pireisetrseer tse ites battunne decenusets ies iestssseas eit S genre rieae a oeeters BESSY epeseiduabssssseses: # SHEEN epesesgressteseteree f B Sf tiie! Se = . 7 J ‘ 7 : » 2 ", | as 4 : am) : : : J 5 ina 2 Nias 4 ! t ) Lf 7 iy * r 2 - a 4 « ‘ r, \ eran | iu, ‘ 5 « “ot . De - id , oy aoe MRANSACTIONS OF THE POY @. SoOcintTyY EDINBURGH. VOL. XXV. EDINBURGH: PUBLISHED BY ROBERT GRANT & SON, 54 PRINCES STREET. AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. MDCCCLXIX. 7 ‘ ' 7) S > P P . oe Lay = x : : 4 . . FR ORIG aoa | CHP Ra eer Het OA & VA AAD: FMM Fe | ) eee eh wisoal ate YALA EVP DAMS eH STRIOK “hi ~ . - a . : ——_— —s - ~ > OT Sek, KIRIN | me - - 7 a, : a ; . : a J : Ly I ‘ sd f _ 7 fe weg DA ? a i "sly ee LAWS OF THE ROYAL SOCIETY OF EDINBURGH, AS REVISED 31st OCTOBER 1869. VOL. XXV. PART II. C of : ea : a - et te ah ee je oS en ee aN . bet 2 : Po a : - a ee AIL TO TALE > re heed i . - 7 e i. 7 i ae -o* "RM UE YO Fathi LAWS. [By the Charter of the Society (printed in the Transactions, Vol. VI. p. 5), the Laws cannot be altered, except at a Meeting held one month after that at which the Motion for alteration shall have been proposed. | R THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Honorary Fellows. Il. Kvery Ordinary Fellow, within three months after his election, shall pay Two Guineas as the fee of admission, and Three Guineas as his contribution for the Session in which he has been elected ; and annually at the commencement of every Session, Three Guineas into the hands of the Treasurer. This annual contribution shall continue for ten years after his admission, and it shall be limited to Two Guineas for fifteen years thereafter.* Ti. All Fellows who shall have paid Twenty-five years’ annual contribution shall be exempted from farther payment. IV. The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s., payable on his admission; and in case of any Non-Resident Fellow coming to reside at any time in Scotland, he shall, during each year of his residence, pay the usual annual contribution of £3, 3s., payable by each Resident Fellow ; but after payment of such annual contribution for eight years, he shallbe exempt from any farther payment. In the case of any Resident Fellow ceasing to reside in Scot- * At the Meeting of the Society, on the 5th January 1857, when the reduction of the Contri-. butions from £3, 3s., to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was resolved that the existing Members shall share in this reduction, so far as regards their future annual Contributions. A modification of this rule, in certain cases, was agreed to 3d January 1831. Title. The fees of Ordi- nary Fellows resid- ing in Scotland. Payment to cease after 25 years. Fees of Non-Kesi- dent Ordinary Fellows. Case of Fellows becoming Non-Re- sident. Defaulters. Privileges of Ordinary Fellows. Numbers Un- limited. Fellows entitled to Transactions. Mode of Recom- mending Ordinary Fellows. Honorary Fellows, British and Foreign. x land, and wishing to continue a Fellow of the Society, it shall be in the power of the Council to determine on what terms, in the circumstances of each case, the privilege of remaining a Fellow of the Society shall be continued to such Fellow while out of Scotland. V. Members failing to pay their contributions for three successive years (due application having been made to them by the Treasurer) shall be reported to the Council, and, if they see fit, shall be declared from that period to be no longer Fellows, and the legal means for recovering such arrears shall be employed. VI. None but Ordinary Fellows shall bear any office in the Society, or vote in the choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the Society. Vit The number of Ordinary Fellows shall be unlimited. VIII. The Ordinary Fellows, upon producing an order from the TREASURER, shall be entitled to receive from the Publisher, gratis, the Parts of the Society’s Trans- actions which shall be published subsequent to their admission. IX: No person shall be proposed as an Ordinary Fellow without a recommenda- tion subscribed by One Ordinary Fellow, to the purport below.* This recom- mendation shall be delivered to the Secretary, and by him laid before the Council, and shall afterwards be printed in the circulars for three Ordinary Meetings of the Society, previous to the day of the election, and shall lie upon the table during that time. X. Honorary Fellows shall not be ‘subject to any contribution. This class shall * « A. B., a gentleman well skilled in several branches of Science (or Polite Literature, as the case “may be), being to my knowledge desirous of becoming a Fellow of the Royal Society of Edin- “ burgh, I hereby recommend him as deserving ofthat honour, and as likely to prove a useful and ‘“« valuable Member.” This recommendation to be accompanied by a request of admission signed by the Candidate. xl consist of persons eminently distinguished for science or literature. Its number shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty- six may be subjects of foreign states. Xi. Personages of Royal Blood may be elected Honorary Fellows, without regard to the limitation of numbers specified in Law X. XII. Honorary Fellows may be proposed by the Council, or by a recommendation (in the form given below*) subscribed by three Ordinary Fellows; and in case the Council shall decline to bring this recommendation before the Society, it shall be competent for the proposers to bring the same before a General Meeting. The election shall be by ballot, after the proposal has been communicated viva voce from the Chair at one meeting, and printed in the circulars for two ordinary meetings of the Society, previous to the day of election. XIII. Royal Personages. Recommendation of Honorary Fel- lows. Mode of Election. The election of Ordinary Fellows shall take place at the Ordinary Meetings of Election of Ordi- the Society. The election shall be by ballot, and shall be determined by a majo- rity of at least two-thirds of the votes, provided Twenty-four Fellows be present and vote. XIV. The Ordinary Meetings shall be held on the first and third Mondays of every month from November to June inclusive. Regular Minutes shall be kept of the proceedings, and the Secretaries shall do the duty alternately, or according to such agreement as they may find it convenient to make. XV. The Society shall from time to time publish its Transactions and Proceedings. For this purpose the Council shall select and arrange the papers which they shall * We hereby recommend for the distinction of being made an Honorary Fellow of this Society, declaring that each of us from our own knowledge of his services to (Literature or Science, as the case may be) believe him to be worthy of that honour. (To be signed by three Ordinary Fellows.) To the President and Council of Royal Society of Edinburgh. VOL. XXV. PART II. d nary Fellows. Ordinary Meet- ings. The Transactions. How Published. xii deem it expedient to publish in the Zvransactions of the Society, and shall super- intend the printing of the same. mV A; The Transactions shall be published in Parts or Fasciculi at the close of each ' Session, and the expense shall be defrayed by the Society. The Council. Retiring Council- lors. Election of Office- Bearers. Special Meetings ; how called. Treasurer’s Duties. Auditor, There shall be elected annually, for conducting the publications and regulating the private business of the Society, a Council, consisting of a President; Six Vice- Presidents, two at least of whom shall be resident ; Twelve Councillors, a General Secretary, Two Secretaries to the Ordinary Meetings, a Treasurer, and a Curator of the Museum and Library. XVII. Four Councillors shall go out annually, to be taken according to the order in which they stand on the list of the Council. XVIII. An Extraordinary Meeting for the Election of Office-Bearers shall be held on the fourth Monday of November annually. XIX. Special Meetings of the Society may be called by the Secretary, by direction of the Council; or on a requisition signed by six or more Ordinary Fellows. Notice of not less than two days must be given of such Meetings. XX. The Treasurer shall receive and disburse the money belonging to the Society, eranting the necessary receipts, and collecting the money when due. He shall keep regular accounts of all the cash received and expended, which shall be made up and balanced annually; and at the Extraordinary Meeting in November, he shall present the accounts for the preceding year, duly audited. At this Meeting, the Treasurer shall also lay before the Council a list of all arrears due above two years, and the Council shall thereupon give such directions as they may deem necessary for recovery thereof. AXE At the Extraordinary Meeting in November, a professional accountant shall be chosen to audit the Treasurer’s accounts for that year, and to give the necessary discharge of his intromissions. Xi XXII. The General Secretary shall keep Minutes of the Extraordinary Meetings of General Sratetaays the Society, and of the Meetings of the Council, in two distinct books. He shall, under the direction of the Council, conduct the correspondence of the Society, and superintend its publications. For these purposes, he shall, when necessary, employ a clerk, to be paid by the Society. The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in secretaries to which a full account of the proceedings of these Meetings shall be entered ; they "ny Metine® shall specify all the Donations received, and furnish a list of them, and of the donors’ names, to the Curator of the Library and Museum: they shall likewise furnish the Treasurer with notes of all admissions of Ordinary Fellows. They shall assist the General Secretary in superintending the publications, and in his absence shall take his duty. XXIII. The Curator of the Museum and Library shall have the custody and charge of Curator of Museum all the Books, Manuscripts, objects of Natural History, Scientific Productions, and Speen 2. other articles of a similar description belonging to the Society ; he shall take an account of these when received, and keep a regular catalogue of the whole, which shall lie in the Hall, for the inspection of the Fellows. XXIV. All Articles of the above description shall be open to the inspection of the Use of Museu Fellows at the Hall of the Society, at such times and under such regulations, as “1” the Council from time to time shall appoint. OO A Register shall be kept, in which the names of the Fellows shal! be enrolled Register Book. at their admission, with the date. eae cae a ‘ - , , ; ’ ake ie yur he x rosie Rote ih “ oT . oo 4 a o$ | Aleta. 2dood retibsils cree oid Snir me ie Mork i nb beet is TAA whee mls "he ras un biaoqasreste a “oa " 7 ) J es pare y ie wiht < = > +t a © ae. easy ; I on “ey onabaoatciced 4) intl 3 aulenity: “al whegrty: (eatin 9. dent bovtrt ote ch Ultlabeegeiton bes cach} ie init ic boi ‘roa. nite ‘dai’? ay ater Ae WO Hi1! i knelectenadal z foul bo qed Tuk) Dos, eet vad? ~ swolleil qecitaD hp enoteninha tet Behar “=v nu at biw ae ilewite vg pot agape ar oi rane 4 ioe i } he is ia! : | aA ‘2 \ : eae an ’ ' an é re Seely - e iar _ wrags Dik vive tity wal overt It ant eikar bite a a) we * ay + ” ite dal ‘igerhiost, yidedc ict pare’ tattiightlo.s1s0 he, eat . bh luiily oAyy tide ‘attics tual, Hai) Re per * i) idve bho onEn. vor omy Muar a ond Bum, hovenoos ued om to bn ; ae _ atolls | ve TG, a »oogha § sdf a aac cory a ; Gi hs uamlgt > “i 5 dens we. sani i iG “~ (ike x. ate, ie cor ; gf i}. DUP Uh GO pews anit; OF ooo dh A ‘ibe _ogpapvonate pe sob ; ie wodatiger dave vee Dus asin is iting fa peels ad) Ta lin ed ibey | | a rk tiie cull 0 3) scene i y 4 : » Po 5 DF Be 4 3 . ot i ‘ - iG - Y ‘ j ) ; Si sit he 22 pres et ; 4: A as a ‘ 7 Ln ae [ i ‘toda Rerakihl dekh Wp dotes “0 if dale a dee mi hes im 4 mt a ¥ a” pie . - : y qs = 7 ye Vie @ 4 ‘ js eae R 7 a) { rs as *. » 4 ? . ~ . A é . * - . > _ - r - Z ‘ Ld DIRECTIONS TO THE BINDER FOR PLACING THE PLATES IN THIS VOLUME. Plate li \ Illustrating Sir David Brewster’s Paper on the Motion, Equilibrium, and IT. Forms of Liquid Films, : . To face page Illustrating Mr John Scott’s Paper on the Burning Mirrors of Archi- eal miedo with some Propositions relating to the Concentration of Light produced by Reflectors on different forms, I11.* Ilustrating Professor Sir William Thomson’s Paper on Vortex Motion, . TY. Ve VAR NEL. VAN. re Illustrating Dr W. Carmichael M‘Intosh’s Paper on the Structure of the XT British Nemerteans, and some New British Annelids, XII. DAG XIV. XV. x VI XVI. ae Ilustrating Professor Fleeming Jenkin’s Paper on the Practical Appli- XX cation of Reciprocal Figures to the Calculation of Strains on Frame- XXL work, 3 ; ; : : ; XXII. XXIII. ) Illustrating Dr W. Lauder Lindsay’s Observations on New Lichenicolous XXIV. } Micro-Fungi, ; : ; XXYV. ) Illustrating Mr Alexander Buchan’s Paper on the Mean Pressure of the XXVI. Atmosphere and the ens over the Globe, for the Months XXVII. and for the Year. Part II., : E XXVIII Illustrating Professor Alexander Dickson’s Paper on the Development of XXIX. the Flower of Pinguicula vulgaris, L., with Remarks on the Embryos XXX. of P. vulgaris, P. ees Gs PE: lusitanica, P. caudata, and Utri- : cularia minor, . : ; ; XXXI. Illustrating Mr David Milne-Home’s Paper on the Boulder-Clay of Europe, VOL. XXV. PART II. é 305 . 441 655 ‘ 0, ed ad - ; . y ad _ . EMTIO7 PINT i E. TA SA vega 8 ia S A= i : - & ee | RO ane ee ON «= : ¥ ths abana Gh “ aly iw dey ar ~ te nad aT a i 3 L i i [ : i i ustiweuld ail jg’ tonal ‘ forse hid wb ae Ri" hast enn may? 4 ann oh J > a , ats ag 198K 60 ws eco ~ y 7 ‘ : ; is —— ; ‘i ; gal / ra ; 7 f\i cae i) i a ‘ w 4nd Aut $ 7 Le 4 .* of a * - i é x 1+ 9 twa atginene PG lambansiincs IG) 1 ' awaeel oe ee - ae * | : ‘ a a), ae weal awh sitet met Syriana : ’ a 14 P| Vv ee? AM Pre +, & a ay Ya ahs al a oar =. A . 7 ; 2 cy . a from | ; Ao a ‘ A ‘ ~ + , A ** 9 7 Ne ee a a Fe ; fo a wren if? »'y bagi t iat 70 — toys bf ith - oe é ‘ r F ‘ a pia a ee cat Lett soho chain oe iy A Oo) ee Whang at te . oe b magttnk CFE Ae ee als .@. \ jee cia ‘aA VAR | aah t fma Res : ‘ ; : 7 - | , } : i>) Y wi feteide peat ssl) a Li 7 ee | Me ; wh) ¢ is ’ . ' ' ms Des ‘omer va oh, he nk ; }s of \ é | 7 a" § oa mA 49 ona che = . ae if Pg i ian ¢ yi abner ; es * 7 x aA 7 . ae - sy a sed hae iy eth CONTENTS. PART I. (1868-69.) T.—On Polyzomal Curves, otherwise the Curves JU + /V + &c. = 0. By Professor CayLEY. Communicated by Professor Tarr, I1.—On the Motion, Equilibrium, and Forms of Liquid Films. By the late Sir Davin Brewster, K.H., D.C.L., &c. (Plates I. and II.) Communicated by Francis Deas, Esq., LL.B., . IlI].—On the Temperature of the Common Fowl (Gallus domesticus). By the late Dr Joun Davy, F.R.SS. Lond. & Edin. Communicated by Professor ALLMAN, oe 1V.—On the Burning Mirrors of Archimedes, with some Propositions relating to the Concentration of Light produced by Reflectors of diferent forms. By Joun Scort, Esq., Tain. (Plate III.) Communicated by Professor KELLAND, V.—On the Connection between Chemical Constitution and Physiological Action. Part I.—On the Physiological Action of the Salts of the Ammonium Bases, derived from Strychnia, Bructa, Thebaia, Codeia, Morphia, and Nicotta. By Dr A. Crum Brown and Dr Tuomas R. FRASER, VI.—On the Products of the Destructive Distillation of Animal Sub- stances. Part V. By THomas ANDERson, M.D., Professor of Chemistry in the University of Glasgow, VII.—On Vortex Motion. By Professor Sir W. THomson. (Plate III.*), PAGE 111 119 151 XVill CONTENTS. PART II. (1868-69.) VIII.—On the Rotation of a Rigid a about a, Fited Point. By Pro- fessor TIT, ; ; / IX.—On the Structure of the British Nemerteans, and some New British Annelids. By W. CarmicHareL M‘Intosu, M.D., F.L.S., Murthly, Perthshire. Communicated by Professor TurNER. (Plates IV.-XVL.), : : X.—Observations on the Temperature of Newly-Born Children. By T. J. Mactacan, M.D., Dundee. Communicated by Dr J. MatTtTHEews Duncan, XI.—On the Practical Application of Reciprocal Figures to the Calcula- tion of Strains on Framework. By Professor FLEEMING JENKIN. (Plates XVII.—XXIL), XII.—An Investigation into some previously undescribed Tetanie Symptoms produced by Atropia in Cold-Blooded Animals, with a Com- parison of the Action of Atropia on Cold-Blooded Animals and on Mammals. By Tuomas R. Fraser, M.D., XIT—Hegel and the Metaphysics of the Fluxional Calculus. By W. Ropertson SmitTH, M.A., Assistant to the Professor of Natural Philosophy in the University of Edinburgh. Communicated by Professor Ta1r, é XIV.— Observations on New Lichenicolous Micro-Fungi. By W.LAvupER Linpsay, M.D., F.L.S., &e. (Plates XXIII, XXIV), XV.—On the Thermal Energy of Molecular Vortices. By W. J. Macquorn RankInE, C.E., LL.D., F.R.SS. L. & E., &c., XVI.—On the Alkaloids contained in the Wood of the Bebeceru, or Green- heart Tree (Nectandra Rodicei, Schomb.) By Doveias MaciaGaNn, M.D., F.R.S.E., Professor of Medical Juris- prudence in the University of Edinburgh, and ARTHUR GamcEE, M.D., F.R.S.E., Lecturer on Physiology in Surgeon’s Hall, Edinburgh, PAGE 261 305 435 441 449 491 513 Or Or ~J Or jan) -~] CONTENTS. XVII.—The Mean Pressure of the Atmosphere and the Prevailing Winds over the Globe for the Months and for the Year. Part II. By ALEXANDER Bucnan, M.A., Secretary of the Scottish Meteorological Society. (Plates XXV. to XXVIL.), XVIII.—On the Development of the Flower of Pinguicula vulgaris, L. ; with Remarks on the Embryos of P. vulgaris, P. grandiflora, P. lusitanica, P. caudata, and Utricularia minor. By ALEXANDER Dickson, M.D. Edin. & Dublin; Regius Pro- fessor of Botany in the University of Glasgow. (Plates XXVIII.-XXX.), X1IX.—On the Boulder-Clay of Europe. By Davin Mitne Home, Esq. (Plate XXX1.), XX.—On the Connection between Chemical Constitution and Physiological Action. Part IL—On the Physiological Action of the Anmonium Bases, derived from Atropia and Conia. By Dr A. Crum Brown and Dr THomas R. FRASER, Proceedings of Statutory General Meetings, &c., List of Members Elected, List of the present Ordinary Members AGean ly arran dee. List of the present Ordinary Members in the Order of their Election, List of Non-Resident Members, elected under the Old Laws, Honorary Fellows, » Fellows Deceased and cae Jrom 1867 a 1869, Public Institutions, de., entitled to receive the Transactions and Prececdings of the Society, List of Donations continued aon Vol. XXI V. sD 830. Indez, 9) WO, XXV. PART If. of X1x PAGE 639 655 _ 693 741 745 T47 750 758 758 760 762 765 781 ee iF * Mev PAnat Seon ah hese Pie deal aes sal ah. arlene sie ison” afd je quiere ‘eh ai hie. DIX uot VEE 90 i a ape brea! ease Ae ne sag Segre sie yi 2 epikabuorg « Taiaa dec 3 = ; my y is ae oii ried fgsal J a ah re At sks a * Say Uoinoll patel se sh 4. meopagenl : +f f ‘ ca ies Lo ee Pal naale) Yi Wi ores) rind gs watt a - “+ 7 . HS 5 ee . ’ me a Ae _ é Cid - e y 9 » i a a” s » “a , * ‘es / a ' 7 f 4 H 2 I ivi id * ¢. ich » a \ c .! * ‘ ~ : . ; : , j . , Arie < a o aie , by : > 4 J "hose ‘" e si” 0 7 oy! be a3. - , A Ban =< . wily Wy’. whee’ wae a fO-=. Egat © Kee tri J t Gytto!) ng . wid. viel, Wr eves Ran 44 noite i, at aa pce, 2. 2 et aa E pe Ee ene av, epi a 77 esi ca: Vrithnas stagh i resent ye peabedt eee . a oF), ‘ oe ce Sep Oy! % ot L @1.Ge¥ ‘push ae Seid —. xj Re ON 8 Tey , “ites, avs abr gg ) 7 eis bets Re P a Wks Bn By ae, Bene = . f Saher 5 : Bo’, Lous web ieeaent th wh oxE ¢ ~ . . @ , al ‘iby ; - s ~ all bly he : ACER Y) at Pe ee ee. 7 ” é y ve * + « =e 7. Pa => fe oe rs { 4 _ r! ¢ 4\.94 - a ‘ Jaa ERRATA. In Professor Tarv’s Paper, Page 281, line 6, omit the sign of integration. In Dr Dicxson’s Paper, Page 641, note, line 1, omit “ only.” Page 646, line 3, for “ extremities” read “‘ extremity.” Plate XXIX. fig. 14, for “ pt” read “ pl.” iy KRTEANRS anu Tvisoeatigean y i ef “\otteryadar To Agia cl a wid AE al aay'l Comensll ve ok Rshas™, Heo f sail she Legale, : ‘Ceiba "ery "eat pretins © it BS age ag* heevny “yy “rh RS 1s) CLE tT : TRANSACTIONS. I.—On Polyzomal Curves, otherwise the Curves VU +V/V + &. = 0. By Professor CayLEY. Communicated by Professor Tarr. (Read 16th December 1867.) Ir U, V, &c., are rational and integral functions (*)(2, y, z)’, all of the same degree 7°, in regard to the co-ordinates (7, y, z), then /7 + /V + &c. is a poly- zome, and the curve /U + W/V + &c. = 0a polyzomal curve. Each of the curves / VU = 0,7 V = 0, &c. (or say the curves U = 0, V = 0, &c.) is, on account . of its relation of circumscription to the curve /V + /V + &c. = 0, considered as a girdle thereto (Coua), and we have thence the term “zome” and the derived expressions ‘‘polyzome,” “zomal,” &c. If the number of the zomes /{7, V/V, &c. be = v, then we have a »-zome, and corresponding thereto a v-zomal curve; the curves U = 0, V = 0, &c., are the zomal curves or zomals thereof. The cases v = 1, v = 2, are not, for their own sake, worthy of consideration ; it isin general assumed that vis = 3 at least. It is sometimes convenient to write the general equation in the form //V + &c. = 0, where /, &c. are constants. The Memoir contains researches in regard to the general »-zomal curve; the branches thereof, the order of the curve, its singularities, class, &c.; also in regard to the v-zomal curve / (6 + L@) + &c. = 0, where the zomal curves 6 + Lo = 0, all pass through the points of intersection of the same two curves 6 = 0, = 0 of the orders 7 and r—s respectively ; included herein we have the theory of the depres- sion of order as arising from the ideal factor or factors of a branch or branches. A general theorem is given of ‘the decomposition of a tetrazomal curve,” viz.. if the equation of the curve be VJU + /mV +V¥aW + V pT = 0; then if U, V, W, Tf are in involution, that is, connected by an identical equation aU + bV + cW + d7 = 0, and if /, m, n, p,. satisfy the condition “+ = + ad E = 0, the tetrazomal curve breaks up into two trizomal curves, each expressible by means of any three of the four functions U, V, W, 7; for VOL. XXV. PART I. a 4 PROFESSOR CAYLEY ON POLYZOMAL CURVES. example, in the form // U + /m V+ /p' T= 0. If, in this theorem, we take p = 0, then the original curve is the trizomal /7U + /mV+W/n W = 0, Tis any function = — - (aU +bV+cW), where, considering /, m, 2 as given, a, b, ¢ n c theorem of ‘the variable zomal of a trizomal curve,’’ viz., the equation of the trizomal VJ U + VW V + /n W = 0, may be expressed by means of any two of the three functions U, V, W, and ofa function 7’ determined as above, for example in the form Vl U + Vm’ V + Vn’ T = 0; whehce also it may be expressed in terms of three new functions 7, determined as above. This theorem, which occu- pies a prominent position in the whole theory, was suggested to me by Mr Casey’s theorem, presently referred to, for the construction of a bicircular quartic as the envelope of a variable circle. In the »-zomal curve ViU6+Le) + &c.=0, if @= 0 be a conic, 6= 0 a line. the zomals 6 + L@ = 0, &c. are conics passing through the same two points 9 = 0, 6 = 0, and there is no real loss of generality in taking these to be the circular points at infinity—that is, in taking the conics to be circles. Doing this, and using a special notation A° = 0 for the equation of a circle having its centre at a given point A, and similarly A = 0 for the equation of an evanescent circle, or say of are quantities subject only to the condition +7 +— -—0, and we have the the point A, we have the »-zomal curve V/A° + &c. = 0, and the more special form /7/A + &c.=0. Asregards the last-mentioned curve, //A + &c. = 0, the point A to which the equation A = 0 belongs, is a focus of the curve, viz., in the case v = 3, it is an ordinary focus, and in the case v> 3, it is a special kind of focus, which, if the term were required, might be called a foco-focus; the Memoir contains an explanation of the general theory of the foci of plane curves. For v = 3, the equation VJA + /mB + VnC = 0 is really equivalent to the apparently more general form V/A° + “/mB°.+ /nC° = 0. In fact, this last is in general a bicircular quartic, and, in regard to it, the before-mentioned theorem of the variable zomal becomes Mr Casey’s theorem, that ‘‘ the bicircular quartic (and, as a particular case thereof, the circular cubic) is the envelope of a variable circle having its centre on a given conic and cutting at right angles a given circle.” This theorem is a sufficient basis for the complete theory of the tri- zomal curve /IA° +/“mB° + “nC? =9; and it is thereby very easily seen that the curve V/A° + /mBY + “nC° = 0 can be represented by an equation VUN + Vim'B’ + /n/C’=0. But for »> 3 this is not so, and the curve VIA + &c. = 0 is only a particular form of the curve W/A° + &c. = 0; and the discussion of this general form is scarcely more difficult than that of the special form V/A + &c. = 0, included therein. The investigations in relation to the theory of foci, and in particular to that of the foci of the circular cubic and bicircular quartic, precede in the Memoir the theories of the trizomal curve PROFESSOR CAYLEY ON POLYZOMAL CURVES. 3 VIR? +V mB? +WnC’=9, and the tetrazomal curve //A° + /mB°+Vn0°+V pD* —0, to which the concluding portions relate. I have accordingly divided the Memoir into four parts, viz., these are—Part I, On Polyzomal Curves in general ; Part II., Subsidiary Investigations; Part III, On the Theory of Foci; and Part IV., On the Trizomal and Tetrazomal Curves where the zomals are circles. There is, however, some necessary intermixture of the theories treated of, and the arrangement will appear more in detail from the headings of the several articles. The paragraphs are numbered continuously through the Memoir. There are four Annexes, relating to questions which it seemed to me more convenient to treat of thus separately. It is right that I should explain the very great extent to which, in the com- position of the present Memoir, I am indebted to Mr Casey’s researches. His Paper ‘On the Equations and Properties (1.) of the System of Circles touching three circles in a plane; (2.) of the System of Spheres touching four spheres in space; (3.) of the System of Circles touching three circles on a sphere; (4.) on the System of Conics inscribed in a conic and touching three inscribed conics in a plane,” was read to the Royal Irish Academy, April 9, 1866, and is published in their “ Proceedings.” The fundamental theorem for the equation of the pairs of circles touching three given circles was, previous to the publication of the paper, mentioned to me by Dr Salmon, and I communicated it to Professor Cre- mona, suggesting to him the problem solved in his letter of March 3, 1866, as men- tioned in my paper, “Investigations in connection with Casey’s Equation,” “Quarterly Math. Journal,” t. viii. 1867, pp. 334-341, and as also appears, Annex No. IV. of the present Memoir. In connection with this theorem, I communicated to Mr Casey, in March or April 1867, the theorem No. 164 of the present Memoir, that for any three given circles, centres A, B, C, the equation BOVA® + CA VB° + ABVC° = 0 (where BC, CA, AB, denote the mutual distances of the points A, B, C) belongs to a Cartesian. Mr Casey, in a letter to me dated 30th April 1867, informed me of his own mode of viewing the question as follows :—“ The general equation of the second order (a, 6, ¢, f, g, h) (4, 8, y) =9, where a, 8, y are circles, is a bicircular quartic. If we take the equation (a, }, ¢, f. g, h) (A, », v)’=0 in tangential co-ordi- nates (that is, when 4, «, v are perpendiculars let fall from the centres of a, 8, y on any line), it denotes a conic; denoting this conic by /, and the circle which cuts a, 8, y orthogonally by J, I proved that, if a variable circle moves with its centre on F, and if it cuts J orthogonally, its envelope will be the bicircular quartic whose equation is that written down above;” and among other conse- quences, he mentions that the foci of / are the double foci of the quartic, and the points in which J cuts /'single foci of the quartic, and also the theorem which I had sent him as to the Cartesian, and he refers to his Memoir on Bicircular Quartics as then nearly finished. An Abstract of the Memoir as read before the Royal Irish 4 PROFESSOR CAYLEY ON POLYZOMAL CURVES. “Academy, 10th February 1867, and published in their “ Proceedings,” pp. 44, 45, contains the theorems mentioned in the letter of 50th April, and some other theorems. It is not necessary that I should particularly explain in what manner the present Memoir has been, in the course of writing it, added to or altered in consequence of the information which I have thus had of Mr Casey’s researches; it is enough to say that I have freely availed myself of such information, and that there is no question as to Mr Casey’s priority in anything which there may be in common in his memoir on Bicircular Quartics and in the present Memoir. Part I. (Nos. 1 to 55).—On Potyzomat Curves IN GENERAL. Definition and Preliminary Remarks—Art. Nos. 1 to 4. 1. As already mentioned, U, V, &c. denote rational and integral functions (*) (a, y, 2)”, all of the same degree 7 in the co-ordinates (2, 7, ~), and the equation VU +V7V + &. = 0 then belongs to a polyzomal curve, viz., if the number of the zomes / U7, VV, &c., is = v, then we have av-zomal curve. The radicals, or any of them, may con- tain rational factors, or be of the form P/Q; but in speaking of the curve asa v-zomal, it is assumed that any two terms, such as P VO se PNG. involving the same radical ./Q, are united into a single term, so that the number of distinct radicals is always = v; in particular (7 being even), it is assumed that there is only one rational term P. But the ordinary case, and that which is almost ex- clusively attended to, is that in which the radicals / U7, / V, &c. are distinct irre- ducible radicals without rational factors. 2. The curves U= V = 0, &c. are said to be the zomal curves, or simply the zomals of the polyzomal curve /U + /V + &c. = 0; more strictly, the term zomal would be applied to the functions U, V, &c. It is to be noticed, that al- though the form /U + /V + &c. = 0 is equally general with the form /iU + /mV + &c.=0 (in fact, in the former case, the functions U, V, &c., are con- sidered as implicitly containing the constant factors /, m, &c., which are expressed in the latter case), yet it is frequently convenient to express these factors, and thus write the equation in the form //U + ,/m V + &c. For instance, in speak- ing of any given curves U=0, V = 0, &€., we are apt, disregarding the constant factors which they may involve, to consider U, V, &c. as given functions; but in this case the general equation of the polyzomal with the zomals U = 0, V = 0, &e., is of course J/70 + /m V + &e. = 0. 3. Anticipating in regard to the cases vy = 1, vy = 2, the remark which will be presently made in regard to the »-zomal, that ./77 + ./V + &c. = 0 is the curve represented by the rationalised form of this equation, the monozomal curve /U = 0 is merely the curve U = 0, viz., this is any curve whatever U = 0 of the PROFESSOR CAYLEY ON POLYZOMAL CURVES. 9) order 7; and similarly, the bizomal curve ,./7 + ./V = 0 is merely the curve U— V= 0, viz. this is any curve whatever Q = 0, of the order 7; the zomal curves U = 0, V = 0, taken separately, are not curves standing in any special relation to the curve in question Q = 0, but U = 0 may be any curve whatever of the order 7, and then V = 0 is a curve of the same order 7, in involution with the two curves OQ = 0, U= 0; we may, in fact, write the equation {2 = 0 under the bizomal form /7 + ./9 + U=0. Inthe case 7 even, we may, however, notice the bizomal curve P + ./U = 0 (Ff a rational function of the degree 7); the rational equation is here Q = U— P” = 0, thatis V=Q + P’, viz., Pisany curve whatever of the order 47, and U = 0 is a curve of the order 7, touching the given curve Q = 0 at each of its 37’ intersections with the curve P= 0. I fur- ther remark that the order of the v-zomal curve ,/V + &c. = 0 is =2’—7; this is right in the case of the bizomal curve ,/U + ./V = 0, the order being = 7, but it fails for the monozomal curve ,/U = 0, the order being in this case 7, instead of #7, as given by the formula. The two unimportant and somewhat exceptional cases v = 1, y = 2, are thus disposed of, and in all that follows (except in so far as this is in fact applicable to the cases just referred to), y may be taken to be = 3 at least. 4, It is to be throughout understood that by the curve /U + /V + &c. =0 is meant the curve represented by the rationalised equation— Norm (SU+V7V + &.) 0 viz. the Norm is obtained by attributing to all but one of the zomes ,/U, ./V, &c., each of the two signs +, —, and multiplying together the several resulting values of the polyzome; in the case of a »-zomal curve, the number of factors is thus =2’-1 r (whence, as each factor is of the degree 47, the order of the curve is 2’-! _ 47, = 2’-27,as mentioned above). I expressly mention that, as regards the polyzomal curve, we are not in any wise concerned with the signs of the radicals, which signs are and remain essentially indeterminate; the equation JU + /V + &c. = 0, is a mere symbol for the rationalised equation, Norm (JU + /V + &¢.) = 0. The Branches of a Polyzomal Curve—Art. Nos. 5 to 12. 5. But we may in a different point of view attend to the signs of the radicals; if forall values of the co-ordinates we take the symbol ,/,, » andconsider /U, ./V, &c. as signifying determinately, say the positive values of /U,./V, &c.; then each of the several equations + ./U + ./V'+ &c.=0, or, fixing at pleasure one of the signs, suppose that prefixed to ./V, then each of the several equations JU + JV + &e. = 0, will belong to a branch of the polyzomal curve: a v-zomal curve has thus 2’-! branches corresponding to the 2’—! values respec- VOL. XXV. PART I. B 6 PROFESSOR CAYLEY ON POLYZOMAL CURVES. tively of the polyzome. The separation of the branches depends on the precise fixation of the significations of ./U, ./V, &c., and in regard hereto some further explanation is necessary. 6. When U is real and positive,*./7/ may be taken to be, in the ordinary sense, the positive value of ./V, and so when U is real and negative, ./{7 may be taken to be = 7 into the positive value of ./—U/; and the like as regards JV, &c. The functions U, V, &., are assumed to be real functions of the co-ordinates ; hence, for any real values of the co-ordinates, U, V, &c. are real positive or negative quantities, and the significations of /U, ./V, &c. are com- pletely determined. 7. But the co-ordinates may be imaginary. In this case the functions U, V, &c. will for any given values of the co-ordinates acquire each of them a determinate, in general imaginary, value. If for all real values whatever of a, 6, we select once for all one of the two opposite values of ./a + £7, calling it the positive value, and representing it by ./a + £7, then, for any particular values of the co-ordinates, U being = a + Bi, the value of ./U may be taken to be = /a + Bi; and the like as regards ,/V, &c. ./U, ./V, &c. have thus each of them a determinate signification for any values whatever, real or ima- ginary, of the co-ordinates. The co-ordinates of a given point on the curve JU + /V + &. = 0, will in general satisfy only one of the equations JU + JV &e. = 0; that is, the point will belong to one (but in general only one) of the 2” branches of the curve; the entire series of points the co-ordinates of which satisfy any one of the 2’! equations, will constitute the branch corresponding to that equation. a ang 8. The signification to be attached to the expression ./a + 87 should agree with that previously attached to the like symbol in the case of a positive or negative real quantity; and it should, as far as possible, be subject to the condition of continuity, viz., as a + @2 passes continuously to a’ + 8%, so ./a + Bi should pass continuously to ./a’ + 6’7; but (as is known) it is not possible to satisfy univer- sally this condition of continuity ; viz., if for facility of explanation we consider (a, 8) as the co-ordinates of a point in a plane, and imagine this point to describe a closed curve surrounding the origin or point (0, 0), then it is not possible so to define /a + fi that this quantity, varying continuously as the point moves along the curve, shall, when the point has made a complete circuit, resume its original value. The signification to be attached to /a + Bi is thus in some measure arbitrary, and it would appear that the division of the curve into branches is affected by a corresponding arbitrariness, but this arbitrariness relates only to the imaginary branches of the curve: the notion of a real branch is perfectly definite. 9. It would seem that a branch may be impossible for any series whatever of points real or imaginary. Thus, in the bizomal curve /U + ,/V =0, the branch ee /V = 0is impossible. In fact, for any point whatever, real or PROFESSOR CAYLEY ON POLYZOMAL CURVES. fh imaginary, of the curve, we have U = V, and therefore /U= ./V; the point thus belongs to the other branch Mi J/V= 0, not to the branch JU + ./V = 0; the only points belonging to the last-mentioned branch are the isolated points for which simultaneously JU = 0, J/V= 0; viz., the points of intersection of the two curves VU = 0, V=0. 10. It is not clear to me whether the case is the same in regard to the branch Cre ee Vat x/ W =0 of a trizomal curve. In fact, for each point of the curve /U+ /V + /W=0 we have (U—V—W)’=4 VW, and therefore, U—V—W=+2A/V /W;; there may very well be points for which the sign is +; that is, pointsfor which U=V+ W + 2 /V JW, and for these points we have + /U= /V + \/W;; for real values of the co-ordinates the sign on the left hand must be + (for otherwise the two sides would have opposite signs), but there is no apparent reason, or at least no obviously apparent reason, why this should be so for imaginary values of the co-ordinates, and if the sign be in fact —, then the point will belong to the branch /U + /V + #/ Wak 11. But the branch in question is clearly impossible for any series of real points ; so that, leaving it an open question whether the epithet ‘‘ impossible”’ is to be understood to mean impossible for any series of real points (that is, as a mere synonym of imaginary), or whether it is to mean impossible for any series of points, real or imaginary, whatever, I say that in a »-zomal curve some of the branches are or may be impossible, and that there is at least one impossible branch, viz. the branch /U + /V + &c. = 0. 12. For the purpose of referring to any branch of a polyzomal curve it will be convenient to consider /U as signifying determinately + /U, or else — /U; and the like as regards ,/V, &c., but without any identity or relation between the signs prefixed to the /% Nap &¢., respectively; the equation /U + J/V + &e. = 0, so understood, will denote determinately some one (that is, any one at pleasure) of the equations /U+/V + &. = 0, and it will thus be the equation of some one (that is, any one at pleasure) of the branches of the polyzomal curve — all risk of ambiguity which might otherwise exist will be removed if we speak either of the curve /U7+ ./V, &c. = 0, or else of the branch JU + /V + &. = 0. Observe that by the foregoing convention, when only one branch is considered, we avoid the necessity of any employment of the sign +, or of the sign —; but when two or more branches are consi- dered in connection with each other, it is necessary to employ the sign — with one or more of the radicals ./U, ./V, &c.; thus in the trizomal curve JU + JV + /W = 0, we may have to consider the branches wi tee WW = 0/0 + SV — /W = 0; viz. either ‘of these equations apart from the other denotes any one branch at pleasure of the curve, but when the branch represented by the one equation is fixed, then the branch represented by the other equation is also fixed. 8 PROFESSOR CAYLEY ON POLYZOMAL CURVES. The Points common to Two Branches of a Polyzomal Curve—Art. Nos. 13 to 17. 13. I consider the points which are situate simultaneously on two branches of the »-zomal curve /U + /V + &.= 0. The equations of the two branches may be taken to be JU + &. + (./W + &.) = 0, JU + &. — (./W + &e.) = 0, viz., fixing the significations of ./U7, ./V, ./W, &c. in such wise that in the equation of one branch these shall each of them have the sign +, we may take /U, &e. to be those radicals which, in the equation of the other branch, have the sign +,and ,/W, &c. to be those radicals which have the sign —. The fore- going equations break up into the more simple equations JU + &=—0, /W+ &. = 0, which are the equations of certain branches of the curves ,./U + &c. = 0, and /W + &e. = 0, respectively, and conversely each of the intersections of these two. curves is a point situate simultaneously on some two branches of the original »-zomal curve /U + ./V + &. = 90. Hence, partitioning in any manner the »-zome ./U7 + ,/V + &c. into an a-zome, ,/{7 + &c. and a 6-zome /W + &e. (a + 8 = »), and writing down the equations JU + & =0, /Wt+ & =0 of an a-zomal curve and a $-zomal curve respectively, each of the intersections of these two curves is a point situate simultaneously on two branches of the v-zomal curve; and the points situate simultaneously on two branches of the v-zomal curve are the points of intersection of the several pairs of an a-zomal curve and a 6-zomal curve, which can be formed by any bipartition of the »-zome. 14. There are two cases to be considered :—First, when the parts are 1,v—1(»—lis> 1, except in the case »=2, which may be excluded from consideration), or say when the »-zome is partitioned into a zome and antizome. Secondly, when the parts a, 8, are each > 1 (this implies vy = 4 atleast), or say when the »-zome is partitioned into a pair of complementary parazomes. 15. To fix the ideas, take the tetrazomal curve /U+ /V+ /W+ /Tf — 0, and consider first a point for which /U=0, /V+ /W+ /T=0. The Norm is the product of (2° =) 8 factors; selecting hereout the factors JU+ J0+ JW JT, hed ese fora 8 let the product of these =U0—-(VV+ Jw JT) be called /, and the product of the remaining six factors be called G; the PROFESSOR CAYLEY ON POLYZOMAL CURVES. 9 rationalised equation of the curve is therefore YG = 0. The derived equation is GdF + FdG = 0; at the point in question /G=0, /V+ /W+ /T=0; G and dG are each of them finite (that is, they neither vanish nor become infinite), but we have F=0,dF=dU—(J/V + JW+ VD AV + JV +dWe JW+ dl + JT), =a, and the derived equation is thus GdU = 0, or simply dU = 0. It thus appears that the point in question is an ordinary point on the tetrazomal curve; and, further, that the tetrazomal curve is at this point touched by the zomal curve U=0. And similarly, each of the points of intersection of the two curves JU=9, /V + JW + /T = 9, is an ordinary point on the tetrazomal curve ; and the tetrazomal curve is at each of these points touched by the zomal curve ae 0. 16. Consider, secondly, a point for which /7 + /V=0, /W+./T=0; to form the Norm, taking in this case the two factors LO TNE ST, NO ER i ee i Ot CW eel RY be called F, and the product of the remaining six factors be called G; the rationalised equation is /G' = 0, and the derived equation is FdG' + GdF = 0. At the point in question G and dG are each of them finite (that is, they neither vanish nor become infinite), but we have F=0,dF=(/U+ JV) (dU+ JU+dV + JW-(J/W+ /D(dW+ JW+ dT+ JT), =0, that is, the derived equation becomes identically 0 = 0; the point in question is thus a singular point, and it is easy to see that it is in fact a node, or ordinary double point, on the tetrazomal curve. And similarly, each of the points of intersection of the two curves ./U+./V=09, /W+./7=0 is a node on the tetrazomal curve. 17. The proofs in the foregoing two examples respectively are quite general, and we may, in regard toa »-zomal curve, enunciate the results as follows, viz., in a »-zomal curve, the points situate simultaneously on two branches are either the intersections of a zomal curve and its antizomal curve, or else they are the intersections of a pair of complementary parazomal curves. In the former case, the points in question are ordinary points on the v-zomal, but they are points of contact of the »-zomal with the zomal; it may be added, that the intersections of the zomal and antizomal, each reckoned twice, are all the intersections of the v-zomal and zomal. In the latter case, the points in question are nodes of the v-zomal; it may be added, that the »-zomal has not, im general, any nodes other than the points which are thus the intersections of a pair of complementary para- zomals, and that it has not 7m general any cusps. VOL. XXV. PART I. C let their product 10 PROFESSOR CAYLEY ON POLYZOMAL CURVES. Singularities of a y-comal Curve—Art. Nos. 18 to 21. 18. It has been already shown that the order of the »-zomal curve is = 2”~?7. Considering the case where v is = 3 at least, the curve, as we have just seen, has contacts with each of the zomal curves, and it has also nodes. I proceed to deter- mine the number of these contacts and nodes respectively. 19. Consider first the zomal curve U = 0, and its antizomal,/V + ./W +c. = 0, these are curves of the orders 7 and 2”~—*7 respectively, and they inter- sect therefore in 2”-*7* points. Hence the »-zomal touches the zomal in 2”—*7* points, and reckoning each of these twice, the number of intersections is = 2”—?7*, viz., these are all the intersections of the »-zomal with the zomal U = 0. The number of contacts of the v-zomal with the several zomals / = 0, V = 0, &e., is . of course = 2”—*7°7y. 20. Considering next a pair of complementary parazomal curves, an a-zomal and a 6-zomal respectively (a + 6 = v), these are of the orders 2*—°7 and 2°—?7 respectively, and they intersect therefore in 2«**—‘*7” = 2-47" points, nodes of the v-zomal. This number is independent of the particular partition (a, 6), and the v-zomal has thus this same number, 2”~—‘7°’, of nodes in respect of each pair of complementary parazomals ; hence the total number of nodes is = 2”~‘7* into the number of pairs of complementary parazomals. For the partition (a, 8) the number of pairs is = [v|”+[a]{6]*, or when a = 8, which of course implies » even, it is one-half of this; extending the summation from « = 2 to a =v — 2, each pair is obtained twice, and the number of pairs is thus = 42D) + [a}*(B]*{; the sum extended from « = 0 to a=» is (1 + 1)’,= 2”, but we thus in- clude the terms 1, »,»,1, which are together = 2y + 2, hence the correct value of the sum is = 2” — 2v—2, and the number of pairs is the half of this = 2”~'—v—1. Hence the number of nodes of the »-zomal curve is = (2"—1— y —]1)2"~—47". 21. The »-zomal is thus a curve of the order 2”—?7, with (2’—!— v — 1) 2¥—*r* nodes, but without cusps; the class is therefore = 2" ro + Ir — 2], and the deficiency is =2"~‘*r[ + lr—6] +1. These are the general expressions, but even when the zomal curves U = 0, V = 0, &c., are given, then writing the equation of the »-zomal under the form JiU+ /mV + &c. = 0, the constants /: m: &c., may be so determined as to give rise to nodes or cusps which do not occur in the general case; the formule will also undergo modification in the particular cases next referred to. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 11 Special Case where all the Zomals have a Common Point or Points—Art. Nos. 22 to 27. 22. Consider the case where the zomals U = 0, V = 0 have all of them any number, say &, of common intersections—these may be referred to simply as the common points. Each common point is a 2”’—?-tuple point on the »-zomal curve : it is on each zomal an ordinary point, and on each antizomal a 2”—*-tuple point, and on any a-zomal parazomal a 2*—*-tuple point. Hence, considering first the intersections of any zomal with its antizomal, the common point reckons as 2¥—3 intersections, and the £ common points reckon as 2”—* & intersections; the number of the remaining intersections is therefore = 2”—*(7°— k), and the zomal touches the v-zomal in each of these points. The intersections of the zomal with the »-zomal are the * common points, each of them a 2”—?-tuple point on the v-zomal, and therefore reckoning together as 2”—°s intersections; and the 2¥—% (7? — k) points of contact, each reckoning twice, and therefore together fem2ue (@ — 4%). intersections (2"~*h + 2”~?(r*— ky = 2°97", = 7. 2”—? 4); the total number of contacts with the zomals U=0, V=0, &c., is thus = Be (rT —_— k) Vv. 23. Secondly, considering any pair of complementary parazomals, an «-zomal and a $-zomal, each of the common points, being a 2«—*-tuple point and a 28—?_tuple point on the two curves respectively, counts as 2**+*—4, = 2»—* in- tersections, and the £ common points count as 2”—‘*&# intersections; the number of the remaining intersections is therefore = 2”—‘*(7r’ — k), each of which is a node on the v-zomal curve; and we have thus in all 2”—*(2”—!— »— 1) (7? — &) nodes. 24. There are, besides, the £ common points, each of them a 2”~—?-tuple point on the v-zomal, and therefore each reckoning as $2”—?(2”—?— 1), = 2%—5— Qu—-8 double points, or together as (2””—°— 2”—*)k double points. Reserving the term nde for the above-mentioned nodes or proper double points, and considering, therefore, the double points (dps.) as made up of the nodes and of the 2”—?-tuple points, the total number of dps. is thus 274 (Q”—*— y — 1) (7? — &) + (2 —F— 2%), SDPO ee SS eee (CE ar or finally this is = DP CRW 3 v— 1) 7? + (v _ 1)} so that there is a gain = 2”—*(v — 1)& in the number of dps. arising from the & common points. There is, of course, in the class a diminution equal to twice this number, or 2”~*(v — |); and in the deficiency a diminution equal to this number, or 2’—*(v — 1)k. 25. The zomal curves U = 0, V = 0, &c., may all of them pass through the same »* points; we have then / = 7’, and the expression for the number of dps. 12 PROFESSOR CAYLEY ON POLYZOMAL CURVES. is = (2%—*— 2”—*)p”, viz., this is = 4 2¥—? (2”—?— 1)7”. But in this case the dps. are nothing else than the 7” common points, each of them a 2”—*-tuple point, the v-zomal curve in fact breaking up into a system of 2”—? curves of the order r, each passing through the 7” common points. This is easily verified, for if 6 = 0, 6 = 0 are some two curves of the order 7, then, in the present case, the zomal curves are curves in involution with these curves; that is, they are curves of the form /6 + /@ = 0, me + m’m = 0, &c., and the equation of the »-zomal curve is Jie + lo+ Jme + mot &. = 0. The rationalised equation is obviously an equation of the degree 2”—? in 6, @, giving therefore a constant value for the ratio 6: @; calling this g, or writing 0 = Q®, we have oes Jig+U + Jmq +m’ + &.=0, viz., the rationalised equation is an equation of the degree 2”—? in q, and gives therefore 2”—? values of g. And the »-zomal curve thus breaks up into a system of 2”—? curves each of the form 6 — g@ = 0, that is, each of them in involution with the curves 6 = 0, 6=0. The equation in g may have a multiple root or roots, and the system of curves so contain repetitions of the same curve or curves; an instance of this (in relation to the trizomal curve) will present itself in the sequel; but I do not at present stop to consider the question. 26. A more important case is when the zomal curves are each of them in involution with the same two given curves, one of them of the order 7, the other of an inferior order. Let 6 = 0 be acurve of the order 7, 6 = 0 a curve of an inferior order 7 —s; L = 0, M = 0, &c., curves of the order s ; then the case in question is when the zomal curves are of the form 6 + L@=0, 6 + Mo = 0, &c., the equation of the »-zomal is Jie + Le) + Jno + Me) + &. =0, where /, m, &c., are constants. This is the most convenient form for the equation, and by considering the functions L, M7, &c. as containing implicitly the factors 1-1, m1, &c. respectively, we may take it to includethe form //g + Lo + Jie Tee &c. = 0, which last has the advantage of being immediately applicable to the case where any one or more of the constants /, m, &c. may be = 0. 27. In the case now under consideration we have the 7(7 — s) points of inter- section of; the curves 6 = 0, @ = 0 as common points of all the zomals. Hence, putting in the foregoing formula 4 = r(7 — s), we have a »-zomal curve of the order 2”—?7, having with each zomal 2”—?7s contacts, or with all the zomals 2¥—7sv contacts, having a node at each of the 2”—‘7s intersections (not being common points 6 = 0, @ = 0) of each pair of complementary parazomals; that is, together 2”—*(2”-!— v—1)rs nodes, and having, besides, at each of the PROFESSOR CAYLEY ON POLYZOMAL CURVES. 13 r(r — s) common points, a 2”—?-tuple point, counting as 2?”—°’— 2”—* dps., to- gether as (2””—°— 2”—*) r(7 — s) dps.; whence, taking account of the nodes, the total number of dps. is = 2¥-*9[(2”-1— 2) r — (v—1)s]- Depression of Order of the v-zomal Curve from the Ideal Factor of a Branch or Branches— Art. Nos. 28 to 37. 28. In the case of the 7(7 — s) common points as thus far considered, the order of the v-zomal curve has remained throughout = 2”—?7r, but the order admits of depression, viz., the constants /, m, &c., and those of the functions L, MW, &c., may be such that the norm contains the factor @”; the v-zomal curve then con- tains as part of itself (@’= 0) the curve @ = 0 taken @ times, and this being so, if we discard the factor in question, and consider the residual curve as being the v-zomal, the order of the v-zomal will be = 2”—’r — w (r — s). 29. To explain how such a factor * presents itself, consider the polyzome Jie + Lo) + &c., or, what is the same thing, //7./6 + Lo + &c., belonging to any particular branch of the curve, we may, it is clear, take ./6 + Zo, &c. each in a fixed signification as equivalent to ./6 + Le, &c., respectively, and the particular branch will then be determined by means of the significations attached to /l, ./m, &c. Expanding the several radicals, the polyzome is = lye 2? & l ies Jt{ Je +5 L - L = + &e, 5 + be; or, what is the same thing, it is J6( vi i. &e.) so ene tp &e.) 7 sous (” Ji+ &e.) + &e, which expansion may contain the factor @, or a higher power of @. For in- stance, if we have ,// + &c. = 0, the expansion will then contain the factor @; and if we also have L/7 + &c. = 0 (observe this implies as many equations as there are asyzygetic terms in the whole series of functions Z, JZ, &c.; thus, if L, M, &e., are each of them of the form aP + 6Q + cR, with the same values of P, Q, #, but with different values of the co-efficients «, , c, then it implies the three equations a@,/7 + &.= 0, b,/7 + &. = 0, c,/] + &c. = 0; and so in other cases), if I say Z./7 + &c. be also = 0, then the expansion will contain the factor @*, and so on; the most general supposition being, that the expansion contains as factor a certain power @* of @. Imagine each of the polyzomes expanded in this manner, and let certain of the expansions contain the factors @*, b°, &c., respectively. The produce of the expansions is identically equal to the product of the unexpanded polyzomes—that is, it is equal to the Norm , hence, if a + 6 + &c. = wo, the Norm will contain the factor @~. VOL. XXV. PART I. D 14 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 30. It has been mentioned that the form ./7(6 + Z@) is considered as includ- ing the form //6 + Lo, that is, when / = 0, the form ./Z@. If in the equa- tion of the »-zomal curve there is any such term—for instance, if the equation be /Lo + J/m(o + Mo) + &c. = 0—the radical ./Z@ contains the factor @’; but if Z contains as factor an odd or an even power of @, then ./Z@ will contain the factor * where « is either an integer, or an integer +3. Consider the polyzome /Z@ + /m(6 + Mo) + &c., belonging to any particular branch of the curve; the radical ./Z@ contains, as just mentioned, the factor @, and if the remaining terms ./m(6 + Mo) + &c., are such that the expansion contains as factor the same or any higher power of &, then the expansion of the polyzome JL + J/m(Q + Mo) + &c., belonging to the particular branch will contain the factor @*; and similarly we may have branches containing the factors +, 64, &c., whence, as before, if » = a + 8 + &c., the Norm will contain the factor ”; the only difference is, that now a,(, &c., instead of being of necessity all integers, are each of them an integer, or an integer + 4; of course, in the latter case the integer may be zero, or the index be = 3. It is clear that » must be an integer, and it is, in fact, easy to see that the fractional indices occur in pairs; for observe that « being fractional, the expansion of ./m(@ + Mo) + &c., will con- tain not «, but a higher power, @«*+2, where a + g isan integer; whence each of the polyzomes ./Z@ + (/m(6 + Mo) + &c.) will contain the factor 31. Observe that in every case the factor presents itself as a factor of the expansion of the polyzome corresponding to a particular branch of the curve; the polyzome itself does not contain the factor @*, and we cannot in anywise say that the corresponding branch contains as factor the curve @* = 0; but we may, with great propriety of expression, say that the branch ideally contains the curve *« = 0; and this being so, the general theorem is, that if we have branches ideally containing the curves @* = 0, 6° = 0, &c. respectively, then the »-zomal curve contains not ideally but actually the factor dy = 0 (# =a+6 + &c.), the order of the v-zomal being thus reduced from 2’-27 to 2°-27 — w(7 — s); and conversely, that any such reduction in the order of the v-zomal arises from factors p* = 0, &? = 0, &c., ideally contained in the several branches of the »-zomal. 32. It is worth while to explain the notion of an ideal factor somewhat more generally; an irrational function, taking the irrationalities thereof in a deter- minate manner, may be such that, as well the function itself as all its differential co-efficients up to the order « — 1, vanish when a certain parameter @ contained in the function is put = 0; this is only saying, in other words, that the function expanded in ascending powers of @ contains no power lower than ®*; and, in this case, we say that the irrational function contains ideally the factor @«. The rationalised expression, or Norm, in virtue of the irrational function (taken deter- minately as above) thus ideally containing *, will actually contain the factor PROFESSOR CAYLEY ON POLYZOMAL CURVES. 15 *; and if any other values of the irrational function contain respectively 4, &c., then the Norm will contain the factor p< + 4 + &. 33. A branch ideally containing @* = 0 may for shortness be called integral or fractional, according as the index ¢ is an integer or a fraction; by what precedes the fractional branches present themselves in pairs. If for a moment we consider integral branches only, then if the »-zomal contain @= 0, this can happen in one way only, there must be some one branch ideally containing ® = 0; but if the v-zomal contain ©’ = 0, then this may happen in two ways,—either there is a single branch ideally containing 6 = 0, or else there are two branches, each of them ideally containing @ = 0. And generally, if the »-zomal contain @ = 0, then forming any partition » =a + 6+ &c. (the parts being integral), this may arise from there being branches ideally containing @* = 0, 6 = 0, &e. respectively. The like remarks apply to the case where we attend also to fractional branches,—thus, if the v-zomal contain @ = 0, this may arise (not only, as above mentioned, from a branch ideally containing @ = 0, but also) from a pair of branches, each ideally containing @'= 0. And so in general, if the v-zomal contain @“ = 0, the partition » = a + 8 + &c. is to be made with the parts integral or fractional (= } or integer + 3 as above), but with the fractional terms in pairs; and then the factor @* = 0 may arise from branches ideally con- taining @* = 0, of = 0, &c. respectively. 34. Any zomal, antizomal, or parazomal of a v-zomal curve, af l.O+L@) + &e. = 0, is a polyzomal curve (including in the term a monozomal curve) of the same form as the »-zomal; and may in like manner contain @ = 0, or more gene- rally, @* = 0, viz., ifo = a + 6 + &c. be any partition of » as above, this will be the case if the zomal, antizomal, or parazomal has branches ideally contain- ing @* = 0, @° = 0, &c. respectively. It is to be observed that if a zomal, anti- zomal, or parazomal contain @ = 0, or any higher power 6” = 0, this does not in anywise imply that the zomal contains even @'= 0. But if (attending only to the most simple case)a zomal and its antizomal, or a pair of complementary parazomals, each contain @ = 0 inseparably (that is, through a single branch ideally containing @ = 0), then the »-zomal will have two branches, each ideally containing @ = 0, and it will thus contain @’ = 0. In fact, if in the zomal and antizomal, or in the complementary parazomals, the branches which ideally con- tain @ = 0 are Ji(o + Le) + &.=0, /n(o + N®) + &. = 0 respectively (for a zomal, the + &c. should be omitted, and the first equation be * written ./7(6 + Lp) = 9), then in the »-zomal there will be the two branches (Jo + L%) + &.)+(J/n(o + N®) + &e.) = 0, each ideally containing @ = 0. 16 PROFESSOR CAYLEY ON POLYZOMAL CURVES. Conversely, if a v-zomal contain 6? = 0 by reason that it has two branches each ideally containing @ = 0, then either a zomal and its antizomal will each of them, or else a pair of complementary parazomals will each of them, inseparably contain @ = 0. 35. Reverting to the case of the v-zomal curve Ji(o + Le) + J/m(e + MS) + &. = 0, which does not contain @ = 0, each of the 7(7— s) common points 6 = 0, ® = 0isa 2’—2-tuple point on the v-zomal; each of these counts therefore for 2»—2 intersections of the v-zomal with the curve 6 = 0, and we have thus the com- plete number 2’—? 7 (7 — s) of intersections of the two curves, viz., the curve @=0 meets the »-zomal in the 7(7—s) common points, each of them a 2»—2-tuple point on the v-zomal, and in no other point. 36. But if the v-zomal contains @* = 0, then each of the 7 (7 — s) common points is still a 2’—?-tuple point on the aggregate curve; the ageregate curve therefore passes 2’—? times through each common point; but among these passages are included » passages of the curve @ = 0 through the common point. The residual curve—say the v-zomal—passes therefore only 2’—2 — w times through the common point; that is, each of the 7(7—s) common points is a (2»—2 — w) tuple point on the »-zomal. The curve @ = 0 meets the »-zomal in {2»—2 » — (7 —s)} (r —s) points, viz., these include the 7(7— s) common points, each of them a (2’—? —o) tuple point on the »-zomal, and therefore counting together as (2’—? —w) r(#— s) intersections; there remain conse- quently » s(7 — s) other intersections of the curve 6 = 0 with the v-zomal. 37. In the case where the v-zomal contains the factor @* = 0, then throughout excluding from consideration the 7(7—s) common points 6 = 0, @ = 0, the remaining intersections of any zomal with its antizomal are points of contact of the zomal with the v-zomal, and the »emaining intersections of each pair of com- plementary parazomals are nodes of the »-zomal, it being understood that if any zomal, antizomal, or parazomal contain a power of @6=0, such powers of ® = 0 are to be discarded, and only the residual curves attended to. The num- ber of contacts and of nodes may in any particular case be investigated without difficulty, and some instances will present themselves in the sequel, but on account of the different ways in which the factor @* = 0 may present itself, ideally in a single branch, or in several branches, and the consequent occur- , rence in the latter case of powers of 6=0 in certain of the zomals, anti- zomals, or parazomals, the cases to be considered would be very numerous, and there is no reason to believe that the results could be presented in any moderately concise form; I therefore abstain from entering on the question. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 17 On the Trizomal Curve and the Tetrazomal Curve—Art. Nos. 38 and 39. 38. The trizomal curve VOR SV Bl WS 0 has for its rationalised form of equation U24+ V27+ W2?—2VW —2WU —2UV=0; or as this may also be written, Cee OL ea 0 and we may from this rational equation verify the general results applicable to the case in hand, viz., that the trizomal is a curve of the order 27, and that U = 0, at each of its rv? intersections with V —~ W= 0 Ve 0; »” » W—U=0 W = 0, a : CV =0 respectively touch the trizomal. There are not, in general, any nodes or cusps, and the order being = 27, the class is = 27(27 — 1). 39. The tetrazomal curve J0+ JV+JWt+J/T=0 has for its rationalised form of equation (U274+V27+4+W? + 7? — 2UV — 2UW — 2UT — 2VW— 2VT — 2WT)8 — 64UV WT = 0, and we may hereby verify the fundamental properties, viz., that the tetrazomal is a curve of the order 47, touched by each of the zomals VU = 0, V=0, W=0, T = 0 in 27’ points, viz. by U = 0 at its intersections with /7 + /W+/T = 0, that is, V? + W? + T? —2VW —2VT —2WT = 0; and the like as regards the other zomals), and having 37’ nodes, viz., these are the intersections of (JU + VV =9, JW+ SJT=09),(J0+ JW=9, JV + ST = 9), (JU + /T=90,/V + /W = 9), or, what is the same thing, the intersections of (U—V=0, W—T=0), (U—W =0, V—T= 0), (U— T=0, V—W= 0). There are not in general any cusps, and the class is thus = 47(4r — 1) — 67’, = 107r°— 4r. On the Intersection of two y-Zomals having the same Zomal Curves—Art. Nos. 40 and 41. 40. Without going into any detail, I may notice the question of the intersec- tion of two »-zomals which have the same zomal curves—say the two trizomals JU+NV +/W=09, JIU +/mV +/nW = 9, or two similarly related VOL. XXV. PART I. E 18 PROFESSOR CAYLEY ON POLYZOMAL CURVES. tetrazomals. For the trizomals, writing the equations under the form JO+J0+ J/W=9, SINT + Vin J/V+ Jn JW=9, then, when these equations are considered as existing simultaneously, we may, without loss of generality, attribute to the radicals ./77, ./V, ./W, the same values in the two equations respectively; but doing so, we must in the second equation successively attribute to all but one of the radicals ./7, /m, ./n, each of its two opposite values. For the intersections of the two curves we have thus VU: SVN W = Nm — Nnidn — JSi:Ji— dm, viz., this is one of a system of four equations, obtained from it by changes of sign, say in the radicals ./jm and ,/n. Each of the four equations gives a set of 7° points; we have thus the complete number, = 47°, of the points of intersection of the two curves. 41. But take, in like manner, two tetrazomal curves; writing their equations in the form Lidl ai ot i ICRA +L WV tat =0. Ji JO + Im IV + Jn JW+ VpVTH=0, then /U, /V,/W, /7 may be considered as having the same values in the two equations respectively, but we must in the second equation attribute succes- sively, say to ./m, /n, \/p, each of their two opposite values. For the inter- sections of the two curves we have C/a> J) LV + (la Jt) JW + Jp — JT) IT = 6 (afl = lm) EF +(J/n—- Jm) JW + (Jp — J/m) /T=0 viz., this is one of a system of eight similar pairs of equations, obtained therefrom by changes of sign of the radicals ./m, ./n, /p. The equations represent each of them a trizomal curve, of the order 27; the two curves intersect therefore in Ar’ points, and if each of these was a point of intersection of the two tetrazomals, we should have in all 8 x 47” = 327° intersections. But the tetrazomals are each of them a curve of the order 47, and they intersect therefore in only 167° points. The explanation is, that not all the 47° points, but only 27° of them are intersections of the tetrazomals. In fact, to find a// the intersections of the two trizomals, it is necessary in their two equations to attribute opposite signs to one of the radicals ./W, ./7'; we obtain 27° intersections from the equations as they stand, the remaining 27” intersections from the two equations after we have in the second equation reversed the sign, say of ,/7. Now, from the two equations as they stand we can pass back to the two tetrazomal equations, and the first men- tioned 27” points are thus points of intersection of the two tetrazomal curves — from the two equations after such reversal of the sign of ./7, we cannot pass back to the two tetrazomal equations, and the last-mentioned 27° points are thus PROFESSOR CAYLEY ON POLYZOMAL CURVES. 19 not points of intersection of the two tetrazomal curves. The number of inter- sections of the two curves is thus 8 x 27’, = 167”, as it should be. The Theorem of the Decomposition of a Tetrazomal Curve—Art. Nos. 42 to 45. 42. I consider the tetrazomal curve JIT + JmVit+ JnW+ J/pT=0, where the zomal curves are in involution,—that is, where we have an identical relation, aU +bV+cW+dT=0; and I proceed to show that if /, m, n, p, satisfy the relation mn pa ae b c the curve breaks up into two trizomals. In fact, writing the equation under the form (J17 + /mV + J/nW) — pT =0, and substituting for 7’ its value, in terms of U, V, W, this is (Jd + pa)U + (md + pb)V + (nd + pe) W +2 4/mnd J/VW+2/nid JWU + 2J/imd JUV = 9; or, considering the left-hand side as a quadric function of (,/U, /V, ./JV), the condition for its breaking up into factors is ld + pa, d Jim, d Jin — 0, el erties Suet a md | d Jnl, dJ/nm, nd + pe that is p(lbed + meda + ndab + pabe) = 0 , or finally, the condition is : + ~ +e SI f =. 43. Multiplying by Jd + pa, and observing that in virtue of the relation we have (id + pa) (md + pb) = lmd? — abe pn (Id + pa) (nd + pce) = Ind? — sa pm , the equation becomes (Ud + pa) J+ Alm JT + AJ JW) = = ad ae P( Stirs Un JW). 7 ae PROFESSOR CAYLEY ON POLYZOMAL CURVES. or as this is more conveniently written ‘ ap TT a TT . a at ra as weet ; (( J+ aD JU + JmV + val) = peas (b Ja - - Jn) ? an equation breaking up into two equations, which may be represented by VLO+ JmVt+ J/nw=l, JL0+ Jn,V+ Jn,wW=0, where i ee ap sehy a p Vi = Jl + ay De a a Be J/m,= JVnm—- La wy i i m= jee? oe 1 bed/ ss 2 bed/ a Jag = Sat EP ovm\ ? ny = dd Sale easariss Pp rae, beds Cm where, in the expressions for ,/7, &c., the signs of the radicals J Sm, Jaa) 2 bed Z may be taken determinately in any way whatever at pleasure; the only effect of an alteration of sign would in some cases be to interchange the values of (Jl, /m,, /n,) With those of (./7,, ./m,, /n,). The tetrazomal curve thus breaks up into two trizomals. 44. It is to be noticed that we have ty Pane a) ap\ (1 Pp =(+ @) (~+7+2 +4); nN a mp that is And similarly we have The meaning is, that, taking the trizomal curve /] U + /m,V + /n,W = 09, this regarded as a tetrazomal curve, /l, U + /m,V + /n,W + »/07' = 0, satis- fies the condition fu + = + 2 + += 0 ; and the like as to the trizomal curve 1,0 + /m,V + Jn, W = 0. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 21. 45. The equation by which the decomposition was effected is, it is clear, one of twelve equivalent equations ; four of these are (0+ a vn WY = A 0 \ (We Vents JT) cs d/l eS ES PAN 2 bao — Jin ) (0 ik ae age ) ( : y- 4. Hovw— ‘sary ee ote ty - aa a JIT — 2 lp 0 v) (vi itis ilo p+) ( : y b. ae “(a JmU—bJIP) and the others may be deduced from these by a cyclical permutation of (U, V, W), (a, b, c), (2, m, 2), leaving 7, d, p unaltered. Application to the Trizomal ; the Theorem of the Variable Zomal—Art. Nos. 46 to 51. 46. I take the last equation written under the form a sa b — — d NZ (a Jind — > JIV) = Fe (VipU + VinpV + (p+ PVT)? which, putting therein p = 0, is (a, Jmol — b JI)? = ar, which is in fact the trizomal curve, aJm0~bJI7 + fe ar=o, viz., the trizomal curve /J17 + /mV + /nW = 0,—if a,b, c be any quantities connected by the equation . oe (the ratios a, b,c thus involving a single arbitrary parameter); and if we take 7 a function such that av + bV +cW+d7= 0; that is, 7 = 0, any one of the VOL. XXV. PART I. F 22 PROFESSOR CAYLEY ON POLYZOMAL CURVES. series of curves aU +bV+cW= 0, in involution with the given curves U=0, V=0, W = 0,—has its equation expressible in the form aJmU — b JIT + J nr=o; that is, we have the curve 7’ = 0 (the equation whereof contains a variable para- meter) as a zomal of the given trizomal curve 70 + ./mV + /nW=0; and we have thus from the theorem of the decomposition of a tetrazomal deduced the theorem of the variable zomal of a trizomal. The analytical investigation is somewhat simplified by assuming p = 0 ab initio, and it may be as well to repeat it in this form. 47. Starting, then, with the trizomal curve Ji + JnmV+ JnW =0, and writing aU +bV+cW+d7=0 as the definition of 7, the coefficients being connected by Von ot: ad a) the equation gives lU+mV + 2 /imUV — aW=; or substituting in this equation for W its value in terms of U, V, T, we have (an + cl) U + (bn + em) V + 2c /imUV + nT = 0, which by the given relation between a, b, c, is converted into ac be es =f eS or 2c JimUV +dnT=0 ; that is ates SEM 10/0 a2m U + b21V — 2ab JimUV = ‘Ce nT ; viz., this is Pe OL (a. /mU —b JiV)? = — Me or finally adm —bvI0 +) arso. 48. The result just obtained of course implies that when as above L aU +bV +eW +d7=0,5+5 +2 =0, the trizomal curve ./7U + ./mN + »/nW = 0 can be expressed by means of any three of the four zomals U, V, W, 7, and we may at once write down the four forms PROFESSOR CAYLEY ON POLYZOMAL CURVES. 23 Re ature, WW, 7) 6 ( " z Pere 2’ az’ abe Bs: ie io? az ‘ abe find, fad abe’ abe’ abe’ the last of which is the original equation ./77 + ./mV + /nW = 9. Itmay be added that if the first equation be represented by /m,V + /n,W + J/p,T = 9 —that is, if we have id amps In Fee m ie Nae ea Jim = C2” m= b?’ YP => and therefore, - t44 Fa (att Ee ae =) is (ie or if the second equation be represented by //,U + /n,W + »/p,7 = 0,—that is, if we have = i. Maree 1 AE =a 2? Jig= Js, t= a and therefore or if the third equation be represented by /7,U + /m,V + /p,T = 0,—that is, if we have - [rw i Ji, = ge, Jims = ete a2? JP = = and therefore then the equation of the trizomal may also be expressed in the forms— es alc ane oo “ab ? and ( Fie’ lest, “a Ji, — [mee \ (vu JV. JW. JT)=0 pad — ibd — NJ * , 5] — J» = fe Jip Meek ae mad lbp ey be ’ ac ” VPs» 49, These equations may, however, be expressed in a much more elegant form. Write j b . Cc —d df eee be Se ~ (By8)? — (yu)? (BB)? (aey”)” where, for shortness, (875) = (8 — y) (y — 8) (0 — 8), &e.; (a, 8, y) being arbitrary quantities: or, what is the same thing, a:b:c:d = a(6yd): — b(yéda) : c'(da8) : — d'(aBy) . Assume Lim:n = ga(B—y)? : ob(y—a)? : rc'(a—B); then the equation —— D +2 — = (0) takes the form e(B—y) ate + o(y—a) (8-8) + r(a—B8) (y—8), and the four forms of the equation are found to be ( . , ve@=7), Ve(B—2), Je (y-8)) (V2, VOT Je, VAT) =0 Vr (7- 9), - 9 ve(b—4), Jo(a—y ) Je (8-9), Vo(y—%), Vr (a—B) viz., these are the equivalent forms of the original equation assumed to be (8 —y) JpaU + (y—4) JSob’V + (¢ — 8) /reW = 9. 50. I remark that the theorem of the variable zomal may be obtained as a transformation theorem—viz., comparing the equation /7U + /mV + /nw=0 with the equation //z + /my + »/nz = 0; this last belongs to a conic touched by the three lines z = 0, y = 0, z = 0; the equation of the same conic must, it is clear, be expressible in a similar form by means of any other three tangents PROFESSOR CAYLEY ON POLYZOMAL CURVES. 25 thereof, but the equation of any tangent of the conic is ax + by + cz = 0, where m i) ing az + by + cz + dw = 0, we may introduce w = 0 along with any two of the original zomals « = 0, y = 0, z = 0, or, instead of them, any three functions of the form w; and then the mere change of 2, y, z,w into U, V, W, T gives the theorem. But it is as easy to conduct the analysis with (U, V, W, 7) as with (x, y,%, wv), and, so conducted, it is really the same analysis as that whereby the theorem is established ante, No. 47. 51. It is worth while to exhibit the equation of the curve a, b,c are any quantities satisfying the condition i ++ ~ = (0; whence, writ- JIT + JmVit J/nW = 9, in a form containing three new zomals. Observe that the equation L of er. - =0 b is satisfied by a = /dx, b = mx0, c= nO”, if only 06+ 6+ x=); or say, if 6=a—a, p= a—a, x= a—a'. The equation aA J(a—a)(a—a’\lU + (a —a’) (a —a)mV + (a’—a) (a”—a)nW + J/(b—v) O-VU + WV’) G—b)mV + (VU —b) (’—0)nW +» J/(e=¢) (C—elU + (=e) (’—c)mV + (c’—c) (c’—c)nW = 0 is consequently an equation involving three zomals of the proper form; and we can determine A, “,v in suchwise as to identify this with the original equation JIU + J/mV + J/nW, Viz., writing successively V = 0, V= 0, W = 0, we find (a —a")a+ (V—V’) wt (C—c’)v =0, (a’—a)r~A + (0’—b) wt (—c) v=0, (a—a’)rA+ (b—-U) wt (ec—e v=0, equations which are, as they should be, equivalent to two equations only, and which give FM eT amt) Ha ocala pe jl Fe! Rn Ti at lS bi0\0" GONE COO Oe” G30 100 b, 0’, b” and the equation, with these values of , », v substituted therein, is in fact the equation of the trizomal curve ./W + ./mV + /nW =9 in terms of three new zomals. It is easy to return to the forms involving one new zomal and any two of the original three zomals. Remark as to the Tetrazomal Curve—Art. No. 52. 52. I return for a moment to the case of the tetrazomal curve, in order to show that there is not, in regard to it in general, any theorem such as that of the variable zomal. Considering the form /lz + /my + J/nz + /pw = ° (the co- VOL. XXV. PART I. G 26 PROFESSOR CAYLEY ON POLYZOMAL CURVES. ordinates 2, y,z,m are of course connected by a linear equation, but nothing turns upon this), the curve is here a quartic touched twice by each of the lines a=0, ¥y=0, z=0, w = 0 (viz., each of these is a double tangent of the curve), and having besides the three nodes (z# = y, z = ®), (v=2% Y=W), (T=, Y = 2). But a quartic curve with three nodes, or trinodal quartic, has only four double tangents—that is, besides the lines z = 0, y = 0, z = 0, w = 0, there is no line ax + By + yz + dw = 0 which is a double tangent of the curve; and writing U, V, W, T in place of 2, y, 2, vw, then if U, V, W, 7 are connected by a linear equation (and, @ fortiori, if they are not so connected), there is not any curve aU +BV+yW +0L=0 which is related to the curve in the same way with the lines VU = 0, V=0, W =0, T = 0; or say there is not (besides the curves U=0, V=0, W=0, T=0), any other zomal eU+ BV+yW+ dST=0, of the tetrazomal curve. The proof does not show that for special forms of U,V, W,T there may not be zomals, not of the above forma +6V+yW+d7T=0, but belonging to a separate system. An instance of this will be mentioned in the sequel. The Theorem of the Variable Zomal of a Trizomal Curve reswmed—Art. Nos. 53 to 56. 53. I resume the theorem of the variable zomal of the trizomal curve JIT + /mV + /nW=0. ‘The variable zomal 7 =0 is the curve aU +bV + cW = 0, where a, b, c are connected by the equation : we ks oa “ =0; that is, it belongs to a single series of curves selected in a certain manner out of the double series aU’ + bV + cW = 0 (a double series, as containing the two variable parameters a: b:c). These are the whole series of curves in involution with the given curves U = 0, V = 0, W = 0, or being such that the Jacobian of any three of them is identical with the Jacobian of the three given curves; in particular, the Jacobian of any one of the curves aU + bV + cW = 0, and of two of the three given curves, is identical with the Jacobian of the three given curves. I call to mind that, by the Jacobian of the curves U= 0, V=0, W = 0, is meant the curve d(x, y, 2) hg Vy V=eaV d,W,d,W,d.W viz., the curve obtained by equating to zero the Jacobian or functional deter- minant of the functions U, V, W. Some properties of the Jacobian, which are material as to what follows, are mentioned in the Annex No. I. For the complete statement of the theorem of the variable zomal, it would be necessary to interpret geometrically the condition ‘ ee ; a ~ = 0, thereby PROFESSOR CAYLEY ON POLYZOMAL CURVES. 27 showing how the single series of the variable zomal is selected out of the double series of the curves aU + bV + cW = 0 in involution with the given curves. Such a geometrical interpretation of the condition may be sought for as follows. but it is only in a particular case, as afterwards mentioned, that a convenient geometrical interpretation is thereby obtained. 54. Consider the fixed line 2 = px + qy + rz = 0, and let it be proposed to find the locus of the (r— 1)? poles of the line 2 = 0 in regard to the series of curves aV +bV+cw =), where « As % ae . —(, Take (z,y, z) as the co-ordinates of any one of the poles in question, then in order that (#, y, z) may belong to one of the (7 — 1)? poles of the line 2 = px + qy + 7rz =0 in regard to the curve aU + bV + cW = 0, we must have d(aU +bV+cW):d,aU +bV+cW): dau +bV+eW) =p:¢:7; or, what is the same thing— =ds0r dard, a and these equations give without difficulty abet ICV, We OyICW, U, a) :d(U, Voy, en Sociale “en (aaa 7 whence, substituting in the equation Eat eae Uae have l m nN TVW, a) t 7(W, 0a) * 70 Va" as the locus of the (r—1)’ poles in question. Each of the Jacobians is a func- tion of the order 277 — 2, and the order of the locus is thus = 4r—4. As the given curves U = 0, V = 0, W = 0 belong to the single series of curves, it is clear that the locus passes through the 3(7 — 1)? points which are the (7 — 1)? poles of the fixed line in regard to the curves U = 0, V= 0, W= 0 respectively. 55. In the case where the given trizomal is Jie + Le) + J/m(o + Me) + JVn(o + No=0, s=r—1, that is, where the zomals 96+ ZOb=0, 0+ MG=0,6+4+ NO=0 are each of them curves of the order 7, passing through the 7 intersections of the line @ = O with the curve 6 = 0, then, visti this line » = 0 for the fixed line (2 = 0, we have J(V,W,2) = J(0 + MS, 0 + No, s)=O{M,N}, if, for shortness, {7, V' = J(M-N,0, ©) + @J(M, N,o&), and the like as to the other two Jacobians, so that, attaching the analogous significations to {N, ZL} and {L, M}., the equation of the locus is l m n (wy * EN Zy * {za ° where observe that each of the curves {17, M} = 0, {N, LZ} = 0, {L,M} =0 is 28 PROFESSOR CAYLEY ON POLYZOMAL CURVES. a curve of the order 27 — 3; the order of the locus is thus = 47 — 6, and (as before) this locus passes through the 3(7 — 1)’ points which are the (7 — 1)’ poles of the line @ = 0 in regard to the curves 69 + Lb = 0,6 + Mb = 0,0 + Nb = 0 respectively. 56. In the case 7 = 2, the trizomal is Jio+ Le) + J/m(o+ Me) + Jn(O+ No) =0, where the zomals are the conics 6 + Lo = 0, 9 + MH = 0, 8 + NS = O, each passing through the same two points 6 = 0, 6 = 0; the locus of the pole of the line @ = 0, in regard to the variable zomal, is the conic l m n (W,N}* {NZ} 7 {Za ~°> viz., {M@, N} = 0, {N,L}= 0, {Z,M}=0, are here the lines passing through the poles of the line @ = 0 in regard to the second and third, the third and first, and the first and second of the given conics respectively : treating /, m, n as arbi- trary, the locus is clearly any conic through the poles of the line @ = 0 in regard to the three conics respectively. The Jacobian of the three given conics is a conic related in a special manner to the three given conics, and which might be called the Jacobian conic thereof, and it would be easy to give a complete enunciation of the theorem for the case in hand. (See as to this, Annex No. I, above referred to.) But if, in accordance with the plan adopted in the remainder of the memoir, we at once assume that the points 6 = 0, @ = 0 are the circular points at infinity, then the theorem can be enunciated under a more simple form—viz., if A° = 0, B° = 0, C° = 0 are the equations of any three circles, then in the trizomal VIX + J/mB°+ J/nO°=0, the variable zomal is any circle whatever of the series of circles cutting at right angles the orthotomic circle of the three given circles, and having its centre on a certain conic which passes through the centres of the given circles. Moreover, if the co-efficients /, m, m are not given in the first instance, but are regarded as arbitrary, then the last-mentioned conic is any conic whatever through the three centres, and there belongs to such conic and the series of zomals derived there- from as above, a trizomal curve ,//A° + ./mB° + ./nC° = 0. This is obviously the theorem, that ifa variable circle has its centre on a given conic, and cuts at right angles a given circle, then the envelope of the variable circle is a trizomal curve .//A° + ./mB° + /nC*, where A®= 0, B°=0, C°=0 are any three circles, positions of the variable circle, and /, m, 7 are constant quantities depend- ing on the selected three circles. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 29- Part IT. (Nos. 57 to 104).—SuBsiD1aRy INVESTIGATIONS. Preliminary Remarks—Att. Nos. 57 and 58. 57. We have just been led to consider the conics which pass through two given points. There is no real loss of generality in taking these to be the circular points at infinity, or say the points /, J/—viz., every theorem which in anywise explicitly or implicitly relates to these two points, may, without the necessity of any change in the statement thereof, be understood as a theorem relating instead to any two points P,Q. I call to mind that a circle is a conic passing through the two points /, J, and that lines at right angles to each other are lines har- monically related to the pair of lines from their intersection to the points J, J respectively, so that when (J, /) are replaced by any two given points whatever, the expression a circle must be understood to mean a conic passing through the two given points; and in speaking of lines at right angles to each other, it must be understood that we mean lines harmonically related to the pair of lines from their intersection to the two given points respectively. For instance, the theorem that the Jacobian of any three circles is their orthotomic circle, will mean that the Jacobian of any three conics which each of them passes through the two given points is the orthotomic conic through the same two points, that is, the conic such - that at each of its intersections with any one of the three conics, the two tangents are harmonically related to the pair of lines from this intersection to the two given points respectively. Such extended interpretation of any theorem is appli- cable even to the theorems which involve distances or angles—viz., the terms “distance” and ‘‘ angle” have a determinate signification when interpreted in reference (not to the circular points at infinity, but instead thereof) to any two given points whatever (see as to this my “Sixth Memoir on Quantics,” Nos. 220, et seqg.*) And this being so, the theorem can, without change in the statement thereof, be understood as referring to the two given points. 58. I say then that any theorem (referring explicitly or implicitly) to the cir- cular points at infinity Z, J, may be understood as a theorem referring instead to any two given points. We might of course give the theorems in the first instance in terms explicitly referring to the two given points—(viz., instead of a circle, speak of a conic through the two given points, and so in other instances) ; but, as just explained, this is not really more general, and the theorems would be given in a less concise and familiar form. It would not, on the face of the inves- tigations, be apparent that in treating of the polyzomal curves Ji + 1%) + Jm(@ + Me) + &e. = 0, (9 = 0 a conic, = 0 a line, as above), that we were really treating of the * Phil. Transactions, vol. cxlix. (1859), pp. 61-90. See p. 86, VOL, XXY. PART I, H 30 PROFESSOR CAYLEY ON POLYZOMAL CURVES. curves the zomals whereof are circles, and therein of the theories of foci and focofoci as about to be explained. And for these reasons! shall consider the two points 6 = 0, @ = 0, to be the circular points at infinity J, J, and in the investigations, &c., make use of the terms circle, right angles, &c., which, in their ordinary significations, have implicit reference to these two points. The present Part does not explicitly relate to the theory of polyzomal curves, but contains a series of researches, partly analytical and partly geometrical, which will be made use of in the following Parts III. and IV. of the Memoir. The Circular Points at Infinity ; Rectangular and Circular Co-ordinates—Art. Nos. 59 to 62. 59. The co-ordinates made use of (except in the cases where the general trilinear co-ordinates (2, 7, ), or any other co-ordinates, are explicitly referred to), will be either the ordinary rectangular co-ordinates 2, y, or else, as we may term them, the circular co-ordinates & 7 (= + iy, 2 — iy respectively, 7 = ./ — ] as usual), but in either case I shall introduce for homogeneity the co-ordinate 2, it being understood that this co-ordinate is in fact = 1, and that it may be retained or replaced by this its value, in different investigations or stages of the same investigation, as may for the time being be most convenient. In more con- cise terms, we may say that the co-ordinates are either the rectangular co-ordi- nates x, y, and z ( = 1), or else the circular co-ordinates £, », and z(=1). The equation of the line infinity is 7 = 0; the points J, J are given by the equations (a + iy = 0, z = 0) and (« — wy = 0, z = 0), or, what is the same thing, by the equations (& = 0, z = 0) and (7 = 0, = 0) respectively; or in the rectangular co- ordinates the co-ordinates of these points are ( — 7, 1, 0) and (2, 1, 0) respectively, and in the circular co-ordinates they are (1, 0, 0) and (0, 1, 0) respectively. It is of course, only for points at infinity that the co-ordinate z is = 0 (and observe that for any such point the z and y or € and 7 co-ordinates may be regarded as finite) , for every point whatever not at infinity the co-ordinate z is, as stated above, = 1. 60. Consider a point A, whose co-ordinates (rectangular) are (a, a’, 1) and (circular) (a, a’, 1), viz. a = a+ ai, a =a—av7; then the equations of the lines through A to the points J, J, are x—az+uUy—az)=0, «—az— i(y— az)=0 respectively, or they are -—az= » n—az=0 respectively. These equations, if (a, a’) or (a, a’) are arbitrary, will, it is clear, be the equations of any two lines through the points J, J, respectively. 61. We have from either of the equations in (2, y,z) («— az? + (y—a’z)? =0, that is, the distance from each other of any two points (2, y, 1), and (a,@’,1) ina PROFESSOR CAYLEY ON POLYZOMAL CURVES. dl line through J or Jis=0. And in particular, if z = 0, then 2 + y’ = 0; that is, the distance of the point (@,a@’,1) from J or J is in each case = 0. 62. Consider for a moment any three points P,Q, A; the perpendicular dis- tance of P from QA is = 2 triangle PQA ~ distance QA; if Q be any point on the line through A to either of the points J, J, and in particular if Q be either of the points J, J, then the triangle PQA is finite, but the distance QA is = 0: that is, the perpendicular distance of P from the line through A to either of the points I, J, that is, from any line through either of these points, is = 00. But, as just stated, the triangle PQA is finite, or say the triangles P/A, PJA are each finite; viz., the co-ordinates (rectangular) of P, A being (a, y, z = 1), (a, a’, 1) or (circular) (E,, 2 = 1), (a, a’, 1), the expressions for the doubles of these triangles respec- tively are L,Y, @ 6 “L,Y, @ me ay Ae a, Gal | a, DEAL that is, they are (rectangular co-ordinates) e—az + 1(y— a’ z), x—az—i(y—a@e), or (circular co-ordinates) & — az, » —a’ z. Representing the double areas by PJA, PJA, respectively, and the squared distance of the points A, P by A, we have— A = (a — az)? + (y — a2)? = (& — az) (n — wz), = PIA, PUA. Antipoints ; Definition and Fundamental Properties—Art. No. 63. 63. Two pairs of points (A,B) and (4,,B,) which are such that the lines AB, A,B, bisect each other at right angles in a point O in such wise that OA = OB =1 0A, =i0OB,, are said to be antipoints, each of the other. In rectangular co-ordinates, taking the co-ordinates of (4 B,) to be (a,0,1) and (—a, 0,1), those of (A,, B,) will be (0, a, 1) and (0, — az, 1) respectively, whence joining the points (A, B) with the points (J, -/), the points A,,B, are given as the intersections of the lines AJ and BJ, and of the lines AJ and BI respectively. Or, what is the same thing, in any quadrilateral wherein J, J are opposite angles, the remaining pairs (A,B) and (A,, B,) are antipoints each of the other. 64. In circular co-ordinates, if the co-ordinates of A are (a, a’, 1), and those of B are ((@, 6’, 1), then the equations of ALAJ are §—az=0, 1-—e&z=0 BI, BI ” &—pz= 2 1—6z=0 whence the equations of A,I,A,J are §—az=0, 4—Bz=0 BLBIT , F—-Pze=0, 4-az=0. 32 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 65. Considering any point P the co-ordinates of which are £,,2 (= 1), let A,B,A,,B, be its squared distances from the points A,B, A,,B, respectively; then by what precedes— A = (& — az) (n— a2), B = (§ — 2) (n— 8B), A, = (€ — az) (n — B2), B, = (§ — Bz) (n — 2), and thence A.B=A,.B,; that is, the product of the squared distances of a point P from any two points A, B, is equal to the product of the squared distances of the same point P from the two antipoints A,,.B,. This theorem, which was, I believe, first given by me in the Educational Times (see reprint, vol. vi. 1866, p. 81), is an important one in the theory of foci. It is to be further noticed that we have A+B—A,—B,=(«-8)(/—6)# = K2,=K, if K, = (a — a’) (8 — 8’), be the squared distance of the points A, 6, = — squared distance of points 4,, B,. Antipoints of a Circle—Art. No. 66. 66. A similar notion to that of two pairs of antipoints is as follows, viz., if from the centre of a circle perpendicular to its plane and in opposite senses, we measure off two distances each = 7 into the radius, the extremities of these distances are antipoints of the circle. It is clear that the antipoints of the circle and the extremities of any diameter thereof are (in the plane of these four points) pairs of antipoints. It is to be added that each antipoint is the centre of a sphere radius zero, or say of a cone sphere, passing through the circle: the circle is thus the intersection of the two cone spheres having their centres at the two antipoints respectively. Antipoints in relation to a Pair of Orthotomie Circles—Art. No. 67. 67. It is a well-known property that if any circle pass through the points (A, B), and any other circle through the antipoints (4,, B,), then these two circles cut at right angles. Conversely if a circle pass through the points A, B, then all the orthotomic circles which have their centres on the line AB pass through the antipoints 4,,.B,. In particular, if on AZ as diameter we describe a circle and on A, #, as diameter a circle, then these two circles—being, it is clear, concentric circles with their radii in the ratio 1:7, and as concentric circles touching each other at the points (Z,/)—cut each other at right angles; or say they are con- centric orthotomic circles: PROFESSOR CAYLEY ON POLYZOMAL CURVES. 33 Forms of the Equation of a Circle—Art. Nos. 68 to 71. 68. Tn rectangular co-ordinates the equation of a circle, co-ordinates of centre (a, a’, 1) and radius = a’, is Ao = (a@—az? + (y—a 2)?-a® 2 =0; and in circular co-ordinates, the co-ordinates of the centre being (a, a’, 1), and radius=a’ as before, the equation is A® = (&— az) (n- wz) -—a? 2 =0. 69. I observe in passing, that the origin being at the centre and the radius being=1, then writing also z=1, the equation of the circle is &;=1, that is the circular co-ordinates of any point of the circle, expressed by means of a variable parameter @, are (6, 7 i. 70. Consider a current point P, the co-ordinates of which (rectangular) are 2, y, (=1), and (circular) are &, », 2 (=1), then the foregoing expression = (wx—az)? + (y—a 2)? —a'? = (§—az) (n—a@z) —a'? denotes, it is clear, the square of the tangential distance of the point P from the circle A° = 0. 71. But there is another interpretation of this same function A°, viz., writing — therein z = 1, and then A’ =(x—a)? +(y— a)? + (a1)?, we see that A’ is the squared distance of P from either of the anti-points of the circle (points lying, it will be recollected, out of the plane of the circle), and we have thus the theorem that the square of the tangential distance of any point P from the circle is equal to the square of its distance from either anti-point of the circle. On a System of Sixteen Points—Art. Nos. 72 to 77. 72. Take (A, B, C, D) any four concyclic points, and let the anti-points of (B, C), (A, D) be (By, OC), (Ap Dy) » (C, 4), (BD) » (Cy Ae), (Ba De) » (4, B), (GD) » (As Bs), (Cs, Ds) » then each of the three new sets (4,, B,, C,, D,), (4,, B,, C,, D,), (Ag, B;, Cz, Ds) will be a set of four concyclic points. 73. Let O be the centre of the circle through (A, B, C, D), say of the circle O, and then, the lines BC, AD meeting in R, the lines CA, BD in S, and the lines AB, CD in T, let each of these points be made the centre of a circle orthotomic to O, viz., let these new circles be called the circles R, S, T respectively. As regards the circle #, since its centre lies in BC, the circle passes through (B,, C,); and since the centre lies in AD, the circle passes through (4,, D,), that is, the four points (4,, B,, C,, D,) lie in the circle R. Similarly (4,, B,, C,, D,) lie in the circle S, and (A,, B,, C,, D,) in the circle 7. VOL. XXV. PART I. I 34 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 74. The points #, S, 7 are conjugate points in relation to the circle O; that is, ST, TR, RS are the polars of &, S, 7 respectively in regard to this circle; and they are, consequently, at right angles to the lines OR, OS, OT respectively ; viz., the four centres O, #,S,7 are such that the line joining any two of them cuts at right angles the line joining the other two of them, and we see that the relation between the four sets is in fact a symmetrical one; this is most easily seen by consideration of the circular points at infinity J, J, the four sets of points may be arranged thus :— A,A oe By; Ty, Tie, Pas OL, Us eas BEDS | TEs RS a» Ao, B in such wise that any four of them in the same vertical line pass through J, and any four in the same horizontal line pass through / ; and this being so, starting for instance with (A,, B,, C,,.D,) we have anti-points of (Bs, C,), (Ag, Ds) are (By, Cy), (Ag, Dy), » (Cy Ay), (By Dg)» (Cy Ay) (By Dy); » (Az, Bs), (C;, D,) » (A ? £,), (C , D 7; and similarly if we start from (4,, B,, C,, D,) or (A,, B,, C,, D,). 75. [return for a moment to the construction of (A,, B,, C,, D,); these are points on the circle #, and (B,, C,) are the anti-points of (B, C); that is, they are the intersections of the circle # by the line at right angles to BC from its middle point, or, what is the same thing, by the perpendicular on BC from O. Similarly (A,, D,) are the anti-points of (A, D); that is, they are the intersections of the circle 2 by the perpendicular on AD from O. And the like as to (A,, B,, C,, D,) and (A,, B,, C,, D,) respectively. 76. Hence, starting with the points A, 6, C, D on the circle O, and constructing as above the circles P, Q, #, and constructing also the perpendiculars from O on the six chords AB, AC, &c., the perpendiculars on BC, AD meet circle Rin (B,, C,), (A;, D,), . CA,BD , 4 S 5 (Cz,A2), (By D,), 3 AB OD eee ogee soe) (tebe a so that the whole system is given by means of the circles P, Q, &, and the six perpendiculars. 77. If to fix the ideas (A, 6, C, D) are real points taken in order on the real circle O, then the points #, S, 7 are each of them real; but # and 7 lie outside, S inside the circle O. The circles R and 7 are consequently real, but the circle S imaginary, viz., its radius is = 7 into a real quantity; the imaginary points (A,, B,, C,, D,) are thus given as the intersections of a real circle by a pair of real lines, and the like as to the imaginary points (4,, 6,,C,, D,); but the PROFESSOR CAYLEY OF POLYZOMAL CURVES. 35 imaginary points (A,, B,, C,, D,) are only given as the intersections of an imagin- ary circle (centre real and radius a pure imaginary) by a pair of real lines. The points (C,, A,) gud anti-points of (C, A) are easily constructed as the intersections of a real circle by a real line, and the like as to the points (B,, D.) qua anti-points of (B, D), but the construction for the two pairs of points cannot be effected by means of the same real circle. Property in regard to Four Confocal Conics—Art. Nos. 78 to 80. 78. All the conics which pass through the four concyclic points A, B, C, D, have their axes in fixed directions; but three such conics are the line-pairs (BC, AD), (CA, BD), and (AB, CD), whence the directions of the axes are those of the bisec- tors of the angles formed by any one of these pairs of lines; hence, in particular, considering either axis of a conic through the four points, the lines 4B and CD are equally inclined on opposite sides to this axis, and this leads to th theorem that the anti-points (A,, B,) (C,, D,) are in a conic confocal to the given conic through (A, B, C, D); whence, also, considering any given conic whatever through (A, B, C, D), the points (A,,.B,, C,, D,), (A,, B,, C,, D,) (A;, B,, C,, D;) lie seve- rally in three conics, each of them confocal with the given conic. 79. To prove this, consider any two confocal conics, say an ellipse and a hyper- - bola, and let /' be one of their four intersections; join / with the common centre O, and let OT, ON be parallel to the tangent and normal respectively of the ellipse at the point /. OF, OT are in direction conjugate axes of the ellipse, and OF, ON are in direction conjugate axes of the hyperbola; and if they are also the axes in magnitude, that is, if the points 7, NV are the intersections of OT with the ellipse and of ON with the hyperbola respectively, then it is easy to show that OT? +0N?=0. And this being so, imagine on the ellipse any two points A, B such that the chord AB is parallel to OT, that is conjugate to OF; AB is bisected by OF, say in a point K, or we have parallel to O7 the semichords or ordinates KA=KEB; and we may, perpendicularly to this or parallel to ON, draw through K in the hyperbolaa chord A,B,, which chord will be bisected in K, or we shall have KA, = KB,. Hence KA, KA, are in the ellipse and the hyperbola respec- tively ordinates conjugate to the same diameter O/’, and the semi-diameters con- jugate to OF being OT, ON respectively, we have KA?(—KB’): KA; (=KB?’) = OF : ON’, that is, KA7=KB’= — KA = — KB’; or (A,, B,) will be the anti-points of (A, B). 80. Conversely, if in the ellipse we have the two points (A, B), then drawing the diameter OF’ conjugate to A, and through its extremity /, the confocal hyperbola, then the anti-points (A,, B,) will lie on the hyperbola. And similarly, if on the ellipse we have the two points (C,D), then drawing the diameter OG conjugate to CD, and through its extremity G a confocal hyperbola, the 36 PROFESSOR CAYLEY ON POLYZOMAL CURVES, anti-points (C,, D,) will lie on the hyperbola. Suppose (A, B, C, D) are concyclic, then, as noticed, AB and CD will be equally inclined on opposite sides to the transverse axis of the ellipse—the conjugate diameters OF, OG will therefore be equally inclined on opposite sides of the transverse axis—and the points / and @ will therefore be situate symmetrically on opposite sides of the transverse axis, that is, the points / and @ will respectively determine the same confocal hyper- bola, and we have thus the required theorem, viz., if (A, B,C, D) are any four concyclic points on an ellipse, or say on a conic, and if (A,, B,) are the anti- points of (A, B), and (C,, D,) the anti-points of (C, D), then (A,, B,, C,, D;) will lie on a conic confocal with the given conic. System of the Sixteen Points, the Axial Case—Art. Nos. 81 to 85. 81. The theorems hold good when the four points A, B, C, D are ina line; the anti-points (B,, C,) of (B, C), &c., are in this case situate symmetrically on oppo- site sides of the line, so that it is evident at sight that we have (A,, B,, C,, D,), (A,, B,, C,, D,), (A;, B;, C;, D;), each set in a circle; and that the centres R, S, T of these circles lie in the line. The construction for the general case becomes, however, indeterminate, and must therefore be varied. If in the general case we take any circle through (B, C), and any circle through (A, JD), then the circle # cuts at right angles these two circles, and has, consequently, its centre # in the radical axis of the two circles; whence, when the four points are ina line, taking any circle through (4,C), or in particular the circle on BC as diameter, and any circle through (A, J), or in particular the circle on AD as diameter,—the radical axis of these two circles intersects the line in the required centre /, and the circle # is the circle with this centre cutting at right angles the two circles respectively; the circles S and 7 are, of course, obtained by the like construction in regard to the combinations (C, A ; B, D) and (A, B; C,D, respectively. It may be added, that we have R extremities R BGs. A, D, S kent and | of diameter S | sicojngt points of involutions GU, 4, B,D, g of circles TZ Ay B.D and that (as in the general case) the circles R, S, 7 intersect each pair of them at right angles; and they are evidently each intersected at right angles by the line ABCD (or axis of the figure), which replaces the circle O in the general case. 82. If the points 4, B,C, D are taken in order on the line, then the points Rk, S, T are all real, viz., the point £ is situate, on one side or the other, outside AD, but the points S and 7’ are each of them situate between B and C; the circles & and 7 are real, but the circle S has its radius a pure imaginary quantity. 83. If one of the four points, suppose D, is at infinity on the line, then the anti-points of (A, D), of (B, D), and of (C, D) are each of them the two points PROFESSOR CAYLEY ON POLYZOMAL CURVES. Sif (Z,J). It would at first sight appear that the only conditions for the circles R, S, T were the conditions of passing through the anti-points of (B, C), of (C, A), and of (A, B) respectively, and that these circles thus became indeterminate ; but in fact the definition of the circles is then as follows, viz., # has its centre at A, and passes through the anti-points of (B,C): (whence squared radius =AB.AC). And similarly, S has its centre at B,and passes through anti-points of (C, A), (squared radius = BA.BC); and 7 has its centre at C, and passes through anti-points of (A, &), (squared radius = C'A . CB); these three circles cut each other at right angles. As before, 4, B, C being in order on the line, the circles 2, 7 are real, but the circle S has its radius a pure imaginary quantity. 84. That the circles are as just mentioned appears as follows: taking the line as axis of z, and a, b,c, d for the « co-ordinates of the four points respectively, then the co-ordinates of A,, D, are t(a + d), +4i(a — a); whence, m being arbitrary, the general equation of a circle through 4,, D, is a + y® — 2mxz + [m(a + d) — ad] =0 , writing herein 0 — this becomes - 2 2 e+ ye 2(« — 7) + G —k? — <)#=0 ; d viz., for d = o it is which is a circle having 4 for its centre, and its radius an arbitrary quantity &. If the circle passes through the anti-points of B, C, the co-ordinates of these are 4(64+¢),+Mb-o), and we find ke = [3(0 + ec) — a}?— 400 -— OF =(@— bla — 0). 85. Reverting to the general case of four points A, B,C,D on a line, the theorem as to the confocal conics holds good under the form that, drawing any conic whatever through (4,, B,, C,, D,) the points (4,, B,, C,, D,), and (A,, B,, C;, D,) lie in confocal conics, these conics have their centre on the line, and axes in the direction of and perpendicular to the line. When D is at infinity, the confocal conics become any three concentric circles through (B,,C,), (C,, A.) and (A,, B,) respectively. The Involution of Four Circles——Art. Nos. 86 to 91. 86. Consider any four points A, B,C, D, the centres of circles denoted by these same letters, and let A°, B°, C°, D° signify as usual, viz., if (in orthogonal VOL. XXV. PART I. K 38 PROFESSOR CAYLEY ON POLYZOMAL CURVES. co-ordinates) (a, a’, 1) are the co-ordinates of the centre, and a” the radius of the circle A, then A° stands for (2 — az)? + (y—az) —a”’~, and the like for B’, C°, D°. Write also a:b:e:d=BCD: —CDA : DAB: — ABC, where BCD, &c., are the triangles formed by the points (B,C, D), &c.; the analytical expressions are as bsats th] 0, OS bis) Gee, 2 d,d, 1 | — | aa, 1 | iw fae | 4d, 1 a, @ 4 bo, Y, 1 | | hs sill a els |. Cy yh Db ¥, yk oat; 4.\) so that a +b itetd> =F, aa + bb + ce + dd = 0, aa + bb’ + ce + dd = 0; this being so, it is clear that we have aA° + bB° + cC°® + dD® = 2[a(a? + a?—a'?) + b(0?+0?—-b) + (2? +07 — 0") + dP +d*- d®)) = KZ,=K, a constant. 87. I am not aware that in the general case there is any convenient expres- sion for this constant A ; it is = 0 when the four circles have the same ortho- tomic circle; in fact, taking as origin the centre of the orthotomic circle, and its radius to be = 1, we have a2 + a® — a? = 1, &., whence K= s+ b+¢.44=0; that is, if the circles 4, B, C, Dhave the same orthotomic circle, then A’, B°, C°, D®, a, b, ¢, d, signifying as above, we have aA° + bB° + cC° + dD°= 0, and, in particular, if the circles reduce themselves to the points 4, 5, C, D re- spectively, then (writing as usual A, B,C, D in place of A’, B’, C°, D°) if the four points A, 6, C, D are on a circle, we have aA + bB +00 +dD=0. 88. This last theorem may be regarded as a particular case of the theorem aA + bB+cC + dD= Kk? = K, viz., the four circles reducing themselves to the points A, B, C, D, we can find for the constant A an expression which will of course vanish when the points are onacircle. For this purpose, let the lines BC,AD meet in AR, the lines PROFESSOR CAYLEY ON POLYZOMAL CURVES. 39 CA, BD in S, and the lines Ab, CD in T; we may, to fix the ideas, consider ABCD as forming a convex quadrilateral, R and 7’ will then be the exterior centres, S the interior centre; a, b, c,d, may be taken equal to BCD, — CDA, DAB, — ABC, where the areas BCD, &c., are each taken positively. The expression aA + bB + cC + dD has the same value, whatever is the position of the point P (z, y, z = 1); taking this point at #, and writing for a moment ha = 7 = 0, Ro = y, AD = 3, then BCD = (RCD — RED) =}RD (RC — LB) sin k = (y—B)ésin £, with similar expressions for the other triangles; and we thus have , . &(y¥—Bd eco ae ane) 8? Ca acts Bey — wdyly — 4 eG / &. 77(8 — «)8 ame, Yi a nog B)(6 ae — Py — Ba that is, replacing a, 6, y, 0, by their values, and writing also z = 1, we have aA + bB + cC +dD=4sinR. (RB. RC — RA. RD)BC. AD, where 4sin &.BC.AD is in fact the area of the quadrilateral ABCD ; we have thus aA + bB + cO + dD = (RB.RC—RA.RD)O = (SC .SA —SB.SD)5 ' = (TA.TB-—TC.TD)O where it is to be observed that SA, SC being measured in opposite directions from S, must be considered, one as positive, the other as negative, and the like as regards SB, SD. This expression for the value of the constant is due to Mr Crofton. In the particular case where A, 6, C, D, are on acircle, we have as before aA + bB+cC +dD=0. 89. If the four points A, 6, C, D, are on a circle, then, taking as origin the centre of this circle and its radius as unity, the circular co-ordinates of the four points will be ; (<3); 622): 34) Gh) the corresponding forms of A, &c., being | A° = (2 — az) (1 aa 2) — W?2, &e. the expressions for a, b, c,d, observing that we have 1 = Bye (By8), &e. +0) PROFESSOR CAYLEY ON POLYZOMAL CURVES. if (By0), &c., denote (8 — y) (y — 9) (6 — B), &c., become a:b:c:d = a(Byd): — B(yda) : y(da8): — b(aBy), which are convenient formule for the case in question. 90. If the points A, B, C, D, are on a line, then taking this line for the axis of a, we may write A°=(# —az) +y*°—a@’2, &c. It is to be remarked here that we can, without any relation whatever between the radii of the circles, satisfy the equation aA® + bB° + cC° + dD° = 0; in fact this will be the case if we have a ze 0) + ¢ 2d 0, aul + bb + ce +dd=0, a(a? — a’*) + b(b? — b”) + ee? — ce”) + dd? — d”) = 0, equations which determine the ratios a: b:c:d. In the case where the circles reduce themselves to the points A, B, C, ), these equations become a+b +e++d =0, aa + bb +cc +dd =0, aa? + bb? + cc? + dd? = 0, giving a:b:ce:d = (bed): — (eda): (dab): — (abe); if for shortness (Jed), &c. stand for (b — c)(e — d)(d — b), &c.; and for these values, we have aA + bB + cO0 + dD=0. 91. A very noticeable case is when the four circles are such that the foregoing values of (a, b, c, d) also satisfy the equation aA° + bB° + cC° + dD®° = 0; the condition for this is obviously aa”? + bb’? + ce’? + dd’ = 0; or, as it may also be written, a Up} b”2 2 qd’? G-)G-da8) ConC-D0Lo Haie=ate =n On a Locus connected with the foregoing Properties.—Art. No. 92. 92. lf, as above, A, B, C, Dareany four points, and A, B, C, D are the squared distances of a current point P from the four points respectively, then the locus of the foci of the conics which pass through the four points is the tetrazomal curve aJ/A+b/B+c/6+d/D=0. In fact the sum aA + bB + cC + dD has, it has been seen, a constant value for PROFESSOR CAYLEY ON POLYZOMAL CURVES. 41 all positions of the point P; taking P to be the other focus, its squared distances are (k —,/A)’, &c., whence for the first-mentioned focus we have aA + bB + cC + dD = a(t — JA)? + bE — VB)? + ck — JOY + d(k— JD); or recollecting that a+b+e¢e+d=0, we have for the locus in question a/A+b,/B + ¢./C + 4,/D = 90; this locus will be discussed in the sequel. I remark here, that in the case where the four points are on a circle, then (as mentioned above), the axes of the several conics are in the same fixed directions ; there are thus two sets of foci, those on the axis in one direction, and those on the axis in the other direction; it might therefore be anticipated, and it will appear, that in this case the tetrazomal breaks up into two trizomal curves. Formule as to the two Sets (A, B, C, D), and (A,, B,, Cy, D,), each of four Concyclic Points—Art. Nos. 98 to 98. 93. Consider the four points A, B, C, D ona circle, then taking, as before, their circular co-ordinates to be (a, a’, 1), (8, 6’, 1), (vy, y, 1), (6, 6 1), the condition that the points may be on a circle is eee ncusmecce | == 4) 1, B, B, BR’ Ly 7,97 eect viz., this equation may be written (8 — vy) (@— 8): (y— 4) (8 — 8): (@— 8B) (y — 8) = (8 — 7) (#—8) : (y¥—@’) (8-8) : (a —B) (7'—8) ; or, if for shortness, we take nee ke fy fe 8, b=y—4, g=P—s4, a g =B-8, ec=a—PB, h=y—6, ¢d=a@—-P, VW=y7-3, and consequently af+bg+ch=0, af +Ug +ch =0, a=g-h, w=g-h, = h— if, C= h — f, c=f—g, eé=f—g, atb+c=0, wv+04+ce=0, then the equation is asg:th=arsbg ich . 94. Let a,b,c,d, denote as before (a:b:c:d= BCD:—CDA:DAB:—ABC), then we have aye Drees ee hs Bye Ws |hOn On Wilts ell ten ce, L | Pee ON aL! he ot! 18.8.1) siya a,a@,1| |6, 8,1 Ae se VOL. XXV. PART I. L 42 PROFESSOR CAYLEY ON POLYZOMAL CURVES. and we may write a= ; ah’ —ah, af —ag, gi —gh, b = bh’ — Uh, . , bf —Vf, hf —Xf, c= — 4, of — cf, : 7 Ie —J9:; d=cl' — cb, ad —aec, ba — Va, viz., the expressions in the same horizontal line are equal, and a, b, ¢, d are pro- portional to the expressions in the four lines respectively. 95. I say that we have of, of, £9 ge a. na ab 9? viz., this will be the case if b'a = hyd, ach = hf'd, abe = fia, and selecting the convenient expressions for a, b, c, d, these equations become be’ (gh’ — gh) = g/h (cb — eb), ad (hf —Wf)=fh(aé — ac), ab (ff —f9) = Ji (ba' — ba), viz, these equations are respectively bgc’h’ = b’g’ch, chaf = cWaf, aft'g' =a'f'bg, and are consequently satisfied. It thus appears that the equation Lm An. ‘'p ah io eae is transformable into which is of course one of a system of similar forms. 96. Take (A,, D,) the anti-points of A, D; (B,, C,) the anti-points of (B, C); or say that the circular co-ordinates of A,, 6,, C,, D, are (a, 0’, 1), (8, 7, 1), (y, BY, 1), (6, @, 1) respectively; the points A,, B,, C,, D, are, as above mentioned, on a circle, the condition that this may be so being in fact 1, a, 8, ad 1, B, ¥ By 1ly,B xB | 1, 6, a, da’ = 0, equivalent to af :tg: ch = af «0g =ch.. ‘97. Let (a,,b,,¢,,d,) be the corresponding quantities to (a, b, c, d), viz. aeD ee, :d, = BCD, > — C04. DA BA we have a, ib, .¢,2:d, = 18 9.11: — 1 ee, Le) eee ee ae ee | y> BG 1 6, a’, J a, é, ; B, y; 1| cya fee cANt «vil B, 7, 11 y, By 1) PROFESSOR CAYLEY ON POLYZOMAL CURVES. 43 giving rise to a similar set of forms ae . ,-aé +h, ag+va,—¢g —Oh, b, = — ¢b — gh, . 4 ,-fb—gff,—fht+ cf, = Uet+hg—fert hf, 5s FG RGS d= gct+hb,—ha+ ac, —ab—ga, and leading to CEA ES OE OE a ie ae ay —— = cg Dy — ae Cy —— wg er ; ste ice) We solleg Near ig CD ‘ : so that the equation Taye tes tan les transformable into 1 i 1 1 Gs Gs COD Pans Uhdideee as we! eg’ M+ af’ 1 ag ji = 0 98. Let A, B, C, D, be, as above, points on a circle; (4,, D,) and (B,, C,) the anti-points of (A, B), (B, C) respectively. Write A = (& — az) (m — wz) , A, = (& — az) (4 — 82), B= (€ — B2)(n— 82) , B, = - 8) (1-72), C= (E — yz) (n— yz) , ©, = (E — 92) (4 — Bz), D = (& — 82)(m — dz) , D, = (§ — 82) (4 — 32); then we have identically (6—a)(d—a) B =(8—8) (8-6) A+ (B—a) (B —a) D—(B—8) (B—a) A,—(B—a) (8 —3’/) D, , (@—a) (8—a’) © =(y~8) (/—¥) A+ (y—2) (/—a') D—(y—8) (¥ — 2’) A, (ya) (¥-8)D, , (6—a) (6 —a’) B, =(8—8) (7-8) A+ (B—a) (7 —a’) D—(8—8) (y'— a’) A, —(8B—«) (7'—8) D, . (6—a) (8 —a) ©, =(y—8) (B'—8) A+(y—a) (8 —a’) D=(y—8) (B —a’) A, —(y—a@) (B'—8) D, , or in the foregoing notation Sf B = 9A + c’D + gcA, + cgD, , ff'C =hWVA + WD — WA, — WD, , Tf B, = gVA — c’D — GA, + ch’'D,, Sf C, = 7A — béD + heA, — d7'D,. Further Properties in relation to the same Sets (A, B, C,D) and (Ay, By, Cy, Dy)— Art. Nos. 99 to 104. 99. It is be shown that in virtue of these equations, and if moreover 7 culers F Tad “ = = + f = 0, then it is possible to find 4, 7, m, p,, such that we have identically — 1A + mB + nC — pD + 1,A,— m,B,— 1,0, + p,D, = 9. +4 PROFESSOR CAYLEY ON POLYZOMAL CURVES. This equation will in fact be identically true if only — ffl + gfm + hi'n cem + bln — ff'p gem — hb'n com — bhin + fh — ghim, — ghn, — + chm, + ben, = 0, + gm, — he n, = + chim, + bf n, + ff'py = 0. From the first and second equations eliminating m, or m, , the other of these quantities disappears of itself, and we thus obtain two equations which must be equivalent to a single one, viz., we have béffl + cgafm + bhafn+ ghffp =0, beffl + gafm + bhafn + ghffp = 0; which equations may also be written of uf, £9 aaa Ae. A lth a of cy af arn al’ ie a af’ ay? ea and it thus appears that the equations are equivalent to each other, and to the assumed relation l m N P a b ; 100. Similarly, from the third and fourth equations eliminating m or n, the other of these quantities disappears of itself, and we find og ffl, — egafm, + afegn, — cgff'p, = DW f{fl, — afU him, + bha'f'n, — Uhff'p, = 9, equations which may be written ff Digg 4 Se ae cg af’ ga? sa ee ei ap pl ah Gy ae ape =? where we see that the two equations are equivalent to each other and to the equation ; tig ag ee ay 1 ei dy It thus appears that the quantities /,, 7, 7, ,, must satisfy this last equation. It is to be observed that the first and second equations being, as we have seen, equivalent to a single equation, either of the quantities m,, m, may be assumed at pleasure, but the other is then determined; the third and fourth equations then give /,, p,; and oe quantities /,, 72, 2, 7, so obtained, satisfy identically the : Une ay ge ne equation oN 1s cae é fae 0. i | PROFESSOR CAYLEY ON POLYZOMAL CURVES. 45 101. Now writing Tl, = — gem + U'm,) + hn + en) , LTP, = — gm — hm.) + b(h’n— g'n,) , and p= cem+t+ Um) + 00n+ cn), Tl = gK¢m—Wm) + hhn—- gn), we find It (40, — 'p) = — (bg + ch) [(em + Vm, )(hin = — gn) + (om — Wm) (Yn + en,)] = (bg + ch) (Uy + ch’ )(mn, — mn) = aaff (mn, — mn) that is, Gp, — 'p) = aa'(myny — mn) viz., this equation is satisfied identically by the values of /,, m,, n,, p, determined as above. 102. Hence if m, n, = mn, we have also /, p, = /p, and we can determine m,, 7,, so that m,n, shall = mn, viz., in the first or second of the four equations (these two being equivalent to each other, as already mentioned), writing m, = 9n, and therefore 7, = 5m we have 1 — fl + gm + hh'n — gh'nd — ghm .= Om Amel cem + bon — fi'p + ch'nd + bem ,= Ou: which are, in fact, the same quadric equation in 0, viz., we have —fl+g7m+hhn_ _ gh _ _ gh cm + bln — fp Gb eeuy ey The final result is that there are two sets of values of /,, m,, 2,, p,, each satisfying the identity — IA + mB + nC — pD + /1,A, — mB, —7,C, + p,D, = 0, and for each of which we have Y m eet ee ee AS 0 6p, Hb, mn, = mM : a, Mice d, WO a ety 103. Consider, in particular, the case where p = 0; the relation (ae. Geese Sa i Ls ea eee 8 a @ b s c i; d here becomes / ‘h ‘=— se) oe q of if VOL. XXV. PART I. M 46 PROFESSOR CAYLEY ON POLYZOMAL CURVES. The equation in 0 is (ccm + bb’n)d + cb’'n® + bem = 0 , viz., this is (c6 + &m)(U'nd + 6) = 0 , giving b bn cm G@=—= 5 nh, = — — (ee c 2 c : b ¥ or else Pema em eC ie cm a got b'n b'n ? 1 b/ , 1 Py Ps Since in the present case /,p, = 0, we have either /, = 0, or else p, = 0, and as might be anticipated, the two values of 6 correspond to these two cases re- spectively, viz., proceeding to find the values of /,, »,, the completed systems are b ae 7 ry bn em = — er = bo (cm — bb n) = = tu nm = ae 5 14= cm cm n a é= — ian TS — eS ee ‘m — bb’ Wy? v; ae 7 oP weF ce’m — bbin ) , so that for the first system we have bg ts ea 0, myn, = mn, —/A + mB + nC = —1,A, + mB, + 1,C,, ae Vi ee and for the second system in a ice fa =0,m n= mn, — 1A + mB + nC = —p',D,+m',B, + 7\C, . 1 Cy 1 104. The whole of the foregoing investigation would have assumed a more simple form if the circular co-ordinates had been taken with reference to the centre of the circle A6CD as origin, and the radius of this circle been put = 1; we should then have a’ = _ &c., and consequently fate 1 5 ye ee oe ee ere! 5 zy ce 4e 5 ae a ae re dae = i ie a = me but the symmetrical relation of the circles ABCD and A,6,C\D, would not have been so clearly shown. I will however give the investigation in this simplified form, for the identity —lA + mB + 27C = —1.A+4+™,B + 7,C; viz., in this case we have L_ _ m(8— 9) (8 — 2). 26 =7) G2 a B(y—a)(@—8) y(a—B)(a—y)’ PROFESSOR CAYLEY ON POLYZOMAL CURVES. 47 and the identity to be satisfied is — 1l(é — az) (7 = ) = —1(§- a2) = 5*) + m(& — Bz) (7 = Z) + ms(E—B2) (1 _ 5°) + n(& — 72) (> = 2) + m4 (§ — n(n a 3°) ; ae Sis 1 writing € = az, 7= 3% we find m,, and writing — = az, 7 = : z, we find n,, and it is then easy to obtain the value of /,, viz., the results are ee AO ENS 7) AR Nye), YO ial 6 Biy—a)@—8) y@—BP)@—a’ * «—B a ae and therefore m,”, = mn; it may be added that we have viz., this is the form assumed by the equation © te = + a = 0. 1 1 2 Part III. (Nos. 105 to 157.)—On THE THEORY oF Foct. Explanation of the General Theory—Art. Nos. 105 to 110. 105. If from a focus of a conic we draw two tangents to the curve, these pass respectively through the two circular points at infinity, and we have thence the generalised definition of a focus as established by PLUCKER, viz., in any curve a focus is a point such that the lines joining it with the two circular points at infinity are respectively tangents to the curve; or, what is the same thing, if from each of the circular points at infinity, say from the points J, J, tangents are drawn to the curve, the intersections of each tangent from the one point with each tangent from the other point are the foci of the curve. A curve of the class has thus in general n° foci. It is to be added that, as in the conic the line join- ing the points of contact of the two tangents from a focus is the directrix cor- responding to that focus, so in general the line joining the points of contact of the tangents from the focus through the points J, J respectively is the directrix corresponding to the focus in question. 106. A circular point at infinity 7 or J, may be an ordinary or a singular point on the curve, and the tangent at this point then counts, or, in the case of a multiple point, the tangents at this point count a certain number of times, say q times, among the tangents which can be drawn to the curve from the point ; the number of the remaining tangents is thus = »— gq. In particular, if the circular point at infinity be an ordinary point, then the tangent counts twice, or 48 PROFESSOR CAYLEY ON POLYZOMAL CURVES. we have g = 2; if it be a node, each of the tangents count twice, or g = 4; if it be a cusp, the tangent counts three times, or g = 3. Similarly, if the other circular point at infinity be an ordinary or a singular point on the curve, the tangent or tangents there count a certain number of times, say 7 times, among the tangents to the curve from this point; the number of the remaining tangents is thus = 2—g. And if as usual we disregard the tangents at the two points J, J respectively, and attend only to the remaining tangents, the number of the foci is = (n—g) (n—q). 107. Among the tangents from the point / or J there may bea tangent which, either from its being a multiple tangent (that is, a tangent having ordinary con- tact at two or more distinct points), or from being an osculating tangent at one or more points, counts a certain number of times, say 7", among the tangents from the point in question. Similarly, if among the tangents from the other point J or J, there is a tangent which counts 7” times, then the foci are made up as follows, viz. we have— Intersections of the two singular tangents counting as 7 foci. Intersections of the first singular tangent with each of the ordinary tangents from the other circular point at infinity, as : ; : (n—g—ryr ,, Do. for second singular patent : ; (n—q—r)y” ,, Intersections of the ordinary tangents, . ; (n—q—?r)(n—q—7) ,, Giving together the : (n—q) (n—q’) foci : and the like observation applies to the more general case where the tangents from each of the points /, / include more than one singular tangent. 108. There is yet another case to be considered ; the line infinity may be an ordinary or a singular tangent to the curve: assuming that it counts s times among the tangents from either of the circular points at infinity, the numbers of the remaining tangents are n —q—s, n—gq’—s from the two points /, J respectively, and the number of foci is = (x — g —s)(n— q—s). 109. In the case of a real curve the two points /, J are related in the same manner to the curve, and we have therefore 7 = q'; the singular tangents (if any) from the two points respectively being the same as well in character as in num- ber. Writing » —¢—s =n —¢qd—s, = p, and not for the present attending to the case of singular tangents, I shall assume that the number of tangents to the curve from each of the two points is = py; the number of foci is thus = p*; and to each focus there corresponds a directrix, viz., this is the line through the points of contact of the tangents from the focus to the two points J, J respectively. 110. Consider any two foci A, B not in lined with either of the points J, J, then joining these with the points /, J, and taking A,, B, the intersections of AI, BJ and of AJ, BI (A,, B, being therefore by a foregoing definition the anti- PROFESSOR CAYLEY ON POLYZOMAL CURVES. 49 points of (A, B) ), then A,, B, are, it is clear, foci of the curve. We may out of the p’ foci select, and that in 1.2..p different ways, a system of p foci such that no two of them lie in lined with either of the points /,/; and this being so, taking the anti-points of each of the 4+(p — 1) pairs out of the p foci, we have, inclusively of the p foci, in all p + 2.4p(p—1), that is p* foci, the entire system of foci. On the Foci of Conics—Art. Nos. 111 to 117. 111. A conic is a curve of the class 2, and the number of foci is thus = 4. Taking as foci any two points A, B, the remaining two foci will be the anti-points A,, B,. In order that a given point A may be a focus, the conic must.touch the lines AJ, AJ; similarly, in order that a given point B may be a focus, the conic must touch the lines B/, BJ; the equation of a conic having the given points A, B for foci contains therefore a single arbitrary parameter. 112. In the case, however, of the parabola the curve touches the line infinity; there is consequently from each of the points J, J only a single tangent to the curve, and consequently only one focus: the parabola having a given point A for its focus is a conic touching the line infinity and the lines AJ, AJ, or say the three sides of the triangle A/J; its equation contains therefore two arbitrary parameters. 113. Returning to the general conic, there are certain trizomal forms of the focal equation, not of any great interest, but which may be mentioned. Using circular co-ordinates, and taking (a, a’, 1) and (8, 6’, 1) for the co-ordinates of the given foci A, B respectively, the conic touches the lines €—az=0, ,—a’z=0, ——Bz=0, »—6’z =0; the equation of a conic touching the first three lines is VIE — az) + Vm(E — B2) + VW n(n — az) = 0, where /, m, m are arbitrary, and it is easy to obtain, in order that the conic may touch the fourth line 7 — 6’z = 0, the condition B— «a p—a io 114. In fact, 2 having this value, the equation gives U(E — a2) + m(E - Be) + 2VIm(E— a) E— B= — Fs (m—D (1-82 + (BK — ap), and taking over the term i mie — (m—1) (8 — az, =(B— a) (m—Ipz, this gives LE ~ Be — (m — 1) (n—B2), VOL. XXV. PART I. N 50 PROFESSOR CAYLEY ON POLYZOMAL CURVES. which puts in evidence the tangent 7 — 6’z. It is easy to see that the equation may be written in any one of the four forms STE a8) + 7 mE— Be) + nf — B=* (om —0) (1 a2) =0, J iniz—az) + S1(E— Bz) + a Lea Foe —l)(,-Bz) =0, VA 1(n — az) + Vin(n—82) + a a= (m—1)(E-az)=0, Vig a+ V8) + nf 2" m9 G8) = 0. viz., in forms containing any three of the four radicals /—az, /£— Gz, Jn —a’z, Jn —Bz. The conic is thus expressed as a trizomal curve, the zomals being each a line, viz., they are any three out of the four focal tangents; the order of the curve, as deduced from the general expression 2” *7, is = 2; so that there is here no depression of order. 115. But the ordinary form of the focal equation is a more interesting one: viz., A, B being as usual the squared distances of the current point from the two given foci respectively, say A = (& — az) — a2), B = (§ — 8:)1 — 82), then 2a being an arbitrary parameter, the equation is 2az + VA + /B = 0, viz., the equation is here that of a trizomal curve, the zomals being curves of the second order, that is, the zomals are (z’= 0) the line infinity twice, and the line-pairs AI, AJ and BI, BJ respectively: the general expression 2” ~ 7 gives therefore the order = 4; but in the present case there are two branches, viz., the branches 2aze + VA — VB = 0, 202 —-VA + VB = 0, each ideally containing (z = 0) the line infinity; the curve contains therefore ( 1, we have a real representation of (w—qae? + y? + BG’ —1), as the squared distance of the point (z, y) from a point (X, 0, Z) out of the plane of the figure, viz., putting this =(@—-XP+¥4+7, we have qae= X, Z*7 = bq? — 1), whence or what is the same thing, that is, the locus is the focal hyperbola, viz., a hyperbola in the plane of zz, having its vertices at the foci, and its foci at the vertices of the ellipse. 122. If instead of the form first considered, we start from the trizomal form Qbe + Ja? + (y — aciz)? + Ja? + (y + acz? =90, then we have the zomal or circle of double contact under the form x? + (y — gaei)’ = a%(1 — 9”) ; or putting herein g = — itanq, this is, x? + (y — aetang)* = a*sec’9 ; so that we have the ellipse as the envelope of a variable circle having its centre on the minor axis of the ellipse, distance from the centre = aetan®, and radius _ ee PROFESSOR CAYLEY ON POLYZOMAL CURVES. 53 =asecp. This is, in fact, Gergonne’s theorem, according to which the ellipse is the secondary caustic or orthogonal trajectory of rays issuing from a point and - refracted at a right line into a rarer medium. It is to be remarked that for tang = + >; the equation of the circle is a? 2 at #+(~t0-5)) = viz., this is the circle of curvature at one or other extremitity of the minor axis; from @ = 0 to? = + tan’ = , the intersections of the consecutive circles are 1 real, and give the entire real ellipse; from d@ = + tan — 75 to ¢ = + 90°, the circles are still real, but the intersections of consecutive circles are imagi- nary. 123. If in the equation of the generating circle we interchange a, y, a, b, the equation becomes (x — aeitang)? + 7? = bsec?o , which is (as it should be) equivalent to the former equation (x — aesiné)? + y? = b?cosé , the identity being established by means of the equation , and .. sind=c " symmetrical, { and each of these kinds may be general, nodal, or cuspidal—viz., for the two last mentioned kinds there may be a node or a cusp at a real point of the curve. 135. In the case of a node, say the point NV; first if the curve (circular cubic or bicircular quartic) be twisted—then of the four foci A, 6, C, D we have two, suppose B and C, coinciding with V; and the sixteen foci are as follows, viz. B, Oy ALD ware N,N, ALD; Bin Ay bie tN oaAnti-pts. of (4, D):; C,,A,, B,D, . Anti-pts. of (WV, A), Anti-pts. of (W, D) ; Wallis Aor IDS Do. do. _ viz., we have the points (A, D) each once, the node JW four times, the anti-points of (A, D) once, and the anti-points of (NV, A) and of (JN, D), each pair twice. But properly there are only four foci, viz., the points A, D and their anti-points. The circle O subsists as in the general case, and so does the circle & (BC, AD), viz., this has for centre the intersection of the line AD by the tangent at WN to the circle O, and it passes through the point JV, of course cutting the circle O at right angles: the circles S and 7 each reduce themselves each to the point V considered as an evanescent circle, or what is the same thing to the line-pair V/, WJ. VOL. XXV. PART I. P 58 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 136. The case is nearly the same if the curve be symmetrical, but in the case of the bicircular quartic excluding the Cartesian: viz., we have on the axis the foci B, C coinciding at NV, and the other two foci A, D; the sixteen foci are as above—and the circle # is determined by the proper construction as applied to the case in hand, viz., the centre £ is the intersection of the axis by the radical axis of the point WV (considered as an evanescent circle) and the circle on AD as diameter; that is RV’ = RA.RD. And the circles S and 7 reduce themselves each to the point VV considered as an evanescent circle. 137. Next if we have a cusp, say the point A: first if the curve (circular cubic or bicircular quartic) be twisted—then of the four foci A, B, C, D, three, suppose A, B, C, coincide with KX ; and the sixteen foci are as follows, viz., B, 0, A, D «re\| K,K,K,D, B,,C,,4,D, , K,K, Anti-points of (K, D), Cj Bae aS Do. do. Bg, Bg a ng wig Do. do. viz., we have the point D once, the point A nine times, and the anti-points of K, D three times. But properly the point J is the only focus. The circle 0 is, it would appear, any circle through A, D, but possibly the particular circle which touches the cuspidal tangent may be a better representative of the circle O of the general case—the circles #, S, 7’'reduce themselves each to the point A considered as an evanescent point. 138. The like is the case if the curve be symmetrical, but in the case of the bicircular quartic excluding the Cartesian; the circle 0 is here the axis, which is in fact the cuspidal tangent. 139. For the Cartesian, if there is a node 1; then of the three foci A, B, C, two, suppose B and C, coincide with V; the nine foci are A once, N four times, and the anti-points of NW, A twice: but properly the point A is the only focus. And if there be a cusp A; then all the three foci A, B, C coincide with A ; and the nine foci are A nine times; but in fact there is no proper focus. 140. A circular cubic cannot have two nodes unless it break up into a line and circle; and similarly a bicircular quartic cannot have two nodes (exclusive of course of the points /, /) unless it break up into two circles; the last-mentioned case will be considered in the sequel in reference to the problem of tactions. As to the Analytical Theory for the Circular Cubic and the Bicircular Quartie respectively— Art. No. 141. 141. It may be remarked in regard to the analytical theory about to be given, that although the investigation is very similar for the circular cubic and for the bicircular quartic, yet the former cannot be deduced from the latter case. In fact if for the bicircular quartic, using a form somewhat more general than that —— —— ee PROFESSOR CAYLEY ON POLYZOMAL CURVES. 59 which is ultimately adopted, we suppose that for the two nodes respectively 0, 2=0)fand 3] = 0, 2=0), then if JE +m=0, 12+ mz = 0, mm + pz=0, my + pz = 0 are the tangents at the two nodes respectively, the equation will be (1E + mz) (VE + m’z) (nn + pz) (n'n + p’z) + cen + 28 (aE + bn) + c2* = 0, and if (in order to make this equation divisible by z, and the curve so to break up into the line zg = 0 and a cubic) we write / = 0 or m = 0, then the curve will indeed break up as required, but we shall have, not the general cubic through the two points (€ = 0, 2 = 0), (7 = 0, 2 = 0), but in each case a nodal cubic, viz., if 7= 0 there will be a node at the point (, = 0,2= 0), and ifz=0Oa node at the point (€ = 0, z= 0). Analytical Theory for the Circular Cubic—Art. Nos. 142 to 144. 142. I consider then the two cases separately; and first the circular cubic. The equation may be taken to be En(p& + qn) + cen + 2 (aE + bn + cz?) = 0, or what is the same thing En(pé + gn + cz) + 2(aE + bn + cz) = O, viz. (€, 7, 2) being any co-ordinates whatever, this is the general equation of a cubic passing through the points (E=0, z=0), (7=0, z=0), and at these points touched by the lines €=0, » = O respectively. And if (&, 7, 2 = 1) be circular co-ordinates, then we have the genera] equation of a circular cubic having the lines € = 0, » = O for its asymptotes, or say the point €=0, 7 =0 for its centre; the equation of the remaining asymptote is evidently pé + qn + ez = 0; to make the curve real we must have (p, 7) and (a, 6) conjugate imaginaries, e and ¢ real. 143. Taking in any case the points /, J to be the points & = 0, e = 0 and 4=0, z=0 respectively, for the equation of a tangent from / write p& = 0z; then we have Oy (02 + Qn + ez) + 2(abz + bpn + cpz) = 0, that is 2? (ad + cp) + n2z(6? + €6 + bp) + 1°.gd = 0, and the line will be a tangent if only (0? + cd + bp)? — 49d (ad + cp) = 0, that is, the four tangents from / are the lines p& = 02, where @ is any root of this equation. Similarly the four tangents from J are the lines g7 = ¢z, where @ is any root of the equation (9? + ep + ag)?— 4po(bp + cq) = 0, 60 PROFESSOR CAYLEY ON POLYZOMAL CURVES. writing the two reaped under the forms é we , | | ey eee (6, 1)4 rs On 2aq — 4bp, + (9, 1)* =0, | 3ebp — 6epq, 3 eng an L 6 Bp? 6a2q?, the equations have the same invariants ; viz., for the first equation the invariants are easily found to be I= 3@ — 4bp — 4aq)? + 72(ce — 2ab)pq, J = — (? — 4bp — 4aq)8 — 36 (ce — 2ab)pg(e — 4bp — 4aq) — 21607 p*9? and then by symmetry the other equation has the same invariants. The absolute invariant /°*+ J” has therefore the same value in the two equations; that is, the equations are linearly transformable the one into the other, which is the before-mentioned theorem that the two pencils are homographic. 144. The two equations will be satisfied by 9 = ¢, if only bp = aq; that is, if b : : ie : P=7-9= j.3 Putting for convenience ; in place of ¢, the equation of the curve is then En (aE + bn + cz) + ke* (aE + bn + cz) = 0. In this case the pencils of tangents are a& = k6z, bn = kOz, where 0 is deter- mined by a quartic equation, or taking the corresponding lines (which by their intersections determine the foci A, B, C, D) to be (a& = k0,2, bn = k0,z), &c., these four points lie in the line a — 6, = 0, which is a line through the centre of the curve, or point € = 0, 7 = 0: the formule just obtained belong therefore to the symmetrical case of the circular cubic. Passing to rectangular co-ordinates, writing z = 1, and taking y = 0 for the equation of the axis, it is easy to see that the equation may be written (2? + v(x —a)+ k(x —b) = 0; | | or, changing the origin and constants, ay? + («7 — a\«e—b)(@—ec)=0. Analytical Theory for the Bicireular Quartic—Art. Nos. 145 to 149. | 145. The equation for the bicircular quartic may be taken to be h(E — a2?) (m? — B22”) + e2?&y + 22(aE + bn) + ce*# = 0, viz. (& 7, 2) being any co-ordinates whatever, this is the equation of a quartic : curve eae a node at each of the points (& = 0, 2 = 0) and (7 = 0,2 = 0): the equations of the two tangents at the one node are —az= 0, €+ az = 0; and | those of the two tangents at the other node are 7 — 6z = 0,7 + B2 = 0; €=0 is thus the harmonic of the line z = 0 in regard to the tangents at (& = 0, 2 = 0), PROFESSOR CAYLEY ON POLYZOMAL CURVES. 61 and 7 = 0 is the harmonic of the same line z = 0 in regard to the tangents at (7 =0,2=0). If(& 1, 2 = 1) be circular co-ordinates, then we have the general equation of the bicircular quartic having the lines & + az = 0, & — az = 0 for one pair, and the lines » —8z=0, 7 + 82 =O for the other pair of parallel asymptotes; and therefore the point € = 0, »=0 for centre, and the lines BE — an = 0, BE + ay = O for nodal axes. In order that the curve may be real we must have (a, @), (a, 6) conjugate imaginaries, 4,¢,c real. The points (2-0, 2 = 0) and (, = 0, ¢ = 0) are as before the points J, J. If « = 0, the node at J becomes a cusp, and so if 6 = 0, the node at J becomes a cusp; the form thus includes the case of a bicuspidal or Cartesian curve. 146. To find the tangents from J, writing in the equation of the curve € = 6az, we have ) ko? (62 — 1)(m? — B?2”) + eadnz + z(audz + bn) + cz? =0; that is n? . ka?(d? — 1), + mz. ead + b, +27. — hea? ?(0 — 1) + aad+c=0, and the condition of tangency is Ake(g? — 1) {ka?6? (0? — 1) — aad—c} + (c + >) = 08 viz., the tangents from J are € = 0az, where @ is any root of this equation. Similarly, if we have 2 4k (9? — 1) {ka?B? (p— 1) — bBe — ct + (eg + 3) ==:0), the tangents from J are , = $8z, where ¢ is any root of this equation. 147. The two equations may be written 24k? a? B? , 247078? , ) — 6kae, — 6k0£, — 8ka36? — 4ke + ¢? , — 8k'a’p?— 4ke + e, : pt 0), L@ 1lt=0, | 6aa + me @ 1) 6kbB + 30 3 (1) L 24.h2078? + 24ke + ge eA 24h7a28? + 24ke + 6 which equations have the same invariants; in fact for the first equation the invariants are found to be as follows, viz., if for shortness CO = — 8ha26? — Ake + &, then T = 576k4a'6* + 57648ca26? + 14422(a2a2 + 026%) + 72hkab + 30? , J = Cf{576ktatB! + 576 1%c026? + 14442(a2a? + 028%) + 36heae — 07} — 8641? caba?6? — 216 ke? (a®a? + 6767) — 216h7070? , and then by symmetry the other equation has the same invariants. The VOL. XXV. PART I. Q 62 PROFESSOR CAYLEY ON POLYZOMAL CURVES. absolute invariant 7° + J* has thus the same value in the two equations, that is, the equations are linearly transformable the one into the other, which is the before-mentioned theorem that the pencils are homographic. 148. The equations will be satisfied by = > if only aa = 88, that is, if a,b =m, ma; or by 0 = — dif only aa = — 0G, that is, if a,b = mB, — ma: the equation of the curve is these two cases respectively— (E? — a2) (q? — 82?) + oz?&q + m2z3(BE + an) + ct = 0, h(E — az”) (9? — 82?) + c2?&q + mz*®(BE — an) text =0. If to fix the ideas we attend to the first case, then the equation in @ is 24}? 07,37, — 6kma8, — 8h?a?B?— Ake + e?, (6, 1)* = @* 6khma8 + 3me, 24h7a78? + 24ke + 6m? and we may take as corresponding tangents through the two nodes respectively & = Oaz, » = 082; the foci A, B, C, D, which are the intersections of the pairs of lines (& = 0,az, 1 = 0,82), &c., lie, it is clear, in the line B — ay = 0, whichis one of the nodal axes of the curve. Similarly, in the second case, if 6 be determined by the foregoing equation, we may take as corresponding tangents through the two nodes respectively —& = 6az, y = — 08z; the foci (A, B, C, D), which are the intersections of the pairs of lines (& = 6,az, 7 = — 6,82), &c., lie in the line BE + ayn = 0, which is the other of the nodal axes of the curve. In either case the foci A, B, C, D lie ina line, that is, we have the curve symmetrical; and, as we have just seen, the focal axis, or axis of symmetry, is one or other of the nodal axes. 149. In the case of the Cartesian, or when a=0, 8=0, viz., the equation aa=b@ is satisfied identically, and this seems to show that the Cartesian is symmetrical ; it is to be observed, however, that for «=0, 8 =0 the foregoing formule fail, and it is proper to repeat the investigation for the special case in question. Writing a=0, 0=0 the equation of the curve is hE? n? + czEq 4 23 (aE + bn) + cz* = 0, and then, taking = 6@bz for the equation of the tangent from /, we have a. ke + nz. b(e6 + 1) +27 .abb+c=0. and the condition of tangency is 4h0? (abd + c)—(ce6 + 1)? =0; viz , we have here a cubic equation. Similarly, if we have »=0az for the equa- tion of a tangent from J, then 4k? (abp + c) — (ep + 1)? =0. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 63 Hence 6 being determined by the cubic equation as above, we may take #=80, and consequently the equations of the corresponding tangents will be €=0bz, »=6az, viz., the foci A,B,C will be given as the intersections of the pairs of lines (E=0,bz, 7»=0,az), &c. The foci lie therefore in the line a—by=0; or the curve is symmetrical, the focal axis, or axis of symmetry, passing through the centre. On the Property that the Points of Contact of the Tangents from a Pair of Concyclie Foci lie in a Circle—Art. Nos. 150 to 158. 150. We have seen that the foci form four concyclic sets (A, B, C, D), (A,, B,, G)),(A,, B,,C,, D,),(A,, B,, C,, D,), that-is, A,B, C,D are in a circle. We may, if we please, say that any one focusis concyclic—viz., it lies in a circle with three other foci; but any two foci taken at random are not concyclic; it is only a pair such as (A, B) taken out of a set of four concyclic foci which are concyclic, viz., there exist two other foci lying with them in a circle. The number of such pairs is, it is clear = 24. Let A, B be any two concyclic foci, I say that the points of contact of the tangents AJ, AJ, BI, BJ, lie in a circle. 151. Consider the case of the bi-circular quartic, and take as before (& = 0, z = 0), and (7 = 0, z = 0) for the co-ordinates of the points J, J respectively. Let the two tangents from the focus A be & — az = 0, 1 —a’z = 0, say for shortness p = 0, p’ = 0, then the equation of the curve is expressible in the form pp’U = V**, where U = 0, V =O are each of them circles, viz., UY and V are each of them quadric functions containing the terms 2’, zy, z&, and &. ‘Taking an inde- terminate coefficient \, the equation may be written pp (U + 2aV + pp’) = (V+ app’), and then \ may be so determined that V+ 2\V + )’pp’ =0, shall be a 0-circle, or pair of lines through J and J. It is easy to see that we have thus for \ a cubic equation, that is, there are three values of \, for each of which the function U + 2\V + ’pp’ assumes the form (¢ — Gz) (» — 6’z), =qq’ suppose : taking any one of these, and changing the value of V so as that we may have V in place of V +rpp’, the equation is pp’gq + V*, where V=0 isas before a circle, the equation shows that the points of contact of the tangents p = 0, 7p = 0,¢g = 0, 7 = 0 lie in this circle V = 0. The circumstance that \ is determined by a cubic equation would suggest that the focus g = 0, g = 0 is one of the three foci B, C, D con- eyclic with A; but this is the very thing which we wish to prove, and the inves- tigation, though somewhat long, is an interesting one. 152. Starting from the form pp’qq/ = V’, then introducing as before an arbitrary coefficient A, the equation may be written pe’ (aq + 20V + rpp') = (V+ App')?, * This investigation is similar to that in Salmon’s Higher Plane Curves, p. 196, in regard to the double tangents of a quartic curve. 64 PROFESSOR CAYLEY ON POLYZOMAL CURVES. and we may determine \ so that gq7/ + 2\V + *pp’ = 0 shall be a pair of lines. Writing V = Hi —LIn — L’& + M2’, and substituting for pp’ and gq’ their values (£ —az) (y — a’z) and (€ —Gz) (n — §’2), the equation in question is (1 + 20H + 2?) En — (B+2aL + a) nz — (8 + 2a’ + 27a’) Ez+ (BB + 20M + 2200’)? =0, and the required condition is (1 + 2aH + 2”) (BB + 20M +270’) = (8 + 2aL + da) (R’ + 2ALl’ + a2a’); or reducing, this is (2M + 2HBe — 21/6 — 218) + 2((a — 8) (@’ — 8) + 4HM — 4LL’) +22 (2M + 2Haa’ — 21a — 21a’) = 0, viz., is determined by a quadric equation. Calling its roots ,, and A,, the foregoing equation, substituting therein successively these values, becomes (€ — yz)(1—vz)=9, and (€ — dz)(y — d’z) = 0 respectively, say 77’=0 and ss’= 0. 153. We have to show that the four foci (p= 0, p’ = 0), (g = 0, 7 = 0), (r = 0,7” = 0), (s = 0, s' = 0) are a set of concyclic foci; that is, that the lines p=, g=90,7 =0, s=0 correspond homographically to the lines p’ = 0, g = 0,7’ = 0, s’ = 0; or, what is the same thing, that we have | 1, a, 6,20 | =O 1, 8,8’, BB Lyre | ie Rear or, as it will be convenient to write this equation, he ee ae a—By—s a—d B—y 154. We have _B+2,2+a%a |, B+ 2a, + ro’ . 1+ 2Ha,+A,7 ” ? 1 + 2d, + a,? 3 —B + 2A,0 + A,%u ya Bt 2d! + 22a! 1+ 2H, +2, ” 1+ 2H, +22 © The expressions of a — 0, &c., are severally fractions, the denominators of which disappear from the equation; the numerators are fora — 38, = a(1 + 2a, + a,?)—(84+ 2aL + a,*), =o) BoP + 21, (eb f)- forB—y, = #(1+ 2,H +2?) - 6+ 2a, + aa,?), = {26H - L) (a - 8}; fory —8 = (6 + 22a, + oa,”) (1 + 2M, + a,?) — (B + 2Ld, + ad”) (1 + 2Ha, + 22), (a! — 6) {2H?a8 — 2HL(a + B) + 20? + 4 (a — B)?} PROFESSOR CAYLEY ON POLYZOMAL CURVES. 65 and it hence easily appears that the equation to be verified is 2H?o8 — 2HL(a + 8) + 207+}4(@-B)? _«-B+2@H-L)r, 2(GH-L)-(a-8B)a, 2H?a/e’ — 2HL (a + B)2L7 +4 —- BP w- B+ 2WH-TL)a,° 2CH-L)-(a-B)a, 155. This is Gee B ice Chote Dae B’-C A’ + Bret Cr, + Dry,’ if for shortness A=2(a-8)(GH-L), A’= 2(e¢ -B)(BH-L) , B= -(a—£) » bB=-¢- 6) ; C=4(eH-L(8-—L, C’'= 4(H-L)(wH-L), D=-2(e-—fP)\e¢H—L) D= —2(¢-6)wH-TL), and the equation then is AB’ — A'B + CA’ — C'A — (a, + 24) (BC — BO) + 2,2, (CD' - C'D - (BD - B'D)). 156. Calculating AB’ — A’B, CA’ — C'A, CD’ — CD, BD’ — BD, these are at once seen to divide by {(a8’ — a8) H + L (a’— 8’) —L'(a —8’)} ; we have, moreover, BO — BC = —4(a — 6)? WH — L) (6H - L’) + 4(0’ — 8)? (aH - L) (BH — L) a t (aa — PB)H—L (a —6')- L'(a—B)} {(a' -«8)H+ L(a'-B)-L’'(a-8)}, viz., this also contains the same factor; and omitting it, the equation is found to be t(@ — B)(# — B) — 4(BH — L) (BH — L)} —2{ (aa! — BB')H — L(a' — B) — L'(a — B)} (A, + Ag) +{-(@—P)@— #’) + 4(¢H — L) wWH— L’)} aa, = 0; viz., substituting for A,+ A, and ,A, their values, this is {(a — 8) («’ — 6’) — 4(8H — L) (eH — L)} (M+ How’ — La’ — La) —{(aa' — 8G’) T— L(a’ — B)} {(@ — 8) (@ — 8’) + 40M — 421} +{-(@—®)@—6)+4@¢H —Lh@wH—-TL)} {M+ Hee — Le — Lp} = 0, which should be identically true. Multiplying by H, and writing in the form {(a—) («’ — 6) — 4(@H — L) @H — L)} (AM — LL’ + (@H — L) (eH L)) —{(@@H — L) (/H—L) — (@H — L) @H —L’)} ((@— 8) (@ — 8) + 4H — LL) +{—(«— 6) (@—f’) + 4@H — L) (wH — L/)} (HM — LI’ + (6H — 1) (6'H - io) ai) we at once see that this is so, and the theorem is thus proved, viz., that the equa- tion being pp'gq’ = V’, the foci (p = 0, p’= 0) and (¢ = 0, g’= 0) are concyclic. 157. By what precedes, \ being a root of the foregoing quadric equation, we may write q¢ + 20AV + pp’ = K? rr’, VOL. XXV. PART I. R 66 PROFESSOR CAYLEY ON POLYZOMAL CURVES. where the focus 7 = 0, 7’= 0 is concyclic with the other two foci; but from the equation of the curve V = /pp'q7, that is we have gy + 20 Vpp'qy' + pp’ = Kir’, or, what is the same thing, av pp + Ja + Kr’ =0, viz., this is a form of the equation of the curve; substituting for p, p’, g.9q/, 7,7" their values, writing also A = (& — az) (n— az), B= ( — 8) (1 — 82), C=(€—)(1— 72), and changing the constants , K (viz. \:1:K =J/1: /m: s/n) the equation is JIA + J/mB + JVnC = 0, viz., we have the theorem that for a bicircular quartic if (& — az = 0, 7 — a’z =0), (E — Bz =0, n — Bz = 0, (E — yz = 0), 1» — y’z = 0) be any three concyclic foci, then the equation is as just mentioned ; that is, the curve is a trizomal curve, the zomals being the three given foci regarded as 0-circles. The same theorem holds in regard to the circular cubic, and a similar demonstration would apply to this case. 158. It may be noticed that we might, without proving as above that the two foci (p = 0, p’ = 0), (¢ = 0, g’ = 0) were concyclic, have passed at once from the form pp'gq = V, to the form App’ + Vqq + KNrr’ =0 (or JIA = /mB = J/nC = 0), and then by the application of the theorem of the variable zomal (thereby establishing the existence of a fourth focus concyclic with the three) have shown that the original two foci were concyclic. But it seemed the more orderly course to effect the demonstration without the aid furnished by the reduction of the equation to the trizomal form. Part IV. (Nos. 159 To 206).—On TRIZOMAL AND TETRAZOMAL CURVES WHERE THE ZOMALS ARE CIRCLES. The Trizomal Curve—The Tangents at I, J, éc—Art. Nos. 159 to 165. 159. I consider the trizomal JiR + /mB’ + ./n° = 0, where A, B, C being the centres of three given circles, A°, &c. denote as before, viz., in rectangular and in circular co-ordinates respectively, we have A® = (@ — a2)? + (y — az)? — a, = (E — 2) (n — wz) — 22, B’ (a Te bz)? a (y — bz)? — aa => (§ ai Bz) (n = Bz) sz "222, O° = (@— oe? + (y — ex)? — 2, = (EF — 92) (1 — 2) — CH. Il PROFESSOR CAYLEY ON POLYZOMAL CURVES. 67 By what precedes, the curve is of the order = 4, touching each of the given circles twice, and having a double point, or node, at each of the points J, J; that is, it is a bicircular quartic: but if for any determinate values of the radicals Jl, /m, /n, we have lt + fmt fn = 0, UN ae! ie 0. containing (¢ = 0) the line infinity; and the order is here = 3: viz., the curve here passes through each of the points /, J and through another point at infinity (that is, there is an asymptote), and is thus a circular cubic. 160. I commence by investigating the equations of the nodal tangents at the points J, J respectively; using for this purpose the circular co-ordinates (&, », 2 = 1), it is to be observed that, in the rationalised equation, for finding the tangents at (£ = 0, z = 0) we have only to attend to the terms of the second order in (&, 2), and similarly for finding the tangents at (, = 0, 2 = 0) we have only to attend to the terms of the second order in (7,2). But it is easy to see that on any term involving @’, 0", or c’ will be of the third order at least in (é, 2), and similarly of the third order at least in (7, z); hence for finding the tangents we may reject the terms in question, or, what is the same thing, we may write a’,b’,c’ each = 0, thus reducing the three circles to their respective centres. The equation thus becomes SIE = a2) a — dz) + J/m(E— B) (9 — B2) + Jn E- Q— 72) = 0. For finding the tangents at (€ = 0, 2 = 0) we have in the rationalised equation to attend only to the terms of the second order in (&, 2); and it is easy to see that any term involving «’, @’, 7 will be of the third order at least in (é,2), that is, we may reduce a’, 8’, y’ each to zero; the irrational equation then becomes divisible by , and throwing out this factor, it is SUE — a2) + /mE — B2) + J/nE— yz) = 0, viz., this equation which evidently belongs to a pair of lines through the point (€ = 0, 2 = 0) gives the tangents at the point in question; and similarly the tangents at the point (7 = 0, 2 = 0) are given by the equation Jin = v2) + rfm(n — Bz) + RG — vz)=0. 161. To complete the solution, attending to the tangents at (& = 0, z = 0), and putting for shortness then there is a branch A= l—-m—n, w= —-lim —n, y= —1 —™m ar WO 5 A= F4m?+nv* — 2mn — 2nl — 2lm, 68 PROFESSOR CAYLEY ON POLYZOMAL CURVES. the rationalised equation is easily found to be adie — 2&2z(lka + mpB + nvy) + 2(Pa? + mR? + ny? — 2mnBy — 2nlya — 2lmaB) = 0. And it is to be noticed that in the case of the circular cubic or when Jl + /m + /n =0, then A=0, so that the equation contains the factor z, and throwing this out, the equation gives a single line, which is in fact the tangent of the circular cubic. 162. Returning to the bicircular quartic, we may seek for the condition in order that the node may be a cusp: the required condition is obviously A(l?a? + mB? + 247? — 2mnBy — 2nlya — 2linaB) — (law + muB + nvy)? = 0, or observing that A—Ww= — 4mn, &e. A+ w = — 21a, &e. this is la? + mB? + ny* + By + wya + B= 0, or substituting for A, u, v, their values, it is L(a — B) (a— y) + m(B— 7) (B— a) + n(y— a) (y— 8) = 0, or as it is more simply written 1 m n =—— + — + =O. B-y ya a— 163. If the node at (7 = 0, z = 0) be also a cusp, then we have in like manner wp A MED Th B—y ya a —f Now observing that ae et | p;-B; i 7, ¥, 1 y—9) @ 8) = —*) @—- 2s = («— 8) (8 —y/) — («—8B) (B—y), (B—¥) (7 -—@) — @—9'/) (y—-2), = () suppose: the two equations give Lim:n = aA(8—y) (B—y) : U(y—4@) (y'— a): Aa —8) (a — 8’); or if Q is not = 0, then Lim:n = (B—y) (8-7): (y—@) (x —@) : (a8) (#8). 164. If 2= we 0' rg B, B, 1 7,4 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 69 or, what is the same thing, if , pins oon Om Cua 2 C, Zi): the centres A, B, C are in a line; taking it as the axis of x, we have a=a =a, B=’ =), y=y'=c; and the conditions for the cusps at J, J respectively reduce themselves to the single condition l mM n b—e Cc—a a—b = (I). so that this condition being satisfied, the curve Wi@—a +a] + /mie—ky +y—vAl + Jawa) + fo] = 0 is a Cartesian ; viz., given any three circles with their centres on a line, there are a singly infinite series of Cartesians, each touched by the three circles respectively ; the line of centres is the axis of the curve, but the centres 4, B, C are not the foci, except in the case a’= 0, b= 0, c'= 0, where the circles vanish, The con- dition for /, m, is satisfied if /: m:n = (b — cc)’: (ec — a)’: (a —b)’; these values writing /7: /m: /n = 6—c¢:c—a:a—b, give not only /] + /m + /n = 9, but also a,/] + b,/m + ¢r/n = 0; these are the conditions for a branch contain- ing (2? = 0) the line infinity twice; the equation (b—c) n/(a—a2z)? +? — a? + (c—a) J (a—b)? + y? — 02? + (a—b) J (c— 2)? + — C72 =0, is thus that of a conic, and if a’ = 0, 6" = 0, c’ = 0, then the curve reduces itself to y° = 0, the axis twice. 165. If Q is not = 0, then we have L:m:n = (8 — y)(B— 7) = (y— @)(7'— @) = (a — B)(a’ — 6), viz., J, m, n are as the squared distances BC’, C/A’, AB’, say as f?:97:h’; or when the centres of the given circles A, B, Care not in a line, then f, g, h being the distances BC, CA, AB of these centres from each other, we have, touching each of the given circles twice, the single Cartesian Tin Be + 9/B° + De Cr 0 ; which, in the particular case where the radii a’, 6’, c’ are each = 0, becomes FJ/A+9/B+h,/6 = 0, viz., this is the circle through the points A, B, C, say the circle A BC, twice. VOL. XXV. PART I. S 70 PROFESSOR CAYLEY ON POLYZOMAL CURVES. Investigation of the Foci of a Conic represented by an Equation in Areal Co-ordinates— Art. Nos. 166 to 169. 166. I premise as follows: Let A, B,C be any given points, and in regard to the triangle ABC let the areal co-ordinates of a current point P be u, v, w: that is, writing PBC, &c., for the areas of these triangles, take the co-ordinates to be 295 = PRO: PCA = PAB ; or, what is the same thing in the rectangular co-ordinates (z, y, z = 1), if (a, a, 1), (6,8, 1), ( ¢,1), be the co-ordinates of A, B, C respectively, take WIV DW =e, yy, 2) F/B Wee) 1B Hs ! a | ie, 6, 4 8,64 ed, 7 | |a,a’,1 Jag pans | 7 or in the circular co-ordinates (£ 7,2 = 1), if (a,a’, 1), (8, 6’, 1), (y, 7’, 1) be the co-ordinates of the three points respectively, then * U:v:w=| a z | &, 4-2 le a 2 | 8, B11 y, 7,1) a a, 1 bsitgied a, a, L B, BY, 1 167. For the point / we have (&, 7, z) = (0,1, 0), and hence if its areal co- ordinates be (w,, %; 2%), we have Uy iUyi@ =B—-y:y—a:a—B, and hence also, (w, v, w) referring to the current point P, we find YW — Wy = (y — a)[(@ — B)(E — az) — (a —B)(n — @2)] — (@ — B)[(7 — @)(E — az) — (y — a) (n— a2)] = OF — azz) , if 2 = (y—a) (@ —B)—(@— B)(y¥ —2) = |a, a’, 1) 5 B, By % 7,1] whence Vy — WyV 2 Wy — Wig i UyY — WY, =F —az:E— Pz :E—yxz, and in precisely the same manner, if w,’, v,’, 7,’ refer to the point J, then Wyityiw,=P—-x7:7¥—a@:ae—f’, and Vw —Wyv: wou — wu, Wav — Ww, =n — a2:n— Bein— yz. _ 168. Consider the conic (a, 6, ¢, f, 9, h)(u, v, w)? = 0, PROFESSOR CAYLEY ON POLYZOMAL CURVES. 71 where w, v, wv are any trilinear co-ordinates whatever; and take the inverse co-efficients to be (A, B, C, F,G, H) (A =be —f’, &c.), then for any given point the co-ordinates of which are (w,, v,, 2,), the equation of the tangents from this point to the conic is, as is well known, (A, BC, F, G, Av,w — wor, wy — UW, Uv — vyu)y?=0; consequently for the conic GoaeLgh@ga,wyY = 0, where (#, v, v) are areal co-ordinates referring, as above, to any three given points A, B, C, the equation of the pair of tangents from the point- J to the conic is (A, B, Ce G, H)(g — a2, & — Bz, & cane 92) = 0), and that of the pair of tangents from J is (A, B, O, F, G, H)(n— wz, — P2,n-—72)?=0, these two line-pairs intersecting, of course, in the foci of the conic. 169. In particular, if the conic is a conic passing through the points A, B, C, then taking its equation to be low + mwu + nu =0, the inverse co-efficients are as (/?, m?, n?, — 2mn, — 2nl, — 2/m), and we have for the equations of the two line-pairs Jie — a2) + J mE — B2) + J/nE— 72) = 9; Jin — #2) + n(n — B2) + J nln — 72) = 9 - The Theorem of the Variable Zomal—Art. No. 170. 170. Consider the four circles A’ = 0, B= 0, C° = 0, D? = 0 (A° = (a — az)? + (y — wz)? — a'?2*, &e.), which have a common orthotomic circle; so that as before aA° + bB° + cC° + dD° = 0, where DCB OU —iO DA DAB — ABO . I consider the first three circles as given, and the fourth circle as a variable circle cutting at right angles the orthotomic circle of the three given circles; this being so, attending only to the ratios a:b: c, we may write aabpee = DBO. DCA. DAB. that is, (a, b, c) are proportional to the areal co-ordinates of the centre of the vari- able circle in regard to the triangle A BC. 72 PROFESSOR CAYLEY OF POLYZOMAL CURVES. 171. Suppose that the centre of the variable circle is situate on a given conic, then expressing the equation of this conic in areal co-ordinates in regard to the triangle A BC, we have between (a, b,c) the equation obtained by substituting these values for the co-ordinates in the equation of the conic; that is, the equation of the variable circle is aA° + bB° + cC°=0, where (a, b, c) are connected by an equation, (a, 6,655 9, AG, b, cf =.0. Hence (A,B,C, F,G, H) being the inverse co-efficients, the equation of the envelope of the variable circle is (A, 8, C, F, G, H(A’, B’, Cc’)? = ? and, in particular, if the conic be a conic passing through the points A, B, C, and such that its equation in the areal co-ordinates (wu, v, w) in regard to the triangle ABC is lw + mwu + nuv =0, then the equation of the envelope is (7, m?, n?, — mn, — nl, — Im)(A®, B’, C°)? = 0; that is, it is (1, 1,1, — 1,—1, — 1)(/A’, mB’, nC°)? = 0, or, what is the same thing, it is SIR + /mB° + ,/n0° = 0. 172. It has been seen that the equations of the nodal tangents at the points I, J respectively are respectively JE = az) + Jm(E—82) + Jn(E-y2) =0, Jin —az)+ Jm(n — B2) Ea Vania —yz)=0, and that these are the equations of the tangents to the conic low + miu + nuv = 0 from the points J,.J respectively. We have thus Casey’s theorem for the generation of the bi-circular quartic as follows :—The envelope of a variable circle which cuts at right angles the orthotomic circle of three given circles A° = 0, B’ = 0, C° = 0, and has its centre on the conic /vw + miu + nuv = 0 which passes through the centres of the three given circles is the bicircular quartic, or trizomal JiR + JmB° + J/nC*= 0, which has its nodo-foci coincident with the foci of the conic. 173. To complete the analytical theory, it is proper to express the equation of PROFESSOR CAYLEY ON POLYZOMAL CURVES. 73 the orthotomic circle by means of the areal co-ordinates (w, v,w). Writing for shortness a + a” — ad” = 4a, &c., and therefore A° = a? + y? — 2auz — 2a'yz — a2", &e., then if as before VeVi UW) D2 | | CeOt Z\s5| COLY, e Ws , / / b,.6, 1 @, el CANO Nea Goo el a,a,1 G, Url and therefore eiy:2=aut+bt+ew:dutbo+cwiut+vt+u, the equation of the orthotomic circle is Z—az,y—az, axn+vy—az|=0 z— bey — Vz, bu + Vy — V2 L— ,u— cz, a+ Cy— Cz 3 viz., throwing out the factor z, this is ulaxw + ay — az) + vibe + Vy — bz) + Wea + Cy — ez) = 0, or what is the same thing, it is (au + bv + ewha + (aut bv + ecw)y— (dust bv +cw)z = 0, viz.,it is (au + bv + ewP+ (wu + bv + cw)? — (wu + bv + cw) (U+04w) =), that is, substituting for a’, b', c their values, it is ay? 4. by? + ¢/?* + (07% 4 c%—(b-cP — — ¢)?) ww + (ce? + a’ — (¢ — a)? — (¢ — ’)*) wu + (a? + bv’? — (a — b)? — (a — b’)?) w = 0, and it may be observed that using for a moment a, 6, y to denote the angles at which the three circles taken in pairs respectively intersect, then we have 26’ c' cosa = 6" + &” — (b—c)’ — (lV — €)’, &c., and the equation of the ortho- tomic circle thus is (1, 1, 1, cos a, cos B, cosy) (au, b’v, cw)? = 0. 174. We have in the foregoing enunciation of the theorem made use of the three given circles A, B, C, but it is clear that these are in fact any three circles in the series of the variable circle, and that the theorem may be otherwise stated thus :— The envelope of a variable circle which has its centre in a given conic, and cuts at right angles a given circle, is a bi-circular quartic, such that its nodofoci are the foci of the conic. VOL. XXV. PART I. T 74 PROFESSOR CAYLEY ON POLYZOMAL CURVES. Properties depending on the relation between the Conic and Circle— Art. Nos. 175 to 177. 175. I refer to the conic of the theorem simply as the conic, and to the fixed circle simply as the circle, or when any ambiguity might otherwise arise, then as the orthotomic circle. This being so, I consider the effect in regard to the trizomal curve, of the various special relations which may exist between the circle and the conic. If the conic touch the circle, the curve has a node at the point of contact. If the conic has with the circle a contact of the second order, the curve has a cusp at the point of contact. If the centre of the circle lie on an axis of the conic, then the four intersec- tions lie in pairs symmetrically in regard to this axis, or the curve has this axis as an axis of symmetry. If the conic has double contact with the circle (this implies that the centre of the circle is situate on an axis of the conic) the curve has a node at each of the points of contact, viz., it breaks up into two circles intersecting in these two points. The centres of the two circles respectively are the two foci of the conic, which foci lie on the axis in question. Observe that in the general case there are at each of the circular points at infinity two tangents, without any cor- respondence of the tangents of the one pair singly to those of the other pair, and there are thus four intersections, the four foci of the conic; in the present case, where the curve is a pair of circles, the two tangents to the same circle corre- spond to each other, and intersect in the two foci on the axis in question. The other two foci, or anti-points of these, are each of them the intersection of a tangent of the one circle by a tangent of the other circle. If the conic has with the circle a contact of the third order (this implies that the circle is a circle of maximum or minimum curvature, at the extremity of an axis of the conic), then the curve has at this point a tacnode, viz., it breaks up into - two circles touching each other and the conic at the point in question, and having their centres at the two foci situate on that axis of the conic respectively. 176. If the conic is a parabola, then the curve is a circular cubic having the four intersections of the parabola and circle for a set of concyclic foci, and having the focus of the parabola for centre. The like particular cases arise, viz., lf the circle touch the parabola, the curve has a node at the point of contact. If the circle has, with the parabola, a contact of the second order, the curve has a cusp at the point of contact. If the centre of the circle is situate on the axis of the parabola, then the four intersections are situate in pairs symmetrically in regard to this axis, and the curve has this axis for an axis of symmetry. If the circle has double contact with the parabola (which, of course, implies PROFESSOR CAYLEY ON POLYZOMAL CURVES. 75 that the centre lies on the axis), then the curve has a node at each of the points of contact, viz., the curve breaks up into a line and circle intersecting at the two points of contact, and the circle has its centre at the focus of the parabola. If the circle has with the parabola a contact of the third order (this implies that the circle is the circle of maximum curvature, touching the parabola at its vertex), then the curve has a tacnode, viz., it breaks up into a line and circle touching each other and the parabola at the vertex, that is, the line is the tangent to the parabola at its vertex, and the circle is the circle having the focus of the parabola for its centre, and passing through the vertex, or what is the same thing, having its radius = } of the semi-latus rectum of the parabola. 177. If the conic be a circle, then the curve is a bi-circular quartic such that its four nodo-foci coincide together at the centre of the circle; viz., the curve is a cartesian having the centre of the conic for its cuspo-focus, that is, for the inter- section of the cuspidal tangents of the cartesian. The intersections of the conic with the other circle, or say with the orthotomic circle, are a pair of non-axial foci of the cartesian; viz., the anti-points of these are two of the axial foci. The third axial focus is the centre of the orthotomic circle. Case of Double Contact, Casey's Equation in the Problem of Tactions—Art. No. 178. 178. In the case where the conic has double contact with the orthotomic circle, then (as we have seen) the envelope of the variable circle is a pair of circles, each touching the variable circle; or, if we start with three given circles and a conic through their centres, then the envelope is a pair of circles, each of them touch- ing each of the three given circles; that is, we have a solution of the problem of tactions. Multiplying by 2, the equation found ante, No. 173, for the variable circle, and then for the moment representing it by (a, b, c, f, g, h) (u,v, wy = 0; then attributing any signs at pleasure to the radicals /a, /b, s/c, the equation of a conic through the centres of the given circles, and having double contact with the orthotomic circle, will be (a, bc, f, g, h) (uw, , w)? —(w Jat v/b+w/c)?=0, viz.. representing this equation as before by lew + mwu+ nuv=0, we have l:m:n=f—J/be:g —Jca:h — Jab, that is, substituting for a, b,c, f, g, h their values, and taking, for instance, a, b, c Ba 20 2. On) 2, we find i:m:n= 6" -— ec — G— oF —C' —- ¢? :(c’ — a’)? — (¢ — a)? — ( — a’)? : (a” — 6”)? — (a — 6)? — (a — BY, 76 PROFESSOR CAYLEY ON POLYZOMAL CURVES. that is, 7,m, m are as the squares of the tangential distances (direct) of the three circles taken in pairs, and this being so, the equation of a pair of circles touch- ing each of the three given circles is //A° + /mB° + /nC° = 0. It is clear that, instead of taking the three direct tangential distances, we may take one direct tangential distance and two inverse tangential distances, viz., the tan- gential distances corresponding to any three centres of similitude which lie in a line; we have thus in all the equations of four pairs of circles, viz., of the eight circles which touch the three given circles. This is Casey’s theorem in the problem of tactions. The Intersections of the Conic and Orthotomic Circle are a set of four Coneyclie Foci— Art. No. 179. 179. The conic of centres intersects the orthotomic circle in four points, and for each of these the radius of the variable circle is = 0, that is, the points in question are a set of four concyclic foci (A, B, C, D) of the curve. Regarding the foci as given, the circle which contains them is of course the orthotomic circle; and there are a singly infinite series of curves, viz., these correspond to the singly infinite series of conics which can be drawn through the given foci. As for a given curve there are four sets of concyclic foci, there are four different constructions for the curve, viz., the orthotomic circle may be any one of the four circles O, R, S, 7, which contain the four sets of concyclic foci respectively ; and the conic of centres is a conic through the corresponding set of four concyclic foci. We have thus four conics, but the foci of each of them coincide with the nodofoci of the curve, that is, the conics are confocal; that such confocal conics exist has been shown, ante, Nos. 78 to 80. Remark as to the Construction of the Symmetrical Curve—Art. Nos. 180 and 181. 180. It is to be observed that in applying as above the theorem of the variable zomal to the construction of a symmetrical curve, the orthotomic circle made use of was one of the circles 2, S, 7, not the circle 0, which is in this case the axis; in fact, we should then have the conic and the orthotomic circle each of them coinciding with the axis. And the variable circle, gud circle having its centre on the axis, cuts the axis at right angles whatever the radius may be; that is, the variable circle is no longer sufficiently determined by the theorem. The curve may nevertheless be constructed as the envelope of a variable circle having its centre on the axis; viz., writing A° = (¢—az’?+y—a’e, &e., and starting with the form Jih® + ./mB + ./nC° = 0, then recurring to the demonstration of the theorem (ante, No. 47), the equation of the variable circle is aA° + bB° + cC° = 0, where a, b, ¢ are any quantities PROFESSOR CAYLEY ON POLYZOMAL CURVES. 77 satisfying - + 5 + = = 0, or, what is the same thing, taking g an arbitrary para- meter, and writing { =1+4, ~ = 1-49, ~ = — 2, the equation of the variable circle is IAP pe i BPs FHP 0) 1 1 tg 1—gq Compare Nos. 118-123 for the like mode of construction of a conic; but it is proper to consider this in a somewhat different form. 181. Assume that the equation of the variable circle is Do =@—dyP+7— ad? = 0; we have therefore identically aA®° + bB° + cC° + dD° = 0, viz., this gives a+b+ece= -—d, aa+bb+ce = — dd, a(a? — a’) + b(0? — 0) +e? —¢?) = —d(d’ —d”), and from these equations we obtain a, b, c equal respectively to given multiples of d; substituting these values in the equation : -- e + = = 0, d divides out, and we have an equation involving the parameters of the given circles, and also d, d’, the parameters of the variable circle; viz., an equation determining d’, the radius of the variable circle, in terms of d, the co-ordinate of its centre. I consider in particular the case where the given circles are points; that is, where the given equation is RODE Af ME! + /nc = 0. The equations here are a +h +¢,.=-d aa + bb + cc = — dd aa? + bb? + cc? = — d(d*—d”), and from these we obtain a(a—b)(a—c) = —d((d—2) @—¢)-a”) b(@ — 0) (b—a) = —d((d- 0) (d-a) -d”) c (¢ —a)(¢ ~d) = —d((d-a) (d—b)-d”), ™ so that the equation : tapes = = 0 becomes L(a—b) (a—c) m(b—c) (b—a) TC (G—0) (d—b) (d—e)—d”® ~ d—c) @—ay—d” * —a) (d—b)—d® ~ VOL ex, PART I. U 0, 78 PROFESSOR CAYLEY ON POLYZOMAL CURVES. or, as this is more conveniently written l 1 4 ee | seg he ! b—c (d—b) (d—c)—d” * c—a (d—c)(d—a)—d” * a—b (d—a) (d—b)—d” =), viz., considering d,d' as the abscissa and ordinate of a point on a curve, and representing them by 2, y respectively, the equation of this curve is pn : ee: 4 mone d Bs b—c (2—b) (a—e)—y® ~ c—a (2@—c) (x—a)—y? * c—a (4—a) (x—b)-7? which is a certain quartic curve; and we have the original curve JIA + /mB + ./ne = 0, as the envelope of a variable circle having for its diameter the double ordinate of this quartic curve. . U m n Write for shortness ——_, —_, — b—c’ c—a’ a—b tion of the quartic curve may be written = LI, M,N respectively, then the equa- = L [(w—a)? (x—d) (w@—e) — y*(w—a) (2a—b-c) + y*] = 0, viz., this is ZL | «(e—a) @—b) @—e) — y?( 2a? —(a+tb+cer+ (ab + ac + be)) +7 — a (w—a) («@—b)(a—c) + y (ax + be) | oD or what is the same thing, the equation is (L+M+N) [ «(z—a) (a—b) (w—c)—y? (20? —(at+b+c)r+ ab +ac+be) a y* | — (La+Mb+ Ne) (x—a) (x—b) (xe) + y*{La+Mb+Ne)x + Lhe+Mca+ Nab} = 0. In the particular case where L + M+ N = 0, that is, where l m n b—e c—a i TB 0, the quartic curve becomes a cubic, viz., putting for shortness — _ Lhe + Mca + Nab ~ La+ Mb+ Ne ’ the equation of the cubic is fe (x—a) (x—b) (x—e) y eee viz., this is a cubic curve having three real asymptotes, and a diameter at right angles to one of the asymptotes, and at the inclinations + 45°, — 45° to the other two asymptotes respectively—say that it is a “ rectangular” cubic. The relation PROFESSOR CAYLEY ON POLYZOMAL CURVES. i) ae “+ —_=0 implies that the curve JIA+ JmB+ JnC =0 is a C—O a cartesian, and we have thus the theorem that the envelope of a variable circle having for diameter the double ordinate of a rectangular cubic is a cartesian. I remark that using a particular origin, and writing the equation of the rect- 2 : : angular cubic in the form y* = 2” — 2mx +a + 2 the equation of the vari- able circle is 92 (ed +P =P — Ind tar that is 2 a A aN ga he ENO d where d is the variable parameter. Forming the derived equation in regard to d, we have eas a ss Mm ~ q?? and thence e+ y? — oo — =) a 2 @ ar y? = Aree == IGA (a = m), dl that is, the equation of the envelope is (az? + y’ — «a)* = 16 A (w — m) = 0, which is a known form of the equation of a Cartesian. Focal Formule for the General Curve—Art. Nos. 182 and 183. 182. Considering any three circles centres A, B,C, and taking A’, &c., to denote as usual, let the equation of the curve be JID + /mB° + Vn0° = 0; then considering a fourth circle, centre D,a position of the variable circle, and having therefore the same orthotomic circle with the given circles, so that as before aA® + bB° + cC° + dD°= 0, the formule No. 47 (changing only U, V, W, T into A’, B°’, C’, D°) are at once applicable to express the equation of the curve in terms of any three of the four circles A, B, C, D. In particular, the circles may reduce themselves to the four points A, B, 0, D, a set of concyclic foci, and here, the equation being originally given in the form JIA + J/mB + JnO = 0, the same formule are applicable to express the equation in terms of any three of the four foci. 80 PROFESSOR CAYLEY ON POLYZOMAL CURVES. 183. It is to be observed that in this case if the positions of the four foci are given by means of the circular co-ordinates (« = ) &e. which refer to the centre of the circle A BCD as origin, and with the radius of this circle taken as unity, then the values of a, b, c, d (ante, No. 90), are given in the form adapted to the formulee of No. 49, viz., we have a:b:c:d = a(Byd): — B yéda): y (da8) : — b (aby) , where (673) = (8 — yy — 38 —B), &e- The relation < + + ” = 0, put. ting therein /:m:n = pa(B—y)*?:cB8(y —a)*:ty(a — 8), (or, what is the same thing, taking the equation of the curve to be given in the form (8 —y) JSpaA + (y — a) /cBB + (a —B) /7tyC = 0), becomes e(B— y)(a—8 + oy —a)(B— 8) +<(@—-B)(y—8=0, viz., this equation, considering p, 7, t, «, 2, y as given, determines the position of the fourth focus D, or when A, B, C, D are given, it is the relation which must exist between p, o,7; and the four forms of the equation are ; sr (8— 9), Ve(B — 8), Ve(y — B)) (aA, /BB, /7C, /0D) = 0, ve(y—3, . Ned — a), Jo(a—y) Jo(8 — 8) Ve(a — 8), , /r(6 — @) | Ve (8 - 7), Ve.7— a), Vr (a — 8), viz., the curve is represented by means of any one of these four equations involv- ing each of them three out of the four given foci A, B, C, D. Case of the Circular Cubic—Art. Nos. 184 and 185. 184. In the case of a circular cubic, we must have @(8 — y) (a — 8) + «(y —a) (8 —8) + r(a— B) (y — 8) = 0, a/oe(8 — y) + n/ Boy — a) ate / yz (a — B) iy which, when the foci A, B,C, D are given, determine the values of p:o:7 in order that the curve may bea circular cubic. We see at once that there are two sets of values, and consequently two circular cubics having each of them the given points A, B,C, D for a set of concyclic foci. The two systems may be written Ve:Vo:Vr = Vad — / By: “Ba = Jya:7 78 — V of, viz., it being understood that »/ad means Ja 4/0, &c., then, according as /3 has one or other of its two opposite values, we have one or other of the two PROFESSOR CAYLEY ON POLYZOMAL CURVES. 81 systems of values of p:o+: 7. To verify this, observe that writing the equation under the form Vag? VB: V7 yr = 0/8 — VaBy: 8/8 — Joby :7¥ V3 — VaBy , the second equation is verified ; and that writing them under the form e:o:r=—(B+y7)(2+d+M:—(vt+ a) (B+HN4+M:-@ +P) y+ H+, where ee M = By + cb + ya + 66+ o8 + 76 — 2 J aby » the second equation is also verified. 185. Ifwe assume fora momenta = cosa +7sin a = e”, &c., viz., if a,b,c, d be the inclinations to any fixed line of the radii through A, B, C, D respectively, then we have mee Gy eet Tee COT ae Ne rete Mee cya rt et 4, 20-98 _ g-}@-95 iy and thence Jag (8 — 7): VBo(y — 0): J yr (a — 8) = cosj(a +d — b— oe) sin} (b— oc) :cos }(6 + d— c— a) sin} (¢—a) :cos }(a+d—a-— b)sin} (a— J); or else = sini (a +d —-b — c) sin} (6 — ¢) :sin} (b+ d— ¢ —a) sin} (¢ — a) :sin}(¢c+d—a — 6)sin } (a — D). Putting in these formule, t(a—b—c=A, then we have B-— C=}(b- 0), 16—c —a)=B, : C— A=}(c —a), d(c -a—b)= 0, ‘5 A-— B=}(a — b), and for either set of values the verification of the relation rJag(B — 7) + SBoly — @) + r/yr(a— 8) = 0, will depend on the two identical equations sin 4 sin(B — C) + sm Bsn (C — A) + smCsm(4 — B) = 0, cos A sin(B — C) + cos B sin (C — A) + cosCsin(A — B) = 0: although the foregoing solution for the case of a circular cubic is the most elegant one, I will presently return to the question and give the solution in a different form. Focal Formule for the Symmetrical Curve—Art. No. 186. 186. In the symmetrical case, where the foci A, 6, C, D are on a line, then if, as usual, a, 6, c,d denote the distances from a fixed point, we have the ex- VOL. XXV. PART I. x 82 PROFESSOR CAYLEY ON POLYZOMAL CURVES. pressions of (a, b, c, d) in a form adapted to the formule of No. 49, viz., a:b:c¢:d=(b—c)(¢—d)(d—b) :—(e—d)(d—a)(a—c) : (d—a)(a —b)(b—d) : —(a—b) (b—c)(e—a) , so that, assuming l:m:n = ob —c)?: o¢—a)?: ea — bP, : l the equation aif - + = 0, becomes e(b — ea — d) +0¢ — a) (b—d) + x(a — be —d) = 0, and the equation of the curve may be presented under any one of the four forms ( +» 4 oe@=o, Seb-4), ree — 2) ) (SK, JB, SC, JD )= 0. ORD GE Ns , Or d,a, — dc, — ¢,), + od, = 0; 1 ae aap: i that is b, | (+d, > tal ate = Sho; 2 b l b— & and hence ‘ Bo(— bye, + Oy? + aydy — dy”) + Oy(— Bydy + dy + Me, — dy) = 0, that is by (c,? — d,”) + ¢, (a,c, — b,d,) = 0, but aye, — dyd, = Eee — d,”), 1 or the equation gives 3, + 2%, =0, orsay}b,:¢,=6,: —d,, and this with 1 aS Cie Oy fo 2, gives all the ratios, or we have a,—d, d 2 Ws My : bg : Cy : dy = 0, (a, — d,) : 0, (6, — ¢,): — dy (a, — d,) : — d,(b, — ¢,). We have then for example by — Cy 3 Cy — Ay 3 My — 09d, — Cy 2, — 4, : a, — 4b; &e., showing the identity of the forms in (a,, 0,, ¢,, d,) and (2, be, C2, de) - Transformation to a New Set of Concyclic Foct.—Art. No. 193. 193. Consider the equation JIA + JmB+ Jn0 =0, which refers to the foci A,B, C, and taking D the fourth concyclic focus, let VOL: &XV. PART I. Y 86 PROFESSOR CAYLEY ON POLYZOMAL CURVES. (A,, D,) be the antipoints of (A, D) and (B,,C,) the antipoints of (B, C); so that (4,,B,, ¢,, D,) are another set of concyclic foci. We have B,.C,=B. C, and it appears, ante No. 104, that we can find /,, m,,7,, such that identically —/A+ mB + 20 = — 1,A,+ m,B,+ 7,0, and that m,”, = mn. ‘The equation of the curve gives — (A+ mB + 2C +2 J/mnBO = 0, we have therefore — 1,A,+ m,B,+ 2,0+ 2 /m,n,B,C, =0, that is, J1,A, + Jm,B, + J/n,C, =0, viz., this is the equation of the curve expressed in terms of the concyclic foci An, Bois The Tetrazomal Curve, Decomposable or Indecomposable—Art. No. 194. 194. I consider the tetrazomal curve JI? + JmB° + JnC® + JpD? =0, where the zomals are circles described about any given points A, B, 0, D as centres. There is not, in general, any identical equation aA°+ bB°+ cC°+ dD°= 0, but when such relation exists, and when we have also- BF sel += op Be 0, then the b d curve breaks up into two trizomals. When the conditions in question do not subsist, the curve is indecomposable. But there may exist between /, m, n, p re- lations in virtue of which a branch or branches ideally contain (z*= 0) the line infinity a certain number of times, and which thus cause a depression in the order of the curve. The several cases are as follows :— Cases of the Indecomposable Curve-—Art. No. 195. 195. I. The general case; /, 1m, n, p not subjected to any condition. The curve is here of the order = 8; it has a quadruple point at each of the points J, J (and there is consequently no other point at infinity) ; it is touched four times by each of the circles A, B,C, D; and it has six nodes, viz., these are the intersections of the pairs of circles | JmB? + JnO? = 0, JIA + J/pD?=0, Lie? fie =4, J mBe + /pD° = OF Jie + J/mB°= 0, /nC? + JpD°=0; the number of dps. is 6 + 2.6, = 18, and there are no cusps, hence the class is = 20, and the deficiency is = 3. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 87 II. We may have JtI+ Jn + Jnt+ Jp =9; there is in this case a single branch ideally containing (z = 0) the line infinity ; the order is = 7. Each of the points J, J is a triple point, there is consequently one other point at infinity; viz., this is a real point, or the curve has a real asymptote. There are 6 nodes as before; dps. are 6 + 2.3,= 12; class = 18, deficiency = 3. III. We may have Jit+ J/m=0, Jn + Jp =0; there are then two branches each ideally containing (z = 0) the line infinity; the order is = 6. Lach of the points J, J is a double point, and there are therefore two more points at infinity. These may be real or imaginary; viz., the curve may have (besides the asymptotes at J, J) two real or imaginary asymptotes. The circles //A + /mB = 9, /nC + W/pD = 0, each contain (z = 0) the line infinity, or they reduce themselves to two lines, so that in place of two nodes we have a single node at the intersection of these lines; number of nodes is = 5. Hence dps. are 5 + 2.1,= 7. Classis = 16, deficiency = 3. IV. We may have a/ Uist De 5) fs Vp =a:b:c:d there is here a single branch containing (z*= 0) the line infinity twice; the order is = 6. Each of the points /, J is a double point, and there are therefore two more points at infinity, that is (besides the asymptotes at J, J), there are two (real or imaginary) asymptotes. The number of nodes, as in the general case, is = 6. Hence dps. are6 + 2.1, = 8; class is = 14; deficiency = 2. I notice the included particular case where the circles reduce themselves to their centres ; viz., we have here the curve aJA+b/B+cJ/6+d/D=0, which (see ante No. 93) is in fact the curve which is the locus of the foci of the conics which pass through the four points 4, B,C,D. Itis at present assumed that the four points are not a circle; this case will be considered post No. 199. If we have BC, AD meeting in R; CA, BD in S, and AB, CD in T, then these points £, S, 7 are three of the six nodes. In fact, writing down the equations of the two circles | bVB4+cVGC=0,a/A4+d/D= 0, and observing that when the current point is taken at R, we have B:C = RB’: RO?=(BAD): (CAD) = c?:b’, and similarly A:D = RA®: RD? = (ABC) : (DBC)’= d’: a’, we see that each of the two circles passes through 88 PROFESSOR CAYLEY ON POLYZOMAL CURVES. the point R, or this point is a node. Similarly, the points Sand 7 are each of them a node. VIE Jl= Nm = VJn= Jp, there are here three branches, each ideally containing (z = 0) the line infinity; the order is thus = 5. Each of the points J, J is an ordinary point on the curve; there are besides at infinity three points, all real, or one real and two imaginary ; that is (besides the asymptotes at J,J) there are three asymptotes, all real, or one real and two imaginary. Each of the circles /A + /B = 0, &c., contains the line infinity, and is thus reduced to a line; the number of nodes is therefore = 8. Hence also, dps. = 3; class = 14; deficiency = 3. Cases of the Indecomposable Curve, the Centres being in a Line.—Art. No. 196. 196. There are some peculiarities in the case where the centres A, B, C, D are on a line; taking as usual (a, b, c,d) for the 2x-co-ordinates or distances of the four centres from a fixed point on the line, I enumerate the cases as follows :— I. No relation between /, m, ,p ; corresponds to I. supra. Il. J/7+ J/m+ /n + Jp = 0; corresponds to II. supra. Il. Wl + /m = 0,/n + Sp = 0; corresponds to III. supra. IV. J0+ JS/m+ Jn + Sp =0, al + bm + cro/n + dr/p = 0; corre- sponds to IV. supra, viz., there is a branch ideally containing (z*= 0) the line infinity twice. But, observe that whereas in IV. supra, in order that this might be so, it was necessary to impose on /, m, n, p three conditions giving the definite systems of values //: /m: /n: /p = a:b:c:4d, in the present case only two conditions are imposed, so that a single arbitrary parameter is left. V. Ji = J/m= J/n = ./p; corresponds to V. supra. VI. Ji + f/m = 0, Jn t+ Sp = 0, 4 fl + da/m + ¢/n + d,/p = 0, OF what is the same thing, .//: ./m: /n: /p = ¢—d:d—c:b—a:a—b; the equation is thus (¢c — d)(,/A° — ./B°) — (@— 8)(,/A° — ./B°) = 0. There is here one branch ideally containing (z* = 0) the line infinity twice, and another branch ideally containing (z = 0) the line infinity once; order is = 5. Each of the points J, J is an ordinary point on the curve, the remaining points at infinity are a node (A° = B°, C° = D°), as presently mentioned, counting as three points, viz., one branch has for its tangent the line infinity, and the other branch has for its tangent a line perpendicular to the axis; or what is the same thing, there is a hyperbolic branch having an asymptote perpendicular to the axis, and a parabolic branch ultimately perpendicular to the axis. The number of nodes is = 5, viz., there is the node A° = B°, C° = D° just referred to; and the two pairs of nodes ((¢ — d) /A° — (a — b),./C° = 0, — (¢—d),/B° + (4 —b),/D° = 0) and (c — d),/A° + (a—b) /D° = 9, (¢ — d),/B° + (a — b). /G° = 0), each PROFESSOR CAYLEY ON POLYZOMAL CURVES. 89 pair symmetrically situate in regard to the axis. Hence alsodps. = 5; class = 10; deficiency = }. And there is apparently a seventh case, which, however, | exclude from the present investigation, viz., this would be if we had bye oa Hd \ WO way Seay 20" laps Pa Cie Ole es ee as, eee Gi ene Oe, that is, a, b, c, d denoting as before, if we had me Jus jp—arbr,e¢d, and aa” + bb? + ce? +dd?%=0. For observe that in this case we have PATHE =e oCle dD’ = 0, and 24 42s? = 0. Ae Salcy ie eal that is, the supposition in question belongs to the decomposable case. The Decomposable Curve—Art. No. 197. 197. We have next to consider the decomposable case, viz., when we have aA® + bB° + cC® + dD°® = see ante, Nos. 87 et seqg.—it there appears that (unless the centres A, B, C, D are in a line) the condition signifies that the four circles have a common ortho- tomic circle; and when we have also foe. mG nee 5 + 8 i ts aA 05 The formule for the decomposition are given ante, Nos. 42 a seg. Writing therein A°, B°, C°, D® in place of U, V, W, T respectively, it thereby appears that the tetrazomal curve //A° + /mB° + /nC° + »/pD° = 9, breaks up into the two trizomal curves JIA? + Jm,B° ar /n,C° = 0, JT," + J/m,B° ar /n,O c= where Fags 2 2 none ae i Alber cg ag Vi= Jl + yp pean ee a, a p Jn, = lm be sag Na Jim, = /m + NES 5 bJ/n, ‘= a p a ta Pp al ty = Jn + were Clim , NEP = aca 7 oN and where we have VOL. XXV. PART I. Z 90 PROFESSOR CAYLEY ON POLYZOMAL CURVES. Cases of the Decomposable Curve, Centres not in a line—Art. Nos. 198 to 203. 198. I assume, in the first instance, that the centres of the circles are not in a line; we have the following cases :— I. No further relation between /, m, n, p; the order of the tetrazomal is = 8 the order of each of the trizomals is = 4, that is each of them is a bicircular quartic. I. J+ /m+ J/n+ »/p = 9; the order of the tetrazomal is = 7, that of one of the trizomals must be = 3. To verify this, observe that we have Ji, + Sm, + vn, = Jit J/m +t Jat ths Le peat (cJ/m—bJ/n), or substituting for ./7 + i + »/n the value — ,/p, this is =a 3 a —ayi+ J™ (Jin — bin}, and similarly for ./7, + /m, + s/n,, the only change being in the sign of the radical , hs . But from the two conditions satisfied by /, m, n, p itis easy to deduce (aJp— VIP — © ed — bay = 0, and hence one or other of the two functions Wi bolt weg eee apie eee ee that is, one of the trizomal curves is a cubic. TW. /0 + /p=9, /m+ /n = 9; order of the tetrazomal is = 6; and hence order of each of the trizomals is = 3. To verify this, observe that here 1s Oe ot Sie iG +a) +™Gt5)=o which since a + b +c + d = 0, gives x = — so that properly fixing the sign of the radical, we may write Ji - Jsh Sin = 0. We have then Vu= PFS Mt, Jaa + dmg = J b+ 0S PROFESSOR CAYLEY ON POLYZOMAL CURVES. 91 which last equation, using er = to denote as above, but properly selecting the signification of +, may be written Jing + dng = OT 8 in. Hence VIF (lia, + Vn) =={ +4 Jit 040) [84 in} 1 1 1 a N/ be =!491 n+ J yw} mo, viz., /l, = (/m, + /n,) with a properly selected signification. of the sign = is = 0; and similarly //, = (./m, + /n,) with a properly selected signification of the sign + is = 0; that is, each of the trizomals is a cubic. HOO, TV. Ji: n/m: n/n: /p = a:b:c:d (values which, be it observed, satisfy of themselves the above assumed equation “+ a a = 0) ; the order of the tetrazomal is = 6; and the order of each of the trizomals is here again = 3. We in fact have /7 =a+d, W/m, + /n, = b+, and there- fore /7, + J/m, + /n, = 9; and similarly //, + /m, + /n, = 9; that is, each of the trizomals is a cubic. I attend, in particular, to the case where the four circles reduces themselves to the points A, B, C, D; these four points are then in a circle; and the curve under consideration is aJA+b/B+c/C6d/D=0; in the general case where the points A, B, C, D are not on a circle, this is, as has been seen, a sextic curve, the locus of the foci of the conics which pass through the four given points; in the case where the points are in a circle then the sextic breaks up into two cubics (viz., observing that the curve under considera- tion is //A + /mB + /nC + »/pD = 0, where /i: /m: J/n:/p = a:b:0e:4, these values do of themselves satisfy the condition of decomposability : + a + “ + ‘ = 0), that is, the locus of the foci of the conics which pass through four points on a circle is composed of two circular cubics, each of them having the four points for a set of concyclic foci. It is easy to see why the sextic, thus defined as a locus of foci, must break up into two cubics; in fact, as we have seen, the conics which pass through the four concyclic points A, B, C, D have their axes in two fixed directions; there is consequently a locus of the foci situate on the axes which are in one of the fixed directions, and a separate locus of the foci 92 PROFESSOR CAYLEY ON POLYZOMAL CURVES. . situate on the axes which lie in the other of the fixed directions; viz., each of these loci is a circular cubic. 200. Adopting the notation of No. 188, or writing RA =, RB=b,, BC =¢, RD=d, , (and therefore b,c, = a,d,) we have a:b:e:d = — d,(0,—¢,) : ¢(a,—d,) : —b,(a,—d,) + a,(6,—¢,). Moreover Ji =ard | fi =erd, aa bed wes bed fai Wen eS . Jim, =v — Jf, bed = beb gape sala Rs Jing = 6 + aie and we have bed b,¢ bed == (a,—d,)? ware =2,7(a,—d,)*, eS = —a,(a,—d,) suppose; and thence n/ly = (a,—d,) (b,—4) , Jl = (a,—4,)( b,-4) n/m, = (4, —A,) (¢,— 4%), n/ ity = (a,—d,)(_ 4 +4) Jn, = (a,—d,) (a,—4,), n/N = (a,—d,)(—a,—4,), that is Jl, : Sm, / ny = b,—¢,:¢,—a,: a,—5,, nly: n/m: Jing = b,—e, : ¢, +4, : — a,—b,; agreeing with the formule No. 188. The tetrazomal curve —d,(b,—¢) JA + ¢(a,—d,) /B—),(a,—4d,) /C + a,(b,—¢) /D = 0 is thus decomposed into the two trizomals (b;—¢y) JA + (¢,—4) /B + (a —4,) Wc (6; —¢y) JA + (¢, +4) /B — (a@,+,) /C 201. Observe that the tetrazomal equation is a consequence of either of the trizomal equations; taking for instance the first trizomal equation, this gives the tetrazomal equation, and consequently any combination of the trizomal equation and the tetrazomal equation is satisfied if only the trizomal equation is satisfied. 0, OR PROFESSOR CAYLEY ON POLYZOMAL CURVES. 93 Multiply the trizomal equation by — a, + d, and add it to the tetrazomal equa- tion ; the resulting equation contains the factor a,, and omitting this, it is (0,—4) (— JA + /D)+(4—4,) (/B— JC) = 9, where observe that 6,—c, is the distance BC, and a,—d, the distance AD. But in like manner multiplying the second trizomal equation by — a, + d,, and adding it to the original tetrazomal equation, the resulting equation, omitting the factor @,, is (0-4 )(— JA + /D )— (-4,)(/B — JC) = 9; viz., it is in fact the same tetrazomal equation as was obtained by means of the first trizomal equation. 201. The new tetrazomal equation, say Ce wks D) + Gy — a) JB /e)= 9, is thus equivalent to the original tetrazomal equation; observe that it is an equation of the form .,/7A + ./mB +r/nC + /pD=9 , where Jb=—-O,-—¢), Jm=4—d,, Jn=(%—4), Jp =%)—-4, and where consequently /7+./p=90, /m+./n = 9, that is an equation of the form (198) III., decomposable, as it should be, into the equations of two circular cubics. Writing See WE Neo. >) a, — dy by — ty where @ is an arbitrary parameter, the curve is obtained as the locus of the inter- sections of two similar conics having respectively the foci (A, D) and the foci (B, C); (see Satmon, /Tigher Plane Curves, p. 174): whence we have the theorem, that if A, B, C, D are any four points on a circle, the two circular cubics which are the locus of the foci of the conics which pass through the four points A, B, C, D, are also the locus of the intersections of the similar conics, which have for their foci (A, D) and (B, C) respectively; and of the similar conics with the foci (B, D) and (C, A) respectively; and of the similar conics with the foci (C, D) and (A, B) respectively. — 202. V. /lI=/m=J/n=A/p. The order of the tetrazomal is = 5, whence those of the trizomals should be = 3 and = 2 respectively. To verify this observe that the equation : a ae ap : aF 4 = 0 gives : ar : “ic : TF : =0, and combining with a+b+c+d=0, these are only satisfied by one of the systems VOL. XXV. PART I. 2A 94 PROFESSOR CAYLEY ON POLYZOMAL CURVES. (a+b=0,c+d=0), (a+e=0, b+d=0), (a+d=0, b+c=0). Select- ing to fix the ideas the first of these, or writing . (a, b,c, d) = (a, ~ a, c, — Cc), so that we have identically a(4° — B°) + c(C° — D’)=0, an equation which signifies that the radical axis of the ee A, B is also the radical axis of the circles C, D; then, writing as we may do, / a ae re ae 5)= 5 3 we have jew a — a et ee Jmy=1—-, Jn, Ny a A ie Ja, =1-1,=0. Here ./i, + /m,— Jn, = 0, which gives one of the trizomals a cubic, viz.. this is the trizomal (1-2) VAP + (1 + 8) JB + 20= 0. The other trizomal reduces itself to the bizomal ,/A° + ./B°= 0, which regarded as a trizomal, or written under the form (,/A° + ./B’)’ = 0, is the line A°— B’= 0 twice, viz., this is the radical axis of the circles 4,, B, twice; and the order is thus=2. By what precedes, the line in question is in fact the common radical axis of the circles A, B and of the circles C, D. Cases of the Decomposable Curve, the Centres in a Line—Art. Nos. 203 to 206. 203. We have yet to consider the decomposable case when the centres A, B,C, D are on a line; the equation aA°+ bB’+ cC°+ dD°=0 here subsists universally, whatever be the radii w’, b”, ce’, d’. We establish as before the relation < d -+> 3 Esk pe aie: P _Q. The cases are as follows :— 1. No eae ines between J, m,n, p, order of tetrazomal = 8, of trizomals 4 and 4. I. J/2+/m+/n + /p =0; order of tetrazomal=7 ; of trizomals — 4 and 3; same as II. supra. WT. /0+/p=9, /m+/n=0; order of tetrazomal = 6; of trizomals 3 and 3; same as III. supra. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 95 204. 1V. Ji + Jin t+ /n t+ Jp = 9, an/l + bi/m + Cr/n + Aa/p = 0; order of tetrazomal = 6; this is a remarkable case, the orders of the trizomals are either 3, 3 or else 4, 2. To explain how this is, it is to be noticed that in the absence of any special relation between the radii, the above conditions combined with § ate - ua : Eee () give /1: /m: /n:/p=a:b:c:d*; when J, m, n,p have these values, the case is the same as IV. supra, and the orders of the trizomals are 3,3. But if the radii of the circles satisfy the condition a? , b?, c2, d? Ges Ge. C= dq then the two conditions satisfy of themselves the remaining condition af . + ‘ +4 = 0, and the ratios /J: ./m: ./n: »/p instead of being deter- minate as above, depend on an arbitrary parameter. We have NE x8 F, ding= lm 2? bv lage J+ EB esha and between /, m,n, p only the relations Ji+ Jn + J/n+ Jp=0, adnt+bj/m+eNn+dJ/p=0. We find first V1, + Jim + Vay = VE+ dm + Jn - “ef Jp ~ Nig (ovn—e Wn) } =- “2 {Favi- adn — 2 ova—evm} * Writing a”, y?, 2?, w? in place of Vt Jm, Jn, /p, we have to find 2, y, z, w from the conditions e+y +2+w =0, az + by +cez2+dw=0, ey kw ae =F bh AF ¢ + d ? where the constants are connected by the relation aa 25 (i) 2h ge 45 abl = 0), It readily appears that the line represented by the first two equations touches the quadric surface in the point x: y:¢:w=a:b:e:d, so that these are in general the only values of ./J: /m: Jn: J/p- In the case next referred to in the text the line lies in the surface, and the values are not determined. 96 PROFESSOR CAYLEY ON POLYZOMAL CURVES. and then ei he (d—a) Jl =(b—d)J/m+ (c—d) Vn, (d—a) Jp = (a—b)J/m+ (a—c) Jn, whence @Ji-adp = 7—_0va— Vm): and we have thus Jig + Jin, + dig= 2B (2=* — f°) ae), d Ji \d And See : = Vp (b—¢, fad eee ae (observe that in the case not under consideration b/n — cx/m = 0, and therefore JI, + /m, + Sn, = 0, Sl, + /m, + /n,= 0). In the present case we have a:b:c:d=(b—c) (e—d)(d—b):—(c—d) (d—a) (a—b) :—(d—a)(a—b)(b—d): — (a—b) (b—c)(e—a), and thence so that only one of the two sums V1, + /m, + Jn,, V1, + Sm, + Jn, is=0, viz., assuming we have Ji + dm, + vn, =0. And then also a Jl, + b/m, +eJ/n, =aJs/i+b/mteJ/n p YE {tale of (0a wap) = at =(dd /t — aa,/p) — es = (bb Jn — com) | ; but we find dd JI — aa Jp = =" Jn — co Vin) and thence alt, + Jin, + evn, = Ph (S=*— J) Gh Ja = ce ni) = 9, ee in virtue of J*t ——. Hence /1,: + - ++ E = 0. Taking (A,, D,) the anti-points of (A, D); (B,, C,) the anti-points of (B, C); then A, D, = AD, B, C, = BC (No. 65) and referring to the formule, anie, Nos. 100 e seq., it appears that we can find /,, m,, n,, p, such that identically —lA+mB + 70 — pD = —1,A, + m,B, + 1,C, — p,D,, and moreover that /p = /, p,, mn = m, n, . The equation of the curve gives — (A + mB + 20 — pD — 2 JipAD +2./mnBC = 0, which may consequently be written — LA, + m,B, + 2,0, — p,D, — 2,/i,p,A,D, + 2./mn,B,C, = 0; viz., this is . ree JTA, + /m,B, + /n,C, + /p,D, oy hs that is, the two trizomals expressed by the original tetrazomal equation involving the set of concyclic foci (A, B,C, D) are thus expressed by a new tetrazomal equation involving the different set of concyclic foci (4,, B,, C,, D,); and we might of course in like manner express the equation in terms of the other two sets of concyclic foci (A,, B,, C,, D,) and (A,, B,, C,, D,) respectively. It might have been anticipated that such a transformation existed, for we could as regards each of the component trizomals separately pass from the original set to a different set of concyclic foci, and the two trizomal equations thus obtained would, it might be presumed, be capable of composition into a single tetrazomal equation ; but the direct transformation of the tetrazomal equation is not on this account less interesting. ANNEX I.—On the Theory of the Jacobian. Consider any three curves U= 0, V= 0, W = 0, of the same order 7, then writing dU, dgV, deW dy U, dyV, dyW d,U, d,V, d,W AE CHCOE ETI Rs NOE d(a, Y, 2) = 2 we have the Jacobian curve J(U, V, W) = 0, of the order 37 — 3. A fundamental property is that if the curves U = 0, V = 0, W= 0 have any common point, this is a point on the Jacobian, and not only so, but it is a node, or double point, that is, for the point in question we have J = 0, and also Ca 0, 6, = 0, df = 0. It follows that for the three curves /90+ Lo=0, m9 + MS—0, n0 + Nb=—0 (Q = 0 of the order r—s’, 6=0 of the order r—s, 1 = 0, m= 0, n = 0 each of 100 PROFESSOR CAYLEY ON POLYZOMAL CURVES. the order s’, L = 0, M=0, N=0 each of the order s) which have in common the (7 — s’) (7 — s) points of intersection of the curves 6 = 0, 6 = 0, each of these points is a node on the Jacobian, and hence that the Jacobian must be of the form J(10+ Le, m+ Me, no+ Ne) = Ao’? +2bo0a+Ce*= 0, where obviously the degrees of A, B, C must be 7+ 2s —3, r+s+s’—3, r+2s—3 respectively. In the particular case where s’=0, that is where /, m, m are con- stants, we have 4 =0; the Jacobian curve then contains as a factor (b=0), and throwing this out, the curve is BO + CH=0, viz., this is a curve of the order 2r + s—3 passing through each of 7(7 — s) points of intersection of the curves e=0,f6=0. In particular, if »=2,s=1, that is, if the curves are the conics 6+ l0e=0,0+ Mb =0, 0+ Nb = 0, passing through the two points of intersection of the conic 6 = 0 by the line @ = 0, then the Jacobian is a conic passing through these same two points, viz., its equation is of the form 9+Q26=0. This intersects any one of the given conics, say 9 + Lm = O in the points 6 = 0, @ = 0, and in two other points 96 + OQ = 0, Q—L=0; at each of the last-mentioned points, the tangents to the two curves, and the lines drawn to the two points 6 = 0, @ = 0, form a harmonic pencil. Although this is, in fact, the known theorem that the Jacobian of three circles is their orthotomic circle, yet it is, I think, worth while to give a demonstration of the theorem as above stated in reference to the conics through two given points. Taking (2 = 0, x = 0)(z = 0, y = 0) for the two given points 6 = 0, @ = 0, the general equation of a conic through the two points is a quadric equation con- taining terms in 2”, zz, zy, zy; taking any two such conics cz + 2fyz + 2gex + 2hay =0, C2 + 2Fyz + 2Gzx + 2Hxy = 0, these intersect in the two points (zx = 0, z = 0), (y = 0, z = 0) and in two other points; let (z, y, z) be co-ordinates of either of the last-mentioned points, and take (X, Y, Z) as current co-ordinates, the equations of the lines to the fixed points and of the two tangents are Xz — Ze =0, Ye-—-W=0, (hy +92) (Xz— Zz) + (he + fe) (Vz —-Zy) =0, (Hy + Gz) (Xz — Ze) + (Hx + Fz) (Vz — Zy) =0, whence the condition for the harmonic relation is (hy + g2)(Ha + Fz) + (he + fz) (Hy + G2) = 0, that is (/G + gf)2 + (AF + fH) yz + (gH + hG)ex + 2hHaey=0, PROFESSOR CAYLEY ON POLYZOMAL CURVES. 101 but from the equations of the two conics multiplying by 4H, 3h and adding, we have 4H +10)2 4+ (AF + fA)yz + GA + h@)ea + 2hHay = 0; viz., the condition is thus reduced to cH +hO—2(f6+ GF) =0, so that being satisfied for one of the points in question, it will be satisfied for the other of them. Now for the three conics cz" + 2fyz + 29ee + 2hey =0, C22 + 2fye + 2g’zx + 2h’ay OF ca + 2f’ye + 2g’ea + 2h’ay = 0, II forming the Jacobian, and throwing out the factor z, we may write the equation in the form CP 4+ 2Fyz + 2Gee+2Hay =0, where the values are OG Re Cet Gg Gioe—se) + 9-( fe — fe), , H=gllif’ — Wh) +g WF ~ Mf) +9" — Kf). 2F=h( fe’ —f') + (fre—fe)th'(fe —fo , 24 =h(cg” — ce’) +N C%"9 — eg) +h’ (eg — cg) ; and we thence obtain cH + hO =— (fo — f'9) (ch — ch’) + (fo — fq’) cl’ — ch) = f+ gF), viz., the condition is satisfied in regard to the Jacobian and the first of the three conics; and it is therefore also satisfied in regard to the Jacobian and the other two conics respectively. I do not know any general theorem in regard to the Jacobian which gives the foregoing theorem of the orthotomic circle. It may be remarked that the use in the Memoir of the theorem of the orthotomic circle is not so great as would at first sight appear: it fixes the ideas to speak of the orthotomic circle of three given circles rather than of their Jacobian, but we are concerned with the ortho- tomic circle less as the circle which cuts at right angles the given circles than as a circle standing in a known relation to the given circles. ANNEX IJ.—On Casty’s Theorem for the Circle which touches three given Circles. The following two problems are identical :— 1. To find a circle touching three given circles. 2. To find a cone-sphere (sphere the radius of which is = 0) passing through three given points in space. VOL. XXV. PART I. 2€ 102 PROFESSOR CAYLEY ON POLYZOMAL CURVES. In fact, in the first problem if we use z to denote a given constant (which may be = 0), then taking a, a’ and 2(z — a’) for the co-ordinates of the centre and for the radius of one of the given circles; and similarly }, 0’, i(z — 0"); ¢, ¢, uWz—e) for the other two given circles; and S, S’,i(z — S”) for the required circle; the equations of the given circles will be (@— a +y—aP+@—af=0, (7 — bP + (y— VP + (2— VP =0, (@—eP+y—¢P +(e—e")*¥=0, and that of the required circle will be (a—S)? + (y—S’)? + @—S’)? = 0. In order that this may touch the given circles, the distances of its centre from the centres of the given circles must be 7(S’—a’), i(S’—b’), iS’—c’) respectively; the conditions of contact then are (S—a)? + (S’-a? + (S’— a’? (S — b? + (S’— UY)? + (S"— HF = 0, (S— co)? + (S’—c)? + (S’— ec’? = 0, 0, | or we have from these equations to determine S, S’, S’. But taking (a, a’, a’), (0, 0’, b’), (c, &, ec) for the co-ordinates of three given points in space, and (S, S’, S") for the co-ordinates of the centre of the cone-sphere through these points, we have the very same equations for the determination of (S, S’, 8”), and the identity of the two problems thus appears. I will presently give the direct analytical solution of this system of equations. But to obtain a solution in the form required, I remark that the equation of the cone-sphere in question is nothing else than the relation that exists between the co-ordinates of any four points on a cone-sphere; to find this, consider any five points in space, 1, 2, 3, 4,5; and let 12, &c. denote the distances between the points 1 and 2, &c.; then we have between the distances of the five points the relation pa ie Na ch ert alia Oe ee ae, Le oT, 0, 335. 08 25 , O25 W ; a4, 35" a er ay aS Sal 58+, Bae 6 whence taking 5 to be the centre of the cone-sphere through the points 1, 2, 3, 4, PROFESSOR CAYLEY ON POLYZOMAL CURVES. 108 — we have 15 = 25 = 35 = 45 = 0; and the equation becomes OR 2215, ee 0 211.05, 23°, 24? 1% So 0 2 34” es, 0 which is the relation between the distances of any four points on a cone-sphere ; this equation may be written under the irrational form . OFC Te 4231, 94 4194 Taking (a, a’, a’), (0, 0’, 0"), (¢, ¢, c’), (x, y, ) for the co-ordinates of the four points respectively, we have = J(b-cP + U—e) + ees 14 = J/(@—a? + y—a)? + a’) , = /(¢—a)? + (—a) + (=a, 24 = f/(a—bP + (y—by + (20, JMa=b? + (a 0 + (a0 = 34 = J/(z—c)? + (y—ey + @—ey, NI oo eal . or the symbols having these significations, we have 23.14 + 31.24+ 12.34 = 0 for the equation of the cone-sphere through the three points; or rather (since the rational equation is of the order 4 in the co-ordinates (2, y, z)) this is the equation of the pair of cone-spheres through the three given points; and similarly it is in the first problem the equation of a pair of circles each touching the three given circles respectively. In the first problem the radii of the given circles were u(z—a’), u(z—0’), i(z—c’) respectively; denoting these radii by a, 6, y, or taking the equations of the given circles to be (c—a)? + (y—-aP—a? = 0, (a— bP + y—by = Be = 0, Gy + y-—c? —7 = 0, the symbols then are = Jb— oF + © cP — (6-7, = JS@—aP + yap —e’, a Coes ey Chee (y—a)?, 24 = eran by + (y= ne B’, S (SX) al fg and the equation of the pair of circles is as before 14 + 31.24 412.34.= 0; esl 104 PROFESSOR CAYLEY ON POLYZOMAL CURVES. where it is to be noticed that 23, 31, 12 are the tangential distances of the circles 2 and 3, 3 and 1, 1 and 2 respectively; viz., if a, 8, y are the radii taken positively, then these are the direct tangential distances. By taking the radii positively or negatively at pleasure, we obtain in all four equations—the tangential distances being all direct as above, or else any one is direct, and the other two are inverse ; we have thus the four pairs of tangent circles. The cone-spheres which pass through a given circle are the two spheres which have their centres in the two anti-points of the given circle; and it is easy to see that the foregoing investigation gives the following (imaginary) construction of the tangent circles; viz., given any three circles A, B, Cin the same plane, to draw the tangent circles. Taking the anti-points of the three circles, then select- ing any three anti-points (one for each circle) so as to form a triad, we have in all four complementary pairs of triads. Through a triad, and through the com- plementary triad draw two circles, these are situate symmetrically on opposite sides of the plane; and combining each anti-point of the first circle with the symmetrically situated anti-point of the second circle, we have two pairs of points, the points of each pair being symmetrically situate in regard to the plane, and having therefore an anti-circle in this plane; these two anti-circles are a pair of tangent circles; and the four pairs of complementary triads give in this manner the four pairs of tangent circles. I return to the equations (@ — S)?+ (y —8)?+ @ —8")? =0, (a — 8)? + (a — 8)? + (a” — 8”)? = 0, (6 —S8)?+(0¢—S)?+ 0 — 8’)? =0, ( — 8) + (¢— 8+" — 8) =0; by eliminating (S, S’, S”) from these equations we shall obtain the equation of the pair of cone-spheres through the points (a, a’, a’), (0, 0’, b’), (¢, ¢, ¢’). Write «—S,y—S',z—S" = X, Y, Z, then we have AF 4} Y2 +77 = 0, and if, for shortness, we put A=(a—2)? +(@ —y)*?+(@—-2)?, . B= (0 —2)* a — 9) i — 22, CHa + PFC 2, then by means of the equation just obtained the other three equations become A+2(@-a)XL4+(—-y)V+ (a —2Z]=0, B+2[@-2) +0 -—y V+ -2Z]=0, C+2[( —a) X+( —y) V+ (c’ —2)Z] =0. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 105 These last equations give A:V:Z= rMA+4B4 IC >: AA+WB+/C NA+ u4B+4+/C , where A=0e" —Vd+(¢ —Ve -— (—-O'\y, w=ca—cad+(a—cej —(a—ey, yp =al’— a+ U—a)ze— "ay, N= b’e — be’ +(e’ — Da — (e — dz, w=la—ca +(e’—c)je-—(a-— cz, y =a’b — ab” + (0’ —a’)x— (b — az, w= bl —Ue + (¢ —djyy —(¢ — U)a, we =e — Ca+ (a —cjyy —W— ca, ab — ab + (6 —ajyy —(U —a)z; = and the result of the elimination then is (a A+,.B +» cy +(* A+ 4¢B+y/C? +(VWA+n'B4+ /CP =0. But substituting for A, B, C their values, and writing, for shortness, a 4 — bc’ cee bc’ + cal ar, a + ab” z. a’b ; —j =U’c — be’ + c’a — ca” +’) — ab’, —k =be —Ue +cev —ca +ab’ —ab, A =a(l'c’ — b’c) + a’ (bc — be”) + abe’ — Ue) , —p = (Uc’ — ’c) (a? + aw? + a”) + (a”—e'd’) (0? +02 +0") + (vb —a'd’) (2? +67 +c) , —q = (bc — be’) (a* + a? + a”) + (ca —ca” ) (0? +07+0"?) + (ab —ab’) (PP? +07 +c) , —r = (bec —0U'c)(a* + a7 + a”) + (ca —ca ) (0? +07+0"7) + (ab’ —ab’ ) (ce? +67 +0) , —l = (ce —b )(a?+a% +a") +(a —c )(0?+07+0"?) + (0 —a )(P+c%+4c%) , —m= (¢ —-0U )\(®+a%74+ 0%) 4+ (a -—c )\U407+0%) + (0 -a’ ) (+e? +c%) , —n = (ce —b’)(@ +a? +0) 4+ (a’—c’ )(P+b74+0"7) + (0 —a’ ) (@+c7+0%), we find AA + 2B + 9C = — Ua + xy? + 2°) + 2a(a? + y? + 27) — 2a(iw + jy + ke) — 2ax+ ny—mze—p, with similar expressions for \’A + v’B + C, »’A + «’B + »’C, and the re- sult is {u(a? + y? + 2”) — 2u(aw + jy + hz) — 2da+ ny — mz— ph? + fie? + y? + 2?) — 2y(iae + jy + ke) — na — 2by+ le— gh? + {k(a? + y? + 2?) — Qed + jy + ke) + ma— ly—2az—7rh?=0, VOL. XXV. PART I. 2D 106 PROFESSOR CAYLEY ON POLYZOMAL CURVES. viz., this is (a? + y? + 27)? (i? + 7? + kh?) + (a? + y? + 2?) {dain + jy + ke + 2(i(ny — mz) + j(lz — na) + (ma — ly) + 44? — 2p + jq + kr) + (7? + m? + n?)h — (le + my + nz)? + A(ia + jy + kez) (pu + gy + 72) + 4A(px + qy +72) — 2(p(ny — mz) + g(lz — nv) + 7(mx — ly)) +r? +7+r=0. viz., this is in the rational form the equation of the pair of cone-spheres. The function on the left hand side must, it is clear, be save to a numerical factor the norm of VO— oF + We + Ue. J a—a?l + Ya? + &=e'P + Sea + C= aF + a}. SOO GP + CUP + J(a—b? + @—0P + W VP. Je—o? + Y— oP + — eF,” the numerical factor of the expression in question is in fact =— 4, that is, the norm is =— 4074+ 74+ 27 (P+ 7? + 2) + &.; so that attending only to the highest powers in (a, y, z) we ought to have Norm {/(b—c)*+ (U —¢/)? + (U’ — "P+ V(c—a)? + (¢ —a')* + (0” — 0")? +N (a—b)* + (a —U) + (a —0")} = —4(? +7? +h’) . It is easy to see that the norm is in fact composed of the terms WW —e{ OF — C—aP — (a HF}, + 2(¢ —a'? {—(b—e? + (¢—a?— (a— BY}, + 2(a’—¥)2 {—(b— 0)? — (¢— a}? + (a—BF}, and of the similar terms (a, 0, c), (a, 6, &) and in (a, 0c’), (a, 6, c’); the above written terms are = — 4 into W— ¢)? (a—2) (a—0) + (¢—a)? 6 —0)(b —a) + (a —0')? (ce —a)(a—b), which is = a? (b—c)? + 07 (e—a) + &? (a—b)? + 20’c' (a —b) (ec—a) + 2ca' (b—c) (a—b) + 2ad’ (ce —4) (b—c) = {a(b—c) + U(ec—a) + c(a—d)}? Sie and the value of the norm is thus = — 4(2? + 7? + £°), as it should be. PROFESSOR CAYLEY ON POLYZOMAL CURVES. 107 Annex IIL.—On the Norm of (b—c),/A°+ (c— a), /B°+ (a— 6), /C°, when the Centres are in a Line. The norm of /U+,/V+,/W is = (pall eel = —81).(U, Vy We): whence that of /U+0’ + /V+WVt+/W+W’ is Sd ee ee ee (Ge VW) ag Ds I is RE Wa ORs 30 Vel ee I, ee VC, BWP, where the last term is = 2 into | oT 7=W) ROIS (= Ue W +W(—-U=V4W). And the norm of /U+0’+U" + /V4+V+V'+J/W+W’+ W’" is obviously composed in a similar manner. Now, applying the formula to obtain the norm of O-0) JF Fotat C—O JP +I+B + (W-)) JE F047, the expression contains six terms, two of which are at once seen to vanish ; and writing for shortness (,, ) in place of (1, 1,1, —1,— 1, — 1) the remaining terms are (,)(G@—6)%« , (¢e—a)?8, (a—b)*¥ ye +2 (,;) ((o- c)?a , (¢c—a)*B, (a—b)*y )(@ —c)*a?, (c—a)?b?, (a— b)?c?) + 24(,,)((6—¢)?a , (¢—a)?8, (w~—b)?7 )(G—c)? , (c—a)? , (a—0)? ) + 26(,,) (@—«)?a?, (¢ — a)?0?, (a—b)?c?) (o— 0)? ,(e—a)? , @—bd)? ); the first of these terms requires no reduction ; the second, omitting the factor 2, is (b—c)’a | (6—c)?a® — (¢—a)?b? — (a—b)%c? | + (c—a)’p (= (—e)?a? + (¢—a)?b? — (a—b)?c? | ; + (a—b)?y [—@—90?a? — (¢c—a)?b? + (@=b)7e?|; which is = 2(a — b) (b — c) ¢ — a) [ bc (b — ¢) a+ca(e—a)B+ab(a— b)y | ’ Similarly the third term, omitting the factor 20, is (b— ca [ (6—c)? —(—a??—-(a— b)? | + (c — a)*B[—(@ — 0)? + ¢ — a)? — (a — | + (a — by |—-G@- oF —-C-af +(@—d)], 108 PROFESSOR CAYLEY ON POLYZOMAL CURVES. which is = 2(a — b) (6 —¢) (c—a) [@—cat (c — a) B+ (a — Dy], and for the last term, omitting the factor 20, this may be deduced therefrom by writing (a’, 6’, c*) in place of (a, 8, y), viz., it is = — 2(a — b)* (b — ce? (ec — a)’. Hence, restoring the omitted factors, and collecting, we find Norm {(} — e) Na+ 6+at(c—a)/P +6484 (a — b) Je +o+ x} = (b—c)*a? + (c—a)*B? + (a—b)'y? — 2(e—a)? (a—b)*By — 2(a—b)? (b—c)*ya—2(b—c)? (c—a)*aB + 46(a—b) (b—c) (c—a) [ (b—c)a+(c—a) B+(a—D)y] + 4 (a—b) (b—e) (c—a) [ (be (b—c) a +ea (c—a) B+ab (a—D)y] — 46(a—b) (b—c)? (e—a)*. Hence, first writing a— az, b—«2,¢—~wz in place of a,b,c; then 7’ for 6, and (— a”,— b”,— c’”) for (a, 8, y); and finally introducing 2 for homogeneity, we find Norm {(b —c) Va — az)? + y? — a2 + (¢ — a) ye (a — b) J} = 27 into 22((b — c)ta”t + (¢ — a8" + (a — byte” — 2c — a)? (a — b)?b'9c"? — 2(a — b)* (b — ¢)?e”4a”? — 2(b — c)? (¢ — a)Pa’b"?) —4y? (b — c) (e— a) (a — Dd) a (b— ec) a? + (c—a)l” +a— b)e"?] —4 (b—c)(c—a)(a—b) { (b—oc) a” be —w(b+c) +2’) +(¢c—a)b” (ca — zz (¢ + a) + 2") +(a—b)c” (#ab—z(a + 0) + a?)} —4y (b—c) (ec—a) (a—b). so that the equation (6 — c) ./A° + (¢—a) ./B° + (a —b) ./C° = 0, in its rationalised form, contains (2? = 0) the line infinity twice, and the curve is thus aconic. If @?=0?= c’= k”, then the expression of the norm is = 2 into — 4(a — B)? (& — 0)? (¢ — a)? (y — Bh), viz., when the three circles have each of them the same radius #”, the curve is the pair of parallel lines y*? — &”z*? = 0; and in particular when s’ = 0, or the circles reduce themselves each to a point, then the curve is y’ = 0, the axis twice. ANNEX IV.—On the Trizomal Curves /JiU+ /mV + »./nW = 9, which have a Cusp, or two Nodes. The trizomal curve ./7U + ./mV+/nW= 9, has notin general any nodes or cusps: in the particular case where the zomal curves are circles, we have PROFESSOR CAYLEY ON POLYZOMAL CURVES. 109 however seen how the ratios / : m:n may be determined so that the curve shall acquire a node, two nodes, or a cusp; viz., regarding a, b, c as current areal co- ordinates, we have here a conic : + + + : = 0, the locus of the centres of the variable circle, and the solution depends on establishing a relation between this conic and the orthotomic circle or Jacobian of the three given circles. I have in my paper “ Investigations in connection with Casry’s Equation,” Quart. Math. Jour. vol. viii. (1867), pp. 334-342, given, after Professor CrEMona, a solution of the general question to find the number of the curves /7U + /mV +/nW= 9, which have a cusp, or which have two nodes, and I will here reproduce the leading points of the investigation. I remark, that although one of the loci involved in it is the same as that occurring in the case of the three circles (viz., we have in each case the Jacobian of the given curves), the other two loci > and A, which present themselves, seem to have no relation to the conic of centres which is made use of in the particular case. We have the curves U= 0, V=0, W=0, each of the same order 7; and considering a point the co-ordinates whereof are (/, m, ), we regard as corres- ponding to this point the curve 707+ /mV+ /nW= 0, say for shortness, the curve Q, being as above a curve of the order 27, having 7” contacts with each of the given curves V= 0, V=0, W=0. As long as the point (/, m, 2) is arbitrary, the curve (2 has not any node, and in order that this curve may have a node, it is necessary that the point (/, m, 7) shall lie on a certain curve A; this being so, the node will, it is easy to see, lie on the curve J, the Jacobian of the three given curves; and the curves J and A will correspond to each other point to point, viz., taking for (J, m, n) any point whatever on the curve A, the curve Q will have a node at some one point of J; and conversely, in order that the curve Q may be a curve having a node at a given point of J, the point (/, m, n) must be at some one point of the curve A. The curve A has, however, nodes and cusps; each node of A corresponds to two points of J, viz., for (/, m, n) at a node of A, the curve () is a binodal curve having a node at each of the corresponding points of ./; each cusp of A corresponds to two coincident points of J, viz. for (/, m, n) at a cusp of A, the curve Q has anode at the corresponding point of /. The number of the binodal curves Q is thus equal to the number of the nodes of A, and the number of the cuspidal curves Q is equal to the number of the cusps of A; and the question is to find the Pluckerian numbers of the curve A. This Professor CREMONA accomplished in a very ingenious manner, by bringing the curve A into connexion with another curve = (viz., = is the locus of-the nodes of those curves VOL. XXV. PART I. 25 110 PROFESSOR CAYLEY ON POLYZOMAL CURVES. lU+ mV + nW = 0 which have a node), and the result arrived at is that for the curve A ’ Order = 3(r—1) (8-2), Class = 6(r—1)?, Nodes = $(r—1) (27r*® — 637? + 227 + 16) , Cusps = 3(r—1) (7ir—8), Double tangents = % (r — 1) (1273 — 36r? + 197 + 16), Inflexions = 12 (r —1) (r- 2); so that, finally, the number of the cuspidal curves 707 + ./mV + /nW=0, is = 3 (r — 1) (77 — 8), and the number of the binodal curves of the same form is = 3 (7 — 1) (277° — 637" + 22r + 16). When the given curves are conics, or for r = 2, these numbers are = 18 and 36 respectively; but the formule are not applicable to the case where the conics have a point or points of intersection in common ; nor, consequently, to the case of the three circles. ae te Gal bug) Il.—On the Motion, Equilibrium, and Forms of Liquid Films. By the late Sir Davip Brewster, K.H., D.C.L., &e. (Plates I. and IL) Communicated by Francis Dzas, Esq., LL.B. (Read 6th April 1868.) [This paper was transmitted to the Council by Sir Davin Brewster, on the 8th February 1868, with the following remarks :—“ I have tried in vain to finish the two most important of my papers on Liquid Films, but the most beautiful drawings of all the phenomena which its purpose was to describe have been finished. I think, therefore, that my friend Mr Deas will, by means of these drawings, produce an interesting paper. The drawings are numerous and large, but many of them may be reduced in size. As this is the last of my papers, I hope the Council will not grudge the expense of having them well lithographed.” In another letter, Sir Davin BREwstTER expresses a wish, that in the event of the paper being printed in the ‘‘ Transactions,” notice should be taken of the fact that the drawings were executed by his friend Miss DickENson. | I. On some Transformations in Films when brought in contact with Surfaces of Glass.* (1.) Let a film be formed on the rim of a cylindrical wine-glass, at or very near its margin; cover it immediately with a watch-glass, and holding the latter firmly in its place, invert the whole, so that the film is placed in a vertical position. The film will now attach itself to the watch-glass at the lowest point where it is in contact with the margin of the wine-glass, and will run up the concave surface of the former. At the same time, the film will leave the margin of the wine- glass at its upper edge, and retreat into the glass, running down its inner sur- face. 7 in the preceding expressions, and 6 = 0, then ¢ = 0, 2 = p — r, and ; ; kl’ intensity at O=—y x mr’ = Al. : (5). If, therefore, the circle ADPB falls wholly within the circle ABG, the in- tensity of the illumination on the circular space, whose centre is F and radius p— 7, is constant and equal to that of the beam when it leaves the mirror, or the intensity is the same as if all the rays from the sun’s disc were parallel to one another. When p = 7, then, z= 0, and F is the only point whose intensity = Al’. Next when p < rand 6 = z, then ¢ = z,z =7 — p, and intensity = = x pa ==} 5 (6). This formula expresses the intensity throughout the circle, whose radius is T — p. When z = r + p, the intensity vanishes. 130 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. The preceding limiting cases are also evident from the geometrical considera- tion of the problem taken in connection with equation 2; and the same principles can be applied to find the intensity, whatever the shape of the perpendicular section of the incident beam. ARTICLE 3.—When there are m mirrors similar to the preceding, the light from each making an angle of incidence 7, with the perpendicular to the plane on which it is thrown, the intensity of the central spot in each of the preceding cases becomes— In 1st case, nkl’ cos 2, : é é . (1). 12 « In 2d case, BENE SOE, é ; ' 6 (2). r ARTICLE 4.—Prop. A Small Luminous Sphere has its centre in one of the foci of a Prolate Elliptic Mirror, to find the Intensity on any Small Plane surface situated in the other Focus. Let / (fig. 3) represent the luminous sphere. (& = the angle which the small plane at F makes with FX: the axis of z coinciding with the axis ofthe mirror, and the plane of xz being perpendicular to the small plane passing through F; the axis of y, which is at right angles to the plane of xz, will therefore coincide with the small plane which passes through F. oP. 6 = the angle PFZ. ¢ = the angle which the projection of 7 on the plane of zy make with FX. a = radius of the luminous sphere at / V = the angle which 7 makes with the normal to the small plane at F. I = the intensity of the light at the surface of the small sphere. Since the well-known differential of a volume 7’ sin 6 d@ df dr has for its perpendicular section, at the surface of the spheroid, 7” sin 6 d@ dp; we may sup- pose the whole surface of the elliptic mirror to be divided into small areas, each of which receives from the sphere at f, and reflects to F, a pencil of light, whose perpendicular section, at any point P of the mirror, is 7” a 6 dé do. Moreover, the intensity at P Soa to Py = — = (by Art. 1, eur 3), and after reflection it becomes © P 7” The cone of rays reflected from the increment of surface at P, in the direction PF, will have expanded at F into a oe (perpendicular to the radius vector), rar? whose radius by similar triangles is >, o 7 and area = pyr By Art. 1. Equa. 6, the intensity of the light on this circle at F = 7° sin 6 dé 2 Qprd dp x prt a = ET sin 0 ddd. MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 131 and e sin 6 d0 dp cos V = its intensity at F on the small plane, whose equation is z cos 8B — asin B = 0, : , (1), €os-V = “ cos B —* sin B = cos 6 cos 9 — sin B sin @ cos ¢. Substituting for cos V its value we obtain for the whole intensity at F, on the small plane, EL fos 6 cos 6— sin sin 4 cos g) sin 4 dé dg, ; : (2). Denoting this integral by u, Uw = fe f (cos sin? + sin 6 sin é cos @ cos g — é sin 8 cos 9) dp + C. Now cot 6 = tan@ cos¢, when V = 90’, that is, when PF coincides with the plane denoted by Equation 1, .. 6 = cot —1(tan 6 cos ¢) 1 sin = (1 + tan? B cos? 9)! nae tan 6 cos 9 (1 + tan? 6 cos? 9)? Taking the integral between the limits 9 = 0, and 6 = cot—’ (tan cos ®), Pol ee 6 (1 + tan? B cos? 9) i On I + tan? 6 cos? 9 = iB! ; dy : ar sin 6 tan B sm pol =e { feos 8 dep sin 8 sin g cot—* (tan 6 cos 9) +f Tae Gas Gos Bee E : 2 seep dey} mais f feos 6 do — sin B sin g cot—! (tan B cos 9) —fcosB dp + see Gar tate 1 — cot—? (tan 6 cos g) sin cos S do. = = { tan (cos B tan 9) — sin f sin 9g cot—! (tan 6 cos 9) } + C. and between the limits ¢ = 0 and ¢ = 90", u = 575 sin 6 ), = = (1 —sin @), which is the intensity at F of the light reflected from that portion of the spheroid bounded by the planes passing through the co-ordinate axes of + xand + 2, + y and + z, and the small plane produced. Similarly ao + sin 8) gives the intensity of the light, from that portion enclosed by the planes passing through the axes — # and + z, + yand + 2, and the small plane at F produced. Hence the intensity of all the light which can fall on the side of the small plane towards A (fig. 3). fills ; j 5 t : (3). VOL, XXV. PART I. Dale 132 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. Also - sin 6 is the intensity at F due to the light reflected from the part of the mirror intercepted between the small plane produced, and the co-ordinate plane of xy. In the same manner it can be shown, that the intensity of the light concen- trated at F, on the opposite side of the small surface, and reflected from the remaining portion of the spheroid, is also equal to Al. These results are independent of a, the radius of the luminous sphere, and are equally true for all spheroids which have F for one of their foci, wherever the other may be situated. It appears then, in conclusion, that the light emanating from a small luminous sphere, with its centre in one of the foci of a prolate elliptic mirror, produces at the other focus a nucleus of radiant light and heat, equal in intensity to the radiation at the luminous surface diminished by the quantity lost by reflection. Again, putting 6 = 0 (in Equation 2), we obtain intensity kI F =" [fsin costdodo, . (4). Integrating between g = 0, and 22; : ; a Sat intensity = 2n x — fein cos 6 dé , = 2kI Jsin 6 cosé dé; and between 6°, and zero, = Aisin oy 7 ’ ; : (5). This expresses the intensity at the focus of the light reflected from a segment of the spheroid intercepted between the vertex and a plane perpendicular to the axis; and the intensity produced by a zone intercepted between two planes, per- endicular to the axis of revolution, is kI (sin 76 — sin? 6’) ; : : (6). ARTICLE 5.—The preceding proposition is true, independently of the size and form of the luminous body in the focus / (figs. 3 and 4). Since radiant light and heat diminish in the inverse ratio of the square of the distance, it follows that the quantities received from circular areas of equal angular magnitudes are equal, whatever their absolute magnitudes, when the intensities at the radiating surfaces are equal. Taking this principle in connection with the fact, that a luminous surface appears equally bright when viewed at any angle, the light emanating from CD, part of the surface of DCE, will therefore have at F _ the same intensity as if it had proceeded from the small sphere AB (fig. 4). But the light reflected from P to F can only emanate from some part of the surface DC, which lies within the cone described by PA, revolving about Pf Hence the MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 133 intensity at F of the light radiating from DC, and reflected at P, is equal to that which would have resulted from the sphere AB; and the same is true for every increment of the elliptic mirror. Therefore, the total illumination at F, from the luminous surface DCE, is equivalent to that from the small sphere AB. From this and the preceding article, we infer that a zone or segment of an elliptic reflector may be used as a pyrometer. For if such a zone, contained between two planes perpendicular to the axis, be placed before an opening in a furnace, the place of the focus f falling within the heated body, the heat reflected to F may be reduced, by diminishing the breadth of the zone, until it can be measured by a Fahrenheit thermometer ; and I, the intensity of the total radiation from any point f within the furnace, can be determined in degrees of Fahrenheit by Art. 4, Equa. 6. Articrz 6.—Prop. When a Parabolic Reflector has its axis directed to the centre of the Sun, to find the intensity of the converging Rays which fall on a small Plane Disc at the Focus. Let « = angular diameter of the sun, which is about 32’, ce = the distance at which the reflected image of the sun expands into a circle equal to unity in diameter, being about 107°4, j—— Pi (fig. 5), Y’ = intensity of the sun’s rays at the earth’s surface, I = intensity at the surface of the sun, u, k, 8, 8, p, and V = the same as in proposition (Art. 4). 2 Then aa = area of the circle, which the light reflected at P occupies at F perpendicular to PF. The intensity of the light reflected from the increment of surface at P on this circle by Art. 1, Equa. 6. : ye emer? =r’ sind dddg x kl See 27! uz y sin 6 dé do ; : 4c7kl’ . and on the small disc at F, = —— sin 4 dé do cos V. cos V = cos cos 6 — sin 6 sin é Cos @, 2 7 ? us = fico 8 cos @ — sin B sin 4 cos 9) sin é dé dg, (1). Integrating as in Article 4, we obtain for the intensity of the light reflected from the corresponding sections of the parobolic mirror kV (l—sin®), . , F ; (2). and kl’ (1+sin8), . ; (3). Hence the total intensity at F (fig. 5) on the side of the plane disc towards 134 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. A, resulting from the light reflected from the segment of the paraboloid cut off by the plane of the disc produced, = 2PkI'(1 —sinB) + PkI'(1 + sinB)} = 40°’ = KI . (4), I being the intensity at surface of the sun. But c = 107 nearly, therefore the numerical value of this equation = 45796kI’ nearly, which is a degree of concentration several times that of the most powerful burning glass ever constructed. Again putting 6 = 0 (in Equation 1), ail he “= AOE | fsivscoseas do; and integrating as in Article 4, Equation 4, u = Ac7kI’ sin? 6 ; ; : : . (5), which gives the intensity at the focus of the light reflected from a segment of a paraboloid, intercepted between the vertex and a plane perpendicular to the axis; and the intensity produced by a zone, intercepted between two planes perpendicular to the axis, is 4(?k]' (sin?é— sin?¢’) = AI (sin?6— sin?é’) ; (6). Equation 5 shows that the concentration at the focus varies as sin’@: it is a maximum when @ = 90°, and is independent of the parameter of the parabola. It may therefore be inferred that a reflector employed to detect the heat of the lunar rays should be as large a segment of a paraboloid as possible; and the same condition is essential in improving to its utmost limit the space-penetrating power of the reflecting telescope. Again, suppose the parabolic mirror to extend to infinity, it can also be shown that the light concentrated at the focus on the other side of the small disc is equal to 4c°Al’=£I. What has been proved respecting the intensity at the focus is approximately true for every point on the plane of the small disc not farther from F than + , the quantity = being the radius of the sun’s image reflected from the vertex of the paraboloid, and p the parameter of the generating para- bola. Thus, in every position in space, when the axis of a parabolic mirror, whose extent of surface is not less than that cut off by a plane passing through the focus, is directed to the sun, a circle of radiant light and heat is formed equal in intensity to the radiation at the solar surface minus the quantity lost by reflection. MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 135 ARTICLE 7.—The intensity at the focus of a parabolic reflector is independent both of the form and distance of the luminous body. Let BAC (fig. 6) represent a section of the parabolic reflector, and GH that of a luminous surface of uniform intensity; it can be shown, as in the case of the spheroid (Art. 5), that the concentration at F produced by the only rays which can fall on it, namely, those emanating from GH parallel to the axis AF, is equal to the intensity at the luminous surface GH, minus the quantity lost by reflection. It is evident that the section of the luminous body must not be less than CB. Arricir 8.—Prop. When the Axis of a Mirror in the form of a Right Cone is directed to the centre of the Sun, to find the Intensity of the reflected Light on any point in a Plane placed perpendicular to its Axis. Let CAD (fig. 7) represent a section of the mirror, O the point on which we wish to determine the intensity of the reflected light. Every small increment of the mirror gives rise to a cone of rays which casts an ellipse of light on the plane at F, the major axis of which passes through the point F. The light of all these ellipses, whose centres fall within a certain distance of the point O, will overspread it and increase the intensity at that point. | If P (fig. 8) be the centre of one of these ellipses NOM, considerably magnified, whose circumference passes through O, then P is a point in the curve within which must fall the centres of all the ellipses whose light can overspread O. To find the equation to this curve, let 19) eel p FO =¢z a and 6 = the co-ordinates of P, referred to rectangular axes whose origin is at O, 6 = the angle PFO. Now ay’ +0°x’ = a’b’ is the equation to the ellipse NOM, the centre being the origin. When referred to the axes OX and OY; by substituting, y = (y — 8B) cosé— (a — a) sind, we = (y’—8) siné + (v’—«)cosé, fan = abe , we obtain z+a (a? cos? 6 + b? sin?) (y’— B)? + (a? sin?6 + b?.cos? 4) (x — a)? — 2(a? —b?) (y’— 8’) (av — @) sind cosd = 020?, Putting z’=0, y’=0, there results the equation to the required curve, which is . VOL. XXV. PART I. 2M 136 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. the locus of the centres of all the preceding ellipses whose transverse axes intersect in F and their circumferences in O, (a? cos? 6 + 6? sin? 6) 6? + (a? sin” 4 + b? cos? 6) a? — 2 (a? —b?) a8 sind cosé = a*D? (1), . (a? +0? tan? 6) B? + (a? tan? 6+ 0?) a? —2(a?—b*) a8 tan d = a?b?(1+ tan? 4). Substituting for tan 6 its value, we obtain {a?(z+ a)? + b7B?18? + {0287 + b7(z + a)? }a? — 2(a? —b?) (2+ «) a3? = a7b*{(z+a)?+ 87}, UPB 4+0 fe +a(e+a)}? = wb {(e+a)? +B}. : ; (2). By substituting in this z+a=p cos @, and 8=p, sin 0, we have the polar equation to the curve, F being the origin, 9 “ a? 2” 9 sin? 6 + b?(¢” sin? 6 + ¢” cos? d— zecos 6)? = a*b? 6, 72 9? sin? 6+ 676? (2 — 2 cos 6)? = ab?” , 2 and e=zcosdta(l— 7 sin? 6)! ; ; é (3). It is evident that the form of the curve represented by the Equations 2 and 3 will vary with the relative values of the constants a, b, and z; but in every case it is symmetrical with respect to the axis FX (fig. 8). When z=0, the point O is situated on the axis of the mirror, and the curve becomes the circle p=a. And if z=), the equation breaks up into two circles whose centres lie in the line FO, and which touch one another externally at the point F’, their diameters being a+ 6 and a— 6d respectively. When the point F falls without the curve, the radius vector becomes a tangent for the value sin 6= : : Putting 6=0 in Equation (1), we get for a plane mirror CP+0a =a'l’, an ellipse with O for its centre, and equivalent to ay + Bat = al. Now, if PHG (figs. 9 and 10) represent the curve, considerably magnified, expressed by equation 3, in deducing the intensity at O the proposition divides itself into cases depending on the relative positions of the points F and O (as in figs. 9 and 10). Case 1. When the distance FO from the axis (fig. 7) is so small compared with FB that the distance of any point within the curve similar to PHG from CB, that part of the mirror where the light which overspreads O is reflected, may be considered equal to FB. MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 137 Let 7 = angle of incidence on the mirror, R = perpendicular distance of B from the axis, 7 = perpendicular distance of any point in the curve similar to HPG (fig. 9), as represented by FQ, v = FA = FB, because BFA is an isosceles triangle (fig. 7), wu = intensity at O, I’ = intensity of the sun’s light at the earth’s surface ; then 27 = angle BFA, 90°—7z = angle BAF, a = bsec 22, 7ab = wb’ sec 27 = area of ellipse, semi-axes @ and 3, z = FO, in this case less than 0. Since the rays reflected from C and D (fig. 7) fall upon the same point O, the circumference of the circle described by O in its revolution about the axis is illuminated by the light reflected from the two annuli described by C and D. Besides the point O is situated so near the axis, that the perpendicular distances of C and D from the axis may be considered as equal to one another. Thus, to find the concentration which results from the converging of the rays to the axis, we have, 2RI’ Qar:4cR:: 1’: intensity at distance r from F, (= = the intensities being estimated on planes perpendicular to the rays. Wherefore the intensity on the plane at F of the reflected light 2RI’ . 2kRI' cos 22 = lex z A es a aa ae which would give the intensity on the increment at Q (figs. 9 and 10), if the sun’s rays were perfectly parallel. But instead of this light being confined to the increment at Q, it is spread over an ellipse whose area = 7’ sec 27, and hence the intensity at O due to this increment es 2k RY cos 2% 7 adr dé im 2k RY cos? 22 7 ? x Fb? sec dt ox 02 r de ; and the same is true for a corresponding increment on the other side of the axis GH (figs. 9 and 10), -/] 2k RI’ cos 22 rdr dé OP Sy | DN Se ae 8 We vi ax 0? sec 22 4k RI’ cos? 27 e = Scare aia | kl drdé (7). 138 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. This, taken between the limits 7 = p, and r = 0; and 6 = z, and @ = 0, gives the total intensity 4k RI’ cos? 27 a xb? e dé. 2 } Now, from Equa. 3, p = zcos9 + a(1 — ~~ sin 26 ), 2 being less than b, ’ q b g i 2 3 = HRT cos! 26 f 4 (1 — Fesinta) + #0086 | a0. 0 ab? Expressed in terms of elliptic functions, “= ee [ « E, _ @) + z8ind | + C. Eee RI’ cos? 27 =i ak z (x) : ; : . (8). But by Art. 1, R cosec 22: ¢:: 6:4, (R cosec 27 being = FB, fig. 7), R cosee 27 = 2c a page! A nn 2esime27,.” and | a = bsec 20 = To55; ¢ Substituting in Equation 8, we get = 8ck I’ sin 27 cos 22 E, (s), z z _ 4ckT’ sin 47 Ee (n) . (9). An expression which may be put in the following form :—If a circle be described with Fas a centre (figs. 7,8, or 9) and 26 as a diameter, and an ellipse with O for one of its foci and the same diameter as a major axis; the circumference of the circle will be to the circumference of the ellipse as the intensity at the axis to the intensity at O. When z = 0, then Ez (7) = 7 6 _ 4ck T' sin 47 a and < r= 4c sia, : (10), which is the expression for the intensity at the axis, and shows that in the same conical mirror it is constant at every point in the axis ; whereas, in conical mirrors MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 139 of different inclinations, there are two which produce a maximum effect at the axis, viz., when 42 = 90° and 270° (in Equa. 10), that is, when BAF (fig. 7) = 674° or 224°. When z = 6 (Kqua. 9), E, (7) = 2, 6 and Use ee ——— (11). If% = 4, the maximum intensity at the axis expressed numerically is w= Achl sin 904. x 107, x FT S2147 . When & = 3 and 47 = 2° 36’, it can be shown by Equa. 10 that w = 101’ nearly, a heat sufficient to ignite wood and other combustibles. This can be effected at a distance of 130 feet with a segment of the reflector 18 inches broad, and having a mean diameter of 6 feet. , Case 2. When the point O is situated at a considerable distance from the axis, z being much greater than 0, the distances CO and DO will now differ perceptibly from one another and from FA = FB = » (fig. 7). Let R and R’ represent the distances of the points C and D respectively from the axis, then R = fC sin 27 = (v + 2 cot 22) sin 27, and CO= fc—fO=FA+F f— f0 = + acot 2d — zcosec 27 = 4 — ztan?. Similarly for the point D, R’ = (v — cot 22) sin 22 , and DO = v0 + ¢ tan 2. The ellipses of light which overspread O reflected from each increment of the space around C have for their minor and major axes respectively, b vy —ztan?d v —ztanz = Se 2 SSS 2c 2 2ccos2z ’ and the corresponding quantities with respect to the space around D are _v+aztanz a = Ub atant rh 2¢ : ~ Qecos2t © VOL X XV. PART I 2N b’ 140 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. It can be shown, as in Case 1, Equa. 7, that the concentration at O, due to the light reflected from the space around C, is , 2 a drdé, and taken between g, and g,, 2h RI’ cos? 27 = rb? ee ay ee 2) a8 , 2 4k Rl’acos Sere he — =, sin? do, ab because (fig. 10) a = FP = 2 c0s6+a(1— 5 sin’ 6)? , pe zc0sd—a(1— 5 _ aie 6)? , 21 —%=201-% a) saat G b . Taking the integral between the required limits sin 6 = ~, and 6 = 0 we obtain 4kRI’ 294 Tra ag ay AE oy tances ~ (A — H), denoting the difference between the asymptote and the infinite hyper- 3 bolic arc whose major axis is unity, and eccentricity 7 a finite quantity, though A and H are severally infinite. But, if the distance from the centre to the focus be equal to unity, the transverse axis is : and (A — H), = ; (A — H), which D expressed in complete elliptic functions of the second order gives Ee —s je ’ (A—P), = Ac Swe e being put for ° , the relation between the moduli ¢ and ¢,, being ale Onlta 10> ee: Fi ae and ¢’ and é,, denoting the corresponding quantities when 0’ is put for 0. Substituting in Equation 12, we get for the light reflected from the space around C, 4kRVa ae +b pe — E. = EE} 5 Fae MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 141 and similarly the light reflected from the space around D, _ 4kRTa a2 a | Be, — 7 Bef - Hence the total intensity at O is AkRIacos? 27 (2+b \ 4kR’Va' cos? 27 {ae Z— ) Se — 58 Pi ab? b’ E., Gare. and substituting for a, 0, a’, 0’, R, and R’ 4c(v+z cot 2)kI’sin4i { v + Qe—tanz)z 2cz \ = : . e — = Ez, r(v—z tan?) UL v—z tané 1 v—ztant eee ee 2cz | io a(v + ztanz) v+zetant “% v+z tant Hee Ge), the values of the moduli in terms of ¢, v, z, and 2 being i 2 ./2cz(v — 2 tant) _ v—ztant o! _ 2n/2c2(v +z tant). at v+ztanz mpeer@e—tani)z” ~~ .2ez 7.1 v+(2c+taniz * A AN Ree Since the value of w will not be altered by substituting for 7 and 2 any two quantities having the same ratio, it follows that the intensity of the reflected light is uniform along the line which joins A and O (fig. 7). ARTICLE 9.—Corollary. The value of 4, the fraction which expresses the relation between the intensities of the reflected and incident rays, may be found by means of a conical reflector, thus :— Let R = distance from the axis of a small zone described by AB (fig. 11). r = distance from the axis at which the reflected light or heat becomes, by convergence to its axis, equal in intensity to the incident. Then PB, Ase eleue, Up , We al ==. 4 amd ie = R: This result, calculated on the assumption that all the rays emanating from the sun are parallel, will not deviate perceptibly from the truth, except when r is small compared with R. The value of & may also be found by using the combination of m plane mirrors. By Article 3, Equation 2, intensity _ nkI'e? cost Se 142 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. but if the direct rays of the sun fall on the same plane with the light reflected by the combination, the intensity will be re 2 nkI ae ae. Bringing the combination nearer the plane on which the light is thrown, the intensity of the » mirrors can be made equal to the above equation by diminishing the value of r. Hence pls Bd = ad Bi ay 7 72 Cas ne (v2 — r?) cost ° As these results are independent of the absolute value of I’, the equality of temperature may be detected by a Fahrenheit thermometer, or any more delicate means of indicating equal temperature. When £ is accurately known, this combination, or the conical reflector, may obviously be used to ascertain the intensity of the solar beams at different hours of the day and different periods of the year, and will thereby furnish data for estimating accurately the heat or light absorbed by the atmosphere. The light lost by the solar rays in penetrating the atmosphere being known, the intensity of the radiation at different parts of the solar disc may be found by (Article 6, Equation 6), if a zone or segment of a parabolic reflector can be constructed having a focal length of 70 or 80 feet. ArticLeE 10.—Prop. When two Conical Mirrors have a common Axis, their Surfaces being either perpendicular or parallel, if the rays incident on the exterior Reflector parallel to the Axis meet after rejlection the interior one, they will be again reflected parallel to the Axis in a beam of increased intensity. Let AB (figs. 12 and 13) be the common axis of two conical reflectors described by the revolution of the lines MN and CD about the axis AB, CD being either perpendicular or parallel to MN. When AB (fig. 12) is directed to the centre of the sun, the rays which fall on the surface described by MN will make with it the angle SKN = MKH = KHD = FHC = DCB, because DCB = SKN, therefore FH is parallel to AB (Euclid, 1-27). The intensity of the finally reflected beam at H is to that incident at K as the perpen- dicular distance of K from AB is to the perpendicular distance of H from MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 143 AB. Since every cylindrical annulus of rays incident on the exterior mirror forms after reflection from the interior a cylindrical annulus of equal thickness, the intensities must be inversely as the mean radii, the loss from reflection being neglected, or, if taken into account, equal to 4° times the preceding intensity nearly. ArticLE 11.—The preceding annulus of rays may be thrown upon a circular area whose. diameter is equal to the breadth of the zone, which forms a section of the annulus. To effect this, we have only so to increase the angle DCB, that the rays may meet the axis at the required distance, as shown in fig. 14. In like manner, the parallel rays, from any extent of reflecting surface may be thrown upon the area whose section is F/ (fig. 15) by constructing one or both of the conical mirrors of frustums having the required extent of curved surface and the requisite inclination, the same axis being common to all. But when the breadths of the annuli are small compared with the distance of the focus F/ from the reflectors, the diameter of the circular area mentioned must be increased by the diameter of the sun’s image for that distance. Cor. When the number of lines CD, DE, EG, &c. (fig. 15), is indefinitely increased, their lengths being diminished, CDEG becomes part of a parabola. ArticiE 12.—Prop. If two Parabolic Reflectors have a common Focus, the Solar Rays which are made to converge by reflection from the eaterior Mirror will again form a beam of parallel Rays by reflection from the surface of the interior one. Let MKN and DHC (fig. 16) be sections of two confocal parabolic reflectors of which AB is the axis of the exterior and CE that of the interior, / being their common focus. When AB is directed to a point in the sun’s disc, the rays which fall on the exterior mirror parallel to the axis AB, in converging to f, will meet the surface of the interior mirror, and be reflected parallel to its axis fCE, as indicated by the course of the rays SKHF. Thus the solar beam of light which falls on the exterior and larger mirror is again reflected into a beam of parallel rays, and the intensity of the final beam will be greater than that of the incident, as explained in the preceding article. Moreover, since the axis fE of the interior mirror may make any angle with AB the axis of the exterior, the final beam may be thrown in any direction. VOL. XXV. PART I. 20 144 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. ArticLe 13.—Prop. The Rays which converge to the focus of the exterior Parabolic Mirror may be thrown by a second reflection on a given circular space, by constructing the interior reflector in the following manner :— Let DH and H’D (fig. 17) be parts of parabolas, whose common focus is /, their axes being respectively /U parallel to RG, and fC’ to QG. By causing these to revolve about the line fA, a surface will be described, such that the rays converging to f and falling on DH, will be reflected parallel to /C, and fall on the plane FF’. In like manner, the rays converging to fand falling on H’D, will be reflected parallel to fC’, and will intersect the axis of revolution at G, and fall upon the plane FF’. If this surface be substituted for the inner reflector DHC (fig. 16), the rays reflected from the outer mirror whose axis is directed to the sun, when con- verging to 7, will meet the inner reflector described by H’QDH, and be reflected (as indicated in fig. 17) so as to intersect its axis of revolution at G, and fall upon the plane FF’. And this is true, whatever angle fG makes with the axis of the exterior reflector. Cor. When the number of parts in H’QDRH are indefinitely increased, and their lengths diminished, it evidently becomes the are of a hyperbola whose foci are f and G. ARTICLE 14. The convergence of the solar rays upon a given area can also be effected by combining a number of exterior reflectors, each with its correspond- ing interior, as indicated in fig. 16, the axes of all the exterior parabolic reflectors being directed to the centre of the sun’s disc, while the axes of the interior are directed to the centre of the given spot, on which the light has to be cast. Neither is it necessary that the respective reflectors should be complete symme- trical paraboloids: the exterior may consist of a series of large plates, each form- ing a part of a paraboloid of revolution, witha corresponding plate cut from a less paraboloid for its inner reflector. If the axes of all the exterior plates be in the same straight line, such a combination may have a common focus, each interior having that diameter of its generating parabola, which passes through the centre of the plate directed to the spot on which the light is required to fall. The practicability of such a combination is evident, from fig. 16, where K may be viewed as the centre of one of the exterior plates, and H that of its correspond- ing interior, having the diameter of its generating parabola, which passes through H, directed to the plane on which the light is concentrated. The exterior plates may be joined together to move as one piece, and in like manner the interior. This combination is capable of casting the finally reflected beam in a direction MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 145 making any angle with the axis of the exterior plates; and by a readjustment of the inner plates, the distance at which the rays finally meet may be varied at pleasure. ARTICLE 15. It is stated that the Archimedean burning mirror was hexagonal. Let us consider if the combinations we have been illustrating can be made to conform to that figure. The term hexagonal may have reference either to the appearance of the mirror as a whole, or to the form of each individual reflector. Figs. 14 and 15 will correspond to the former; for if the external and internal conical frustums be each divided into six equal segments, with sufficient space between the segments to admit of free motion, the combination, viewed at a dis- tance, will resemble a hexagonal polygon. Assuming the other meaning to be the correct one, we have only to suppose the form of the parabolic plates, which constitute the exterior and interior reflectors previously explained, to be hexagonal. From this would result two advantages:—they could be so formed that the different six-sided figures would unite together without leaving any interval, and the section of the beam cast by each on the required spot, approximating to a circle, would approach more nearly to the maximum effect with a given section of solar light. ArticLe 16.—Prop. As the Hxpansion of the Sun’s image is in proportion to the distance Jrom the Point of Reflection, no greater accuracy is required for the construction of curved surfaces, capable of producing Combustion at distances of 150, 200, and 300 feet, than for those of a focal length of only a few inches. The expansion being about 1 foot in diameter for every 108 feet of focal distance, it follows that a reflector is sufficiently accurate for a burning glass, if it can concentrate the rays which fall on each part of its surface from the centre of the sun’s disc, within a circular area, whose diameter is the same multiple or part of 1 foot which its focal length is of 108 feet. The same principle may be exhibited in another and more definite form. Burn- ing-glasses, which produce at the focus an intensity equal to parabolic ones, may be constructed of plane reflectors arranged as tangent planes to a paraboloid of revolution. kV6A area of circle DE ( Since the increment of intensity is Art. 1, Kqua.6, fig. 1), if we take a portion of the surface of the paraboloid subtending an angle at the focus not greater than the sun’s disc, the denominator of the foregoing frac- tion may be considered constant; and the intensity at the focus reflected from such an extent will be kl’ area of circle DE area of circle DE a 146 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. But a plane mirror which is a tangent to the paraboloid at the same spot, and of just sufficient area to reflect the circular beam of light whose section is equal to the circle DE, will also produce at the focus an intensity equal to AI’ (Art. 2, Equa. 5); that is, the concentration at the focus is the same, whether a circular beam of the section mentioned be reflected from the surface of. the paraboloid or from its tangent plane; and the same will evidently apply to any polygonal beam capable of being inscribed in the circular. Hence a burning mirror, scarcely inferior in its effects to a parabolic one, may be formed of plane hexagonal reflectors, their sizes, of course, depending on the distance of the focus. For example, as the sun’s image overspreads an area of 1 inch in diameter at a distance of 9 feet, a burning mirror of that focal length may be formed of plane hexagonal pieces, each side about half an inch; whereas at 108 feet distance, the sides of the plane hexagonal plates need not be less than half a foot, and so on in proportion. Plates of the latter size being greater than those with which Burron performed his experiments, we infer that his combination, at distances exceeding 100 feet, would be little inferior in power to a parabolic segment of equal focal length, and capable of reflecting exactly the same sectional area of the solar beams. Again, what has been proved true of plane mirrors, tangents to a paraboloid of revolution, must be equally true of a series of tangential circumscribing conical frustums. In all these cases, however, it is probable that the advantage in practice will remain with the parabolic figure, from the light at its focus having a greater area of maximum intensity. From these results, as well as from independent calculations, we con-_ clude that refracting burning-glasses may be constructed, by placing at some distance from an axis a series of acute-angled conical zones, or wedge-shaped pieces of glass (fig. 18), built up like the compound lens of Brewster, which will produce combustion at as great distances as Burron’s combination of reflectors. ARTICLE 17. That the practibility of the Archimedean mirror may be made still more apparent, we shall now apply Equations 1 and 2, Article 3, to find the numerical intensity of the light in the focus of Burron’s combination. This was attempted by PEyrarp, but his conclusions are vitiated by the false premises from which he set out. He assumed that the intensity is uniform at every part of the luminous image reflected by a plane mirror,—a supposition proved incorrect by Art. 2. In our calculation we shall suppose that each of Burron’s mirrors, which were 8 inches by 6, produced an effect equivalent to a circular beam of 6 inches diameter, when it leaves the mirror. Taking 4 = 4, and cos7 = 1, we obtain by substitution, in the equations of Art. 3, the following results :— MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 147 40 x 3 x 62 On 23d March, heat produced by 40 glasses at 66 ft. French = (S) = taro 9 Do. do. 98 fhe tt. =. oi 3d April, 4 p.m, do. 112 Ay, bao! Ete = ool 1 10th April, after 12 noon, do. 128 ee lO tts == 8:29 1 10th April, 2°30 p.m., do. 148 Ft LOOT, = 9-95.) 11th April, 2°30 p.m., do. 21 “ 20 ft.=21 x 3 ’=10°5 I'(by Art.3, Hq.1) Do. 2:30PM, do. 12 3 20 tt. = 12) x tr Sam: In the first experiment, on the 23d March at noon, tarred beech was ignited with the 40 glasses; but the mirror not being mounted on a stand, acted at a dis- advantage. On the same day, when 98 glasses ignited a plank smeared with tar and brimstone, the mirror is said to have been still more disadvantageously placed. The experiment on the 3d April was at 4 o’clock P.m., with the mirror mounted, and placed on its stand. The sun being weak, a slight inflammation was produced on a plank covered with threads of wool. On the 10th April, with a clear sun, the 128 glasses very suddenly kindled a plank of tarred fir. At half-past 2 o’clock on the same day, the combination of 148 glasses was tried on a plank of beech tarred in part, and covered in some places with shreads of wool. The inflammation, which was very sudden, com- menced on those parts of the wood which were uncovered. Beech previously charred was the material ignited with 21 glasses, and little combustible materials were the substances set on fire by 12 glasses, on the 11th April. An inspection of the results in the preceding table shows that if /= 4 be correct, wood done over in the manner mentioned can be ignited by a heat varying from eight to nine times that of the direct mid-day rays of the sun at Paris in April, and finely divided combustible substances by a heat consider-— ably less, as proved by the experiment with 12 mirrors. But if we assume k = 2,which is probably nearer the truth, the heat required to produce the same effect will vary between ten and eleven times the sun’s mid-day heat. If the number in the right-hand column of the preceding table be multiplied by 5 it gives the minimum number of plane mirrors capable in each case of producing ignition—that is, the number of mirrors which come under Equa. 1, Art. 3. Supposing 4 = 4, we find the numbers, for the first five experiments adduced, to be respectively 26:6, 18, 16:58, 17:14, and 19:18. The sizes of these mirrors will, of course, depend on the distance of the focus, and the angle at which they receive the incident light. When the distance is about 108 feet, each of them should have an extent sufficient to reflect a beam of solar light, not less than one foot in diameter, and their dimensions vary in the same ratio for other focal lengths. As these minimum combinations have been calculated on the assumption VOL. XXV. PART I. 2P 148 MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. that the centre of the luminous circle reflected by each of the mirrors can be directed with precision to a given point, which in practice is not attainable, their number, or the size of each, must be somewhat increased, to compensate for defective adjustment. After making such an allowance, it will appear that at distances not exceeding 150 feet, between 16 and 20 plane mirrors, each 25 by 14 feet, may be substituted for the numerous combinations of Burron, the adjust- ment of which required so much time and trouble. What has been shown respecting the power of the solar rays to produce com- bustion after one reflection, can easily be extended to the case in which the light undergoes two reflections, the intensity of the final beam being then reduced to about one-fourth that of the direct solar rays. To compensate for this diminu- tion, the exterior reflectors must have about twice the area of Burron’s com- bination. Taking, for example, the 128 plane mirrors which kindled combustibles at 150 feet, the reflecting surface of the combination ‘is paren. = 422 square feet, and the sectional area of solar light, which we supposed it to reflect, was A x 6? x 128 + 144 = 25 square feet nearly. It seems then, that about 80 feet of reflecting surface, or an extent capable of reflecting 50 square feet of solar light, will be more than sufficient to inflame such a material as tarred wood, &c., at the distance of 150 feet, after having undergone two reflections,—an extent of surface not too great to be united in one compound mirror, constructed in the manner explained in the foregoing articles. Considering the scepticism which has prevailed respecting the Archimedean achievement in the most favourable circumstances, we are the less surprised to find that some recent authors, in quoting the passage from TzeTzEs, omit the statement which refers to the burning of the Roman ships in winter. Instead of ignoring these winter attacks, let us examine them in the light which Burron’s experiments supply. That performed with 112 mirrors, at the distance of 138 feet, was at 4 o’clock on the afternoon of the 3d April, at which time the altitude of the sun in the sky of Paris would nearly correspond to his meridian altitude at mid-winter in the more southern latitude of Syracuse; and as the difference between the meridian altitude of the sun at the summer and winter solstice amounts to above 46°, it must be admitted that this additional fact corroborates in a striking manner the evidence already adduced. Having now shown how compound burning mirrors can be constructed corre- sponding in every respect to the description which TzEeTzzs gives of the one invented by ARcHIMEDES, and that every statement in the passage is in accord- ance with well-established facts, we conclude that his narrative is no fiction, but, on the contrary, a true account of a real mirror, capable of producing all the effects ascribed to it. While this ancient discovery can be tried, after the lapse MR JOHN SCOTT ON THE BURNING MIRRORS OF ARCHIMEDES. 149 of two thousand years, by the light of modern science, and pass with credit through the ordeal, the pretended discoveries of comparatively modern times, when subjected to the same test, fall to pieces. An instance may be given without digressing from the subject of our paper. THomas DicGes, who republished in 1591 a work by his father, LEonHarp Diecss, entitled ‘“‘Pantometria,” would make us believe, in the preface to this edition, that he had seen his father at sundry times fire gunpowder and discharge ordnance at a distance of half-a-mile or more, by means of the sun’s beams. Had he been aware that to accomplish such a feat would require at least four thousand square feet of reflecting surface, we may venture to affirm that he would not have overstepped so far the Archimedean range. We may observe, in conclusion, that the experiments of Burron, taken in connection with the preceding deductions, are calculated to produce a strong conviction that, in clear and comparatively warm climates, the sun’s rays may be made, at a small expense, to supersede in some respects the fires employed in culinary operations. Further, when it is considered with what ease a combina- tion of plane mirrors, or a series of conical reflecting zones, can be constructed, capable of producing a heat exceeding that of the most intense furnace (Art. 16), we infer that the solar beams may also be turned to account by the chemist and metallurgist. For these purposes, one reflection only is required, as the reflected light can be made to fall always on the same spot, by directing the axis of the reflector to the centre of the sun’s disc, and causing it to follow the sun’s motion in the heavens, by revolving round a fixed axis parallel to that of the earth. (ine) \ V.—On the Connection between Chemical Constitution and Physiological Action. Part. lL—On the Physiological Action of the Salts of the Ammonium Bases, derived from Strychnia, Brucia, Thebaia, Codeia, Morphia, and Nicotia. By Dr A. Crum Brown and Dr Tuomas R. FRasEr. (Read 6th January 1868, under the title ‘‘ On the Changes produced by direct Chemical Addition on the Physiological Action of certain Poisons.”) There can be no reasonable doubt that a relation exists between the physiolo- gical action of a substance and its chemical composition and constitution, under- standing by the latter term the mutual relations of the atoms in the substance. There are numerous indications of such a relation, and attempts have been made to express it formally in certain cases. Thus it has been long observed, that the salts of the same base have a common physiological action, and it has been pointed out by Mr Biake* that, with some exceptions, the salts of isomorphous bases havea similar action. A corresponding likeness in physiological action may be traced in salts having the same acid, but beyond these generalisations we are not aware that any approach has been made to the statement of a law con- necting the physiological action of a substance with its chemical constitution. Some observers have endeavoured to connect physiological action with com- position, looking for the cause of the peculiar action of substances in the presence or proportion of particular elements. It is a sufficient answer to this to point to isomeric or polymeric bodies—bodies having identically the same composition— which differ totally in action, such as acetic acid (C,H,O,), and sugar (C,H,,0,); glycocoll (C,H,NO,), and nitrite of ethyl (C,H,NO,); or to instance kakodylic acid, which is inert, although perfectly soluble, and containing more than 54 per cent. of metallic arsenic. . Examples such as these clearly show that composition alone is guite insuf- ficient to explain physiological action, and that constitution must also be taken into account in every attempt to connect the chemistry of substances with their action on the animal body. The most direct way of making such an attempt would obviously be to com- pare physiological action and chemical constitution in a sufficiently large number of cases, and by classifying the results to deduce a law; but, unfortunately, the data which we possess are quite insufficient for this. We know, indeed, the “structure” of a considerable number of substances; that is, we know the order . Proceedings of the Royal Society of London, vol. iv. Jan, 28, 1841, p. 285. VOL. XXV. PART I. 2Q 152. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN in which the atoms of these substances are related to each other, but something more than this is implied in the term constitution, as we have used it above. For this involves not only the “structure,” or the arrangement of the equivalents in atoms and in mutually united pairs, but also what we may call the potential of each pair of united equivalents.* For instance, the structural formula of formic acid is ©-O-9 ©) @) which indicates—1lst, That the four carbon equivalents form one atom, the four oxygen equivalents two atoms, and the two hydrogen equivalents two atoms; 2d, that these equivalents are united in pairs, thus—co, co, co, ch, ho, but it does not in any way indicate (and we do not know) what is the potential of each of these pairs—that is, how much energy would be required to separate the equiva- lents from each other. We know that this potential depends upon the structure, and we can to a certain extent trace the nature of this dependence, but we cannot as yet express the potential numerically, or give a rule for finding its value from the structure, and till we can do this we do not fully know the constitution. But even the structure of the majority of substances is not at all, or only very imperfectly known, and this is especially the case with those whose physiological action has been most fully investigated, such as the natural alkaloids. Seeing, then, that we could not follow the direct road of induction, it occurred to us that a by-path might be found, by making use of a method resembling in its main features a mathematical calculus of jinite variations. This method con- sists in performing upon a substance a chemical operation which shall introduce a known change into its constitution, and then examining and comparing the physiological action of the substance before and after the change. We may express this in mathematical language thus:—Let C represent the constitution of the original substance and @ its physiological action. After the operation, C becomes C + AC and ©, @ + A®. Here AC, o, and @ + A® are known, and by applying the method to a sufficient number of substances, and by varying AC, we might hope to determine what function ® is of C. The only reason why this method is not a strictly mathematical one is, that we cannot express our known terms AC, @, and @ + A® with sufficient definiteness to make them the subjects of calculation. But although, on this account, we cannot obtain an accurate mathematical definition of fin the equation @ = fC, we may be able, in an approxi- mate manner, to discover the nature of the relation. In applying this method, we must select a chemical operation which satisfies * More correctly, ‘“ the exhaustion of the potential energy” of each pair of united equivalents. See THomson and Tait’s Treatise in Natural Philosophy, § 547. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 133° the following conditions :—1s¢, That it is unambiguous; that is, that the change of structure produced by it is susceptible of only one interpretation. 2d, That the change of sérwctwre produced by the operation is, in all cases investigated, the same, and the change of constitution (AC)—that is, the change of structure and potential—as nearly as possible the same. 3d, That the operation is completely under our control, so that it cannot be either performed or reversed spontaneously, in ordinary circumstances, within the animal body. 4th, That the substance is equally suitable for absorption into the system before and after the change (that is, that @ and @ + A@ are observed under similar conditions); and 5th, That a decided change of physiological action is, in some cases at least, produced (that is, that A® is not always = 0). Chemical operations may be divided into two classes—ls?, operations of sub- stitution; and 2d, operations of addition or subtraction. In the first, an atom or group of atoms is replaced by an equivalent atom or group of atoms, without any change taking place in the active atomicity of any atom or radical in the substance. In the case of addition (and by subtraction we mean to express merely the - Inverse operation to addition), the active atomicity of one or more atoms or radicals in the compound is increased, and the bonds thus set free, or rendered active, are saturated by atoms or radicals (the sum of whose active atomicity is of course an even number), which are thus added to the substance. We shall apply the name condensation to capability of being added to in whatever way the addition takes place, and distinguish two kinds of condensation, zntra-atomic and inter-atomic; in the first of which it is an atom, and in the second a compound radical, the active atomicity of which is increased. Thus, carbonic oxide, sulphide of methyl, and protochloride of tin, are examples of intra-atomic condensation; olefiant gas, the dibasic anhydrous acids, and allylic alcohol, of zuter-atomic con- densation ; while hydrocyanic acid (if we assume for it the formula @-@)=@ ) shows both. Many operations of addition and also of substitution satisfy the Ist, 2d. 3d, and 4th of the five conditions mentioned above; but when we examine them in reference to the 5th condition, we find a marked difference. Operations of substitution (satisfying the lst, 2d, 3d, and 4th conditions) do not appear greatly to change the physiological activity of a substance, except, Ist, where the activity depends on direct local action; or 2d, where the operation removes or introduces an atom or radical, the compounds of which are as arule active. As examples of the first exception, we may take sulphuric acid (H,SO,) and caustic soda (HNaO), both poisonous; while sulphate of soda (Na,SO,) and water (H,O) are not: as examples of the second, acetate of lead and cyanide of sodium, both poisonous, acetate of potash and chloride of sodium not. Besides the exceptions which can be reduced to the two classes just mentioned, there are several isolated °154 pRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN cases of change of activity produced by replacement, such as the singular inert- ness of ferrocyanide of potassium and of the analogous double cyanides, as com- pared with the activity of cyanide of potassium and its analogues. On the other hand, operations of addition, particularly where the condensation diminished by the addition is intra-atomic, seem, in many cases, to produce very decided change both in the kind and in the degree of the physiological activity of the substance acted on. The following examples will illustrate this statement. Some are cases of direct and some of indirect addition, and in all of them the change of structure produced is known, and there is in none of them much risk of fallacy arising from the change taking place spontaneously in the animal system. The first column contains the names and formule of the substances before addition, the second the atoms or groups added, and the third the names and formulee of the substances produced. I, if Tis. Carbonic oxide, CO O Carbonic acid, CO, Hydrocyanic acid, HCN 2H, + HCl Hydrochlorate of methylamine, CNH,CI. Arsenious acid, As,O,, [HAsO,] (CH,), Kakodylic acid, AsC,H,0, * Strychnia, C,,H,,N,O, (CH, (HO)) Methyl-strychnia (hydrate), C,,H,,N,O, ft Brucia, C,,H,,N,O, (CH, (HO) ) Methyl-brucia (hydrate), C,,H,,N,O; ¢ It will be observed that all the substances in the first column are highly poisonous, while those in the third column are either quite inert, or possess an action entirely different in kind from that of the bodies from which they are derived, and very much less in degree. A consideration of the hitherto isolated facts collected in the above table leads not unnaturally to a suspicion that condensation (and in particular zntra- atomic condensation) is in some way connected with physiological activity, as the first is, and the second appears to be, diminished or removed by chemical addi- tion. This suspicion is strengthened when we observe that in a very large pro- portion of the cases as yet investigated saturated bodies (that is, bodies whose condensation is 0) are inert, or nearly so. Kakodylic acid, as already mentioned, is a remarkable example of this, and the salts of tetrethyl-arsonium § seem to be equally inert. Similarly, the salts of tetramethyl-stibonium || are not emetic. So that, as far as experiment goes, it | would seem that the stable compounds of pentatomic arsenic and antimony have avery different and much less strongly marked action than the compounds in which these elements are contained as triads, or than those (such as arsenic acid) * Bunsen, Annalen der Chemie and Pharmacie, vol. xlvi. p. 10 (1848). { Sranutscumipr, Poggendorff’s Annalen, vol. eviil. p. 523 (1859). ¢ Ibid. p. 541. § Lanpott, Annalen der Chemie und Pharmacie, vol. Ixxxix. p. 331 (1854). || Ibid. vol. Ixxxiv. p. 49 (1852). CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 155- in which, although present as pentads, they are easily reduced by subtraction to the state of triads. In reference to this, we cannot avoid referring to a very remarkable passage in BuNsEN’s admirable paper on kakodylic acid. After describing the experi- ments by which he proved the inert character of this acid, he says, ‘* Gehen wir auf den Grund dieser unerwarteten Erscheinung zuriick, so bietet sich dafiir nur in der Annahme eine Erklirung dar, dass die Verbindungsweise des Arseniks im Kakody] eine andere ist, als in seinen unorganischen Verbindungen. Indem es darin aufgehort hat, fiir sich einen Angriffspunkt der Verwandtschaft zu bilden, hat es zugleich seine Reaction auf den Organismus verloren.”’ (Annalen, vol. xlvi. 1843, p. 11.) While it is plain that Bunsen does not here refer to the different degree of saturation of the arsenic in arsenious and kakodylic acids, both because the whole theory of saturation is of a much later date, and because he makes no distinction between the mode of combination of the arsenic in those compounds in which kakodyl is monad and arsenic triad, and those in which kakodyl is triad and arsenic pentad, he points out in an exceedingly clear manner the striking coincidence of peculiar chemical constitution and peculiar physiological action in the case of kakodylic acid. While, however, the cases mentioned incline us to believe that physiological activity is related to condensation, the occurrence of saturated substances, such as alcohol, corrosive sublimate, and oxalic acid, having a well marked poisonous action, and of condensed substances, such as benzoic acid and salicine, which are comparatively inert, shows that condensation is not the only condition of physiological activity. There can, at the same time, be little doubt that if the effect of condensation were discovered and eliminated, the other conditions might be much more hopefully sought for. Under these circumstances, we turned our attention, in the first place, to the effect of chemical addition in altering the physiological action of the natural alkaloids. Wewere led to do so, partly by a consideration of the ease with which, by means of iodide of methyl, the nitrogen of nitrile bases can be rendered stably pentatomic, and partly by the hope, grounded on the obser- vations of STAHLSCHMIDT in reference to the salts methyl-strychnium and methyl-brucium, that we should obtain marked changes of physiological action. The great majority of natural alkaloids belong to the class of nztrile bases, that is, they contain one or more atoms of triatomic nitrogen directly united to carbon by three bonds. This nitrogen atom (or, in the case of poly-acid bases, atoms) can become pentatomic, as in the formation of salts; thus in the forma- tion of hydrochlorate of morphia the nitrogen takes up H and Cl, thus becom- ing pentatomic, united by three bonds to carbon, by one to hydrogen, and by one to chlorine. But by this change it is not rendered permanently or stably VOL. XXV. PART I. 2k 156 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN pentatomic; it easily loses the hydrogen and chlorine it has acquired, and returns to the triatomic state. The action of allalies, or, in many cases, even of alka- line carbonates, is sufficient to effect this, and reprecipitate the alkaloid. It is obvious, therefore, that the chemical addition of an acid does not satisfy the third condition mentioned above, for it is certain that the addition can be per- formed in the stomach, which is acid, and very probable that it may be reversed in the blood and other alkaline fluids of the body. But if, instead of an acid, we make use of such a substance as iodide of methyl, we find that while the triatomic nitrogen takes up CH, and I, and becomes pentatomic (just as in the former case it took up H and Cl), it does not lose these newly-acquired atoms when the substance is treated with alkalies, but remains pentatomic even when subjected to attacks more violent than any to which it can be exposed in the animal system. ‘This operation, the addition of iodide of methyl to nitrile bases, satisfies the first condition, for we know precisely what change of structure is produced. It satisfies the second, for the change of structure is the same in all nitrile bases; and the change of potential, as far as can be judged from a very rough estimate of the heat produced by the change, and from the general character of the substances produced, is not very different in different cases. It satisfies the third, as we have seen above; and as the iodides of the compound ammoniums thus formed from the alkaloids are all tolerably soluble in warm water, and can easily be transformed into other salts very readily soluble, it satisfies the fourth condition; and the observations of SranHLscumipT show, and the sequel of this paper will further prove, that it satisfies the fifth. It deserves to be noted that this operation. only removes the condensation of the typical nitrogen (that is, of one atom of nitrogen for each molecule of a mono-basic acid that the alkaloid can saturate), and leaves any other condensa- tion which may exist in the substance unaffected; so that even if physiological action should depend upon condensation, it would be unreasonable to expect @ + 4@ to be in all cases zero, that is, that the new bodies should be quite inert. In the present paper we communicate the results of the application of the method described to strychnia, brucia, thebaia, codeia, morphia, and nicotia. In each case we shall first describe the action of the alkaloid itself. then give the method of preparing the derived substances, and describe their physical char- acters, and, with some detail, their physiological action. Our investigation of the physiological action of these substances has been chiefly directed to the deter- mination of their poisonous activity, and of the most prominent differences between the nature of their action and that of the alkaloids from which they are derived. . CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 157 STRYCHNIA. It is well known that strychnia acts on the living economy in a distinctly defined and characteristic manner, and that it is one of the most active of poisons. When administered subcutaneously, doses varying from one-twentieth to one- fiftieth of a grain rapidly produce in rabbits the most violent tetanic convulsions, and in a few minutes kill the animal. Few poisons have been more carefully studied, and it is now almost undoubtedly established that the phenomena pro- duced by strychnia are due to a localisation of its action on the spinal cord. Iodide of methyl-strychnium.—Strychnia (C,,H,,N,0,) is a mono-acid nitrile base, that is, it contains one atom of nitrogen united by three bonds to carbon ; the structure of the radical or radicals (C,,H,,NO,)” is unknown. How first demonstrated that strychnia is a nitrile base by subjecting it to the action of iodide of ethyl, and described, in a paper read before this Society,* the ethyl- strychnium and amyl-strychnium compounds. STAHLScHMIDT subsequently pre- pared and described the compounds of methyl-strychnium.; We prepared the iodide of methyl-strychnium by STaHLscHmipT’s method. Strychnia, in fine powder, was treated, in a flask, with excess of pure iodide of methyl;{ the flask was allowed to stand in the cold for some hours, then heated in the water- bath, the excess of iodide of methyl distilled off, and the iodide of methyl- strychnium dissolved in boiling water, filtered, and recrystallised. Iodide of methyl-strychnium (C,,H,,N,0,CH,I) crystallises in brilliant white scales, tastes distinctly bitter, though not so strongly or persistently so as strychnia, and when treated with strong sulphuric acid and peroxide of man- ganese, or bichromate of potash, it gives the colour reaction of strychnia, some- what obscured by the presence of free iodine. It dissolves in 133 parts of water at 37° C., and in 385 parts of water at 9° C. SrautscHmMipT has published a statement to the effect that the methyl- strychnium compounds are inert. As the sequel will show, we do not confirm this assertion ; but it is proper to admit that our investigation arose principally from it. . We first examined the effects of this substance by subcutaneous administra- tion. For this purpose, it was reduced to the form of very fine powder, suspended and dissolved in warm distilled water, and injected into a previously formed * Transactions, vol. xxi, p. 32 (1854). } Pocernporrr’s Annalen, vol. cviii. p. 513 (1859). t As iodide of methyl prepared directly from pyroxylic spirit is apt to become acid, it is advisable, if such impure iodide of methyl be used, to add a small quantity of an alkali (such as carbonate of potash), in order to prevent any of the strychnia being converted into a salt, and thus remaining unacted on by the iodide of methyl. 158 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN cavity in the subcutaneous cellular tissue. In this way, bya series of pro- gressively increasing doses, it was found that as much as twelve grains could be given to a rabbit, weighing three pounds and four ounces, without any effect what- ever. Fifteen grains, however, produced serious symptoms, though followed by recovery, and death was caused by the exhibition of twenty grains. Short abstracts of the majority of the experiments will be found in the table at the end of this paper; we shall, however, give some details of several experiments, in order to illustrate the mode of action. ExPERIMENT VIJ.—Two very small incisions were made through the skin, one in either flank, of a rabbit, weighing three pounds and eight ounces; and by in- serting an aneurism needle into these incisions, two cavities were formed in the cellular tissue. Into each of these we injected seven and a-half grains of iodide of methyl-strychnium (in all fifteen grains), suspended and dissolved in warm distilled water. No effect was caused until forty-five minutes, when the rabbit moved about uneasily, the limbs gradually yielded, and it soon lay on its chin and abdomen. When placed on the side, it remained quiet, without any efforts to recover anormal posture. Irritation did not cause any spasm nor give the slightest evidence of any increase in the reflex excitability. In one hour, when lifted by the ears, it hung in a perfectly flaccid and unresisting condition; the respirations were sixty-four per minute; and there were no voluntary move- ments. In one hour and thirteen minutes, a few spontaneous movements occurred in the limbs, but these, apparently, were merely feeble efforts to change its position. The external temperature appeared to be somewhat elevated, and the respirations were sixty-five per minute. In an hour and twenty-two minutes, a few twitches of the body, and especially of the abdominal muscles, occurred during the respiratory movements, which were now at the rate of sixty-six per minute; the eyelids did not contract when the conjunctiva or cornea was touched: but the animal was still conscious. In two hours, the condition was nearly the same as at last note, except that faint twitches of the eyelids could be excited by gentle irritation of their edges. In two hours and fifteen minutes, a number of very feeble spasmodic-like movements of the limbs occurred along with the twitches of the body, and these could also be excited by irritation. In two hours and thirty-five minutes, the condition of the rabbit had greatly improved. Efforts to rise were frequently made, in the intervals between which it lay perfectly quiet and flaccid, and the sensibility of the conjunctiva and cornea appeared to be normal. The observations were now stopped until the following morning, when the rabbit was found jumping actively about, and apparently in a perfectly normal — condition. ExprerIMent VIII.—We injected ten grains of iodide of methyl-strychnium, suspended and dissolved in warm distilled water, into each of two subcutaneous CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 159 cavities (twenty grains in all) of a rabbit, weighing three pounds and two and a-half ounces. Fifty minutes afterwards, the animal was lying flaccid, and ex- hibited the continuance of life only by slow and laboured respiratory movements. In one hour, tremulous movements of the body and limbs accompanied the respirations; and it was extremely difficult to excite even a feeble reflex move- ment by pretty strong stimulation. In one hour and ten minutes, the rabbit was dead. The autopsy was immediately made: the heart was contracting with regularity and considerable force, at the rate of 160 beats per minute; the intestinal peristalsis seemed normal; galvanic stimulation of the exposed muscles caused energetic contractions, and continued to do so until more than thirty minutes after death; and similar stimulation of the exposed sciatic nerves caused contractions of the posterior extremities at four minutes after death, but ceased to do so in other five minutes. These experiments are sufficient to illustrate the physiological effects that are produced when iodide of methyl-strychnium is administered to rabbits by sub- cutaneous injection. We have made similar experiments, with exactly analogous results, on dogs and cats, the more important details of which are mentioned in the table at the end of this paper. The effects of internal administration were examined by passing a gum-elastic catheter down the cesophagus of a rabbit, and so injecting iodide of methyl-strych- nium, suspended and dissolved in warm distilled water. It is unnecessary to give any description of these experiments, at this place, as no effect was produced by this method of exhibition, although as much as thirty grains was given at one _ time, and it was inconvenient, as well as unnecessary, to give larger doses. It is well known that to produce symptoms with a poison in a rabbit, a much larger quantity is required when it is administered by the stomach than when it is injected subcutaneously. The contrast between the action of iodide of methyl- strychnium and strychnia itself was, however, well shown in the rabbit to which thirty grains of the former had been given without any effect; for one-tenth of a grain of strychnia, also administered by the stomach, quickly produced violent tetanic convulsions, and, in a few minutes, killed the animal. As iodide of methyl-strychnium is a sparingly soluble substance, it appeared proper, in conformity with our fourth condition, and in order to compare the actions of strychnia and of methyl-strychnium, that the properties of the sulphate of the latter, which is extremely soluble, should be examined. Sulphate of methyl-strychnium ((C,,H,,N,0,CH,),SO,) was prepared by precipita- ting a hot aqueous solution of the iodide by a hot solution of sulphate of silver, the slight excess of the latter was precipitated by chloride of sodium, the filtrate evaporated to dryness, and the sulphate of methyl-strychnium extracted by means of alcohol. It erystallises in delicate white needles, is very soluble in cold VOL. XXV. PART I. 25 160 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWFEN water, tastes like the iodide, and gives the usual strychnia-reaction with oxidising agents. As had been anticipated, it is much more active than the iodide. One grain, dissolved in water, and injected under the skin of a small rabbit, caused its death in eighteen minutes. Half-a-grain, however, produced no effect. When eight- tenths of a grain was similarly administered, the following symptoms were pro- duced, but death did not result. Experiment X XIII.—Eight-tenths of a grain of sulphate of methyl-strychnium, dissolved in a few minims of distilled water, was injected into the subcutaneous tissue over the abdomen of a rabbit, weighing three pounds and three and a-half ounces. It caused no immediate uneasiness, and the animal was unaffected for about twenty-five minutes, after which, however, it became restless. In twenty- eight minutes, movements of the limbs were made with obvious difficulty, and the rabbit occasionally stumbled. In twenty-nine minutes, the limbs could no longer support the body, and a position was assumed in which the rabbit lay on the abdo- men with the chin resting on the table. It was now perfectly flaccid, and remained on the side when so placed. There was no evidence of exaggeration in the reflex motor function; indeed, an extremely violent stimulus was required to produce even a faint reflex movement. In thirty-two minutes, slight quiverings occurred, and the respirations were laboured, and at the rate of sixty-eight per minute. This condition continued until one hour after the administration, and during all this time consciousness seemed unaffected, and sensibility was not lost, as was shown by stimulation of the conjunctiva or cornea causing movements of the eyelids. Repeated efforts were, however, now made to recover a normal posture, and the frequency of the respirations increased. In one hour and eleven minutes, the head was raised from the table; and in eleven minutes afterwards, the rabbit succeeded in rising on its feet and maintained itself thus, though at first some- what unsteadily. In one hour and twenty-two minutes, all the symptoms had disappeared. The rabbit was perfectly well on the following morning. ‘The sequence of symptoms to a fatal termination, and the post mortem appear- ances, are well shown in the experiment where one grain was exhibited (Experi- ment XXV.). EXPERIMENT XXV.—We dissolved one grain of sulphate of methyl-strych- nium in fifteen minims of distilled water, and injected this solution into the sub- cutaneous tissue of a rabbit, weighing two pounds and fourteen ounces. In eleven minutes, the first symptom, unsteadiness, appeared. In twelve minutes, the rabbit was lying on the abdomen and chest, with the lower jaw resting on the table. There were no voluntary movements; strong irritation caused feeble reflex movements only, and the respirations were shallow and laboured, and at the rate of sixty per minute. In sixteen minutes, quivering movements of the chest and abdomi- nal muscles occurred, from which it was nearly impossible to distinguish the CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 161 respiratory movements; and the sensibility of the eyeball was greatly im- paired. In seventeen minutes, there were no movements, except occasional faint twitches of the muscles of the body, while irritation of the skin or of the eye- - ball did not cause any reflex movements. The rabbit was quite dead in eighteen minutes. Four minutes after death, the heart was contracting in proper rhythm and with regularity, at the rate of 164 beats per minute, and the intestinal peristalsis was well marked; the heart had however ceased to contract in other twenty-four minutes, but the intestinal peristalsis continued for some time after this. Six minutes after death, the gluteal muscles were exposed, and exposure caused them to twitch. The sciatic nerves were at the same time stimulated with galvanism and mechanical irritation, but no contractions were produced. igor mortis com- menced about two hours and forty minutes after death. When sulphate of methyl-strychnium is administered to rabbits by the stomach, twenty-five grains appears to be about the minimum fatal dose. The symptoms and mode of death are the same as those that result from subcutaneous injection. These experiments clearly prove that the methyl derivatives of strychnia possess a very different action from strychnia itself. In none of our experiments, ~ not even in the fatal cases, were the symptoms those of strychnia-poisoning; no starts nor spasms occurred, nor did stimulation give evidence of the slightest _ increase of reflex excitability. In fact, a condition exactly the reverse of that produced by strychnia was produced by these compounds. In place of violent spasmodic contractions and muscular rigidity, the appearances were those of paralysis, with a perfectly flaccid condition of the muscles. The limbs of the animal first yielded, its head gradually sank until it rested on the table, by- and-by, it lay in a perfectly relaxed condition, and when death occurred, it was due to stoppage of the respiratory movements. In the autopsis, further evi- dence was obtained to distinguish the effects of the methyl-strychnium com- pounds from those of strychnia. The heart was found acting with nearly its normal rapidity; the spinal motor nerves were either paralysed or nearly so; | and, in place of the almost immediate occurrence of 72gor mortis that follows the | action of strychnia, the muscles continued flaccid, contractile, and alkaline for many hours. These symptoms are sufficient to suggest a close resemblance between the action of the methyl derivatives of strychnia and that of curare (wourali), a well _ known and elaborately studied poison. In a recent publication, Professor Scurorr, of Vienna, has indicated a resemblance of this kind between the nitrate of methyl- strychnium and curare.* Both substances undoubtedly produce a condition of * Wochenblatt der Zeitschrift der k. k. Gesellschaft der Aertze in Wien; vi. Band, 1866, pp. 157-162. 162 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN general paralysis; but the special characteristic of curare-poisoning is, that this paralysis is the result of an impairment or destruction of the function of the peripheral terminations (end-organs) of the motor nerves. It is impossible to demonstrate such an action without undertaking experiments of a special character. We, accordingly, extended our research for the purpose of examining this question. ExrertmMent XXVIII.—The sciatic artery and vein were tied at the knee of a frog, and one-tenth of a grain of sulphate of methyl-strychnium, dissolved in distilled water, was injected under the skin of the back. Eight minutes after- wards, the frog was lying in a perfectly flaccid state, and, in ten minutes, irrita- tion of any portion of the skin produced energetic movements of the tied limb, below the points of ligature, but nowhere else. The sciatic nerve of the untied limb was now exposed, and on stimulating it with a weak, interrupted galvanic current, movements occurred in the tied limb only; not the slightest effect occurred in any part to which the poison had access. At the same time, the muscles were everywhere active, and freely contracted when directly stimulated. The sciatic nerve was then exposed in the tied limb, above the points of ligature, and on stimulating it, energetic movements occurred below the knee of that limb, and there only. The heart was, at this time, acting at the rate of fifty per minute. This experiment was repeated with one grain of iodide of methyl-strychnium, and the same general results were obtained. The evidence that was thus acquired in favour of an action on the peripheral terminations of the motor nerves was strengthened by a modification of this method of experiment. EXPERIMENT XXIX—The right gastrocnemius muscle of a frog was carefully dissected from its connections, excepting that its origin and insertion, and the nerve- fibres entering it, were untouched, and that all its blood-vessels were ligatured. One-tenth of a grain of sulphate of methyl-strychnium, dissolved in five minims of distilled water, was then injected under the skin of the back. Twenty minutes afterwards, the animal] being in a perfectly relaxed and motionless condition, the two sciatic nerves were exposed. Galvanism of the left produced no movement in the left limb, while galvanism of the right produced energetic movements of the right limb, which were seen to be due solely to contractions of the right gas- trocnemius muscle, the other muscle remaining motionless. At the same time, direct stimulation by galvanism caused contractions as freely in the poisoned muscles as in the non-poisoned right gastrocnemius. In an experiment, in which iodide of methyl-strychnium was substituted for sulphate, the effects were the same. We have, therefore, demonstrated that the methyl-strychnium derivatives produce paralysis and death by destroying the function of the motor nerve end-organs, and that their mode of action is, there- fore, identical with that of curare. This conclusion is an extremely curious and CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 163 interesting one. It is difficult to imagine a more decided modification in the action of any substance than has been produced by the addition of iodide or sulphate of methyl to strychnia. The striking characteristic of strychnia-action is the great and uncontrollable activity of the muscular system ; that of curare, of iodide, and sulphate of methyl-strychnium, and, as we shall presently see, of several other similarly modified poisons, is the flaccid and motionless condition caused by the impossibility of exciting muscular action through the nervous. system. So opposite are their effects that physiologists look upon curare as a powerful counteragent to strychnia, while physicians have employed it with success in the treatment of strychnia-poisoning and of tetanus. It is remarkable that by so simple a chemical process so thorough a change should be produced in physiological action. The experiments we have already described have also shown that this change in chemical constitution has greatly reduced the poisonous activity of strychnia. This effect is still more clearly exhibited in the following table :— eo ® Substance Animal and its Method of employed. weight. exhibition. Ese: Effect. VII. |Lodide of methyl-| Rabbit, 3 lbs. 8 oz. | Subeutaneously.|15 ers. (contain-| Paralysis in 50 minutes, strychnium. ing 10°5 grs.| continuing for more than of strychnia). | 2 hours, and followed by recovery. XIII. | Strychnia (sus-| Do. (same rabbit | Subcutaneously.| 0:05 gr. Tetanus in 15 minutes; pended in dis- | as in Expt. VII.) death in 30 minutes. tilled water). XVII. |Iodide of methyl-| Do., 3lbs.130z. |By stomach. | 30grs. (contain-! No effect. strychnium. ing 211 grs. of strychnia). XIX. Strychnia (as Do., (same rabbit | By stomach. Ol gr. Tetanus in 22 minutes; hydrochlorate).| asin Ex. XVII.) death in 31 minutes. XXIII. | Sulphate of me-| Do., 3 lbs. 33 oz. | Subcutaneously.|0'8 gr. (contain-| Paralysis in 29 minutes, thyl-strych- ing 0.67 gr. of| continuing for 53 minutes, nium. strychnia). and followed by recovery. XXXIII. | Sulphate of me-| Do., 3 lbs. 5? oz. | By stomach. 20 ers. (contain-| No effect. thyl-strych- ing 16:8 grs. nium. of strychnia). We have made experiments with nitrate of methyl-strychnium and hydro- chlorate of ethyl-strychnium, and have found that their action is identical with that of the iodide or sulphate of methyl-strychnium. * The numbers in this, and in the other short tables that are appended to the description of the physiological action of the derivatives of each alkaloid, have reference, in common with the numbers in the text, to the arrangement in the complete table at the end of the paper. VOL. XXV. PART I. 2p 164 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN BRUCIA. Brucia is a poisonous alkaloid derived from some plants belonging to the genus Strychnos. It possesses a physiological action exactly similar in character to that of strychnia, but less in degree. Todide of methyl-brucium (C,,H,,N,0,CH,I +8H,O).—Brucia (C,,H,,N,0, + 4H,O) is, like strychnia, a mono-acid nitrile base: here also the structure of the group (C,,H,,NO,)” is unknown, but the action of nitric acid on brucia renders it probable that it contains the radical 6) 0S) The ethyl-brucium compounds @ were discovered and described by GUNNING,* and the methyl-brucium compounds by Srautscumipt.t We prepared the iodide of methyl-brucium by adding excess of iodide of methyl to a saturated solution of brucia in rectified spirit, allowing the mixture to stand for some hours, evaporating, and recrystallising from hot water. It forms thin white scales, and dissolves in 79 parts of water at 37°C, and in 225 parts of water at 9°C. Its taste resembles that of the corresponding strychnia compound. When administered by subcutaneous injection, iodide of methyl-brucium was reduced to the form of a very fine powder, and suspended and dissolved in warm distilled water. In a series of experiments, it was found that as much as twelve grains could be thus given to a rabbit without any effect, that fifteen grains produced marked symptoms, and that eighteen grains was about the minimum fatal dose. Its method of action is well shown in the following experiment. EXPERIMENT XL.—We injected seven and a-half grains of iodide of methyl- brucium, suspended and dissolved in warm distilled water, into each of two cavities (fifteen grains in all) previously formed in the subcutaneous cellular tissue over the abdomen of a rabbit, weighing four pounds. This did not pro- duce the slightest effect until two hours and forty-three minutes after the administration, when the rabbit’s movements became sluggish. Shortly after, a difficulty was observed in standing, and this posture soon become impossible on account of the increasing feebleness of the limbs. In three hours and three minutes, the rabbit subsided on the abdomen and chest, with the lower jaw rest- ing on the table. The condition was one of perfect quietness, there being no twitches; and, though frequently tested, the reflex excitability appeared normal. * Journal fiir praktische Chemie, vol. Ixvii. p. 46. + Poaesnporrr’s Annalen, vol. evil. p. 535 (1859). CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 165 It remained on the side when so placed, but unsuccessful resistance was made to this change of position. In three hours and thirty-eight minutes, the flaccid state was even more marked, the position was changed without any resistance on the part of the rabbit, severe pinching only occasionally excited a reflex movement, but the respiratory movements were at the rate of sixty-eight per minute. These symptoms continued for other twenty minutes, when some volun- tary movements were made, and soon after, the flaccid condition had nearly dis- appeared. On the following morning, the animal appeared to be perfectly well. In the experiment we next give, a fatal dose was administered. EXPERIMENT XLI.—We injected, in all, eighteen grains of iodide of methyl- brucium, suspended and dissolved in warm distilled water, into two subcu- taneous cavities formed over the abdomen of a rabbit, weighing three pounds and twelve ounces. No result was observed until twenty-seven minutes, when uneasiness was manifested by restless movements, and slight quivers were seen in the muscles of the neck. In thirty minutes, there was great difficulty in supporting the head, which shook tremulously, and frequently fell on the table, where it eventually remained at thirty-two minutes. The body was still supported on the limbs, though by no means steadily. In thirty-seven minutes, it lay on the table and remained on the side, unresisting and flaccid. The respirations were, at this time, at the rate of forty-eight per minute, and were occasionally interrupted by faint quivering movements, but these had no spasmodic char- acter. In forty-five minutes, the respirations were thirty-six per minute, and the heart’s contractions 160 per minute. In one hour, the respirations were twenty-five per minute; and irritation of the conjunctiva did not now cause any movements of the eyelids. In one hour and seven minutes, the respiratory movements were irregular and shallow, only about sixteen occurring in the minute, while the heart was contracting at the rate of 120 per minute. The limbs were perfectly flaccid and motionless. The respiratory movements gra- dually became less apparent, a series of feeble quivers occurred in the muscles of the face, and death immediately afterwards occurred, one hour and thirteen minutes after the administration. In the autopsy, the cardiac action was found to be regular and rhythmical, though only at the rate of seventy-four per minute. In three minutes after death, galvanism of the sciatic, phrenic, and other nerves, did not produce any muscular contraction; while it was found by direct galvanism that the muscles retained their contractibility for many minutes afterwards. Rigor mortis did not occur until more than one hour after death. For the purpose of contrasting these symptoms with those that are caused by brucia itself, we shall describe, very briefly, an experiment in which the rabbit, that recovered after the administration of fifteen grains of iodide of methyl- brucium, was rapidly killed by a somewhat large dose of brucia. 166 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN Experiment XLII1.—One-fifth of a grain of brucia was dissolved in ten minims of very dilute hydrochloric acid, and injected, with Woonp’s syringe, into the subcutaneous tissue of the rabbit that had, some days previously, been subjected to an experiment with fifteen grains of iodide of methyl-brucium. In seven minutes, a constrained position was assumed by the rabbit, and the slightest touch caused a sudden spasmodic contraction of the four limbs by which the body was swiftly elevated. In eight minutes, the rabbit sprang to a considerable height, and fell in a well-marked tetanic convulsion, which lasted about fifteen seconds. After this, a series of violent tetanic convulsions, of a distinctly opisthotonic character, followed each other in rapid succession; and at the termination of one of these, eighteen minutes and thirty seconds after the injec- tion of the poison, the rabbit died. There was distinct igor mortis thirty minutes after death. For internal administration, the iodide of methyl-brucium was also reduced to a very fine powder, and suspended and dissolved in warm distilled water. It was then introduced into the stomach, by means of a gum-elastic catheter. In this way, we performed several experiments, but never succeeded in producing any effect, although as large a dose as thirty grains was at one time admin- istered. It is well known that there is considerable difficulty in affecting a rabbit by a poison introduced into the stomach. That this difficulty was not due, in the present instance, to any recognised cause peculiar to the stomach of the rabbit, was shown by an experiment in which we produced tetanic symptoms and death by introducing two grains of brucia into the stomach of the rabbit that had previously received thirty grains of iodide of methyl- brucium without any effect whatever. Sulphate of methyl-brucium ((C,,H,,N,0,CH,),SO,, dried at 100°C) was pre- pared by precipitating a hot solution of the iodide by means of sulphate of silver. It forms a white crystalline mass, readily soluble in water, and, as well as the iodide, gives the ordinary brucia reaction with nitric acid. It is freely soluble in cold water. We examined the effects of this substance by subcutaneous injection and by introduction into the stomach. For the former purpose, it was dissolved in a few minims of distilled water, and injected under the skin with a Woop’s syringe. In a rabbit, one grain could be thus given without any effect, two grains caused marked effects, which were not, however, fatal; while two grains and a-half soon killed the animal. The symptoms were the same as those of the iodide, and, therefore, very different from the exaggerated reflex action, convulsions, and tetanus, which are caused by brucia itself. They are illustrated in the following experiments. EXPERIMENT LIII.—We injected two grains of sulphate of methyl-brucium, dis- solved in fifteen minims of distilled water, under the skin of a rabbit, weighing two ~ CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 167 pounds and thirteen ounces and three-quarters. In ten minutes, the animal had obviously some difficulty in moving about, and it could not stand steadily. The limbs soon after yielded, and it lay down on the abdomen, chest, and lower jaw ; while occasional quivering movements occurred in the muscles of the body. In thirty-four minutes, it lay unresisting and quiet on the side, and the respira- tions were at the rate of seventy-four per minute. In forty minutes, the respirations were at the rate of fifty-four per minute.. It lay in a perfectly relaxed and quiet condition, and when the skin was severely irritated, only extremely feeble reflex movements followed. In one hour and two minutes, the respirations were at the rate of forty-eight per minute; and though irritation of the cornea or conjunctiva did not cause any movement of the eyelids, reflex movements could be excited by severe pinching of the skin. This condition of helpless prostration continued for about thirty minutes, during which some faint twitches of the body and jerking movements of the limbs occasionally occurred. Soon after this, however, a marked improvement was observed : the respirations became fuller and more frequent ; irritation of the eyeball was followed by con- tractions of the eyelids; and, at last, well-directed efforts were made to recover a normal position, and these ultimately proved successful at about two hours after the poison had been injected. The rabbit recovered perfectly. Experiment L1V.—Two and a-half-grains of sulphate of methyl-brucium was dissolved in fifteen minims of distilled water, and administered by subcutaneous injection to a rabbit, weighing three pounds and fourteen ounces and a-half. In twenty-two minutes, the animal was lying on the abdomen and chest, but the head was still supported by the muscles of the neck; there was distinct congestion of the ears and conjunctiva. In thirty-five minutes, the head had fallen on the table, and the rabbit was perfectly flaccid, and apparently unable to make any voluntary movements. The respirations were at the rate of eighty-two per minute. In fifty-three minutes, the number of the respirations had diminished to twenty-four per minute, while their character was extremely feeble and shallow. In one hour and two minutes, the respiratory movements occurred at long intervals, and were accompanied with a faint tremor of the body and limbs; and it was ascertained that the cardiac contractions were occurring regularly, at. the rate of 160 beats per minute. In one hour and ten minutes, the respirations altogether ceased, and death occurred. During the progress of the symptoms, the reflex excitability was frequently tested, with the result that not the slightest increase was ever observed. The autopsy was immediately made: the heart was found contracting at the rate of 120 per minute; the vermicular action of the intestines was well marked ; the conductivity of the sciatic nerves was lost three minutes after death ; and idio- muscular irritability persisted for more than twenty minutes afterwards. Rigor mortis had not commenced forty minutes after death. VOL. XXV. PART I. 2U 168 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN For administration by the stomach, we dissolved this substance in warm dis- tilled water, and introduced the solution through a gum-elastic catheter. We found that as much as twenty grains could be thus given without any effect, and it was not considered advisable to increase this dose. Its magnitude is apparent when we recollect that it contains about seventeen grains of brucia; and we have already seen that when two grains of this alkaloid is introduced into the stomach of a rabbit, the most violent tetanic convulsions are quickly produced, and death soon follows. The short account we have given of a few of our experiments with iodide and sulphate of methyl-brucium is sufficient to show that these substances have an action that is very different from that of brucia itself. Brucia is a violent con- vulsant poison, and it causes death by either exhaustion or asphyxia; its methyl derivatives never produce convulsions, nor do they even increase the reflex activity ; and although they cause death by asphyxia, this asphyxia, in place of being the result of prolonged and continuous muscular action, due to abnormal nerve activity, is the result of muscular paralysis, due to partial or complete absence of normal nerve activity. We have demonstrated the latter effect by the following experiments, which further show that the influence of the methyl deri- vatives of brucia is exercised on the terminations of the motor nerves. Exrertment LVI.—tThe left iliac artery ofa frog, weighing 608 grains, was tied, after exposing it by removing a portion of the sacrum, and one-fifth of a grain of sulphate of methyl-brucium, dissolved in ten minims of distilled water, was then injected into the abdomen. In four minutes, every portion of the frog except the left leg was paralysed. In five minutes and thirty seconds, weak interrupted galvanism, applied to any portion of the skin, caused violent movements of the left leg, and of it alone, every other part of the body remaining motionless. The heart, as ascertained by its impulse, was contracting thirty times per minute. In seven minutes, the right sciatic nerve was exposed—the incisions neces- sary for which excited energetic reflex movements of the left limb—and on gal- vanising it, strong contractions of the left limb occurred, but no movement occurred in the right limb. The muscles were everywhere in a normal state, and freely responded to direct galvanic stimulation; and the heart still con- tracted at the rate of thirty beats per minute. In a similar experiment, with half a grain of iodide of methyl-brucium, the same effects were observed. It is, therefore, apparent that these substances do not directly influence the action of the heart, of the muscles, of the spinal cord, or of the sensory (afferent) nerves, but that the paralysis, which they so promi- nently cause, is the result of an action on the motor nerves. In the above experiment, the whole course of the sciatic nerve, from the pelvis to the extremity of the left posterior limb, was protected from the influence of the poison. The experiment does not, therefore. show if the methyl-brucium compounds have — CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 169 an elective action for any special portion of the nerve. In the next experi- ment, a much more limited portion of the nerve was protected from the poisonous action. EXPERIMENT LVII.—In a frog, weighing 542 grains, the right gastrocnemius muscle was exposed; the muscle was separated from all its connections, excepting its origin and insertion and the nerve-fibres that entered it. One- sixth of a grain of sulphate of methyl-brucium, dissolved in ten minims of distilled water, was then injected into the abdomen. In twenty minutes, a condition of complete paralysis was present everywhere except in the right leg. The two sciatic nerves were exposed, and on galvanising the left nerve, feeble movements occurred in the right leg, and there only. When the right nerve was galvanised, movements occurred in the right leg, which were observed to be solely due to contractions in the right gastrocnemius muscle. In this experiment, the terminations of the sciatic nerve in the right gastroc- nemius muscle were alone protected from the direct influence of sulphate of methyl-brucium. This substance had access to all the other terminations of the right sciatic nerve, to the trunk of this nerve, and to all the other nerves of the body. No manifestation of vitality was obtained anywhere, except in the right limb, and it was restricted to contractions of one muscle of that limb. As these contractions could be produced by a stimulus originated in and conducted along the nerve trunk, it is obvious that the vitality of this portion of the nerve was not lost. And as the stimulus produced no effect on the termi- nations of the nerves to which sulphate of methyl-brucium had access, while it produced an effect on those that were protected from its direct influence, it is evident that this poison acts on the peripheral terminations of the motor nerves. The physiological action of brucia is, therefore, completely changed by the addition of iodide or sulphate of methyl. It is also apparent that its activity as a poison is greatly lessened; and the following table, which contains a succinct statement of some of the previously-mentioned facts, will clearly illustrate this :— 170 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN No. of Substance Animal and its Method of ence Effect. Experiment. employed. weight. exhibition. XL. |Iodide of methyl-| Rabbit, 4 Ibs. Subcutaneously.|15 grs. (contain-| Paralysis in 3 hours and brucium. ing 87 grs. of| 3 minutes, continuing dry brucia). for more than 28 minutes, and followed by recovery. XLIII. | Brucia (erystal- | Do. (same rabbit | Subcutaneously.|0-2 gr. (contain- | Tetanus in 8 minutes; lised). as in Experi- ing 0°17 gr.of | death in 18 minutes 30 ment XL.) dry brucia). seconds. XLVI. [Iodide of methyl-| Do.,4Ibs.20z. | By stomach. 30 grs. (contain- | No effect. brucium. ing 17:4 ers. of dry brucia). LI. Brucia (crystal- | Do. (same rabbit | By stomach. 2 grs. (contain- | Tetanus in 44 minutes; lised). as in Experi- ing 1‘7 gr. of | death after 3 hours. ment XLVI.) dry brucia). LIII. | Sulphate of me- | Do.,2 Ibs. 133 oz. Subcutaneously.| 2 grs. (contain- | Paralysis in 20 minutes, thyl-brucium, ing 1:7 gr. of | continuing for about 1 dried. dry brucia). hour and 40 minutes, and followed by recovery. LVIII. | Sulphate of me- | Do.,41bs.20z. |By stomach. 20 grs. (contain-| No effect. thyl-brucium, ing17-2ers. of dried. dry brucia). THEBATA. One of the active principles of opium possesses an action in all respects the same in character as that of strychnia or brucia. We principally owe our know- ledge of the method in which thebaia acts to the admirable researches of CLAUDE BerNARD. ‘This distinguished physiologist has further demonstrated that thebaia does not possess any soporific property, that it is the most active toxic principle in opium, and that it ranks first among the alkaloids of this drug that havea ~ convulsant action.* From our experience of its properties, we should assign to it a lower rank than brucia as a toxic and convulsant substance. Lodide of methyl-thebaium—tThe close analogy in physiological action that exists between thebaia (C,,H,,NO,) on the one hand, and strychnia and brucia on the other, led us to subject this alkaloid to the action of iodide of methyl. The method adopted was the same as that described for the preparation of iodide of methyl-brucium, and the reaction takes place as readily. The product crystallises from alcohol in hard, shining, transparent crystals, which, when air-dried, have the composition (C,,H,,NO,CH,1). They dissolve in 16-5 parts of water at 37°C., and in 63°5 parts of water at 9°C.+ When a hot, saturated, aqueous solution is allowed to cool, it gelatinises, and the jelly, when left to itself, in some hours, and, when stirred, in a few minutes, is converted into a mass of minute silky needles, which when dried in the air, have the same composition as the crystals obtained from the alcoholic solution. * Comptes Rendus, vol. lix. 1864, p. 413. ¢ The methyl derivatives of thebaia have not been described. We shall take some other oppor- tunity of giving details of their chemical relations. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 171 It is much more soluble in water than the iodides of methyl-strychnium and methyl-brucium, and, on this account, we commenced its administration in relatively small quantities. We found that doses of one, five, and six grains, nearly completely dissolved in very dilute spirit, and administered to rabbits by subcutaneous injection, produced absolutely no effect. When, however, the dose was increased to ten grains, partial and then complete paralysis was caused, and death quickly occurred; while serious symptoms were caused by eight grains, but they did not terminate fatally. We shall give some details of these two experiments. EXPERIMENT LXII.—We dissolved eight grains of iodide of methyl-thebaium in very dilute alcohol, and injected the solution, with Woon’s syringe, into the subcutaneous cellular tissue of a rabbit, weighing two pounds and twelve ounces. Symptoms of uneasiness occurred in thirty minutes, and were soon followed by quivering movements of the head and ears, and, to a slight extent, of the rest of the body. It was soon apparent that the neck muscles were scarcely able to support the head, for it frequently fell on the table,but the rabbit did not permit it to remain there until forty-five minutes after the administration. At this time, the respirations were at the rate of seventy-eight per minute, and, although the head was resting on the table, the body of the animal was supported, in a comparatively normal posture, on the limbs. There were occasional tremulous movements of the body, but no exaggeration of the reflex function could be dis- covered. The rabbit remained in this state for about thirty minutes; but soon after this, the tremulous movements disappeared, the head was raised and supported normally, and a perfectly natural posture was assumed. Every symptom had disappeared within two hours after the administration. EXPERIMENT LXIII.—Ten grains of iodide of methyl-thebaium, reduced to a very fine powder, was partially dissolved and partially suspended in very dilute alcohol, and injected under the skin of a rabbit, weighing two pounds and eleven ounces. There was no obvious effect until ten minutes, when it was observed that the animal moved with difficulty. Tremulous movements then occurred, the limbs occasionally yielded, and the head frequently fell. In twelve minutes, the rabbit lay on the abdomen and chest, with the lower jaw resting on the table; and the tremulous movements only occurred at intervals. It could now be lifted without any struggles. In nineteen minutes, the condition was one of complete flaccidity, the only movements were an occasional gasping respiration, but common sensibility was still retained. It continued thus, on the very verge of death, for about four minutes, when a few quivering contractions occurred in the muscles of the face and neck, and the respirations altogether ceased. During the course of the symptoms, there was never the slightest trace of any exaggeration in the reflex activity, nor of spasmodic or convulsive movements. VOL, XXV. PART I. 2X 172 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN The autopsy was immediately made. The heart was found contracting, in normal rhythm, at the rate of eighty-five per minute, and its spontaneous contractions did not cease until eight minutes; and the intestinal peristalsis was active. The sciatic nerves were exposed four minutes after death, and stimulated with weak and strong currents of interrupted galvanism, but no muscular contractions were thereby caused. The muscles themselves readily contracted when the poles were applied directly to their surface, and continued to do so for more than fifteen minutes after death. There was no appearance of rigor mortis one hour and five minutes after death, and the muscles were, at this time, alkaline in reaction. We administered to the rabbit, which had survived the administration of eight erains of iodide of methyl-thebaium (Experiment LXII.), a fatal dose of the thebaia from some of which the methyl compound had been prepared. The striking contrast in the symptoms that were produced will be seen from the following account of the Experiment. EXPERIMENT LX VI.—We injected one-fifth of a grain of thebaia, dissolved in very dilute hydrochloric acid, into the subcutaneous cellular tissue of the rabbit, which had been subjected to an experiment, some days previously, with eight grains of iodide of methyl-thebaium. The injection did not appear to cause much annoyance, as the animal jumped about naturally for forty minutes after it. Soon after, however, its movements became more constrained and cautious, and occasional twitches occurred in the muscles of the back. These gradually became more marked and powerful, and in forty-eight minutes, they assumed the character of spasmodic starts. In forty-nine minutes, a touch, even when very gentle, of any portion of the skin excited a violent spasmodic jump, and in fifty-two minutes, a spontaneous violent opisthotonic convulsion took place, and continued for forty-five seconds. The rabbit now lay on its side; every respiratory move- ment provoked a short fit of tetanus, while, occasionally, a violent and prolonged fit occurred. This condition lasted for two minutes, when, at the termination of one of the more violent of these fits, death occurred,—fifty-four minutes after the administration of the poison. It was found, in the autopsy, that the sciatic nerves retained their motor con_ ductivity for at least fifteen minutes after death. A certain degree of muscular rigidity was observed at twenty-eight minutes, and rigor mortis was perfectly established at forty minutes, when all the muscles were acid in reaction, although the temperature of the abdominal cavity was as high as 95° F. The internal administration of iodide of methyl-thebaium was effected in the same way as we have described for the corresponding strychnia and brucia com- pounds. It was found that, with this substance also, so large a dose as thirty grains could be introduced into the stomach of a rabbit without any effect. Well- marked symptoms were produced in the same animal by three, and, on another CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 173 occasion, by three and a-half grains of thebaia similarly administered, but it recovered after both doses. Four grains was, however, a fatal dose, as will be seen from the following Experiment. EXPERIMENT LX XIV.—Four grains of thebaia, almost completely dissolved in very dilute hydrochloric acid, was introduced, by a gum-elastic catheter, into the stomach of the rabbit that had received thirty grains of iodide of methyl-thebaium (Experiment LXXI.) In six minutes, a violent tetanic convulsion occurred ; after this, the rabbit remained on the side, and convulsion succeeded convulsion until its death, nineteen minutes after the administration of thebaia. Azgor mortis, with an acid reaction of the muscles, was completely established at thirty-seven minutes after death. Sulphate of methyl-thebaium ((C,,H,,NO,CH,),SO,, dried at 100° C.), was pre- pared by precipitating an aqueous solution of the iodide by means of sulphate of silver. It forms a white, indistinctly crystalline mass. It dissolves readily in water, and gives, with sulphuric acid, the reaction of thebaia. We found it to be a less active substance than the corresponding derivative of either strychnia or brucia, as doses of four and of four-and-a-half grains were not fatal, though they produced symptoms, when injected into the subcutaneous cellular tissue of rabbits. Five grains appears to be about the smallest quantity that can produce death when administered to rabbits in this manner. The expe- riments in which four and a-half and five grains were given are sufficient to illus- trate the general physiological effects of this substance. EXPERIMENT LXXVII.—We dissolved four and a-half grains of sulphate of methyl-thebaium in fifteen minims of distilled water, and injected this solution into the subcutaneous tissue at the flank of a rabbit, weighing three pounds and eleven ounces and a-half. In seventeen minutes, the rabbit had some difficulty in jumping about, for it occasionally stumbled, and rested for a few seconds on the chest. In twenty-one minutes, it was lying on the abdomen, with the lower jaw resting on the table; and, occasionally, a series of shivering tremors took place in the muscles of the back. In thirty minutes, it remained on the side, when so placed, and was perfectly flaccid. The respirations were at the rate of sixty per minute. In forty-one minutes, the respirations had diminished in frequency to forty per minute, and during inspiration the abdominal muscles contracted in a tremulous manner. In fifty-five minutes, the respirations had increased in number to seventy-one per minute, and in one hour and thirty minutes, they appeared to have regained their normal rapidity; but it was impossible to ascertain this definitely, on account of frequent interrup- tions by tremulous movements of the abdominal muscles. The rabbit was still lying on the side in a perfectly flaccid state. In one hour and thirty-two minutes, however, it suddenly raised the head, rose, and assumed a normal posture ; but the trembling continued. This trembling, very faint and not at 174 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN all spasmodic, was the last symptom to disappear, which it did about two hours and thirty minutes after the injection of the poison. We frequently tested the condition of the reflex activity, and did not find it increased at any period during the experiment. Experiment LX XVIII. —Five grains of sulphate of methyl-thebaium was dis- solved in thirty minims of distilled water, and injected under the skin of a rabbit, weighing four pounds and half an ounce. Its effects began to be seen in thirteen minutes, when, after a few restless movements, the rabbit subsided on the abdo- men and chest. Complete flaccidity soon after occurred; and the respirations be- came shallow and gasping, and they diminished in frequency until, at twenty-five minutes after the injection, they were only at the rate of twenty-three per minute. Occasional, very weak, tremulous movements occurred at this time. In thirty-five minutes, severe pinching of the skin caused only a feeble reflex movement, while the contraction of the eyelids, after irritation of the eyeball, was almost imper- ceptible. ‘The rabbit appeared still to retain consciousness. In fifty minutes, no movement followed severe pinching of the skin, or irritation of the eyeball, and the respirations were gasping and infrequent. In fifty minutes, a few twitches occurred in the muscles of the face, and either immediately before or during these the rabbit expired. In the autopsy, which was immediately performed, the heart was seen con- tracting at the rate of seventy-eight per minute, and the intestinal peristalsis seemed normal. Four and a-half minutes after death, neither a weak nora powerful galvanic current could excite any muscular contraction when applied to the trunk of a sciatic nerve; but idio-muscular irritability was not lost for many minutes after this. At two hours and thirty minutes after death, the rabbit was still perfectly flaccid, and there was not the slightest appearance of muscular rigidity. We have not observed any symptoms follow the internal administration 0 this substance, as no effect was produced when we introduced twenty grains, dis- solved in warm water, into the stomach of arabbit. It has been shown by Experi- ment LXXIV. that four grains of thebaia is a fatal dose when thus exhibited. The experiments we have narrated contain the most satisfactory proof that the chemical addition of iodide and sulphate of methyl has produced a complete change in the physiological action of thebaia. The nature of the change appears to be identical with that we have described as occurring under similar circum- stances in strychnia and brucia. Thebaia acts in the same way as these alkaloids; for it causes increase of the reflex activity, convulsions, and tetanus by an action on the spinal cord. The action of iodide and sulphate of methyl-thebaium is strik- ingly different; for they diminish reflex excitability, and produce a condition of paralysis in which death occurs by asphyxia. This paralysis, as we have seen, is dependent on an effect on the spinal nerve system. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 175 We will now describe an experiment in which we endeavoured to determine what portion of this system is affected. ExpPERIMENT LX XIX.—The sciatic artery and the two principal veins were tied in the right thigh of a frog, weighing 420 grains, and one-fifth of a grain of sulphate of methyl-thebaium, dissolved in seven minims of distilled water, was injected into the abdominal cavity. In six minutes, the animal was flaccid and motionless, and in other four minutes the respiratory movements of the chest and abdomen had ceased, while those of the throat continued, and did so for several minutes longer. In sixteen minutes, galvanic stimulation by an inter- rupted current, applied to any portion of the skin, caused movements of the right leg below the points of ligature, but nowhere else. In twenty-one minutes, the left sciatic nerve was exposed, and on galvanising it, energetic movements occurred in the right leg, while the left leg and every other part of the body remained motionless. The heart was now contracting at the rate of thirty-six beats in the minute. The muscles that had been laid bare in the left leg, by the dissection necessary for the exposure of the left sciatic nerve, were stimulated by the direct application of an interrupted galvanic current, and they contracted powerfully. This condition continued during other two days; on the second day, even a feeble stimulus applied to the left sciatic nerve was followed by well- marked contractions of the right leg, below the points of ligature; while it caused no movements in those parts of the frog that had been directly acted upon by the poison, although the muscles everywhere contracted when directly stimulated. We learn from this experiment that sulphate of methyl-thebaium produces paralysis by destroying the conductivity of the motor nerves, and not by inter- fering with the function of the spinal cord, or of the sensory (afferent) nerves. The next experiment was made with.the view to determine what portion of the motor nerve is paralysed by this substance. EXPERIMENT LXXX.—The left gastrocnemius muscle was exposed in the leg of a frog, weighing 604 grains. The blood-vessels that entered it were ligatured or twisted, and it was carefully separated from all its connections, excepting that its origin and insertion were untouched, and that the nerve fibres that entered it were not divided. Immediately after this somewhat tedious preparation, one-fifth of a grain of sulphate of methyl-thebaium, dissolved in ten minims of distilled water, was injected in the abdomen. Omitting the details of the effects that ensued, it is sufficient to mention that, at thirty minutes after this injection, the sciatic nerve was exposed in each thigh and galvanised, with the result that in the case of the right nerve movements followed in the left leg alone, and in the case of the left nerve movements followed in the left leg, and there only. It was seen that these movements in the left leg were entirely caused by contractions of the left gastrocnemius muscle, that is, of the muscle which had been protected from the direct influence of the poison. VOL. XXV. PART I. ZN, 176 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN We obtained the same results on repeating these experiments with half-grain doses of iodide of methyl-thebaium. These experiments demonstrate clearly that the methyl derivatives of thebaia produce their principal physiological effects by impairing and destroying the function of the peripheral termination of the motor nerves—an action that is very different from that:of thebaia itself. They also differ from thebaia in being con- siderably less potent as poisons. Several of these characters are summarised in the appended table. No. of Substance Animal and its Method of Experiment. employed. weight. exhibition. Diese Effect. LXII. | Iodideof methyl-| Rabbit, 2 Ibs. 120z.) Subeutaneously. | 8 grs. (contain-| Paralysis in 45 minutes, thebaium. ing 5°5 grs. of| continuing for about 30 thebaia). minutes, and followed by recovery. LXVI. | Thebaia. Do. (same rabbit | Subcutaneously, | 02 gr. Tetanus in 52 minutes, as in Experiment and death in 54 minutes. LXIL) LXXI. | Iodide of methyl-| Do., 4 lbs. 6 oz. | By stomach. 30 grs. (contain-| No effect. thebaium. ing 20°6 grs. of thebaia), LXXIV. | Thebaia. Do. (same rabbit! By stomach. 4 ors. Tetanus in 6 minutes, and asin Exp. LXXI.)| death in 19 minutes. LXXVII, | Sulphate of me-| Do., 3 lbs. 11} 0z. | Subeutaneously. | 4*5grs.(contain-| Paralysis in 21 minutes, thyl-thebaium. ing 3°7 grs. of| continuing for 2 hours thebaia). and 9 minutes, and fol- lowed by recovery. LXXXI. | Sulphate of me-|Do., 4 Ibs,40z. | By stomach. 20 ers. (contain-| No effect. thyl-thebaium. ing 16°6 grs. of thebaia). CODEIA (C,,H,,NO, + H,0). We have examined the effect of the addition of iodide and sulphate of methyl to codeia—an opium alkaloid, which, according to CLAUDE BERNARD, is the second in toxic activity, and possesses distinct convulsant but feeble soporific properties.* Lodide of methyl-codeium.—How } obtained by the action of iodide of ethyl on codeia, iodide of ethyl-codeium, and from it a number of ethyl-codeium com- pounds, and proved that codeia is a nitrile base. As was to be expected, iodide of methyl acts even more readily on codeia.{ It is only necessary to heat codeia with a little alcohol and an excess of iodide of methyl to 100°C. for an hour, in a sealed tube, to complete the reaction. The excess of iodide of methyl is distilled off, the alcohol evaporated, and the product crystallised from hot water. It * Comptes Rendus, vol, lix. (1864) p. 418. + Chemical Society’s Quarterly Journal, vol. vi. (18538) p. 134. { We shall give details of the chemical relations of the methyl derivatives of codeia on some other occasion, CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. ar forms large transparent prisms, soluble in 14:5 parts of water at 37°C., and in 49 parts of water at 9°C. Its solution is not precipitated by caustic potash, and in all respects, except in the appearance of its crystals, agrees with iodide of ethyl-codeium. As iodide of methyl-codeium is tolerably soluble in warm water, we could administer it by subcutaneous injection in the form of solution. It was found, in rabbits, that a dose of five grains was quite inert, that one of fifteen grains caused prolonged and serious symptoms which were recovered from, and that one of twenty grains produced death in a short time. The following details include the principal symptoms that appeared when fifteen and twenty grains were thus administered. Exprrtmment LXXXIV.—Fifteen grains of iodide of methyl-codeium was dissolved in some warm distilled water, to which a few drops of rectified spirit had been added, and the solution was injected into the subcutaneous cellular tissue of a rabbit, weighing two pounds and fourteen ounces. The rabbit remained sitting quietly until twenty-two minutes afterwards, but in a few seconds more it had some difficulty in retaining a sitting posture, and, on standing, the fore-limbs occasionally yielded, until, at twenty-five minutes, it subsided on the abdomen, chest, and lower jaw. In thirty minutes, it remained on the side without strug- -gling; and now, after considerable intervals, faint twitches occurred in the body and limbs, which, however, had no convulsive character. In thirty-seven minutes, irritation of the cornea or conjunctiva did not cause any movement in the eyelids, but the respirations, though weak, shallow, and somewhat jerking, were at the rate of sixty-seven in the minute. In forty-five minutes, the frequency of the re- spirations had diminished to sixty in the minute, and there were now no twitches. The rabbit continued to lie in this flaccid state for about two hours longer ; at the end of which time, twitches reappeared, at first extremely faint, but, by-and-by, of considerable strength, and involving the muscles of the abdomen, chest, neck, and limbs. In four hours and twenty minutes, the rabbit was again in a perfectly quiet state, the twitches had disappeared, and the common sensibility was in a normally active condition. Frequent attempts were made, soon after, to recover a natural position, and success was at Jength attained, four hours and twenty-five minutes after the injection of the poison. There were no further symptoms. EXPERIMENT LXXXV.—We injected twenty grains of iodide of methyl-codeium, dissolved as in the preceding experiment, into the subcutaneous cellular tissue of a rabbit, weighing two pounds and twelve ounces and a-half. The animal began to tremble in thirteen minutes, and the head, after being unsteadily sup- ported for a short time, fell on the table. In fifteen minutes, the rabbit remained on the side; the respirations were weak and irregular, and slight starts occurred occasionally. Severe irritation of the skin was now required to cause 178 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN even an extremely feeble reflex movement. In twenty-four minutes, no move- ment followed irritation of either the skin or eyeball, and the respirations were mere gasping jerks. In thirty-two minutes, a series of feeble twitches occurred in the face-muscles, and then the respirations entirely ceased. We immediately exposed the sciatic nerves, and examined their condition : when they were stimulated with galvanism, slight movements followed in the hind limbs at one minute after death; but no movement could be excited at one minute and thirty seconds. The heart was found to be contracting in regular rhythm, at the rate of eighty-two in the minute. Forty-five minutes after death, the body was perfectly flaccid, and there was not the slightest ap- pearance of muscular rigidity. We may best display the marked differences between these physiological effects and those that are caused by codeia, by describing an experiment in which the rabbit that survived the administration of fifteen grains of iodide of methyl- codeium, was quickly killed by the subcutaneous injection of one grain of codeia. EXPERIMENT LXXXIX.—We dissolved one grain of codeia in some warm distilled water, to which a few drops of rectified spirit had been added, and in- jected the solution into the subcutaneous tissue of the rabbit, which was some days previously the subject of Experiment LXXXIV. In fifteen minutes, faint twitches occurred in some of the muscles of the back ; and, soon after, a slight touch excited a violent start. Spontaneous spasmodic starts now followed each other, until one hour and eleven minutes, when a violent tetanic convulsion of an opis- thotonic character occurred. For some time before this, it was observed that the hind limbs trailed slightly when movements were attempted, indicating, apparently, a slight degree of motor paralysis. The first tetanic convulsion was followed by trismus, which lasted for a few seconds, and by a succession of slight spasms; and soon after its occurrence, unsuccessful efforts were made to recover a normal position. In one hour and thirty minutes, a second violent tetanic con- vulsion took place, and this presented the character of emprosthotonos rather than of opisthotonos. Such convulsions now recurred after intervals of a few minutes, and at the termination of one of them, one hour and forty-five minutes after the administration of the poison, the rabbit died. In fifteen minutes after death, strong 7gor mortis was present. We introduced iodide of methyl-codeium into the stomach of rabbits on two occasions. In one of these, fifteen grains were thus administered, and in the other, thirty grains; but no effect was produced by either dose. Codeia itself, how- ever, is by no means a violent poison when given to rabbits in this manner. We made a considerable number of experiments, but did not succeed in causing death even with fifteen grains. In the following experiment we employed ten grains. EXPERIMENT XCIV.—By means of a gum-elastic catheter, we injected ten grains of codeia, dissolved in warm distilled water to which a few drops of | PHYSICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 179 dilute hydrochloric acid had been added, into the stomach of a rabbit, weighing three pounds and thirteen ounces. In twenty-four minutes, some symptoms of sleepiness were observed, which chiefly manifested themselves by nodding movements of the head. In thirty-nine minutes, the reflex excitability seemed increased, as a slight touch caused a sudden, somewhat spasmodic start. In one hour, the sleepy condition had so far increased, that the head rested on the table, and the eyelids were semi-closed. In one hour and twenty minutes, the rabbit could be placed in almost any position, provided physical rest were allowed; and it would remain sleeping in these attitudes until roused by sounds or by pretty violent irritations. It continued in this condition for more than two hours; but in three hours, the sleepiness was less marked, and on the following morning the rabbit was in a perfectly natural state. Sulphate of methyl-codeitum was prepared from the iodide, by precipitating it by means of sulphate of silver. It forms a white crystalline mass, readily soluble in cold water. It is ‘a rather more active poison than the iodide, for we found that ten grains, exhibited subcutaneously, was sufficient to kill a rabbit. We observed only slight symptoms with eight grains. EXPERIMENT XCVI.—Eight grains of sulphate of methyl-codeium was dissolved in twenty minims of distilled water, and injected under the skin of a rabbit, weighing four pounds. No distinct effect was observed until thirty minutes, when some uneasiness was shown by restless movements of the limbs; and, soon after, a little trembling occurred. Weakness of the limbs was then exhibited by occasional stumbles, and, in thirty-three minutes, the rabbit fell, and remained rest- ing on the abdomen, with the lower jaw on the table. There were no starts nor spasms, and even the trembling had now ceased; while severe irritation of the © skin caused merely slight reflex movements. After remaining in this state for twenty minutes, the symptoms gradually improved, and the rabbit appeared to be quite well two hours after it had received the poison. EXPERIMENT XCVII.—Ten grains of the sulphate of methyl-codeium was dis- solved in distilled water, and injected under the skin of a rabbit, weighing four pounds and four ounces. In twenty-three minutes, the head and portions of the body shook in a quivering manner ; and, gradually, the head sank until it rested on the table. In twenty-five minutes, the legs gave way, and the animal fell; faint twitches occurred over the body, but otherwise the condition was one of complete flaccidity. In thirty-five minutes, it remained on the side, without any resistance. In thirty-eight minutes, the respirations were laboured, and at the rate of thirty-six per minute; and in other four minutes, they had fallen to twenty per minute. In forty-one minutes, these movements were extremely shallow and irregular; and in forty-two minutes, they altogether ceased. In the course of this experiment, no convulsive symptoms occurred, and no hypnotism was observed. VOL. XXV. PART I. 22 180 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN In the autopsy, the heart was seen acting, one minute after death, at the rate : of 160 beats per minute, and the intestinal peristalsis was found to be normal. __ The motor conductivity of the sciatic nerves was retained at three minutes after death, but it had disappeared in other four minutes; while the idio-muscular irritability was not lost until more than sixty minutes after death. | For internal administration, we followed the plan already described. No | symptom whatever was observed when the large dose of twenty grains was ~ introduced into the stomach of a rabbit. We did not, accordingly, consider it advisable to continue this method of administration any further. . As we have already stated, and as the experiments we have narrated clearly _ show, the principal effects that are caused by codeia are convulsions and hypno- : tism. In our experiments with rabbits, the latter effect was manifested only when large doses were introduced into the stomach. It was not seen when this alkaloid was administered by subcutaneous injection, probably because sleep was then prevented by the spasmodic starts and convulsions that were so prominently caused. We learn from our experiments that the iodide and sulphate of methyl- codeium have a very different action from codeia. We have never observed any hypnotic effect follow their administration, and, in place of convulsions, we have seen that they produce paralysis. This, indeed, is the only marked symptom that follows their administration, and it is apparent that it does not depend on an effect on the muscles, nor on the cerebral lobes. We endeavoured to determine the exact cause of this paralysis by experiments with localised poisoning on frogs. EXPERIMENT XCVIII.—Having tied the right sciatic artery and vein of a frog, weighing 722 grains, one grain of sulphate of methyl-codeium, dissolved in distilled water, was injected into the abdominal cavity. In fifteen minutes, voluntary movements had disappeared, and the frog was lying on the abdomen, in a flaccid state. In thirty minutes, pinching of the skin with a pair of forceps excited movements in all the limbs, but these were most energetic in the right posterior extremity. In one hour and thirty minutes, similar stimula- tion excited no movement except in the right posterior extremity (where the vessels had been tied). The application of an interrupted galvanic current to the exposed trunk of the. left sciatic nerve was now followed by active movements of the right leg, but of no other part; while, at the same time, the muscles in the poisoned regions freely responded to galvanic stimulation directly applied to them. In two hours and forty minutes, the condition was the same, and, judging from the cardiac impulse, the heart was contracting at the rate of thirty-five per minute. We need not again enter into the reasons for concluding from such an experi- ment that the paralysis caused by sulphate of methyl-codeium is due to an action on the motor nerves. As has been already done with the corresponding sub- stances treated of in the previous portion of this paper, we, in the next place, — determined what portion of the motor nerve—trunk or periphery—is acted on. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 181 EXPERIMENT XCIX.—In a frog, weighing 694 grains, the left gastrocnemius muscle was prepared in the manner described in Experiments XXIX., LVIL, and LXXX., and one grain of sulphate of methyl-codeium, dissolved in distilled water, was injected into the abdomen by means of a Woop’s syringe. In one hour after this, a condition of flaccidity being present, the trunks of the two sciatic nerves were exposed, and stimulated with an interrupted galvanic current. When the right nerve was thus treated, some contractions followed in the left leg, and nowhere else; and when the left nerve was thus treated, vigorous contractions followed in the left leg; and it was observed that the movements of the left leg were caused by contractions restricted to its gastrocnemius muscle, that is, the muscle to which the poison had no direct access. At this time, the muscles in all parts of the body contracted freely when the poles of the battery were applied to their surfaces, and continued to do so for many hours longer. We repeated these last experiments with iodide of methyl-codeium, and obtained the same general results. We have, therefore, demonstrated that iodide and sulphate of methyl-codeium produce paralysis, by destroying the function of the peripheral terminations (end- organs) of the motor nerves—a mode of action that distinguishes them, as physiological agents, in a most striking manner from codeia. It will also be seen from the following table, that the poisonous (toxic) activity of the codeia in these methyl-compounds is considerably diminished. No. of Substance Animal and its Method of Experiment. employed. weight. exhibition. Dove: paba LXXXIV. Iodide of metnyl-) Rabbit, 21bs, 140z.) Subeutaneously.| 15 grs. (contain-| Paralysis in 25 minutes. codeium. ing 10-2 grs.of| continuing for about 3 dry codeia). hours, and followed by recovery. LXXXIX.| Codeia (crystal-| Do. (same rabbit as| Subcutaneously.|1 gr. (contain-| Spontaneous twitches in lised). in Ex. LXXXIYV.) ing 0:94 gr.| 15 minutes, tetanus in of dry codeia).| 1 hour and 11 minutes, and death in 1 hour and 45 minutes. XCI. |Lodide of methyl-| Do., 2 lbs. 13 oz. | By stomach. 30 gers. (contain-| No effect. codeium. ing 20°3 grs. of dry codeia). XCIV. | Codeia (crystal-| Do. (same rabbit as| By stomach. 10 grs. (contain-| Sleepiness in 24 minutes, lised), in Ex. XCL.) ing 9°4 gers. of} increase of reflex exci- dry codeia), tability in 39 minutes, and followed by recovery in more than 3 hours. XCVI. | Sulphate of me-| Do., 4 lbs, Subcutaneously.|8 grs. (contain-| Paralysis in 33 minutes, thyl-codeium. ing 6°6 gers. of| continuing for more than dry codeia). 20 minutes, and followed by recovery. C. Sulphate of me-|Do., 41bs.130z. | By stomach. 20 grs. (contain-| No effect. thyl-codeium. ing 16°5 grs. of dry codeia). 182 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN - MORPHIA. The most recent and trustworthy investigations show that, among the opium alkaloids, morphia (C,,H,,NO,+H,O) is next in activity as a soporific to narceia, that it possesses a less convulsant action than codeia, and that its fatal dose is one of the largest of those of the active principles of opium. * Lodide of methyl-morphium (C,,H,,NO,CH,1)—How subjected morphia to the action of iodide of ethyl and of iodide of methyl, prepared and described a number of the ethyl-morphium and methyl-morphium compounds, and proved that morphia is a nitrile base.t We prepared the iodide of methyl-morphium by How’s method, viz., by treating morphia with alcohol and an excess of iodide of methyl in a sealed tube, at 100° C., for an hour, distilling off the excess of iodide of methyl, and recrystallising from hot water. It forms long, transparent, prismatic needles; and dissolves in 34 parts of water at 37° C., and in 88°5 parts of water at 9° C. As it is well known that comparatively large doses of morphia are required to produce any symptom in such animals as rabbits, we at once commenced the administration of iodide of methyl-morphium in very large doses. We were unable to produce any effect whatever when so large a dose as twenty grains was — injected under the skin of a small rabbit; and, as this could only be adminis- tered as a fine powder, suspended in warm distilled water, it was extremely inconvenient to give any larger quantity in a form necessarily so bulky. Eight grains of morphia was afterwards exhibited, in the same way, to this rabbit, and it caused the usual symptoms and death. It may be interesting and satisfactory to give some details of these two experiments. EXxPEerRtMENT CI.—Twenty grains of iodide of methyl-morphium was reduced to a fine powder, mixed with two drachms of warm distilled water, and injected into two previously formed subcutaneous cavities at the flanks of a rabbit, weigh- ing two pounds and fourteen ounces. The rabbit was carefully observed for four hours, but no symptom occurred during this time. It was perfectly well on the following morning. ExPERIMENT CV.—Eight grains of morphia, suspended in warm distilled water, was introduced into the subcutaneous cellular tissue of the rabbit that had been employed,two days previously, in Experiment CI. In one hour and four minutes, an inclination to sleep was observed, the eyelids closed, and the head sank on the table, but a slight sound immediately roused the rabbit. In two hours, the soporific effect was more marked; and the animal remained in almost any position in which it could be placed, provided the change was made gradually and gently; * Craupe Bernarp, Comptes Rendus, vol. lix. 1864, p, 413. + Chemical Society’s Quarterly Journal, vol. vi, (1853) p. 126. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 183 and, however unnatural the position might seem to be, if it were consistent with rest, sleep immediately occurred. In three hours, there was some difficulty in rousing it, and when this was done, it remained awake for afew seconds only. In six hours, the respirations had fallen to the slow rate of twenty-six in the minute. This condition lasted, altogether, for about forty-eight hours, when spasms made their appearance, which, by-and-by, assumed all the characters of epileptiform convulsions. These epileptic fits frequently recurred, and could be excited, at any time, by pinching the skin. They consisted of tonic spasms of the limbs and of the abdominal muscles, followed by twisting of the head to the right, grinding movements of the lower jaw, and violent opisthotonos. The rabbit was found dead on the morning of the third day after the administration. The two subcutaneous cavities into which the morphia had been introduced were laid open, and a small quantity of unabsorbed morphia was found in both. The cavities into which iodide of methyl-morphium had been introduced were also laid open, but none of this substance was found. We were unsuccessful in producing any symptoms by the internal administra- tion of iodide of methyl-morphium. Thirty grains was found to be perfectly inert when exhibited by the stomach, while the same rabbit was decidedly narcotised with five grains of morphia similarly exhibited. It is interesting, for the purpose of comparison, to give a short account of these two Experiments. EXPERIMENT CVI.—We suspended thirty grains of finely-powdered iodide of methyl-morphium in distilled water, and injected the mixture into the stomach of a rabbit, weighing three pounds and twelve ounces. It was observed for more than two hours, but no symptoms could be detected. EXPERIMENT CVII.— We suspended five grains of finely-powdered morphia in distilled water, and injected the mixture into the stomach of the rabbit that was used, two days previously, in Experiment CVI. In one hour and six minutes, the rabbit was observed to be sleepy, and it soon after laid its head on the table. This sleepy condition became gradually more marked: in one hour and twenty- five minutes, the rabbit could be placed in almost any position, and slept thus ; while about the same time, a condition resembling that of catalepsy was present, for when we placed the rabbit on the back and raised the fore legs perpendicu- larly upwards, it remained in this extraordinary attitude for several minutes. In two hours and forty-one minutes, it was observed that the pupils, which were small, did not contract on the approach of a bright light, nor did this stimulus excite any movement of the body; but the common sensibility was not lost. The condition of cataleptic-like hypnotism lasted, altogether, about three hours and twenty minutes. Soon after this, some voluntary movements were made, and the rabbit gradually recovered to a perfectly normal state. Any conclusion drawn from experiments on such animals as rabbits, with a substance whose predominating action is a soporific one, are always liable to VOL. XXV. PART I. OA 184 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN objection. For this reason, we were induced to try the effect of iodide of methyl- morphium on man. One of us,* who is perfectly susceptible to the action of morphia, took on one occasion, half a grain of iodide of methyl-morphium, in the form of powder; but this produced no effect. On another occasion, one grain was taken, also as a powder; but not the slightest soporific or other action was caused. The latter dose contained about three-fourths of a grain of morphia, and this is certainly much above the usual narcotic dose of this substance. It is important to mention, that although we have failed in causing any symptoms in warm-blooded animals with this substance, we have found that it acts with considerable energy on frogs. The nature of this action will be explained in the description of the effects of sulphate of methyl-morphium. Sulphate of methyl-morphium ((C,,H,,NO,CH,),SO,), was prepared by pre- cipitating a solution of the iodide by means of sulphate of silver. It forms a white crystalline mass, very soluble in water. It gives the ordinary blue colour- reaction of morphia with persalts of iron. This salt of methyl-morphium is much more active than the iodide. By subcutaneous injection, doses of two, three, four, five and eight grains caused marked symptoms; while a dose of ten grains was sufficient to kill a large rabbit. The effects of eight and of ten grains are described in the two following Experiments. EXPERIMENT CXII.—Eight grains of sulphate of methyl-morphium, dissolved in distilled water, was injected under the skin, over the two flanks of a rabbit, weighing three pounds and one ounce. In twelve minutes, it appeared to be rather sleepy, and disinclined to move. In fourteen minutes, the head fell on the table, and the animal remained in this position, without any movements, except those that were necessary for respiration. In twenty-five minutes, the hypnotism was extremely well-marked; it was possible to place the animal in any position, and if this were compatible with stability, sound sleep occurred. A considerable stimulus was now required before the rabbit could be roused from _ sleep. In two hours and twenty minutes, this condition still continued, but the — observations were now discontinued. On the following morning, the rabbit appeared to be perfectly well. No convulsive symptoms nor exaggeration of reflex activity was observed in this Experiment. EXPERIMENT CXIII.—We dissolved ten grains of sulphate of methyl-morphium in 200 minims of distilled water,and injected the solution under the skin of a rabbit, weighing three pounds and eight ounces. In seven minutes, difficulty in moving about was observed; and, in rapid succession, some stumbles occurred, the limbs yielded, and the animal lay in a state of flaccidity, on the abdomen, chest, and lower jaw. It could now be placed without any resistance in almost * Dr FRASER. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 185 any position. In twenty-four minutes, the respirations were very feeble and shallow, and at the rate of twenty-four in the minute; the rabbit was perfectly quiet and flaccid; and severe pinching of the skin excited only feeble refiex movements. There was not the slightest appearance of muscular rigidity, nor of starts, spasms, or even quivering movements. In forty-seven minutes, the respir- ations were extremely weak and jerky, and at the rate of ten per minute, while the sensibility of the conjunctiva and cornea had greatly diminished. In fifty-six minutes, the respirations occurred only eight times in the minute, and no move- ment of the eyelids could be excited by irritating the conjunctiva or cornea. Exophthalmos was now markedly present. Death occurred in one hour and two minutes after the administration of the poison. In the autopsy, the heart was found to be distended, and acting irregularly and slowly. There was no appearance of 77gor two hours after death. When administered by the stomach, twenty grains of sulphate of methyl- morphium produced no effect on a rabbit. Our experiments with morphia confirmed the observations made by others, which show that this alkaloid has two prominent actions on rabbits—a convul- sant and ahypnotic one. We shall now consider how far each of these is modified by the addition of sulphate of methyl to morphia. The addition of iodide of methyl appears, no doubt, to have produced a very important change, but as ‘this is rather in the direction of diminishing, or, as our experiments indicate, altogether destroying, the physiological activity of morphia, the iodide of methy]- morphium may, in the mean time, be removed from consideration. It has been proved, in a most satisfactory manner, that sulphate of methy!- morphium possesses no convulsant action; for neither in the experiments we have described in detail, nor in any of the others we performed with this substance, was there any trace of spasmodic action or of exaggeration of the reflex function. It, however, undoubtedly causes hypnotic symptoms. In small non-fatal doses, hypnotism was chiefly manifested, and this rendered it somewhat difficult to judge whether paralysis were present or not. In large non-fatal doses, and in fatal doses, on the other hand, paralysis appeared to be the chief effect, though hypnotism was also present. It would, therefore, seem that sulphate of methy]- morphium agrees with morphia in possessing a hypnotic action, but differs from it in producing paralysis, and in being free from all convulsant action. It is obvious that an objection might be urged against the latter part of this statement ; for both the absence of convulsions and the production of paralysis might be merely the effects of hypnotism. Though we were ourselves convinced, from our experiments on rabbits, that such is not the case, we made some experiments on frogs to determine this more clearly. EXPERIMENTS CXV. and CXX.—The blood-vessels were tied in one limb near the knee of two frogs, selected because of their resemblance to each other in weight 186 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN and in activity. One grain of sulphate of methyl-morphium, in solution, was injected into the abdominal cavity of one of these frogs (a), and three-fourths of a grain of morphia, dissolved in very dilute sulphuric acid, into the abdominal cavity of the other (0). (a). Frog with Sulphate of Methyl-morphium. (b). Frog with Sulphate of Morphia. In eight minutes, the limbs yielded, and the frog | In sixteen minutes, some slight sprawling occur- subsided on the abdomen and chest. red, before which the frog was jumping about In twenty minutes, it was perfectly flaccid, and vigorously. the respirations had entirely ceased. Pinching | In fifty minutes, pinching of the skin occasioned of any portion of the’ skin excited energetic a series of clonic spasms, in which both poste- movements of the leg whose vessels were tied, rior extremities were forcibly and slowly ex- and feeble movements in various other parts. tended and then withdrawn, somewhat regu- In thirty minutes, the two sciatic nerves were larly, during three or four minutes, about four exposed; galvanism applied to their trunks times in the minute. The movements then caused contractions of the tied limb, below the | _ ceased, but they could be again excited. ligatures, and nowhere else. The heart was | In one hour, there was marked increase of the now acting at the rate of forty-two in the reflex excitability, a slight touch causing a minute, and the idio-muscular irritability was spasmodic start. normal everywhere. In one hour and thirty-eight minutes, a slight In twenty-four hours, the frog was still perfectly touch of the skin excited a short tetanic con- flaccid, the heart was contracting at the rate vulsion. of thirty per minute, and the muscles of the | In two hours, the same condition existed, and a poisoned and non-poisoned regions contracted tetanic convulsion could be at any time excited when directly galvanised. Galvanism of the by aslight touch. During these convulsions, sciatic nerve of the poisoned leg, however, pro- the muscles in the non-poisoned limb were duced no movement; but galvanism of the contracted as forcibly as those in the poisoned sciatic nerve of the non-poisoned leg, even regions, when applied to a part where the poison had | In twenty-four hours, the frog was found dead, access, still caused vigorous movements below with all its muscles rigid. the ligatures, These experiments prove distinctly that sulphate of methyl-morphium does not possess, in any degree, the convulsant action of morphia, but that it causes paralysis in place of convulsions. They also prove that this paralysis is due to an effect on the motor nerves. We have further determined, by the same method of experiment as has been already frequently described, that the peripheral terminations are the parts of the motor nerves which are primarily affected. Iodide of methyl-morphium produces the same effects on frogs as sulphate, only a larger dose is required. The poisonous activity of sulphate of methyl-morphium does not appear to be very different from that of a salt of morphia; for we have seen that for rabbits ten grains is about the minimum fatal dose of the former by subcutaneous injection, and this contains about eight grains of morphia, which is little above the fatal dose when subcutaneously exhibited. We have placed these and several other results, in a form convenient for comparison, in the following table. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 187 No. of Substance Animal and its Method of apne Dose. Effect. Experiment. employed. weight. exhibition. CI. Iodide of methy1-| Rabbit, 2 lbs. 140z.| Subcutaneously. | 20ers. (contain-| No effect. morphium. ing 133 grs. of dry morphia), CY. Morphia. Do. (same rabbit | Subcutaneously. | 8 grs. (contain- | Sleep in 1 hour and 4 as in Experiment ing 7‘Sgrs. of| minutes, epileptic con- CI.) dry morphia).| vulsions in about 48 hours, and death some hours afterwards. CVI. Iodide of methyl-| Do., 3 1bs. 12 0z. | By stomach. 30ers. (contain- | No effect. morphium. ing 20 grs. of dry morphia). CVII. | Morphia. Do. (same rabbit| By stomach. 5 ers. (contain-| Sleep in 1 hour and 6 as in Experiment ing 4°7 grs. of| minutes, and catalepsy CVI.) dry morphia).| inlhourand 25minutes; thesesymptoms lasted for nearly 3 hours and 30 minutes, and were fol- lowed by recovery. CXII. | Sulphate of me-|Do.,3 Ibs. 1 oz. | Subeutaneously. | 8 grs. (contain- | Sleep and partial paralysis thyl-morphium. ing 6°6 grs. of| in 14 minutes, continu- dry morphia).| ing for more than 2 hours and 16 minutes, and followed by recovery. CXIII. | Sulphate of me-| Do., 3 lbs. 8 oz. | Subeutaneously. | 10 grs. (contain-| Paralysisin 8 minutes, and thy-morphium. ing 8:2 grs. of| doubtful sleepiness in 10 dry morphia), | minutes; the paralysis became gradually more complete, andterminated in death, at 1 hour and 2 minutes after the admini- stration of the poison. CXXI. |Sulphate of me- | Do., 4 lbs. 33 oz. | By stomach. 20 grs. (contain-| No effect. thyl-morphium. ing 16:4 grs. of dry morphia). NICOTIA. The last substance in which we have now to describe the modifications pro- duced by chemical addition is nicotia. This is a liquid alkaloid of great poisonous energy, derived from tobacco. It is a di-acid nitrile base, and has the formula (C,H, ,N,). Lodide of methyl-nicotiwm.—Von PLANTA and KEKkvuii* investigated the action of iodide of ethyl on nicotia, and described a number of the ethyl-nicotium salts. The compounds of methyl-nicotium were investigated and described by STaHL- scHMIpT.t When excess of iodide of methyl is added to nicotia, a considerable amount of heat is developed, and it is advisable to immerse the flask in which the mixture is made in cold water, in order to moderate the action; by this means the product (iodide of methyl-nicotium (C,,H,,N,(CH,D),) is obtained nearly colourless, and crystallises almost as soon as it is cold. The crystalline * Annalen der Chemie und Pharmacie, vol. Ixxxvii, p. 1 (1858). + Ibid. vol. xe. p. 222 (1854). VOL. XXV. PART I. 3B 188 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN powder is washed with a little cold alcohol, and crystallised from hot rectified spirit. Thus obtained, it forms tolerably large prismatic crystals, perfectly trans- parent and colourless, and free from the peculiar odour of nicotia. It is ex- tremely soluble in water, so that for our purpose it was scarcely necessary to prepare the sulphate. More for the sake of symmetry, however, than because we expected to find any difference in action, we did so. A dose of five grains of iodide of methyl-nicotium, exhibited by subcutaneous injection, produced no effect on a rabbit. Ten grains caused trembling and slight impairment of motility; and the same symptoms occurred, in a somewhat exaggerated form, after the administration of fifteen grains: but recovery took place after both doses. The subcutaneous injection of twenty grains was fol- lowed, after several hours, by death. In the following account of the experiments in which fifteen and twenty grains were exhibited, it will be seen that no convul- sive movements occurred during the progress of the symptoms. EXPERIMENT CXXVII.— We injected fifteen grains of iodide of methyl-nicotium, dissolved in ninety minims of distilled water, into the subcutaneous cellular tissue of a rabbit, weighing three pounds. In eleven minutes, some trembling occurred, which, however, did not continue long; but it recurred in twenty- three minutes. In thirty minutes, it was observed that the head was supported with great difficulty, and shortly after it fell on the table, and the rabbit assumed a crouching attitude. There was no trembling so long as it was not disturbed; but whenever this was done, and when attempts were spontaneously made to assume some different position, the trembling recommenced. It continued in this condition for about an hour; soon afterwards the head was raised, and the trembling ceased. The rabbit was jumping about in a perfectly normal state two hours and three minutes after the administration. EXPERIMENT CXXVIII—We injected twenty grains of iodide of methyl- — nicotium, dissolved in ninety minims of distilled water, into the subcutaneous cellular tissue of a rabbit, weighing about three pounds. In eight minutes, some trembling. of the fore-legs was observed, which, however, soon ceased, and the rabbit sat down and remained quiet. In twenty minutes, the head fell upon the — table, the neck muscle being apparently unable to support it ; and in twenty-eight minutes, the paralysis had so far extended to the body that the rabbit, being unable to maintain even a crouching attitude, fell on the side. In one hour, it © was in the flaccid condition of the last note, but the respiratory movements were — few and feeble. In two hours and ten minutes, the respirations consisted of occasional gasps merely, and death appeared imminent. The observationswere unfortunately now (4 p.m.) interrupted until the following morning, when (10°15 a.m.) the rabbit was dead, and in rigor mortis. In accordance with the plan followed in this investigation, we shall no CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 189 describe the effects that are produced by nicotia itself,—and in order to obtain as exactly comparable data as possible, a portion of the nicotia used in the prepara- tion of the iodide of methyl-nicotium employed in Experiments CX XVII. and CXXVIII. was administered to the rabbit which recovered from fifteen grains of the latter substance. EXPERIMENT CXXXII.—One half-minim of nicotia (about 0°5 grain) was dis- solved in fifteen minims of very dilute sulphuric acid, and the solution was injected into the subcutaneous cellular tissue of the rabbit employed, a week pre- viously, in Experiment CXXVII. Symptoms were rapidly produced. In two minutes, spasmodic contractions occurred in the four limbs, which became extended, and raised the body ina convulsive manner. In three minutes, violent tremors occurred, and the whole body was convulsively agitated. In a few seconds afterwards, the limbs altogether yielded ; the rabbit lay on the abdomen ; and strong twitches occurred in the muscles of the neck, by which the head was jerked upwards, and in the limbs, by which the body was partially raised. This condition continued until ten minutes, when the spasmodic twitches ceased, and the rabbit fell on the side. It was now perfectly flaccid, with only twenty-five laboured respirations in the minute. In fourteen minutes, the respiratory movements were so feeble as to be scarcely visible; and, in fifteen minutes, they altogether ceased. In the autopsy, the heart was tound contracting, five minutes after death, at the rate of 160 per minute, but its contractions were feeble. The vermicular movements of the intestines appeared to be normal. The trunk of a sciatic nerve was irritated, ten minutes after death, and energetic movements followed in the limb to which the nerve was distributed. Having found, in the case of iodide of methyl-nicotium, that so large doses of an extremely soluble substance were necessary to affect a rabbit by subcutaneous injection, we did not consider it advisable to determine how much was required to produce symptoms when it is exhibited by the stomach. For it may be almost positively asserted that, in the latter case, a much larger dose would be necessary; and while the administration of this would be inconvenient, because of its bulki- ness, and of the difficulty of obtaining a large quantity in a perfectly pure form, the data obtained by subcutaneous injection are sufficient to prove the principal change that the addition of iodide of methyl produces in the physiological action of nicotia—namely, a great diminution in its poisonous activity. Sulphate of methyl-nicotium (C,,H,,N,(CH,),SO,) was prepared by precipi- tating a solution of the iodide by means of sulphate of silver. It forms a white, crystalline mass, extremely soluble in water. On account of the readiness with which iodide of methyl-nicotium dissolves in water, it was not to be expected that any change in poisonous activity would be caused by its conversion into a sulphate; and the following experiment con- 190 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN firms this surmise, by showing that the activity of the sulphate is apparently no greater than that of the iodide. EXPERIMENT CXXXIII.—Ten grains of sulphate of methyl-nicotium, dissolved in ninety minims of distilled water, was injected into the subcutaneous cellular | tissue of a rabbit, weighing four pounds and three ounces. In ten minutes, some trembling occurred, accompanied with partial paralysis of the fore-legs. In twenty minutes, the head fell on the table, and, at intervals, series of tremors shook the whole body. It continued in this condition, the body being still sup- ported by the legs, until fifty minutes, when ineffectual attempts were made to raise the head. These attempts were frequently repeated, and were finally successful at one hour and ten minutes; but the trembling, though now very slight, did not altogether cease until one hour and twenty minutes. After this, the rabbit seemed perfectly well. In the absence of any very trustworthy or complete investigation into the mode in which nicotia acts, we cannot ascertain exactly how far its physiological properties are modified by chemical addition. It would appear, however, that the convulsive movements which are described as always occurring during nicotia poisoning, and which were well marked in Experiment CXXXIL. are not among the symptoms produced by either iodide or sulphate of methyl-nicotium. The action of these substances is characterised by paralysis, accompanied with tremors, but unattended with spasms or convulsions. We performed the follow- ing experiments on frogs, in order to determine if this change were due not only to the disappearance of convulsive action, but also to the appearance of a paralysing action on motor nerves, similar to that so prominently possessed by the methyl derivatives of the other alkaloids examined in this paper. EXPERIMENT CXXX.—The blood-vessels were tied in the left thigh of a frog, weighing 430 grains, and one grain of iodide of methyl-nicotium, dissolved in fifteen minims of distilled water, was then injected into the abdomen. In ten minutes, the anterior extremities had become so weak that they could not alto- gether support the thorax, but still the frog jumped about with considerable activity. In twenty-five minutes, the movements were sluggish, and the jumps were by no means so active as formerly, while some trailing of the posterior extremities was observed. The heart was acting at the rate of forty-two in the minute. In thirty-five minutes, irritation of any portion of the skin was followed by contractions of all the limbs, but these appeared to be rather more energetic in the left posterior (non-poisoned) limb than in the others. In forty minutes, the respirations were feeble, but the frog was sufficiently powerful to turn itself — when placed on the back. In fifty-five minutes, severe pinching caused only slight reflex movements, of nearly equal strength, in both posterior extremities. — In fifty-seven minutes, it was unable to turn when placed on the back, and the heart’s contractions were at the rate of thirty-seven per minute. In one hourand ~ CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 191 thirty-nine minutes, irritation of any portion of the skin was followed by feeble, but nearly equal, movements of the four limbs. The observations were now interrupted. On the following morning the frog was jumping about normally. EXPERIMENT CXXXI.—The blood-vessels were tied at the right knee of a frog, weighing 630 grains, and three grains of iodide of methyl-nicotium, dissolved in twenty minims of distilled water, was injected into the abdomen. In twenty-six minutes, the frog was lying, flaccid, on the abdomen and chest; and when the skin was irritated, reflex movements of equal strength were caused in the four limbs. In one hour and sixteen minutes, the flaccid state had become more marked, and, now, a somewhat stronger irritation was requisite in order to cause reflex movements, while these appeared to be of greatest strength in the right posterior (non-poisoned) limb. In two hours and forty-six minutes, the condi- tion was exactly the same as last noted. The observations were now inter- rupted ; and on the following morning the frog was found dead, and in rigor. We obtained similar results with the sulphate. It would, therefore, appear that though the convulsant effects of nicotia are not produced by its methyl derivatives, these derivatives do not possess any paralysing action on motor nerves. The change that is produced in the physio- logical action of nicotia is not the same as that which we have described in strychnia, brucia, thebaia, codeia, and morphia. We are inclined to believe, on account of this difference, that the convulsions of nicotia are not due to the same cause as in the other alkaloids we have examined. A great diminution in physiological activity has, however, been produced by this chemical addition, and this will be at once recognised by referring to the following table :— No. of Substance Animal and its Method of : Dose. liffect. _+| Experiment. employed. weight. exhibition. Qs - CXXVII. | Iodide of methyl-| Rabbit, 3 lbs. | Subcutaneously.| 15 grs. (contain-| Trembling in 11 minutes, nicotium. 5°4 grs. of ni-| and partial paralysis in cotia). 30 minutes; these con- tinued for about 49 and 50 minutes respectively, and a perfect recovery afterwards occurred. CXXXII. | Nicotia (as sul- | Do. (same rabbit| Subcutaneously.| 0°5 min. (0.5 gr.| Convulsions in 3 minutes, phate). as in Experi- nearly), and partial paralysis in mentCXXVIT.) less than 4 minutes ; fol- lowed by death, 15 min- utes after administration. CXXXIII.| Sulphate of me- | Do., 4 lbs, 3 oz.|Subcutaneously.| 10 grs. (contain-| Trembling in 10 minutes, thyl-nicotium. ing 5°6 grs. of| slight paralysis in 20 nicotia). ininutes ; perfect recov- ery in 1 hour and 20 min- utes after administration. VOL. XXV. PART I. 30 192 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN Some experiments were made to determine, for our satisfaction, the physio- logical effects of iodide of methyl. The only bearing of these on the present investigation is, that no evidence was obtained in support of the extremely impro- bable hypothesis, that some of the changes produced in the action of the sub- stances we have described might have been due to addition of the physiological action of the methyl compounds. We have thus shown that chemical addition produces some important modi- fications in the action of those poisons which have been treated of in this com- munication. The action of strychnia, brucia, thebaia, codeia, morphia, and nicotia is evidently greatly diminished in degree, and, at the same time, strikingly changed in character. The former effect is shown with all these alkaloids, especially when their action is compared with that of the iodides of their methyl derivatives. As all these iodides are much less soluble than the salts of the alkaloids themselves, it might be supposed that the diminution in activity could be explained by this difference in solubility. Some support is given to this supposition, by examining the relations between various of the substances included in this investigation. Thus, it has been demonstrated, on the one hand, that, for rabbits, the fatal dose of iodide of methyl-strychnium administered subcutaneously, is about twenty grains, and that of iodide of methyl-thebaium is about ten grains ; while the former is soluble in 133 parts of distilled water, at a temperature of 37° C., and the latter in 16-5 parts at the same temperature. On the other hand, the fatal dose for rabbits, of sulphate of methyl-strychnium, is about four-fifths of a grain, and that of sulphate of methyl-thebaium is about five grains ; while both substances are freely soluble, and with nearly equal readi- ness, in cold water. In these examples, the greater activity of strychnia over thebaia is manifested when a soluble salt of the methyl derivative of strychnia_ is employed ; but when an extremely insoluble salt—the iodide—is employed, its activity is nearly the same as that of a corresponding preparation of thebaia; although the latter alkaloid is itself considerably less energetic than strychnia. It is, therefore, apparent that poisonous activity may be modified by the degree of solubility,—a well-recognised principle in toxicological physiology. But while the diminished activity of the iodides of many of these methyl deriva- tives may be greatly due to the difficulty of dissolving them, this explanation is inapplicable to iodide of methyl-nicotium,—an extremely soluble substance,—and it is insufficient to account for the differences of activity between the majority of the sulphates of the methyl] derivatives and the salts of the alkaloids themselves. Our investigation has not furnished us with any explanation of the change in these sulphates. There are several possible explanations, but we shall not — specially allude to them, as their discussion can only be properly undertaken after experimental examination of a laborious and difficult nature, and but indi- — CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 193 rectly connected with our present subject. When, however, we compare the activity of the sulphates of the majority of the ammonium bases considered in this paper with that of the corresponding iodides, we observe striking differences, which cannot be explained by differences of solubility alone, but which, we believe, must be also due to the remarkable stability possessed by these iodides. Strychnia is a much less soluble substance than iodide of methyl-strychnium, and yet a rabbit that survived the administration of fifteen grains of iodide of methyl-strychium, was killed in a few minutes by the administration of one- twentieth of a grain of strychnia. Before absorption, the strychnia may have been converted into a more soluble form, and this change may have facilitated its absorption, and permitted it to be carried by the blood-stream to the tissues it affects; but the great stability of the iodide of methyl-strychnium prevents its conversion into a more soluble form, and so impedes greatly the absorption. Just as in the more familiar case of the salts of lead, the sulphate is inert while the carbonate is poisonous, although they are both insoluble; and this difference of physiological action is undoubtedly due to the fact, that the carbonate, on account of its instability, is readily converted in the stomach into a soluble salt, while no such change takes place in the case of the sulphate. Stability may also influence the physiological activity of these iodides, even after their absorp- tion, by preventing those chemical actions on the tissues by which many of the effects of poisons are probably caused. The change in the character of the physiological action is remarkably illus- trated by strychnia, brucia, and thebaia, whose purely spinal-stimulant action is converted into a paralysing action on the periphery (end-organs) of motor nerves ; it is apparent in codeia and morphia, whose convulsant action is also converted into a paralysing action on motor nerve end-organs, and whose hypnotic action is apparently altogether destroyed in the case of codeia, and certainly greatly | diminished in that of morphia; and it is obviously, though less so than with the others, in the case of nicotia, whose convulsant action is diminished if not alto- 'gether removed. We may conclude from these facts, that when a nitrile base | possesses a strychnia-like action, the salts of the corresponding ammonium bases ‘have an action identical with that of curare. |. It is well known that curare and strychnia are derived from plants belong- ‘ing to the same genus, and it is, therefore, interesting to observe such a irelationship. It may not, however, be altogether superfluous to add, that istrychnia, brucia, and the other spinal-stimulant alkaloids examined in this ipaper, have not been converted by chemical addition into curarina,—the ‘active principle of curare. The action of the methyl derivatives of these |system, but the degrees of their activity are very different. If we confine our 194 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN attention to the salts of the methyl! derivatives of strychnia, brucia, and thebaia, where the action is uncomplicated, we observe that they form a series in which the fatal dose varies for each, while this dose in the case of the most active of the three is considerably above that of curare, and greatly above that of curarina. Besides, curarina has a characteristic colour reaction that belongs to none of these bodies; and the latter further prove this dissimilarity by each of them possessing special colour reactions by which they may be distinguished from each other. It is not only of great interest, but probably of some practical value, that five new compounds should be found having the physiological action of curare. The ereat difficulty of obtaining this substance has hitherto proved a serious barrier to its therapeutical employment. Although none of the compounds that we have shown to act as curare does are so energetic as that substance, three of them—sulphate of methyl-strychnium, sulphate of methyl-brucium, and sulphate of methyl-thebaium—are sufficiently so to fulfil all possible therapuetical require- ments, and even to rank as powerful poisons. Moreover, they may be readily obtained in a state of perfect purity, and, therefore, of constant strength; and, in this respect, they possess a great advantage over curare. The six alkaloids we have examined may be divided into two classes, accord- ing to the readiness with which they combine with iodide of methyl. The one — class includes strychnia, brucia, thebaia, and nicotia; and the other, codeia and morphia; and the combination is much more easy with the former than with the latter class. Without attaching any general significance to the occurrence, it — may not be altogether unworthy of being pointed out that in our experience, therefore, the more active poisons are the more readily acted upon by iodide of methyl. It is curious, though not unexpected, that the ordinary colour reactions of the alkaloids are retained by their methyl derivatives. This may possibly prove of some importance to the medical jurist ; and as these compounds are not preci- — pitated by alkalies, nor by the carbonates of the alkalies, some difficulty may be met with in discovering their presence in cases of poisoning. 195 CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. (TAX Juoursedxq) tmuniayokrs - [Aqyour JO aprpor jo ‘sid OZ POATAINS sv yIqqvs ouleg “AX Juourrodxy } 10}Jv SINOY QF epeur j -odxq + =“jiqqea ouleg (ITA Juoursedxq) umnruyoX14s-[Aq}our Jo OPIPOL JO “sid GT POAlA “Ins se 4iqqeit soured e014} Wo “4Iqqvt ouIeg *S9]ONT ‘sojnurut LE *SOJNUIUL GF *paArTosqo JON *poaresqo40Ny *so]NUIU 0G *sanoy S Ueyy e10j *sumojduds jo uoljeing "So|NULULZZ Ul WoroUuNy ‘SUOIS[NAWOD OIUL TO} xnpez jo | puesuseds snorounu uorjeressexy | Aq pepessid ‘yyroq ; “OO NT ‘QUON “OUONT ONE *SUOIS[NATOD O1UP}0} sno1ounu pure suseds ‘sojnutm g | Aq popoosord ‘yyveq *SOJNUIUL ZT *stsA[eieg *SO|NULUL TT. ‘stsk[Rieg *OUONT ONG *stsAyered ‘soynuimt QZ | Aq poposard ‘yyeoq *‘£19A0001 ‘soynutut Gp | fq pomojoy stsdyTereg DIONE an ‘QUONT "ou0 NT LONE *om0N *ou0N ‘suojd fs jo JuotWooMeU -U100 puv UOT}e.14 Borhicg -SIUIMIPe Ody -0q [eAIOJUT "13 610-0 ‘sd OG "Sid OZ ‘sa3 CT ‘sIS ZI "I3 0.0 IS ¢.0 13 ‘sa3 ¢ "13 T ‘S18 0G *s13 CT "SIs ZI ‘sIS QOL ‘sI3 Q ‘sI8 9 ‘SIS 9 ’ “4X04 OY} UL poyerodioour u9eq GALT, MOT} JO MOj V JO STIVIOp O17} 4ey} POATAsqo oq [IIA I puw systrojse uv Aq poysinsuystp ore Loy, ‘roded oy} Jo Surpvor oy} Io}ye powmtojiod o10M O[qUT, SIU UL pepnpoUr syuoumtLedxe ot} Jo [eIIAEG y ai 6a “OGL “oC “qoemoys Aq -o” a ‘pofoydure quetared xny * eourysqug JO “ON = Se) > VI.—On the Products of the Destructive Distillation of Animal Substances. Part V. By THomas ANDERSON, M.D., Professor of Chemistry in the University of Glasgow. (Read 20th April 1868.—Sent for publication, November 1868). In the fourth part of these researches, I described a new base produced by the action of sodium upon picoline, to which I gave the name of Parapicoline, because it has the same composition as picoline, although the circumstances of its formation appeared to show that it had been produced by the combination of two molecules of that substance, so that its true formula would be C,,H,,N,. Unfortunately, its high boiling point, and tendency to decompose when distilled, made it impossible to determine its vapour density, which afforded the only means of ascertaining whether this hypothesis was correct; and it was only assumed, because similar cases of polymerisation had been established beyond a doubt in the case of other classes of organic compounds. In the hope of obtaining a similar base of lower boiling point, and therefore better adapted to the necessary experiments, I have submitted pyridine to the action of sodium, and the results of the inquiry are contained in the following pages. My earlier experiments were conducted in precisely the same manner as those with picoline. Dry pyridine was heated to its boiling point along with small pieces of sodium, amounting to about one-fifth of its weight, in a flask furnished with a long cohobating tube. As the temperature rose, the pieces of sodium became covered with a brown coating; purple streaks appeared in the fluid, which, however, soon disappeared again; and after some hours the whole fluid was converted into a dark-brown or black mass, which was viscous when hot, and on cooling solidified into a hard brittle resin. In this a few white powdery nodules are disseminated, which explode violently when brought in contact with water. A large portion of the sodium employed remains unacted on, and if _ the operation has been well performed, is generally found collected into one or two large pieces, which can be easily separated from the resinous mass. After | the sodium has been removed as thoroughly as possible, the crude product is | thrown into water in small successive portions, so as to avoid the risk of explo- 'sions from any particles of sodium which may have remained disseminated | through it. The water soon becomes alkaline, owing to the presence of caustic | soda; unchanged pyridine makes itself manifest by its powerful smell, and the | resin is slowly converted into a thick, viscid oil of dark-brown colour, and nearly, | or altogether, insoluble in water, which collects at the bottom of the vessel. This | oil is washed several times with water, dried over calcic-chloride, and distilled. | The distillation is best effected in a current of hydrogen, and at a temperature VOL. XXV. PART I. 3 G 206 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE below the boiling point of the oil. A little unchanged pyridine distils at first, accompanied by a small quantity of a light oil, insoluble in water, having a pun- gent smell similar to, and yet appreciably different from, that of pyridine; and which, as we shall afterwards see, appears to be a mixture of several bases. As the temperature rises, a thick, heavy, and yellowish oil, having a peculiar smell, in no degree pungent, but dull, heavy, and somewhat resembling that of soot, passes over. As the distillation proceeds, crystals make their appearance in the neck of the retort. Ata certain stage of the process the product becomes nearly solid, and on cooling, crystals are deposited from the fluid distillate. Towards the close of the distillation some ammonia and very volatile bases are evolved, obvi- ously produced by the decomposition of the oil passing over; and adark resinous mass remains in the retort, which can be forced over by raising the temperature, in doing which a large part of it is decomposed, and a residue of charcoal is left in the retort. The products of the action being obviously complicated, the whole was cautiously redistilled, and the portion which solidified in the neck of the retort collected apart, while the fluid portions having been introduced into a freezing mixture of snow and salt, soon gave an abundant crop of crystals. These were purified by pressure between folds of filtering paper, and crystallisation from water or alcohol, in both of which they are soluble, until they have lost the smell of the oil by which they are accompanied. After having proceeded some way in the investigation, I found that the same substances could be obtained with greater certainty by a modification of the pro- cess just described. It is by no means necessary to heat the sodium and pyridine together, for the action takes place in the cold; but in this case it is slower, and the phenomena are somewhat different. The brown appearance on the surface of the sodium and the purple streaks appear in the fluid at the beginning of the action, but the pyridine does not become brown, it retains its colour, and the sodium is covered with a black crust, which, after two or three days, exceeds it in bulk, is quite brittle, and sometimes shows a tendency to separate into layers. The pyridine acquires a yellowish tint, and then contains in solution an oil insoluble in water. When the action is judged to have gone sufficiently far, the sodium with its crust is removed from the fluid and washed with a small quantity of pure pyridine, so as to get rid of any of the oily base which may remain attached to it. The crust is then detached as thoroughly as possible from the sodium and thrown into water, any sodium still adhering to it burns, and a dark gray, almost black, powder falls to the bottom of the glass. This is washed first by decanta- tion, and afterwards on a cloth filter until it is free from soda, and on being opened out and exposed for some time to the air, it is entirely converted into a snow-white mass of interlaced acicular crystals identical with those obtained by the first process. = ee DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 207 DIPYRIDINE. The substance so obtained is a base to which, for reasons that will be imme- diately apparent, I give the name of dipyridine. It forms white crystals fusing at 108° Cent., and solidifies on cooling into a crystalline mass. It volatilises slowly at 100°, and sublimes unchanged at a high temperature, giving long needle-shaped crystals. It is rather sparingly soluble in cold but readily in boiling water, and the fluid, on cooling, becomes filled with a mass of interlaced needles. It is readily soluble in alcohol and ether, and the boiling solutions give acicular crystals on cooling. It likewise dissolves in pyridine and in volatile oils. From the oily base along with which it distils in the first process of preparation, it crystallises in short, thick, four-sided prisms, which are transparent so long as they remain in the fluid, but soon become opaque when they are removed from it. When well purified they are inodorous, but in general they have a faint smell, due, apparently, to a trace of the fluid base adhering to them. Dipyridine is a very stable com- pound. Itis not decomposed by hydrochloric, sulphuric, or nitric acids. Potash and ammonia precipitate it from its solutions in acids as a mass of minute crystals. Its aqueous solution gives no precipitates with solutions of sulphate of magnesia, zinc, nickel, acetate of lead, or perchloride of iron. With sulphate of copper it gives a pale bluish-white precipitate, with corrosive sublimate a white amorphous powder insoluble in boiling water, and with nitrate of silver a white precipitate insoluble in cold and sparingly in boiling water, from which the compound is obtained in crystals on cooling. Its most characteristic reactions, however, are those it gives with the ferro- and ferri-cyanides of potassium. If a few drops of the ferrocyanide of potassium be added to a not too dilute solution of the dipyridine hydrochlorate, a pale precipitate makes its appearance, which rapidly changes to a dirty indigo colour, increasing at the same time in quantity. Ifthe proper concentration is hit, the precipitate consists entirely of very minute needle-shaped crystals having a dark indigo colour. They dissolve in boiling water, forming a very deep and rather dull purple solution, and are again deposited on cooling; but if the boiling be continued for some time, the compound appears to undergo some change, for the fluid retains its red colour at ordinary temperatures, though a great part of the substance is still deposited in crystals. A saturated cold solution of dipyridine in water gives no precipitate with ferrocyanide of potassium, but on the addition to the mixture of a drop or two of hydrochloric acid the dark precipitate instantly makes its appearance, and is deposited in small crystals. The precipitate is readily soluble in excess of hydrochloric acid. When ferricyanide of potassium is added to dipyridine hydrochlorate no immediate effect is observed, but on standing, the interior of the test-tube becomes lined with minute prisms of sulphur yellow colour and high lustre. If the solution be boiled, it acquires a dark colour, and partial decomposition takes place. 208 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE Dipyridine carefully dried in the water bath was found on analysis to give these results :— 0:2802 gramme dipyridine gave I 0-7782 ... carbonic acid, and ( O:1497° ... water. 0:3600 gramme dipyridine gave 10 i 0°8367 ... carbonic acid, and 0:1575 ... water. Experiment. Calculation. Sxipils i Carbon, F . 75°74 76:07 75:94 C, 60 Hydrogen, . . 5:94 5°83 633 4H, 5 Nitrogen, , in coe 17°73 N 14 100-00 79 These numbers lead to the formula C,H,N, which is that of pyridine itself. The platinum compound of the base, which is thrown down as a yellow crystalline powder, gave the following results :— L { 0°3345 gramme gave 01175 ... platinum. u 0:2007 gramme gave ; 0:0685 ... platinum. IIL. 0:4335 gramme gave 0:1473 =~... ~— platinum. 0'4052 gramme gave IV. 0°3087 ... carbonic acid, and 0:0905 ... —~water. Experiment. Calculation. ie IL. III. Carbon, : ; eee a8 20:78 21-02 Ch 120 Hydrogen, . é one ah 2°48 2:10 Hs 12 Nitrogen, . : sae hae ae 4:90 Ne 28 Chlorine, . : ae Ae sep 37°30 Cl, 213 Platinum, . : 34:11 34:12 34:03 34:68 Pt 197-4 100-00 570-4 This agrees with the formula (C,H, NHC1),PtCl,, which is identical with that of the pyridine salt. In order to fix the true constitution of the base, it was necessary to determine its vapour density, and as its boiling point was beyond the range of the mercurial thermometer, it was necessary to use a bath of metallic lead and an air thermometer. The air thermometer was a bulb of the same size as that used for containing the vapour, and the details of the experiment were as fol- lows :— | | q DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. Weight of vapour bulb empty, full of vapour, Temperature at ‘weighing, Barometer, Volume of bulb, Residual air, Hence Weight of bulb and vapour, air displaced, Weight of bulb and vapour in vacuo, bulb, 22-2530 22°4806 B59 753 mm. 197-1 CC 0-2 C.C. 22°4806 0°1552 22-6358 22-5230 0°3828 Residual air, Weight of vapour, Weight of air thermometer, : partly full of mercury, Barometer 753 — 67:5 . : Temperature, Air thermometer full of mercury, Hence ieee of mercury partially filling bulb, completely, and 26666 — 14127 = 12539. Now, we have here in the formula WCE nag ee ta se We he wil’ W = 26666 w = 12539 H = 753 h = 685°5 a = 0:00366 k = 0:00003 free 175 whence t = 414°4 Cent. Now 1271 — 05 = 126°5,* d 126°5 753 1:29366 an 1 4 4144 x 0:00366 * 760 * 1000 0:3825 and |. 0:0003 0°3825 264 = grains. 14391 685°5 mm. by aC: 26930 14127 26666 = 0:0646, 09 The formula C,,H,,N, requires 5:46. This result is as close as could be expected under the circumstances, and proves that the base must be formed by the com- * 0:6 is the volume of the residual air at 414°. VOL.EXOaVy. PARD Ir 210 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE bination of two molecules of pyridine, and hence the name of dipyridine which I have applied to it. Salts of Dipyridine.—Though dipyridine is not a very powerful base, it gives a number of salts, most of which crystallise well, though some of them are not easily obtained of definite composition. Hydrochlorate of Dipyridine.—This salt is best obtained by adding a slight excess of hydrochloric acid to the aqueous solution of the base and evaporating to crystallisation; the crystals, after being pressed and recrystallised from water, are sufficiently pure for analysis. They are flat needles readily soluble in water, especially when hot—insoluble in ether. The salt is very apt to retain hydro- chloric acid, and it is advisable to heat it to 130° for analysis. 0-6104 gramme of the hydrochlorate gave 0:7633 iodide of silver. Experiment. Calculation. Carbon, 51:94 Cio 120 Hydrogen, 519 is De 12 Nitrogen, me 12-13 N, 28 Chlorine, 30:93 30°74 Cl, 7 100-00 231 Sulphate of Dipyridine.—Dipyridine is added in slight excess to dilute sul- phuric acid, and this fluid is evaporated nearly to dryness; on cooling, crystals of the sulphate are deposited; they are washed with alcohol, in which they are scarcely soluble, and again crystallised from water. It is thus obtained in needle-shaped crystals, which deliquesce in moist air. One determination of sulphuric acid was made of a specimen of this salt dried in vacuo over sulphuric acid, which gave 26°85 per cent. of SO,.. This would correspond with a salt containing two molecules of water of crystallisation with the formula C,,H,,N,H,SO, + 2H,0, which requires 27:39 per cent. Nitrate of Dipyridine is obtained by adding a slight excess of nitric acid to solution of dipyridine, evaporating on the water-bath and recrystallising. It forms pale yellow needles of moderate solubility in water. When exposed for some time to a temperature of 100°, it acquires an orange colour, but is not sensibly decomposed. A combustion of this salt gave 0°5162 gramme of the nitrate gave it, 0:7915 of carbonic acid, and 0:1820 of water. Experiment. Calculation. Carbon, 41°81 42°25 Cc. 120 Hydrogen, 3°92 3°92 fa 12 Nitrogen, aie 20°38 Ny, 56 Oxygen, 33°45 O, 96 100-00 284 DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 211 Double Salt mith Chloride of Zinc.—This substance is prepared by adding to dipyridine a mixture of hydrochloric acid and zinc chloride, and allowing it to stand for some time, when small prismatic crystals are deposited. Their formation is materially assisted by the addition of alcohol and ether. The compound may even be obtained from the crude product, in which the dipyridine is mixed with the oily base distilling along with it. For this purpose zine chloride, along with hydrochloric acid and a considerable excess of alcohol and ether, must be added to the crude product, when, especially on stirring, the zinc salt deposits, and can be purified by crystallisation from water. This process can even be em- ployed for separating the two bases. The salt is in long white needles, soluble in eight times their weight of water, less so in alcohol, and quite insoluble in ether. On the addition of potassic hydrate in excess it gives the pure base in minute crystals. A chlorine determination gave foie gramme zinc salt gave 05755 ... dichloride of zine. Experiment. Calculation. — = , Carbon, ; . oof 32°70 Cio 120 Hydrogen, , one 3°27 lees 12 Nitrogen, ; : 23 762 N, 28 Chlorine, ; é 38°90 38°68 Cl, 142 Zinc, . é 5 ss emo Zn. 65 100:00 367 Double Salt with Nitrate of Silver—This salt is best obtained by mixing hot solutions of dipyridine hydrochlorate, and silver nitrate, the latter being in excess, and at once filtering off the precipitated silver chloride. On cooling, the salt is deposited in brilliant needles, of sparing solubility in water. This com- _ pound could not be obtained of constant composition, but one specimen gave 35°09 per cent. of silver, while the formula C,,H,,N,(HNO,),(AgNO,), requires 34°61. Platino-chloride of Dipyridine—The analysis of this salt has been already given. It is obtained as a crystalline yellow powder of very sparing solubility. Palladio-chloride of Dipyridine is obtained as an orange precipitate on mixing the hydrochlorates. DERIVATIVES OF DIPYRIDINE. Diethylo-Dipyridine.—The compounds of this base were obtained in the usual manner. The ethyl-iodide is easily prepared by exposing dry dipyridine with iodide of ethyl to the temperature of 100° in hermetically sealed tubes. The action is complete in half an hour. It is obtained in acicular crystals, which are brilliant and perfectly colourless if they have not been exposed to the air. They are very soluble in water, much less so in alcohol and in ether. 212 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE 0:3997 gramme ethyl-iodide gave I 0:5195 ... carbonic acid, and 01530 ... water. Il 03512 gramme gave f 0:3513 ... iodide of silver. Experiment. Calculation. — SS Carbon, : : , 85°44 35°74 Cy, 168 Hydrogen, . ; 4°25 4:26 7 20 Nitrogen, . : : a5 5°96 Ne 28 Iodine, : : : 54:05 54:04 i, 254 100-00 470 Corresponding with the formula C,,H,,N,(C,H.I),. Heated with silver chloride and water this salt was converted into the chloride, which, on the addition of platinic-chloride gave the platino-chloride in very sparingly soluble small red needles. 02780 gramme platino-chloride gave 0:0685 ... platinum. This corresponds with 31:12 per cent., and the formula C,,H,,N,(C,H,Cl),PtCl, requires 30°44. The base itself, when separated from the iodide by silver oxide, forms a highly alkaline solution, having generally a red or purple colour, which, on evaporation, leaves a dark-coloured uncrystallised residue. It obviously belongs to the class of ammonium bases, but I have not pursued its investigation further. Dibromo-Dipyridine.—This base is thrown down when bromine is added to a solution of dipyridine hydrochlorate, or hydrobromate, as a white powder, insoluble in water, sparingly soluble in cold, more so in hot alcohol, from which it is depo- sited in flattened needles on cooling. If too much bromine has been used in its preparation, these crystals are pink. Its basic properties are extremely feeble, and it is a somewhat unstable compound; for, on boiling with water, or with hydrochloric acid, the original base appears to be more or less completely rege- nerated. An analysis, in which the hydrogen was lost, gave L ee gramme dibromo-dipyridine gave 04902 ... carbonic acid. ll -0°3420 gramme gave O40 7E ee: silver iodide. Experiment. Calculation. EE SEE Carbon, : : ; 37°56 37°97 Cio 120 Hydrogen, : bse 2:53 H, 8 Nitrogen, ‘ : dios 8°87 N, 28 Bromine, : ; : 50:74 50°87 Br, 160 100-00 316 DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 213 Its platinum compound could not be obtained in a state fitted for analysis. On boiling with hydrochloric acid, and adding platinic-chloride, a yellow precipi- tate was obtained, which, in one experiment, gave 32°39 per cent. of platinum ; and in another, in which the boiling was continued longer, 33°53 per cent. was obtained. Dibromo-dipyridine requires 30°94, and dipyridine itself 34°68; so that there can be little doubt that the latter has been regenerated. OILy BASE. The oily base from which the dipyridine was deposited in crystals, has been as yet but imperfectly examined. It was purified by redistillation and cooling, by which it yielded a small additional quantity of dipyridine, and this was re- peated as long as it gave crystals. The base so obtained is a rather thick, pale- yellow oil, heavier than water, having a peculiar heavy smell, quite distinct from that of pyridine. Itis insoluble in water, but dissolves with great ease in alcohol and ether. It boils at a high temperature, and if distilled rapidly, it undergoes partial decomposition, yielding a small quantity of what appears to be a mixture of several bases with pungent smell, and sparingly soluble in water. If, how- ever, the distillation be carried on very cautiously at a temperature below its boiling point, it passes over unchanged. It dissolves in acids and forms salts, most of which, however, are uncrystallisable. and dry up into gummy masses. It was prepared for analysis by drying over calcic-chloride, distilling and separat- ing the first part of the distillate which might retain moisture. 0:3420 gramme of the base gave I. ¢ 09605 ... carbonic acid. 021385) 2.) ) water. 03662 gramme of the base gave II. ¢ 10140 ... carbonic acid. 0:2300 =... ~ + water. Experiment. Calculation. tesa ei le. Carbon, . ; 76:59 7551 75:94 C, 60 Hydrogen, ; 6:94 6°98 6:33 Hi. 5 Nitrogen, . ' a a 17°73 N 14 100-00 a These results, it will be seen, correspond with those given by pyridine and di- pyridine, and they are confirmed by the analysis of a platinum salt, prepared in the usual way. heaiets gramme of the platinum salt gave 01015... _ platinum. This corresponds to 33:94, and calculation for the formula (C,H,NHCl),PtCl, requires 34:68. It is obvious, therefore, that this is another polymer of the VOL. XXV. PART I. 31 214 PROFESSOR T. ANDERSON ON THE PRODUCTS OF THE original pyridine; but, unfortunately, there is no means by which its molecular constitution can be determined. It is impossible to determine its vapour density, because it undergoes partial decomposition at its boiling point ; and as its salts do not crystallise, and probably, like the platinum compound, all correspond with those of the original pyridine, there is no prospect of satisfactory conclusions being drawn from them. In the absence of experimental evidence, any assump- | tion may be made regarding the constitution of this base, and at first sight the most reasonable view of the matter is to suppose it to be the product of afurther polymerisation, and to be formed by the combination of three or four molecules of the original pyridine. Its boiling point, which is certainly lower than that of dipyridine, however, appears to militate against this view; and taking its proper- ties and those of its compounds into consideration, I am inclined to believe it to be another dipyridine, and an example of those cases of physical isomerism of which so many are now known. As there was no means of ascertaining the constitution of this base, and the properties of its compounds were not encourag- ing, I have not pursued their investigation further. Licgut BaAsEs. It has been stated at the commencement of this paper that when dipyridine was prepared by the first of the processes there described, that a light basic oil was obtained at the beginning of the rectification of the crude product. This oil, which is insoluble in water, was collected, dried, and rectified when it was found to consist of several bases. ‘The distillate was collected in several frac- tions, which were analysed, but the quantity was far too small to admit of any systematic attempt to separatethem. ‘The results, both of the combustion of the bases themselves and of the platinum determinations in their platinum com- pounds, seem to show that they are a class of bases isologous with the pyri- dine series. I give here the results of these analyses :— O83s a Eee. ... earbonic acid, and 0°3025 gramme of base boiling between 225° and 240° F. gave I 0:2302 i... ows | WAUEES 0:4120 gramme of base boiling between 270° and 290° F. gave LN38Or ser ... carbonic acid, and ONS 230i. oo. ... Water. 0:2711 gramme of base boiling about 291° F. gave TE Oo Aae sere ... carbonic acid, and 0:1984 Py: ... water. 0:2708 gramme of base boiling between 287° and 291° F, gave Omiotle “Sere ... carbonic acid, and O20 92 ea. ... water. 0:2355 gramme of base boiling between 291° and 360° F. gave 06690... ... carbonic acid, MOTOR ee, ... Water. IV. V. DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 215 i TE Tae IV. Vv. Carbon, } re7orol 75°36 76:18 74:23 7747 Hydrogen, . . 8-46 8-71 8:13 8°58 8:47 Nitrogen, . - 16:03 15:93 15°69 T7A9 14:06 —— ———— ed ———— oy 10000 100:00 100-00 10000 100-00 It must be distinctly understood that all the substances analysed were obviously mixtures, and the degrees above given do not denote true boiling points, but only that the fractions they represent were collected at these points. It will be observed that all these analyses are characterised by yielding a per- centage of hydrogen far above that contained in pyridine, or any of its homo- logues. To render this more obvious, I place here the calculated numbers for pyridine and picoline, along with those required by bases containing two atoms of hydrogen more than these compounds :— C,H.N C,H,N OHN. CHUN Carbon, . 75°94 77-42 74:04 75°75 Hydrogen, . A 38/3) 7:53 8°64 9:47 Nitrogen, . Sa Meio 15:05 17:32 14-78 100:00 100-00 100:00 100:00 The experimental results above given are manifestly incompatible with the first two of these formula, but would agree tolerably with a mixture of substances containing more hydrogen, and this is further confirmed by several platinum determinations in platinum compounds obtained from these substances. These results appear to indicate the existence of a series of bases having the general formula C,H,,_,;N. The further investigation of these substances would be of interest, but as they are obtained only in minute quantity, and are clearly secondary products of the action of sodium on pyridine, it is scarcely possible to obtain them in sufficient quantity for this purpose. At the beginning of this paper, mention has been made of a black or dark-gray substance, obtained in the second process for preparing dipyridine. This com- pound was only obtained towards the close of the investigation, and I have not had time to examine its properties and relations minutely. It is a black amorphous powder, quite insoluble in water. When exposed to the air, it is rapidly converted into a mass of crystals of pure dipyridine. I was at first _ disposed to consider this substance to be a sodium compound of dipyridine, but I soon found that this was not the case, and that its properties more nearly corres- _ponded with a hydrogen compound of that base ; and it seems probable that its formula will turn out to be C,,H,,N,, in which case it would be related to 216 DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. dipyridine in the same manner as ammonium is to ammonia. Should this view be correct, it seems probable that, on the addition of hydrochloric acid, it should, like a metal, evolve hydrogen. An experiment was made to ascertain whether this occurred by introducing a quantity of the compound into a jar over mercury, and bringing hydrochloric acid in contact with it; but the anticipated result was not obtained—no hydrogen was evolved, but a brownish precipitate appeared in the fluid, and the gray powder at once disappeared. I have been unable to pursue this subject further, but propose to return to it on a future occasion. Numerous experiments have been made, in the hope of throwing light on the nature of the chemical changes occurring during the first process of preparing dipyridine; but it is obviously of a very complex kind, and some of the products must be the result of secondary decompositions. My impression is, that sodio- dipyridine must be first formed, probably C,,H,Na,N,. In this case hydrogen must be given off during the action, and this is actually the case, as was estab- lished by direct experiment; but the quantity evolved is trifling compared with that of the sodium consumed, so that if the action takes place in this way, a large part of the hydrogen must be converted into some other compounds within the mixture itself. The light bases already mentioned might account for this, if it were not that they are produced in very small quantity. Altogether I am inclined to think that, in the first process, a number of secondary reactions take place, which greatly complicate matters, and that it is through some modifica- tion of the second by which an explanation will most probably be obtained. I am still engaged with the subject, and have already nearly perfected a process by which some of the products can be obtained with greater certainty and in larger quantity than by either of those described in this paper, and which I hope will enable me to subject the constitution and relations of these curious com- pounds to a more minute examination. ‘ ic c Diagram showing stream lines traversing circular ring. Pe i nme = ace nites ia — _ < : Ky : a nie Wee. | i. COLA )\ mn LO ee 1 | | ne \ | PY ——— LS — a a—\.-\4 Soe LN Ge QUT VI.—On Vortex Motion. By Sir W. THomson. (Read 29th April 1867.) (2 2 1-59 recast and augmented 28th August to 12th November 1868.) 1. The mathematical work of the present paper has been performed to illus- trate the hypothesis, that space is continuously occupied by an incompressible frictionless liquid acted on by no force, and that material phenomena of every kind depend solely on motions created in this liquid. But I take, in the first place, as subject of investigation, a finite mass of incompressible frictionless* fluid completely enclosed in a rigid fixed boundary. 2. The containing vessel may be either simply or multiply continuous.; And I shall frequently consider solids surrounded by the liquid, which also may be either simply or multiply continuous. It will not be necessary to exclude the sup- ‘ position that any such solid may touch the outer boundary over some finite area, in which case it is not surrounded by the liquid; but each such solid, whether surrounded by the liquid or not, and whether moveable or fixed, must be con- sidered as a part of the whole boundary of the liquid. 3. Let the whole fluid be given at rest, and let no force, except pressure from the containing vessel, or from the surfaces of solids immersed in it, ever act on any part of it. Let there be any number of solids, perfectly incompressible, and of the same density as the fluid; but either perfectly rigid, or more or less flexible, with perfect or imperfect elasticity. Some of these may at times be supposed to lose rigidity, and become perfectly liquid; and portions of the liquid may be supposed to acquire rigidity, and thus to constitute solids. Let the solids act on one another with any forces, pressures, frictions, or mutual distant actions, subject only to the law of ‘‘action and reaction.” Let motions originate among them and in the liquid, either by the natural mutual actions of the solids or by the arbitrary application of forces to them during some limited time. It is of no consequence to us whether these forces have reactions on matter outside the con- taining vessel, so that they might be called “ natural forces” in the present state of science (which admits action and reaction at a distance); or are applied arbitrarily by supernatural action without reaction. To avoid circumlocution, * A frictionless fluid is defined as a mass continuously occupying space, whose contiguous portions press on one another everywhere exactly in the direction perpendicular to the surface separating them. | Heitmuoirz— Ueber Inteyrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen: Crelle (1858); translated by Tarr in Phil, Mag. 1867, i, Riemann—Lehrsdtze aus der Analysis situs, §c. Crelle (1857). See also § 58, below. VOL. XXV. PART I. uk 218 SIR W. THOMSON ON VORTEX MOTION. and, at the same time, to conform to a common usage, we shall call them impressed forces. 4. From the homogeneousness as to density of the contents of the fixed bounding vessel, it follows that the centre of inertia of the whole system of liquid and solids immersed in it remains at rest; in other words, the integral momentum of the motion is zero. Hence (THomson and Tart’s “ Natural Philosophy,” § 297) the time integral of the sum of the components of pressure on the containing vessel, parallel to any fixed line, is equal to the time-integral of the sum of the com- ponents of zmpressed forces parallel to the same line. This equality exists, of course, at each instant during the action of the impressed forces, and continues to exist for the constant values of their time integrals, after they have ceased. Thus, in the subsequent motion of the solids, and of the fluids compelled to yield to them, whatever pressure may come to act on the containing vessel, whether from the fluid or from some of the solids coming in contact with it, the components of this pressure, parallel to any fixed line, summed for every element of the inner surface of the vessel, must vanish for every interval of time during which no im- pressed forces act. If, for example, one of the solids strikes the containing vessel, there will be an impulsive pressure of the fluid over all the rest of the fixed con- taining surface, having the sum of its components parallel to any line, equal and contrary* to the corresponding component of the impulsive pressure of the solid on the part of this surface which it strikes [see § 8, and consider oblique impulse of an inner moving solid, on the fixed solid spherical boundary]. But, after the impressed forces cease to act, and as long as the containing vessel is not touched by any of the solids, the integral amount of the component of fiuid pressure on it, parallel to any line, vanishes. 5. If now forces be applied to stop the whole motion of fluid and solids [as (§ 62) is done, if the solids are brought to rest by forces applied to themselves only], the time integrals of the sums of the components of these forces, parallel to any stated lines, may or may not in general be equal and contrary to the time integrals of the corresponding sums of components of the initiating impressed forces (§ 3). But we shall see (§§ 19, 21), that if the containing vessel be infinitely large, and all of the moving solids be infinitely distant from it during the whole motion, there must be not merely the equality in question between the time integrals of the components in contrary directions of the initiating and stopping impressed forces, but there must be (§ 21) completely equilibrating opposition between the tivo systems. 6. To avoid circumlocution, henceforth I shall use the unqualified term impulse to signify a system of impulsive forces, to be dealt with as if acting on a rigid body. Thus the most general impulse may be reduced to an impulsive force, and couple * T shall use the word contrary to designate merely directional opposition; and reserve the unqualified word opposite, to signify contrary and in one line. SIR W. THOMSON ON VORTEX MOTION. 219 in plane perpendicular to it, according to PornsoT; or to two impulsive forces in lines not meeting, according to his predecessors. Further, I shall designate by the impulse of the motion at any instant, in our present subject, the system of impulsive forces on the moveable solids which would generate it from rest; or any other system which would be equivalent to that one if the solids were all rigid and rigidly connected with one another, as, for instance, the Pornsor resultant impulsive force and minimum couple. The line of this resultant impulsive force will be called the resultant axis of the motion, and the moment of the minimum couple (whose plane is perpendicular to this line) will be called the rotational moment of the motion. 7. But, having thus defined the terms I intend to use, I must, to warn against errors that might be fallen into, remark that the momentum of the whole motions of solids and liquid is not equal to what I have defined as the impulse, but (§ 4) is equal to zero; being the force-resultant of ‘‘ the impulse” and the impulsive pressure exerted on the tiquid by the containing vessel during the generation of the motion: and that the moment of momentum of the whole motion round the centre of inertia of the contents of the vessel is not equal to the rotational moment, as 1 have defined it, but is equal to the moment of the couple constituted by “ the impulse” and the impulsive pressure of the containing vessel on the liquid. It must be borne in mind that however large, and however distant all round from the moveable solids, the containing vessel may be, it exercises a finite influence on the momentum and moment of momentum of the whole motion within it. But if it is infinitely large, and infinitely distant all round from the solids, it does so by infinitely slow motion through an infinitely large mass of fluid, and exercises no finite influence on the finite motion of the solids or of the neighbouring fluid. This will be readily understood, if for an instant we suppose the rigid containing vessel to be not fixed, but quite free to move as arigid body without mass. The momentum of the whole motion will then be not zero, but exactly equal to the force-resultant of the impulse on the solids; and the moment of momentum of the whole motion round the centre of inertia will be precisely equal to the resultant impulsive couple found by transposing the constituent impulsive forces to this point after the manner of Poinsot. But the finite motion of the immersed solids, and of the fluid in their neighbourhood which we shall call the jield of motion, will not be altered by any finite difference, whether the containing vessel be held fixed or left free, provided it be infinitely distant from them all round. It is, therefore, essentially indifferent whether we keep it fixed or let it be free. The former supposition is more convenient in some respects, the latter in others ; but it would be inconvenient to leave any ambiguity, and I shall adhere (§ 1) to the former in all that follows. 8. To further illustrate the impulse of the motion, and its resultant impulsive force and couple, according to the previous definitions, as distinguished from 220 "SIR W. THOMSON ON VORTEX MOTION. the momentum, and the moment of momentum, of the whole contents of the vessel, let the vessel be spherical. Its impulsive pressure on the liquid will always be reducible to a single resultant in a line.through its centre, which (§ 4) will be equal and contrary to the force-resultant of “the impulse ;” and, therefore, with it will constitute in general a couple. The resultant, of this couple and the couple-resultant of the impulse, will be equal to the moment of momentum of the whole motion round the centre of the sphere (which is the centre of inertia). But if the vessel be infinitely large, and infinitely distant all round from the moveable solids, the moment of momentum of the whole motion is irrelevant; and what is essentially important, is the impulse and its force and couple-resultants, as defined above. 9. The following way of stating (S§ 10, 12), and proving (§§ 11—15), a funda- mental proposition in fluid motion will be useful to us for the theory of the impulse, whether of the moveable solids we have hitherto considered or of vortices. 10. The moment of momentum of every spherical portion of a liquid mass in motion, relatively to the centre of the sphere, is always zero, if it is so at any one instant for every spherical portion of the same mass. 11. To prove this, it is first to be remarked, that the moment of momentum of that part of the liquid which at any instant occupies a certain fixed spherical space can experience no change, at that instant (or its vate of change vanishes at that instant), because the fluid pressure on it (§ 1), being perpendicular to its surface, is everywhere precisely towards its centre. Hence, if the moment of momentum of the matter in the fixed spherical space varies, it must be by the moment of momentum of the matter which enters it not balancing exactly that of the matter which leaves it. We shall see later (§§ 20, 17, 18) that this balancing is vitiated by the entry of either a moving solid, or of some of the liquid, if any there is, of which spherical portions possess moment of momentum, into the fixed spherical space; but it is perfect under the condition of § 10, as will be proved in § 15. 12. First, I shall prove the following purely mathematical lemmas; using the ordinary notation wu, v, w for the components of fluid velocity at any point (@, 'Y, 2). Lemma (1.) The condition (last clause) of § 10 requires that udx + vdy + wdz be a complete differential,* at whatever instant and through whatever part of the fluid the condition holds. Lemma (2.) Ifwdax + vdy + wdz be a complete differential of a single valued function of x, y, z, through any finite space of the fluid, at any instant, the con- dition of § 10 holds through that space at that instant. * This proposition was, I believe, first proved by Stokes in his paper “ On the Friction of Fluids in Motion, and the Equilibrium and Motion of Elastic Solids.” Cambridge Philosophical Transactions,” 14th April 1845. SIR W. THOMSON ON VORTEX MOTION. 221 13. The following is Sroxes’ proof of Lemma (1):—First, for any motion whatever, whether subject to the condition of § 10 or not, let L be the component moment of momentum round OX of an infinitesimal sphere with its centre at O. Denoting by /// integration through this space, we have = /{f (wy — v2z)dxdy dz : : : (1). Now let (Ge) i &c. denote the values at O of the differential coefficients. We have, by Mactaurin’s theorem, on Ne dat Y \ dy dz i , and so for v. Hence, remembering that (Z , &c. are constants for the space 0 w=2 through which the integration is performed, we have fda dy dzwy = =) Sf ay dx dy dz + (=) fy? da dy dz + we =) Sf zy da dy dz. 0 0 The first and third of the triple integrals vanish, because every diameter of a homogeneous sphere is a principal axis; and if A denote moment of momentum of the spherical volume round its centre, we have for the second Lfy? dedydz=A.. Dealing similarly with vz in the expression for 2 we find =34[(%) -(3 ale . (2). But L must be zero according to the condition of § 10; and, therefore, as the centre of the infinitesimal sphere now considered may be taken at any point of space through which this condition holds at any instant, we must have, through- out that space, do _ do _ dy dz | 2 ae du OB x. and similarly rie ee PUREE Aare 2 EM BY: dv du _ a dy which proves Lemma (1.) 14. To prove Lemma (2.), let _ _ dp _ do “u= ae v= dy , w= ae . 5 ° . ci (4) 3 and let L denote the component moment of momentum round OX, through any spherical space with O in centre. We have [ (1) of § 13], VOL. XXV. PART I. 3.1L 222 SIR W. THOMSON ON VORTEX MOTION. L=S{f da dy dz (wy — v2) . ) : ; (5), // denoting integration throughout this space (not now infinitesimal). But by (4) d d d yo—u=(y 5-25, )0= Fe (6); if Hy denote differentiation with reference to , in the system of co-ordinate 2, p, , such that. y=ecos),z=esiny . ; 5 : (73: Hence, transforming (5) to this system of co-ordinates, we have L=fff dx de ed a . : . . : (8). Now, as the whole space is spherical, with the origin of co-ordinates in its centre, we may divide it into infinitesimal circular rings with OX for axis, having each for normal section an infinitesimal rectangle with dz and dp for sides. Inte- grating first through one of these rings, we have ; 2Qar dg die dee f a which vanishes, because ¢ is a single-valued function of the co-ordinates. Hence L = 0, which proves Lemma (2.). 15. Returning now to the dynamical proposition, stated at the conclusion of § 11; for the promised proof, let R denote the radial component velocity of the fluid across any element, dc, of the spherical surface, situated at (a, y, z); and let u, v, w be the three components of the resultant velocity at this point; so that sty o & Res US ee RO . : : z : { (yr The volume of fluid leaving the hollow spherical space across de in an infinitesimal time, di is Rde . dt, and the moment of momentum of this moving mass round the centre has, for component round OX, (wy — vz) Rde dt. Hence, if L denote the component of the moment of momentum of the whole, mass within the spherical surface at any instant, ¢, we have (§ 11), = = ff wy — vz) R de, . : : : (10). Now, using Lemma (1.) of § 12, and the notation of § 14, we have " WY — Ve — He) dap ’ SIR W. THOMSON ON VORTEX MOTION. 223 and, by (9), = ae dr where e denotes rate of variation per unit length perpendicular to the spherical Lr surface, that is differentiation with reference to 7, the other two co-ordinates being directional relatively to the centre. Hence, using ordinary polar co-ordinates, 7, 0, ~, we have : oo Lit yO ae d ; af fF re sinddédp : : : (11). But the “equation of continuity” for an incompressible liquid (being du dv dw de * dy i oy, Ti gives* vy’ p =—0, for every point within the spherical space; and therefore [THom- son & Tait, App. B] =e 9=8,+S8,7r+ 8,7? + &. 7 : p ; @2) a converging series, where S, denotes a constant, and §,, S,, &c., surface harmo- nics of the orders indicated. Hence d R= $=8, +28, +37°8,4+&. © . (18) And it is clear from the synthesis of the most general surface saga by zonal, sectional, and tesseral harmonics [THomson & Tarr, $781}, that “ a is a surface harmonic of the same order as §,:} from which [THomson & Tarr, App. B (16)], _ it follows that, d? ae ae da? * dy? + + This follows, of course, from the known analytical theorem that the operations yv? and * By v? we shall always understand | (y = — 2% a) are commutative, which is proved thus :— | By differentiation we have ddp_ dd dy dz” dz dy’ v(: dp do vi 7 da eB 7) -*9" dy VEO ‘ay ae | and therefore, since OY Vv? “6 ee 7)? = (v 5 v2 9 dz * dy Cn ¢ | p being any function whatever. Hence, if vy? 9 = 0 we have 224 SIR W. THOMSON ON VORTEX MOTION. d8Sv . sé sin 6dédp=—0O, except when 7?’ =7. But this is true also when ¢’ = 7 because and therefore, as in § 14, the integration for .), from W = 0 to W = 2 = gives zeru. Hence (11) gives aL _ a Pals This and § 11 establish § 10. 16. Lemma (1) of § 11, and § 10 now proved, show that in any motion whatever of an incompressible liquid, whether with solids immersed in it or not, wda+ cdy +wdz is always a complete differential through any portion of the fluid, for which it is a complete differential at any instant, to whatever shape and position of space this portion may be brought in the course of the motion. This is the ordinary statement of the fundamental proposition of fluid motion referred to in § 9, which was first discovered by Lacrancs. (For another proof see § 60.) Ihave given the preceding demonstration, not so much because it is useful to look at mathematical structures from many different points of view, but (§ 19) because the dynamical considerations and the formule I have used are immediately available for establishing the theory of the impulse (S$ 3 . . . 8), of which a fundamental pro- position was stated above (§5). To prove this proposition (in § 19) I now proceed. 17. Imagine any spherical surfaces to be described round a moveable solid or solids immersed in a liquid. The surrounding fluid can only press (§ 1) perpen- dicularly; and therefore when any motion is (§ 3) generated by impulsive forces applied to the solids, the moment round any diameter of the momentum of the — matter within the spherical surface at the first instant, must be exactly equal to the moment of those impulsive forces round this line. And the moment. round this line, of the momentum of the matter in the space between any two concentric spherical surfaces is zero, provided neither cuts any solid, and provided that, if there are any solids in this space, no impulse acts on them. | 18. Hence, considering what we have defined as ‘“‘the impulse of the motion,” (§ 6), we see that its moment round any line is equal to the moment of momen- tum round the same line, of all the motion within any spherical surface having its centre in this line, and enclosing all the matter to which any constituent of the — impulse is applied. This will still hold, though there are other solids not in the neighbourhood, and impulses are applied to them: provided the moments of mo- mentum of those only which are within S are taken into account, and provided none of them is cut by S. 19. The statements of § 11, regarding fluid occupying at any instant a fixed spherical surface, are applicable without change to the fluids and solids occupying SIR W. THOMSON ON VORTEX MOTION. 225 the space bounded by S, because of our present condition, that no solid is cut by S. Hence every statement and formula of § 15, as far as equation (11), may be now applied to the matter within 8; but instead of (12) we now have [THomson & Tair, § 736], if we denote by T,, T,, &c., another set of surface spherical harmonics, g9=S,+8,7 +837? + &e. $7 toot Ty r—* + &e } ee for all space between the greatest and smallest spherical surface concentric with S, and having no solids in it, because through all this space, § 16, and the equa- tion of continuity prove that 77 ¢ = 0. Hence, instead of (13), we now have Fe Se Coop Ries Siti, &e, ) dr 2 3 fie (15). Hence finally es ee Pelle dS; . dt = see ffs E 8; ap — (@ + 1) T; 7a sin 6d bdL 5 (16). Now if, as assumed in § 5, neither any moveable solids, nor any part of the _ boundary exist within any finite distance of S allround; §,, 8,, &c., must each _ be infinitely small: and therefore (16) gives eDi- his proves the proposition at asserted in § 5: because a system of forces cannot have zero moment round _ every line drawn through any finite portion of space, without having force-resul- — tant and couple-resultant each equal to zero 20. As the rigidity of the solids has not been taken into account, all or any of them may be liquefied (§ 3) without violating the demonstration of $19. To save circumlocutions, I now define a vortex as a portion of fluid having any motion that it could not acquire by fluid pressure transmitted through itself from its boundary. Often, merely for brevity, I shall use the expression a body to denote either a solid or a vortex, or a group of solids or vortices. 21. The proposition thus proved may be now stated in terms of the definitions of § 6, which were not used in § 5, and so becomes simply this:—The impulse of the motion of a solid or group of solids or vortices and the surrounding liquid remains constant as long as no disturbance is suffered from the influence of other solids or vortices, or of the containing vessel. This implies, of course (§ 6), that the magnitudes of the force-resultant and _ the rotational moment of the impulse remain constant, and the position of its axis invariable. A iy : ere : * There is no term at because this would give, in the integral of flow across the whole sphe- rical surface, a finite amount of flow out of or into the space within, implying a generation or destruction of matter. VOL, XV. PART I. 3M 226 SIR W. THOMSON ON VORTEX MOTION. _ 22. In Pornsot’s system of the statics of a rigid body we may pass from the resultant force and couple along and round the central axis to an equal resultant force along the parallel line through any point, and a greater couple the resultant of the former (or minimum) couple, and a couple in the plane of the two parallels, having its moment equal to the product of their distance intp the resultant force. So we may pass from the force-resultant and rotational moment of the impulse along and round its axis, to an equal force-resultant and greater moment of im- pulse, by transferring the former to any point, Q, not in the axis (§ 6) of the motion. This greater moment is (§ 18) equal to the moment of momentum round the point Q, of the motion within any spherical surface described from Q as centre, which encloses all the vortices or moving solids. 23. Hence a group of solids or vortices which always keep within a spherical surface of finite radius, or a single body, moving in an infinite liquid, can have no permanent average motion of translation in any direction oblique to the direc- tion of the force-resultant of the impulse, if there is a finite force-resultant. For the matter within a finite spherical surface enclosing the moving bodies or body, cannot have moment of momentum round the centre increasing to infinity. 24. But there may be motion of translation when the force-resultant of the impulse vanishes; and there will be, for example, in the case of a solid, shaped like the screw-propeller of a steamer, immersed in an infinite homogeneous liquid, and set in motion by a couple in a plane perpendicular to the axis of the screw. 25. And when the force-resultant of the impulse does not vanish, there may be no motion of translation, or there may even be translation in the direction opposite to it. Thus, for example, a rigid ring, with cyclic motion, established (§ 63) through it, will, if left at rest, remain at rest. And if at any time urged by an impulse in either direction in the line of the force-resultant of the impulse of the cyclic motion, it will commence and continue moving with an average motion of trans- lation in that direction ; a motion which will be uniform, and the same as if there were no cyclic motion, when the ring is symmetrical. If the translatory impulse is contrary to the cyclic impulse, but less in magnitude, the translation will be contrary to the whole force-resultant impulse. If the translatory impulse is equal and opposite to the cyclic impulse, there will be translation with zero force-resultant impulse—another example of what is asserted in § 24. In this case, if the ring is plane and symmetrical, or of any other shape such that the cyclic motion (which, to fix ideas, we have sup- posed given first, with the ring at rest,) must have had only a force-resultant, and no rotational moment, we have a solid moving with a uniform motion of translation through a fluid, and both force and couple resultant of the whole impulse zero. “@ 26. From §§ 21 and 4, we see that, however long the time of application of — the impressed forces may be—provided only that, during the whole of it, the — SIR W. THOMSON ON VORTEX MOTION. 224 solid or group of solids has been at an infinite distance from all other solids and from the containing vessel—the time integrals of the impressed forces parallel to three fixed axes, and of their moments round these lines, are equal to the six corresponding components of “‘ the impulse” (§ 6). 27. If two groups, at first so far asunder as to exercise no sensible influence on one another, come together, the “impulse” of the whole system remains un- changed by any disturbance each may experience from the other, whether by im- pacts of the solids, or through motion and pressure of the surrounding fluid; and (§ 6) it is always reducible to the force-resultant along the central axis, and the minimum couple-resultant, of the two impulses reckoned as if applied to one rigid body. The same holds, of course, if one group separates into two so distant as to no longer exert any sensible influence on one another. 28. Hence whatever is lost of impulse perpendicular to a fixed plane, or of component rotational movement round a fixed line, by one group through collision with another, is gained by the other. 29. Two of the moveable solids, or two groups, will be said to be zn collision when, having been so far asunder as not to disturb one another’s motions sen- sibly, they are so near as to do so. ‘This disturbance will generally be supposed to be through fiuid pressure only, but impacts of solids on solids may take place during a collision. 30. We are now prepared to investigate (§§ 30, 31, 32) the influence of a fixed solid on the impulse of a moveable solid, or of a vortex, or of a group of solids or vortices, passing near it, thus—If during such collisions or separations as are con- sidered in S§ 27, 28, forces are impressed on any one or more of the solids, their alteration of the whole impulse is (§ 26) to be reckoned by adding to each of its rectangular components the time integral of the corresponding component of — these impressed forces. Now, let us suppose such forces to be impressed on any one of the moveable solids as shall keep it at rest. These forces are zero as long as no moving solid is within a finite distance. But if a moving solid or vortex, or group of solids or vortices, passes near the fixed solid, the change of pressure due to the motion of the fluid will tend to move it, and the impression of force on it becomes necessary to keep it fixed. Let do be an element of its surface; (x, y, 2), the co-ordinates of the centre of this element; a, 8, y the inclinations of the normal at (2, y, z) to the three rectangular axes; and p the fluid pressure at time ¢, and point (a, y, z). The six components of force and couple required to hold the body fixed at time #, are f[do. cosa.p, ffde.cosB.p, ff/de. cosy. p; ; Ide (y cosy — zcosB)p , [fde(zcosa — xcosy)p , [/do(xcosB — y cos x)p , a): | If in these expressions we substitute Spat ’ Hey 228 SIR W. THOMSON ON VORTEX MOTION. in place of p ( /dt denoting a time integral from any era of reckoning before the disturbance became sensible, up to time 7, which may be any instant during the collision, or after it is finished), we have the changes in the corresponding com- ponents of the impulse up to time ¢, provided there has been no impact of move- able solid on the fixed solid. 31. Let now the “ velocity potential” (as we shall call it, in conformity witha German usage which has been adopted by HeLMHoLTZ,) be denoted by ¢; that is (S$ 16), let » be such a function of (a, y, z, ¢) that _ do ___ ap _ do Use oi, Siti , : ; (3). and let @ (or ?) denote its rate of variation per unit of time at any instant ¢, for the point (z, y, 2) regarded as fixed. Also, let g denote the resultant fluid velocity, so that ‘ do* do* dg? G@=aw+e¢qdwv= f =F ae + oa . : (4). The ordinary hydro-dynamical formula gives p=u-$-3¢ . (5) ; where II denotes the constant pressure in all sensibly quiescent parts of the fluid. 32. The constant term II disappears from p in each of the integrals (1) of § 30, because a solid is equilibrated by equal pressure around. And in the time integral (2), we have Sedt =o : : (Oy; and therefere if (XYZ) (LMN) denote the changes in the force-and couple-com- ponents of the impulse produced by the collision up to time ¢, we have X = —ffdecosa (9 + £/q? di), Y= &.,Z= &e., 7) L = — ffdo (y cos y — 2 cos B) (9 + 4/¢? dt), M = &., N= &c., But because the fluid is quiescent in the neighbourhood of the fixed body when the moving body or group of bodies is infinitely distant from it; it follows that before the commencement and after the end of the collision we have ¢ = 0 at every point of the surface of the fixed body. Hence, for every value of ¢ represent- ing a time after the completion of the collision, the preceding expressions become X= —-—iffdecosa/gdt, Y= &., Z= &e., | L = — }ffdo(y cosy — zc0s 8) fe? dt, M = &., N = &.,, (8); which express that the integral change of impulse experienced by a body or group of bodies, in passing beside a fixed body without striking it, may be regarded as a SIR W. THOMSON ON VORTEX MOTION. 229 system of impulsive attractions towards the latter, everywhere in the direction of the normal, and amounting to 4 /a°dt per unit of area. But it must not be forgotten that the term ¢ in the expression [§ 31 (5)] for p produces, as shown in § 30 (1), an influence during the collision, the integral effect of which only disappears from the expression [§ 32 (7)] for the impulse after the collision 1s completed ; that is (§ 29) after the moving system has passed away so far as to leave no sensible fluid motion in the neighbourhood of the fixed body. 33. Hence, and from § 23, we see that when there is no impact of moving solid against the fixed body, and when the moving solid or group of solids passes altogether on one side of the fixed body, the direction of the translation will be deflected, as if there were, on the whole, an attraction towards the fixed body, or a repulsion from i, according as (§ 25) the translation is in the direction of the impulse or opposite to it. For, in each case, the impulse is altered by the intro- duction of an impulse towards the fixed body upon the moving body or bodies as they pass it; and (§ 23) the translation before and after the collision is always along the line of the impulse, and is altered in direction accordingly. This will be easily understood from the diagrams, where, in each case 5 represents the fixed body, the dotted line ITT’, and arrow-heads I I’, the directions of the force- resultant of the impulse at successive times, and the full arrow-heads T 1’, the directions of the translation. Fig.1 ag Fig. 2 LAT BAS Fide Av’ Vr " i ) N 1! ‘ “A vee f ai | van Pee Zoe \ All ordinary cases belong to the class illustrated by fig. 1. The case of a rigid ring, with cyclic motion (§ 25) established round it as core, belongs to the class illustrated by fig. 2, if the ring be projected through the fluid in the direc- tion perpendicular to its own plane, and contrary to the cyclic motion through its centre. 34. When (§ 66) we substitute vortices for the moving solids, we shall see (§ 67) that the translation is probably always in the direction with the impulse. Hence, as illustrated by fig. 1, there is always the deflection, as if by attraction, when a group of vortices pass all on one side of a fixed body. Thisis easily observed, for a simple Helmholtz ring, by sending smoke rings on a large scale, according to VOL. XXV. PART I. oN 230 SIR W. THOMSON ON VORTEX MOTION. Professor Tait’s plan, in such directions as to pass very near a convex fixed sur- face. An ordinary 12-inch globe, taken off its bearings and hung by a thin cord, answers very well for the fixed body. 35. The investigation of §§ 30, 31, 32, is clearly applicable to a vortex or a moving body, or of a group of vortices or moving bodies, which keep always near one another (§ 23), passing near a projecting part of the fixed boundary, and being, before and after this collision (§ 29), at a very great distance from every part of the fixed boundary. Thus,a Helmholtz ring projected so as to pass near a projecting angle of two walls, shows a deflection of its course, as if caused by attraction towards the corner. 36. In every case the force-resultant of the impulse is, as we shall presently see (§ 37), determinate when the flow of the liquid across every element of any surface completely enclosing the solids or vortices is given ; but not so, from such data, either the axis (§ 6) or the rotational moment, as we see at once by con- sidering the case of a solid sphere (which may afterwards be supposed liquefied) set in motion by a force in any line not through the centre, and a couple in a plane perpendicular to it. For this line will be the “axis,” and the impulsive couple will be the rotational moment of the whole motion of the solid and liquid. But the liquid, on all sides, will move exactly as it would if the impulse were merely an impulsive force of equal amount in a parallel line through the centre of the sphere, with therefore this second line for “ axis” and zero for rotational moment. For illustration of rotational moment remaining latent in a liquid (with or with- out solids) until made manifest by actions, tending to alter its axis, or showing effects of centrifugal force due to it; see § 66, and others later. 37. The component impulse in any direction is equal to the corresponding component momentum of the mass enclosed within the surface S, containing all the places of application of the impulse, together with that of the impulsive pressure outwards on this surface. But asthe matter enclosed by S (whether all — liquid or partly liquid and partly solid) is of uniform density, its momentum will be equal to its mass multiplied into the velocity of the centre of gravity of the — space within the surface S supposed to vary so as to enclose always the same matter, and will therefore depend solely on the normal motion of 8; that is to say, on the component of the fiuid velocity in the direction of the normal at every point of 8. And the impulsive fluid pressure, corresponding to the generation of the actual motion from rest, being the time integral of the pressure during the instantaneous generation of the motion, is (S§ 31, 32) equal to — ¢, the velocity potential; which (§ 61) is determinate for every point of S, and of the exterior space when the normal component of the fluid motion is given for every point of S. Hence the proposition asserted in § 36. Denoting by de any element of 8; N the normal component of the fluid velocity; a the inclination to OX, of the normal drawn outwards through do ; and X the z-component of the impulse; we SIR W. THOMSON ON VORTEX MOTION. 231 have for the two parts of this quantity considered above, and its whole value, the following expressions; of which the first is taken in anticipation from § 42— xz-momentum of matter, within §, = iff Na de (8) of § 42 ax-component of impulsive pressure on §, outwards, = — //p cos ade (1). X =//(Nx — 9cosa) do . . , ; : ; ; (2). It is worthy of remark that this expression holds for the impulse of all the solids or vortices within S, even if there be others in the immediate neighbourhood out- side: and that therefore its value must be zero if there be no solids or vortices within S, and N and ¢ are due solely to those outside. 38. If > be the potential of a magnet or group of magnets, some within S and others outside it, and N the normal component magnetic force, at any point of S, the preceding expression (2) is equal to the z-component of the magnetic moment of all the magnets within S, multiplied by 47. For let p be the density of any continuous distribution of positive and negative matter, having for potential, and normal component force, ¢ and N respectively, at every point of S. We have [THomson & Tait, § 491 (c)] ¢ = — a v’? 9, and therefore 1 ag do Va" fe dx dy dz= — rae (Fe = dy + Ga) de dy dz ; (3). Now, integrating by parts,* as usual with such expressions, we have d? d u u fe Guyuaf[fo FZ aya: —f{f} das dy de =ff (eZ —) dy dz . Hence, integrating each of the other two terms of (3) once simply, and reducing as usual [THomson & Tait, App. A (q@)] to a surface integral, we have il W[fewuus-a (Nzx—gcosa)do . 4); which proves the proposition, and also, of course, that if there be no matter within S, the value of the second member is zero. 39. Hence, considering the magnetic and hydrokinetic analogous systems with the sole condition that at every point of some particular closed surface, the magnetic potential is equal to the velocity potential, we conclude that 47 times the magnetic moment of all the magnetism within any surface, in the magnetic system, is equal to the force-resultant of the impulse of the solids or vortices within the corresponding surface in the hydrokinetic system ; and that the direc- tions of the magnetic axis and of the force-resultant of the impulse are the same. For the theory of magnetism, it is interesting to remark that indeterminate dis- tributions of magnetism within the solids, or portions of fluid to which initiating * The process here described leads merely to the equation obtained by taking the last two equal members of App. A (1) (THomson & Tarr) for the casea = 1,U = 9, U'= «. 232 SIR W. THOMSON ON VORTEX MOTION. forces (§3) were applied, or determinate distributions in infinitely thin layers at their surfaces, may be found, which through all the space external to them shall produce the same potential as the velocity-potential, and therefore the same distribution of force as the distribution of velocity through the whole fluid. But inasmuch as when the magnetic force in the interior of a magnet is defined in the manner explained in § 48 (2) of my ‘‘ Mathematical Theory of Magnetism,’’* it is expressible through all space by the differential coefficients of a potential; and, on the contrary, for the kinetic system w dz + v dy + w dzis not a complete differential generally through the spaces occupied by the solids, the agreement between resultant force and resultant flow holds only through the space exterior to the magnets and solids in the magnetic and kinetic systems respectively. But if the other definition of resultant force within a magnet, [‘‘Math. Theory of Magnetism,” § 77, foot-note, and § 78], published in preparation for a 6th chapter ‘On Electro-magnets” (still in my hands in manuscript, not quite completed), and which alone can be adopted for spaces occupied by non-mag- netic matter traversed by electric currents, the magnetic force has not a potential within such spaces; and we shall see (§68) that determinate distributions of closed electric currents through spaces corresponding to the solids of the hydro- kinetic system can be found which shall give for every point of space, whether traversed by electric currents or not, a resultant magnetic force, agreeing in magnitude and direction with the velocity, whether of solid or fluid, at the cor- responding point of the hydrokinetic system. This thorough agreement for all space renders the electro-magnetic analogue preferable to the magnetic; and, having begun with the magnetic analogous system only because of its convenience for the demonstration of § 38, we shall henceforth chiefly use the purely electro- magnetic analogue. 40. To prove the formula used in anticipation, in § 37 (1) we must now (S§ 41, 42, 43) find the momentum of the whole matter—fiuid, fluid and solid, or even solid alone—at any instant within a closed surface S, in terms of the normal component velocity of the matter at any point of this surface, or, which is the same, the normal velocity of this surface itself, if we suppose it to vary so _ as to enclose always the same matter. ; 41. Let V be the volume of the space bounded by any varying closed surface S. As yet we need not suppose V constant. Let #, y, 2 be the co-ordinates of of the centre of gravity. We have Vzst/fl[edydz] . ; : : (5), where[ _] indicates that the expression within it is to be taken between proper limits for S. Now as S varies with the time, the area through which //dy dz is — taken will in general vary; but the increments or decrements which it experiences * Trans. R.S. Lond., 1851; or “ THomson’s Electrical Papers.” Macmillan. 1869. SIR W. THOMSON ON VORTEX MOTION. 233 at different parts of the boundary of this area, in the infinitely small time di, contribute no increments or decrements to //[a°dy dz], as we see most easily by first supposing S to be a surface everywhere convex outwards. Hence di Sg [a* dy dz] =f; ie [ee dyd: | = 2 ff ia & PP * dy dz] : (6). But if N denote the velocity with which the surface moves in the direction of its outward normal at («, y, %), we have, in the preceding expression dx a N seca : : : : (7), if a be the inclination of the outward normal to OX. Hence ane = f[fton sec a dy dz]. But the condition as to limits indicated by [ ] are clearly satisfied, if, de denoting an element of the surface, such that dy dz = cos ade, we simply take //dc over the whole surface. Thus we have Boe =ffon 2 ae (7) ; 42. In any case in which V is constant, this becomes ie ea) eM ehan ee hic ital ob vit rook If now the varying surface, S, is the boundary of a portion of the matter—fluid or solid—of uniform density unity, with er motions we are occupied, the a-component momentum of this portion is Wee Fi a and, therefore, equation (8) is the required (§ 40) expression. | 43. The same formule (7) and (8) are proved more shortly of course by the _ regular analytical process given by Porsson* and GREEN t+ in dealing with such | subjects; thus, in short. Let w, v, w be the components of velocity, of any matter, | compressible or incompressible, at any point (#, y, z) within S; and let ¢ denote dv dw | the value at this point of 4 +7 +7, So that dy i Obie. dv , dw pe =C dy + az , > : s (9). | We have, for the component momentum of the whole matter within S, if of unit | density at the instant considered, Sf fede ay ae = =e [ [vz dy dz ~f ffs 7, dedy dz a CLO) * Théorie de la Chaleur, § 60, + Essay on Electricity and Magnetism. VOL. XXV. PART I. 30 234 SIR W. THOMSON ON VORTEX MOTION. But by (9) ST fa away ds = ff fox au dy ae S]fe (2+ Ow dee dy da and by simple integrations, SS fe (G+ + Gp) dedy de = [fa(vdeds + waedy), Using these in (10), and altering the expression to a surface integral, as in THomson & Tait, App. A (@), we have eae y te = {fx (udy dz + vdzdx + w dx dy) — //fcx dx dy dz =/f[uNds—f{fexdxdydz . . : 3 (11), which clearly agrees with (7). When this mass is incompressible, we have c=o by the formula so ill named the equation ‘ of continuity” (THomson & Tarr, § 191), and we fall upon by ) The proper analytical interpretation of the differential coefficients 5 ” ites and of the equation of continuity, when, as at the surfaces of separation a fluid and solids, w, v, w are discontinuous functions, having abruptly varying values, presents no difficulty. 44. In the theory of the impulse applied to the collision (§ 29) of solids or vortices moving through a liquid, the force-resultant of the impulse corresponds, as we have seen, precisely to the resultant momentum of a solid in the ordinary theory of impact. Some difficulty may be felt in understanding how the zero- momentum (§ 4) of the whole mass is composed; there being clearly positive momentum of solids and fluids in the direction of the impulse in some localities near the place of its application, and negative in others. [Consider, for example, the simple case of a solid of revolution struck by a single impulse in the line of — its axis. The fluid moves in the direction of the impulse, before and behind the body, but in the contrary direction in the space round its-middle.] Three modes of dividing the whole moving mass present themselves as illustrative of the dis- tribution of momentum through it; and the following propositions (§ 45) with reference to them are readily proved (§§ 46, 47, 48). 45. I. Imagine any cylinder of finite periphery, not necessarily circular, com- — pletely surrounding the vortices (or moving solids), and any other surrounding none, and consider the infinitely long prisms of variously moving matter at any instant surrounded by these two cylinders. The component momentum parallel to the length of the first is equal to the component of the impulse parallel to the same direction ; and that of the second is zero. iI. Imagine any two finite spherical surfaces, one sea all the vortices SIR W. THOMSON ON VORTEX MOTION. 235 or moving solids, and the other none. The resultant-momentum of the whole matter enclosed by the first is in the direction of the impulse, and is equal to 2 of its value. The resultant-momentum of the whole fluid enclosed by the second is the same as if it all moved with the same velocity, and in the same direction, as at its centre. III. Imagine any two infinite planes at a finite distance from one another and from the field of motion, but neither cutting any solid or vortex. The com- ponent perpendicular to them of the momentum of the matter occupying at any instant the space between them (whether this includes none, some, or all of the vortices or moving solids) is zero. 46. To prove these propositions :— I. Consider in either case a finite length of the prism extending to a very great distance in each direction from the field of motion, and terminated by plane or curved ends. Then, the motion being, as we may suppose (§ 61) started from rest by impulsive pressures on the solids [or (§ 66) on the portions of fluid constituting the vortices]; the impulsive fluid pressure on the cylindrical surface can generate no momentum parallel to the length; and to generate momentum in this direction there will be, in case 1, the impressed impulsive forces on the solids, and the impulsive fluid pressures on the ends; but in case 2 there will be only the impulsive fluid pressure on the ends. Now, the impulsive fluid pressures on the ends diminish [§ 50 (15)] according to the inverse square of the distance from the field of motion, when the prism is prolonged in each direction, and are therefore infinitely small when the prisms are infinitely long each way. Whence the proposition I. 47. By using the harmonic expansions § 19, (14), (15), in the several expres- sions (1), (2), of § 37, (1), (2); and the fundamental theorem [2:8 do=0, of the harmonic analysis [THomson & Tart, App. B. (16)]; and putting S, = 0 for one case, and T; = 0 for the other; we prove the two parts of Prop. II., § 45 immediately. 48. To prove Prop. II., § 45, the well-known theory of electric images in a plane conductor* may be conveniently referred to. It shows that if N, denotes the normal component force at any point of an infinite plane due to any distribu- tion, “, of matter in the space lying on one side of the plane, a distribution of matter over the plane having = N, for surface density at each point exerts the same force as » through all the space on the other side of the plane, and therefore that the whole quantity of matter in that surface distribution is equal to the * Tuomson, Camb. and Dub. Math. Journal, 1849; Liovvitix’s Journal, 1845 and 1847; or Reprints of Electrical Papers, (Macmillan, 1869.) 236 SIR W. THOMSON ON VORTEX MOTION. whole quantity of matter in «.* Hence, // dc, denoting integration over the infinite plane [If N,de= 0 ‘ ‘ f : ; ; (12). if the whole quantity of matter in » be zero. Hence, if N be the normal force due to matter through space on both sides of the plane, ae the whole quan- tity of matter on each side separately is zero, (20 en rere since N is the sum of two parts, for each of which separately (12) holds. This translated into hydrokinetics, shows that the whole flow of matter across any infinite plane is zero at every instant when it cuts no solids or vortices. Hence, and from the uniformity of density which (§ 3), we assume, the centre of gravity of the matter between any two infinite fixed parallel planes, has no motion in the direction perpendicular to them at any time when no vortex or moving solid is cut by either: which is Prop. III. of § 4 in other words. 49. The integral flow of matter across any surface whatever, imagined to divide the whole volume of the finite fixed containing vessel of § 1 into two parts is necessarily zero, because of the uniformity of density; and therefore the momen- tum of all the matter bounded by two parallel planes, extending to the inner surface of the containing vessel, and the portion of this surface intercepted between them has always zero for its component perpendicular to these planes, whether or not moving solids or vortices are cut by either or both these planes. But it is remarkable that when any moving solid or vortex is cut by a plane, the integral flow of matter across this plane (if the containing vessel is infinitely distant on all sides from the field of motion), converges to a generally jinite value, as the plane is extended to very great distances all round from the field of motion, which are still infinitely small in comparison with the distances to the containing vessel; and diminishes from that finite value to zero by another con- vergence, when the distances to which the plane is extended all round begin to be comparable with, and ultimately become equal to, the distances of the curve in which it cuts the containing vessel. Hence we see how it is that the condition of neither plane cutting any moving solid or vortex is necessary to allow § 46, III. to be stated without reference to the containing vessel, and are reminded that * This is verified synthetically with ease, by direct integrations showing (whether by Cartesian or polar plane co-ordinates), that eto s*. ae And taking = of this, we have 2) Ayre pe ee he oie Oe iy ae 9p. ue. (a? + y? + 27)§ the synthesis of (12). SIR WILLIAM THOMSON ON VORTEX MOTION. 237 the equality to zero asserted in this proposition is proved in § 48 to be approxi- mated to when the planes are extended to distances all round, which, though infi- nitely short of the distances to the containing vessel, are very great in comparison with their perpendicular distances from the most distant parts of the field of motion. 50. The convergencies concerned in § 46, I., III. may be analysed thus. Per- pendicular to the resultant impulse draw any two planes on the two sides of the field of motion, with all the moving solids and vortices between them, and divide a portion of the space between them into finite prismatic portions by cylindrical (or plane) surfaces perpendicular to them. Suppose now one of these prismatic portions to include all the moving solids and vortices, and without altering the prismatic boundary, let the parallel planes be removed in opposite directions to distances each infinite (or very great) in comparison with distance of the most distant of the moving solids or vortices. By § 46, I., the momentum of the motion within this prismatic space is (approximately) equal to the force-resultant, I, of the impulse, and that of the motion within any one of the others is (approximately) zero. But the sum of these (approximately) zero values must, on account of § 46, II1., be equal to —I, if the portions of the planes containing the ends of the prismatic spaces be extended to distances very great in comparison with the dis- tance between the planes. To understand this, we have only to remark that if denotes the velocity potential at a point distant D from the middle of the field, and « from a plane through the middle perpendicular to the impulse, we have (§ 53) approximately, la Cee edu ny mane Ui bat yl thetey, provided D be great in comparison with the radius of the smallest sphere enclos- ing all the moving solids or vortices. Hence, putting 2 = +a for the two planes under consideration, denoting by A the area of either end of one of the prismatic portions, and calling D the proper mean distance for this area, we have (§ 46) for the momentum of the fluid motion within this prismatic space, provided it con- tains no moving solids or vortices, la — 2 72D: OR tLe we Ameer Meet 16), bes This vanishes when & is an infinitely small fraction (as D D is at most unity); but it is finite if p: 3s finite, provided . be not infinitely small. And its integral value (compare § 48, footnote) converges to — I, when the portion of area in- a cluded in the integration is extended till —p 3S infinitely small for all points of its boundary. VOL. XV. PART 1. 3 P 238 SIR WILLIAM THOMSON ON VORTEX MOTION. 51. Both as regards the mathematical theory of the convergence of definite integrals, and as illustrating the distribution of momentum in a fluid, it is inter- esting to remark that, w denoting component velocity parallel to x, at any point (z, y, 2), the integral //u dx dy dz, expressing momentum, may, as is readily proved, have any value from —o to + according to the portions of space through which it is taken. 52. As a last illustration of the distribution of momentum, let the containing vessel be spherical of finite radius a. We have, as in § 19, g9=8,+ 5,7 +827? + &e., (14), + T,r-? + T, 7-7? + &e., each series converging, provided 7 is less than a, and greater than the radius of the smallest concentric spherical surface enclosing all the solids or vortices. Now, by the condition that there be no flow across the fixed containing surface. we must have oe - 0, when7 =a : : : : : (15), which gives a+1 T; . S; = ag : 2 i : « ele and (14) becomes 4 r® T 3 Pr p= (1425)4+ 3(1455) + & entaany: But [§ 37 (1) ]if the whole amount of the w-component of impulsive pressure exerted by the fluid within the spherical surface of radius 7, upon the fluid round it be denoted by I, we have F = — f/9 cos bdo : a (2) 6 being the inclination to OX of the radius through dc. Now cos @ is a surface harmonic of the first order, and therefore all the terms of the harmonic expan- sion, except the first, disappear in the integral, which consequently becomes 3 d P= - (1425) [[Treose S . as _ Aw + By + Cz r Now let ie (20), this being [THomson & Tair, App. B, §§ i, j] the most general expression for a sur- face harmonic of the first order. We have cosé =<; and therefore (by spheri- cal harmonics, or by the elementary analysis of moments of inertia of a uniform spherical surface), SIR WILLIAM THOMSON ON VORTEX MOTION. 239 aff, cos 1% = Af fea= Oi: as F= (1425). | . | (22): Whence, if X denote the z-momentum of the fluid at any instant in the space between concentric spherical surfaces of radius 7 and 7”, and (19) becomes 3 nf 4A es If 7 and 7’ be each infinitely small in comparison with a, this expression vanishes, as it ought to do, in accordance with § 45, I]. But if Li ee ss (24), it becomes X = —3.4cA fulfilling § 4, by showing in the fluid outside the spherical surface of radius 7” a momentum equal and opposite to that (§ 45, II.) of the whole matter, whether fluid or solid, within that surface. 53, Comparing § 47 and § 52, we see that ff X, Y, Z be rectangular com- ponents of the force-resultant of the impulse, the term T, 7~—? of the harmonic expansion (14) is as follows :-— T, po? = ee + Vy + Ze Ag v8 : provided all the solids and vortices taken into account are within a spherical surface whose radius is very small in comparison with the distances of all other vortices or moving solids, and with the shortest distance to the fixed bounding surface. 54, HELMHOLTZ, in his splendid paper on Vortex Motion, has made the very important remark, that a certain fundamental theorem of GREEN’s, which has been used to demonstrate the determinateness of solutions in hydrokinetics, is subject to exception when the functions involved have multiple values. This calls for a serious correction and extension of elementary hydrokinetic theory, to ' which I now proceed. 55. In the general theorem (1) of THomson & Tait, App. A leta=1. It becomes dp do’ poe de’ dodg = ff R be whee de dx * dy dy * dz i) dedy de = | /dsone ff fix dy dz9v 2 =f/ eee ail DO Oe Cian tially mane os ts) es a (1); which is true without exception if ~ and ¢’ denote any two single-valued functions of 2, y,2; ///dx dy dz integration through the space enclosed by any finite closed (25), 240 SIR WILLIAM THOMSON ON VORTEX MOTION. surface, S; //do integration over the area of this surface; and 0 rate of variation per unit of length in the normal direction at any point of it. This is GREEN’s original theorem, with HELMHOLTz’s limitation added (in italics.) The reader may verify it for himself. 56. But if either ¢ or ¢’ is a many-valued function, and the differential co- . d 19" ‘ : efficients “ye tees - » +++» each single-valued, the double equation (1) cannot be generally true. Its first member is essentially unambiguous; but the process of integration by which the second member or the third member is found, would introduce ambiguity if > or if ¢’ is many-valued. In one case the first member, though not equal to the ambiguous second, would be equal to the third, provided ? is not also many-valued ; and in the other, the first member, though not equal to the third, would be equal to the second, provided ¢ is not many-valued. For example, let Y=—t ary Y/ 9 i ae : (2). and let S consist of the portions of two planes perpendicular to OZ, intercepted between two circular cylinders having OZ for axis, and the portions of these cylinders intercepted between the two planes. The inner cylindrical boundary excludes from the space bounded by S, the line OZ where ¢’ has an infinite 19’ dy’ , ante number of values, and -, and a have infinite values. We have bl Spleen (3) da a +y?’ dy x? + y? : ; : ; and at every point of S, dp’ = 0. Then, if ¢ be single-valued, there is no failure in the process proving the equality between the first and second members of (1), which becomes d d Mf te ee dzdyde=0. . : ‘ (4). Compare § 14 (6) to end. The third member of (1) becomes [fa tan-? ve [ffi ‘ V'odxdydz . (5), which is no result of unambiguous integration of the first member through the space enclosed by 8S, as we see by examining, in this case, the particular mean- ing of each step of the ordinary process in rectangular co-ordinates for proving GREEN’s theorem. It is thus seen that we must add to (5) a term on ff ax dz (2) ; dy] y=0 SIR WILLIAM THOMSON ON VORTEX MOTION. 241 ek if in its other terms the value of tan“*~ is reckoned continuously round from one side of the plane ZOX to the other: or dg ies anf fay a(P) _, 5 if the continuity be from one side of ZOY to the other ; to render it really equal to the first member of (1). Thus, taking for example the first form of the added term, we now have for the corrected double equation (1) for the case of = tan?! , ¢ any single valued function, and S the surface, composed of the two co-axal cylinders and two parallel planes specified above: dp = 7) Ba: da Z da dy dz =0 = an |) da a(e 4. aH i de tan Ya a2 + y y=0 OG ff dx dy dz tant! v%— : é (6). But if we annex to S any barrier stopping circulation round the inner cylindrical core, all ambiguity becomes impossible, and the double equa- tion (1) holds. For instance, if the barrier be the portion of the plane ZOX, intercepted between the co-axal gylinders and parallel planes constituting the S of § 55, so that //do must now include integration over each side of this rectangular area; (6) becomes simply the strict application of (1) to the case in question. 57. The difficulty of the exceptional interpretation of GREEN’s theorem for the class of cases exemplified in §§ 55 and 56, depends on the fact that /Fds may have different values when reckoned along the lengths of different curves, drawn within the space bounded by S, from a point P to a point Q;: ds being an infinitesimal element of the curve, and F the rate of variation of ¢ per unit of length along it. Let PCQ, PC’Q be two curves for which the /Fds has different values; and let both lie wholly within S. If we draw any curve from P to Q; make it first coincide with PCQ, and then vary it gradually until it coincides with PC’Q; it must in some of its intermediate forms cut the bounding surface S: for we have do do do Hes == da 4 = sates ers da + ay dy + > dz throughout the space contained within 8, and pe ea! al are each of them a” dy’ de unambiguous by hypothesis; which implies that /Fds has equal values for all VOL. XXV. PART I. 3Q 242 SIR WILLIAM THOMSON ON VORTEX MOTION. gradual variations of one curve between P and Q, each lying wholly within S. Now, in a simply continuous space, a curve joining the points P and Q may be gradually varied from any curve PCQ to any other PC’Q, and therefore if the space contained within S be simply continuous, the difficulty depending on the multiplicity of value of ¢ or ¢’ cannot exist. And however multiply continuous (§ 58) the space may be, the difficulty may be evaded if we annex to S a surface or surfaces stopping every aperture or passage on the openness of which ~ its multiple continuity depends; for these annexed surfaces, as each of them occupies no space, do not disturb the triple integrations (1), and will, therefore, not alter the values of its first member; but by removing the multiplicity of con- tinuity, they free each of the integrations by parts, by which its second or third members are obtained, from all ambiguity. To avoid circumlocution, we shall call 6 the addition thus made to S; and further, when the space within § is ($58) not merely doubly but triply, or quadruply, or more multiply, continuous, we shall designate by 8,, 6,; or 6,, 8,, 8,; and so on; the several parts of 6 re- quired in any case to stop all multiple continuity of the space. These parts of 6 may be quite detached from one another, as when the multiple continuity is that due to detached rings, or separate single tunnels in a solid. But one part 6, may cut through part of another, 6,, as when two rings (§ 58, diagram) linked into one another without touching constitute part of the boundary of the space considered. And we shall denote by //ds, integration over the surface 8, or over any one of its parts, 6,, 8,, &c. Let now P and Q be each infinitely near a point B, of 6, but on the two sides of this surface. Let « denote the value of /Fds along any curve lying wholly in the space bounded by §, and joining PQ without cutting the barrier; this value being the same for all such curves, and for all positions of B to which it may be brought without leaving 8, and without making either P or Q pass through any part of 8. That is to say, « is a single constant when the space is not more than doubly continuous; but it denotes one or other of m constants Ky) Ko, ++ + Ky Which may be all different from one another, when the space is 7-ply continuous. Lastly, let «’ denote the same element, relatively to ¢’, as « relatively to >. We find that the first steps of the integrations by parts now introduce, without ambiguity, the additions saffds ye, and 3x’ //ds yo : : : (6), to the second and third numbers of (1): = denoting summation of the integra- tions for the different constituents 6,, 6,,... of 8; but only a single term when the space is (§ 58) not more than doubly continuous. GreEEN’s theorem thus corrected becomes do dq’ do dy do +) =/f: ff] “ F Ee + a + ly dy * Eda) ye do pug + xx// dsdo’ wi ovo dx dy dz = ff ac gdp + xt [fisry iff} 9 Vv" 9 dx dy dz : (7). SIR WILLIAM THOMSON ON VORTEX MOTION. 243 58. Adopting the terminology of Riemann, as known to me through Heim- HOLTZ, I shall call a finite position of space n-ply continuous when its bounding surface is such that there are m irreconcilable paths between anytwo points in it. To prevent any misunderstanding, I add (1), that by a portion of space I mean such a portion that any point of it may be travelled to from any other point of it, without cutting the bounding'surface; (2), that the ‘* paths” spoken of all lie within the portion of space referred to; and (3), that by irreconcilable paths between two points P and Q; I mean paths such, that a line drawn first along one of them cannot be gradually changed till it coincides with the other, being always kept passing through P and Q, and always wholly within the portion of space considered. ‘Thus, when all the paths between any two points are recon- cilable, the space is simply continuous. When there are just two sets of paths, so that each of one set is irreconcilable with any one of the other set, the space is doubly continuous; when there are three such sets it is triply continuous, and soon. To avoid circumlocutions, we shall suppose S to be the boundary of a hollow space in the interior of a solid mass, so thick that no operations which we shall consider shall ever make an opening to the space outside it. A tunnel through this solid opening at each end into the interior space constitutes the whole space doubly continuous ; and if more tunnels be made, every new one adds one to the degree of multiple continuity. When one such tunnel has been made, the surface of the tunnel is continuous with the whole bounding surface of the space con- © sidered; and in reckoning degrees of continuity, it is of no consequence whether the ends of any fresh tunnel be in one part or another of this whole surface. Thus, if two tunnels be made side by side, a hole anywhere opening from one of them into the other adds one to the degree of multiple continuity. Any solid detached from the outer bounding solid, and left, whether fixed or movable in the interior space, adds to the bounding surface an isolated portion, but does not in- terfere with the reckoning of multiple continuity. Thus, if we begin with a simply continuous space bounded outside by the inner surface of the supposed exter- nal solid, and internally by the boundary of the detached solid in its interior, and if we drill a hole in this solid we produce double continuity. Two holes, or two solids in the interior each with one hole (such as two ordinary solid rings), constitute triple continuity, and so on. A sponge-like solid whose pores communicate with one another, illustrates a high degree of multiple con- tinuity, and it is of no consequence whether it is attached to the external bounding solid or is an isolated solid in the interior. Another type of multiple continuity, that presented by two rings linked in one another, was referred to in § 57. When many rings are linked into one another in various combinations, there are complicated mutual intersections of the several partial barriers 6,, 6,, . . required to stop all multiple continuity. But without having any portion of the 244 SIR WILLIAM THOMSON ON VORTEX MOTION. bounding solid detached, as in that case in which one at least of the two rings is loose, we have varieties of multiple continuity curiously different from that illus- trated by a single ordinary straight or bent tunnel, illustrated sufficiently by the simplest types, which are obtained by boring a tunnel along a line agreeing in form with the axis of a cord or wire on which a simple knot is tied; and by fixing the two ends of wire with a knot on it to the bounding solid, so that the surface of the wire shall become part of the bounding surface of the space considered, the knot not being pulled tight, and the wire being arranged not to touch itself in any point; or by placing a knotted wire, with its ends united, in the interior of the space. No amount of knotting or knitting, however complex, in the cord whose axis indicates the line of tunnel, complicates in any way the continuity of the space considered, or alters the simplicity of the barrier surface required to stop the circulation. But it is otherwise when a knotted or knitted wire forms - part of the bounding solid. A single simple knot, though giving only double con- tinuity, requires a curiously self-cutting surface for stopping barrier: which, in its form of minimum area, is beautifully shown by the liquid film adhering to an endless wire, like the first figure, dipped in a soap solution and removed. But no complication of these types, or of combinations of them with one another, eludes — the statements and formule of § 57. 59. I shall now give a dynamical lemma, for the immediate object of preparing to apply GrEEN’s corrected theorem (§ 57) to the motion of a liquid through a multiply continuous space. But later we shall be led by it to very simple demonstrations of HretmHoitz’s fundamental theorems of vortex motion; and shall see that it may be used as a substitute for the common equations of hydrokinetics. ‘ (Lemma). An endless finite tube* of infinitesimal normal section, being given full of liquid (whether circulating round through it, or at rest) is altered in shape, * A finite length of tube with its ends done away by uniting them together. SIR WILLIAM THOMSON ON VORTEX MOTION. 245 Instalment, received Nov.—Dec. 1869 [§ 59 -§ 64 (5)]. length, and normal section, in any way, and with any speed. The average value of the component velocity of the fluid along the tube, reckoned all round the circuit (irrespectively of the normal section), varies inversely as the length of the circuit. 59. (a). To prove this, consider first a single particle of unit mass, acted on by any force, and moving along a smooth guiding curve, which is moved and bent about quite arbitrarily. Let e be the radius of curvature, and €, y the component velocities of the guiding curve, towards the centre of curvature, and perpen- dicular to the plane of curvature, at the point P, through which the moving particle is passing at any instant. Let ¢ be the component velocity of the particle itself, along the instantaneous direction of the tangent through P. Thus &, », ¢ are three rectangular components of the velocity of the particle itself. Let Z be the component in the direction of ¢, of the whole force on P. We have, by elementary kinetics, ay dé dy ae ee ‘ : : (i);* * This theorem (not hitherto published 2) will be given in the second volume of Tuomson and Tarr’s “Natural Philosophy.” It may be proved analytically from the general equations of the motion of a particle along a varying guide-curve (Watron, “‘ Cambridge Mathematical Journal,” 1842, February); or more synthetically, thus—Let 7, m, n be the direction cosines of PT, the tangent to the guide at the point through which the particle is passing at any instant; (2, y, z) the co-ordinates of this point, and («, 7, 2) its component velocities parallel to fixed rectangular axes. We have C=le+my+nz; and Z = lz + mij + nd, and from this we = lé+ mij +nitléie+ nyt nz=Z+le+ my + nz. But it is readily proved (Tomson and Tart’s “ Natural Philosophy, § 9, to be made more explicit on this point in a second edition) that the angular velocity with which PT changes direction is equal to /(? + mr? + n), and, if this be denoted by w, that t m n ® @ @ are the direction cosines of the line PK, perpendicular to PT in the plane in which PT changes direction, and on the side towards which it turns. Hence, dé yet Ke if « denote the component velocity of P along PK. Now, if the curve were fixed we should have o= by the kinematic definition of curvature (Tomson and Tarr, § 5); and the plane in which PT changes direction would be the plane of curvature. But in the ease actually supposed, there is also in this plane an additional angular velocity equal to = , and a component angular velocity ds in the plane of PT and 7, equal to = ; due to the normal motion of the varying curve. Hence the whole angular velocity « is the resultant of two components, Cf dé g a ds VOL. XXV. PART II. Bae 3 in the plane of €, 246 SIR WILLIAM THOMSON ON VORTEX MOTION. : dé d: ee where e denotes the radius of curvature, and = = rates of variation of € and 7 from point to point along the curve at one time. 59. (b). Now, instead of a single particle of unit mass, let an infinitesimal portion, », of a liquid, filling the supposed endless tube, be considered. Let o be the area of the normal section of the tube in the place where p is, and és the length _ along the tube of the space occupied by it, at any instant; so that (as the density of the fluid is called unity), b= wos - Further, let a denote the rate of variation of the fluid pressure along the tube, — so that Thus we have, by (1), ay te a :o = Bs _ dp a ae . 7. ae : : : : (2). (c). Now, because the two ends of the arc ds move with the fluid, we have, by the kinematics of a varying curve, dés _ dé E ‘ = = a, 8s = BOS acae ; . (3); eee Eis +6(Ga- 7) a and, therefore, Substituting in this for ® its value by (2), we have ad(fss) _ (dé dn cg eg a (56s) dt “p +t Os 5 or = O(4g?—p) . : ’ : : (5), if g denote the resultant fiuid velocity; and 6, differences for the two ends of the arc 6s. Integrating this through the length of any finite arc P,P, of the fluid, its: ends P,, P,, moving with the fluid, we have PS) = Gapping os the suffixes denoting the values of the bracketed function, at the points P, and. and ay. — fn. de it the plane of 7 Hence | Cased dn e(j “+ 2) +0 Fra as and the formula (1) of the text is proved. SIR WILLIAM THOMSON ON VORTEX MOTION. 247 P,, respectively; and =; denoting integration along the arc from P; to P,. Let now P, be moved forward, or P, backward, till these points coincide, and the arc P,P, becomes the complete circuit; and let 2 denote integration round the whole closed circuit. (6) becomes d>(&€s) dt and we conclude that >fés remains constant, however the tube be varied. This is the proposition to be proved, as the “average velocity’”’ referred to is found by dividing >(65s) by the length of the tube. | 59. (d). The tube, imagined in the preceding, has had no other effect than exert- ing, by its inner surface, normal pressure on the contained ring of fluid. Hence the proposition®* at the beginning of § 59 is applicable to any closed ring of fluid forming part of an incompressible fluid mass extending in all directions through any finite or infinite space, and moving in any possible way; and the formule (5) and (6) are applicable to any infinitesimal or infinite arc of it with two ends not met. Thus in words— Prop. (1.) The line-integral of the tangential component velocity round any closed curve of a moving fluid remains constant through all time. And, Prop. (2), The rate of augmentation, per unit of time, of the space integral of the velocity along any terminated arc of the fluid is equal to the * Equation (6), from which, as we have seen, that proposition follows immediately, may be proved with greater ease, and not merely for an incompressible fluid, but for any fluid in which the density is a function of the pressure, by the method of rectilineal rectangular co-ordinates from the ordinary hydrokinetic equations. These equations are— Du da Dw da Dw da Dian ae PED manreyoib: § nedey if Di denote rate of variation per unit of time, of any function depending on a point or points moving with the fluid; and z= he es e denoting density. In terms of rectangular rectilineal co-ordinates we have Gs = udu + vdy + wez. Hence D(&s) Du Dox br= pi & + up, + &e. Now Dé. DS. Déz Spa, = =). and = bu. These and the kinetic equations reduce the preceding to D (fs) da da da sae Sl ee Oa Ue ae ON che tut) = ae pCa igs whence, by integration, equation (6) generalised to apply to compressible fluids. 248 SIR WILLIAM THOMSON ON VORTEX MOTION. excess of the value of 3g” — p, at the end towards which tangential velocity is reckoned as positive, above its value at the other end. 59. (e). The condition that wu dz +vdy + dz is a complete differential [proved above (§ 13) to be the criterion of irrotational motion] means simply That the flow (defined § 60 (a)] is the same in all different mutually recon- cilable lines from one to another of any two points in the fluid ; or, which is the same thing, That the circulation [§ 60 (a)] is zero round every closed curve capable of being contracted to a point without passing out of a portion of the fluid through which the criterion holds. From Proposition (1), just proved, we see that this condition holds through all time for any portion of a moving fluid for which it holds at any instant; and thus we have another proof of LAGRANGE’s celebrated theorem (§ 16), giving us a new view of its dynamical significance, which [see for example § 60 (g)] we shall find of much importance in the theory of vortex motion. (f). But itis only ina closed curve, capable of being contracted to a point without passing out of space occupied by irrotationally moving fluid, that the circulation is necessarily zero, in irrotational motion. In § 57 we saw that a continuous fluid mass, occupying doubly or multiply continuous space, may move altogether irro- tationally, yet so as to have finite circulation in a closed curve PP’QQ’P, provided PP’Q and PQQ are “ irreconcilable paths” between P and Q. That the circula- tion must be the same in all mutually reconcilable closed curves (compare § 57), is an immediate consequence from the now proved [§ 59 (Prop. 2)] equality of the flows [§ 60 (a@)] in all mutually reconcilable conterminous arcs. For by leaving one part of a closed curve unchanged, and varying the remaining arc continuously, no change is produced in the flow, in this part; and, by — repetitions of the process, a closed curve may be changed to any other recon- cilable with it. 60. Definitions and elementary propositions (a). The line-integral of the tangential component velocity along any finite line, straight or curved, in a moving fluid, is called the flow in that line. If the line is endless (that is, if it forms a closed curve or polygon), the flow is called circulation. The use of these terms abbreviates the statements of Propositions (2) and (1) of § 59 to the following :— : [$ 59, Prop. (2)]. The rate of augmentation, per unit of time, of the flow in any terminated line which moves with the fluid, is equal to the excess of the value of 3q° — p at the end from which, above its value at the end towards which, — positive flow is reckoned. [§ 59, Prop. (1)]. The circulation in any closed line moving with the fluid, remains constant through all time. (0). If any open finite surface, lying altogether within a fluid, be cut into SIR WILLIAM THOMSON ON VORTEX MOTION. 249 parts by lines drawn across it, the circulation in the boundary of the whole is equal to the sum of the circulations in the boundaries of the parts. This is obvious, as the latter sum consists of an equal positive and negative flow in each portion of boundary common to two parts, added to the sum of the flows in all the parts into which the single boundary of the whole is divided. 60. (c). Hence the circulation round the boundaries of infinitesimal areas, infinitely near one another in one plane, are simply proportional to these areas. (d). Proposition. Let any part of the fluid rotate as a solid (that is, without changing shape); or consider simply the rotation of a solid. The “ circulation”’ in the boundary of any plane figure moving with it is equal to twice the area enclosed, multiplied by the component angular velocity in that plane (or round an axis perpendicular to that plane). For, taking 7, @ to denote polar co-ordinates of any point in the boundary, A the enclosed area, and » the component angular velocity in the plane, and continuing the notation of § 59, we have and therefore > 40 ds 200s = otr” — és = w2r"6d = @ x 2A. (e). Definition. (For a fluid moving in any manner), the circulation round the boundary of an infinitesimal plane area, divided by double the area, is called the component rotation in that plane (or round an axis perpendicular to that plane) of the neighbouring fluid. In this statement, the single word “rotation” is used for angular velocity of rotation: and the definition is justified by (c) and (d); also by § 13 (2) above, applied to (p) below. It agrees, in virtue of (p), with the definition of rotation in fluid motion given first of all, I believe, by SroxeEs, and used by HeLmMuoitz in his memorable “ Vortex Motion,” also in THomson and Tart’s “ Natural Philosophy,” §§ 182 and 190 (7). (f). Proposition. If €, n, ¢ be the components of rotation at any point, P, of | a fluid, round three axes at right angles to one another, and » the component | round an axis, making with them angles whose cosines are /, m, n, o= &+nm+ &. _.To prove this, let a plane perpendicular to the last-mentioned axis cut the other | three in A, B, C. The circulation in the periphery of the triangle ABC is, by (0), | equal to the sum of the circuJations in the peripheries PBC, PCA, and PAB. Hence, calling A and a, 8, y the areas of these four triangles, we have, by (@), oA = fa+nB+ &%. VOL. XXV. PART IT. 35 250 SIR WILLIAM THOMSON ON VORTEX MOTION. . But a, 8, y are the projections of A on the ee of the pairs of the rectangular axes; and so the proposition is proved. It follows, of course, that the composition of rotations in a fluid fulfils the law of the compositions of angular velocities of a solid, of linear velocities, of forces, &c. 60. (g). Hence, in any infinitesimal part of the fluid, the circulation is zero in the periphery of every plane area passing through a certain line ;—the resultant axis of rotation of that part of the fluid. But (a) the circulation remains zero in every closed line moving with the fluid, for which it is zero at any time. Hence (h). The axial lines [defined (z)] move with the fluid. (2). Definition. An axial line through a. fluid moving rotationally, is a line (straight or curved) whose direction at every point coincides with the resultant axis of rotation through that point. (7). Proposition. The resultant rotation of any part of the fluid varies in simple proportion to the length of an infinitesimal arc of the axial line through | it, terminated by points moving with the fluid. To prove this, consider any in- finitesimal plane area, A, moving with the fluid. Let w be the resultant rotation, and @ the angle between its axis and the perpendicular to the plane of A. This makes w cos @ the component rotation in the plane of A; and therefore Aw cos @ remains constant. Now, draw axial lines through all points of the boundary of A, forming a tube whose area of normal section is A cos @. The resultant rota- tion must vary inversely as this area, and therefore (in consequence of the in- compressibility of the fluid) directly as the length of an infinitesimal line along the axis. (4). Form a surface by axial lines drawn through all points of any curve in the fluid. The circulation is zero round the boundary of any infinitesimal area of this surface; and therefore (0) it is zero round the boundary of any finite area of it. (2). Let the curve of (£) be closed, and therefore the surface tubular. On this surface let ABCA, A’B’C’A’ be any two curves closed round the tube, and ADA’ any arc from A to A’.. The circulation in the closed path, ADA’B’C’A’/DACBA, is zero by (hk). Hence the circulation in ABCA is equal to the circulation in A'B'C’A’—that is to say, The circulations are equal in all circuits of a vortex tube. (m). Definitions. An axial surface is a surface made up of axial lines. A cortex tube is an axial surface through every point of which a finite endless path, cutting every axial line it meets, can be drawn. Any such path, passing just once round, is called a circuit, or the circuit of the tube. The rotation of a vorter tube is the circulation in its circuit. A vortex shect is (a portion as it were of a collapsed vortex tube) a surface on the two sides of which the fluid moves with different tangential component velocities. SIR WILLIAM THOMSON ON VORTEX MOTION. Zot 60. (z.) Draw any surface cutting a vortex tube, and bounded by it. The surface integral of the component rotation round the normal has the same value for all such surfaces; and this common value is what we now call the rotation of the tube. (0). In an unbounded infinite fluid, an axial tube must be either finite and endless or infinitely long in each direction.* In an infinite fluid with a boundary (for instance, the surface of an enclosed solid), an axial tube may have two ends, each in the boundary surface; or it may have one end in the boundary surface, and no other; or it may be infinitely long in each direction, or it may be finite and endless. In a finite fluid mass, an axial tube may be endless, or may have one end, but, if so, must have another, both in the boundary surface. (p). Proposition. Applying the notation of (/), to axes parallel to those of co-ordinates 2, y, z, and denoting, as formerly, by w, v, 2, the components of the fluid velocity at (z, y, z), we have— ab dw dv be du dw =e dv du f= dy a)» aie Hae)? ae LC TO ae The proof is obvious, according to the plan of notation, &c., followed in § 13 above. (q). Hence by (/), (e), and (2)— dw dv du dw QE iio b> Tf add a a as {u( = — =) +n (E- ae aed (‘i gen Sf (uae + vdy + wdz). where //dS denotes integration over any portion of surface bounded by a closed curve; J(udx + &c.) integration round the whole of this curve; and (/, m, n) the direction cosines of any point (z, y, ~) in the surface. It is worthy of remark that the equation of continuity for an incompressible fluid does not enter into the demonstration of this proposition, and therefore w, v, 7 may be any functions. whatever of a, y,z. In a purely analytical light, the result has an important bearing on the theory of the integration of complete or incomplete differentials. It was first given, with the indication of a more analytical proof than the pre- ceding, in THomson and Tart’s “ Natural Philosophy,” § 190 (7). (7). Propositions (2) (7) (”) (0) of the present section (§ 60) are due to HELM- HOLTZ; and with his ae, for associated rotational and cyclic irrotational motion in an unbounded fluid, to be given below, constitute his general theory of vortex motion. (m) and (0) are purely kinematical; (/) and (7) are dynamical. _ (s). Henceforth I shall call a circuit any closed curve not continuously reducible to a point, in a multiply continuous space. I shall call diferent circuits, any * Vortex tubes apparently ending in the fluid, for instance, a portion of fluid bounded by a figure of revolution, revolving round its axis as a solid, constitute no exception. Each infinitesimal vortex tube in this case is completed by a strip of vortex sheet and so is endless, 252 SIR WILLIAM THOMSON ON VORTEX MOTION. two such closed curves if mutually irreconcilable (§ 58); but different mutually reconcilable closed curves will not be called different circuits. 60. (¢). Thus, (72+1)ply continuous space, is a space for which there are 7, and only n, different circuits. This is merely the definition of § 58, abbreviated by the definite use of the word circuit, which I now propose. The general termin- ology regarding simply and multiply continuous spaces is, as I have found since § 58 was written, altogether due to HetmHoLTz; RremaAnn’s suggestion, to which he refers, having been confined to two-dimensional space. I have deviated some- what from the form of definition originally given by HELMHOLTZ, involving, as it does, the difficult conception of a stopping barrier;* and substituted for it the definition by reconcilable and irreconcilable paths. It is not easy to conceive the stopping barrier of any one of the first three diagrams of § 58, or to understand its singleness; but it is easy to see that in each of those three cases, any two closed curves drawn round the solid wire represented in the diagrams are recon- cilable, according to the definition of this term given in § 58, and therefore, that the presence of any such solid adds only one to the degree of continuity of the space in which it is placed. (w). If we call a partition, a surface which separates a closed space into two parts, and, as hitherto, a barrier, any surface edged by the boundary of the space, HELMHOLTz’s definition of multiple continuity may be stated shortly thus :— A space is (n+1)ply continuous if n barriers can be drain across it, none of which is a partition. (v). HetMHoutz has pointed out the importance in hydrokinetics of many-— valued functions, such as tan ~, which have no place in the theories of gravi- tation, electricity, or magnetism, but are required to express electro-magnetic potentials, and the velocity potentials for the part of the fluid which moves irro- tationally in vortex motion. It is, therefore, convenient, before going farther, that we should fix upon a terminology, with reference to functions of that kind, — which may save us circumlocutions hereafter. (w). A function ¢ (a, y, z) will be called cyclic if it experiences a constant — augmentation every time a point P, of which a, y, z are rectangular rectilineal co-ordinates, is carried from any position round a certain circuit to the same — position again, without passing through any position for which either = a or dd q, becomes infinite. The value of this augmentation will be called the cyclic * But without this conception we can make no use of the theory of multiple continuity in hydrokinetics (see §§ 61-63), and Hztmuottz’s definition is, therefore, perhaps preferable after all to that which I have substituted for it. Mr Crerk Maxwe zt tells me that J. B. Listine has more recently treated the subject of multiple continuity in a very complete manner in an article entitled “ Der Census raumlicher Complexe.”—Kdénigl. Ges. Gittingen, 1861. See also Prof. Cayzzy “ On the Partition of a Close.”’—Phil. Mag. 1861. SIR WILLIAM THOMSON ON VORTEX MOTION. 253 constant for that particular circuit. The cyclic constant must clearly have the same value for all circuits mutually reconcilable (§ 58), in space throughout which the three differential coefficients remain all finite. 60. (z). When the function is cyclic with reference to several different mutually irreconcilable circuits, it is called polycyclic. When it is cyclic for only one set of circuits, it is called monocyclic. EXAMPLE.—The apparent area of a circle as seen from a point (2, y, 2) anywhere in space, is a monocyclic function of x, y, z, of which the cyclic con- stant is 47. The apparent area of a plane curve of the (2n)th degree, consisting of 2 detached closed (that is finite endless) branches (some of which might be enclosed within others) is an »-cyclic function, of which the » cyclic constants are essen- tially equal, being each 47. Algebraic equations among three variables (2, y, ~), may easily be found to represent tortuous curves, constituting one or more finite, isolated, endless branches (which may be knotted, as shown in the first three diagrams of § 58, or linked into one another, as in the fourth and fifth). The integral expressing what, for brevity, we shall call the apparent area of such a curve, is a cyclic function, which, if polycyclic, has essentially equal values for all its cyclic con- stants. By the apparent area of a finite endless curve (tortuous or plane), I mean the sum of the apparent areas of all barriers edged by it, which we can draw without making a partition. It is worthy of notice that every polycyclic function may be reduced to a sum of monocyclic functions. (y). Fluid motion is called cyclic unless the circulation is zero in every closed path through the fluid, when it is called acyclic. Rotational motion is (e) essen- tially cyclic. (z). Irrotational motion may [ § 59 (/)] be either acyclic or cyclic. If cyclic it is monocyclic if there is only one distinct circuit, or polycyclic if there are several distinct circuits, in which there is circulation. It is purely cyclic if the boundary of the space occupied by irrotationally moving fluid is at rest. If the boundary moves and the motion of the fluid is cyclic, it is acyclic compounded mith cyclic. 61. (a). We are now prepared to investigate the most general possible irrota- tional motion ofa single continuous fluid mass, occupying either simply or multiply continuous space, with for every point of the boundary a normal component velocity given arbitrarily, subject only to the condition that the whole volume remains unaltered. | (0).” Genesis of acyclic motion. Commencing, as in § 3, with a fluid mass at rest throughout, let all multiplicity of the continuity of the space occupied by it be done away with by temporary barrier surfaces, 6,, 8, ... stopping the circuits, as described in § 57. The bounding surface of the fluid, which ordinarily consists VOL. XXV. PART Il. : 37 254 SIR WILLIAM THOMSON ON VORTEX MOTION. of the inner surface of the containing vessel, will thus be temporarily extended to include each side of each of these barriers. Let now, as in § 3, any possible motion be arbitrarily given to the bounding surface. The liquid is consequently set in motion, purely through fluid pressure ; and the motion is [$§ 10-15, or 60, 59] _ throughout irrotational. Hence irrotational motion fulfilling the prescribed sur- face conditions is possible, and the actual motion is, of course (as the solution of every real problem is), unambiguous. But from this bare physical principle we could not even suspect, what the following simple application of GREEN’s equation proves, that the surface normal velocity at any instant determines the interior motion irrespectively of the previous history of the motion from rest. 61. (c). Determinacy of irrotational motion in simply continuous space. In § 57 (1), which is mney applicable, as the volume is now simply continuous, make 9 = 9, and put y’9 = 0, so that 9 may be the velocity potential of an incompressible fluid. That double naetion becomes the following single equa- tion— ho fe dg? Sf Gtr e + 5 de dy dz= [| done ; where the surface integration //do must now include each side of each of the barrier surfaces 6,, 8,..... Hence, if te = 0 for every point of the bounding surface, we must have d dg? dg? SSS (Ge + Ge + Fe) eyo, dg. do de ~ ip. which requires that that is to say, if there is no motion of the boundary surface in the direction of the normal, there can be no motion of the irrotational species in the interior ; whence — it follows that there cannot be two different internal irrotational motions with the same surface normal component velocities. Thus, as a particular case, beginning with a fluid at rest, let its boundary be set in motion; and brought again to rest at any instant, after having been changed in shape to any extent, through any series of motions. The whole liquid comes to rest at that instant. A demonstration of this important theorem, which differs essentially from the preceding, and includes what the preceding does not include, a purely analytical proof of the possibility of irrotational motion throughout the fluid, fulfilling the arbitrary surface-condition specified above, was first published in THomson and Tair’s “ Natural Philosophy,” § 317 (8), and is to be given below, with some variation and extension. In the meantime, however, we satisfy ourselves as to the possibility of irrotational motions fulfilling the various surface-conditions with which we are concerned, because the surface motions are possible and require the fluid to move, and [§§ 10-15, or § 59] because the fluid cannot acquire SIR WILLIAM THOMSON ON VORTEX MOTION. 255 rotational motion through fluid pressure from the motion of its boundary; and we go on, by aid of Green’s extended formula [§ 57 (7)], to prove the determinate- ness of the interior motion under conditions now to be specified for multiply continuous space, as we have done by his unaltered formula [§ 57 (1)] for simply continuous space. 62. Genesis of Cyclic Irrotational Motion.—In the case of motion considered in § 61, the value of the normal component velocity is not independently arbitrary over the whole boundary, but has equal arbitrary values, positive and negative, on the two sides of each of the barriers 6,, 8,, &c. We must now introduce a fresh restriction in order that, when the barriers are liquefied, the motion of the fluid may be irrotational throughout the space thus re-opened into multiple continuity. For although we have secured that the normal component velocity is equal everywhere on the two sides of each barrier, we have hitherto left the tangential velocity. unheeded. If they are not equal on the two sides, and in the same direction, there will be a finite slipping of fluid on fluid across the surface left by the dissolution of the infinitely thin barrier membrane; constitut- ing [§ 60 (mm) above], as Hetmuoutz has shown, a “ vortex sheet.” The analytical expression of the condition of equality between the tangential velocities is that the variation of the velocity potential in tangential directions shall be equal on the two sides of each barrier. Hence, by integration, we see that the difference between the values of the velocity potential on the two sides must be the same over the whole of each barrier. This condition requires that the initiating pres- sure be equal over the whole membrane. For, at any time during the instituting of the motion, let p,, p, be the pressures at two points P,, P, of the fluid, and moving with the fluid, infinitely near one another on the two sides of one of the membranes, so that the pressure 7, which must be applied to the membrane to produce this difference of fluid pressure on the two sides, is equal to p, — p, in the direction opposed to p,. And let ¢,, 9, be the velocity potentials at P, and P,, so that if /ds denote integration from P, to P,, along any path P,PP, what- ever from P, to P,, altogether through the fluid (and therefore cutting none of the membranes), and ¢ the component of fluid velocity along the tangent at any point of this curve, we have oe Mite cenas elt Genk) (0: Hence, by (6) of § 59, eee ave re fo) 0), where q,, g, denote the resultant fluid velocities at P, and P,. Now, the normal component velocities at P, and P, are necessarily equal; and therefore, if the components parallel to the tangent plane of the intervening membrane are also equal, we have he oD, 256 SIR WILLIAM THOMSON ON VORTEX MOTION. and the preceding becomes sid ee ee vires, hoe But if the tangential component velocities at P, and P, are not only equal, but in the same direction, g,— 9, must, as we have seen, be constant over the membrane, and therefore 7 must also be constant. Suppose now that after pressure has been applied for any time in the manner described, of uniform value all over the membrane at each instant, it is applied no longer, and the membrane (having no longer any influence) is done away with. The fluid mass is left for ever after in a state of motion, which is irrota- tional throughout, but cyclic. The “circulation” [§ 60(a)], or the cyclic constant being equal to ¢, — ¢,, for every circuit reconcilable with P,PP,P, is given by the equation %—-%,=—fadt . ; ; : : : (4), /dt denoting a time-integral extended through the whole period during which = had any finite value. The same kind of operation may be performed, on each of the 7 barriers temporarily introduced in § 61 to reduce the (x+1)fold continuity of the space occupied by the fluid, to simple continuity. The velocity potential at any point of the fluid will then be a polycyclic func- tion [§ 60 (z)] equal to the sum of the separate values corresponding to the pressure separately applied to the several barriers. ‘Thus we see how a state of irrotational motion, cyclic with reference to every one of the different circuits of a multiply continuous space, and having arbitrary values for the corresponding cyclic constants, or circulations, may be generated. But the proof of the possibility of fluid motion fulfilling such conditions, founded on this planning out of a genesis of it, leaves us to imagine that it might be different according to the infinitely varied choice we may make of surfaces for the initial forms of the barriers, or according to the order and the duration of the applications of pressure to them in virtue of which these figures may be changed more or less, — and in various ways, before the initiating pressures all cease; and hitherto we have seen no reason even to suspect the following proposition to the con- trary. 63. (Prop.) The motion of a liquid moving irrotationally within an (7+1)ply continuous space is determinate when the normal velocity at every point of the boundary, and the values of the circulations in the » circuits, are given. This is proved by an application of Green’s extended formula (7) of § 57, showing, as the simple formula (1) of the same section showed us in § 61 for simply continuous space, that the difference of the velocity potentials of two motions, each fulfilling this condition, is necessarily zero throughout the whole SIR WILLIAM THOMSON ON VORTEX MOTION. 257 fluid. Let 9, 9 be the velocity potentials of two motions fulfilling the prescribed conditions, and let ; p=e-—¢. At every point of the boundary (the barriers not included) the prescribed con- ditions require that }9=2¢’, and therefore »=0. Again, the cyclic constants for 9’ are equal to those for g; those for {, being their differences, must there- fore vanish. Hence, if the 9 and 9’ of § 57 (7) be made equal to one another and to avoid confusion with our present notation we substitute & for each, the second members of that double equation vanish, and it becomes simply Tigao lard yoit _ of HE + Oy dz? diz dy dz ==(() p which, as before (§ 61), proves that /=0, and therefore 9 —9; and so establishes our present proposition. ExampLe (1). The solution ¢= tan“ considered in § 56, fulfils LapLacr’s equa- tion, V’9=0; and obviously satisfies the surface condition, not merely for the annular space with rectangular meridional section there considered, but for the hollow space bounded by the figure of revolution obtained by carrying a closed curve of any shape round any axis (OZ) not cutting the curve; which, for brevity, we shall in future call a hollow circular ring. Hence the irrotational motion possible within a fixed hollow circular ring is such that the velocity poten- tial is proportional to the angle between the meridian plane through any point, and a fixed meridian. EXAMPLE (2). The solid angle, a, subtended at any point (a, y, z), by an infinitesimal plane area, A, in any fixed position, fulfils LapLace’s equation y?a=0. This well-known proposition may be proved by taking A at the origin, and per- pendicular to OX, when we have —gayem “eee rey 8 oO for which V’a = 0 is verified. The solid angle subtended at (z, y, z) by any single closed circuit is the sum of those subtended at the same point by all parts into which we may divide any limited surface having this curve for its bounding edge. [Consider particularly curves such as those represented by the first three diagrams of § 58.] Hence if we call ¢ the solid angle subtended at (2, y, z) by this surface, LAPLAcE’s equa- v’¢ is fulfilled. Hence ¢ represents the velocity potential of the irrotational motion possible for a liquid contained in an infinite fixed closed vessel, within which is fixed, at an infinite distance from the outer bounding surface, an in- finitely thin wire bent into the form of the closed curve in question. VOL. XXV, PART Il. 3U 258 SIR WILLIAM THOMSON ON VORTEX MOTION. The particular case of this example for which the curve is a circle, presents us with the simplest specimen of cyclic irrotational motion not confined [as that. of Example (1) is] to a set of parallel planes. The velocity potential being the apparent area of a circular disc (or the area of a spherical ellipse) is readily found, and shown to be expressible readily in terms of a complete elliptic integral of the third class, and therefore in terms of incomplete elliptic functions of the first and second classes. The equi-potential surfaces are therefore traceable by aid of LrecENDRE's tables. But it is to HeLtmMHotrz that we owe the remarkable and useful discovery, that the equations of the stream lines (or lines perpendicular to the equi-potential surfaces) are expressible in terms of complete integrals of the first and second classes. They are therefore easily traceable by aid of LEGENDRE’s tables. The annexed diagram, of which we shall make much use later, show these curves as calculated and drawn by Mr Macraruane from HELMHOLTZ’s. formula, expressed in terms of rectangular co-ordinates. An improved method of tracing them is described in a note by Mr CLerK MaxweE tt, which he has kindly allowed me to append to this paper. EXAMPLE 3. The motion described in Example 2 will remain unchanged out- side any solid ring formed by solidifying and reducing to rest a portion of the fluid bounded by stream lines surrounding the infinitely thin wire. Thus we have a solid thick endless wire or bar forming a ring, or an endless knot as illustrated in the first three diagrams of § 59, of peculiar sectional figure depend- ing on the stream lines round the arbitrary curve of Example 2; and the cyclic irrotational motion which, if placed in an infinite liquid it permits, is that whose velocity potential is proportional to the solid angle defined geometrically in the general solution given under Example 2. 64. Kinetic energy of compounded acyclic and polycyclic irrotational motion— — kinetico-statics. ‘The work done in the operation described in § 62 is calculated directly by summing the products of the pressure into an infinitesimal area of the surface, into the space through which the fluid contiguous with this area moves in the direction of the normal, for all parts of the surface, whether boundary or internal barrier, where the genetic pressure is applied, and for all infinitesimal divisions of the whole time from the commencement of the motion. (a). Let w denote the work done, and /dé time-integration, from the beginning of motion up to any instant. At any previous instant let p be the pressure, q the velocity, and @ the velocity potential, of the fluid contiguous to any element do of the bounding surface, /& the difference of fluid pressures on the two sides of any element, ds, of one of the internal barriers, and N the normal com- ponent of the fluid velocity contiguous to either do or ds. The preceding state- _ ment expressed in symbols is W =/at[—ffpNdo + S/fkNds] . ee SIR WILLIAM THOMSON ON VORTEX MOTION. 259 > denoting summation for the several barriers if there are more than one. According to the general hydrokinetic theorem for irrotational motion [§ 59 (6) compare with § 31 (5)], with 9 expressed in terms of the co-ordinates of a point moving with the fluid, we have do ; eS eee oth eames reser 3 i: Now, let us suppose the pressure to be impulsive, so that there is infinitely little change of shape either of the bounding surface or of the barriers during the time /d¢. This will also imply that 2S is infinitely great in comparison with 4q°; so that d LS a . a . c c ° (8). And according to the notation of § 57 we have Ne Dcuemecet cis he Uk oy cee hs Also & is constant over each barrier surface. Hence (6) becomes Ww fal fe veda + 3k ffveus | Lote aay 64. (0). The initiating motion of the bounding surface and the pressures on the barriers may be varied quite arbitrarily from the beginning to the end of the impulse; so that the history within that: period of the acquisition of the pre- scribed final velocity may be altogether different, and not even simultaneous, in different parts of the bounding surface. Thus 4, and &, may be quite different functions of ¢; provided only /4,dt and /k,dt have the prescribed values, which we shall denote by &, and &, respectively. : (c). But, for one example, we may suppose ¢ to have at each instant of /dt everywhere one and the same proportion of its final value; so that if the latter denoted by ®, and if we put BA SS FN: . 4 . . ° ° Gy m is independent of co-ordinates of position, but may of course be any arbitrary function of the time. Hence, observing that as the final value of m is 1, (10) becomes Wil fPvbde + Skea] . . . . (12). (d). The second member of this equation doubled agrees with the two equal 260 SIR WILLIAM THOMSON ON VORTEX MOTION. second members of (7) § 57 with 9 and 9’ each made equal to ®. And the first member of that equation becomes twice the kinetic energy of the whole motion. Hence, when 9’=¢, and V’9=0, (7) of § 57 expresses the equation of energy for the impulsive generation, of the fluid motion corresponding to velocity potential 9, by pressures varying throughout according to the same function of the time ; the first member being twice the kinetic energy of the motion generated, and the second twice the work done in the process. 64. (e). As another example, let us suppose the initiating pressures to be so applied as first to generate a motion corresponding to velocity potential 9, and after that to change the velocity potential from 9 to 9+’, denoting by ¢ and ¢’ any two functions, such that 9+9’=©’, and each fulfilling Lapiace’s equation: and let the augmentation from zero to 9, and again from ¢ to 9+¢’ be uniform through the whole fluid. The work done in the first process, found as above (12), Lf [fod do+ x [de ds] as) i ie if x,, «,, &c., denote the cyclic constants relative to 9, as k,, &,, &c., relatively to ®, and the additional work done in the second process, similarly found, is 4 //o' (209 +09’) do+ zx //(29 +309’) ds] : : (14). (f). Now, as we have seen (§ 63) that the actual fluid motion depends at each instant wholly on the normal velocity at each point of the bounding surface and the values of the cyclic constants, it follows that the work done in generating it ought to be independent of the order and law, of the acquisition of velocity at the bounding surface, and of the attainment of the values of the several cyclic constants. Hence, the the sum of (13) and (14) ought to be equal to (12). But if, for ® in (12) we substitute 9+’, the difference between its value and that of the sum of (13) and (14) is found to be 4L//(9d9 —9'00) do+ UK/de'ds—K' [/Beds)] . s : (15); which, being the half the difference between the two equal second members of (7) § 57 for the case of v7e=0 and y7o’=0, is equal to zero. Hence, the equality of the second members of (7) § 57, con- stitutes the analytical reconciliation of the equations of energy for different modes of generation of the same fluid motion. a eae ap ieeee ee @RaEt? y VIIl—On the Rotation of a Rigid Body about a Fixed Point. By Professor Tarr. (Received October 13th, Read December 21st, 1868.) Although it is very improbable that there remains to be discovered any new, and at the same time simple, fact connected with a question which has been elaborately treated by many of the greatest mathematicians of this and the pre- ceding century, the employment of a new mathematical method may enable us to present some of their results in a more intelligible form, and with far less expenditure of analytical power than has hitherto been deemed necessary ; and it may give us such an insight into the question, that we shall be able easily to discover the mutual relations among the various processes which have been already employed; so far, at least, as these differ in principle, and not merely in the peculiar co-ordinates assumed for the purpose of simplifying the equations. Such a method is that of Quaternions, which seems to be expressly fitted for the symmetrical evolution of truths which are usually obtained by the ordinary Car- tesian methods only after great labour of calculation, and by modes of attack so indirect, and at first sight so purposeless, as to bewilder all but a very small class of readers. Quaternions afford so clear a view of the nature of the question they are applied to, that even the student, if he have some little knowledge of them, can often see why a transformation is made, whose object he would have been unable to discover had the problem. been masked in the unnecessarily arti- ficial difficulties of Cartesian geometry, or the outrageously repulsive formule of spherical trigonometry. By far the most elegant and most easily intelligible representations of the motion of a solid body yet discovered, are due to Pornsot. With the following extract from his splendid work, Théorie Nouvelle de la Rotation des Corps (Liou- ville’s Journal, 1851), I most cordially agree,— though it appears to me that, when he does condescend to use analytical methods, he is by no means so happy as others have been, who, trusting to mathematical analysis alone, had not the benefit of his beautiful geometrical representations. But in perusing the extract, let the reader bear in mind that a guaternion equation is quite as suggestively in- telligible, to those who understand it, as any geometrical diagram can possibly be. In fact, Imight almost say, that it is more readily intelligible than diagrams usually VOL. XXV. PART II. 3X 262 PROFESSOR TAIT ON THE ROTATION OF A are; for, in reading a work illustrated by figures, we have generally to go through a laborious explanation of what the figure is intended to represent before we can make use of it for further developments. On the other hand, a purely quaternion formula draws, as it were, its own figure in the reader’s mind, and saves him at least the trouble just mentioned. In this way every one has his figures drawn so as best to suit himself, and is not perplexed by having to pick up the prin- ciples on which they have been drawn for him by another, very probably of a different mode of thought. Still, such words as the following, when properly applied, not to quaternions but, to ordinary so-called analysis, must always convey a much-needed warning :—“ Gardons-nous de croire qu’une science soit faite quand _ on l’a réduite 4 des formules analytiques. Rien ne nous dispense d’étudier les choses en elles-mémes, et de nous bien rendre compte des idées qui font objet de nos spéculations. N’oublions point que les résultats de nos calculs ont pres- que toujours besoin d’étre vérifiés, d’un autre cété, par quelque raisonnement simple, ou par l’expérience. Que si le calcul seul peut quelquefois nous offrir une vérité nouvelle, il ne faut pas croire que, sur ce point méme, lesprit n/ait plus rien a faire: mais, au contraire, il faut songer que, cette vérité étant indé- pendante des méthodes ou des artifices qui ont pu nous y conduire, il existe certainement quelque démonstration simple qui pourrait la porter a l’évidence: ce qui doit étre le grand objet et le dernier résultat de la science mathématique.” : “Ce n’est qu'une apparente fécondité de cette méthode de pur led qu’on appelle assez improprement l’analyse. Car si les théorémes sont déja connus on découvre bien vite les transformations 4 faire pour que les équa- tions y répondent; mais quand on n’a aucune idée de ces théoremes, on ne trans- forme guere qu’au hazard, et le plus souvent on n’arrive 4 rien. La vraie analyse est dans l’examen attentif du probleme a résoudre, et dans ces premiers raison- nements qu’on fait pour le mettre en équations. ‘Transformer ensuite ces équa- tions, c’est-a-dire les combiner ensemble, ou en poser d’autres évidentes que Yon combine avec elles, n’est au fond que de la synthése; 4 moins que Vidée de chaque transformation ne nous soit donnée par quelque vue nouvelle de l’esprit, — ou quelque nouveau raisonnement,ce qui nous fait rentrer dans la véritable analyse. Hors de cette voie lumineuse, il n’y a donc plus d’analyse, mais une obscure synthése de formules algébriques que l’on pose, pour ainsi dire, lune sur l’autre, et sans trop prévoir ce que pourra donner cette combinaison. Voila les idées nettes qu'il faut attacher aux mots: et c’est au fond ce que tout le monde parait sentir, puisqu’on dit trés-bien une hewreuse transformation, et qu’on ne dit point un heureux raisonnement, ni une hewreuse analyse.” | I was led to the following investigations by a desire to simplify, if possible, — by asymmetrical process, the usual modes of treating the rotation of a rigid body. The methods ordinarily employed are essentially unsymmetrical, ¢.g. the determi- nation, by means of three angles, of the position of the body at a given time, when RIGID BODY ABOUT A FIXED POINT. 263 its angular velocities about its principal axes are given, or can be found. It was not till after my investigations were nearly completed, and the chief fundamental equations had been communicated to the British Association at Norwich, that I became aware of the existence of Professor CayLry’s* admirable Second Report on Theoretical Dynamics, which contains an immense amount of valuable informa- tion, especially bearing on the present subject. From this I found that the notion of attaining symmetry, by seeking the single rotation which would bring the body from some initial position to its actual position at a given time, which had been suggested to me by Hamitron’s} beautiful results, is due to EULER; and I ‘also found that, by the help of certain formule due to RopRicuEs, CAYLEY has completely solved the question in the ‘‘ Cambridge Mathematical Journal,” vol. iii. (1843).{ Comparative symmetry, however, is only attained by means of a brilliant display of analytical power at a great expense of time and bewilder- ment to the ordinary reader. In the ‘“‘ Philosophical Magazine,” 1848, ii., Cay- LEY has translated some of his formule into quaternions, and has thus arrived, though by a very circuitous route, at the fundamental kinematical equation of the present paper (§ 7 below). He does not give it in its simplest form, and he remarks that he has “ not ascertained whether it leads to any results of import- ance.” Under these circumstances, I have had no hesitation in laying this paper before the Society; for although many of its more important results have been otherwise obtained, few, with the exception of those due to Hamitton (which will be given in their turn), have hitherto been arrived at so easily or in such simple forms. As symmetry has been the particular object which I have had in view, by far the greater part of the investigation bears upon the determination of the qua- ternion, by which the transition can at one step be effected from any initial position to the actual position of the body at a given time; and a good many results have been retained, which are of more interest as properties of quater- nions, than as regards their connection with the physical question. In the kine- matical part of the paper, to which I proceed as a necessary preliminary, I have exhibited, for facility of comparison with other works on the subject, the values of this quaternion in terms of the various sets of co-ordinates usually employed. This, I need hardly say, does not lead to very simple or elegant results; but the fault is due, not to quaternions, but to the wanaturalness and want of symmetry of these common methods of attacking the problem. On the other hand, nothing can be neater than the set of formule which are suggested directly by quaternions. * Report on the Progress of the Solution of certain Special Problems of Dynamics.—Brit. Ass. Report, 1862. t Proc. R. I. A., 1846. See also §§ 1 and 4 below. ¢ See also Cambridge and Dublin Math. Journal, vol i. (1846). 264 PROFESSOR TAIT ON THE ROTATION OF A §§ 1-14. Kinematics of a Rigid System with one Point fixed. 1, If ¢ represent the instantaneous axis of a rigid body, its length being employed to denote the angular velocity about it; then, = being the vector of any point of the body, drawn to a point in the axis as origin, we obviously have (using NEwTon’s convenient notation) ee a Ver es This formula was given long ago by Hamitton. 2. Every infinitely small displacement of a Rigid System, one point of which is fixed, takes place about an instantaneous axis. Let z, 7,, be the vectors of any two points of the system, referred to the fixed point as origin; then, whatever displacements may occur, we must have (on account of the rigidity of the system) ) Ta = const., Ta, = const. , Saaz, = const. Hence, differentiating with respect to ¢, Sax = 0, Saaz, = 9, Saa, + Sas, = 0 : ; : (2). The first shows that a = Ver, where ¢ is some vector. With this the third gives 6 a Veey = 10; which must be true for all values of «. Hence we have also a, =, Vem. This is consistent with the second of equations (2), so that the existence of the — instantaneous axis is proved. From the fact of its existence follows at once the representation of the motion, in every case, by the rolling of a cone fixed in the rigid system upon another cone fixed in space. The case of finite displacements will be treated farther on (§ 5 below). 3. To find the instantancous axis, when the vectors, and vector-velocities, of — any tivo points of the system are given. Here we have to find ¢ from the two equations Za Niece aN ear They give by inspection Vase, =— Sau, = sSaa,, or, more symmetrically, RIGID BODY ABOUT A FIXED POINT. 265 4, If q be any quaternion, the operator GG igs turns the vector, quaternion, or system, to which it is applied, about the axis of q through double the angle of q. This was one of HamiLTon’s early* discoveries in his new calculus, but it was independently obtained by Cayuey (only a month or two later)} by the help of the formule of RopricuEs already referred to. Conversely, when its truth has been established by an independent process, these formule may be at once derived from it: not only far more simply, but even in a somewhat improved form. The quaternion g may obviously be considered as a mere versor, since its tensor does not appear in the operatorg( )q”, and a glance at the annexed figure proves, by the multiplication of versor arcs, the theorem above stated. (See Tarr’s Quaternions, § 353, or Hamitton’s Lectures, § 282, and Elements, § 308 (9).) 5. In quaternions we have, of course, whatever be g and 7, (qr) a= pogo, Hence Tigi vir ds =a Gn, which shows how to combine any two rotations into a single one. 6. Given the initial and final positions of any two vectors. of a rigid system, drawn from the fixed point; to find the quaternion operator by which the rotation can be effected. Let them be a, 8, a,,@,, and let g be the required quaternion, then Gi) maaan rGOd > —: 6, <; or q@=ag,9e=6q . : : : : (3). Hence S(a—-a)q=0, S(P—-B,)¢ =0, or Vq || Vi@— #,) (B— By) * Proc. R. I. A. November 11, 1844. + Phil. Mag. Feb. 1845. VOL. XXV. PART II. 3 Y 266 PROFESSOR TAIT ON THE ROTATION OF A as we might at once have seen by the geometry of the question. Hence qg=2%+ yV(a—«,)(B—B,). By the help of this, the first of equations (3) becomes 0 =a(a—m) + y {V(a—%) (B—B,).«~ a, Via — a) (B—B,)} or 0O=a2+yS(ata,)(B—B,). [ The second of equations (3) merely gives us a condition which is equivalent to this, because S(a + a,)(@—B,) =—S/a - a,)(B + B,) or SaB = Sa,8,. | Thus, finally, = y(—S(a+«,)(@-B,) + V@ - a) (8—-8B,)) =—y[(@-B,)«+ «,(8—8,)] where, as was to be expected, the tensor is left indeterminate. 7. Given the instantaneous axis in terms of the time, it is required to find the single rotation which will bring the body from any initial position to its position at a given time. If a be the initial vector of a point of the body, = the value of the same at time ¢, and g the required quaternion, we have a= gag L 3 é AP at - ~ (4). ‘Differentiating with respect to ¢, this gives a = gag — gag! gq , = gq. gag — gag. gq , = 2V (Vag — . gag). But e=Vew=YV., eqag —! - Hence, as gag~! may be any vector whatever in the displaced body, we must have sseveg=) 2"! .. .- ves ee This is the fundamental kinematical relation already referred to. CAayLEy’s* quaternion form of it (which will be understood by the help of § 13 below) is ~(ip +jq + kr) = 2 32 =. * Phil. Mag., Sept. 1848. be. RIGID BODY ABOUT A FIXED POINT. 267 where A=1+ art jut ky. 8. The result of § 7 may be stated in even a simpler form than (5), for we have always, whatever quaternion g may be, and, therefore, if we suppose the tensor of g, which may have any value what- ever, to be a constant (unity, for instance), we may write (5) in the form Se i, ORES, TSO CAE Ne A ANG. An immediate consequence, which will be of use to us later, is GiGpre = 2g”. : (7). 9. It may appear to some that the demonstration of § 7, founded on the differentiation of quaternions, is not very convincing. For such it is easy to put it in an expanded form in which no process of differentiation of a function of a quaternion is alluded to—though in principle it is the same proof. Let g become g+~7 in the indefinitely short interval tr. Then the change of position of the extremity of (op = (6050) me may be expressed either as Veo .r or as (+7) «@(q+7r) — gag. Hence rV.egag-* = (9 + r)a(y + r)~* — gag’, lig ad tgs) + — alg, = pate (ta) e+ Keo) - 14 NDE Ka) = ros (a + ry (Ve-*r. a) grt. But 7 is the change of q in time 7, and we may therefore write AG) Substituting, expanding, and neglecting small quantities of the orders 7? and upwards, we have 268 PROFESSOR TAIT ON THE ROTATION OF A V.. eqag- = 29 Vi(Vo 9 e)g = q((Vq-"¢.4—«aVq'¢)q = 9(Vq-*¢)q—*. gag * — gag-*.q(Vq-*q)q-* = Vagq-* . gag—* — gag-* . Vaq-* = 2V (Vag *. gag") the same equation as in § 7. 9*, [Inserted Dec. 19th, 1868.] A geometrical investigation may also easily be given, if for no other purpose than to serve as an instance of the justice of my introductory remarks on diagrams as compared with quaternion equations. Let Q, Q’ be the poles, on the unit-sphere, of the versor angles BQE’, BQ'E’,, whose bounding arcs intersect in E’; and let P, P’ be the poles of these bounding arcs, A the pole of QQ’B [A coincides with the projection of O, the centre of the sphere]. Then evidently AP (=q) and AP’ (=q’) are the versor ares, correspond- ing to the above versor angles. Obviously the point E’ is deduced from a point é — on the other side of the sphere [whose projection coincides with that of E’], by a rotation about Q through double of BQE’, or about Q’ through double of BQ’E. Hence we have obviously RIGID BODY ABOUT A FIXED POINT, 269 Thus a rigid body may pass from the position g( )q~* to the position g( )q, whatever be q and 7, by a rotation about OH’. Also, by g( )qg7,Q remains fixed; but by g'( ) gq’ it moves to R, where . Here the vectors 7, 7, & in the original position of the body correspond to A OA, OB, OC, respectively, at time ¢. The transposition is effected by—/irst, a rotation ~ about £; second, a rotation 6 about the new position of the line VOL. XXV. PART II. oz 270 PROFESSOR TAIT ON THE ROTATION OF A originally coinciding with 7; third, a rotation } about the final position of the line at first coinciding with /. Let 2, 7, & be taken as the initial directions of the three vectors which at time ¢ terminate at A, B, C respectively. The rotation \ about & has the operator Wy w Pat he: ce: This converts 7 into 7, where ie 2a ae =j cos ~—7sin yp. The body next rotates about 7 through an-angle 6. This has the operator It converts / into 8 OG {7 ate ae 6 aa © 6 238 C= 0S35 = CoS 5 + 1SiN 5 k cos 5 — 78IN 5 =kcosé+ sin 6(i cos) +7 sin Y). The body now turns through the angle ¢ about ¢, the operator being ? =p Caen jee Hence poy Q=Cn = (cos 3 + ¢sin 5) (cos - +7 sin 3) (cos = + ksin ¥) = (‘cos $ + ¢sin $Y [cos 5 cos + keos§ sin} + sin § cos 5) ¥ (jeos - ésinyy) aide 3 sin z ¥ (i cos w.+ 7 sin v)] ty 8 = (cos $ + ¢sin5 $ ) [eos § 3 008 = — ising sin § + 7 sin 3 COs ¥ + Ieeos § sm ¥] = eos $ cos 5 cos +sin$ sin § sin Y sin @ cos — sin $ sin 5 cosy sin @ sin yy — sin $ cos 5 sin 4 cos @ + i(- cos & sin 5 sin + sin $ cos $ cos + sin 6 cos - sin ® sin $ cos % cos + sin ¥ cos § sin & sin Osinwp) + j (cos F sin § cos-¥ + sin $ cos & cos “¥ sin 6 sinw — sin & sin $ sin 5 cos — sin cos 5 sin ‘5 sin @ cos yr) ‘ + ie( cos 8 cos § sin & + sin? cos $ cos ¥ cos +sin & sin & sin sino sin + sin ® sin $ cos sin 6 cos Wr) St ile 0G 4 peep) Od irae es pty —-w 0 = cos gy «COS FH VSN “Sin 5 + J cos PS ™ in § + Hesin 7 085 which is, of course, essentially unsymmetrical. RIGID BODY ABOUT A FIXED POINT. 11. To jind the usual equations connecting b, 9, > with the angular velocities about three rectangular axes fixed in the body. Having the value of ¢ in last section in terms of the three angles, it may be useful to employ it, in conjunction with equation (6) of § 8, partly as a verifi- cation of that equation. Of course, this is an exceedingly roundabout process, and does not in the least resemble the simple one which is immediately suggested by quaternions. whence or We have = lice Lag 29 = eq = {w, OA + w, OB+ w,0C} Q, 2g-1g = ¢*{u, OA + o, OB +o, OC}, 2g = q (ta, + jo, + ks). This breaks up into the four (equivalent to three independent) equations t) 5 O= t) 0 LS cos # + cos 5) = — a, sin 2 sin 5 — a, cos ® ee, sin tt cos 6 ) : 25,(sin 25 ¥ sin 5) = a, cos 4 ™ cos 5 —a,sin *F™ cos? +a, 008 *5 A a d = a 2n0 - Ot) G+ 0 ; aan) 25,(cos > sin 5) = , SID - cos 4 3 +4, cos —> cos 5 —, sin * kd 9 3 s1n. 3 = sin 2+ ae 5) == a, cos *—* sin § = + w, sin es =e sin 3 + a, cos ®t cos 5 From the second and third eliminate ¢—, and we get by inspection diy pil. 6 cos 5. d= (a, sin + w, Cos 4) COS 5» or = w, sin ¢ + w, cos , : : ; 3 (8). Similarly, by eliminating 6 between the same two equations, sin : (¢@—1) =a, sin 5 + a, 00S 9 cos 5 — , Sl) g cos 5. And from the first and last of the group of four cos : (@+ b) = a, cos — 0 cos ¢sin 5 + , sin gsin 5. These last two equations give OPP ancOS tone on ee | (9). ¢ cos 6+ =(— a, cos ? + w, sin ¢) sin 6 + , cos 6. From the last two we have psind=—a,coo?to, sng . . . . (10). (8), (9), (10) are the forms in which the equations are usually given. Ziel 272 PROFESSOR TAIT ON THE ROTATION OF A 12, The essential want of symmetry, in the system of three angles usually employed, has led me to try various other systems. None of them, however, were quite symmetrical, and I therefore introduce only one of them here. Suppose the position of the body to be determined by the angles y, 4, ¢, through which it has been made to turn about three rectangular axes which are fixed in it; and which may be considered as : ‘i w, dt, : As o, dt, : ve o,dt respec- | tively; @,, ©,, ©, having values in general different from ,, »,, ©,, but easily deducible from them. The essential difference between this process and the ordinary one (just treated), consists in using rotations about each of the three axes fixed in the body, instead of one about one axis, followed by another about a second, and then a final rotation about the jist axis instead of the third. We have first a rotation \ about 7, next 6 about the new position of y, and finally @ about the final position of 4. ue Y ° oy ix( )@~ = is the operator due to the rotation about 7. It converts 7 into n=jcos) +ksnwy kcosy —jsiny. Next, the operator due to the rotation 6 is and & into Z at! ce Oa and this converts £ cos) —jsin~ into = isiné + (kcos) — jsiny) cos 6. a a . eee See y a) _ @ r) a ~ ae + , q=C n i* = (cos$ + sin) (cos 5 + nsin 5 COS 5 Rear an 4 Thus RIGID BODY ABOUT A FIXED POINT. 273 Substituting the above values of ¢ and 7, multiplying out and arranging, we find finally Ph by ab v MO be ee roe eg ee 5 PAT SR ee Ce + i( cos $ cos 5 sas) rene only OCs ; sell : 0. ate (cos $ sin 3 cos ¥ = pbb) chika sin. *) Vidcwn UC paral an a Ra + i (cos$ sin 5 sin 5 + sin 5 cos 5 cos 5 ). The expressions for ,, ,,, 1m terms of ¢, 0, + and their differential co- efficients are not very simple, and can scarcely be of any use. We see by the equation of § 11 that — w, = 28. igg. If we put gq=wt iat yy + kz this gives — a, = 2(aw — wi + yz — 27) from which the required expression may be obtained. I have not examined the question, but I fancy that to deduce the constituents of the above value of g by means of spherical trigonometry would not be very easy. 13. To deduce expressions for the direction-cosines of a set of rectangular axes in any position in terms of rational functions of three quantities only. Let a, 8, y be unit-vectors in the directions of these axes. Let q be, as in § 7, the requisite quaternion operator for turning the co-ordinate axes into the position of this rectangular system. Then q=wtut+ytez where, as in § 8, we may write Ll=w? +a? + yy? +27. Then we have gqt=w-m—y—e, _ and therefore a= gig-*=(wi-x2—yk+z) (w—xw— yj — zk) = (w? + a — y? — 2?)i +2 (we + ay) i +2 (ez -— wy)k, | where the coefficients of 2, 7, £ are the direction-cosines of a as required. A simi- | lar process gives by inspection those of 8 and y. | As given by Cayury, after Ropricuzs, they have a slightly different and VOL. XXV. PART I. 4a rr 274 PROFESSOR TAIT ON THE ROTATION OF A somewhat less simple form—to which, however, they are easily reduced by putting The geometrical interpretation of either set is obvious from the nature of quaternions. For (taking CayLey’s notation) if 6 be the angle of rotation: cos f, cos g, cos h, the direction-cosines of the axis, we have gq=wt+a+t+y+2k =cos ; + sin § (é cos f +7 cos g + keos h) so that as WIa x = sin 5 cos f y = sin 5 cosg sel 2 =sin=cosh. 2 From these we pass at once to Ropricugs’ subsidiary formule, me Da be eee a 2 2 Be She 6 oS Ses an 5 cos f &e. = &e, 14, In the system of three angles, corresponding to that usually employed in . astronomy—viz., 9 the longitude of node, ¢ the inclination of orbit, 7 the angle — from node in plane of orbit—to find the quaternion operator. ee Here we relapse into the essential asymmetry of the method of § 10. First, . RIGID BODY ABOUT A FIXED POINT. 275 a rotation @ about 7; second, a rotation ¢ about the new position of 4; third, a rotation + about the final position of what was originally 7. The connection of this process with that of § 10 is sufficiently obvious. , | Herejz(_) jos is the operator for 0, and converts & into OS Ose eh, 8) 6 Bene) n= (008 5 + jsin 5) & (cos 5 —jsin5) =isiné + kcosé. OG, Next, the operator for ¢ is 2 w nr ( ) 4 7? and converts 7 into OB= 7 = (cos $ +sin $ (ésin +h c080)) a (cos $ —sin $ (isin + cos 6) ) =—Zsin cos é+j7cosf?+hksin¢ sin é. Hence we have = [ cos 5 + sin 3( - isin g cos 0 + joos @ + ksin sin 6) | (cos $ + sin $i sin @ + k eos €)) (cos 5 + jsin 5) 6 = [ cos 5 + sin 5( - ésing cos0 + jos. + k sing sin®) |( cos $ cosy + isin § sing +5 cos $ sing + ksin $ cosg) 6— () Q- = 03 Fo cos 2 + isin “G7 sin +jsin cos $ + k cos z sin 5 _ As a verification, we have by § 11 OA = gig! = (w?4+ 27 -y?— 2)i4+2(we+2y)7 +2 (xz—wy)k = [ cos (6 +7) cos? £ — cos (8 — 7) sin? a + cost sings + [ sin (0 - x) sin? — sin (0 + +) cost? | k = (cos @ cos rT cos @ — sin@ sin r) 7 + cost sing j + ( — sin@ cos tT cos m — cosO@ sin z)k. The coefficients of 2, 7, £, in this are the usual expressions for three of the direction-cosines. The other six may be obtained by the same process. To express the angular velocities about OA, OB, OC in terms of the three angles 0, ¢, 7, we have at once a= 28. 4¢4¢ = 2(aw — wi + yz — 2y) =— dcosrsing—¢sin r. _| And the others can be found in a similar manner. 276 PROFESSOR TAIT ON THE ROTATION OF A §§ 15-60. Kinetics of a Rigid Body with one Point Fixed. 15. Having premised these kinematical theorems, we pass to the consi- deration of the motion of a rigid mass. It was of course at once obvious to Hamitton (Proc. R. I. A. 1847), that if « be (as in § 7) the vector of the portion m of the mass referred to the fixed point, @ the vector-force acting at m, LAGRANGE’s general equation of motion takes in quaternions the form >. Va(ma — B) = 0, or, if we put ) = 3. Vae so that ~ denotes the vector-couple acting on the body, >. mVes = J A. 1. ae This is our sole dynamical equation. 16. Integrating once with respect to 7, we have, putting y¥ =f dt = . : . : . (12), SimVetSy. Ue. 5) where, if we please, we may omit the V, as == is necessarily a vector. Now, by the kinematical relation in § 1, if ¢ be the vector-instantaneous axis, we may write (13) as >. maVer=y : , z : : (14). 17. From these equations Hamirton has deduced, in an extremely simple way, many known results of great interest. For instance, if ~ vanish, 2.¢., if there be no applied forces, y is a constant vector, and (operating on (14) or (13). by S. «) Sey = 2. m(Ver*=Ime?=—-W . «ww SC a constant, by the principle of conservation of energy. Of these equations 2m(Ver)? = — h? denotes obviously an ellipsoid fixed in the body, and such that ¢ is a radius-vector of it. The tangent plane to it at the extremity of « is easily seen to be the fixed © plane Sey = —/?. Hence we have at once Pornsor’s beautiful construction of the motion, by the rolling of the central ellipsoid on the invariable plane. But this, although extremely elegant, is not well adapted to assist us in the determination of the position of the body in space after a given time. 18. In most of the investigations which follow, we shall use the form (14) RIGID BODY ABOUT A FIXED POINT. 207 as given by Hamitton; and we shall omit for the present the consideration of whether y is a constant vector or not. 19. Let a be the initial position of 7, g the quaternion by which the body can be at one step transferred from its initial position to its position at time 7. Then == gag and HamiLTon’s equation (14) becomes x. mgag . sgeqt=y, or x. mg {aS . aq eq — gq eqa*} gq =y. Let ge= 2. m(aSag—a?e) . ; ; ‘ ; (16), _ where ¢ is a self-conjugate linear and vector function, whose constituent vectors are fixed in the body in its initial position. Then the previous equation may be written g(q Dy" =y7, or | oq g=T'10- _ For simplicity let us write i = vite "| (17). gq" 79=C Then Hamiutow’s dynamical equation becomes simply sie een Mememnns SANE he i Meng, | 20. It is easy to see what the new vectors 7 and ¢ represent. For we may _ write (17) in the form | Reap a mo ert salt uit in Hae oe _ from which it is obvious that » is that vector in the initial position of the body _ which, at time ¢, becomes the instantaneous axis in the moving body. When no | forces act, y is constant, and ¢ is the initial position of the vector which, at time ¢, | is perpendicular to the invariable plane. 21. The complete solution of the problem is contained in equations (7), (17), | (18).* Writing them again we have, attending to (17), while introducing » instead of « into (7), * To these it is unnecessary to add Tq = constant , as this constancy of Tq is proved by the form of (7). For, had Tq been variable, there must have | been a quaternion in place of the vector 7. In fact, = (Tq)? = 28.qKq = (Tq) Sn = 0. VOL. XXV. PART II. 4B 278 PROFESSOR TAIT ON THE ROTATION OF A . Qn = 29 , : ; : : ‘ (7), be ee ee ee We have only to eliminate ¢ and », and we get al ae aie) er in which qg is now the only unknown; y, if variable, being supposed known in terms of g and z. It is hardly conceivable that any simpler, or more easily inter- pretable, equation for g can be presented until symbols are devised far more com- prehensive in their meaning than any we yet have. 22. Before entering into considerations as to the integration of this equation, we may investigate some other consequences of the group of equations in § 21. Thus, for instance, differentiating (17), we have Wt w=H+ah, ~ and, eliminating g by means of (7) gn + Wig = qnt + 29% whence C=Vin+ g19; which gives, in the case when no forces act, the forms Gaim : , : ' , (20), and (as = 9) gon = — V. non : : : , : (21). To each of these the term g~'yq, or g~'Wq, must be added on the right, if forces — act. 23. It is now desirable to examine the formation of the function ¢. By its definition (16) we have $e = L.m (aSag — ae) , =>— D2 : ma V ae c Hence i — Sege = 2. m (TVae)?, _— so that — Sede is the moment of inertia of the body about the vector e, multiplied by the square of the tensor of g. Thus the equation Sege=— hi, evidently belongs to an ellipsoid, of which the radii-vectores are inversely as the RIGID BODY ABOUT A FIXED POINT. 279 square roots of the moments of inertia about them ;* so that, if 2, 7, & be taken as unit vectors in the directions of its axes respectively, we have Sigv=—A, S7o7 =— B, (22), A, B, C, being the principal moments of inertia. Consequently op =—{AiSie + BjSje + ChShe} . . 3 . (28). Thus the equation (21) for 7 breaks up, if we put 1 = 10, + Jo, + ko, into the three following scalar equations Aw, + (C — B)a,w, = 0, Ba, + (A — C)a,o, = 0, Ca, +(B— A)aw, = 0, which are the same as those of Euter.~ Only, it is to be understood that the equations just written are not primarily to be considered as equations of rotation. They rather express, with reference to fixed axes in the initial position of the body, the motion of the extremity, ,, »,, »,, of the vector corresponding to the instan- taneous axis in the moving body. If, however, we consider ©,, ,, », as standing for their values in terms of m, x, y, z (§ 27 below), or any other coordinates employed to refer the body to fixed axes, they are the equations of motion. Similar remarks apply to the equation which determines ¢, for if we put C= ta, + Jag + kay, | (20) may be reduced to three scalar equations of the form “+ (G- 5) = 0. | 24, EuLer’s equations in their usual form are easily deduced from what pre- | cedes. For, let ee = 9h (9 *e)9 | whatever be e; that is, let 9 represent with reference to the moving principal | axes what ¢ represents with reference to the principal axes in the initial position | of the body, and we have ge = Gog tga = 9o(nq =a = gV (2o-Z)q— * For further information about this equation, see Hamitton, Proc. R. I. A. 1847, and Elements | of Quaternions, p. 755. Also Tait, Quaternions, § 367. 280 PROFESSOR TAIT ON THE ROTATION OF A = — ¥V(ndn)q~ = — V. gno(n)q~ = — V.gnq~ 99(q~* #9) 9g =— V. «ge, which is the required expression. But perhaps the simplest mode of obtaining this equation is to start with Hamitton’s unintegrated equation (11), which for the case of no forces is simply >. mVao = 0. But from a= Vea we deduce x= Veo + Via = ae — Sea + Via A so that 2. m(VerSex — tw’ + aSia) = 0. If we look at equation (16), and remember that 9 differs from ¢ simply in having 2 substituted for a, we see that this may be written Vege + pe = 0, the equation before obtained. The first mode of arriving at it has been given because it leads to an interesting set of transformations, for which reason we append other two. . By (17) Y= 914 sae therefore 0 = gq. g@q + gq — gta" aq, qéq— = 2V.yVqqr = Vy o or But, by the beginning of this section, and by (14), this is again the equation lately proved. Perhaps, however, the following is neater.* By (14) ge = 7. Hence ge — ge =— Sy; é Ma Vew ae a Vea) =— 2. maSen =— Ved. maSea = — Vege. * [Inserted Dec, 19,1868.] Ihave lately found that Hamitron, in his Elements of Quaternions (1866), has obtained this equation in a manner almost identical with that last given. RIGID BODY ABOUT A FIXED POINT. 281 25. However they are obtained, such equations as those of § 23 were shown long ago by Evuuer to be integrable as follows. Putting 2 [a0 0, dt Sl we have Ao? = AQ,? + (B— C)s with other two equations of the same form. Hence Odi ds aa a BEC N? Cane A= Pine (22+ a :) (O24 B s) (02+ G s) : so that 7 is known in terms of s by an elliptic integral. Thus, finally, 7 or ¢ may be expressed in terms of ¢; and in some of the succeeding investigations for ¢ we shall suppose this to have been done. It is with this integration, or an equivalent one, that most writers on the farther development of the subject have commenced their investigations. 26. By § 16, y is evidently the vector moment of momentum of the rigid body; and the kinetic energy is, as in § 17, —4>.maz? =— hSey. But Sey =S.g egg yq = SnZ, so that when no forces act S212 = Sagn = — 1’. But, by (17), we have also TC =lys orii¢n Ty; so that we have, for the equations of the cones described in the initial position of the body by » and ¢, that is, for the cones described in the moving body by the ‘Instantaneous axis and by the perpendicular to the invariable plane, We FSO 17 = 0, h?(n)? + y*Sn¢n = 0. This is on the supposition that y and / are constants. If forces act, these quantities are functions of 7, and the equations of the cones then described in the body must be found by eliminating ¢ between the respective equations. The final results to which such a process will lead must, of course, depend entirely upon the way in which ¢ is involved in these equations, and therefore no general statement on the subject can be made. 27. Recurring to our equations for the determination of g, and taking first the case of no forces, we see that, if we assume 7 to have been found (as in § 25) by means of elliptic integrals, we have to solve the equation VOL. XXV. PART Il. 4c 282 PROFESSOR TAIT ON THE ROTATION OF A qni= 2g 3* | that is, we have to integrate a system of four other differential equations harder ~ than the first. Putting, as in § 23, n= tw, + joy + kas , where ,, ,, , are supposed to be known functions of ¢, and g=wtiuat+yy t+ kz, this system is 1 dw dz a) dz 2 W. Kew me where W =— 4,2 — ay — a2, X= aw + wy — a2, Y= ww+oz— a7, Z= O3W + WL — WY. or, as suggested by Cay ey to bring out the skew symmetry, X= . ay —a~+ ww, Y=o-o7 . +a,2%+0,.v, VS er WL—-WY . + 0,W, W =— at — ayy — wz Here, of course, one integral is uw? + 2 + y* + 2* = constant. * To get an idea of the nature of this equation, let us integrate it on the supposition that 7 is a constant vector. By differentiation and substitution, we get 2g = qn = 3n°q. Hence ¢g= pet a sug ny Hee Substituting in the given equation we have Ta(- Q, sin — + Q, cos 3!) = (a cos “2 + Q, sin OLE Ty. Q, = Qi, = T7.Q, = Qa which are virtually the same equation—and thus Hence af Ty 2) Ny (cos 3° + Uysin z) 7Tn = Q,(Un) = . And the interpretation of g(_ —_) q~ will obviously then be a rotation about 7 through the angle tT, together with any other arbitrary rotation whatever. Thus any position whatever may be taker as the initial one of the body—and Q, (_ _) Q,— brings it to its required position at time t=0 s RIGID BODY ABOUT A FIXED POINT. 283 It may suffice thus to have alluded to a possible mode of solution, which, except for very simple values of 7, involves very great difficulties. The quaternion solution, when » is of constant length and revolves uniformly in a right cone, will be given later. 28. If, on the other hand, we eliminate , we have to integrate qo (ah) =24, so that one integration theoretically suffices. But, in consequence of the present imperfect development of the quaternion calculus, the only known method of effecting this is to reduce the quaternion equation to a set of four ordinary differ- ential equations of the first order. It may be interesting to form these equations. Put gaH=wtmtyjy tke, and y= 10 +b + ke, then, by ordinary quaternion multiplication, we easily reduce the given equation to the following set :— ga ee ag am CS where W = —- 2a — yB — 2€ or pe yf —2B+wAa X= wa+ y€ — 2B Y =—2€ +244 wh Y= wB+2A-—xc€ L= «B-yA . +w€ Z= w€+cB —yA W =—- 2A — yB — 2€ and A= Z| a(ut — 08 — 9 — A) + Qo(ew 4 by +) + Bw Oe — ey) | 1 2 2 2 2 B= =| bw —xv—y — #) + 2y (an + by + 2) + Dw (en — a2) | ‘ . @= 5 ow — 2 —y — 2) + 22 (ax + by + cz) + 2 (ay — ta) | W, X, Y, Z are thus homogeneous functions of 7, x, y, z of the third degree. Perhaps the simplest way of obtaining these equations is to translate the group of § 21 into », 2, y, z at once—instead of using the equation from which ¢ and » are eliminated. We thus see that 7=144+78 +E. One obvious integral of these equations ought to be wu? + wo 4+ y? + 27 = constant , 284 PROFESSOR TAIT ON THE ROTATION OF A which has been assumed all along. In fact, we see at once that wW+eX+yY + 2Z=0 identically, which leads to the above integral. These equations appear to be worthy of attention, partly because of the homo- geneity of the denominators W, X, Y, Z, but particularly as they afford (what does not appear to have been sought) the means of solving this celebrated problem at one step, that is, without the previous integration of HuLER’s equations (§ 23). A set of equations identical with these, but not in a homogeneous form (being expressed, in fact, in terms of «, A, u,v of § 13, instead of w, 2, y, z), is given by Cayiey (Camb. and Dub. Math. Journal, vol. i. 1846), and completely integrated (in the sense of being reduced to quadratures) by assuming EuLeEr’s equations to have been previously integrated.. (Compare § 27.) CayLey’s method may be even more easily applied to the above equations than to his own; and I therefore leave this part of the development to the reader, who will at once see (as in § 27) that A, B, € correspond to,, ,, , of the 7 type § 23. 29. It may be well to notice, in connection with the formule for direction cosines in § 13 above, that we may write A= al (w? + a? — y? — 2) + 20 (wy + we) + 2¢ (az - wy) | : 6 — al 24 (zy — we) + b(w? — a? + y? — 2%) + Qc(yz + wa) | 4 C= a | 20 (az + wy) + 2b (yz-— we) +e(w? -#-— 7 + 2) | : These expressions may be considerably simplified by the usual assumption, that one of the fixed unit-vectors (¢ suppose) is perpendicular to the invariable plane, which amounts to assigning definitely the initial position of one line in the body ; and which gives the relations b=0,c=0. 30. When forces act, y is variable, and the quantities a, 6, c will in general involve all the variables 1, z, y, z, t, so that the equations of last section become much more complicated. The type, however, remains the same if y involves 7? only; if it involve g we must differentiate the equation, put in the form y= 2449 “Dq, and we thus easily obtain the differential equation of the second order | V=4V.49.¢7 a7 + OV ga; if we recollect that, because 7~*¢ is a vector, we have 5.99 = (9"9)’ - RIGID BODY ABOUT A FIXED POINT. 285 Though remarkably simple, this formula, in the present state of the development of quaternions, must be looked on as intractable, except in certain very particular cases. 31. Instead of solving the diferential equation (7) of the group in § 21, having previously eliminated » from it by means of the other two, we may solve the second equation of the group, 7 = 9 : é f b J (17), for g, and treat as known in terms of ¢. {, of course, is to be regarded as found by the processes of §§ 23, 25. As this mode of attack leads to a determination of g by aset of three new differential equations, instead of the four of § 27, it may be useful to consider it briefly, but only for the case of y = constant. Its interest seems to be derived entirely from the quaternion investigation to which it leads. 32. In consequence of (17), just cited, we may write q=yit . ; , : ; : (25), which will be found to satisfy that equation, whatever value is assigned to 0. But dis really not unrestricted in value; for, if we exhibit it as the sum of two vectors, thus One of which 6, satisfies the equation 7% + 66=0, or, which is the same thing, the pair Sé(7¥ + 2)=0 ! Va(y — 7) =9 b\ly — ¢ satisfies both. [This depends on the fact that TC = Ty]. Hence 6 must be de- prived of its resolved part parallel to y — ¢: or we must have we see that SAG es 0: ee OA NY, Bh sar) 33. By differentiation of (25) we have ' Gg = yo + Bf + 8Z. Substituting in (7) we have 2(y8 + 6% + 82) = yon + 0Zn. C= Ven, tm — 20 = xf, But, § 22, whence and the above equation becomes . 2 (6 ae 60) = yin+ onf . : ; : (27), VOL. XXV. PART II, 4D 286 PROFESSOR TAIT ON THE ROTATION OF A of which a particular solution is evidently 26 = oy. But this must be completed by the addition (to the second member) of a solution of the equation yr +7Z=0, since any such term in the value of 6 would disappear from the differential equation. Such a solution is easily found, by putting — ¢ for ¢ in (17), and attending to § 32, in the form oe a a with (as in § 32) the condition S(7+.04 =) short vyloae-Bus bes ee Hence, finally, 28 = on ya — ar ||) Ee which, by taking the scalar, gives Sy Oa=— Sin: Abiss co -le ot 34, By differentiation of (26) we have Sly — Ob = Sol = S. dfn. Substituting the value of 3 from (30) we have S.(y — Yan + 2S. y%a = 2S. din, te IS .yLa=—S8. (y+ Lan Sets oe nn From (29), (81), and (32), we find A by the usual quaternion process in the form 2AS .(y — Oly + Q)V7Z = — Voy — Oly + DS. (y + Dan — 2V . (y + CV yeSen; QAV2yf = — VytS. (y +.2)8n + (y — 0) (7? + Sy@)Sen . «SS (83), or where, in transforming the last term, we must recollect the equation T¢ = Ty. From this we deduce at once (yd — AL)V?¥ l= — (yV7l — VoZ. 2S. (y + O80 + [yy — 2) — (y — O21” + Syf)Sen, 2(yA — ALYV? yf= (y — O)(y? + SyZ)S - (y + 280 + 2(7? — 70)(97 + Syf)Sén, or, finally, remembering that Wel = So 6 IG 7 AyA — AL) Syf — 7")'= (y — OS. (y + Fon + Ay? — 72) Son. 35. Substituting this in (30), we get, after a slight transformation, consistin; in omitting the scalar parts of the right hand side, whose sum is zero, 28(Syf — 9”) = (Syf — 97) Vin + $y — ZS. (y + Con — VyGSon. or RIGID BODY ABOUT A FIXED POINT. 287 This may easily be put in the simpler form = Ven VaGee OVS = Oe ee. (BA), Reduced to scalars, this gives three linear differential equations of the first order, the coefficients being functions of 7. These can, of course, be reduced to depend upon one linear differential equation of the third order with coefficients functions of ¢. 36. As a verification of the preceding work, we may try whether the result is consistent, as it ought to be, with the condition (assumed throughout). Constant = (Tq)? = 2776? + 28. ydZ. This expression gives, by differentiation, 0 =— &Sy% + 2(7? — Syf)Sdd + 48y5Sy0. Substituting for 6 its value from (34), we have 0 =— BSyf +S. dyfSdn + 2Syd(S. yan — 48. (y + C)én) =— PSy% +S. dy%Sdn + SydS. yin — SydS. Lon =— Sof 4+ 8. df{nS. 72d + CS. ayd + yS. Zand} =— 6Sy% +S. (6S. fn) which is true, because by (20) | C= Vea. 37. Another mode of attacking the problem, at first sight entirely different from that in § 19, but in reality identical with it, is to seek the linear and vector function which expresses the Homogeneous Strain which the body must undergo to pass from its initial position to its position at time 7. Let a Ke a being (as in § 19) the initial position of a vector of the body, =a its position at time 7. In this case x is a linear and vector function. (Tait’s Quaternions, § 355.) Then, obviously, we have, ~, being the vector of some other point, which had initially the value a, , Sea, = 8S. xaxa, = San, (a particular case of which is La = Tye = Ta) and Van, = V. xaxe, = Vee, . 288 PROFESSOR TAIT ON THE ROTATION OF A These are necessary properties of the strain-function x, depending on the fact that in the present application the system is rigid. 38. The kinematical equation a= Vea becomes ye = V. exe, (the function x being formed from x by the differentiation of its constituents with respect to #). HamiLton’s kinetic equation >.maVer=y, becomes > .myaV .exa= y. This may be written >. m(xyaS.exa — ea”) = x, or a. m(aS.ay’e—x-16.07) = x14, where x’ is the conjugate of x. But, because S. xaxa, = Sam, , we have Saa, =S. ay'xa, , whatever be a and a, , so that f —1 Xx =X Hence > -m(aS..ay—1s— y—le. a”) = y—Iy, or, by § 19, —1 4 8= xX 17: 39. Thus we have, as the analogues of (17), (17’), the equations ree ae Mee =e, and the former result ya =V. enya becomes ye = V.xnye = xVia0. This is our equation to determine x, 7 being supposed known. To find 7 ¥ may remark that Om =i RIGID BODY ABOUT A FIXED POINT. 289 and C=x'y- But a a so that ZR KG eae ho 0), Hence ; Naty les ee = er = VC OW GSC or ' $i = — V non. These are the equations we obtained before. Having found » from the last we have to find x from the condition % 1 xa = Vie. 40. We might, however, have eliminated 7 so as to obtain an equation con- taining x alone, and corresponding to that of § 21. For this purpuse we have ere CER ey; so that, finally, —1 uy Mee ND ye or Ka = Vx taggly, which may easily be formed from the preceding equation by putting y—'« for a, and attending to the value of _ given in last section. 41, We have given this process, though really a disguised form of that in S§ 19, 21, and though the final equations to which it leads are not quite so easily attacked in the way of integration as those there arrived at, mainly to show how free a use we can make of symbolic functional operators in quaternions without risk of error. It would be very interesting, however, to have the problem worked out afresh from this point of view by the help of the old analytical methods: as several new forms of long-known equations, and some useful transformations, would certainly be obtained. 42. As a verification, let us now try to pass from the final equation, in x alone, of § 40 to that of § 21 in g alone. We have, obviously, , a= q a Ve = Xe which gives the relation between g and x. VOL. XXV. PART II. AR 290 PROFESSOR TAIT ON THE ROTATION OF A [It shows, for instance, that, as S.Pya =S.ayx’B while S.Bya = S. Bgag—1 =S . ag—1Bq , we have xB = 49-87 , XB = o(q—*Bq)q-' = 8 , and therefore that x xX or x =x, as above. | Differentiating, we have gay" — gag—*4qq-* = xa . Hence x xe = gga — agg = 2V.V(q—3g)a. Also g- 4 "7 = 9 G90); so that the equation of § 40 becomes 2V ..Vg~*g)a = V.g-(q- 199) , or, aS a may have any value whatever, ee, 2V.9q-'G = 9"(q-"99) ; which, if we put Ty = constant as was originally assumed, may be written : 24 = 99"(9"7) as in § 21. 43, Let ¢ be the vector joining the opiremnity of ¢ to the intersection of y with the invariable plane. Then etay=e. Operating by S. y, and remembering the condition eT Sey = — 1, we have ay? = — I; so that 2 en tee. In the initial position of the body this vector, considered as being drawn from the fixed point, was } RIGID BODY ABOUT A FIXED POINT. 291 In the initial position of the body, therefore, this vector passes through the in- tersection of the ellipsoid 2\ — ON asst S, (o 4 ia 6997 Be iB ps ONT es ee Y if with a second ellipsoid ans T(97 +5) C=C = Ty. It therefore lies on the cone ® -1 2\—1 2-1 OK il 78. (o> +5) so-(9 +5) c+ 18.9445) «(97+5) s=0, 2\—1 8.694 +5 a= i). or [We might have saved the last seven lines by noticing that Sye = 0 } in the present position of the body, involves Si = 0 in the initial state, which, with the value of ¢ in terms of « above, gives the result at once. | 44, This cone is seen at once to be normal to the ¢-cone in the initial body, viz., by § 26, s.-~=-"e Deis, or . Ie Ne 14 )¢=0.* i(o +5) The vector > constantly changes so as to be perpendicular to ¢. Hence in the * Tn fact any equation such as Seve == '(0!, where ») is a constant self-conjugate linear and vector function, gives Sede = 0, whence y= be where » represents the normal-vector. For its locus, we have a= vy 3 and by substitution for e and ./g in the given equation, we have Swpy= 0. 292 PROFESSOR TAIT ON THE ROTATION OF A moving body, the vector p, which is always in the plane through the fixed point | and perpendicular to , belongs to a cone of which y is a normal, and which there- fore rolls on that plane. But the cone also slides, because the vector p which is” in contact with the plane is not the instantaneous axis of the body. This con- struction for the illustration of the motion is also due to Pornsor, and the com- plete analytical solution of the problem has been given, from this point of view, by Ruep and Jacosr.* It is easy to see that the angular velocity of the sliding motion is the constant resolved angular velocity of the body about the fixed line Y; which has the value 2 5 p20 = 7 . 45. When two of the moments of inertia of the rigid body are equal, 7.¢. when the symbolical cubic in ¢ or ¢ has two equal roots, all the previous dynamical work becomes immensely simplified. In fact, if we now take a, B, y as unit- vectors coinciding with the principal axes of the moving body, we have by (23) 92 =— AaSag — BBSGe — BySye. But g =— aSag— BSB — 7Sye, so that ge = Be— (A— B) aSag t : : ; : (35), and thus depends upon the position of the one vector a. We may attempt to determine the motion without at first introducing the consideration of the quaternion which has been our principal object of study in this paper. 46. The general equation of § 24 pe =— Vege becomes, by substituting for 9 from (35), Bi — (A— B)aSae =—(A— B)VaeSae ‘ : s (36). Operating by S.a, we have | Sae = 0 ; ; ; ; 4 . 37). Omitting, therefore, this term from (36) and operating by S.¢, we have Se = 0, whose integral is -” = constant =—Q?, suppose, ; (38). But we have always by § 1 a a= Veu because a is fixed in the body. From this we see that P Sea 16). * See Caytzy, B. A. Report, 1862. RIGID BODY ABOUT A FIXED POINT. 293 This, taken in conjunction with (37), gives Sat + Sea = O, whose integral is Sae = constant. =— Qcos®, suppose, : é ‘ (39). Equation (86) may now be written Be = —(A—B) Qé cos B, or Be =—(A—B)Qa cos B + constant vector. But we have always, by (14), (see § 24) Pee or by, (85), (36), (39), Be + (A— B)aQ cos 8B = x ; , : (40). So that the constant vector is y. Thus we see that a and « are always coplanar with y, and that each remains constantly at the same inclination to it. 47, Operating on (40) by S.<, S.a, S.y, respectively, we have — BO? — (A — B)Q* cos? 8 = — H?, — BQ cosB— (A — B)Q cos B = Say, — Bh? + (A—B)Say Q cos 8 = 9’, and these give, in order, (A cos? B+ B sin? B)Q? = h?, — AQ cos B = Say, — (A? cos? 6 + B? sin? 8) Q? = 9’. The first and third determine 8 and ® in terms of the given constants h and Ty, and the second gives the value of the constant inclination of a to the fixed line y. Introducing — a’, which is unity, as a multiplier of y’ in the third equation, and adding to its members the squares of the corresponding members of the second, we have — BQ)? sin? B = Vay. | 48. We get equations immediately derivable from these by seeking at once _ the equations of the fixed and rolling cones, by which the motion may be exhi- | bited. Thus the locus of ¢ in the body, 7.¢., the rolling cone, has by (14) and (38) the equation QT ge = TyT: , VOL. XXV. PART II. 4F 294 PROFESSOR TAIT ON THE ROTATION OF A which may be transformed as follows— Q? {B? — 2B (A — B) Sta — (A — B)?S%ae} = — 72? QQ? (B? 7 _ (A? — B?) Sae) =-—y7’, (BQ? + 7”) 2 — (A? — B?) Q? S2ae = 0, and finally e* cos?B + S?ae = 0. This might have been written down at once by inspection of (38) and (39). The locus of ¢ in space, 2.¢., the fixed cone, has the equation S?ye + 2 oe 49. In the preceding solution we began with the very simple equation for «, which immediately presented itself Let us now apply to the same problem the general equation of § 21, viz., 2g = 9¢—* (q~""79) - Here, of course, we have ee ee i Sea = a ee ae I3@ — 3 BSke , Hence which, because a= gig", becomes which is (40) of § 46, as we see by substituting for Say from § 47. 50. Employing this value of ¢ in the kinetic equation a= Vea, we have a= aVye Hence 1 : 1 a BY” = Be V-7Vre RIGID BODY ABOUT A FIXED POINT. 295 of which the integral is obviously a=y Say + woos 52 t + asin 32, where « and ) are vector constants of integration. The two last terms must be, together, equal to y I Vye, and, as they vanish alternately, the tensors of « and ’ must be equal. Also unless Sxa = 0 the tensor of this part of « will vary. Hence aw =— Uy SaUy + TVaUy. (Ux cos 52 t + Ua sin fe). Let us, for simplicity, take the usual z, 7, £ of quaternions as coinciding with Uy, Ux, Ud, and let — SaUy = cos. Then TVaUy = sin B. Also let ye B ——aie Thus we have a —icosB + (j cos nt + & sin nt) sin B whence , il : : : 5 ao (3 = . 2B cos B [i cos B + (jcos nt + k sin nt) sin B| + 2ai + 2b(j cos nt + & sin nt), where ars = cos 6 sin 8 — BS a= cos?B + n=n (sins + = cos?) dl, For the complete solution of the problem, it remains that we integrate the equation above, which we may write as g = [ai + 0(j cos nt + k sin nt)] q = (ai + ba)g . (Al), if we put a =jcos nt + ksin nt. 296 PROFESSOR TAIT ON THE ROTATION OF A This gives at once the following results, which are necessary in the elimination of = by differentiation, a=—1 ) z= Na, aa mM ) le =— Na, z=—n'a. ‘ Also, because Sia = 0, we have (ai + ba)? =— (a? + 0”). Differentiating (41), and simplifying at every step by the above auxiliary equa- . tions, we have gG = (a + ba)g g=—(@ + B)q + bag Gg =— (a + &)q — bn? aq + bn (am — bi)g ices (Fh 4 D2) 9 = On? dna) eg a On? = ina) (F% + ») 4 vn( — a +22)9 =— (a? + 0*)G — (bn? — 2bna + ba? + D)aq + Bn?q. Eliminating +7 from the last equation by means of the second, we have for the determination of g the linear equation of the fourth order with constant co- efficients G+ [22 + 0?) + n? — 2na] 4G + [(a? + 0)? + (a? + 0?) (n? — 2na) — bn? |g =0 (42). Assume, as a particular integral, gq — Qe”, where Q is an arbitrary, but constant, quaternion, and ¢ is the base of NAPIER’S Logarithms. Then we find for m the equation m* + [ 2(a? + 07) + n? — 2na | m? + (a? + 0? — na)? = 0; m? + a? + 0? — na =A arf — min’. Hence m is imaginary, so we may write | m = Wr/—1, ween a+? —na, 2 w=ts5+,| a-5 + 07. By § 50 this may be written or and our equation gives whence pots {ie (1-5 cos > ZZ RIGID BODY ABOUT A FIXED POINT. 297 These values may be called +u,, +-m,, and we have fy + Mg = 1. 52. The complete solution of the equation (42) is therefore q = Q, cos wt + Q, sin wt + Q, cos wt + Q, sin wt. This, however, is far too general for the solution of the original problem, for it involves sivtcen arbitrary constants instead of four. But it is a mere piece of ordinary analysis to find twelve of these in terms of the other four. Thus, let us write Q,=40,+114+49,7+ KA, Q, = H, + 1,4 + J,7 + KF, Q, = H, + 1,7 + J,7 + K,k, Q, =H, +1it+Jd 7+ Ke. If these values be substituted in the above expression for g, and the resulting value of ¢ be used in the equation i= [ ai + b(j cos nt + k sin nt) |q : we find, on replacing products of sines and cosines of multiples of ¢ by swms of sines or cosines, two sets of terms. One of these is of the type cos (m — (y)t, which, being equal to COS fyb, may be allowed to remain in the equation. ‘The other set is of the type cos (n + m,)t, and the terms introducing it must vanish identically. This consideration gives us the following relations among the sixteen con- stants above We ce el ea aida Kag,, Kd. eee dK, KS; so that the values of eight are assigned in terms of the remainder. Next, by equating coefficients of each such distinct term as 4cos ut, ksin wt, &c., we obtain sixteen additional equations, of which, however, eight are mere repeti- tions of the other eight. Rejecting them, we find the remainder to be VOL. XXV. PART Il. 4G 298 PROFESSOR TAIT ON THE ROTATION OF A bH, = (a — mw) K, ; bK, = — (a — »,) H, bl, = (a — wm) I, bJ, =—(a—4,)I, J, =—(a—m,)I, 61, = (@ — wm) J, bK, = — (a — w,) H, bH, = (a —.u,)K, . These are, again, identical in pairs; for each pair containing the same two constants agrees with the others in giving or a? + BF — (wy + fy) @ + My, = 0. But, by (43), we have and the condition is satisfied identically. The final value of the quaternion in the case of the uniform rolling of one right cone on another is therefore q = (H, + 1,7 + Jy7 + KA) cos w,t —(W, —Hz+ Ky = J,k) sin pyt + 581K, + Jy — Lj — Hyh) 008 gt a 5 (J, — Kyi — Hj + 12) singe * | Putting gq=wtititt+yjy + kz, the ordinary differential equations, corresponding to that just solved, are * The tensor of g has been assumed constant. Accordingly we find by this formula ; se 2 = 2 [H cos mt — I, sinuyé + = D A (x, cos jt — J, sin nt) | + [1 cos w4,¢ + H, sin pt + Z 5 = (3, cos wt + K, sin nt) } a- 2 2 : a— : + [J, cos wt — K, sin pyé — ah cos pt — H, sin ut) | + [K cos w,é + J, sin py, ¢ == (& cos wot + I, sin ut) | o— 2 re (He aT il ae J? a K,*) [1 + ( b >) ] =(H: Pee igs yt K,) (a = Za) ‘ RIGID BODY ABOUT A FIXED POINT. 299 w= — ax — by cos nt — bzsin nt, zc = aw + becosnt — by sin nt, y = bweos nt + basin nt — az, 2 = bwsin nt + ay — bxcos nt. By substitution in these the above result may be verified. 538. Consider, as an example of applied forces, a homogeneous solid of revolu- tion. moving about a fixed point in tts axis, which is not its centre of gravity. To determine the motion. . If a, a unit-vector, represent at time ¢ the position of the axis of the solid, we may choose the tensor of y, a vertical vector, so that the couple due to gravity is Vay. Hence the equation of motion is §§ 24, 22, ge + Vege = Vay. But ge = Be— (A — B) a Sag , so that Be — (A — B) aSaé — (A — B) Vea Sae = Vay : : : (44). This, with the kinematical relation @. == N em . : , : : : (ts contains the complete solution of the problem. 54, Operating on (44) by S.a, we have See = (0. But, by (1), we have ‘ Sc = 0. Hence See ‘constant = @Q. . : (45) _ (that is, the angular velocity about the axis of revolution of the solid is constant) | and (44) is reduced to the form Beat Om Vays. 9! 5) a ye) (AB). | But, by (45) and (1), i Og. ) or . = aOretady tal of) Le AN. Since aa is a vector, we have (as in § 30) Sore ectamed he Bawah nha ly pottingiieend vl! (AB), 300 PROFESSOR TAIT ON THE ROTATION OF A so that the substitution in (46) of the value of « from (47) gives BVa=AQES Vay 3 *. an extremely simple equation to determine a. It is curious to remark that this is the equation of motion of a simple pendulum, disturbed by a force constantly perpendicular to the cone described by the string, and proportional to the rate at which the area of the surface of the cone is swept out by the suspending cord. When A =0 it becomes that of the undisturbed motion,* and gives a number of curious theorems relating to the curvature of the general path of a simple pendulum. These we need not at present consider; though we may mention that the corresponding equation for the motion of FoucauLt’s pendulum may be written in the form : Va(é+6) = eVa8, where £ is a vector known in terms of ¢. 55. If we suppose a determined in terms of ¢ from this equation, (46) gives « in the form Be = (A—B)Qa — V. y/fadt. This equation may be obtained, even more simply, from (47). 56. But, without finding either a or ¢, we may deduce various facts connected with the motion. Thus operating on (46) by S. ¢, we get Bse = Sl eey = Sye . which gives ee — 2Sya +C : : : : 5 (50). But, by operating on the same equation by S.+¥ and integrating, we have BSye — (A— B)QSya = C, Z : ; : (51), which may be written in the form Sepy = Syge = C, : : : : : (51Y. By (50) and (51) ae hip Dogan Ce so that ¢ is a vector of a fixed sphere, of which however the centre is not at the fixed point. * If m be the mass of the pendulum bob, « the vector representing the string, © its tension, and y’ the acceleration due to gravity ma = my — Ua, or, eliminating @, Vee = Vay, It is well to observe that this is the equation of motion of a pendulum bob, acted on by no forces, ie ¥ be the acceleration of the point of suspension. RIGID BODY ABOUT A FIXED POINT. 301 57. From (49) we have at once, by operating by S. y and integrating, BS. yae = AQSya + C’ : ' ‘ (52). Also, operating by 8. Vya, BS .yaVae = AQS. yaa — (Vay)? : , : (53), or B(—Sya — SyaSaau) = AQS. yac + a®y? — Stay ALO? ~ AQC’ =e Sya + E — 7° —Say, by (52). This may be written iE Sya — Sya(— QQ? — aug’ = A Sy + ne — 9° —Say, which leads, by integration, to the ordinary expression for Sya in terms of an elliptic function. It is to be observed, however, that this quantity is not one which the quaternion calculus directly points out as an object of research; the propriety of seeking « in the first place being clearly indicated. 58. From the above equations all the ordinary results connected with this problem may be at once deduced by any one who has a little skill in quaternion analysis: but the determination of the quaternion which gives the position of the body at any time does not appear, so far as I have yet examined the question, to lead to any very simple expressions. If we could, generally, integrate equation (49), ¢« would be at once given by (47), and the determination of the motion would be reduced to comparative sim- plicity. The equation for the direct determination of ¢ may be formed as follows, but it is not so simple as that for a. From the equation Be — (A — B)QOVew = Vay, we have, by operating by V . <, the result BVe — (A — B)Q(ae? — eQ) = Qy — aSye, which gives _ BVee + (A — B)Q?e — Qy Tie (A — B)Qe? — Sye ; The condition a— Veu gives, by substituting this value of a, BYV24(A.— BYO?s— (A — B)Qe? — Sye = Bree? — See) — OVey . VOL. XXV. PART IL. 4H BVé + (A — B)Q?2 — Cie ROG Sy) 302 PROFESSOR TAIT ON THE ROTATION OF A 59. Processes very similar to these may be applied to the motions of. the Gyroscope and to Precession and Nutation. I confine myself at present to the — formation of the equation for the latter question, reserving for another com- munication the details of the solutions of these three problems; as they involve some curious and delicate points of quaternion analysis. 60. To form the equation for Precession and Nutation. Let a be the vector, from the centre of inertia of the earth, to a particle m of its mass: and let ¢ be the vector of the disturbing body, whose mass is M. The vector-couple produced is evidently U(e —«a MS.mvV. amis . Vag = M2. ma MV ae T%e (1+ a m=) 38a Tp - &e.) : = MS. =Mz.7, ; . To . : no farther terms being necessary, since = is always small in the actual cases g presented in nature. But, because a is measured from the centre of inertia, >.me=0. Also, as in § 19, de = Pap m(aSag = 7p) : Thus the vector-couple required is 3M Referred to co-ordinates moving with the body, @ becomes ¢ as in § 24, and | § 24 gives ts Salone JW bee p= y= 3M fae dt. Introducing the value of ¢ from § 53—1.¢., assuming that the earth has two pu cipal axes of equal moment of inertia, we have Be — (A — B)aSae = 3M(A — nf 4 ~ dt . This gives, as in § 54, See const. — 0 , whence e=>—Qataa, : RIGID BODY ABOUT A FIXED POINT. 303 so that, finally, BVaa — AQa = T (A — B)SagVae . The most striking peculiarity of this equation is that the form of the solution is entirely changed, not modified as in ordinary cases of disturbed motion, accord- ing to the nature of the value of e. Thus, when the right hand side vanishes, we have the equation (49) with the restriction that the body moves about its centre of inertia (easily seen to be identical with that at the beginning of § 50); which, in the case of the earth, would represent the rolling of a cone fixed in the earth on one fixed in space, the angles of both being exceedingly small. If ¢ be finite, but constant, we have a case nearly the same as that of the top © in §§ 53, 54, the axis on the whole revolving conically about ¢. But if we assume the expression e=7(jcos mt + kcos mt) (which represents a circular orbit described with uniform velocity) « revolves on the whole conically about the vector 2, perpendicular to the plane in which ¢ lies. I hope, on a future occasion, to give detailed solutions of these problems, to a sufficient degree of approximation. ( 305 ) 1X.—On the Structure of the British Nemerteans, and some New British Annelids. By W. CarmicHaEL M'‘Inrosn, M.D., F.L.S., Murthly, Perthshire. Com- municated by Professor TuRNER. (Plates 1V.-XVI) (Read 20th April 1868.) The anatomy of the soft worms variously arranged under the Nemertean Order has, even in recent times, not been carried out with that completeness necessary for their thorough elucidation, a state of matters partly due to the confounding of the structure of one family with another, and predicating of the series what investigation has but proved in one group. Few British comparative anatomists have paid much attention to these animals; indeed, Dr GEorGE JoHN- ston,* Mr Harry Goopsir,t and Dr Tuomas WIL.IAMs,{ are the only three who have left researches of any moment on the subject. The observations of the first- mentioned naturalist were made many years ago, with the aid of inferior instru- ments, and, though conscientious enough, are very meagre and unsatisfactory; and those of Dr Witu1ams, while also showing the defects just noted, bear evident traces of imagination. Mr H. Goonpsir’s interpretation of structures was, from his limited observations, likewise very erroneous. On the Continent, again, the investigators have been more numerous, and a long list of distinguished names attest the interest which the subject has received at their hands. I do not deem it necessary on the present occasion to enumerate the older writers at full length, since this has already been accomplished very satisfactorily by MM. DE QuaTRE- FAGESS and KEFERsSTEIN,|| but shall refer to such of their views under the respec- tive heads as may be required for the complete elucidation of the subject. Of those, however, who led the way to a more correct appreciation of the structure of these animals, I may particularise MM. Duck&s,4{ BLancuarp,** and DE QuaTRE- FAGES,§ in France; EuREeNBERG,}}+ RatTHKe,}{ Max Scuuirze,§§ and KErer- * Mag. Zool. and Bot. vol. i. 1837; and Catalogue of Worms, 1865. + Annals N. Hist. xv. 1845. t Report Brit. Assoc. 1851. § Annales des Soc. Nat. 3™° ser. vi. 1846; and Voyage en Sicilie, vol. ii. par MM. Epwarps, DE QUATREFAGES, and BLANCHARD. || Zeitschrift fiir wiss. Zool. xii, 1863. { Annales des Sc. nat. tom. xxi. 1830. ** Annales des Sc. nat. 3me ser xii. 1849. tt Symbole Physice, 1831. tt Neueste Schrift. der Naturforsch. in Danzig, 1842. §§ Beitrige zur Naturg. der Turbellarien, 1851; and Zeitsch. fiir wiss, Zool. iv. 1853, &e. VOL. XXV. PART II. 41 306 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE STEIN,* in Germany; CERSTED,t in Denmark; Van BENEDEN,+{ in Belgium ; CLAPAREDE,S in Switzerland ; and DELLE Cutz, || in Italy. The confusion in regard to the structural characteristics of the order is well illustrated in the descriptions given in the lately published “ Catalogue of the British Museum,” and in the first chapter of Dr CopsoLp’s “‘ Entozoa,” where little else than an array of doubts is produced as a solution of this question. In France, again, the valuable Lectures of M. Mitnse Epwarps,{ for instance, are chiefly of interest on the subject of the Nemerteans as stimulants for further investigation. An examination of the discrepancies existing between the comparatively recent and excellent researches of MM. bE QuaTREFAGES,** Max ScHULTZE, CLAPAREDE, Van BENEDEN, and KEFERSTEIN, demonstrate the same necessity for further elucidation. MM. ne QuatreracEes, VAN BENEDEN, and KEFERSTEIN have, per- haps, gone more minutely than the others into the question, but all have confounded the structure, or certain parts of the structure, of the Ommatopleans with the Borlasians, whether one or both groups have been examined. M. DE QUATREFAGES investigated the Ommatoplean group more extensively than the Borlasian; while Prof. KEFERSTEIN paid more attention to the latter; but he has not entered so minutely into structural detail as the former, though his observa- tions are, on the whole, more exact. VAN BENEDEN likewise predicated of one group what he had found in the other, and hence sometimes gave an erroneous interpretation of the parts. While thus reviewing the labours of these distin- guished naturalists, it must not be understood that I in the least degree under- value their investigations ; but rather, that from a more continued series of obser- vations,structures—about which they were in doubt—have been more clearly determined, and many additional facts brought to light. Indeed, no one who is acquainted with the patience and experience necessary for unravelling the anatomy of these delicate creatures, will wonder at the occurrence of errors of omission or commission, either in the labours of others or hisown. Ever restless when alive, prone to rapid dissolution when dead or too much pressed, and comparatively few of the requisite transparency for examination, it is only by a happy com- bination of circumstances that the structure of these animals can be successfully demonstrated. One of the main objects of this paper is to show the essential differences between the Ommatopleans and the Borlasians, from the skin even to the micro- * Zeitschrift fiir wiss. Zool. xii. 1863. + Entwurf einer Syst., &c., der Plattwiirmer, 1844. t{ Memoires des Sc. des Acad. Roy. de Belgique, tom. xxxi. 1861. § Recherches Anatomiques, &c., dans les Hebrides, 1861. || Mem. sulle Storia, &., vol. ii, Naples, 1825. { Lecons sur la Physiol. et Anat, Comparée, tom. 5™°, pp. 460-65. ** Tn his “ General Outline of the Animal Kingdom,’ 3d edit. 1861, Professor Rymer Jones — strictly follows this author. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 307 scopic structure of the proboscis, as well as to advance our knowledge of the minute anatomy of these animals and their immediate allies. I use the terms Ommatopleans and Borlasians provisionally in the mean- time, because the majority of these soft animals group themselves round two centres, represented respectively by the common Ommatoplea alba and Borlasia olivacea. The terms, indeed, are nearly equivalent to Max Scuuttze’s Hnopla and Anopla, and to Prof. KErerstEIn’s 7remacephalide and Rhochmocephalidw. I do not think it advisable to call by the name of Borlasia, as the last-mentioned author has done, a family whose structure is quite different from that of the animal originally so termed, and hence I have preferred EHRENBERG’sS name, Ommatoplea, on the one hand, and substituted Borlasia for KererstE1n’s Nemertes, on the other, both because it ( Borlasia) has the priority, was applied to an animal similar in structure, and because there are strong claims to perpetuate the name of the early English zoologist. So comprehensive are the above terms, that almost in every minute particular all the known British forms, with the exception of Cephalothrix and another, resolve themselves at once = their respective heads. Ommatoplea alba (and variety rosea) may, as above mentioned, be con- veniently taken as the type of the Ommatoplean group, both from its size and abundance, and accordingly a systematic examination of its anatomy shall first engage our attention, the additional observations made on its immediate allies being appended and contrasted therewith. It is also fair to state, that I could not have pursued the following inquiries if a liberal and ever-ready supply of living animals from the St Andrews’ rocks had not been perseveringly forwarded by a relative, to whom I owe the deepest obligations in this and other depart- ments of zoology. Dermal Tissues—The body of the animal, like that of each in the Order, is universally covered with cilia, some longer ones being present at the proboscidian aperture and mouth, and others at the tip of the tail. The ciliary motion is most active at the openings of the cephalic pits. In Tetrastemma variegatum, it is in- teresting to watch the cilia at the anterior end, especially around the aperture of the proboscis, as the long cilia bend outwards and inwards with a less rapid motion than the shorter. Those at the posterior end cause a complete vortex, the longer cilia often remaining quiescent. The granules in the surrounding water are directed by the cilia of the sides of the tail towards the tip, where, after coming in contact. the two opposing currents dash outwards, frequently again to curve round, and cause their granules to come under the action of the lateral cilia. The whole appearances very much resemble the currents of water in a vessel after the application of heat. This action would be of little service to an animal whose posterior end was quite closed. The cilia, as long known, perform a respiratory function ; at least there exist no other special organs for the purpose. 308 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE The skin is somewhat opaque, and presents a cellular or cellulo-granular appearance. In a small living specimen it is represented as atransparent object in Plate IV. fig. 8, the entire field being definitely covered with glandular cells, and the reddish pigment grouped here and there in varying and irregular granular masses. On snipping a portion of skin from an adult living specimen, and placing it under moderate pressure (Plate IV. fig. 3), it presents the aspect of a series of ovate or spathulate cells, which contain soft and minutely granular con- tents, interspersed with large clear masses of mucus (like oil) of a somewhat similar figure, the latter becoming more numerous as the pressure increases. There are also numerous pigment and other granules scattered over the field. Changes, however, rapidly ensue in this delicate texture, as noted by M. DE QuATREFAGES, both in this group and in Planaria, and the masses of mucus pass rapidly to the nearest free border and there accumulate, the granular contents of the cells following a similar course, but not coalescing. Some of these free globules are shown in Plate IV. fig. 7, @ being the granular masses, and d a group of mucous globules like oil. The former structures, though very mobile, are less so than the latter. A transparent gelatinous basis-substance, often of a reticulated aspect, remains after the extrusion of the foregoing elements from the skin. When a transverse section is made of an animal hardened in spirit and mounted in chloride of calcium, the appearance of the dermal textures (Plate IV. fig. 2) is as follows:—In rapidly prepared and newly mounted specimens, a structureless film is sometimes observed to separate from the exterior of the skin, as indicated by the double line at the edge of the figure. Chloride of calcium would seem to destroy this delicate structure, as after a time it becomes indis- tinct, and I have not seen it in those hardened in chromic acid. The cellular cutis (a) is found to have undergone an alteration, being streaked perpendicularly, an appearance due to the collapsed state of the areolz and cells, whose contents to a greater or less degree have escaped, and thus given greater prominence to the hyaline intercellular substance. It is granular throughout, and rather more so towards the outer and inner edges. In most of the transverse sections, the pressure of the cover has caused flattening of the skin, so that the increased cellular appearance of the outer edge is partly due to the fact that the texture is seen from the surface, and not laterally. Towards the inner edge, the skin in this state sometimes assumes a crenate aspect, and adjoins a pale and structureless basis-layer (b), which separates it from the subjacent muscular walls of the body. In longitudinal sections of the textures, especially in those much hardened or | slightly exposed to air, spurious annulations are caused by the folding inwards or — wrinkling of the skin, but such crenations do not affect the muscular layers, and have no connection with the segmentation of the digestive chamber, or true annuli. A thin longitudinal section from the surface of the skin shows a series of meshes with crenated edges, the size of the spaces being variable. In Omma- BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 309 toplea purpurea and O. gracilis the cells of the skin are much smaller than in O. alba. In 0. gracilis, indeed, the skin resembles microscopic mosaic work, from the granules and plaits in each space or cell. The function of this elaborate glandular arrangement is doubtless the secre- tion of the abundant mucus so characteristic of these animals, and which is often of a most tenacious description. I have seen a specimen rapidly form a sandy investment by this means, when placed in a vessel containing a little sand; and whether the sand particles simply adhered to the gelatinous mucus by accident or not, the animal took full advantage of the protection. The same habit is exten- sively followed by the Ommatopleans of our southern shores, apparently to protect themselves from the increased danger of desiccation. On placing a living speci- men on a glass slip, and causing it to emit some mucus, the secretion proved to be a minutely granular fluid, intermingled with a few larger corpuscles. The silky sheaths formed by Jetrastemma variegatum and others are well-known examples of this cutaneous secretion. The tube constructed by Polia involuta, VAN Brn.,* is the densest yet seen, and it has an areolar aspect, from the granules or globules being set in a hyaline matrix, sometimes at considerable intervals from each other. Moreover, when viewed in profile, these globules are found to be elevated above the external surface, like a series of low pale warts. M. BENEDEN says it is simply tesselated. The tube is attached to the hairs of the abdominal feet of female crabs (C. maenas) bearing ova, and is evidently of intrinsic importance to the species, both as a protection against injury and desiccation. That some of the characters of this group of worms are due to the thick and soft cutaneous layers is demonstrated by the appearance which they present when such are removed, as by improper preservation. Two specimens of 0. pulchra, dredged off the Hebrides by Mr Jerrreys, were in this condition; and as the proboscis had been thrown off in the one first examined, it appeared like a new type of non-bristled worms, characterised by the simple arrangement of its digestive system, and its glisten- ing and elastic investment, so different from the dull, whitish, and non-elastic covering of an ordinary preparation.+ Another interesting feature in regard to the skin of the Ommatopleans (in common with the Borlasians), is the reaction which ensues on testing with litmus-paper. In this group an acid reaction occurs in O. alba, O. melanocephala, and O. gracilis; while, on the other hand, a reaction not less distinctly alkaline characterises O. purpurea and O. pulchra. M. DE QuATREFAGES’ description of the tegumentary structures differs mate- rially from that just given, a discrepancy arising partly from his confounding the * Nemertes carcinophilus, Kolliker. t The comparison of the external tissues of certain remarkable processes, occurring on a new Annelid from the Gulf of Suez, to the Nemertean skin, as described by M. tp Dr Lion Vaitianr in the “ Ann. des Sc. nat.” for 1865, is certainly far fetched and unlikely. The processes referred to are considered buds, but they seem to me to be no more buds or parasites, than the processes on the long tentacles of our British Mea mirabilis. MOM exes PART IT; 4K 310 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE structure of Ommatoplea (his Polia) with Borlasia, and partly from incorrect observations. He refers to the cells or areolee of the integument as “simples vacuoles ovoides ou arrondies,’’ which refract light, takes no note of their con- tents, and apparently considers them empty. His separation of the skin into two layers, the exterior composed of smaller, the interior of larger cells, is not evident in Ommatoplea. Smaller cells sometimes do occur towards the ciliated surface, but the entire integument-proper is continuous as a single layer. The only representative of his ‘“ fibrous’’ layer, which is described as lying within the former, is our structureless basement-layer. Dr ScuuLtTzs* figures a small por- tion of the skin of his Tetrastemma obscurum, showing a series of large cells under the epidermis, with a few granular bodies interspersed, but the view is diagram- matic. Prof. KErersTein’s observations on the cutaneous and muscular struc- tures apply almost entirely to our Borlasians. Muscular Layers of the Body.—A very distinct belt of circular muscular fibres (Plate IV. fig. 2, c) occurs next the basement-layer of the cutis. They (the fibres) are compact throughout, and less bulky than the next coat, with which their fila- ments donot mix. The succeeding layer (d) forms a powerful wall of longitudinal muscular fibres, which, in transverse sections, is generally somewhat crenated on its inner border, and fasciculated throughout. ‘The interfascicular substance is transparent and structureless, and evidently as mobile and contractile as the fibres themselves. Numerous fibrous bands stretch from the inner surface in connection with the various contents of the body. The muscular coats in Tetra- stemma are formed on the same plan as the foregoing. The appearances of these muscles in transverse section resemble those recently given by Professor Ko.- LIKER of the muscles in crabs.+ Thus there are only two distinct muscular coats of non-striated fibres around the body of the Ommatopleans, making an essential difference in this respect between them and the Borlasians, to which (latter) previous observers have for the most part confined their investigations. M. DE QUATREFAGES describes the muscular coats both in Borlasia and Nemertes (specially instancing Nemertes balmea, our Ommatoplea gracilis), as consisting of ‘external longitudinal and internal transverse’ fibres. In Ommatoplea, as just — described, it is exactly the reverse, the circular fibres being external, and the longitudinal internal. He also speaks of another layer, within the internal, as forming an aponeurosis, apparently referring to the fibrous prolongations from — the internal or longitudinal coat.{ Thus Sig. DELLE Cutagz, instead of being in error, as averred by M. DE QUATREFAGES, is correct in stating that the external — coat is circular, and the internal longitudinal. Physiologically, it is certainly a_ * Beitriige zur Naturges. der Turbellarien, tab. vi. fig. 4. + Zeitsch. fur wiss. Zool. bd. xvi. 1866, p. 375 I + Vaw Der Hoeven, apparently from following M. pz Quarreraces, makes the same errors — —Handbuch der Zoologie, vol. 1. p. 212. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 311 better arrangement for such an animal, which has only two muscular coats, to have the longitudinal fibres internal, for, on the occurrence of rupture, they, as well as the other tissues, are constricted by the circular; whereas, in the supposed arrangement of M. pr QuaTREFAGES, the longitudinal are beyond the reach of the constricting belt. Other organs also in the same animal, such as the proboscidian sheath and long posterior gland, have their circular fibres exterior to the longi- tudinal. The actions of this muscular system are very varied, and include swim- ming or floating on the surface of the water, an action performed, as in the Nudi- branchiate mollusca, by aid of the mucous exudation, and not, as stated by M. DE QUATREFAGES, chiefly by the cilia. Anteriorly the body-wall terminates in a rounded snout—of the usual cuta- neous textures, presenting in transverse section an areolar and granular appear- ance, the soft contents of the areole having for the most part escaped. The aperture for the proboscis lies at the ventral border of such a section. Somewhat behind this, but yet in front of the ganglia, a remarkable interlacement of fibres (Plate IV. fig. 1), occupying almost the entire cephalic region, occurs. Powerful bands of fibres (1) pass below both the buccal cavity and the tube for the pro- boscis, meet, and cross each other in an oblique manner, forming afterwards, by their divergence, extensive lateral connections ; indeed, it will be observed, that towards the inner muscular layer the fibres just mentioned form a broad fan- shaped arrangement. Some of the fibres (2) pass upwards by the side of the central canal, and mingle with those descending from this region; while others (3) curve downwards to the ventral wall. The fibres (4) that meet above the central canal cross each other obliquely in the middle line, so as to form a firm arch; and, besides, there are some transverse fibres (5) that cross over the canal, and spread out on each side. Other bands of fibres (6) slant downwards and in- wards on each side of the cavity, and meet inferiorly. The arrangement of these bands and fibres is so intricate, that each seems to blend with the other, and form a continuous anastomosis of contractile meshes. In addition to these oblique and radiating fibres, there is a powerful series of longitudinal fibres interwoven with them in an intricate manner, besides the denser grouping (¢) at the margin (which indicates the inner muscular coat of the body), and the glandular masses in the centre. It will be observed that the bands which pass beneath the central canal are the most powerful, and afford a much greater resistance to the bulging of the proboscis and its sheath than the superior fibres, so that in extrusion the organ is mainly directed upwards. This will be understood by referring to Plate IV. fig. 5, which represents a section of an animal which had protruded a small portion of its proboscis after chloroforming and immersion in spirit. The inferior commissure of the ganglion is thus somewhat protected by the arrangement of the fibres in front of it. The blood-vessel (Plate IV. fig. 1, 7) lies on each side in a sheltered position, in an angle between two series of fibres; and its calibre 312 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE would not seem to be much interfered with except in extreme protrusion of the proboscis. All the oblique or transverse fibres are connected with the body-wall and the inner muscular layer, as are also the longitudinal at the tip of the snout. This elaborate interlacement provides in the best possible manner for the varied changes which this region undergoes during protrusion and retraction of the proboscis, and the ordinary motions ofa tactile and mobile, yet not too yield- ing snout. The arrangement of the oblique and circular fibres around the longi- tudinal layer of the central canal also must act the part of a constrictor, and adapt the cavity to its ever-varying calibre. On the whole, the stroma in this group, from the greater predominance of granular elements. is Jess dense than in Borlasia, and the interlacing of the fibres, though not more complex, is more beautiful, because possessing greater distinctness and regularity. The posterior end of the body has no such intricate arrangement, but the muscular fibres blend together at the tip and close in the cavity, with the exception of the small and sometimes indistinct opening of the great longitu- dinal digestive chamber. The modes of fracture of these muscular coats in some of the Ommatopleans in a sick and perishing condition are interesting, the body being separated into a number of beads from the constriction and rupture of the body-wall at somewhat regular intervals. My observations would lead me to follow a different arrangement in the description of the cavities within the body-wall, from that pursued by MM. bE (YUATREFAGES, KEFERSTEIN, and VAN BENEDEN, since there exist some differences as regards interpretation of structures. Instead of speaking ofa ‘‘ general cavity of the body,” I shall first refer to that chamber in which the proboscis lies, and which may be termed the cavity of the proboscidian sheath. Cavity of Proboscidian Sheath—In Ommatoplea alba as well as in Tetrastemma, this chamber commences just in front of the ganglionic commissures, and con- tinues without interruption nearly to the posterior end of the worm. It is recog- nised in the living animal under the lens, or even with the naked eye, as that forming a pale dorsal streak, and containing a transparent fluid. The commence- ment of the chamber is shown in Plate VI. fig. 1, where a fold (a) from the tube of the proboscis becomes attached to the parenchyma of the head, or where, in- stead of a canal (ab) simply hollowed out in the tissues of the head, free and dictinct walls to the proboscis become apparent. This reflection is the anterior boundary of the proboscidian sheath under ordinary circumstances, and it is against this obstruction that the wave of proboscidian fluid first impinges in the evolution of the proboscis. The cavity gradually increases in diameter, and again diminishes towards the posterior end, where it terminates in a distinct cul- de-sac, a short distance in front of the tail. Its general appearance, when viewed from above, as a transparent object, is seen in Plate VI. figs. 3 and 8, but it varies much according to the position, degree of extension or contraction of the BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 313 animal, sometimes almost clasping the elongated proboscis, at others being attenuated over the doubled organ. The various transverse sections of the worms also render the relations of the cavity more apparent. Like the proboscis, its anterior end passes through the ring formed by the arching of the superior commissure, the inferior commissure, and the sides of the ganglia. The nervous matter must thus occasionally undergo very great stretching, or else the proboscis is rarely launched out. This will be more particularly noticed in the description of the ganglia, and a reference to Plate IV. fig. 5, will suffice in the present instance. The inferior commissure separates it entirely from the chamber of the great ciliated esophagus. The rela- tion of the parts in the ganglionic region is represented in Plate V. fig. 1, o being the wall of the proboscidian sheath somewhat compressed, so as to show both longitudinal and circular fibres; for it may be mentioned, that the structure of the chamber wall is powerfully muscular, as evinced by its ever-varying condition. At this point, however, the fibres have not attained a great degree of develop- ment. In a section made further back (as in Plate V. fig. 2, 0), and in the other transverse sections, this muscularity is more distinctly exhibited, though, of course, the spirit has shrivelled all the~ parts, especially the muscular. Exter- nally the wall of the chamber is furnished with a layer of circular, and inter- nally with a series of longitudinal fibres, both becoming thinner posteriorly. The comparatively large size of the cavity during life has doubtless caused several observers to err, by confounding it with the supposed general cavity of the body. The presence of ova or sperm-sacs has a considerable influence in modifying the size of the chamber, which in the ripe animal is pressed upwards and towards the median line, while in the spawned worm it expands freely in all directions. Itis a mistake, however, to suppose, with M. pr QuUATREFAGES, that no cavity exists pos- teriorly in the ripe animal, for this chamber holds the same anatomical relations from the ganglia to the tail as at other seasons, only its calibre is encroached on posteriorly, and the consequent distention by the proboscis and fluid makes it more conspicuous in front. The chamber is absent in the aberrant form Pola involuta, VAN BENEDEN. In the foregoing cavity the proboscis floats in a clear fluid, rich in large flattened discs, which have a minutely granular appearance. In the living animal, these generally have a fusiform outline, from a slight thickening in the middle (Plate IV. fig. 9, 5). They are accompanied by certain granules and globules, which are also represented in this figure. The discs vary in size, and adhere to- gether in a dying animal very easily, from the highly coagulable nature of the transparent fluid in which they float; and occasionally fibrinous shreds may be observed attached to them under the same circumstances. The fluid, indeed, is highly organised, and very different from sea-water, to which Dr T. WILLiAMs compares it. When the proboscis has been gently protruded under chloroform, VOL. XXV. PART II. 41 314 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE the discs in the interspace may by-and-by be seen grouping together, so as to form stellate bodies, resembling miniature solasters, spiked bodies like thorn apples, flattened structures with pectinate ends, and various other forms. In O. melan- cephala the discs are comparatively small, some being clear, spindle-shaped bodies, others granular and rounded. The enormous increase of cells and granular masses in the proboscidian fluid, after the discarding of a proboscis, is well seen in this species. In Tetrastemma the discs (Plate IV. fig. 14), though similar in shape to those of O. alba, are comparatively large ; and ina variety of 7. varicolor, which I am at present inclined to regard as the Polia sunguirubra of M. DE QUATREFAGES, they are tinged pinkish or reddish by transmitted light (Plate IV. fig. 11). They are not all similarly tinted, some being pale, others yellowish, while many are bright red—the colour in all cases being in the nuclei. Circular bodies and granules are present, as in Ommatoplea. The skin of this specimen contained many minute reddish pigment specks, so that to the naked eye it had a delicate salmon-pink appearance. Reddish granular masses occasionally occur in the proboscidian chamber of O. alba, and in other species of Tetrastemma, generally associated with reddish specks in the skin; and it is curious that a cast-off pro- boscis in 7. algw, and other species, assumes the same hue by transmitted light. — With the foregoing exceptions, the only changes noticed in the colour of the discs — were those caused by refraction of the rays of light. After extrusion into the water, their shape soon alters, and they adhere together, and become translucent. M. CixstTED* gives a small figure of a transverse section of his Notospermus Jiaccidus, and characterises the proboscidian cavity as “ canalis in quo penis est,” indicating by a blank beneath what might have been the digestive.tract. His interpretation of structures, however, is more distinct in his section explana- tory of the Family Amphiporina,} in which the digestive cavity is correctly alluded to. The reflection of the walls of the proboscis before-mentioned, in front of the ganglionic commissures, is the only barrier (and a very effectual one) I have — observed separating the proboscidian chamber from the tissues of the head. In no species examined has such a cephalic diaphragm as described by M. DE QuATRE- FAGES been found; but the peculiar ciliated chamber or cesophagus, to be described — hereafter, takes its place, and leads one to infer that the distinguished naturalist has misinterpreted the structure. Besides, the head is not a hollow organ, requiring such definition from the other parts of the body. This author, while ex- plaining a transverse section through Nemertes Borlasii{ (vel Borlasia Anglie), shows a canal surrounding the proboscis; but in his description he confounds it with the general cavity of the body, and figures (fig. 5 same plate) the proboscis as — * Entwurf einer syst. Hintheilung, &c. der Plattwiirmer, tab. iii. fig. 51. } Entwurf &c., p. 94, fig. 18 (woodcut). t Recherches Anat. and Zool. vol, ii, pl. xviii. fig. 4. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 315 occupying the centre of the general cavity posteriorly. This description, no doubt, refers to a Borlasian; but he states that the same arrangement occurs in the Ommatopleans, and represents in Polia* a series of transverse fibres as forming a platform (plancher) at the anterior and upper portion of the general cavity of the body, indicating its presence in his figures by a dark shading. No such arrangement of transverse fibres has been seen by me, but the characteristic ciliated oesophagus occupies this situation, and has probably misled the observer. The somewhat erroneous views he entertained with respect to the relations of the corpusculated fluid of the proboscidian chamber may be seen by a glance at one of his figures,} which depicts in Polka sanguirubra the proboscidian bodies as floating in what he calls the genital cavity, and in which the genital ceca are supposed to lie. I cannot corroborate his statement that these discs become much more numerous at the epoch of reproductive activity. The diminished size of the chamber may cause a slight crowding anteriorly, but this is not an increase. He did not recognise the complete muscular sheath for the proboscis and the proboscidian fluid. Dr Jonnsron likewise confounded the cavity-proper of the proboscis with the general cavity of the body ; and Dr Wittrams,{ who styled the canal the oesophageal intestine, stated that it opened externally on the side of the body, not far from the head, after the manner of the Sipunculide. M. Van BENEDEN,§ however, alludes to the sheath for the proboscis in Polia obscura, and compares the fluid and discs therein to pale blood. Professor KEFERSTEIN,]|| again, follows the majority of his predecessors, in so far as he also describes the proboscidian discs as floating in the general cavity of the body, in which, more- over, he locates the proboscis (Riissel); thus ignoring the special and complete muscular sheath just described. The structure of the proboscidian discs, and the highly organised condition of the transparent liquid in which they float, point them out as being, in all proba- bility, concerned in nutrition, as first mentioned by M. pz Quarreraces, though he likewise associated generation therewith. Some very interesting questions, how- ever, are raised by their entire absence in the curious Polia involuta, VAN BEn., especially to those who, like the late Dr W1nt1Ams, consider the fluid analogous to the peritoneal or perivisceral fluid in the true Annelids—a fluid, we may remark, which Professor HuxLey 4 considers as the true blood, while he thinks the red fluid in the branching vessels analogous to the water vascular system in the Annuloida. Ifin Polia mvoluta the proboscidian fiuid had been more important in nutrition than that in the vessels, it certainly would not have given way to the latter. It is to be remembered, too, that this absence coincides with the EaOpeciaug. l. pl. xvai, and figs 1; ploxix. + Op. cit. pl. xxii, fig. 1. t Report, Brit. Assoc. 1851, § Op. cit. p. 26. | Zeitsch. fiir wiss. Zool. xii. pp. 69 and 71. {| Notes of Lectures at the Roy. Coll. Surgeons, Med. Times and Gaz., March 7, 1868. 316 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE atrophied condition of the proboscis itself and all its apparatus. It cannot be affirmed, also, of the Nemerteans, that the fluid in the so-called blood-vessels is — devoid of corpuscles, for they occur in several species. Again, I think there can be — no doubt the fluid and discs exercise a very important influence on the reproduction of the proboscis, a process hereafter to be described, as well as promote the absorp- tion of the debris of the discarded organ when it happens to be included in the chamber. But while thus affirming the fluid has a certain influence on, and bears a certain relation to, the development of the proboscis, it cannot be said to be indispensable for the appearance of the latter, since there is a small proboscis in P. involuta, where the fiuid is altogether absent. The views of Dr THomas Wi.1aMs in regard to this corpusculated liquid, which he termed the “‘chylaqueous fluid,” are so much at variance with accuracy, that 1 cannot pass them over in silence. He says—“ In the case of the Borlasiadze, Planiariadee, and Liniadz, the chylaqueous fiuid is contained in the digestive czeca and diverticula. In some of the Planariadz, however, I have proved that a space does actually. exist between the digestive diverticula and the solid structure of the body, mwhich.is lined by a vibra- tile epithelium, and into which probably the external water is in some way ad- mitted. By this water, thus situated, the contents of the digestive ceca are aérated. The fluid oscillating in these ceecal appendages of the stomach is thickly charged with corpuscles, which, from their regular character, prove this fluid to have already reached a high standard of organisation. They occur as elliptical cells in the Borlasia from which the illustration (fig. 25) was taken; the fluid — abounded also in small orbicular points, constituting the ‘ molecular basis’ of the digestive product. In this worm, it is this fluid, and not the true blood, that is aérated ; the latter system is too little developed.”* The above clearly shows that he was quite unaware that the so-called “ elliptical cells” are always con- fined within the cavity of the proboscidian sheath, as well as points out the errone- ous notion he entertained of the true digestive tract, which in all cases can readily admit salt water (by mouth or anus), if such is required, but certainly not for the purpose of converting it into ‘‘ a vital organised fluid.” The proboscidian fluid and discs, as I have previously shown, are very far removed from sea-water. In the Ommatopleans, the aperture for the extrusion of the proboscis is situ- ated towards the ventral edge of the tip of the snout, and under favourable circumstances in the living animal, may be seen as a terminal pore, surrounded by a closely set series of radiating lines; as, for instance, when the snout is bent upwards towards the tube of the microscope (Plate IV. fig. 13). It is furnished with longer cilia even in the young animal; and in the adult these (cilia) form, when the lips are slightly pouting, a very pretty arrangement (Plate VI. fig. 1, ae), similar to the analogous opening in Borlasia (Plate X. fig. 1). The striated ring * Phil. Trans. Part ii. 1852, p. 627, pl. xxxii. fig. 25. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 317 surrounding this orifice in transverse sections of the tip of the snout indicates the special muscular coat pertaining thereto. The canal proceeds in a straight line backwards from this aperture to a point in front of the commissures of the ganglia, where it meets the differentiated walls of the proboscis, as shown in Plate VI. fig. 1, ab; and the cilia can be traced backwards to this region, but no further. This canal is simply hollowed out in the tissues of the head, and is quite inde- pendent of the motions of the proboscis. It is furnished with a series of longi- tudinal muscular fibres beneath the ciliated mucous surface, and the strong oblique and circular bands (Plate IV. fig. 1) form a very efficient constricting invest- ment. When the proboscis is about to be ejected, it commences to fold over like the turning of the finger of a glove inside out, at the point (Plate VI. fig. 1, a) in front of the ganglionic commissures, and not at the tip of the snout, a fact which has escaped previous observers. In withdrawal also, it may be noticed that, to- wards the conclusion of the process, the last wrinkle of the proboscis glides within the terminal aperture, and is seen slowly passing backwards till this point is reached, when the wrinkle ceases, and the organ is once more in its ordinary condition, any change that afterwards ensues being due to the stretch- ing of the shortened organ backwards—a process of simple elongation. Thus the anterior portion structurally and functionally differs from the succeeding, the walls of the proboscis always intervening between it and the proboscidian fluid. The attenuated coats of the proboscis curve outwards all round, and become fixed to the walls of the foregoing canal and other cephalic tissues just in front _of the ganglia; and so the reflection constitutes the point dappui against which the wave of proboscidian fluid impinges, when the organ is about to be extruded. The thin anterior walls of the proboscis unroll, the terminal canal is distended by a pouch of fluid, and then the organ is rapidly launched forth. To judge from the description and drawings of M. pz QuaTReEFAGES, the entire force of this liquid would dash against the posterior part of his nerve-ganglia, and the straitened border of his hypothetical ‘‘ diaphragm” would not pass further forwards. In my specimens, the waves of the proboscidian fluid debouch readily into the yield- ing anterior canal in front of the commissures, and then externally into the loop of the extruded proboscis. I have never seen the very pretty lozenge-shaped arrangement of muscular bands in the snout, as figured* by M. pE QUATREFAGES, and whose function, he says, is to dilate the “‘ oral’’ orifice, and carry the ‘ gullet”’ forwards; but the elaborate stroma, shown in Plate IV. fig. 1, would amply suffice for this. During the motions of the proboscis, the reflection in front of the ganglia assumes various postures, and it frequently does stretch obliquely forwards and outwards from the tube, especially when that is drawn backwards. On the other hand, when the tube is thrust forwards, the fibres slope forwards and inwards. Dr Jounston, M. DE QUATREFAGES, and Dr WiLLiAms agreed in considering * Op. ct. pl xix. fig. 1. VOL. XXV. PART II. 4M 318 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE the terminal aperture the mouth, and indeed it could not be otherwise, since the proboscis was regarded by them as the true alimentary organ. My observations, while leading me to differfrom M. Van BrenrepENn and Professor KEFERSTEIN, who aver that the Ommatoplean mouth is situated on the under surface behind the ganglia, as in the Borlasians, coincide with the three former only in so far as this anterior opening lies close to the real mouth (communicating with the ciliated sac or oesophagus). Dr Max ScuuurTze, almost alone amongst foreign authors, seems to have noticed the true position of the mouth in his Tetrastemma obscurum. The aperture for the proboscis lies just at the ventral border of the snout, while the mouth forms a slit on the ventral surface immediately behind the former. In this respect, therefore, there is a marked distinction between the Ommato- plea and its allies on the one hand, and Borlasia and Cephalothrix on the other, the mouth in the first group opening quite in front of the ganglia, while in the other it is situated considerably behind the ganglia. Analogy gives no grounds for supposing the proboscis to be the alimentary organ. I shall divide, for convenience of description, the Ommatoplean proboscis into three regions, viz., the anterior, middle, and posterior. The first (Plate VI. fig. 3, A) comprehends that somewhat cylindrical portion between the reflection in front of the ganglionic commissures and the commencement of the stylet-region —the trompe of M. pE QuaTreraces; the second (B) includes the stylet-region proper and the well-marked swelling of the great muscular sac—the oesophagus of M. DE QuAaTREFAGES; and the third (C) is represented by the long posterior gland—the intestin of M. DE QUATREFAGES. Anterior Region of Proboscis—From the point of reflection backwards, the proboscis (trompe, Riissel) gradually increases in diameter until its full size is attained. The entire organ is proportionally on a larger scale than in Borlasia, and its anatomy more apparent ; though I doubt, even in this group, if we can assign it the ideal office of a vertebral column. The general appearance of the commencement of the organ in O. alba is seen in Plate VI. fig. 3, and in Tétra- stemma alge, in Plate VIII. fig. 3. At the point of reflection there is sometimes seen a kind of os, from the slight turning over of the lips of the organ in the early stage of ejection (Plate VI. fig. 1, a). This figure also represents the longitudinal fibres of the proboscis as most conspicuous in thisregion. Sometimes the organ assumes a twisted position under examination, so as to give the fibres a spiral appearance, and in such a state the structure might fancifully be likened to the spiral arrangement — of the muscular fibres in the oesophagus of the higher animals, but the condition is _ purely accidental. I fear, however, it has led M. Dz QuaTREFAGEs into an erroneous — interpretation of the anatomy of the organ in Polia glauca,* which (organ) is described and figured as having regular spiral belts at its commencement. * Op. cit. plate xx. fig. 3. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 319 The anterior fibres of the proboscis, as further shown in the various transverse sections, and in the ruptured organ when extruded, are chiefly longitudinal, and while the thinness of the coats renders the exact structure of this region in trans- verse section less distinct, a very definite arrangement is observable as soon as the tube has attained larger proportions. Dr Jounston, indeed, considered the organ to be homogeneous ;* and M. DE QuaTREFAGES describes its commencement in Polia mutabilis as consisting of two longitudinal muscular coats, separated from each other by a cellular layer, which, he explains, is a provision for enabling these muscular coats to act independently. He also observes, that no circular fibres were seen in this species, in P. jiJum, and some others. In very small specimens of the British examples the transparency of the tissues renders definition of the coats somewhat obscure, especially after mounting in chloride of calcium, but, so far as I have observed, the structure is as follows :—Externally, there is a layer of what appears to be elastic tissue (Plate IV. fig. 4, g, Plate V. fig. 4, g, &c.). It is more distinctly striated in transverse than in longitudinal sections of the organ, hence it may be inferred that its fibres are chiefly circular in direction, as seen on comparing the last-mentioned figures. Towards its free border, also, certain obscure granular markings observed in the longitudinal section (Plate IV. fig. 4), show that the direction of the external fibres is different from the others ; indeed, in some views, the appearance is such as to raise a suspicion of the presence of the cut ends of a few fine circular muscular fibres, the rest being nearly homogeneous. Within this is a somewhat narrow belt of longitudinal muscular fibres (/, same figures), which may be termed the external longitudinal muscular coat. It consists of pale, unstriped muscular fibres, whose cut ends are seen in Plate V. fig. +. Intervening between this coat and the other longitudinal layer is a remarkable stratum, the reticulated or beaded layer (e), in the same figures, which in transverse sections (Plate V. fig. 4) assumes a regularly monili- form appearance, from an increase of its constituent substance at certain points. In longitudinal sections, I was for a time puzzled by the appearance of the cut ends of fibres in this layer, as if it had been composed of circular fibres; and a more minute examination showed that such was due to certain intermediate bands which passed between the thicker or beaded portions. If a thin longitudinal slice from the organ in O. pulchra is hardened and mounted in chloride of calcium, numerous well-marked homogeneous longitudinal belts are seen at regular intervals, from one end of the anterior region of the proboscis to the other, and between them are many connecting transverse fibres, which pass from each edge of the belt. The cut ends of the fibres in the longitudinal sections have therefore been caused by the knife severing the transverse meshes between two longitu- dinal belts. Thus the tube is surrounded by a complete investment of this * Catalogue Brit. Museum, p. 285. 320 | DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE homogeneous though complex layer, which, doubtless, has its physiological use in the varied movements of the organ. The next layer (d, same figures) consists — of a strong coat of longitudinal fibres, fully twice as thick as the external longitu- dinal layer, and which may be termed the znner longitudinal muscular coat. In essential structure it resembles the exterior, differing only in bulk. In sections prepared by hardening in alcohol, these fibres, in common with others in this organ, present a much coarser appearance in transverse section than after harden- ing in chromic acid. It may be mentioned also, that there is a considerable histological difference between these muscular fibres and those in the higher animals, such as absence of nuclei and greater homogeneousness. The fifth layer from without inwards is a strong band of circular fibres (c, same figures), the circular muscular coat, which forms a counterpoise to the preceding. . Lying on the inner side of these fibres is a basement-layer of pale translucent texture, best observed in the longitudinal sections (Plate IV. fig. 4), where it is marked 2. In transverse sections this coat is apt to be confounded with the inner layer of © circular fibres, but the distinction between the two is sufficiently apparent in longitudinal sections. It has, on the whole, a cheesy or cartilaginous aspect. Upon this layer rest the peculiar glandular papillee, which arise from a distinct margin on its inner edge, as indicated at b in the last-mentioned figure, where some of the basal streaks of the papille are represented. A glance at the other figures will show the relations and proportions of these organs. In the ordinary transverse sections of the proboscis they form en masse a somewhat foliated or frilled arrangement, often more strictly symmetrical than the view here given (Plate V. fig. 4). In some contracted specimens they block up the entire cavity, or else a — transparent mucous film which has exuded from them does so. The form of the glands in the fresh specimen under pressure is seen in O. a/ba in Plate V. fig. 7, and in Tetrastemma in Plate VY. figs.6 and 11. The largest glands are situated some distance in front of the stylets, for towards this region they become smaller, and — finally the fundus is clothed only by minute papille. In typical examples of Tetrastemma variegatum the glandular papille are leaf-shaped, and somewhat crenated at the free border, where there is a regularly streaked appearance from the ~ arrangement of the globules. Under pressure they are granular in the interior, and furnished with numerous globular or wedge-shaped mucous niasses, that refract the light like oil. Sometimes in O. alba they present a coarsely fringed appearance, with large granules in their interior; and when the tube has been turned inside out, they have a villous aspect, the tough mucosity adverted to above projecting in strings from the papillze under the slightest pressure. I have 4 generally observed also, towards the first portion of the protruded organ, fine motionless processes like cilia projecting from the apices of the glands, and they are probably homologous with the minute spikes which occur on the glands of the posterior region after rupture from pressure. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 321 The foregoing description of the structure of this region differs much from that given by M. pE QuaTrReFaGEs, almost the only author who has entered into the minute anatomy of the Ommatoplean proboscis. He states, like Mr H. Goopsir,* that externally the tube is furnished with a series of transverse muscular bridles, which maintain it in position within the body of the worm, and he gives a section of the parts in Nemertes balmea, which bears out his description very well; but he did not observe that if such bridles exist, they would have to pass through the muscular sheath in which the proboscis glides, before reaching the body-wall of the animal. Apparently he has not made out the two diverse structures. His minute anatomy of the proboscis is chiefly taken from the examination of Borlasia Anglic, and hence cannot apply in any degree to the Ommatopleans, though he considered it the type of both. He makes out only two muscular layers in the wall of this organ, and though in his section from B. Anglic he indicates ‘traces de fibres transversales,” by a few lines crossing these longitudinal coats, he distinctly observes that they are not apparent in the smaller species. These longitudinal coats are separated, says he, by a transparent homogeneous tissue, which forms a great number of bridles of very elastic fleshy columns, making, in other words, an elastic cellular layer; and he figures this in the before-men- tioned section, adding that this lax cellular coat will give the two longitudinal muscular coats that independence of action necessary for the proper perform- ance of their functions. No such cellular layer has been seen in the British species, but between the two longitudinal coats there is found the remarkable reticulated layer. He mentions a transparent homogeneous coat within his longi- tudinal muscular layer, corresponding to the mucous coat of the higher animals, and adds that the papillee of the latter are all covered with vibratile cilia. M. DE QUATREFAGES thus describes only four coats, viz., mucous, internal longitu- dinal, elastic cellular, and external longitudinal; and if the stays or bridles which he notes as connecting the tube to the body-wall be taken into account, it may be surmised that the muscular sheath for the proboscis is included in his reckoning. No cilia are present in this organ. Professor KEFERSTEIN does not enter into the structure of this region in Ommatoplea. Middie Region —tThe elongated chamber just described terminates posteriorly in a sort of cul-de-sac, into which three small apertures converge—one at each side from the lateral stylet-sacs, and a central one in the pit of the cavity con- nected with the peculiar reservoir which succeeds. The walls of the proboscis undergo a considerable change in this region, especially in regard to the deeper layers. Externally there is the investing coat continued from the anterior region on to the commencement of the reservoir (Plate IX. fig. 11), and which has acrenated border in the contracted state of the * Ann. Nat. Hist. xv. 1845. VOL. XXV. PART II. 4N 322 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE parts, with transverse markings or rugee; but such an appearance does not of necessity mean that it is composed of circular fibres, for the contraction of the longitudinal layer underneath would cause even a very feebly elastic coat to assume similar markings. The thin subjacent layer of longitudinal fibres is likewise continued to a similar extent on the reservoir-region, and assists in connecting the divisions. These two layers lie exterior to the stylet-sacs. The structure of the pit or termination of the anterior chamber (7, Plate LX. fig. 3) merits special notice, since it has certain important functions to per- form. The large glands of the inner wall gradually diminish in size until the floor is covered only by small, densely arranged, and minutely granular pro- cesses, so that the whole forms a somewhat sharply defined border, which in the ordinary state of the parts knuckles backwards all round the central stylet in the manner shown in the figure, becomes firmly bound together so as to constitute asphincter for the aperture, and gently bending outwards and backwards, is lost in the obscurity of the parts, caused by the external circlet of glands—somewhat behind the anterior termination of the wedge-shaped investment of the sac at the base of the stylet. This floor of the chamber © is composed of a series of muscular fibres, whose direction, in the ordinary — state of the parts, is outwards and backwards, as shown in the drawing, but which assume various aspects during the motions of the organ. Thus the floor passes from the conical form with the apex directed backwards to that of a transverse platform; and in the everted condition forms a cone whose apex is directed forwards (Plate VI. fig. 2). In the latter position the secure binding of the fibres which knuckle round the central aperture just permits the stylet to project, but no more. The whole arrangement constitutes a large muscular pit with — very powerful and mobile walls, capable of many and varied alterations of form. In firm contraction of the region the floor or pit of the cavity is pouted forwards (Plate XII. fig. 9), causing a radiated or slanting appearance of the fibres. A firm constriction of the tube just in front of the stylet-region often takes place, separat- ing the pit of the organ from the more glandular region in front, and causing a double swelling of the parts. Just in front of the stylet-sacs lie some coarse granular glands, which, however, are less conspicuous than in O. gracilis and others. Professor KEFERSTEIN* speaks of this region as having only a longitudinal muscular coat (though the crenated border of the anterior chamber is continued thereon in his figure), and as possessing much pigmentary and granular matter. © The latter is not well marked in Ommatoplea alba or Tetrastemma, as the entire apparatus is either translucent or white; but in certain species, as will hereafter be shown, an increase in the granular matter occurs. The longitudinal fibres of the last-mentioned author end at the posterior border of the stylet-region. The Lateral Stylet-Sacs—poches styligénes, QuaTreF., Taschen, Ker., &c. * Op. cit. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 329 (v, Plate LX. fig. 3)—occupy the exterior portion (covered only by the elastic coat and external longitudinal fibres) of the somewhat solid wall of the section imme- diately succeeding the foregoing cavity, and in some views cause a distinct bulg- ing. They are conspicuous by their aqueous translucency, as well as by the nail-shaped stylets in their interior, though the exact position of their long axes is rather difficult to determine. In ordinary views, when the animal is examined as a transparent object under pressure, their long diameter is antero-posterior, or slightly oblique; but when the worm has been killed and hardened in alcohol, their long diameter is often found to be transverse (Plate V. fig. 5). Each sac is somewhat ovoid in outline, has a thin, transparent, contractile investment (suffi- ciently tough to prevent the points of the stylets piercing it during the motion of the worm), which lies immediately under the superficial layers of the section, and a duct passing from its central region to communicate with the pit of the anterior chamber of the proboscis. The direction of this duct under ordinary circumstances (2.e. when the animal is viewed from above asatransparent object) is forwards and inwards, but, like other structures pertaining to this mobile organ, it is liable to many alterations, and is occasionally much stretched and attenuated. It is also slightly narrowed on approaching the sac, and has at its junction therewith a series of protecting fibres (Plate VI. fig. 9, a). MM. pe QuatTREeraces and Max Scuutrze do not notice the duct at all, and M. CLaparkpe’s figure* shows it dis- torted from pressure in Tetrastemma, but M. KEFrEersTEIn’s representation is more accurate. Each sac contains a variable number of the characteristic nail-shaped stylets (8), from three to five, more or less—in different stages of development, as well as certain clear fluid vesicles (€), globules and granules, and is quite filled by a transparent fluid. The relations of the sac and its contents are shown in the various figures. In Tetrastemma alge I have seen, besides the ordinary stylets, a group of minute crystalline spinets, which had no connection with the clear vesicle of the sac. The stylets very much resemble a lath-nail, and are formed of a translucent calcareous secretion ; indeed, they appear like spikes of the purest glass. The head is bulged, rounded at the edges, and somewhat flattened on the top, from which an elongated conical spike proceeds to a sharp apex. The per- fect spike or spikes in these sacs are usually about the size of the central stylet, and there are often three or four that can scarcely be distinguished from each other. Besides the perfect spikes, there are some with heads not fully developed, but complete in other respects; others again present the form of simple spikes of various lengths devoid of any head. In some instances the centre both of the head and point of the stylet is granular, while the superficial portion is of the usual homogeneous aspect. These stylets are secreted by the sac, yet I do not think they are always developed originally in one of the contained globules, as Dr ScHULTZE says; and this would not signify much, since the entire cavity must * Recherches Anat. sur les Annélides, &c. plate v. fig. 6. 324 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE act as a secreting chamber, else the large ones could receive no increase after they had outgrown the capacities of the globules. They seem to be formed by gradual increase of layer upon layer of the calcareous glassy secretion, as is well shown in some specimens mounted in chloride of calcium, where they have assumed a stratified or laminated appearance. Sometimes a process (Plate IV. fig. 10), probably a remnant of the globule, passes from the head down the shaft of the spike for a short distance, as indicated by Dr Scuuttze in Tetrastemma,* though seldom to such an extent in the adult stylet. The knob on the head figured by this author must be rare, and probably represents a casual globule. The stylets are dissolved in weak acetic acid, as first noted by M. DE QUATREFAGES, and are roughened or corroded by strong liquor potassee. In a large animal an interesting arrangement of the stylet-sacs occurred on one side, for there were two of nearly equal size, which communicated with each other at one end, so that an interchange of fluid and granular contents took place. Only one had a duct of communication with the anterior chamber of the proboscis. The opposite side had a single sac of the usual formation, containing two large and perfect stylets, and a shorter without a head. On the abnormal side the outer sac (in this view) had two fully formed stylets, a larger and a smaller clear globule, besides some other minute globules and granules; the inner, which possessed the duct of communication, had one stylet as large as the preceding, and fully formed; another somewhat less, but also having a head; a third slender spike of greater length than the latter, but headless; and a fourth, rather more than half the length of the last mentioned. No globule existed in the inner sac. It is interesting to notice the different degrees of per- fection of these spikes in relation to what Dr ScHuLTzE avers as to their develop- ment, viz., that they are the products of the smaller contained vesicles. In the one there were two large globules, and two perfect stylets, yet no trace of a de- veloping spike; in the other there were three completely formed stylets, yet each varied in length; while the long spike without a head was fully as long as the largest in that sac—head included. The stylets in the outer sac were quite as large as the central stylet. Thus at present, though I have often seen spikes inside, and connected with the fluid vesicles, I cannot support Dr ScHULTZE’S notion that the spikes must be developed therein. M. CLaparEDE says he has never seen the spikes inside those vesicles,} but I observe, in a more recent publi- cation,{ he figures a developing stylet in a globule in Prosorhochmus Claparedit. In a specimen that had often been under the microscope, I found on one occasion a pair of stylets, apparently from the lateral sac of one side, advanced nearly to the ganglionic portion of the proboscis. One lateral pouch, as it * Beitrage zur Naturges der Turb. tab. vi. fig. 10, a. + Recherches Anat., &. p. 79. ; { Beobachtungen itiber Anat. und Entwicklung, &c., 1863. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 325 happened, was thus emptied, while the other retained its three stylets. The loose stylets were very slowly moved forwards, scarcely any progress being made during an hour’s observation. At this time the sac from which they had been. liberated contained numerous granules, but no circular or ovoid vesicle. Twenty- four hours after, the stylets had disappeared. The sac is now observed to be much less than its fellow of the opposite side, and somewhat shrivelled and undefined ; but it contains a small ovoid vesicle, which is traversed by a minute slender spike, whose long diameter exceeds that of the globule, and therefore it cannot be supposed to be within it. In addition, there is a free spike about a third the length of the larger one. The former has assumed the shape of a stylet without a head ; the latter is as yet nearly cylindrical (Plate VI. fig. 4). What- ever the function of these stylets in the lateral sacs may be, there can be no doubt they have nothing to do with the supply of the central apparatus, for that fur- nishes its own stylet. The middle or stylet-region is likewise the seat of other structures of import- ance, viz., the central stylet and its basal sac, the ejaculatory duct or canal of com- munication with the reservoir, and the circlet of granular glands. It is of the same vitreous translucency posteriorly as the succeeding region, while both the anterior chamber and the posterior region are of an opaque white in the fresh specimen. Externally there is the investing layer (Plate IX. fig. 3, 7), continued from the anterior chamber, and which passes backwards to the next region. Beneath this lies a series of very powerful and conspicuous longitudinal muscular fibres (7, same plate), apparently to some extent continuous with the more bulky longitudinal layer of the preceding region, but few of which pass on to the next. Internally oblique and radiating fibres occur, the former slanting forwards and outwards from the setting of the central stylet, and forming a kind of mus- cular sling, well marked in O. melanocephala (Plate VI. fig. 7). This layer is dis- tinctly separated at its posterior border from the succeeding region or reservoir by a pale boundary-line under pressure, so that the parts have a somewhat jointed appearance. In transverse section, the complicated structure of this part is well observed (Plate V. fig. 5). The longitudinal fibres form a thick belt exteriorly, and send gradually diminishing bundles inwards towards the central point. ‘This peculiar appearance in transverse section must be due to some difference in the arrangement of the ultimate fibres, as such sections of other muscles usually show a much coarser, more fasciculated, and less granular aspect. There can be no mistake as to the true structure and arrangement of these fibres, since I have cut them both obliquely and transversely in the same specimen. The last-mentioned transverse section also shows a complicated arrangement round the central stylet-apparatus; exteriorly there is a firm setting, next a layer which seems to be closely united with the coat of the ejaculatory duct in front, and other two more immediately connected with the granular sac itself. Some of VOL. XV. PART Il. 40 326 DR W. CARMICHAEL M‘SINTOSH ON THE STRUCTURE OF THE these appearances may have been due to the action of the chemicals in mount- ing, but they were very distinct. The ejaculatory duct has a single ring or coat surrounding it. The exact arrangement of the fibres of this region is difficult to unravel, but some evidently curve across the region, while those at the sides bend backwards, the latter in some views simulating the walls of a cavity. In Tetrastemma vermiculus (as a living transparent object) the region has its deep mass formed of fibres which curve outwards and forwards from the central set- ting (Plate IX. fig. 12). Through this region the ejaculatory duct (js) passes to the point where it opens into the muscular space behind the constrictor of the central aperture in the floor of the anterior chamber. The aperture of the duct pw) is generally obscured by the central stylet-apparatus, unless the observer sees it at the moment of contraction of the powerful muscular walls of the reservoir, when the mucous or villous lining is driven forward so as to render the channel more apparent, and a vigorous jet of the minutely granular fluid is propelled into the muscular sac, and then through the stylet-aperture into the floor of the anterior chamber. Closer observation, even when such convulsive contractions are absent, occasionally shows the minutely granular fluid passing onwards to the anterior chamber; and when the ejaculatory duct is not obscured by the glands, the dancing granules of this peculiar fluid are seen therein. Moreover, when the large compound cells (Plate V. fig. 3) have been detached under pres- sure, and squeezed forwards into the reservoir and along the duct, the calibre of the opening into the muscular sac may be ascertained with tolerable accuracy, and, so far as I could see, is such that only a single file of cells at atime can be transmitted. The duct has a bent-conical form, a shape that avoids inter- ference with the basal sac of the stylet, which occupies the centre of the region ; and its posterior end (that opening into the reservoir) is capable of a certain amount of constriction, as indicated in one of M. CLapareEpe’s figures, but I have rarely met with the organ in this position. In the latter state the inner or convex side of the duct is glandular, while the outer or concave side is not. A layer of longitudinal fibres, continued from the reservoir posteriorly, consti- tutes the proper wall of the tube, and is represented in transverse section in Plate V. fig. 3. Internally the tube has a mucous lining, which anteriorly is for the most part quite free from glandular papille; a few small glands, however, are generally observed towards its posterior end. Its wall is not very dilatable, the cavity becoming elongated, but not much increased in diameter, even under violent expansive force. It can be firmly closed by the contrac- tion of the region surrounding it, so as to be marked by a mere central streak — (Plate XII. fig. 9, »). The villous lining of the reservoir is often pushed forwards along the duct during violent contractions. The whole structure of the channel, and its relations to surrounding parts, show that it is formed, not for transmitting — fluids from before backwards, but entirely in the opposite direction. The mobile BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 327 muscular space (e, various figures) into which this duct opens, forms a kind of sac that is occasionally distended with the cells and granules, before they reach, through the central pore, the pit of the anterior chamber. The cavity or reservoir (0, Plate IX. fig. 3, and other figures), from which the duct proceeds, is a somewhat globular or ovoid chamber, with its long diameter for the most part directed transversely ; or it may be compared to the bowl of a short and wide wine-glass, the stem being formed by the peculiar channel of communication with the long posterior chamber. It is liable to much variation in shape, from the contractility of its inner wall, independently of the action of the massive exterior muscular investment. Extreme contraction of the region transforms the globular cavity into amere transverse slit. Its inner surface is provided with a series of glands, the larger and more distinct having minutely eranular contents (Plate IX. fig. 3, +), and easily distinguished from those of the anterior chamber or long posterior gland. Towards the opening of the ejaculatory duct the glands are smaller than in the swollen part of the reservoir, and they again decrease in size before the organ narrows to its posterior channel of com- munication. In this comparatively large chamber the dancing granules, hereafter to be described, have free scope for the display of their movements, and not only do they move themselves, but they cause such large bodies as the compound gland- cells from the posterior chamber, when they happen to be present, to revolve and jerk also, a state of matters that has probably helped to mislead M. pg QuaTRE- FAGES as to the ciliation of the organ. Such, however, is very distinct from ciliary motion. The reservoir diminishes posteriorly, so as to form in the con- tracted state of the parts a very narrow duct (?), which by-and-by expands, and becomes continuous with the long glandular posterior chamber, the whole form- ing an hour-glass contraction, as represented in the various figures. Before, however, proceeding with the description of the posterior chamber, it may be as well to complete the narration of the structure of the two translucent regions in which the foregoing duct and cavity lie. In addition to the ejaculatory duct of the reservoir, the anterior division possesses also the central stylet and its peculiar arrangements, with the external circlet of granular glands. The former projects straight forward in the usual state of the parts, and is generally about the same size as the largest stylet in the lateral pouches, with which it likewise agrees in structure and composition (Plate IX. fig. 3, &c.). Its point under examination seems generally: to project into the pit of the anterior chamber, though the thick muscular floor occasion- ally closes round it. The base of the stylet is fixed to the granular sac (A) ; the arrangement being not inaptly likened by Dr JoHNnsTon to an awl, the anterior or smaller end of the sac sending its investing substance over the head of the stylet, and grasping part of the spike. The basal sac (or awl-handle) is narrowed anteriorly, gradually widens backwards, is then marked by a constriction, and 328 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE again is terminated by a wider portion, which may represent the butt of the awl. — This structure is shorter in proportion to the stylet, and has its constriction placed further backwards than in Tetrastemma alge. The entire sac is opaque white, and coarsely granular from an early age, the granules disappearing with effervescence under the action of weak acetic acid, and rendered paler (in some cases dissolved) by liquor potassee. These granules would not seem to be simply inclosed in the structure, as if in an ordinary sac, but they adhere together and form a consistent whole, as proved, amongst other things, by their not falling out of the fragment when the anterior part is cast off with the stylet, as will be here- _ after described. I have also seen the stylet and its granular basal sac thrown off together in a discarded proboscis in the proboscidian chamber of O. melano- cephala and other species. This peculiar body or sac is set in a firm wedge of translucent yet compact muscular substance (marked 6 in the various figures) which often has its posterior border curved in a saddle-shaped manner, projecting backwards in the middle, and with a curve on each side directed forwards. The — anterior part of this wedge proceeds about as far forwards as the shoulder of the first swelling of the awl-handle, and there becomes lost on the coat of the latter. Though this generally appears like a wedge of translucent and structureless car- tilage, the addition of liquor potassee and acetic acid shows distinct strize, chiefly — of atransverse character when viewed under pressure, and therefore of a radiating — nature with regard to the central granular sac. In front of the wedge-shaped division hes the muscular cavity (e, Plate IX. fig. 3), into which the ejaculatory — duct opens (at py’). This cavity is formed by the knuckling outwards of the floor of the anterior chamber all round, and it is furnished with a distinct inner mus- cular coat. The walls are thus very mobile, and I have seen them form an hour- glass contraction in the middle, quite distinct from the narrowing between the sac (whose greatest diameter is in front) and the firm wedge behind. Its anterior border can be projected to the tip of the central stylet; while in the extruded state of the parts (e, Plate VI. fig. 2) it forms, when seen from above, a com- pressed process at each side of the basal sac of the central stylet ; more correctly, however, and if viewed from the front, it has the shape of a muscular umbrella, which slopes all round the anterior portion of the basal sac. M. CLAPAREDE does not mention this arrangement at all, and M. p—E QuaTREFAGES seems to have | mistaken it for a pair of glands, which, he explains, probably secrete poison for cankering the wounds inflicted by the stylet, a supposition unsupported by any | anatomical basis as regards this spot. Prof. KerersTEIn’s anatomy of the region also requires correction, since he does not distinguish the separation between this cavity and the floor of the anterior chamber; thus in his representation* of the extruded proboscis, the central stylet projects smoothly into the water, and the ejaculatory duct opens directly into the latter at a short distance from the stylet. — * Op. cit. tab. v. fig. 3. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 329 A very interesting condition was found in two specimens of Tetrastemma vari- color, which directly bears on the physiology of this region. In each a fragment of the granular sac, with the central stylet attached, lay towards the anterior end of the first region of the proboscis ; and since injury would scarcely have caused a result so systematic, it is evident the stylet had been thrown off by the animal. In both instances the central stylet-apparatus was complete, only in one the anterior part of the basal sac appeared paler, and there was a slight irregularity in its outline, similar to that in fig. 14, Plate V. In each, the lateral stylet-sacs had their full complement of stylets, one or two of which equalled the central stylet in size. There appears to be only one explanation of this state of matters, viz., the fact that the central stylet can be thrown off, and somewhat rapidly regenerated; for it is unlikely that in each case it found its way there from without, and it is still less likely to have been driven in by an enemy. Former experience in regard to the stylets from the lateral sacs shows that such bodies take some time to gain the exterior of the worm, and hence our surprise is Jessened at the perfection of the new structures while the old have not yet escaped from the proboscis. Besides, the structure of the parts in O. pulchra will by-and-by throw still farther light on this subject. Lastly, across this region passes the belt of granular glands (7, various figures), which have the form of lobules, with their long axes parallel to that of the proboscis, and are situated beneath the two external layers of the part. The granules are proportionally larger in Tetrastemma. I have not found any struc- tural guide to their function, though they are invariably present in the Omma- topleans. A curious appearance was noticed in a small specimen of Tetrastemma varicolor, which had its stylet-region in front of the granular glands covered by an external coating of large cells, with a nucleus and faintly granular contents; such, however, may have been due to an abnormality. The structure of the next division—that of the great Reservoir—has now to be examined (0, Plate IX. fig. 3). On reaching the point previously mentioned (a, Plate IX. fig. 11), the elastic coat and the external longitudinal muscular fibres of the proboscis for the most part cease. Before this occurs, however, the muscular fibres (+) peculiar to the*region arise, sweep backwards in a beautiful fan-like manner over the reservoir, loop round and meet those from the opposite side, and leave only a small space in the centre posteriorly, through which the channel of communication with the third region passes. When viewed as a trans- parent object under pressure, or in longitudinal section, the direction of these fibres is backwards and inwards. This great muscular mass does not receive accessions from the outer wall, but the whole of the loops come from the front. _ By the varied crossings of these fibres, a felted aspect is produced under examina- tion in some species, such as O. purpurea and O. alba (Plate IX. fig. 11), and is doubtless present in all. In addition, there are circular and longitudinal fibres VoL. XXV. PART II. 4p 330 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE within the former, and to whose presence the independent wrinkles of the inner structures are due. The longitudinal layer (70) is innermost, and forms a kind of spindle-shaped arrangement; the anterior fibres—commencing with the ejacu- latory duct (of which they form the special wall)—soon spread out to cover the dilated cavity of the reservoir, then become narrowed as they surround the channel of conmunication, and proceeding backwards, merge into the longitudinal coat of the posterior chamber. In some positions, these fibres assume a crossed or spiral aspect in the channel of communication; but, as in the case of the gan-— glionic region of the proboscis, this is purely accidental. The margins of the reser- voir and the channel of communication are marked under pressure by the ends of muscular fasciculi, especially posteriorly; an appearance due to the doubling of the looped fibres, but also partly to the presence of the thin circular coat, which lies without the longitudinal. By the contraction of these various fibres, the chamber of the reservoir is squeezed with great force in every direction, like a thick caoutchoue — ball or globular syringe in the hand. Its transverse diameter is lessened, and still more, its antero-posterior, while ajet of the minutely granular fluid is squirted into the anterior chamber; and, in spasmodic efforts, even a prolapsus of its glan- dular lining occurs. In contraction, the entire region is much shortened, and the mass of the looping muscle increased posteriorly. Not only does the peculiar looping of the fibres cause most powerful squeezing of the cavity, but the posterior aperture has a tendency to be closed, and slightly carried forwards, the anterior being less subject to interference. The closing of the posterior aperture (channel — of communication) is also greatly assisted by the circular fibres which are situated — outside the longitudinal. The varying conditions of the reservoir may be under- stood by comparing Plate IX. fig. 3 with Plate XII. fig. 9, the former show-— ing the organ in its ordinary state, the latter in a somewhat contracted con-— dition. ’ The peculiar looping of the fibres of the reservoir causes a transverse section through its posterior part (Plate IX. fig. 10) to assume a finely radiated spiral arrangement, the whole reminding one strongly of Dr Prerricrew’s beautiful diagrams of the arrangement of the muscular fibres of the heart ; and in this case ~ - no better structure could have been devised for the complete and forcible evacua- tion of the chamber. Professor KrrerstTErn describes only oblique and longitu- dinal muscular fibres in this region. Posterior Region.—Behind the translucent region just described, the opaque white long posterior chamber (C) (éntestin, QuaTREF., Drusentheils of the Germans) occurs. It communicates with the reservoir in front, as previously mentioned, but its posterior end is cecal. The contractile nature of the parts renders com- parison uncertain, but it is generally not much shorter than the anterior chamber in the perfect animal. Sometimes, indeed, it exceeds the latter chamber in length, the simpler structure of its walls giving greater extensibility. In young BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 331 specimens and in regenerating organs, again, it assumes a nearly globular form in contraction. Externally, it is covered by a very delicate investing layer. Within this lies a series of powerful circular muscular fibres, which towards the taper-., ing posterior end become indistinct, and finally disappear altogether, after the czecal tip is reached (Plate VII. fig. 4). The next coat is formed of an equally strong series of longitudinal fibres, the anterior or primary ones being continuous with the longitudinal layer of the reservoir, as previously mentioned. These run throughout the entire length of the posterior chamber, becoming proportionally more developed as the central cavity diminishes towards the cecal end, and finally merging into the muscular ribands which terminate the organ. The mucous layer with its glands lies within the latter, though in several views, both in the living animal and in transverse sections, I fancied some sub-mucous circular fibres were present ; they are at any rate insignificant, and the two chief layers explain all the motions which ensue in this division. This mucous layer in con- traction of the organ forms many rounded folds, which are especially distinct in O. gracilis (Plate IX. fig. 16). A transverse section of the chamber is repre- sented in Plate IX. fig. 14, and the great increase of the glandular mucous layer in contraction is conspicuous. The two muscular coats are about equal in thick- ness. From the commencement of the region behind the translucent reservoir almost, but not quite, to its czecal tip, its entire inner surface is covered with a series of glandular papillee, which differ materially in structure from those of the previous regions. Viewed as a transparent object under moderate pressure (Plate V. fig. 9), the field is found to be covered with globular glands containing clear rounded vesicles in their interior. In contraction, and when the wall is less compressed, the glands have an enlarged and coarse appearance, only the external wall of each being visible. When the pressure has been increased, these glands, especially towards the posterior end (where, from their lessened numbers, ‘a clearer view can be obtained), alter their shape apparently by bursting (fig. 10, same plate), and seem like a double ring of a minutely hirsute aspect, while the contained globules are scattered over the membrane. If the organ has been rup- tured and partly inverted, the free edge of the laceration and the shrivelled glands have the appearance shown in fig. 8, same plate. ‘The globules from the glandular papille (fig. 3) and glands whose contents have been evacuated (and which are minutely hirsute) readily pass forwards to the reservoir, and roll through the ejaculatory duct under pressure. The function of the vast array of glands in this chamber would seem to be the formation and elaboration of the remarkable | fluid with the dancing granules previously alluded to. This secretion is produced in considerable quantities, and towards the posterior portion frequently distends the organ into a translucent pouch (Plate VII. fig. 4, @), wherein the moving granules are in full action, and even the experienced are apt to err in regard to the nature of the movements, so like are they to those caused by ciliary currents. 332 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Under a high power (700-1000 diam.), the moving bodies appear as mere specks or points, and they retain this remarkable motion for upwards of twenty-four hours after extrusion from the cavity into the surrounding salt water. There is thus a peculiar fluid rich in these granules secreted by the posterior chamber or gland; and continued observation, and the whole anatomy of the parts, show that this fluid passes forwards into the reservoir, where it is probably mixed with a small quantity of another secretion from the glandular walls-.of the latter, and then propelled with force through the ejaculatory duct into the anterior chamber. What its peculiar function in the anterior chamber, or when discharged into the surrounding medium in the extruded state of the parts, may be, can only be con- jectured at present; but from the elaborate structure of the parts concerned in its economy its action would seem to be important. I have no observations in support of the view that this granular fluid is poisonous. It cannot pass into a wound at any rate until the stylet is withdrawn; and if it really acts as a poison to animals when introduced into their tissues, it might reasonably be supposed to affect them injuriously when discharged into the water around them. Whether the fluid has any influence on the secretion of the stylets in the lateral sacs, or in — the central apparatus, Iam unable to say; but, as already mentioned, a minutely granular fluid has been seen in the former, and a large though imperfect stylet in the posterior chamber of 0. pulchra. MM. ve QuATREFAGES, VAN BENEDEN, and others, state that the proboscis and the foregoing apparatus are used in attacking prey ; but, we may ask, Do the Borlasians use their feeble and unarmed structure for the same purpose? So far as I have seen, the proboscis is a somewhat pre- carious aggressive weapon, since it frequently adheres to the attacking body, and is thrown off. It is true we may assign, with an air of probability, an aggressive function to the central stylet; but we cannot do so with the very same organs in the lateral sacs; for, being developed in a free condition within almost closed — cavities, they are quite useless as offensive weapons. In extrusion of the proboscis (Plate VI. fig. 2), the entire spike of the stylet | projects, the floor of the anterior chamber forms all round a thick and powerful umbrella-shaped cushion (whose independent structure has escaped Prof. KEFER- STEIN), the lateral stylet-sacs are under cover, and the region of the reservoir is — shortened and widened. The position of the muscular chamber (e), which forms — a second small umbrella round the apex of the basal sac of the central stylet, has already been mentioned. The separation between the longitudinal fibres of the — stylet-region proper (v) and the looping fibres (7) of the reservoir is well marked in this condition. It will also be observed that the stylet-region is widened 7 by the forcible wedging forwards of the reservoir. ' The walls of the posterior chamber, after forming the cul-de-sac, are continued — backwards in the form of one or two long translucent muscular ribands of extreme flexibility and contractility (), fig. 4, Plate VIII.), and which are attached to the BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 339 walls of the proboscidian sheath, rather behind the middle of the animal, the fibres spreading out in a fan-shaped manner, and mingling with those of the tube. The motions of these muscular bands is most interesting, now jerking into nume- rous graceful folds or coils, by a sudden contraction, like the stalk of a Vorticella, now shortening more gradually—the curves being thickened here and there by the bulging of the fibrille. They are simply muscular fasciculi, with very fine longitudinal lines—the marks of the fibrillee, and seem to restrain the irregular protrusion of the proboscis and assist in its retraction. This muscular arrange- ment is also the wltimum moriens, showing contractions when all other signs of life have fled. In a young Tetrastemma variegatum, in which the riband had been ruptured from its attachment, the fibres (Plate VI. fig. 6, 1) had assumed a clavate aspect from contraction, and only very faint longitudinal markings were visible. Before reviewing the statements of previous investigators with regard to the general structure of the foregoing parts, a description of the peculiarities of the regions in other species of Ommatoplea will be narrated. In Ommatoplea melanocephala (Jounst.), the proboscis is somewhat larger in proportion than in 0. alba ; and, while the type of structure is adhered to, there are several important differences in detail. The stylet-region (Plate VI. fig. 7) is peculiar in having the lateral stylet-sacs carried considerably forwards, so that they lie quite in front of the central apparatus, and the floor of the anterior region has consequently to form a deep pit to reach the spike of the stylet. In this figure the organ is shown comparatively free from pressure, and the encroach- ments of the lateral sacs on the cavity may thus be correctly estimated. The basal sac of the central stylet is proportionally large, while its wedge-shaped setting is comparatively meagre. The powerful series of oblique or radiating fibres which pass outwards and forwards from the latter, in the usual position of the organ under pressure, are very distinctly shown, and, as it appears, sling the apparatus. The points of the stylets (central and lateral) are rather blunt, and their shape, on the whole, resembles that found in Tetrastemma alge. Some of the looped muscular fibres of the reservoir seemed to pass inwards beyond the exterior ring in front, so that a continuous series of fibres would thus be formed, as in certain viscera* (bladder, &c.) of the higher animals, and the chamber environed with the exception of the anterior and posterior openings. The circlet of granular glands is much developed in this species, and often renders the subjacent parts obscure. The remarks and figures of M. DE QuaTREFAGES fF relating to this species (his - Polia coronata) require amendment. He mentions that it is the only exception * Vide the admirable Researches of Dr Pettigrew, Philos. Trans. part ii. 1867. + Recherches Anat. &c, p. 166. VOL. XXV. PART II. 4Q 334 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE he has met with to the uniform arrangement of the stylet-apparatus, as, in addition to the forward position of the lateral stylet-sacs, the central stylet and its surroundings are placed in his second cesophageal cavity—that is, in our reservoir; and his figure* bears out his description, representing, moreover, the organ as placed at the commencement of the posterior channel. ‘The species is easily identified by the position of the lateral stylet-sacs and other peculiarities, and there is certainly no such abnormality of the central apparatus or alteration of type as noted and figured by this naturalist. In a very pretty new species—dredged in Lochmaddy—of a salmon hue, striped down the back with two brown and a white central streak, having also a transverse brown bar at the posterior part of the head, and only two eyes,+ the stylets were similar in shape to those of 0. melanocephala, but decidedly smaller. This shows that while distinctions in size and shape are valuable specifically, they should not be too much relied on. The anterior chamber in O. gracilis (Plate VII. fig. 1) is very short in pro- portion to the great elongation of the animal, the stylet-region being found only a short distance behind the ganglia; indeed, in this respect, it is not far removed from Polia involuta, VAN BENEDEN. ‘The floor of the anterior chamber has generally a bilobed aspect under examination, and hence differs considerably from that of 0. alba. On each side of the floor in front of the stylet-sacs the end of the — proboscis has not the massive muscular structure usually found in this position, but internally has a somewhat opaque mobile lobulated glandular arrangement, which, when the organ is everted, projects as two semi-opaque whitish papille (one on each side), the stylet-sacs being sometimes prolapsed into their interior. The central stylet and its apparatus do not easily project in this condition. The — stylet-region proper, consisting of that part from the floor of the anterior chamber to the border of the reservoir, is somewhat opaque, on account of the glandular nature of the walls anteriorly, and the layer of granular glands posteriorly. The latter are placed far back, and in developing specimens form an opaque granular mass on each side of the ejaculatory duct, sometimes entirely filling up the angle (at a, same fig.), and consist of a dense grouping of minute clear granules, and occasionally coarser particles in lobulated glands, which are apparently homo- logous with the granular glands of other species. The lateral stylet-sacs have very long ducts, and each encloses from seven to ten stylets of a characteristic shape, besides other contents. The central stylet is appended to a basal sac of great length, the sac indeed resembling the outline of some long bone, such as the radius, the stylet being articulated to the head, while the distal extremity of the bone is represented by the swollen posterior end of the sac. The latter has’ * Op. cit. pl. xi. fig. 8. + The Nareda superba of Srimpson has likewise two eyes, but has no longitudinal stripes.— Synopsis Mar. Invert. of G. Manan, N. Brunswick, p. 28, fig. 17, 1853. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 335 the usual granular contents, but the exterior firm setting, so characteristically wedge-shaped in other species, does not proceed half-way forwards, the slender anterior portion having only a thin covering for its support, as indicated in the figure. While in ordinary views the stylet and sac seem straight, both have a decided curve when seen laterally (Plate VI. fig. 12). Just in front of the point where the clear setting of the sac becomes indistinct, the ejaculatory duct opens into the peculiarly elongated muscular cavity (e), which extends forwards to the cir- cular opening in the floor of the anterior chamber. This channel shows a distinct inner layer of longitudinal fibres, which, however, seem to act only in company with the external oblique fibres surrounding them. The presence of this special inner coat demonstrates that it is not the mere doubling of the floor of the anterior chamber that forms this cavity, as indeed certain appearances, previously observed, had led me to suspect. The central and lateral stylets have the same shape, and the majority agree in size. In its usual position the stylet has the form of a spear-head (Plate VI. fig. 13), being sharp-pointed, then dilating gra- dually till near the posterior end, where a slight diminution occurs, and then a marked constriction, just in front of the somewhat small head. If minutely examined, both central and lateral stylets, show a small secondary swelling or ring above the head (Plate VII. fig. 9). The ejaculatory duct is comparatively large and boldly marked, comprising at its posterior end almost the entire region of the reservoir, a slight demarcation, however, marking off the dilated pos- terior end into a portion pertaining to the reservoir, and another to the duct. The widened posterior end is covered with small glands, which are continued along the tube to its opening into the long muscular chamber behind the floor. One peculiarity in the elongated reservoir is the comparative thinness of the looped fibres towards the anterior end, and the thickness of the longitudinal layer, which seems to afford compensation for the diminished strength of the exterior coat. This deviation from the usual structure is doubtless in connection with the enlarged posterior end of the ejaculatory duct, and the gradual con- tinuation of the cavity of the reservoir into it. The bulk of the looped fibres is grouped posteriorly, and in action would seem to compress the reservoir, so as to _ throw its contents forward to the gaping aperture of the duct. On this account also the posterior channel of communication is long. The external layer, con- tinued from the preceding division, passes about half-way backwards over the reservoir. Another peculiarity is the presence of numerous clear cells and granules amongst the looped fibres, most distinctly seen at the posterior part of the chamber. Some of the cells contain nuclei, and others do not. The glandu- lar papillee in the interior of the reservoir are large and prominent. The very great length of the posterior chamber as compared with the anterior is re- markable. M. DE QUATREFAGES seems to have devoted considerable attention to the ana- 336 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE tomy of the foregoing species (his Nemertes balmea), and his deviations from accuracy, therefore, surprise us. He represents* the stylet-region as having the lateral sacs placed rather behind the long central granular sac, each of the former having a carunculated gland attached to its posterior end, while the latter has two longer structures of the same description. None of these carunculated appendages have been seen by me, since it can scarcely be supposed he refers to the opaque granular condition of the angle (at a, fig. 1, Plate VII.), previously described. His description of the contents of the lateral stylet-sacs is erroneous ; for though the position of the stylets is of no moment, the assertion} (and cor- responding figure) that each has a developing sac attached to its extremity is very wide of the correct account. The outline of the stylets given by this author — is inaccurate, since no constriction is represented in front of the head, and no mention is made of their curvature. The other objections to his views are noticed elsewhere. The proboscis in the long purple species, O. purpurea, while approaching that of O. gracilis in slenderness and in tenuity of the posterior region, is yet more closely allied to O. alba in the structure of its comparatively short stylet-region proper. The floor of the anterior chamber in this species is furnished with very minute glands. Notwithstanding the great length of the worm, there is no corresponding elongation of the stylets, and the granular basal sac of the central apparatus is likewise short (A, fig. 2, Plate VII.) The lateral stylet-sacs are small, and somewhat rounded, and their ducts are sometimes spindle-shaped, from marked constrictions situated respectively at the sac and opening into the floor of the anterior cham- ber. The stylets are at once distinguished by their short, stout form and peculiar longitudinal markings, which resemble the longitudinal streaks in polished mahogany (Plate V. fig. 12), and are due to irregularities in the outline. The — granular sac of the central stylet (Plate V. fig. 13, A) has only a slight constric- tion in the middle, so that the lateral line, from the apex of the spike to the base of the sac, is nearly straight. The opening of the ejaculatory duct into the cavity behind the floor of the anterior chamber is wide. The reservoir is much elon- gated, and it may be observed that its fibres, as pressed between glasses, are not seen in a looping series down the sides of the cavity, but form a densely felted — arrangement on each side. When freed from pressure these fibres are observed to — cover the reservoir with most elaborate crossings, from the diverse directions which they pursue. In the same region the longitudinal fibres are much developed anteriorly, though they are only well seen on stretching the parts, otherwise the | felted arrangement of the looping fibres obscures them. The glands of the reservoir are smaller and less distinct than in 0. gracilis, especially anteriorly. The channel * Op. cit. pl. x. fig. 3. + “Quelquefois, surtout chez le Némerte balmée, on apergoit méme un commencement de la tige du stylet.”—Op. cit. p. 166. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 337 of communication with the posterior chamber is somewhat short and wide, and in marked contrast with the same part in the latter form. The long posterior chamber has its inner surface thrown into more prominent ruge than in most species, so that they sometimes appear like large papillze covered with the glands- proper of the cavity. These plaits are not mere wrinkles and folds caused by the contraction of the elongated organ, but are present under severe pressure ; indeed, they are characteristic and original processes of the chamber (Plate IX. fig. 16). The granules of the peculiar fluid therein are also very distinct. It may be mentioned here, that after prolonged confinement the integrity of the proboscis in this and other species is affected, the stylets degenerating, and even disappearing altogether, both from the central and lateral structures. Not only is this the case in the adults themselves, but under the same circumstances the more advanced young in the interior of Prosorhochmus Claparéedi undergo a like degeneration. In a specimen of the former species where this had occurred, the wave of granular fluid driven forward by the contraction of the reservoir distended the muscular cavity in front of the granular basal sac of the central apparatus (which in this instance was devoid of a stylet), and as the aperture into the anterior chamber permitted only a limited discharge at a time, the fluid rushed into the centre of the granular sac, and distended it and its wedge-shaped setting with every impulse. The absence of proper nutriment and free aeration—for the salt water was but rarely changed during the year—are sufficient causes for the above-mentioned degeneration. In O. pulchra (Jounst.) the anterior region of the proboscis has a decidedly pinkish hue, and numerous small clear globules at its commencement, as well as over the reservoir. The large glandular papillae in the anterior chamber have their marginal globules less distinctly marked than in O. alba or Tetrastemma, and hence the structure has a smoother or finer appearance. The lateral stylet-sacs (Plate VII. fig. 3, vy) are very large, and each contains, in well-developed specimens, from five to nine stylets, a large circular globule, and a granular orange pigment- _ mass, besides a fluid rich in moving granules, similar to the secretion from the long posterior chamber. It is, however, in the apparatus of the central stylet that the greatest deviation from the typical structure occurs. The basal sac of the stylet (Plate VI. fig. 11, A) is small, elliptical rather than ovoid, and its granules are very minute. In addition to the ordinary stylet (a) fixed to its anterior end, another stylet (>) projects into its posterior portion, enclosed in a _ kind of sheath, and whose point extends forwards almost to the butt of the an- terior stylet. This reserve-stylet is not in all cases fully formed, but apparently awaits the rejection of its progenitor for complete development. The head of the reserve-stylet projects into a large cavity formed by a peculiar disposition of the fibres composing the setting of the basal sac and the region behind. Instead of the usual wedge-shaped structure, radiating fibres pass outwards from the sides VOL. XXV. PART II. 4R 338 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE of the sac, curve backwards, and arch over a large cavity (Plate VII. fig. 3, oy) filled with a clear fluid, part of the floor being formed by the anterior fibres of the reservoir. In certain states of contraction the central (reserve) stylet may be seen pressed backwards, so that its butt rests on the latter—a position quite easily attained on account of the yielding nature of the cavity and tissues which lie immediately behind and around it. Some granular streaks, probably due to the granular glands, are also observed passing from the central sac along the arch of the fibres. The granular glands themselves are distinct enough if the specimen is not too much pressed. The peculiar cavity behind the central granu- lar sac might be supposed to assist in the rapid formation of the reserve-stylet, yet it cannot be absolutely necessary for its development, since the stylet is as readily replaced in front of the sac in 0. alba, and others, where no such space — exists. Physiologically the cavity may also act as an elastic buffer or cushion © when the stylet is driven into any structure, if such ever occurs. The ejaculatory duct is large, and being surrounded by a yielding region, is more mobile than in the typical forms. The clear globules interspersed amongst the looped fibres of the reservoir are numerous, so that under pressure the cavity seems covered with them; and if pressure is severe, they escape into the reservoir, and pass for- wards into the ejaculatory duct. Posteriorly these looped fibres have a laminated appearance. During examination the walls of the reservoir were frequently con- tracted in the manner shown in the drawing (Plate VII. fig. 3), thus indicating very clearly the presence of circular fibres. The entire region had more trans- lucent walls and greater mobility than in O. a/ba, and the coats were somewhat diminished in total bulk posteriorly, so that the channel of communication was short. The glands are large transparent structures, with clear globules in their interior, and in general aspect differ from any hitherto observed. Those of the posterior chamber of the organ were longer than in 0. alba and Tetrastemma. In one specimen several stylets lay in the cul-de-sac of the latter chamber, show- ing that they had passed along the ejaculatory duct, or else had been formed in the cavity. The muscular and other structures of the anterior region of the proboscis of O. pulchra present, in transverse section, a slight variation from the common type, as seen in O. alba. The beaded layer (Plate VIL. fig. 10, e) is very distinctly marked, and the external angle of the somewhat lozenge-shaped enlargements (longitudinal bands) is connected with the outer layer (g), while a process from the opposite angle passes inwards towards the circular coat (c), so as to cut the great longitudinal layer (d) into a number of separate fascicles, which, in the specimen represented, amount to fourteen. The changes which ensue in the various layers, when the organ is completely everted, are portrayed in the figure; and the characteristic appearance of the beaded layer (¢) is to be noted, as well as th swollen segments of the usually thin external longitudinal Jayer (/). BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 339 Dr Jounstron* observes of this species, that “the structure of the stomach ” (proboscis) “is like that of its congeners, excepting in there being five or six spines on each side of it, instead of three, which is the usual number.” He does not refer at all to the remarkable arrangement of the central stylets, though an incomplete woodcut in one of his early papers} shows that it had not entirely escaped the notice of his accomplished artist. The general arrangement of the proboscis in Tetrastemma algw agrees with that in O. alba, though there are some minor differences in the details of the stylet-region. If under examination the ejaculatory duct is placed on the left of the central stylet-apparatus, an explanation is obtained of the mistake into which M. Cuaparépet had fallen in his description of the region in Tetrastemma vari- color, Girst. (the figure, however, appears to me to be very like that of 7. alge). The central stylet and its sac have been slightly pressed backwards so that the radiating fibres which sling them have been brought out distinctly, and some- times a faint line of demarcation is seen on the right side (in such a position) simulating the presence of a separation; but numerous fibres are prolonged past this, and, moreover, a slight contraction or change of position obliterates this line, while the curved or radiating fibres are rendered more distinct. On the left side the only boundary line to the supposed distinct coat around the wedge- shaped setting is the wall of the ejaculatory duct.. The basal sac of the central stylet in 7. alge (to continue the description) has rather more shape than in 0. melanocephala, and is proportionally more elongated. I thought I could detect a slight difference between this species and 7’. variegatum, for the stylet in 7. alge is generally shorter in proportion to the length of the sac than in 7. varie- gatum. Considerable variations exist in the size of the several stylets in 7. alge, independently of the size of the animal, a fact, perhaps, the less to be wondered at when the reproduction of the tube is remembered; but the greater size is generally diagnostic when compared with other species. In a developing or recently repaired central apparatus (Plate V. fig. 14) the basal sac is thinned off anteriorly from contraction of the parietes, and the difference in size between this central stylet and one from the lateral stylet-sac (Plate V. fig. 15) of the same animal is marked. In Tetrastemma variegatum the structure of the stylet-region, while agreeing generally with O. alba, is yet more particularly allied to 7. alge. The stylets are on the whole more slender than in the latter, and the central longer in proportion to its basal sac. In 7. vermiculus the structure is similar to the two former (Plate IX. fig. 12). The shape of the basal sac of the central apparatus in 7. varicolor is characteristic (Plate VI. fig. 5), the stylet being more slender than in the other two species, larger in proportion to the sac, and the lateral lines _ of the latter nearly straight. The proportionally large size of the glands in the | * Catalogue of Worms, &c. p. 292. t+ Mag. Zool. and Bot. vol. i. p. 531, fig. 4. { Recherches Anat, sur les Annel, Turb., &. p. 81, plate v. fig. 6. 340 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE reservoir in Tetrastemma is well illustrated in this species, where they form very prominent structures with granular contents, and more nearly allied to those in the posterior chamber than in O. alba. In transverse section the micro- scopic structure of the organ in the foregoing species agrees with that in Omma- toplea. In Polia involuta, VAN BENEDEN, the proboscis and its apparatus are reduced toaminimum. ‘The anterior region (Plate VII. fig. 5, a) is very short, and has in general a somewhat conical outline, the base of the cone being formed by the — floor of the chamber. Its walls are proportionally thick and muscular, and internally have a minutely granular aspect, a condition probably due to indica- tions of papillee. Posteriorly it terminates in the usual floor, into which, how- ever, only one aperture leads, viz., that of the central stylet. The next, or stylet- _ region proper, while still retaining the Ommatoplean type, differs much from that of any other British species. Instead of the usual well-defined arrangement of longi- tudinal and radiating fibres, the entire muscular structure is obscured by numerous granular or cellulo-granular bodies (ry), which give a characteristic appearance to the somewhat conical reyion. There is no trace of lateral stylet-sacs. The central stylet is minute, and furnished with an elongated and faintly granular basal sac, which is fixed in the usual transparent muscular setting, the mobile muscular chamber into which the ejaculatory duct opens being situated immediately in front. — Though the whole apparatus is very minute, I have seen the stylet thrust forwards by the contraction of the fibres of its basal setting, so that its point projected into the floor of the anterior chamber of the proboscis. The ejaculatory duct is large, and, owing to its central position in ordinary examinations, causes the stylet-region proper to appear bifid posteriorly ; but this is due only to the greater translucency of the duct, which, for the time being, renders the denser granular masses at the sides more conspicuous. The region of the reservoir is fairly developed, the walls being striated with transparent muscular fibres in the usual manner, and the granular glands lining the inner surface. The walls might be seen now and then contracting with force, and driving the contents forwards into the ejaculatory duct and muscular chamber behind the floor of the first region. The posterior channel of the reservoir led into a posterior chamber of — comparatively small dimensions, but having thicker walls than usually found in — this region, and terminating in a cul-de-sac and rounded end, a short distance — behind the cesophageal apparatus. This chamber had a cellulo-granular lining — internally, and in some specimens the posterior end was observed under pressure to be distended with a transparent fluid containing a few compound cells of similar aspect to those found in other species. This posterior region is kept in position by fibres from the strong bands at the posterior part of the cesophageal apparatus. All that M. Van BENEDEN says with regard to the structure of this organ is BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 341 that it is very short, and bears an ‘‘isolated” stylet, while his enlarged drawing* is incomplete. M. bE QuaTREFAGES considered the posterior chamber of the Ommatoplean proboscis the intestine-proper, but there is no support for this view; and, indeed, his minute anatomy of the organ is somewhat inaccurate. I have not observed that the dilatations and contractions of the channels of the reservoir (his ceso- phagus) vary in the manner he refers to in different species. He describes two bulgings of this “oesophagus,” a large lozenge-shaped one at its commencement, and another corresponding to our reservoir, these dilatations being connected by a straight channel. The former may refer to the mobile muscular chamber behind the stylet-aperture in the floor of the anterior region, but his descriptions and drawings are indistinct. He aptly likens the two central divisions (stylet- region) to crystal; but he says he required the action of hydrochloric and acetic acids to distinguish fibres, which, he observes, have a transverse direction, and he especially notes that he could not see any longitudinal fibres. I have always . been able to see these fibres in the fresh and living animals without any addition to the sea-water in which they happened to float; and, moreover, the presence of longitudinal, looped, and other fibres previously described show how much more complex the structure is than this author imagined. He correctly reports the absence of vibratile cilia from this region; but he again errs by affirming that they occur in the posterior chamber. His figures of the stylets are different from any seen by me, since they exhibit a bulging and then a contraction in front of the head. The basal sac is termed the “body” of the central stylet, and he narrates how in Nemertes balmea (our O. gracilis) this body has an exterior coat com- posed of the same structure as the point. Nothing more than the usual firm muscular setting is really present (see p. 335). Again, the statement that the “body” acquires greater solidity is not borne out in fact, for the granular con- tents of the sac are homogeneous throughout. He speaks of a pouch containing a granular glandular substance in which the stylet and its “ body” are placed in this species, and thinks it probably secretes the latter (body); and, though he has not seen it in Polia, he considers its existence likely. The author has evidently fallen into confusion here, for the granular sac (or so-called “ body’’) is fixed in a clear setting of the firm muscular substance. He next describes and figures other two cavities, which are said to exist at the borders of the “ stylet- pouch,” semi-opaque and glandular in J. balmea, very transparent in Polia; and he considers that these two glandular organs secrete a poisonous fluid for use in offence and defence, which fluid is poured into the pit in front of the stylet-region. Entomostraca, moreover, were killed instantaneously by wounds of the stylet, an effect which could not be due to mechanical injury only, but to the presence of an * Mémoires I’Acad. Roy. &c. pl. iii. fig 6- VOL. XXV. PART II. 4s 342 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE active poison. It is true he was not able to distinguish these glands or their cavities in many species, so that if they existed they must have been confounded with the neighbouring tissues by reason of their transparency. Such glands have never occurred in any of the British species, and the opaque granular substance really present in O. gracilis (NV. balmea, QuatTREF.) totally differs in structure and function from his representations. The folding downwards of the floor of the anterior chamber and the presence of the muscular space behind this have pro- bably caused the error—an opinion shared by Prof. Krererstern; and, indeed, it may be remarked, that the time and opportunities necessary for a correct appre- ciation of these complex structures make those best acquainted with them least surprised at such mistakes. The two muscular bands, also, which M. Dz QUATREFAGES figures and describes as for the probable purpose of carrying forward the stylet-apparatus, and compressing his hypothetical poison-glands, have not been seen, and the explanation of the parts already given renders such useless. With regard to the observation, that the lateral stylet-sacs are free in NV. balmea, but placed in the thick walls of the oesophagus in Polza, I can only state that the type of structure is the same in all, and that they occupy corresponding positions in the species referred to. It is probable also that the finding of only a single lateral stylet-sac in Polia quadrioculata and P. humilis was accidental, and not by any means a characteristic of such species (Zetrastemma). I have also very little doubt that the presence of the toothed cartilaginous plate, which he describes as occupy- ing the usual place of the central stylet in Cerebratulus spectabilis, has been due to some mistake or confusion in his notes. Indeed, the author himself does not speak with certainty on the subject, since he states that he regrets he had mislaid his drawing of the actual relations of this organ to the other parts. The remark, — that in Polia vermiculus one sac was placed on the dorsal and the other on the ventral surface, is of no consequence when the ever-changing condition of this very mobile organ is remembered. This author further describes the “ intestin” (our posterior chamber) as having the same coats entering into its composition as the anterior region, though, he adds, the muscular layers are proportionally thinner. As already stated, the structure of the walls of the two regions is essentially different, just as their functions disagree. He is correct in averring that the cavity ends in a cul-de-sac; but wrong in saying it is ciliated, and that the terminal ribands are attached “a la paroi abdominale.’ His distinguished countryman, M. Mitne Epwarps,* is also in error in regard to both of these points. Lastly, M. pE QuATREFAGES is only certain of the muscularity of these ribands in Polia coronata (O. melanocephala), and he gives a curious figure (which — cannot be verified in the British examples) of their termination in this species— — as a series of arborescent fibres. * Legons sur la Physiol. et Anat. Comp. tome v. p. 464, 1859. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 348 Dr Jounston’s* description of the stylet-region is as follows :—“ First, we perceive on each side a small circular spot or cavity, in each of which are three © spines with their sharp points directed outwards; beneath these there is a cup- shaped organ encircled above with a faintly plaited membrane, and armed in the centre with a strong spine, which can be compared to nothing more aptly than a cobbler’s awl in miniature, the part representing the handle being very dark, and the point transparent and crystalline. This apparatus is placed within the intes- tine, is visible only when this is compressed, and is, as I believe, stomachial, having some distant analogy with the proper digestive organs of Laplysia and Bulla.” His anatomy is thus imperfect, and he, moreover, considered that the “intestine,” as he termed the organ, proceeded to the tip of the body and termi- nated in a distinct anus. Dr Witttams} observes with regard to the proboscis (his alimentary organ), “‘ The extremity of this organ is armed with several styleted jaws, which, from their construction, seem only designed to fix the suctorial end by perforating the alimentary object. When the proboscis is withdrawn into the interior of the body, fitting admirably into a short cesophagus, these sharp instruments are packed and folded upon themselves,” the sides of the tubes closing round them. The correct examination of a single extruded organ would have at. once dispelled such notions. His supposition—that the glands in the interior of this structure furnished an important secretion for the digestive process, which secretion was exuded into the ‘‘ cesophagus” (apparently, judging from his figure,t the pro- boscidian sheath), and thence into the great alimentary organ—rests upon no facts. He is also wrong in stating that the outlet of this organ is situated not far from the cephalic end of the body; but his remark, that there is no open communication between the cesophageal tube (proboscidian sheath) and the ‘alimentary czecum”’ is correct. | Dr Max S. Scuurrze, in his account of Tetrastemma obscurum,§ gives no definite description of the ending of the proboscis, and figures the central stylet as projecting freely into the cavity. He indicates the presence of the muscular space behind this, but confounds its structure with the wedge-shaped setting of the basal sac, the whole forming, he says, a quadrangular mass. He falls into the same error as M. DE QuaTREFAGES and others, in describing the terminal ribands of the organ as attached to the wall of the body. His figure|| of the exserted stylet-region is incomplete in detail, for he omitted to notice the ducts of the lateral stylet-sacs, though he regarded the latter as the producers of the * Mag. of Zool. and Bot, vol. i. p. 530, 1887, copied into “ Catalogue” Brit. Mus. pp. 285-6 1865. t Report Brit. Assoc. 1851. t Op. cit. pl. xi. fig. 64. § Beitrige zur Naturges der Turb. 1851, p. 62, tab. vi. figs. 2-10. | Op. cit. tab, vi. fig. 3, 344 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE stylets for the central organ. He first indicated, however, the connection between ' the developing spikes and the clear globules in the lateral sacs, showing that they are sometimes seen in their interior. Finally, he has not discriminated the structure of the reservoir-region, and its relation to the neighbouring parts; and, indeed, his anatomy of the animal, from the limited nature of his observations, is somewhat imperfect. M. CLAPAREDE,* in his remarks on Tetrastemma varicolor, describes the sac of the central stylet as set in a pale space of a triangular form, and he leaves the stylet-apparatus to hang therein, apparently by its anterior end. He has evi- dently mistaken the translucent wedge-shaped setting of the sac for a cavity, and the triangular muscular structure shown exterior to this has no existence as figured (vide p. 339). He has correctly observed the presence of a duct to the lateral sac, though his figure is somewhat distorted from pressure, and repre- sents the duct by far too wide. He is, moreover, of the opinion that these chambers are not for the sake of furnishing new stylets for the central organ, as Dr ScHULTZE avers, but for the lodgment of those discarded from the latter; a view quite as erroneous as the other. Each supplies its own stylets. He did not observe any connection between the clear globule in the lateral sacs and the developing spikes. His representation of the muscular fibres of the stylet-region is faulty. In mentioning the cavity of our reservoir, he properly describes the presence of a liquid containing minute granules in suspension (but not in motion), and that it (reservoir) communicates with the “‘ trompe” by means of an efferent canal: but he fell into the error of regarding the long posterior chamber as a ““muscle retracteur.”” His figure is inaccurate in other respects, such as in the mode of opening of the ejaculatory duct, and in the absence of the muscular space behind the stylet-aperture in the floor of the anterior chamber. He regards the reservoir as a poison-gland, which squirts its contents along the ejaculatory duct into the wounds inflicted by the stylet. This author is scarcely correct in saying — that M. pre QuaTreraceEs had in reality figured this poison-gland without the efferent canal in Polia mandilla; for the French naturalist figures and describes — the part as one of the bulgings of his cesophagus, and which, therefore, commu- nicated both with the ‘“trompe” and “intestin.”” In a still more recent publi- cation} M. CLaparEDE exhibits the structure of this region in KEFERSTEIN’S Prosorhochmus Clapareédit, a viviparous species, but he gives no details of muscular structure. The central stylet and its sac are placed in the middle of a continuous and apparently homogeneous oblong body, the wedge-shaped enclosure of the basal sac and the muscular cavity in front being confounded. The opening of the ejaculatory duct of his poison-gland (reservoir) has the same position as im his previous figure, viz., at some distance from the stylet, and passing directly * Recherches Anat. sur les Annélides, Turb. &c. 1861, p. 81, pl. v. fig. 6. + Beobach. iiber Anat. und Entwicklung. wirb. Thiere, &c. 1863, p. 23, tab. iv. fig. 10-12. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 345 into the floor of the anterior chamber. He now refers to the posterior chamber, which, he says, occupies the centre of the muscle of the organ, a modified but scarcely satisfactory description. The external granular glands show certain peculiarities when contrasted with other species, viz., complete separation, large number and minute size of the divisions or lobules—modifications that I have not been able to verify. M. Van BENEDEN’s brief remark on the proboscis in Polia involuta has already been adverted to. It may also be stated, however, that, in addition to the in- completeness of his figure, he represents certain lines,* which indicate a sheath (one of his culs-de-sac) around the proboscis—a state that has not been seen in our examples. The structure of the stylet-region, as observed by him in Polia obscura (Tetrastemma varicolor ?), is erroneous. He represents no ducts to the lateral stylet-sacs; no ejaculatory duct. The division of the reservoir has a cavity in the centre, but is likewise furnished with two hypothetical oval vesicles or cavi- ties, and the muscular structure, the floor or ending of the anterior chamber, and other important points, are absent. The statement, that the lateral stylet-sacs contained stylets of a smaller size than the central, and of a different form at the base, shows the learned author did not possess good opportunities for examining these creatures. He follows Dr Scuutrze in calling the lateral sacs _ pouches of replacement, and therefore is not aware of the true physiology of the parts. While he states that the proboscis is enclosed in a separate sheath, he distinctly adds, that its muscular retractor is attached to the skin of the animal posteriorly; and that there may be no misunderstanding on the question, he again repeats the statement when drawing up his conclusions, by erroneously averring that the internal surface of the proboscis is ciliated, and that it is fixed to the bottom of the digestive tube by a retractor muscle, as in the stomach of the Bryozoa.t Prof. Kersrstst’s{ remarks, so far as they go, upon this region in Polia man- dilla, are decidedly in advance of his predecessors. He, however, does not men- tion the minute glands on the floor of the anterior chamber, and shows the central aperture for the stylet in the same by far too large, so that in extrusion the muscular space (€ in our figures) becomes obliterated. The muscular setting of the granular sac is also continued too far forwards in his figure. He indicates no oblique fibres from the pit of the anterior region (as shown in Plate IX. fig. 3), and the thick coat of the reservoir is described as composed of longitudinal fibres. The external granular glands are not distinctly described ; and the dis- proportion between the central and lateral stylets is so great, that I fear some * Mém. de l’Acad. Roy. des Sc. de Belgique, tom, xxxii. pl. iii. fig. 7. T Op. cit. p. 44. Unfortunately this author has not lettered his plates, so that I have often been at a loss as to his interpretation of structures of which no mention is made in the text. { Zeitsch. fiir wiss. Zool. Bd. xii. p. 72, taf. v. fig. 4. ‘ VOL. XXV. PART II. 4T 346 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE slip has occurred in their delineation. Lastly, his crenated border (external elastic coat) does not pass the constriction between the stylet-region and the reservoir-region, whereas, as already shown, both this and the longitudinal coat are continued some distance on the latter division. Reproduction of Proboscis.—So far as 1 am aware, no author has alluded to the reproduction of this organ. The process was first observed in Ommatoplea melanocephala, but it has since been seen in O. gracilis, Tetrastemma alge, and others. In a specimen of the former (O. melanocephala), from which three days before the proboscis had been removed, there existed a pale conical papilla, which projected a short distance behind the ganglionic commissures. Two days after considerable progress had been made, and the organ proceeded backwards — as a slender rod tapered posteriorly (Plate VIII. fig. 1, @). There was a distinct exterior coat from one end to the other, and an inner terminating at the com- mencement of the posterior narrow portion. The former had a crenated edge in contraction. The organ gradually increases in size and complexity, but continues quite free posteriorly for a considerable time, until, indeed, the stylets are well developed. At a further stage of growth (Plate VIII. fig. 2), the walls are defined almost as in the complete structure, but of course are much more delicate and _ plastic; and the extreme contractility and elasticity of the entire organ are most interesting, and raise a doubt as to the identity of its muscular fibres with those of the higher invertebrates, since it so much surpasses them in mobility. The floor of the anterior chamber ends in the usual pit, which is swollen on account of the shortening of the organ. The walls of the muscular cavity behind the floor of the anterior region are not well defined, though the space itself is large, and con- tains a granular fluid. There is no central stylet, and the basal sac is repre- sented by a somewhat triangular group of the usual granules, round which the — radiating fibres are placed. The wedge-shaped setting within the latter (fibres) — is mobile and translucent. A somewhat indistinct streak (/) in the central line indicates the canal for the central stylet, and now and then this became bulged by projected fluid. The lateral stylet-sacs, from the bulging of the chamber in this instance, seem pressed backwards, but in reality they have their distinc- — tive position. Each contained a stylet or two, a few granules, and a clear globule. The reservoir at this stage had assumed its characteristic shape, though its — glands were barely visible. The shortening and bulging of the anterior and pos- terior chambers have annihilated the usual prominent appearance of this part, and the last has encroached very much on the cavity posteriorly. The glands were formed in the posterior chamber, though their contents were not elaborated, and the cavity terminated in the usual czl-de-sac. A few rounded papille at the posterior end indicated the early condition of the muscular retractor or riband. It is clear that at some time or other the latter becomes attached to the wall o : BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 347 the proboscidian sheath, and that, too, in a definite manner, since no great devia- tion in a series of specimens is met with. In the developing organ of O. gracilis, a very good analysis of the somewhat complicated structure is obtained, so that doubtful anatomical points are cleared up satisfactorily. The sac at the base of the central stylet is sometimes seen to be composed of granules in rounded masses; and they are all grouped posteriorly at an early stage, and thus present a similar form to that seen in other species which have no such elongated sac in the complete state. It is curious to witness the accuracy with which the stylets are reproduced in this and other species. There is never any confusion, but each invariably produces them of their respec- tive sizes and curves as infallibly as if they had been struck out of the same mould. Yet these bodies are not in any way organically connected with the tissues of the proboscis, but only spring from a secretion poured into the lateral sacs, or from the central apparatus. In the concentric arrangement of their con- stituent substance, and some other particulars, these spicula are analogous to those of the sponges, whose microscopic anatomy has been so excellently investi- gated by Dr BowrrsBanx.* Indeed, the morphology of the stylets of the Omma- topleans offers elements for deeper reflection than even the hooks and bristles of the higher annelids, which are often so diagnostic of genus and species. Besides the developing organ, the proboscidian chamber contains (unless in cases where the organ has been violently expelled) the cast-off proboscis; and it is a curious sight to observe a fully-developed organ floating freely in the chamber, and still endowed with contractile power, while the new proboscis has advanced to the stage of the advent of stylets. The discarded organ soon becomes opaque, appearing reddish by transmitted light, and the stylets leave their positions. As there is no mode of exit after the new proboscis has begun to develop, the aborted one can only (not to speak of rupture) be removed by disintegration and absorp- tion; and hence in the proboscidian chambers of such animals there is a vast increase of cells, granules, and granular debris. Digestive System.—Though no such transverse muscular plate, as described by M. DE QUATREFAGES, occurs at the anterior part of the body of the worm, yet there exists a very distinct and comparatively large ciliated cesophageal chamber or sac, as first described by Sig. DeLLe Cu1Asz, apparently in a Borlasian.+ The figures of the supposed transverse plate given by the former, indeed, show some degree of doubt, since in the large figure} both wavy and longitudinal fibres are represented, while in the small figure there are only transverse fibres. I fear the wavy longi- tudinal lines owe their presence to those actually existing in the oesophageal sac. Dr Jounston’s figure§ of O. melanocephala indicates this structure, to which he thus * Monograph of the British Spongiade, Ray Society, vol. i. p. 5, et seg. + Mémiorie sulla, &c. vol. ii. 1835. t Op. cit. pl. xix. fig. 1, m. Op. cit. pl. u. a fig. 5.* 348 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE refers under the head of O. pulchra :—‘‘ Immediately under the hearts” (ganglia) — we observe a large, somewhat muscular, viscus, apparently hollow, and lying in the course of the intestine, but seemingly unconnected with it. Of its office — and nature I can form no opinion; but I may remark, that in all the species a greater duskiness in its site shows that a similar organ exists in all.” Prof. KErEr- STEIN’s notice* of the organ in Wrstedia pallida is very brief; and he has abstained from figuring its relations, though affirming that its opening (constitut- ing the mouth) is on the ventral surface behind the ganglia, as in the Borlasians. M. Van BENEDEN,} while indicating an outline of the structure in Polia capitata, makes no reference thereto in his descriptions. The same omission is made by M. CLAPAREDE with regard to his figure of Prosorhochmus Claparédii, Ker. { In every specimen of Ommatoplea and Tetrastemma the great cesophageal organ above-mentioned has been easily observed (Plate VIII. fig. 3, 7) as an elon- gated sac, slightly narrowed posteriorly, and usually thrown into various longi- tudinal wrinkles. In ordinary views from above, it is seen to narrow somewhat abruptly behind the ganglionic commissure, and to pass forwards beneath the inferior one, to open at the tip of the snout just at its ventral border, as a short — longitudinal slit. I have seen the sac turned inside out here, and projecting — beyond the head in an animal which had been subjected to chloroform. Both apertures may frequently be observed at once,—that for the proboscis being cir- cular, while the mouth forms a short longitudinal slit beneath the former. The observations on this point have been often repeated, out of deference to the dis- tinguished foreign authors who hold different views, but I have never seen any other aperture in the British Ommatopleans, and it were hard for such to exist in the free portion of the cesophageal tube behind the ganglia. Moreover, as shown in Plate IV. fig. 1, the narrow anterior part of the glandular cesophagus lies close to the chamber for the proboscis, when the latter is in this region. The two organs, proboscis and cesophagus, become more evidently separated from each other in most sections, just in front of the ganglia, and the interposition of the broad inferior commissure soon renders the distinction more evident; there-— after they have the tunnel of the proboscis as a partywall, together with that portion of the fibrous stroma of the extra-proboscidian region in which the median blood-vessel is situated. The cesophagus, moreover, occupies a special chamber, bounded by a series of well-marked fibres (Plate V. fig. 2, £), which pass down- wards from the upper wall by the side of the proboscidian sheath, and unite in the median line below it. The anterior narrow portion is generally translucent; and just behind the commissure a pursed arrangement is often seen, which is” followed by the more opaque portion with its longitudinal rugee. The pursed arrangement is very similar to that which is caused by tying the mouth of a * Op. cut. p. 10: + Mém. l’Acad. Belgique, pl. iv. fig. 13. t Beobachtungen iiber, &c. pl. v. fig. 10. ph. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 349 leathern bottle, and is due to the narrowing of the sac in front. The pale portion immediately behind the ganglia shows cilia in active motion very distinctly, but I have never seen anything like an aperture; indeed, the great and peculiar stretching of this pale portion, as it is dragged backwards from the region in front of the ganglia during the motions of the animal under pressure, at once demon- strates the fallacy of supposing it connected with any post-ganglionic aperture, as in Borlasia. The wall of the sac evidently contains some contractile fibres, which cause it to dimple inwards here and there during its motions; and in anterior transverse sections the cut ends of longitudinal muscular fibres are shown very distinctly, though they are finer than those of the proboscis. Poste- riorly, the organ opens into the digestive cavity; but the communication is not actually seen in ordinary views, from the folding together of the walls, and I have not been so fortunate as to observe the animals feeding. In Polia involuta, Van BENEDEN, the cesophagus is short and nearly globular under moderate pres- sure, being also conspicuously tied posteriorly by strong transverse bands. In this species the posterior aperture is very apparent. The relations of the oesophagus to surrounding organs may be observed in the sections (Plate IV. fig. 5, and Plate V. fig. 2, at 7). The walls increase in thick- ness after passing the narrowed portion in front, form considerable parietes, and again slightly diminish posteriorly. In transverse sections of specimens hardened in spirit, and mounted in the usual manner, the structure has a streaked and fibrillated aspect, or marked by a series of vertical striz, and minutely granular, an appearance due to the position of the glandular follicles with respect to the inner surface, and the change caused by the preparation. It will also be observed that in these sections the organ is thrown into numerous characteristic longitudinal folds. In life considerable differences in appearance are observed, according to the degree of pressure—as, for instance, between the flattened fol- licles of the organ in a small Yetrastemma, and the thicker structure in a good- sized 0. alba (Plate VIL. fig. 7). In the latter, the inner edge (@) of the glandular tube has a somewhat translucent and well-defined border, garnished with mode- rately long and most vigorous cilia, whose activity is in strong contrast with the motion of the same organs on the epidermis, and which seem to play an im- portant part in the economy of the tube. Under the microscope the fresh speci- men is always thrown into numerous wrinkles, and is crossed by pale streaks— the ciliated edges of the folds (2). The entire organ is studded internally with a series of granular glands or follicles, and numerous brownish pigment-granules. The glands taper towards the free ciliated edge of the ruge. In 0. melanocephala the organ is curiously narrowed posteriorly; and in O. pulchra the granular glands are distinct and large. In 7. varicolor the glandular appearance in a small specimen under pressure is somewhat finer and more translucent, but the structure is essentially the same as in Ommatoplea. VOL. XXV. PART II. 4uU 350 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE This ciliated glandular structure is physiologically and homologically an organ of great interest. It is entirely Ommatoplean in the condition just described, since what is shown here in the complete form is only indicated in Borlasia by the turning inwards of the margins at the junction of the two regions of the ali- mentary canal. The granular glands and cells which coat the latter in Omma- toplea arise (in the case of the cells, at least) on the sides considerably in front of — the posterior end of the cesophageal region—in some cases, indeed, almost touch- ing the ganglia (Plate VIII. fig. 3), and besides, the first region has been demon- strated to occupy a special pouch in which it rolls. The rich ciliation of this cesophageal region, and the somewhat indistinct ciliary movements seen in the posterior division of the alimentary chamber, are points of importance when con- trasted with the arrangement in Bor/lasia, and show that from structure to struc- ture the essential differences between the groups meet the inquirer at every step. — In Vortex, again, the homologue of this region is seen in the “ Schlund”’ of the German authors. The Digestive Cavity-Proper —The detailed description of the general cavity of the worm (all within the muscles) given by M. DE QuaTREFAGES, shows that he had no clear conception of this structure, for, after explaining the hypothetical transverse diaphragm, to which we have already alluded, he goes on to say,*— ‘** Le reste de la cavité générale occupe tout le corps proprement dit; mais les cloisons verticales auxquelles sont suspendus les organes générateurs le parta- gent entrois chambres distinctes, lune médiane, qui renferme le tube digestif dans une portion de son éntendue; les deux autres latérales, dans lequelles flottent les ovaires ou les testicles, et qui 4 l’époque de la reproduction se rem- plissent d’ceufs ou de zoospermes.”’ In his figures} the scalloped shaded portion, which he terms “ ovaires ou testicles,” is, as Prof. KEFERSTEIN has pointed out, the glandular wall of the digestive cavity. Iam ata loss to understand how M. DE _ QuATREFAGES did not correct his error on contrasting his figures of the male and — female elements in his Nemertes balmea (O. gracilis), for the very same organ is made in the one case ovary, and its gland-cells developing ova, and in the other respectively testicle and sperm-cells. Dr Jounston{ recognised the structure as i ‘“a close series of vesicles or cells, formed, in the true Nemertes, apparently by the folds of a membrane.”” The czeca, he adds, are always full of some opaque matter, which varies “in intensity at least according to the nature of the animal’s food.” He thought the structure was connected with the digestive sys- tem, though not in communication with the proboscis (his alimentary organ). Dr Wittrams§ had also an inexact idea of this cavity, for he speaks of it as a great spongy mass, or ‘“‘great alimentary caecum,” which commences anteriorl} * Op! Cit sp. Lode + Op. cit. eg. pl. xviii. fig. 1, and pl. xix. fig. 1. + Mag. Zool. and Bot. vol. i. p. 532. § Report Brit. Assoc. 1851, pp. 244-6, BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 35m immediately behind the hearts (ganglia), under the character of a czecal end, and as ‘‘a perfectly closed sac, containing a milky fluid.” The walls of this cavity, he says, act upon the exuded food, after its passage through the walls of the “oesophagus.” He is correct in denying the ovarian character of the organ, and in showing that the so-called ova consisted only of oil-globules. He has also some reason for considering the transverse segmentation of the organ as an indi- cation of annuli.* Dr Max Scuutrze}+ described it as a straight canal in Tetra- stemma obscurum, ciliated on its inner surface, and opening anteriorly and pos- teriorly, and figures { the cells in its walls as altered by extrusion into the water. M. CraparkgpE, in the before-mentioned figure of Prosorhochmus, shades the region, but makes no mention of it in his description. The digestive cavity is a somewhat moniliform or lamellated canal, in so far as its surface is increased by the numerous diverticula. Its appearance under pressure is well seen in Tetvustemma (Plate VIII. fig. 3) as a lobulated glandular organ, usually of a pale flesh or slightly pinkish hue, extending from a short dis- tance behind the ganglia to the tip of the tail, and forming (in the individual in which the reproductive elements are not developed) a lining to the body-wall, except where interrupted by the proboscidian sheath. In the ripe animal, how- ever, the gradual enlargement of the ova or sperm-sacs pushes in the yielding - organ, so that it occupies a more median position, and has its ventral portion in- creased in bulk. It is also well to bear in mind that the body of the adult worm is only rounded in contraction, and partly so when the ova or spermatozoa are _ minature, but at other times it is flattened, and very mobile; thus, what is space in the transverse section is often filled up in the living animal by the collapsing | and contraction of the yielding tissues in the neighbourhood. Anteriorly the | only opening leading into this chamber is that of the posterior end of the rugose | cesophagus; posteriorly it terminates in an anal pore, less easily seen than the | similar structure in Borlasia, from the absence of the strongly ciliated internal | line. In intimate structure the walls of this cavity resemble the anterior or | esophageal portion, only the gland-cells are larger and more numerous, and | the fatty elements in greater abundance, so that although the type of struc- ture remains, there are considerable differences in microscopic appearances. 1 was for a long time in doubt about the ciliation of this chamber in Ommatoplea, since I have seldom been able to see cilia satisfactorily in the uninjured 0. alba, though in the latter, O. purpurea, Tetrastemma, and especially | in Polia involuta, VAN BENEDEN, peculiar motions of the cells were apparent. When a specimen is kept for some time under pressure, a few moving granules are observed at some particular point; these continue to increase in number, and sometimes a few cells accompany them, the group gradually enlarging and * Philos, Transact. 1858. + Op. cit. p. 64. t Op. cit. taf. 1. fig. 35. 352 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE revolving with great velocity. Such motions are doubtless due to the ciliation of — the chamber. On making a transverse section of the living animal (O. alba), I have seen the inner margin of the digestive cavity cause motion in the surround- ing particles, but the cilia were indistinct, and the appearances very different from the richly ciliated tube of Borlasia, or its own cesophageal portion anteriorly. It is thus much more feebly ciliated than the others. In the walls of this complex cavity are a vast series of gland-cells, which, with M. Van BEnepeEn, I consider as having some analogy with the liver of the higher forms, notwithstanding the adverse opinion of Prof. KerzrstTe1n, who, how- ever, probably refers more particularly to the Porlasians. Microscopically the cells consist of a delicate membrane containing a number of fatty globules (Plate X. fig. 6), the average size of the cell being ,4,th of an inch. Under pressure, and when highly magnified (700 diam.), it is seen to consist of a number of granular fatty bodies (Plate X. fig. 7). After extrusion from a living specimen into salt water, a remarkable motion occasionally ensues in the contents of the cell before breaking up, a condition which causes the observer to fancy the entire organ ciliated. The contained bodies jerk about within the cell, and soon a number of very minute granules appear, having burst from the larger bodies, in which their presence is indicated by obscure markings. The peculiar motions would seem to be due to the action of the water, and ultimately the minute contained | bodies are all set free. The various appearances of the bodies from the cells are shown in Plate X. fig. 8, some being granular, others presenting faint con- centric lines like starch-globules (though probably fatty), while three oil-globules are indicated on the right. The deep port-wine oil-globule is somewhat sparingly scattered throughout the wall of the tract, the yellowish red being abundant, and the pale globule still more plentiful. These cells have a similar structure in Tetrastemma, and often escape under pressure posteriorly. The quantity of deep yellow oil in this organ in 7. alge is unusually great. The foregoing glandular structure undergoes partial absorption at the period of reproductive activity, so- that after spawning the animal is much flattened; but by-and-by it regains its plumpness, and often becomes of a greyish hue, apparently from the increased development of this tissue, which is exuded as a pale, salmon-coloured, semi-fluid — substance on rupture of the body-wall. In O. gracilis the posterior division of the digestive system has a somewhat regularly ramified arrangement, when — viewed from the ventral surface, and this is especially evident some time after spawning, when the animal has regained its condition. The colour of the region is of a deep green by transmitted light, whereas the cesophageal division is brownish. The lamelle of this region in O. pulchra form simple tapering papille under pressure. In Polia involuta, V. BEN., the cavity is greatly developed, both as regards the rest of the body and its individual structures; and it also presents a firmer and more consistent aspect than usual on transverse section. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 309 The absence of the proboscidian sheath and its contents leaves the central space almost entirely at its disposal. In O. alba and rosea Mr E. Ray LanxkestTER* found many Gregarinee, but they were rare in the specimens from St Andrews. In TJetrastemma varicolor a few eregariniform parasites (Plate IV. fig. 12) occurred in the digestive cavity towards the tail. Another parasitic structure was found in January in a large male specimen of Ommatoplea alba in the form of an ovum enveloped in a granular lobulated mass—lying close behind the ganglion of one side (Plate XIV. fig. 9, y), to the exterior of the proboscidian sheath, and altogether unconnected with the ceso- phagus. Externally there was a distinct hyaline capsule or cyst, to which certain fragments of the fibro-granular lobulated covering adhered. The embryo was furnished with a very conspicuous opaque granular mass, and two discs; while the general stroma was cellulo-granular, here and there closely streaked by minute lines, apparently from its external investment. No motion of the included animal was observable, except an alteration of the size and aspect of the pores and discs after a period of eight or nine hours. There was no doubt as to this being a Trematode-larva in its capsule, and by rupturing the latter a complete view of the embryo was obtained (Plate XIV. fig. 10). The oral sucker (c) was considerably smaller than the ventral (0), and this formed a marked feature in the general aspect of the animal. The cesophageal bulb (@) appears as a distinct swelling close behind the margin of the oral disc, and from the tube behind the former the alimentary czeca (¢, ¢) branched off and became lost in the cellular tissues posteriorly. The opaque mass of cells and granules (at @) corre- sponded to those observed in the Trematode-larva of the Carcinus menas,+ though, from the immature condition of this example, these and other structures were much less definite. There were also two large circular granular bodies (generative organs) (f and g); but only a trace of the excretory tubes existed in front near the oral sucker. Microscopically, the alimentary organ has scarcely the regular and firm _ glandular appearance of the same structure in Borlasia, but is more friable and cellular. Its analogy with that of the higher annelids is also borne out; for, although the biliary matter is not arranged as a distinct organ exterior to the alimentary, it is incorporated therewith, and probably has a similar function. The fluid, however, which bathes the liver in the higher forms (if we suppose that inside the sheath for the proboscis to be the homologue of the former), is here separated by the muscular walls of its special tube. The large size of the pro- boscis in the Ommatopleans renders this system very obscure from the dorsal aspect, and it is only when the ventral surface is upturned that a correct know- * Jour. Micros, Sc. 1865. + Jour. Micros. Se. vol. v. N.S., pl. viii. fig. 5, &. VOL. XXV. PART II. 4x 354 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE ledge of its relations is obtained. I have not been able to see O. alba feed in captivity, and have not found any food in the alimentary cavities of those examined. It isa curious fact, that in this group the digestive system lies quite beneath the nervous system anteriorly, whereas the proboscis passes through the nervous collar. Circulatory System.—The circulatory system is composed of three great longi- tudinal trunks—one central and two lateral—besides the cephalic arch and anastomotic vessels. Commencing with the great central trunk posteriorly (Plate VI. fig. 8, p) in Ommatoplea, it is found that the vessel, which in this region is about twice the diameter of the lateral, arises from the point of junction of the two last-mentioned, just within the posterior border of the worm. It travels — forward beneath the proboscidian chamber in a very undulated manner—as © usually seen—to the region behind the ganglionic commissures, where it bifurcates (Plate VI. fig. 3, g), a branch passing to either side to join the lateral trunk (7), which bends inwards to meet it. From this point of junction also a single © vascular arch (cephalic) proceeds forwards into the tissues of the snout (/, same — figure, and in Plate IV. fig. 6, the latter showing the vessels in transverse section), the pillars of the arch thus meeting the lateral and the anastomotic vessels of | each side. From the same point of union each lateral trunk passes backwards under the nerve-cord of its side to the tail, where it meets its fellow of the opposite side, and gives origin to the single central vessel with which the circuit com- — menced. The lateral vessels appear to diminish slightly posteriorily. The median vessel does not actually touch the wall of the proboscidian sheath, though ~ transverse sections usually show a close apposition, but is situated in a layer of transparent elastic tissue which intervenes between this organ and the digestive tract. At the ganglionic region the vessels which go to form the cephalic arch pass below the commissures, and unite in front beneath the channel of the snout. In O. purpurea there are three main longitudinal trunks as in O. alba; but it can be observed that the lateral communicate with the central, as in Borlasia., by transverse branches, which, however, are proportionally smaller. Whether such anastomoses occur in the pale Ommatopleans is thus an open question; but they are distinct enough in this species. Two lateral trunks only could be discovered in Polia involuta, VAN BENEDEN (Plate VIII. fig. 5, 7), which : trunks unite by a very short loop just in front of the commissures. This loop (2) is distinguished from the ordinary arrangement by its not extending forwards into the tissues of the snout. The lateral vessels are not so clear or well defined as in O. alba and Tetrastemma, and are observed to have internal transverse bands or partial septa in front; while the contained fiuid has a few clear granules, as in O. purpurea and others. ‘The contractions in the lateral vessels are very vigorous, and even a minute central vessel could not have been passed over if a trace of such had existed. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 300 The course of the circulation, so far as I can see, is as follows:—Posteriorly a gentle contraction from behind forwards drives the contained fluid along the great central vessel to the front, where it is forced through the anastomotic into the lateral vessels and the cephalic arch. The lateral trunk may be seen to swell with the wave, and the fluid then passes to the posterior end to enter the median as before-mentioned. In addition to the stream poured into the lateral trunks, another passes into the cephalic arch by the vessel on each side, and the counter- currents must meet and commingle, returning again during the diastole of the central vessel. I have not made out any branches in the British species except in O. purpurea ; but this is a somewhat difficult task, on account of the trans- parency of the circulating medium and channels. In many species the fluid contained in these vessels is transparent and homo- geneous. M. DE QuaTREFAGES, however, found corpuscles in his Polia bembix, Prof. KEFERSTEIN small oval discs in the reddish blood of his Borlasia splendida,* and I have seen in Ommatoplea purpurea minute granular corpuscules, but both they and the fluid are colourless. Minute colourless globules also occur in the blood of O. pulchra. : Such, in the Ommatopleans, is a brief outline of the circulation, which, although resembling that of M. pr QuaTREFAGES, in so far as each describes three main trunks, differs considerably in detail. The first point to be noticed in the descriptions of this author is the statement that the lateral trunks pass through the cephalic diaphragm—a structure which has not been seen. He is slightly in error also when he states that the median vessel lies immediately under the sub- | cutaneous muscles. The arrangement shown in his two sections of Borlasia | angliee cannot apply to this group. I have not been able to verify the elaborate | curves which this author gives} each anastomotic division of the central vessel anteriorly, and which may be described as first forming a loop behind the gan- glion, with its curve directed outwards, and a second inversely curved round its | anterior border—in its passage outwards to join the lateral, which is scarcely | bent inwards at all, but occupies a space where no vessel occurs in the British ‘forms. The mere shortening of the anastomotic will not retrieve this anatomical }error. The cephalic arch is also placed otherwise than “immediatement au- |dessous des couches sous-cutanées,” as already described (Plate IV. fig. 1). _He mentions the presence of distinct walls to these vessels, which, however, he learned from Borlasia angliw, and in this I concur (Plate IV. figs. 1 and 6). | The walls are highly contractile, and in the latter figure the vessels have been |cut across just before they complete the cephalic arch; they are observed to be | surrounded by a ring of finely granular texture. M. DE QuatTReEFaGEs likewise * This species has since been found in the Channel Islands, It is the Cerebratulus spectabilis | of M. pe QUATREFAGES, t Op. cit. pl. xviii. fig. 1. and pl. xix. fig. 1; also in his recent Hist. Nat. des Annelés, pl. iv. 2 and 3. a | figs. 306 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE states, that though fixed in front the vessels are elsewhere free, and only con- nected here and there to the body-wall by ligamentous bridles; and in one of his plates* figures the ova between the lateral vessels and the wall of the body. All our transverse sections show that such could hardly occur, for the vessels occupy a secure position beneath the nerve-trunks; and while the ovaries or sperm-sacs sometimes press the vessels downwards towards the ventral surface, and increase the distance between them and the nerve-trunks, they never actually intervene between the latter and the body-wall in the perfect worm. Many of the older authors confounded the ganglia with hearts, such as EHRENBERG, HuscHKE, DELLE CuiAse, DucEs, Cirstep, and more recently our countrymen, Drs Witu1ams and Jounston, The latter mentions that the only blood-vessel he has seen is one ‘“‘ winding down the middle, along the surface of the alimentary canal,” but he can neither trace its origin nor termination. Dr Max ScHuLTzE} seems to have mistaken the edge of the proboscidian sheath under pressure for the blood-system, which he figures as two long straight trunks on each side of the digestive tract. The true blood-vessels he describes as the water-vascular system, but shows neither beginning nor ending, though numerous large branches are represented as issuing from them throughout their course. Prof. KererstEtn} does not distinguish with sufficient clearness the different blood- systems of the Ommatopleans and the Borlasians; and, indeed, applies the definition of the former to the latter; but so far as they go his descriptions and representations of the arrangement in this group are good. He, moreover, shows an elaborate series of minute transverse anastomosing vessels in his Borlasia splendida, whose structure therefore differs from that usually exhibited by the British Ommatopleans. M. CLAPparEDE,§ though his publication is more recent, is less correct than the latter author, for he figures the dorsal vessel as passing above the ganglionic commissure before giving off the anastomotic to join the lateral, — and thus a somewhat stiff square is formed in the cephalic region, while the lateral vessels have to pass to the outside and front of the ganglia before meeting the © anastomotic. The vessel appears also to be placed on the dorsum of the proboscis. Nervous System.—In the living animal two carmine, pinkish, or reddish color- ations are observed on the snout some distance behind the tip: these mark the position of the cephalic ganglia or nervous centres. As previously mentioned not a few authors, misled by their colour, pronounced them to be hearts. The aspect of the ganglia under pressure is indicated in Plate VI. figs. 1 and 3,2; and in large specimens they are pear-shaped under a lens. Hach ganglion consists of two divisions—a superior, shaped somewhat like an almond, and an inferior, continuous with the great nerve-trunks. The first-mentioned portion is chiefly * Op. cit. pl. xxi. fig. 3. Polia sanguirubra. t Op. cit. p. 64, pl. vi. fig. 2. t Zeitsch. fiir wiss. Zool. pp. 85-87, taf. v. & vi. | § Beobach. iiber, &c., taf. v. fig. 10. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 307 cellular, being composed of minutely granular nerve-cells, and is connected with its fellow of the opposite side by the long or superior commissure (Plate V. fig. 1, /), which passes over the proboscis. In ordinary circumstances, this commissure is less than half as broad as the inferior, but it is considerably longer. It is a simple ribbon of transverse fibres. As observed in the living animal, these fibres pass on to the superior lobe, where they diverge, some turning slightly forwards, but the majority passing obliquely backwards to the pale central part of the lobe. The only remark made by M. DE QuaTREFAGES with regard to the physiology of this band is, that it removes the somewhat surprising state of matters of having a brain composed of two lateral masses, and only one (‘‘ sub-cesophageal’’) com- missure. ‘To me, however, this band seems of more importance, since, during the enormous distention which takes place in the extrusion of the proboscis, it is the superior commissure which is stretched to an extreme degree of tenuity. The proboscis, as mentioned, passes through a complete ring of nervous texture, and, during extrusion, forces this outwards in all directions, but chiefly superiorly, the inferior commissure, indeed, being little altered. Nearly half the circum- ference of the proboscis projects above the level of the ganglion (Plate IV. fig. 5), and the superior commissure must be correspondingly elongated ; hence, if this is purely a nervous band, we have a very interesting example of the elasticity of such texture. It may possess elastic as well as nervous fibres, but such are not distinguishable. The inferior commissure consists of a thick mass of nerve-fibres, the majority of which sweep backwards to form the lateral nerve-trunks; thus it becomes an isthmus between these cords. A few of the anterior fibres are connected with the central region of the former division of the ganglion. In long species, such as O. gracilis and O. purpurea, the ganglia are not cor- respondingly lengthened, but are rather rounded. In Yetrastemma the arrange- ment of these organs is very similar to that in O. alba, so that a special descrip- tion need not at present be given, further than by referring to Plate VIII. fig. 7, which represents the ganglia in a small specimen of 7’. varicolor, where the inferior commissure is shorter and broader, and the lobes more elongated. This is also the case in Prosorhochinus. In the aberrant form, Polia involuta, VAN BENED., the ganglia are strictly Ommatoplean in shape, and the lateral nerves, which are not shown by the discoverer of the species, comparatively large. M. BENEDEN’s figure of the anterior branches of the ganglia is erroneous. The lateral nerves _ lie quite within the longitudinal muscular coat. Carefully made transverse sections show how incomplete is the impression conveyed by the examination of the parts in a compressed, though living animal. Instead of forming a fiattened organ, whose greatest transverse diameter is across the plane of the body, each ganglion has its longest (transverse) diameter nearly perpendicular to the latter (Plate IV. fig 5, and Plate V. fig. 1). The nerve-cells do not appear to be confined to the superior portion, but occur in the inferior also VOL. XXV. PART II. ay 358 DR W. CARMICHAEL M*INTOSH ON THE STRUCTURE OF THE (Plate VI. fig. 1), where they are seen on each side of the origin of the great nerve- trunks. In the fresh specimen the sheath of the ganglion is moderately resistant; for under pressure the nerve-cells from the softer interior do not pass through this, | but escape by travelling along a portion of the great lateral trunk, and rushing out at its torn end, or pass along other branches, such as the superior and inferior com- — missures, and the anterior nerves, or through accidental punctures. The nerve- cells are of a yellowish tinge, and minutely granular (Plate VIL. fig, 11), and rapidly alter their appearance after escape into the water. Many contain a larger reddish granule or granules, to which the colour of the organ is partly due; but I cannot say I saw all the numerous larger pigment-granules so located, although they might have been. In the fresh as well as in the prepared condition (Plate IV. fig. 5), the entire ganglion is dotted with minute pigment-specks and granules, which are also continued along the great nerve-trunk for a considerable distance. The superior commissure is faintly tinged with colouring matter, but the inferior more so; both are paler than the masses of the ganglia. The colour of the ganglion is not destroyed by sulphuric ether, but is rendered paler by acetic acid. M. DE QUATREFAGES mentions that in a large Borlasia (angliw ?) he found the cephalic ganglia surrounded by a sheath forming a sort of dura mater, but he could see none in the smaller species. In the Ommatopleans, the muscular and other structures of the head form a somewhat condensed capsule round the ganglia, independently of the delicate sheath-proper of the nervous matter. The longi- tudinal fibres of the former, indeed, form powerful bands between the ganglia and the inner muscular layer of the body-wall. M. DE QUATREFAGES mentions the occurrence of ventricles in the interior of these organs (ganglia), and figures them in Polia berea; such have never appeared in any British form, though, under pressure, collections of oil closely resemble the drawing given by this author. Ihave also never been able to see so many branches proceeding from the ganglia (as he shows)* to the eyes, cephalic fosse, “mouth,” and other tissues from the anterior borders,.in addition to the great trunks and other twigs posteriorly. The arrangement in the British Ommatopleans is represented in Plate VI. fig. 1, and consists of the following, viz., three very distinct branches on each side of the superior lobe anteriorly; two about equal in size; and a third much smaller, to the outer side. Traces of a fourth branch are also present. The outline of the ganglion throughout the rest of its extent is quite smooth. Various branches from these trunks proceed in the direction of the eyes; but the nature of the cephalic tissues renders it very difficult to trace such an object as a pale nerve-branch with certainty. Dr M. Scuutrzr} gives a tolerably correct view of the ganglia and nerve-trunks in Tetrastemma obscurum; no branches, however, occur on the trunks in his figure. This author, in a later publication,{ founded * Op. cit. e.g. pl. xv. fig. 14; pl. xvin. fig. 1; pl. xix. fig. 1; and the whole of pl. xxiv. + Beitrige zur Naturges, Turb., 1851. + Zeitsch. fiir wiss. Zool, iv. 1852. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 359 one of the chief distinctions of his Enopla and Anopla (Tremacephalide and Rhochmocephalidze) on the structure of the ganglia. Prof. KererstErn figures only two branches, proceeding from the anterior part of each superior lobe to the eyes in his Borlasia splendida, but he represents a kind of mesh-work, formed by three or four trunks between the side of the lobe and the cephalic sac, and a pair of nerves from the inferior commissure. No equivalent arrange- ment to the two latter series has been seen in our species. M. CLAPAREDE* figures the proboscis as passing beneath the great or inferior nervous commis- sure in Prosorhochmus Claparedii, and the central blood-vessel as placed above both. The great nerve-trunks (n, in the various transverse sections), springing from the inferior lobes of the cephalic ganglia, pass backwards in this group within the inner (longitudinal) muscular layer of the body-wall to the posterior end of the worm, where they terminate near the tip. They are surrounded by a coat of the usual delicate fibroid stroma of the parts. The branches given off by these trunks are generally pale and indistinct, but by the use of dilute acetic acid in O. alba, and in others without such aid, they can be satisfactorily observed. They are easily seen, for instance, in 0. pulchra, the reddish hue which tinges them at their commencement shining through the translucent integuments. An elaborate plexus of branches from the lateral trunks has also been noticed in the same species. In this form also there remains, even after continued pressure, a peculiar narrowing of the great trunks immediately behind the ganglia, which, if not an original condition, may be due either to comparative immunity from pressure, or a tougher investment. The same constriction is seen in O. purpurea. In transverse section the nerves present a delicately granular appearance from the ends of the cut fibres. No one who has seized on such specimens as O. gra- cilis in semi-contraction (though unwrinkled), and drawn them out to treble the length and upwards, can doubt the peculiar elasticity that must pertain to the lateral nerves in these animals. + The nerve-trunks were said by M. pE QuatREFaGESs to lie “‘ between the external longitudinal and internal transverse muscular fibres” of the body-wall ; a descrip- tion which may in some respects apply to the Borlasians, but is inapplicable to the present group. Frey and Levckartt mention that the lateral trunks lie to the inside of the muscular coats; but while indicating the different arrange- * Beobachtungen, &c. pl. v. figs. 10 and 12. + The arrangement of the nervous system in the curious foreign Turbellarian, described under the names of Bipalium, Stimpson and Gruse, Sphyrocephalus, Scamarpa, and Dunlopea, Perceva Waicut, presents a considerable variation from the foregoing, just as the external form of the head and the digestive system do. Scumarpa represents the cephalic ganglia as quite separated from each other, except by connecting cords, and the great nerve-trunks placed close together in the median line, with an intervening ganglion at regular distances. { Beitrage zur Kenntniss Wirb. Thiere, p. 72. 360 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE ments of the “ brain” in Tetrastemma and Borlasia, they do not explain the dis- tinction in regard to the position of the nerve-trunks in these species. Prof. KErer- STEIN likewise did not observe this essential distinction between the two groups, but considered Cerebratulus the type of the whole. He describes an otolite or two in the middle of the ganglion in a young @rstedia pallida, but I fear such are only pigment-granules and cells, or collections of oil. HE. GRArrFre,* again, in some brief remarks on a Tetrastemma from Nice, states that he found a small cluster of otolite-capsules between the eyes, each capsule containing a crowd of minute otolites. If such were not pigment-cells or structures pertaining to the cephalic sacs, the Mediterranean form shows a most interesting advance on the British in this respect, as well as in having lenses to its eyes. Unfortunately, the author has not figured the structures. The only British Ommatoplean, so far as I have seen, which shows a special structure in its eye-specks, is O. pulchra. In this species the pigment is grouped within a distinct capsule (Plate VII. fig. 8, from a dead, and therefore slightly injured specimen). The eyes in the living animal have a clear patch in the centre, from the projection of the lens-like capsule. In O. gracilis and others, a few of the eye-specks are frequently connected together by bridges of the pigmentary sub- stance. Though a pale portion is sometimes seen in the specks of the former, I have not satisfactorily made out a lenticular structure. In Tetrastemma vermi-— culus, which has frequently been sent me from St Andrews, the eyes of each side are connected by a longitudinal patch of dark pigment, so that in contraction the animal seems only to have two large crescentic eyes, of a very characteristic — appearance. Cephalic Sacs and Furrows.—Midway between the tip of the snout and the anterior border of the ganglion in O. a/ba, a furrow runs inwards and slightly forwards on the dorsum, ceasing, however, before the middle line is reached; and on the ventral surface a similar though shorter furrow exists, the two meeting in a dimple, furnished with longer cilia, on the side (where the cilia are more active and powerful than usual), which depression leads into the cephalic sac. A short distance behind the ganglia two other superficial furrows occur, each slanting backwards and inwards to meet its fellow of the opposite side in the middle line. These furrows — are also continued inferiorly, but with a slightly different direction, so that they meet under the ganglia. The two sets of furrows are very distinctly marked in a flattened head as lateral notches. From the dimple mentioned in connection with — the anterior furrows, a thick-walled ciliated duct on each side leads into a con- siderable ovoid, pyriform, or almond-shaped glandular mass, which lies in front — of and rather exterior to the ganglion of the side (Plate VI. fig. 1, m); and from what is seen in translucent species, such as Tetrastemma vermiculus, it would appear to end in a cul-de-sac, the walls, moreover, under pressure are marked * Beobach. iiber Rad, und Wiirmer in Nizza, Ziirich, 1858. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 361 with transverse ruge. Towards its first part the duct is surrounded by a minutely granular glandular structure, which usually has a somewhat triangular figure. Several glandular masses lie behind, one tothe outer, and another to the inner side in this position. The glandular substance around and behind the posterior part of the ciliated external duct contains numerous granules and finely granular circular cells. From the posterior end of the outer mass in such a view, a structure that appears to be a pale duct passes obliquely towards the superior lobe of the ganglion, crossing this for some distance in a direction inwards and backwards. Traces of a cavity are apparent at its commencement, and, besides, it is distin- guished from the adjoining nerve-trunks under pressure by not being continuous with the ganglion at its edge. In transverse sections of the snout, each sac is seen to occupy a position to the outside of the cephalic blood-vessel, and somewhat above it (Plate IV. fig. 1, m), and to have a special space in the muscular stroma of the head. In large specimens the sacs contain many reddish pigment-granules, and occasionally a large cell filled with coarse granules. Behind the foregoing glan- dular apparatus lie the coiled ciliated ducts (m’), which are sometimes pale and irregularly bulged from included fluid, or else collapsed and minutely granular in aspect. In some specimens of O. alba the commencement of the duct is tinged of a faint reddish hue. There seems to be no ground for the supposition that the sacs are connected with other organs. In O. melanocephala they are less dilated than in O. alba. The coils of the ciliated duct in O. gracilis are most elaborate, and can be traced for a long distance backwards by the side of the nerve-trunk. In O. purpurea* the external apertures are not so evident as in O. alba and Tetrastemma, because the furrows are less distinct when viewed as transparent objects. They are best seen when the ventral surface is upturned, and occur in the angle of the furrow some distance from the margin of the head in this position. The ciliated pit leading inwards is short. Like other parts of the animal, there is a considerable variation in O. pulchra from the typical form in the shape and position of these sacs as well as in regard to the furrows. The latter species has numerous short longitudinal or accessory furrows on the front of the ventral grooves, and in this respect is allied to the Borlasia splendida of Prof. Kererste1n. Instead of lying in front of the ganglia (in the ordinary position under examination), the sacs are situated laterally and pos- teriorly, forming somewhat elongated pyriform organs, which adapt themselves to the curves of the ganglia. Each sac is filled with rounded granular cells, reddish pigment and other granules, has a ciliated duct anteriorly, which opens at the constriction or lateral dimple of the head just in front of the ganglia, and posteriorly ends in a ciliated tube which by-and-by bifurcates and extends for a * IT have a strong suspicion that this is the same species as the Borlasia camillea of M. pr Quarreracss, which he places next B. anglie, an association, if I am correct, founded on erroneous principles, VOL. XXV. PART II. 47 362 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE considerable distance backwards by the side of the lateral nerve-trunk. Besides. these sacs there is in the snout of this worm a series of well-marked glandular organs in front of the ganglia, one of which lies on each side of the blood-vessel, and is connected with a large lobulated mass in the middle line. In structure these glands are allied to the foregoing, having in their interior rounded granular cells, pigment, and other granules. What in some views appeared to be a duct passed from the posterior end of the external lobule towards the cephalic sacs. Traces of similar glandular masses were seen in other species (¢.g. O. alba) near the middle line of the snout, behind the cephalic sacs, and else- where. In Tetrastemma the sacs agree essentially in structure with those of O. alba, and in such translucent specimens as 7’. varicolor the ciliated posterior — ducts are easily traced. The slight furrows just described on the head in this group have been noticed by few investigators, and only Prof. Kererstern* and M. CLAPAREDE} mention the occurrence of the sacs; the former using the term Settenorgane for their signifi- — cation, but his notice is very brief. He figures and describes his B. splendida as furnished with sacs at the side of the ganglia, but without the ciliated ducts posteriorly; while in B. mandilla the latter reach no further back than the ganglia. The former species has a curious series of oblique furrows on the side just behind the snout, which are evidently homologous with those described in O. pulchra. M. CLAPAREDE again figures on each side of the eyes in the young of Prosorhochmus Claparedii a blind sac, apparently unconnected with the ciliated pits above-mentioned; moreover, in the drawing of the adult animal (fig. 10) there is on each sidea ciliated duct, but no sac. M. DE QuATREFAGES only noticed traces of these structures in the Ommatopleans; for he describes bridles or bands as passing outwards to the “ fossettes céphaliques.” In his Polia bembix he represents a large nerve passing from the anterior part of each lateral nerve- column, not far behind the ganglion, and which, after a course directed obliquely — forwards, ends in a swollen granular manner at the cephalic fossa. A similar arrangement occurred in P. humilis; but in this instance the nerve arose from — the superior lobe of the ganglion, passed obliquely forwards and outwards, and ended in several branches at the fossa. In Cerebratulus crassus and Nemertes peronea, again, he figures the nerve as springing from the posterior part of the superior lobe. He does not seem surprised that the nerve-trunks to these fosse should spring from sites so diverse as the front and back of the superior lobe and the lateral trunk. The disposition of an important nerve-branch in species of the same genus, or even in allied genera, is seldom so varied. The structure appears to have been misinterpreted in Ommatoplea, the sac having been over- looked, and the process or duct, which sometimes crosses to the origin of th great nerve-trunk and ganglion of its side, assumed to be a nerve-branch. M. * Zeitsch. fiir wiss. Zool. xii. 1863, pp. 81 and 82. t Beobach. iiber, &c. pl. v. fig. 12. : BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 363 Van BENEDEN, though he noticed the sac in Borlasia, does not mention more than “ fossettes céphaliques” in this group. Organs of Reproduction.—The sexes are separate, and the generative products developed between the inner muscular layer of each lateral region of the body and the glandular digestive chamber, and enclosed in special cavities (Plate XI. fig. 2) formed by transparent membranous sacs (¢), which are connected with the inner muscular layer of the body-wall. In the matured specimen the ova are observed to extend from the cesophagus almost to the tip of the tail, each ovary containing from one to seven ova, which, when fully developed, are seen with the naked eye through the attenuated parietes of the body. They attain a comparatively large size before leaving the body of the parent; and it is curious that they are not much less in bulk in small specimens, though few in number. The female in the ripe state has a greyish-white appearance, with the dorsal tube for the proboscis extending nearly from end to end, though its diameter is lessened posteriorly from the encroachments of the ovaries. The sperm-sacs in the male generally have a pyriform or flask-shaped aspect, especially in the early con- dition, being attached to the body-wall by a narrow tubular neck, which at the proper period doubtless gives transit to the contents of the sac. In the early condition the latter is finely granular, then cellulo-granular; and in the mature state it has a finely fibrous or streaked appearance from the spermatozoa. Some- times both granules and spermatozoa occur in the same sac, and then the former are often observed to be somewhat regularly arranged (Plate VII. fig. 12). The spermatozoa in O. alba (Plate VIII. fig. 13) have a slight curve of the body, which gently widens from the tip and ends in a perceptibly larger rounded knob, from which the long tail proceeds. The mature males are easily distinguished from the females by their whitish or pinkish aspect, and their bodies are less bulged. The spermatozoa of O. gracilis (Plate IX. fig. 8) are most active wriggling struc- tures, of a more slender shape than in O. alba or Tetrastemma (Plate VIII. fig. 14), appearing under a power of 1000 diameters as simple rods, slightly larger towards the end from which the elongated and very fine tail proceeds. The sperm-sacs are very numerous in Polia imvoluta; but the tenuity of the sperma- tozoa (Plate IX. fig. 9) renders their exact structure somewhat obscure. The body of the spermatozoon is elongated, gently curved, and slightly thickened at the end from which the tail proceeds. It is very common, moreover, to observe one or more minute clear globules attached to the body of the spermatozoon, so that the structure seems to have a tail at both ends, or a large flattened head. These appearances have misled even so experienced an observer as M. Van BENEDEN, who figures* these organs as possessed of a somewhat globular body, with a tail at each pole. But, independently of the strange exception which such a condition would make in Nemertean physiology, the frequent occurrence * Recherches, &c. Mém. |’Acad. Belg. t. xxxii. pl. iii. fig. 11. 364 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE of more than one globule on these thread-like organisms, and the comparative steadiness of the body of the spermatozoon, contrasted with the lashing of the tail, might have raised a doubt in the mind of the distinguished foreign author. The spermatozoa in Tetrastemma vermiculus (Plate VIII. fig. 12), though minute, are amongst the most active of the group. These structures are slender at one end, and slightly dilate towards the opposite, which is furnished with a very long tail. Just in front of the posterior end there is in certain views a somewhat abrupt swelling of the body, as if from an adhering globule, but none were observed without the enlargement. The ova and spermatozoa in O. alba would seem to attain full development in February, March, and April; but the breeding- season of other Ommatopleans ranges from the latter month to November. When fully developed, the mode of depositing the ova and spermatozoa may be illus- trated by the following account :—Two specimens, male and female, of O. gracilis were taken from a deep vessel, and subjected to examination in a large glass cell. ‘In a very few minutes after the male had been placed on the bottom of the cell tiny jets or jet-like wreaths of sperm-fluid were observed to issue from the sides of the body, rather past the middle, and gradually increased in number, both in front and behind. The body of the animal was soon enveloped in a wavy cloud of the milky substance, whose borders were slowly commingling with the sur- rounding water, while the numerous coiling jets, like so many miniature wreaths of white smoke from the sides of the worm, were constantly adding to the central mass. This operation lasted only a few minutes, and thereafter the animal crawled about the vessel. The female specimen was now observed to protrude ~ her snout from the mass of sand and mucus in which she was coiled, and crawl- ing to the side of the vessel, deposited in a few minutes a group of ova, about three inches distant from the white edges of the sperm-cloud, and she retired — again under the mass of sand and mucus. The change of water probably caused the male to eject his matured spermatozoa, and some sympathetic influence, it may be the diffusion of the latter, induced the female at once to evacuate her generative organs, so as to afford the ova the benefit of the male element. — A very few ova were found on examination to remain in the body of the female, — and they differed in no respect from those deposited in the vessel. The aper- tures by which the respective elements passed out in these specimens were readily observed as pale specks, each furnished with a central opening, round which ciliation for the time being was well marked. These openings, as in Borlasia, occur a little above the lateral nerve-trunk on each side, and even in — specimens of O. alba not fully ripened, pressure forces the contents of the generative sacs in the same direction, although no aperture is visible. Specimens of O. alba, which had been in confinement for seven months, deposited their ova about the middle of February; and that this is not later than in the free examples, the receipt of many mature specimens from St Andrews at BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 365 the end of March proves. The actual number of ova was not counted; but in one instance the ova of a single specimen covered a circular space of more than half an inch in diameter. Occasionally, in a crowded vessel, they are found above the water-line, adhering to the glass in an irregular mass; but they are not con- nected together by other than accidental mucus, and easily fall asunder. There is, therefore, a marked difference in regard to the deposition of the ova between this group and Borlasia; for in the latter they have a totally different shape, and a special investment of tough mucus. The only exception, so far as I have yet found, in regard to the deposition of the ova in a free condition, occurs in the aberrant form Polia involuta, VAN Ben. The bulk of the worm considerably diminishes after spawning, and the body assumes a flattened form, especially marked in large examples. That impregnation of the ova (in O. alba) takes place only after deposition, is proved by segregating a female ready to spawn, for then it is found that no further change ensues in the egg. Hence the large size of the male organs, as in fishes and other animals that shed their secretion into the surrounding water. It isa mistake to describe, as Dr Jounsron, M. DE QuATREFAGES, and Drs Frey and Leucxart have done, the ova as occurring in a free condition between the body-wall, and the Darm or digestive cavity. They are always contained in ovisacs. M. pE QuATREFAGEs observes that he found at the reproductive season a milky liquid, containing corpuscles of conglomerated globules, in the generative ceeca ; and the succeeding descriptions and illustrations make it clear, as already stated, that he refers to the walls of the digestive cavity, and the special elements contained therein. Thus it is no wonder he had some difficulty in distinguishing the sexes in the early condition of the generative products, since the cells would be identical in every specimen. He indeed gives a tolerable figure of a cell from the wall of the digestive cavity, as one of the true stages in the growth of the spermatozoa ;* and again refers (Plate XXII. fig. 2) to the glandular wall of the said cavity as representing generative ceca. The spermatozoa, therefore, which he shows, had either been discharged externally, or procured from a specimen in such a condition as to leave no room for doubt. His figure} of the spermatozoa of N. balmea is incorrect, for the body is too short and thick. He considered that it was only after the granular corpuscles fell out of the ceca into the lateral cavities that they assumed their special characteristics as sperm-cells. He thus failed to make out the correct anatomy of the parts and the physiology of the process. Dr Wiuui1ams{ states that the ‘‘ segmental organs” in Lineus, Borlasia, and Nemertes correspond in number with the transverse divisions of his great “ alimentary czecum”’ (digestive cavity), and that there is only one British species (Polia quadrioculata) in which it is possible to demonstrate the segmental organs in situ * Op. cit. pl. xxi. fig. 4, and still more plainly in pl. xxii. fig. 2. WiOpacit. pl: xix fie. 6. + Philos. Transact. 1858, p, 131. VOL. XXV. PART II. DA 366 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE as transparent objects. It is almost unnecessary to contradict the last statement, since small specimens of most of the species are more or less translucent. This author also maintains that the group agrees in the structure of its generative organs with the type of the lateral ovarian pouches of the Hirudinei, differing from the latter, however, in having the sexes separate. MM. Van Brenepen and KEFERSTEIN give a correct account of the position of the ova and sperm-sacs in the body of the species examined by them; but the term “biliary ceca” used by the former is objectionable, as tending to confound the generative and digestive systems. M. DE QUATREFAGES makes no mention as to how the ova are extruded, though he points out that (irstEp and DucéEs were wrong in averring that they escaped through the walls of the body. Mirsrep’s observation, however, is cor- rect, as subsequently proved by MM. Benepen and KerersTein. Frey and Leuckarr erroneously conjectured that the ripe ova were shed from the posterior end of the body, ‘‘ as in Arenicola.” The unimpregnated ova in 0. alba (Plate VIII. fig. 8) are pure white, and mea- sure about ~4,d of an inch in diameter, the pale spot just before deposition being about =4,;th of aninch. The ovum has two coats—an external hyaline investment (a), which becomes considerably firmer after extrusion, and an inner membranous — sheath (b) of greater delicacy enveloping the vitellus (c). With the exception of the pale spot the ovum is uniformly granular, the granules on gaining freedom showing very active molecular motion in the surrounding water. Ata particular point there is a very distinct process (micropyle?) (7), as if from the remains of a tube that led through the outer coat. In a few hours after deposition and impregnation the pale spot disappears, the yolk divides into two masses, and shortly afterwards into four. On the second day they are almost all in the © mulberry-stage. In seven or eight days the contained embryo is observed to — - revolve within the capsule by aid of its cilia, and the majority are extruded from _ the 12th to the 14th day. The young animal is furnished with two eyes before bursting the egg (Plate VIII. fig. 11), and the coarse granular matter and globules © of the digestive tract are apparent. In such a condition the wall of the ovum is” readily ruptured, and in several instances the posterior end of the animal emerged ~ first. No sooner did the young get over their labours of extrusion than they ‘glided rapidly off, head first, in a manner that showed no training was necessary — to enable them to progress. Probably the action of the cilia may have some influence in determining their course. In these young animals, which are just — visible to the naked eye as minute specks, the proboscis is marked by a paler space (Plate IX. fig. 1), that has on each side of it a dense mass of the granules | of the digestive canal. To the outside of the latter are two pale stripes, broader in front, caused by the nervous ganglia and trunks. Two longer cilia mark the posterior end. A further stage of development (after an interval of about eight BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 367 days) is shown in Plate IX. fig. 2, under somewhat less pressure. It will now be observed that there are four eyes, the anterior pair of which are largest, and correspond to the first pair. Occasionally a few have an additional pigment- speck or two on one side of the posterior pair. The anterior pair are nearer each other than the posterior, differing in this respect from those of the young Tetras- . temma, whose eyes are equidistant in both pairs.* The two ganglia (4) are large, pale, distinctly outlined, connected by the two commissures, and give off the lateral nerves (n), which approach each other very closely at their posterior termination. The oesophageal sac (7) behind the ganglia is well defined; and two pale streaks mark the cephalic sacs (m). The proboscis has its anterior opening, and the first region (a) its glands, the posterior border being marked by a transverse line (0), after which follows an indistinct stylet and reservoir-region. No stylets are visible until much crushed, and then in one specimen two slender spikes, probably from the lateral sacs, were seen. The posterior region of the proboscis bends forwards, and becomes lost atc. Shortly after this the lateral stylet-pouches become very evident in some, opening by a short and wide tube into the floor of the anterior chamber, and either containing granules or small stylets, while the central apparatus has no stylet (Plate VII. fig. 6). The speci- men had really only granules in its sacs; but to save multiplication of figures one of them was deleted, and filled in with correct drawings of stylets from another example. There is no trace of a central stylet, but the central sac is filled with coarse granules, and they moved with the muscular setting around them, for at this time the latter showed distinct contractions. The muscular space (e) behind the floor of the anterior chamber shows traces of an inner and special lining, which forms a transverse boundary in front. The basal sac is irre- gular in outline at present, and the shape less defined than in the adult, but, as development advances, the form of the ‘‘awl-handle” becomes more characteristic. The lateral stylet-sacs in a few days afterwards were generally furnished with stylets, but these organs were not so sharp and smoothly finished as in the older examples. When the central stylet appears, the granules of the basal sac have a more definite shape than represented in the figure. An outline of the two kinds of stylets is shown in fig. 6, Plate VIII., from the same specimen, and the dispro- portion between them is evident, thus confirming the previous statement, that each apparatus furnishes its own stylets. The central stylet (a) is generally more slender and acute, as well as longer than the lateral (0), which have a more globular head than in.the adult. As the specimen increases in age, the dispro- portion between the two sets of stylets lessens—one or more of the lateral being equal to the central in size. The long posterior chamber of the proboscis now contains the peculiar fluid with moving granules, and the reservoir sometimes con- * It is curious that in the young of Planaria also four eyes should be a common arrangement : indeed, they are present in some species before the embryo leaves the egg. 5368 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE tracted with force, so as to propel the granules, and even the glandular lining of the cavity itself, forwards to the front of the basal sac. The superficial granular — glands of the stylet-region are also well developed. Some weeks afterwards (and there was no difficulty in preserving them for this period, even without a change of water) four eyes were observed in the ma- jority. The head of the worm is distinctly marked in crawling, and the cuticle richly ciliated, a few longer cilia occurring at the snout and tail. Ciliation is also very active in the cephalic pits, whose openings are circular; and there is, moreover, a slight constriction at this point between the two pairsof eyes. The dermal tissues are well seen, and the ganglia are still relatively large. Every structure pertaining to the proboscis now shows considerable advancement; and it may be noted that the posterior glandular organ is wider and shorter in proportion than in the adult. In each lateral stylet-sac (Plate IX. fig. 13) there are at least three well- developed stylets, whose heads still appear somewhat more globular than in the — perfect animal, besides a headless fragment or two. and one or two clear globules. The normal position of these organs in the lateral pouches seems to be transverse. The stylet on the central apparatus is completely formed, and likewise has a somewhat globular head. The muscular cavity (e) is kept in constant jerking contractions under pressure, while the posterior part (@) is quite still. The other structures, such as the cells of the digestive cavity, had made corresponding advancement, but no blood-vessels were apparent. It may be mentioned, in passing, that the cuticular tissues of these domesticated examples become less transparent than in the wild forms brought from the rocks, and the examination of the internal organs is consequently interfered with. In these young animals also (under pressure) the proboscis generally escaped by rupture at the posterior end, as in Tetrastemma variegatum, probably by passing through the anus. In the adult protrusion rarely occurs posteriorly, but almost invariably anteriorly. The ova of O. gracilis (Plate VIII. fig. 9) are much smaller than those of 0. alba, and when first deposited adhere together slightly, so that they may be pushed en masse, but they afterwards lie flatly on the bottom of the vessel. Each likewise possesses two coats. The vitellus is of a dull yellow hue. Though there is no doubt the spermatozoa in this, as in other species, rapidly diffuse themselves throughout a large bulk of water, yet they were applied directly to the ova by means of a pipette. In about four hours many were adhering to the exterior of the hyaline coat, others were within this, while a few seemed to have penetrated — both capsules (Plate VIII. fig. 10). In six hours cleavage had proceeded much farther, so as to cause many to have the usual mulberry-aspect. In 0. pulchra the contents of the ovaries are of a beautiful rose-red colour, with a clear spot in the centre. Each ovisac in the middle of the body contains from twelve to twenty ova, therefore it is unlikely that this is a viviparous species, unless only a single ovum happened to be detained in an ovisac here and there, impregnated and developed. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 369 Numerous specimens of Polia involuta, VAN BEN., were sent from St Andrews in April, loaded with ova, and their development could easily be followed out. The newly deposited eggs (Plate XIV. fig. 1), are somewhat ovoid, about 545th of an inch in their long and 45th to ,},>th in their short diameter, and appear to possess only a single investment. They are not simply enclosed in a sheath, as M. Van BENEDEN says, but the animal, during deposition, envelopes them and its body in a tough hyaline mucus, afterwards withdrawing itself therefrom, as in Borlasia, so that the whole forms a tunnel of mucus, with the ova in its walls. The spiral condition of some of the masses was due to the coiled condi- tion of the animal during deposition. After extrusion the ova pass through the usual stages, and the embryo in each is sometimes ciliated on the tenth day (Plate XIV. fig. 2), although entire dependence cannot be placed on this date, since development occurs within as well as without the body of the parent. In a short time the young are extruded either with a pair of eye-specks, or without them, and furnished with a very long anterior, and a shorter posterior ciliary tuft or whip (Plate XIV. fig. 6). Moreover, numerous adult specimens are found towards the end of April to contain ova with ciliated young, showing that im- pregnation, as may easily be understood, can take place through the genital pores. In many of the ova the embryo had two reddish eyes, and some were extruded from the body of the parent in a free state, so that they sailed about actively through the water as ciliated pyriform bodies. The ciliation of the oesophageal region in those with the eyes was very distinct ; indeed, after the other and apparently more delicate tissues of the animal had become disintegrated, this region was left in active ciliation—dissected out, as it were, by rapid decay. This somewhat globular cesophageal region has probably been mistaken by M. Van BeneDEN for a mouth. The same author fell into the error of supposing that a form having a smooth outline was developed within its progenitor with the long ciliary tuft, the former representing the scolev, and the latter the proglottis; in short, as he says, a case of digenesis, and not a metamorphosis. But his figure* represents the so-called proglottis as furnished with two eyes exactly in the same manner as the scolex, yet he neither mentions having seen the one form inside the other, nor figures this interesting condition. No such mode of development has ever been seen by me, either in the case of those ova deposited in the unimpregnated condition, or in those developed within the body of the parent ; but the same gradual changes ensue in the young of this animal as in Tetras- temma, and, as will afterwards be seen, also in Cephalothrix. Many of the parent-specimens having developing young in their interior are feeble, and almost in a decaying condition inside their sheaths, so that their inert bodies seem but the nidi for the growth of their progeny, each of which, pro- * Op. cit. pl. ii. fig. 28. VOL. XXV. PART II. oB 370 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE vided with two boldly marked eyes, and other differentiated tissues, revolves rapidly within its capsule. This evolution of the ova in these decaying adults is a feature analogous to the elaboration of the respective generative products in the headless fragments of male and female specimens of Lineus longissimus and others—the last efforts of the parental tissues being devoted to the reproduction of the species. In Tetrastemma variegatum the ova are found in the body of the adult in June and August, and are deposited freely in the vessel. The same changes ensue in the egg as in the other forms, and the young are found in swarms beside the adults in the beginning of July and September. These young forms (Plate ‘IX. fig. 15) are so mobile, that one scarce sees the body of the same shape for two consecutive seconds. The surface is coated with long cilia, by whose aid they are piloted through the water like infusorial animalcules ; while, in addi- tion, they are furnished with a single long tuft anteriorly, as described by M. Van BENEDEN, in the young of his Polia involuta. The cutaneous textures are not distinguishable as separate layers, and the entire body has a cellular appear- ance, probably from the individual elements of the digestive cavity and the cuti- cular areole. No eyes are visible. About a week afterwards considerable progress had been made in size, but the cilia had become shorter in proportion to the bulk of the animal; and though the anterior and posterior ends showed a few conspicuous cilia, the long tuft was absent. There are now four eyes. In another week the stylet-region of the proboscis is nearly complete, the lateral often appearing before the central stylets. The usual mode by which the proboscis escapes under pressure is by rupture peranum. ‘Thus there is a slight divergence in the development of this species, whose young move freely as eyeless organisms, each provided with a long ciliary tuft; while in O. alba two well-marked eyes appear in the young in ovo. Dr ScuuLrze* first observed that his Tetrastemma obscurum was viviparous. He likewise stated that, in the development of the proboscis, the lateral stylets appear before the central, and as the animal grows older, he figures it with two loose stylets lying in the pit of the proboscis—an arrangement, as he supposes, for the supply of the central apparatus. I have also seen a loose stylet or two lying in the anterior chamber of the proboscis, but this occurred both when there was, and when there was not, a stylet on the central apparatus. The physiology of the region, as previously explained, demonstrates that there is no connection between the lateral and central stylets, save perhaps in the composition of the fluid — with which both are bathed. Prof. Kererste1n} again details the development of Prosorhochmus Claparediui—a species in which the young animals attain considerable ~ advancement before extrusion, for they are found with four eyes, a well-developed * Op. cit. p. 65, tab. v. figs. 7, 8, and 9. + Op. cit. pp. 89 and 90, taf. vi. figs, 2 and 3. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 371 proboscis, and other organs, before they leave the body of the parent, and on being set free have the same general form as the latter. The larger examples are often doubled within the body of the parent, and apparently invested by the stretched covering of the ovisac, or in large cavities produced by the coalescing of many ovisacs; at any rate, it is clear that to describe them (as Prof. KEFERsTEIN and M. CLapaREDE* have done) as simply within the body-cavity of the worm, is want- ing in structural accuracy. It is certainly a curious sight to see these large young animals moving within the body of the adult, apparently without causing the latter any inconvenience. Such, then, appears to be a further stage of the type of development seen in certain species (¢.g., Polia involuta, VAN BENEDEN), in which, after deposition of the majority, a few ova are left in the body of the parent for subsequent evolution. It remains, however, to be proved whether all the ova in Prosorhochmus are so developed (in which case they must be very few), or whether part are deposited at one or different periods or stages, and the rest evolved in the body of the parent. By the examination of this species, I have been enabled to confirm many of the excellent observations of Prof. KerersTeIn and M. CLAPAREDE; but, on the other hand, the determination of the actual position of the mouth in the same animal shows that it does not deviate from the typical Ommatopleans, and that the organ is situated not behind the ganglia, as asserted. but, like the others previously described, quite in front of the commissures. The mouth, moreover, is the most distinct of any I have examined. It appears to me that such viviparous species do not form a group swé generis. but are connected by insensible gradations with the true oviparous forms. Doubt- less, in the majority, some of the ova only are retained in the ovisacs, impreg- nated by the ubiquitous spermatozoa through the genital pores, developed in the sacs, and space afforded for the growth of the young animals by the stretching or rupturing of the membranous walls of the latter. It is a very interesting fact in connection with this subject, that Prof. Kerersrein+} has lately discovered a Hermaphrodite Nemertean (Borlasia hermaphroditica) at St Malo, in which the anterior sacs were found full of mature spermatozoa, and the. posterior distended with developing ova. This can only be explained in one of two ways—either that the species is truly a hermaphrodite one, or that the spermatozoa are passed from the body of a male (in apposition) into certain sacs of the female through the genital pores, there to remain until the other contents of the female generative organs are evacuated. BORLASIA. Cuticular Tissues.—The skin in this group, for which Borlasia olivacea may be taken as the type, is allied in structure to that of Ommatoplea, though in the living animal its condition is frequently rendered obscure by the much * Beobachtungen iiber Anat., &., p. 23. t Ann, Nat. Hist., 4th ser. vol. i. 1868, p. 229; and Archiv fiir Naturges. 1868. 3712 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE greater development of pigment. The body is everywhere covered with cilia, which are most active in the lateral fissures, but longest on the papille of the snout. They may be seen in active motion under a lens in good light. Sometimes the motion of the cilia in the lateral fissures is suspended, and again set agoing, without evident cause. Dr WILLIAms first asserts that the cilia are confined to the dorsal half of the body,* and then seems to contradict himself by saying farther on that the whole body is ciliated.+ The latter, as above-men- tioned, is the correct view. k In the living animal the cutis has a cellular aspect (Plate IX. fig. 4), the cells or areolee measuring +,)9th of an inch or more, and most distinctly seen towards the tip of the tail in the adult. Sometimes a number of minute clear granules are observed overlying the larger cells, as shown at the lower third of the figure. The pigment-cells and granules reach their greatest development anteriorly, and some of the former contain very dark brownish black pigment in circumscribed masses. The dorsal pigment has in general a longitudinally streaked appearance (Plate IX. fig. 5), a state probably due to the peculiar arrangement of the fibres of the external muscular layer hereafter to be described. In some pale red specimens the coloration is observed to be due to a uniform impregnation of the cutis, and the tint is much deeper than that of the ganglia, which are thus rendered conspicuous by their pallor. Occasionally one or two pigment-cells of exception- ally large size are present anteriorly (Plate IX. fig. 6), and there were three clear granules in the larger of the two figured. The cuticular cells are finer in Borlasia lactea, Mont. MS., and the body is not clouded by the granular pigmentary matter. The superficial arrangement in Meckelia annulata (Plate IX. fig. 7) is similar, though the cells or areolz are smaller, and the pigment-granules do not © form themselves into streaks. There are three tactile papillz on the snout, one of which, from its situation, falls to be described with the opening of the canal for the proboscis. The other two are placed on each side of the central (Plate X. fig. 1), but are not always so prominent. Each is furnished with a series of cilia of greater length than those on the general surface, and which extend from the erected papilla in a radiating or fan-shaped manner. They are probably of great tactile service to the worm. Prof. KErERsTEIN refers to a “transverse” tactile papilla on the snout of his Cephalothrix longissima, which differs from those usually seen in Borlasia, and resembles a slight pouting of the lining membrane of the canal for the proboscis. Under pressure granular masses and globules of mucus resembling oil are ex- truded from the skin, as in Ommatoplea, and often congregate round the borders of fresh transverse sections. But, while in Ommatoplea there are only the ciliated and structureless epidermis, a single layer of cutis-cells and the basement-layer, before * Report Brit. Assoc. 1851, p. 171. t Op. cit. p. 243. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 373 the circular (external) muscular fibres are reached, in Borlasia the structure of the dermal layer is more complicated. Fine tranverse sections of B. olivacea demon- strate that underneath the ciliated epidermis (c, Plate XI. fig. 8), a somewhat thick layer (¢d) composed of granular cells and globules in areole, occurs. From the facility with which these contents escape, the drawings show the parts in a slightly altered condition. Beneath this lies a pale structureless basement-layer (d’), the presence of which in Cerebratulus had misled Prof. KrrersTer into the idea that it was a layer of circular muscular fibres ; but an attentive examination of that genus, as well as the present, demonstrates that, while one may be deceived if only transverse sections are made, no doubt can exist in longitudinal sections. This point may readily be settled without reference to the more explicit, because larger, condition of the parts in the great Lineus longissimus. A thick compound layer is next encountered in B. olivacea, consisting externally of pigment-granules and cuticular globules (d”), and internally of a series of powerful longitudinal muscular fibres (¢). Under a low power, indeed, this com- pound layer in transverse section appears as one, the pigment and other cells, and the cut ends of the muscular fibres, presenting a similar aspect. The amount of pigment varies of course in different specimens, and is always much more developed dorsally than ventrally. Towards the anterior end of the animal this layer of the cutis (d”) becomes thicker, and its reticulations more distinctly marked. Fine longitudinal sections of the snout from above downwards show superficially a series of very beautiful reticulations of a somewhat regular aspect, the chief interstitial bands having a longitudinal direction. ‘Towards the tip of the snout the texture becomes denser in transverse section (Plate X. fig. 4), and the pigmentary matter increases, especially just within the pale external layer of the cutis. A section still further back (Plate XII. fig. 2) exhibits a less dense arrangement, and the pigment is now for the most part grouped into a dorsal and ventral band. The general stroma consists of radiating and longitudinal fibres, the cut ends and granular matter being often situated in the axils of the radiating series. The pigment anteriorly attains its greatest density immediately beneath the pale external layer of the cutis, diminishing in quantity from this point inwards. The snouts of these mobile animals resemble in structure the elaborate arrangements which are sometimes met with in certain organs (such as the tongue) in the higher animals, where extensive and delicate motions are combined with great tactile power. In Cerebratulus bilineatus,* the arrangement of the two white median dorsal stripes is characteristic, for the pigment is strictly confined to the region cor- responding to d” and ¢ in Borlasia; and in transverse section they appear as two patches with an intervening pale space, bounded anteriorly by the basement- * Gordius tenia, DALYELL, Pow. Creat. vol. ii. VOL. XXV. PART II. DC 374 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE layer of the pale exterior coat, and internally by the circular muscular fibres. In transverse section the cutis of Meckelia annulata contains rather small cells (Plate XIV. fig. 11), which retain much of their ordinary shape after mounting. The characteristic opaque white dorsal and lateral pigment-stripes pass through- out the entire thickness of this tissue, while the white touches on the sides that apparently correspond with the openings of some of the ovaries or sperm-sacs do not traverse the entire thickness, but lie towards its inner border. The skin in many of the Borlasians, ¢.g., Zineus longissimus, Borlasia olivacea, B. octoculata, B. lactea, Micrura (Stylus) purpurea and M. fasciolata, gives a marked acid reaction when tested with litmus-paper. Muscular Coats——The longitudinal muscular coat (¢), which is incorporated with the former cutaneous layer at its commencement, is thick and powerful, and has a well-marked fasciculated aspect in transverse section. At the sides of the mouth, where this coat attains great development, and forms a strong lateral — support, there is a very pretty radiated or somewhat arborescent arrangement of the interfascicular substance on transverse section (Plate XI. fig. 1, 2). Sucha condition would permit great stretching in all directions without actual separation of the muscular bundles, and is thus eminently adapted for the functions of the parts. The intimate connection of the outer fibres of this layer with the adjoin- ing coat is well brought out in some superficial longitudinal sections of the body, — which show the outer bundles of fibres quite separated from each other by rows of pigment and other cells and granules,—the whole having a curiously streaked appearance. Anteriorly this longitudinal layer becomes lost in the tissues of the snout. The next coat (¢’) consists of a series of circular muscular fibres of con- siderable thickness, and it is between this and the former that the nerve-trunks are situated. It passes by the sides of the ganglia, and appears to merge into the wall of the passage for the proboscis in front of these organs. In Cerebra- tulus bilineatus this coat is decidedly thicker than usual, a condition which may — be connected with the somewhat rounder form of the body generally in the species. Within the last-mentioned coat is a layer (e’).of longitudinal muscular fibres, similar in structure to the corresponding stratum in Ommatoplea. Like the — former the fibres pass the ganglia to become connected with the muscular channel for the proboscis in the snout. Certain peculiarities are observable in the dermal tissues of the large Lineus longissimus (Borlasia anglize, QUATREF.), and since this species has been taken as” the type of the Nemerteans by M. pE Quatreraces and others, it is necessary to enter somewhat minutely into the anatomy of the parts, as shown in the trans- verse and longitudinal sections (Plate XI. figs. 6 and 7). The external cuticular layer (d) is proportionally thinner than in the common species. The pigmentary - layer \d’, d’) is divided by a definite black band (2), and is distinctly separated from the first or external longitudinal muscular layer. by a curious translucent BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 315 stratum (3, 3), which in transverse section (fig. 6) has a transversely barred arrangement with linear interruptions, which divide it into numerous and some- what regular elongated spaces. In longitudinal section, again (fig. 7), this stratum has a wavy aspect, or, if much contracted, presents a series of moniliform streaks. That this layer, however elastic, is not muscular, a glance at the position of the parts in fig. 7 at once demonstrates. It belongs entirely to the cuticular elements, and with the interior pigmentary layer corresponds to the region d” in B. olivacea, which, in the larger species, attains much greater per- fection, and becomes distinctly separated from the longitudinal muscular fibres. The only peculiarities in the muscular coats consist in the very evident transverse streaking of the external longitudinal layer (fig. 7, ¢), and in the presence of certain parasitic (?) cellular masses in it and the next outer layer. These masses lie in definite spaces, and consist of groups of rounded cells filled with granules. In the contracted state of the animal, as after preservation in spirit, the fibres of the circular coat in longitudinal sections are grouped in a wavy manner (¢, fig. 7), apparently from the extreme shortening of the parts. In the arrangement of the muscular system of the body-wall the curious specimen from Balta is distinguished from all other British forms yet encoun- tered. Externally (Plate X. fig. 2, d’), beneath the basement-layer of the cutis (which in the fragmentary specimen was almost absent), there is a layer of cir- cular fibres (¢’).. Within the latter is a very powerful layer of longitudinal fibres (é), which (layer), however, is not continuous, as in Ommatoplea and Borlasia, but has at least one very distinct point of separation. Upon approaching the middle line of the dorsum in transverse section, this longitudinal coat becomes thinned off, so as to end on each side of the centre in a blunt point. In addition, there is a somewhat triangular portion (ea) cut off by interfascicular substance and fibres. The dorsal curve of the proboscidian sheath is closely applied to this central point of separation, apparently receiving therefrom a few fibres, which retain it in position, while other fibres pass downwards to join the circular layer (ja), which here encloses the space for the digestive tract. The separation of the great longitudinal layer of the body-wall is marked externally by a distinct median line, which is rendered more conspicuous by the occurrence of the trans- verse strize of the dorsum on each side of it. There is also a slightly marked fissure of this muscular coat inferiorly. This arrangement therefore conforms to the Meckelian type, as seen in MW. annulata, in which there are two muscular coats, with intermediate lateral nerve-trunks. The deviations from the ordinary aspect in the Zetlandic specimen may prove to be accidental. The elaborate system of muscles in the body-wall of these worms enables them to perform the most varied and complex motions, so that they have not inaptly been compared to a piece of living caoutchouc. When irritated, the larger species, such as Borlasia lactea, Mont., and the true B. octoculata, suddenly contract in a 376 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE spiral manner like a cork-screw or the stalk of a Vorticella, or twist their bodies into a rope of various strands. The great Lineus longissimus may now and then be observed in its native pools extended between the Fuci of opposite sides in numerous loops, each several yards in length, and so intricately arranged, that — they can scarcely be unravelled by other than the animal itself. The extreme stretching which the body undergoes before it snaps—as in attempting to secure a specimen in an intricate and inaccessible pool—and the extraordinary shorten- ing on immersion in spirit, are only well-marked conditions into which the animal throws its yielding textures at will. A Micrura, again, from the deep water of St Andrews’ Bay, swims freely on its edge like a fresh-water Nephelis, or its own ally O. pulchra, lashing the water with alternate strokes of its muscular and flat- tened posterior extremity. Sir J. G. Datye.t likewise noticed this edge-motion in his great “ Gordius” fragilis, but he was not sure whether it was a natural — condition, or caused by the confined vessel. Meckelia annulata forms in captivity a beautiful silky sheath by its cutaneous secretions, within which it lies in com- parative security, until, tempted perhaps by love of change, it searches for a fresh site, whereon to manufacture a new chamber for its protection. In unhealthy — and slowly dying animals the skin becomes raised into pale bullze, not only from corrugation, but from degeneration of the cutaneous textures. The posterior end of the body in Micrura(Stylus) requires special mention, since there is superadded a peculiar elongated and contractile style. This appendage seems to be formed by a prolongation of the cutaneous and part of the muscular (longitudinal and circular) textures of the body-wall of the animal. The entire organ in contraction has a granular appearance, the coarsest granules, and occa- sionally a few circular masses of brownish pigment, being at the tip. Within these coats is a central chamber, which undergoes various alterations in size, and contains a transparent fluid. This cavity is not connected with the digestive tract, which opens by a terminal pore at the base of the process, nor can pro- boscidian discs be seen therein. I have not as yet ascertained with what system. it communicates, but its connection with the circulatory appears most probable. The style is richly ciliated externally, and undergoes many and varied motions, now forming a verrucose knob, now stretched to an extreme degree of tenuity, and apparently assisted in the latter action by the fixing of the tip, whose warty formations seem to perform the functions of suckers, for the animal may be observed crawling about with a loose style, then the tip of the latter suddenly becomes fixed upon the clean and smooth glass, and the whole organ is elongated accordingly. The fixed portion at the tip is usually more dilated than the suc- ceeding part of the style. + In Cephalothriz, rst. (including Astemma), the dermal tissues, and indeed the entire body-wall, deviate from the ordinary structure in Ommatoplea, Bor lasia, and Meckelia; and while the minute anatomy of this genus bears out th BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 3/7 distinctions—based on external characters, and the form of the nerve-ganglia— given by Prof. KerersTEIN, its independent position can be more satisfactorily demonstrated. Externally (Plate X. fig. 3) there is the usual ciliated coating, whose action is most vigorous in the cephalic region. The cutaneous textures are exceedingly transparent, the pigment, if present, being only developed at the snout in front of the ganglia as a rose-pink or reddish shading within the super- ficial cuticular layer of the parts. The cutis (d), composed of the usual granular cells and gelatinous matter in areole, has along its inner margin a trace of a trans- lucent homogeneous basement-layer. A very thin layer of circular fibres (¢’) comes next, the exact structure of which is best demonstrated in the fresh animals, after the addition of a little dilute acetic acid. The fibres are also evident in fine longi- tudinal sections, but are not satisfactorily seen in transverse sections on account of their tenuity. Beneath this lies a very powerful longitudinal muscular coat (e’), the cut ends of the fibres having the usual fasciculated appearance, the inner being somewhat coarser than the outer. At each side a distinct increase occurs at the region of the nerve, where the coat is separated into two portions by a septum of fibres from the circular coat, the nerve lying in the line of demarcation. This arrangement is quite characteristic, and the position of the nerve-trunk probably points to the compound nature of the great longitudinal layer, viz., as analogous to the two longitudinal layers in Borlasia, the circular muscular coat cutting off only the lateral portions (¢), instead of dividing it completely. This genus shows the mobility of the race even in a greater degree than the others. In crawling about the long yielding snout is used as an exploratory or boring organ, which it stretches hither and thither with ceaseless energy, and by its aid is able to push aside its own mobile body in any direction; while through any narrow loop of mucus the latter is drawn like a thread of semi-fluid, yet coherent substance. These animals also progress readily on the surface of the water. When tested with blue litmus-paper the skin of Cephalothrix gives a most vivid red stain. DELLE Cut14Je’s* description of the structure of the body-wall, if applied to the Ommatopleans, is correct enough, viz., that there is an external layer of circular fibres and an internal longitudinal coat; hence the criticism of M. Dz QUATREFAGES requires qualification. The Polia siphunculus, D. Cu., however, seems to have been a Borlasian, judging from the large triangular slit which lies at a consider- able distance behind the snout. H. Raruxe} gives Borlasia striata two coats,—an epidermis, and a corium,—combining under the latter both the pale and the pig- mentary layers of the skin. He has omitted to notice the external longitudinal muscular layer, and mentions only an outer circular and an inner longitudinal muscular coat. It is somewhat difficult to comprehend the views held by M. bE QUATREFAGES with regard to the same structures, since his descriptions and * Memorie sulla storia, &c., vol. ii, 1825. + Neueste Schriften der Naturforschenden, &c. p. 95, 1842. VOL. XXV. PART II. 5D 378 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE figures do not seem to coincide with each other. He divides the skin into three coats, viz., the ciliated epidermis, cutis, and the fibrous coat. Moreover, the cutis has two layers—an outer, formed of a homogeneous transparent substance, pre- senting in its mass a number of cells or simple rounded vacuoles refracting the light, and an inner, of large elongated cells in a double row; but in his figure* — the muscular elements occupy a bulk so insignificant that some error appears — to have been committed, especially as the third layer of the skin is stated to be a transverse fibrous one. It is at all events difficult to see how the enlarged transverse section just noted agrees with his figures iv. and v., pl. 18. Two mus- cular coats only are described by this author—an external longitudinal and an internal circular—the internal longitudinal being omitted, or rather considered as an aponeurotic layer. He also commits a serious error in affirming that the structure of the dermal tissues in Ommatoplea corresponds with that in Borlasia anglie. Frey and Leucxart likewise describe only two muscular coats—an outer longitudinal and an internal circular. Prof. Krrersrein,} while representing the cutaneous textures of Cerebratulus (a Borlasian) with greater accuracy, also falls into the mistake of applying what he found in this animal to all the Nemer- — teans. He describes the skin as composed of two coats,—a cuticula covered with cilia, and an inner thick, finely granular coat which contains the pigment,—a definition which is scarcely comprehensive enough for the nature of the parts in — such as Lineus longissimus. He mentions the occurrence of crystals of the form of arragonite in the pigmentary layer of Cephalothriz ocellata, but such have not been seen in the British forms, except under the action of chemicals, or after the evaporation of the salt water. His statement, that in Cerebratulus marginatus there are four muscular coats—an external circular under the pigment-layer of the cutis, a longitudinal, a circular, and lastly an internal longitudinal—has already been noticed. No more than three muscular coats are present in the Borlasians. Lastly, Dr ANTON ScHNEIDER, in his remarks on the muscles of — worms, and their importance in the system,{ states that in Nemertes the follow- ing layers occur :—Circular, longitudinal, and circular, besides radiating muscles —a description that is unsatisfactory as regards the British species. Cavity of the Proboscidian Sheath.—This forms a shut sac, as in Ommatoplea, from the bridge of the ganglionic commissure to the posterior end of the worm. The long proboscis glides smoothly in this chamber, whose walls are united with it and other tissues just in front of the commissure. The other contents are the clear proboscidian fluid and its discs. The latter are circular granular bodies, similar to, though smaller than, those of Ommatoplea, and when seen on the edge present a fusiform outline, having a swollen middle and two tapering ends There are also a few small granules and granular cells. ‘The muscular wall of *Opcut (pl, XX, ee le + Op. cit. pp. 66-68. { Miiller’s Archiv fiir Anat. 1864, p. 595. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 379 this chamber and other points agree so closely, both structurally and function- ally, with the same parts in Ommatoplea, that it is unnecessary to describe farther than refer to the aspect of the parts in the living animal (Plate X. fig. 1, 0); and to the various transverse sections, in which the wall of the chamber is lettered 0, and the cavity ao. Sometimes near its diminished posterior end the latter shows a series of moniliform spaces, from internal bridles, and often does not quite reach the tip of the tail either in this group or in Cephalothriz. In Meckelia annulata the proboscidian sheath is not continued to the tip of the tail either, and it is an interesting fact that this absence coincides, as in the last-men- tioned genus, with greatly enlarged lateral vessels. In Cephalothrix the chamber presents certain peculiarities, being subdivided by transverse bands of contractile tissue throughout its entire length, so that during the motions of the worm the anterior region is occasionally thrown into a series of moniliform spaces. These contractile septa (though imperfect in the middle), doubtless prove of much ser- vice during rupture—an occurrence so liable in this lengthened animal. More- over, the wall of the chamber is thin, and the circular muscular fibres of the body not much developed; hence the advantages afforded by these safeguards against the inconvenient bulging of the chamber during the motions of the worm. The transparent liquid of the cavity in this genus (Cephalothrix) contains flask- shaped bodies and minute clear corpuscles. Prof. KEFERSTEIN* seems to have had no definite idea of this chamber as a cavity with special muscular walls, but speaks of the peculiar discs as floating in the body-cavity (Leibeshohle)— an error of some importance. In his two trans- verse sections of Cerebratulus marginatus, he appears to have confounded the wall of the tunnel with that of the proboscis. He is thus less correct than his predecessors Frey and Levcxart,} who noticed the sheath of the proboscis and its contents. Terminal Aperture in the Snout for the Proboscis.—A channel, ciliated for some distance, leads inwards from the terminal pore to the reflection of the proboscis just in front of the commissures. This channel, shortly after its commencement (Plate X. fig. 4, a), is surrounded by an elaborate series of muscular loops (indicated at 2), which, while keeping it closed under ordinary circumstances, permit of rapid and easy dilatation. Immediately within these is a series of longitudinal muscular fibres, which attain a more distinct development some- what posterior to this point (a, Plate XII. fig. 2). A very beautiful group of circular and diverging fibres lies to the outside of the first-mentioned series (2, in the last-mentioned figure), crossing each other in a striking manner superiorly and inferiorly, as well as less distinctly at intermediate points, and forming with the longitudinal and other fibres the intricate stoma of the snout. The terminal * Op cit. pp. 68 and 69. + Beitrige zur Kenntniss, &c. p. 70. 380 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE pore is furnished with a prominent papilla, covered with a fan-shaped brush of cilia, the whole being only occasionally extruded, and no doubt assisting the papillae previously mentioned in the tactile functions of the snout. This central papilla is sometimes bilobed, and each of the divisions supplied with cilia. In spirit-preparations of large examples of Lineus longissimus the proboscidian aperture is distinguished by a slight slit on the inferior surface immediately behind the tip of the snout. | : Proboscis.—The proboscis (Plate X. fig. 1, @) commences as a somewhat slender tube just in front of the commissures, gradually enlarges, continues for a considerable distance of nearly equal calibre, and then, diminishing, terminates posteriorly in a long muscular ribbon (, sometimes bifid), which, curving forwards in the ordinary state of the parts, becomes attached to the wall of the — proboscidian tunnel. Its cavity is continued in front into the canal of the snout, and posteriorly terminates in a cul-de-sac at the commencement of the muscular ribbon. It differs from the Ommatoplean organ in certain respects, such as the absence of the stylets, its more slender proportions, and the shape of the glandular papillee on its internal surface. Experience, indeed, generally enables the observer to distinguish by external characters the proboscis of a Borlasian from that of an Ommatoplean in spirit-preparations, by the abrupt diminution of the calibre at the posterior portion in the latter, caused by the presence of the stylet-region and swollen reservoir; but even where the organ is incomplete, a transverse section at once puts the question beyond doubt. This was illustrated in a well-preserved though shrunken fragmentary specimen brought by Mr Gwyn JErrreys, the distinguished conchologist, from North Unst, Shetland. At first sight it looked like a Borlasian organ, on account of the absence of the stylet and posterior regions, and from its large size I thought it would demonstrate the structure in that family favourably, but a transverse section gave a true Ommatoplean anatomy, with the characteristic beaded and other layers; and an examination of the animal itself at once confirmed its relationship. In the living animal the organ is proportionally longer than in Ommatoplea, and when cast off becomes thrown into numerous screw-like coils. Thus do the two great groups of soft worms q differ in essential characters; and we are taught how unsafe is that classification, — é.g., such as SCHMARDA’Ss,* which proceeds on other than anatomical grounds. A transverse section of the proboscis of a Borlasian (M/zcrura) from St Andrews is represented in Plate XII: fig. 1. Externally there is a coat (a) similar to that | in Ommatoplea, apparently composed of homogeneous elastic tissue, yet showing — some granular markings towards its outer border. This coat is tougher than any of.the others, and often retains its integrity after they have ruptured. A powerful longitudinal muscular layer (0) lies within the former, its cut fibres in transverse * Neue Turbel. Rotat. und Anneliden, vol. i. pt. 1, 1859. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. o8l section having the same histological characters as in Ommatoplea. At opposite or nearly opposite poles of the circle, however, a remarkable interposition severs the continuity of the layer (as seen at g,g’). At one pole, two symmetrical bundles of fibres spring from the succeeding circular layer, and, slanting out- wards, cross each other in such a manner as to disconnect the longitudinal coat just mentioned, and for a portion of its circumference wedge it between two bands of circular fibres. The outer or oblique bands of circular fibres become lost in the external coat of the organ. The longitudinal layer (0) is thus diminished to a blunt point on each side of the crossing of these peculiar fibres, and a region is formed externally which is occupied by a special and somewhat lozenge-shaped group of longitudinal fibres, through which the dotted line g passes. The longitudinal layer, especially near the wedge-shaped ends (where the fibres are often grouped in a thicker mass in these preparations, is marked in the centre by a faint linear streak, as if composed of two layers, but this does not continue all round, and is not apparent in every specimen, nor in B. olivacea. At the other pole there is a variation in this arrangement, for it is found that an elongated portion (g’) is cut off without apparent crossing, the ends of the great longitudinal coat (>) being widely apart. It generally happens that towards this side the bulging of the contracted organ occurs, and, it may be, such forces the edges of the longitudinal coat apart, and aids in causing the above appearances; but it would not account for them all. In contraction this coat is sometimes thrown into a silky belt of regularly waved fibres. Within the longitudinal layer is an equally powerful belt of circular fibres (c) which, at opposite poles in the transverse sections, gives off the peculiar oblique bands previously mentioned. A basement-layer (d), better marked in this species than in the common form (B. olivacea), is situated on the inner surface of the latter. There is also present in this species an incomplete belt of longitudinal fibres (¢) within the basement- layer, and which is not evident in the species just mentioned. Attached to the inner surface of the basement-layer, or in the latter case partly to the incomplete longitudinal layer, is the glandular mucous coat (/), which, from lengthened preservation, has in this case become somewhat altered. The glandular bodies are scattered chiefly towards its inner or free surface. In fresh preparations, 7. ¢., in those made from the organ immediately after extrusion from the living animal, a very pretty radiated arrangement of this coat is constantly observed, as if a series of explosions had occurred in the mucous substance so as to scatter the globules and gelatinous bands in a fan-shaped manner. Indeed, the aspect resembles thick and graceful tufts of grass with large spikes, for the granular glands are mostly at the tips of the streaks of mucus, a state doubtless due to their passage outwards under compression. Prof. KrererstTeIn* figures this in * ‘Op. cit, tat. v. fig. 16. VOL. XXV. PART II. Sm 382 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Borlasia splendida, but he does not refer thereto in his descriptions. In the fresh _ specimen it is found that the glandular papille are much smaller than in Omma- — toplea, and widely different in shape (Plate VI. fig. 10, and Plate X. fig. 5), the former representing them in the extruded proboscis, the latter as viewed from without. Under ordinary circumstances they appear to have an ovoid shape, and to vary from ;,/55th to zo5th of an inch in size. Under pressure they become either flattened circular bodies or assume an elongated and slightly barred aspect; and, after escape into the surrounding water, the contents are club-shaped or rounded (Plate XIII. fig. 9). The usual crossing occurs at one of the poles of the circular section of the proboscis in Lineus longissimus (Plate XIV. fig. 8), but the separated piece at the opposite pole is somewhat larger than in B. olivacea. Like the latter, it also has no inner longitudinal fibres grouped exterior to the mucous layer. In the remarkable form* dredged in 50 fathoms off Balta by Mr Jerrreys—and the structure of whose body-wall coincided with the Meckelian type rather than the Borlasian—the proboscis proceeded backwards from the tip of the snout in the usual manner, but instead of the posterior end diminishing insensibly into the long muscular ribbon, the organ divided into two nearly equal trunks (Plate XIV. fig. 12), each about as — large as the entire portion, and terminated in a somewhat abrupt and swollen end, from which the long muscular ribbon proceeded. The wall of this peculiar proboscis, so far as I could make out from the single and rather unfavourable example, had the following structure :—Externally there was a circular layer which showed a few granules on the outer margin in transverse section; within this lay a powerful and apparently continuous longitudinal muscular coat, from — whose inner surface the granular papillary mucous lining projected. The inner or free margin of the latter was comparatively smooth, a result probably due — to the minuteness of the papillze. Each of the forked portions had the same struc- ture as the anterior region, and the thick longitudinal coat, after bending inwards at the posterior end of the swollen termination, became continuous with the muscular ribbon. The proboscis thus differed from the ordinary Meckelian form in the bifurcation, and in having no distinct circular coat within the longitudinal. It had no closer analogy with the Borlasian or other type. In Micrura (Stylus), a true Borlasian, the organ is furnished with somewhat slender papillee, which, under pressure, became lanceolate and pedicled, fusiform, or rounded with granular contents. When viewed laterally. the rounded or — flattened papille that formerly seemed granular appear to be composed of a series of minute rods set closely together. In some of the elongated structures, how- — ever, under pressure, the striz are longitudinal. When extruded from the organ into the water the elongated bodies in the papillee cling together in some instances like fibrille, and their appearance in the prepared specimens is quite charac- * See p. 375. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 383 teristic, the inner or free surface of the coat being covered with a vast number of these elongated glandular structures. These are the baccillary bodies described by Dr Max. MU.uer,* but I have never observed in the British species any of the urticating organs mentioned by this author. The minute structure of the wall of the proboscis agrees with that in Borlasia, only the lozenge-shaped portion (g, Plate XII. fig. 1) in some specimens was longer than in B. olivacea, from the more gradual slanting of the fibres to the exterior. In Cephalothriz the papille of the proboscis are acicular, and they are longest towards the anterior part of the organ (Plate XI. fig. 9). In transverse section the walls present a simpler structure than in Borlasia; and, though in the living animal an external circular and internal longitudinal muscular coat are apparent, the tissues become so confused after mounting, that I have not yet satisfactorily unravelled them. Under the action of powerful ‘irritants, such as alcohol, the animal detaches, in its spasms, both the anterior and posterior connections of the proboscis at once, so that the extruded organ remains in its ordinary condition when expelled. and is not turned inside out. In Cephalothrixz, again, it sometimes ruptures near the ganglia, and is drawn backwards by the ribbon of attachment and its own elasticity; and the animal seems to be unaffected by the injury, which regeneration soon repairs. I have never seen the worm use the proboscis for any purpose: and though M. Van BENEDEN has observed it extruded in his Cerebratulus @rstedit (which is only DaLYEL’s Gordius tenia), and threatening its prey, I fear it could not do much harm. The life-like vermicular motions of this muscular tube, both in situ and when cast off, have misled Mr Breartie} and others, so that they have described the organ as a young animal, and the possessor as viviparous, or else have considered the expelled portion a parasite. This is at once apparent on examining Mr Breartie’s specimen of the supposed young animal in the British Museum.{ The proboscis is reproduced in the same manner as in Ommatoplea ; and the discarded organ, if not ejected, may be seen floating in the proboscidian eavity amidst much granular debris. Sir J. Dauye.u§ states that the usual colour of the proboscis in Lineus longissismus is vivid red; our specimens have generally had white or faintly pinkish organs. M. Van BENEDEN|| does not mention the tissues to which the muscular retractor of the proboscis is attached in his Nemertes communis, and speaks of it as suspended freely in the cavity of the body, like the digestive tube of the Bryozoa. A further remark with regard to the organ in Cerebratulus Mrstedia (G. tenia, * Observat. Anat. de Vermibus quibusdam Maritimis, Berolini, 1852. {+ Ann. Nat. Hist., 1859. ¢ Dr Bairp, in describing Serpentaria Berryi, n. sp., also alludes to the very common practice of ejecting the proboscis-(not the alimentary canal) after immersion in spirit, It is a habit common to all the Nemerteans.— Proceed. Zool, Soc. Feb. 12, 1866. § Pow. Creat. vol. ii. || Op. cit. p. 10. 384 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE -DALYELL) makes his error still more apparent, for he says, “‘ Toute la trompe se meut librement dans la cavité intestinale.’* Prof. KrrERSTEIN gives a small — figure} of a transverse section of the organ in Cerebratulus marginatus turned inside out; but, though he indicates the lozenge-shaped space formed by the crossing of the fibres, it is misplaced on one side, and the entire figure is too indistinct for reference. Digestive System.—The mouth in Borlasia olivacea is a longitudinal fissure on the ventral surface, situated a short distance behind the ganglia, and varying © in size according to the motions of the animal, and the degree of contraction or relaxation. Its ordinary appearance under examination is represented in Plate X. — fig. 1, w. Certain broad pale lines radiate from the lips of the fissure (which lines in dark specimens are generally pale), an arrangement which led Dr G. Jounston into the error of considering it a nerve-ganglion and branches. These radiating — lines or folds are due to the same structural cause as those in the ciliated ceso- phageal region of Ommatoplea—viz., prominent longitudinal rugze of the thick glandular texture of the organ, which, in this case, permit great dilatation of the parts during ingestion. The number of these ruge varies, as may be observed by a comparison of the figures. In Borlasia lactea, Mont. MS., the mouth is situated very far back, leaving a long space between it and the ganglia. In Cerebratulus, again, the aperture is a longitudinal slit, somewhat less marked than in Borlasia. The mouth leads into a great ciliated cesophageal chamber (7), which commences anteriorly as a cul-de-sac behind the ganglia and cephalic sacs, — and nearly closing in by its anterior wall the vascular lacunz there, while it may be said to terminate posteriorly at a distinct incurving of its wall, by becoming continuous with the digestive cavity-proper. In the transverse section (Plate XI. fig. 1), the anterior part of this chamber is seen under favourable circumstances, © as a thickly folded glandular mass (7), with the ventral slit (z) leading quite freely into it. The cavity has not yet attained its full size, and the mouth is severed at its anterior border. Superiorly, a large space is occupied by the pro- boscidian sheath (a), and the great lacunee (s,s), and indications of some other vascular meshes are seen at the sides. The lips of the mouth (w) curve inwards, © and gradually merge into the ciliated glandular texture of the cavity. A little” further back the glandular substance becomes confined to the inner surface of the body-wall (though actually not closely applied thereto), leaving a large central space. In full perfection the chamber and glandular texture are seen in Plate XIII. fig. 6. The minute structure of the wall of this portion of the digestive cavity is similar to that of the ciliated cesophageal region in Omma- toplea, being composed of a thick layer of granular gland-cells and basement- substance, raised here and there into prominent ruge, and richly ciliated on the E Op. tit. pe le + Op. cit. taf. vii. fig. 5. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 385 inner surface. The turning in of the borders of the region is an interesting cir- cumstance, and demonstrates the distinction between it and the succeeding region, even from the earliest condition of the worm, without for the moment regarding the other cardinal facts relating to the peculiar arrangement of the circulating channels on the walls, the thicker texture of the latter, and the total absence of the gregariniform parasites. Moreover, it is only in this region that the ciliated character of the digestive cavity is apparent, probably because the greater firmness of the walls keeps the chamber somewhat distended. In certain lateral views of the animal, the distinction between the cesophageal and the suc- ceeding region is very evident. Though in the various drawings of transverse sections of Borlasia this chamber (cesophageal) is seen in its normal condition, it is well to remember that it undergoes very marked alterations in size, according to the condition of the proboscidian cavity in its vicinity, for the proboscis most readily distends the latter in this region, and bulges it so much that the walls of the former are pressed flatly together at the ventral surface. In the contracted condition of the worm, as after immersion in spirit, the communication between the cesopha- geal and the succeeding portion of the digestive system is almost obliterated by firm closure. The second or great division of the alimentary tube extends from the point of inflection previously mentioned to the posterior end of the worm, as a ciliated chamber with glandular and sacculated walls; but the cilia, with the exception of a streak near the tip of the tail, are only favourably seen on making a trans- verse section of the living animal, though they are actually longer and more active than those on the cuticular surface. In pale species, such as Borlasia lactea, Mont. MS., the digestive canal is very distinctly divided, for the posterior region is not only more opaque than the oesophageal, on account of the greater development of its glandular elements, but its borders are crenate from the sac- culations. The posterior aperture or anus is situated slightly in front of the tip of the tail, and is well guarded by the muscular structures surrounding it, as may be observed before granular matter escapes, for it requires the impulse of numerous waves of fluid before yielding under pressure. In some favourable specimens masses of cells and debris may be seen revolving within the dilated anus before extrusion. In various examples a distinct anal papilla (Plate XII. fig. 7), furnished with a tuft of longer cilia, is seen projecting posteriorly. In transverse section (Plate XII. fig. 3), the encroachment made on the cavity by the ovaries, during the period of their activity, is well shown, and also the gregariniform parasites, which often occur so abundantly in these worms. The parasites were first alluded to and figured by Dr G. Jonnston,* afterwards * Magaz. Zool. and Botany, vol. i. p. 584, pl. xviii. fig. 1 **. VOL. XXV. PART II. Bea 386 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE - by Frey and Leuckart,* Koiiker,+ Max Scauttze,{ Van BEeNnepEN,§ KErer- STEIN,|| and lately they and certain ova in this species by the author; so that the subject need not be further alluded to here, save to observe that they are strictly confined to the region behind the streaked cesophageal division of the digestive tract, that they hang freely into the cavity, and that the ova mentioned in the last paper probably may not be connected with this particular species of parasite. The occurrence of these ova, however, in specimens so widely different in habitat as St Andrews and South Devon, shows that there is some constancy in their presence. ‘The parasites occur in young specimens scarcely a quarter of — an inch in length, and vary in size. When the animal has regained its condition in its native haunts after spawning, the granular cells of the digestive chamber become largely developed, so that in transverse section the body is rounder, and the entire central region filled up by the mass, with the exception of an irregular fissure in the centre; whereas considerable atrophy of these elements occurs during long confinement, or the exigencies of reproduction. Towards the poste- rior end of the worm, the tract becomes considerably diminished in size, and, in the living animal, more evidently ciliated when viewed from above. The minute structure of the wall of the cavity (Plate XII. fig. 10) has a considerable resem- blance under pressure to that of the ciliated cesophageal region in Ommatoplea, having a basement-substance, in which are imbedded a vast array of granular olands, and with the inner surface richly ciliated. The contents of the glands (Plate XIII. fig. 7) consist of granular cells and globules, which readily escape from the free border of the organ, and are often ejected per anum. In Cephalothrizx the lips of the oral aperture are frequently pouted out- wards in the form of a short funnel, so that the animal resembles an elongated © Distoma, and the ciliation of the entire canal is more apparent than in Bor- lasia. Some circular fibres around the mouth are evident in this genus, and probably exist also in Borlasia. The general arrangement in transverse section is seen in fig. 3, Plate X., and the same gregariniform parasites before mentioned, — as well as an Opalina, likewise occur. In minute structure, the first or ceso- phageal portion has a much more lax and cellular aspect than the succeeding densely granular region; and from the translucency of the animal, the distinc- tions in this respect are more exaggerated than in Borlasia. In one specimen sent from St Andrews in April, the digestive chamber was coloured of a fine pea- green instead of the usual pale pinkish hue—a state due to the uniform tinting of the cellular elements. - It may now be proper to refer to the presence of another parasitic animal which was found in several specimens of Borlasia olivacea from St Andrews in * Beitrage zur Kenntniss, &c. + Zeitsch. f. wiss. Zool. bd. i. pp. 1 and 2, taf. i. fig 4. t Beitraige zur Naturges. Turb., &c. § Op. cit. \|Op. cit. p. 70. { Quart. Jour. Micros. Se. &c., April 1867. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 387 November. The animals infested by this parasite present a remarkable aspect, the posterior half of the dorsum appearing under the lens to be honey-combed and tracked by pale channels in every direction, as if a microscopic Zomicus typographus had been at work in their bodies. Under the microscope the vast net-work of pale channels have a minutely granular appearance, and numerous small, opaque, ovoid granular bodies likewise occurred. Upon rupturing the body of the worm, a large number of the peculiar structures (Plate XII. fig. 4) slid out of their investments, and sailed about in the surrounding water, generally, though not always, with the upper end in the figure first. They differed totally from the gregarinz above-mentioned, many of which, however, were present in the same hosts. Externally, they are coated with long cilia, whose activity in the free state is of somewhat short duration, for after a time the animals remain quiet, and they drop off. The body is distinctly segmented, and tapers slightly towards the posterior end; while the surface is marked by very fine longitudinal lines, as in Opalina, though in a much more minute degree. Anteriorly, there is a conical portion (a), composed of three rather indistinctly-marked segments. Two well-marked annuli (6) succeed, the posterior part of the last being nar- rowed, so as to cause an evident constriction of the body-wall in many positions. Behind these are six nearly equal divisions (c), each of which often appears double, that is, has a broad anterior and a narrow posterior belt, as indicated in the figure. The posterior region (d) consisted of three indistinct segments. The body was minutely granular throughout, and an internal cavity was apparent from the fourth segment to the last; commencing in the former by a rounded end, and terminating just within the border of the latter. No aperture was observed at either end. The opaque ovoid granular bodies (Plate XII. fig. 6), scattered pro- fusely throughout the infected portions of the Borlasian, were evidently young stages in the development of this species, and they too were ciliated. Upon subject- ing them to gentle pressure (Plate XII. fig. 5), transverse segmentation was appa- rent, the number of segments varying according to the degree of advancement. The parasites were very delicate structures; and in the free state soon broke up into cells and granules, after discarding their cilia as above-mentioned. Transverse section of the affected animals showed that they occurred both in the skin and in walls of the digestive tract; their ravages in the pigmentary layer of the former tissue causing the curious appearances which led to their detection. Itis a some- what difficult point to determine whether the skin, muscles of the body-wall, and the digestive canal, constitute the common area of this creature’s depredations ; or if it was piercing the former on its way to the surface, or again passing towards the alimentary cavity to be voided per anum. The differently seg- mented condition of the full-grown specimens, and their internal structure, exhibit a higher type of organisation than the ordinary Opalina and Pachyder- mon, which again are more elevated than the Gregarinee. ‘The ease with which 388 DR W. CARMICHAEL MINTOSH ON TIIE STRUCTURE OF THE so soft and delicate an organism bores through and tunnels the tissues of its host is wonderful. * The Borlasize readily feed upon fragments of mussel (as first noticed by Sir J- G. DALYELL). When a specimen has come in contact with a suitable portion, the mouth is enormously dilated, and the bolus, even though of considerable size, rapidly swallowed. The snout of the animal during this process is curved back- wards, doubtless to afford assistance by its tactile properties, but there is no extrusion of the proboscis. They also feed on dead specimens of Nereis pelagica, ejecting the bristles and indigestible portions afterwards per anum. A specimen measuring about three inches in length boldly seized the head of a large Nephthys, upwards of four inches long, and partially ingulfed its prey. The danger of putting rare specimens, such as Micrure, together in a vessel is great, as the larger generally makes a meal of the smaller. While thus predatory and vora- cious, they are in turn tolerant of much injury; for instance, one specimen had its head and anterior portion seized and held in the stomach of a Sagartia troglo- dytes for ten minutes, yet the worm subsequently got free, and crawled about as if nothing had happened. After being put in spirit, they occasionally turn their bodies inside out, and expose the inner surface of the digestive cavity. In Cepha- lothrix the contents of the latter are easily observed, and often consist of frag- ments of its fellows of the same species. EHRENBERG and DE QUATREFAGES considered the mouth to be the genital orifice, the former observing that a large quantity of mucus was discharged therefrom. Mr H. Goopsir} thought the canal common to the respiratory, diges- tive, and generative systems. ‘ In Serpentaria,” says he, “ it acts almost as an organ of digestion, while in Nemertes there is a trumpet-shaped exsertile pro- boscis, which, contrary to the opinion of RaTHKE and other naturalists, and according to the opinion already expressed by EHRENBERG, is the intestinal canal.” He agreed with EHRENBERG in supposing that the ova escaped into this chamber. His views were rather erroneous, such as supposing that the first region of these worms was composed of a single annulus; but the succeeding or terminal of many, each about an 4th of an inch in length; moreover, that each of the separated annuli contained all the elements of the perfect or original animal, viz.,a male and female generative apparatus, the cavity common to the generative, digestive, and respiratory functions, and a small dorsal vessel analogous to the intestinal canal of Nemertes. Serpentaria, therefore, he explains, ‘‘is a com- * Since the foregoing was communicated to the Society, I find that Prof. KErerstEIN, in a recent paper, gives a drawing of a parasite very similar to the above, but he does not say more about it than simply mention, under the explanation of the plate, that it is an enigmatical body from the stomach of a Leptoplana tremellaris. Beitrage zur Anat. u Entwicklungeschichte Seeplanarien von St. Malo (Der K. Gesellsch. der Wissensch. vorgel. am 4. Januar 1868), p. 37, taf. ii. fig. 8. It is probable that the same parasite, as in the case of the Gregarine, may have a wide distribution. + Annals Nat. Hist. xv. 1845. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 3389 posite animal, each perfect individual consisting of numerous and apparently still unformed or imperfectly formed individuals.” Modern researches do not support any of these suppositions. Of the other British zoologists who have examined these animals, Dr Witt1ams,* while admitting the digestive nature of this chamber, misinterpreted its true relations. He considered the organ as a closed sac filled with a milky fluid, and having many diverticula, into which the nutritive matter passed by exudation from the proboscis. He appears thus to have drawn up his description from an Ommatoplean, which possessed no large slit leading into the chamber. He denied the existence of the proper anus. While thus deviating from the true structure of the parts, he was correct at least in viewing the chamber as digestive, and quite independent of the generative system placed to its exterior. Sir J. G. DALYELL,} whose untiring scrutiny of the habits of such animals is worthy of all praise, saw a Borlasian (his Gordius gesserensis) feeding by the ventral slit, which he therefore correctly termed the mouth. Dr JoHNsToN, in his Catalogue, observes—“ There is another and much larger aperture in front, behind and underneath the head. Long mistaken for the mouth, this has been usually described of late as genital, but the orifice is doubtful.” M. Van BENEDEN does not demonstrate that the so-called biliary elements are simply constituents of the wall of the digestive cavity, and not special czeca attached to the sides of the canal. In Cerebratulus tenia (his C. Grstedii) he states that the digestive canal is divided into three compart- ments—the first short, and corresponding to the cesophagus ; the second twice or thrice the length of the former, and representing the stomach; the third extend- ing to the posterior extremity of the worm and constricted at regular intervals, and corresponding to the intestine. I have not as yet noticed this in the British examples, which agree with the typical Borlasian form in the structure of the chamber, although the external aperture or mouth is somewhat smaller. Prof. KEFERSTEIN’S} description of the cavity as applied to Borlasia, though brief, is good, and his criticism of VaN BENEDEN’S view, in regard to the “liver” in the same group, fair. Nervous System.—The cerebral ganglia or central organs form two large and conspicuous pale red masses situated a short distance behind the snout of the worm (Plate X. fig.1). They differ in shape, as seen under slight pressure, from the same organs in Ommatoplea, each half being narrower and more elongated, so as to cause the entire arrangement to have the appearance of a horse-shoe magnet. In some specimens, instead of being more deeply tinted than the rest of the cephalic tissues, they are paler, on account of the deep red coloration of the latter; while, in others, they can scarcely be distinguished under the dense blackish-green coating of cutaneous pigment. They are surrounded by the usual * Rept. Brit. Assoc, 1851. t Powers of the Creator, vol. ii. p. 73. t Zeitsch. f. wiss. Zool. xii. p. 70. | VOL. XXV. PART II. 5G 390 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE fibres of the cephalic region, besides the sheath-proper of the ganglia. The inferior commissure, often of a deep red hue, is well marked, and placed quite at the front. The anterior curves of the ganglia do not bulge so much forwards on each side as in Ommatoplea, and thus the anterior margin of the system forms a nearly uniform transverse line. The superior commissure is smaller and less distinct; indeed, it is with difficulty seen in the living animal as a transparent preparation. Each ganglion is composed of a superior and an inferior lobe; and in minute structure of the nervous matter agrees with that in Ommatoplea. On making a transverse section through the ganglionic mass just behind the com- missure, the superior lobe is found to be more rounded than the inferior, and to communicate with its fellow of the opposite side by the superior commissure. The inferior is somewhat ovoid, and the great commissure joins it with its fellow; while posteriorly each gives off the great nerve-trunk. In front the two lobes are soldered together, but towards the posterior part a section is now and then found, which shows the posterior end of the upper lobe separated from the inferior. This severing of the end of the upper lobe is not to be confounded with the free rounded sac which lies close behind, as demonstrated in a section in which the knife has cut the left ganglion somewhat further back than the right, and so indicated this separation on that side. The presence of the trumpet- shaped mouths of the ducts of the cephalic sacs in such a section shows that these bodies are posterior and not yet reached by the instrument. Longitudinal sections of the head of the worm exhibit the positions of the ganglia and the cephalic sacs with great clearness, each of the former often presenting different appearances on the respective sides from obliquity of section, but the posterior borders are always distinctly separated from the sacs. In all the sections of the ganglia a peculiar change occurs after mounting in chloride of calcium, the oily matter of the tissue collecting in curious streaks and — circles, and apparently at some parts resisting the penetration of the fluid. Considerable difficulty is experienced in making out the anterior branches of the ganglia, from the opacity of the snout; but three or four trunks of note are occasionally apparent—two large branches superiorly, and one or two smaller beneath. Some twigs seemed to proceed in the direction of the eye-specks, but their ultimate distribution could not be traced. The great nerve-trunks (Plate X. fig. 1, n) leave the posterior end of the inferior lobe as in Ommatoplea, proceed along each side of the body, and termi- nate a little within the tip of the tail. Their calibre slightly diminishes as they course backwards; and their position is nearer the ventral than the dorsal sur- face. Branches no doubt exist, but only faint traces of such are seen in the — longitudinal sections, for the opacity of the textures in the living animal prevents: their being satisfactorily made out. The trunks are imbedded in a fibro-granular matrix of the same reddish hue, and have, in addition, the proper sheath of the — BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 391 nerve. In some pale species they are marked externally as two pinkish dorsal streaks. These trunks, as already indicated, have a very different position from the Ommatoplean nerves, being situated outside the circular muscular coat, and between it and the great longitudinal. Two muscular coats (circular and internal longitudinal) thus intervene between the nerves and the body-cavity and its con- tents, whereas in Ommatoplea the nerves are within all the muscular layers. In Meckelia annulata, the nerve-trunks are not placed as in Cerebratulus tenia, which conforms to the Borlasian type, but lie between the external circular and internal longitudinal muscular coats. This arrangement is characteristic of the Meckelian type. In Cephalothrix, the peculiarity of the ganglia (as first pointed out by Prof. KEFERSTEIN) is the advance of the almond-shaped upper lobes, so that the supe- rior commissure is quite in front of the inferior (Plate XIII. fig. 1). The lateral nerves are placed between an isolated longitudinal fasciculus and the great longi- tudinal muscular coat of the worm. In regard to the innervation of the body by the lateral trunks, it is interesting to observe the very long time during which detached fragments of the body survive in several of the long Borlasians, such as Cerebratulus teenia, DALYELL, and the great Lineus longissimus. A specimen of the latter, for instance, sent from St Andrews in September, broke into pieces on the journey; yet six months afterwards most of the fragments were alive, although the sea-water had not been changed more than once. The head and anterior portion of the worm, which scarcely measured two inches at first, had now grown a body and tail that when crawling measured at least seven inches, and of course capable of much greater extension, so that it looked like an independent animal; and this was accomplished without the aid of any food, except perhaps what it might have acquired from the fragments of its own body in the neighbourhood. Some of the latter measured about a foot in length, and all lay coiled in various ways, with the ends puckered, and in most eases fixed by a whitish cicatrix, which was firmer at one end than the other, and occasionally tapered. A similar power of regeneration was observed in the anterior end of Borlasia, Cerebratulus, Micrura, and Cephalothrix, when only a fragment of the body was left behind the mouth; and in Borlasia octoculata, a very fragile species, reproduction of a complete head upon each of the fragments ensues, if not with rapidity, at least with certainty.* One of the most: remark- able features, to continue the case of LZ. longissimus as a type, was the gradual development and elaboration of the products of the generative organs (in this case the male elements) in the headless fragments, so that when in February they were placed in clean sea-water, some gave exit to milky clouds of perfect spermatozoa. This would seem in these animals to be the main aim of such a provision, since their very length and softness, if not fragility, apparently court * Proced, Linn. Soc., June 1868. 392 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE disseverance. The formation of a complete individual, and the prolonged reten- tion of certain functions by the headless fragments, under circumstances so adverse as the above, may give us some idea of the powers of regeneration and vitality possessed by these worms in their native haunts. Mr H. Goopstr criticises M. DE QuaTREFAGES’ description of the nervous system in Serpentaria and Nemertes, and denies its existence altogether, averring that microscopically the so-called nerve-trunks showed no nervous elements at all, but were the testicles of the worms. I fear, however, this worthy naturalist depended rather upon analogy than actual observation in this case. He accounts for the nervous fibres seen by Ratuxe* (the first who correctly described the Borlasian ganglia) passing out from the cerebral ganglia to the narrow furrows on each side of the head, by supposing them to be seminal tubes on their way to — the furrows (his seminal apertures). M. DE QuaTREFAGEs confined his examina- tions chiefly to Ommatoplean ganglia. FREY and LevcKkart,+ again, confound the cephalic sacs with the posterior part of the ganglia. M. Van BeNnEDEN| makes a curious remark in regard to his Nemertes Quatrefagu—viz., that the “ collier - cesophagien”’ is peculiar for its red colour, which hue, he says, is less marked in — the other species of Nemertes. This colour, he explains, is not due, as believed — for a long time, to the nerve-ganglia, but to the vessels which surround them, and it can easily be understood how the ganglia were confounded with the nerve- trunks. Nothing akin to this has ever come under my observation, and the minute anatomy of the region is adverse to the view. M.Gruse§ had previously made the same remark in describing Nemertes purpurea, JOHNST., a species which (judging from the descriptions) seems to differ very materially from Omma- toplea purpurea, and is apparently a Borlasian form, but I have not as yet seen any British representative. Prof. KrrersTEIN is scarcely accurate in affirming that the ganglia in this group are larger than those of the Ommatopleans. In his — figure of the parts viewed from the dorsum (Taf. vii. fig. 1), the cephalic sacs are not discriminated. : Lateral Fissures.—On each side of the head in Borlasia is situated an exten- — sive fissure (Plate X. fig. 1, and Plate XII. fig. 2, 6), which commences as a shallow groove at the anterior border of the snout, and terminates, as a reddish pit, somewhat abruptly, just beyond the entrance to the cephalic sac. A distinct narrowing of the anterior region occurs behind the fissures in B. olivacea, thus — marking off the cephalic boundary. There is nothing special in the anatomy of © these fissures, for they are formed by a simple extension of the cutaneous ele- | ments superiorly and inferiorly, as represented in the transverse section (Plate | XIL. fig.2). Their entire surface is covered with very active cilia, which, as before mentioned, I have often seen cease abruptly, and again begin to play vigorously. | * Neueste Schriften, &c. + Beitrige zur Kenntniss wirb. Thiere, p. 73, taf. 1. fig. 19. t Op. cit. p. 16. § Archiv fiir Naturges. 1855, p. 150. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 393 The vapour of chloroform, if applied in sufficient quantity, causes them to cease entirely, but they again commence vibration on the partial recovery of the animal. Mr H. Goopsir thought that the fissures were the apertures of the male gener- ative system, a supposition, as mentioned, scarcely requiring refutation. Prof. KEFERSTEIN gives a very good summary of the views of previous observers, but, while agreeing with none, he advances no new interpretation of these structures. He concludes by criticising M. Van BENEDEN’s statements, with which he dis- agrees, but he has scarcely reviewed them at sufficient length. M. Van BENEDEN observes that the cephalic fissures are furnished posteriorly with a pit leading into a ciliated funnel, and that the lateral vessels when they approach the ganglia swell out into vesicules (‘‘ils se renflent la en vesicules’”’), which similate the ganglia, and which lead their contents to the exterior by the ciliated funnel just mentioned.* He considers that the central point of this apparatus lies imme- diately beneath the ganglia on each side; and he has seen, under compression, the pit of the lateral slit adjoin a large canal, which terminated exteriorly by a sort of funnel, and this led into a pouch behind the nerve-ganglia. He did not see any vibratile movement within the vesicle; and states his conviction that this apparatus is similar to that in the Trematoda and Cestoidea. Thus, as Prof. KEFERSTEIN says, he has nearly retrograded to the time of HuscuKe, who regarded these fissures as connected with the lateral nerves, which he took for canals. In his enlarged figure, however, he represents the position of the cephalic sacs fairly, but he has a large blood-vessel running to the exterior of the nerves, and extending to the tip of the snout ; this, of course, is quite at variance with a true interpretation of the structures in Borlasia. The cephalic fissures, as characteristic of the Borlasians, are absent in Aleckelia annulata, their places being supplied by two pale curved grooves on the dorsum and two continuous transverse furrows on the ventral surface of the snout. The furrows are richly ciliated. In the remarkable form from Balta, the snout is surmounted by two curious frilled processes (Plate XIV. fig. 12, 6), which termi- nate posteriorly in a long filament. Whether the latter, however, is a structure Sut generis, or only some normal constituent of the body (such as a nerve) in a peculiar position, the state of the specimen forbids our determining. Cephalic Sacs.—At the posterior end of each lateral fissure, a funnel-shaped tube (m’, Plate X. fig. 1) leads into-a large globular structure (m), often of a pinkish or reddish hue, and the apparent homologue of the cephalic sac in Omma- toplea. This globular sac lies over the origin of the great nerve-trunk on each side, and abuts so closely on the posterior prominence of the upper lobe of the ganglion, as to have led some observers into the error of supposing it only a con- tinuation of the ganglionic texture. Very carefully made preparations and examinations of the adult animal, as well as observations on the young at various * Mém. de l’Acad. Roy. des Sc. de Belgique. + Op. cit. pl. i. fig. 5. VOL. XXY. PART Il. oH 394 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE stages, remove all doubt on this subject, and show that these globular bodies belong neither to the nervous nor the circulatory system. The funnel-shaped duct (m’) is richly ciliated, and the cilia may be traced to the sac, wherein they are continued as a linear streak along its exterior border, but its general mass is not ciliated. The ciliated curve along the external border is well seen in young — specimens, but the exact superficial extent of the ciliation is difficult to deter- mine. In favourable examples the walls are observed to be furnished with finely granular cells, which have a clear and distinct nucleus. These cells are most evident on the inner and posterior curves, the outer curve being pale. The sacs project posteriorly into two large cavities (Plate XI. fig. 1, s,s) on each side of the proboscidian tunnel, and are thus laved by the circulating fluid, which rushes forwards from the walls of the digestive cavity; but there is nothing to support M. Van BENEDEN’S views* as to their continuity with the circulatory system. Their relations to the ganglia have been adverted to previously, and are well shown in some horizontal sections, where one sac has been severed considerably lower than the other. Just in front of the external border of the curved dorsal groove on the snout of J/eckelia annulata is an ovoid body apparently homolo- gous with the foregoing; but I have not yet been able to trace its anatomy, on account of the opacity of the cutaneous tissues in this animal. The functions of these bodies would seem to be excretory. Their gradual advance in position and proportional diminution in size in the developing animal would seem to indicate that their function is more important in the young than in the adult. They are quite absent in Cephalothrix. Prof. KEFERSTEIN does not enter into structural detail with regard to these organs in this group, but states they lie at the posterior end of the lateral fissures. Eyes.—These are simply masses of black pigment, arranged on the sides of the snout with greater or less regularity, and without any special optical struc-_ ture. The textures of the head and nerve-fibres themselves are so unfavourable - for observation that I have had difficulty in making out nerve-branches thereto. A more definite structure is observed in the Ommatopleans, both as regards nervous elements and complexity of organisation. Some Borlasians have no eyes (a remark, however, which does not apply to Lineus longissimus), or have them only temporarily in their young state, like the developing oysters and Terebratule ; while all the Ommatopleans possess them. It is a curious fact that in transverse sections of the snout (such as Plate X. fig. 4) considerable pigment-specks are seen towards the ventral surface. * Op. cit. p. 12.—“ En avant, ces vaisseaux aboutissent au-dessous des ganglions cérébraux, et si nous ne nous trompons, ils se renflent la en vésicules qui semblent appartenir aux ganglions mémes et qui conduisent leur contenu 4 l’extérieur par un court canal excréteur aboutissant au fond de] fossette latérale.” BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 395 Circulatory System.—Vhe circulation in Borlasia diverges considerably from that in Ommatoplea, the vessels differing in definition, size, coiling, and contents. The main vessels indeed somewhat resemble long cavities, with contractile walls, within which floats a transparent fluid with corpuscles. I have referred to this system as the circulatory, but the current is driven by the contraction of the vessels now backwards, now forwards, so that it is rather a kind of oscillation. There are three great longitudinal trunks—confining the description at pre- sent to the region behind the oesophageal division of the digestive tract—a dorsal (p) and two ventral, 7, 7 in the various transverse sections, and in Plate XIII. fig. 2. These three vessels in Borlasia were first mentioned by RatuKke.* The dorsal is a large trunk situated immediately to the outside and to the ventral surface of the proboscidian sheath; while the ventral, also considerable trunks, lie on a lower plane, and nearer the middle line than the nerves. Indeed, when the three trunks are distended in B. olivacea and B. octoculata, they occupy nearly the entire breadth of the worm under gentle pressure. These vessels are frequently swollen in various ways, sometimes being irregularly moniliform from dilatations, crenate, or simply distended as long pale spaces. The three trunks are inti- mately connected by an array of simple and rather large transverse anastomos- ing branches (y, Plate XIII. fig. 2), some of which are forked. These transverse vessels have special contractile walls, and are not mere random channels, as may be seen in the longitudinal sections of the worms (Plate XI. fig. 7, 4). They are subject to the various changes of form noted in the larger trunks. The great longitudinal trunks are further connected by meeting at the tip of the tail (Plate XIII. fig. 2). The dorsal vessel generally contracts from behind forwards, and this causes the corpuscular fluid, not only to rush to the front, but also to flow through the transverse branches into the lateral trunks. The latter propel their contents in both directions. At the posterior end of the cesopbageal division of the alimentary canal the three great vessels, for the most part, lose their individuality, and, so far as I have observed, form an elaborate meshwork of vascular spaces (w, wu, Plate X. fig. 1) around this organ, again meeting in the lacune (s, s) in front of the cavity, and bathing the bulbs of the cephalic sacs which lie therein. These lacune or chan- nels pass forwards to unite at the ganglionic commissures, and the granules of the contained fluid may be seen rushing forwards in the one and backwards in the other. In addition to the smaller meshes surrounding the cesophageal region, two larger spaces are seen on each side of the proboscidian sheath in transverse section, which may be held as the continuations of the dorsal vessel. The reticula- tions formed by this system are seen under favourable conditions in the living animal (¢.g., as represented in Plate X. fig. 1), as well as in numerous transverse * Neueste Schriften, &e. Danzig, 1842. 396 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE sections. I have not been able to see any blood-vessel in the tissues of the head in Borlasia. A distended pale portion may often be noticed in the central line between the snout and the ganglionic commissures, as if the animal had gulped water by the aperture for the proboscis, so as to distend the channel, but this has no connection with the circulatory system. Transverse section demonstrates that there is no other channel in the snout in front of the ganglia than that just referred to. In long pale species, such as Lineus lactea,* Mont. MS., the intervention of an elongated region between the posterior end of the ganglia and the anterior border of the cesophageal region renders a special modification of the circulatory channels necessary. Accordingly, it is found that after the fluid collects in the spaces in front of the alimentary organ, it is conveyed by two long channels for- wards to the ganglia, where the same ending occurs as in the other species. These channels seem to be simple elongations of the ordinary lacune, and are represented in transverse section in Plate XII. fig. 8; thus forming an inter- mediate link between Borlasia olivacea and the still more elongated post- ganglionic region in Cephalothriz. In Meckelia annulata there are two great longitudinal vascular trunks (Plate XIV. fig. 11, 7), which lie within the inner or longitudinal muscular coat opposite the nerve-trunks, and they are peculiar on account of their large size and the granular nature of their contained fluid. They form a coarse network in the cesophageal region as in Borlasia, and are continued forwards just within the border of the snout to meet in a vascular arch. Whatever special function the cesophageal region may perform in regard to — digestion, it is clear that the circulatory fluid bathing its outer wall is placed in | a favourable condition for oxygenation, as the mouth now and then must give entrance and exit to sea-water, under the influence of the powerful ciliary cur- rents caused by the entire surface of this division. Besides, it is evident that during the varied actions of the oral aperture (e.g., during feeding) the circula- tion would sometimes be much interfered with if such a rete mirabile did not exist. In Cephalothrix I can only make out two great longitudinal vessels, whose positions are seen in the transverse section (Plate X. fig. 3, 7), viz., nearly oppo- site the nerve-trunks (), from which they are separated by the chief longitudi- — nal muscular coat. There is thus in this system also a deviation from the ordinary Borlasian type. The size of the vessels is proportionally larger than in — the latter, and their transparent fluid contains a number of minute corpuscles. — In the living animal each lateral vessel may be observed to contract regularly and swiftly from before backwards, sending a wave of fluid towards its posterior — * T am indebted to Mr Parrirt for living specimens of this species from Devonshire. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 397 end, at which the contraction ceases. A reversed movement by-and-by takes place, the contents being propelled towards the snout. Anteriorly the two ves- sels course forwards by the side of the cesophageal portion of the alimentary canal without sub-division, pass along the sides of the proboscidian sheath in special cavities (v), as in Lineus lactea, in front of the former, and reach the ganglia, where they communicate. I have not actually seen a junction pos- teriorly, but analogy would lead us to suppose such to exist. There appeared to be little regularity or rhythm in the movement of the fluid in these vessels, both of which were occasionally seen contracting from before backwards at the same time. Generally, however, the contractions were alternate. In the fragmentary specimen from Balta, transverse section of the anterior region (Plate X. fig. 2) showed a large ovoid and probably vascular tube (7°) placed at the inner border of the great longitudinal muscular coat on each side, while the nerve-trunk (72) lay outside the latter. The cavity was partly filled in the prepa- ration with minute granular cells. This agrees with the arrangement in Meckelia. Both Dr G. Jonnston and Dr WILLIAMs mistook the ganglia for hearts, and the inferior commissure for a connecting vascular trunk. The blood, says the latter author, derived from the cutaneous system of capillaries, is poured by a dorsal vessel into one of the chambers of the heart (the dorsal). From the latter it is sent into the ventral cavity, and thence distributed over the integu- mentary and intestinal systems. He, moreover, says the blood is red, and always devoid of corpuscles. Such remarks are not based on correct observations. . BLANCHARD,* in his examination of Cerebratulus liguricus, describes the nervous centres as lodged in a cavity into which the vascular trunks open, and this can only refer to the post-ganglionic lacune, though such do not by any means sur- round the ganglia. I have not seen any vascular space surrounding the “trompe”’ in front of the commissures, as described and figured by this author ; and the fiuid of the proboscidian cavity could only have been seen there during the ejection of the proboscis. He shows several longitudinal vessels in Nemertes, which are not present in the British forms. I cannot agree with M. Van BENEDEN’S+ views of the circulation in Borlasia, for he describes the lateral ves- sels as swelling out into vesicles when they approach the ganglia, and their con- tents conducted to the exterior by a ciliated funnel. The erroneous nature of this supposition has already been noticed under ‘ Cephalic sacs.’ He also men- tions that each lateral trunk posteriorly communicates only with that of the opposite side, and concludes doubtfully thus:—“Le long des parois du tube digestif, on voit en outre plusieurs vaisseaux, mais dont les aboutissants sont difficiles a décourvir.’”’ Another deviation from accuracy is apparent from his remark (under Cerebratulus cerstedii) that “En arriére un gros vaisseau treés- * Ann. des Sc. Nat. 3™¢ ser, tom viii, pl. ix. fig. 5. + Op. cit. p. 12, &e. VoL. XXV. PART II. 51 398 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE large, 4 parois trés-contractiles, qui parait et disparait par intervalles, occupe la ligne médiane et semble s’ouvrir au bout de la queue.” A reference to his figure* and its explanation at once makes it apparent that he has mistaken the proboscidian sheath for a blood-vessel. Prof. KEFERSTETN again does not enter into detail with regard to the circulation in Borlasia, and his figures and descriptions apply to Ommatoplea, with two exceptions,} which represent transverse sections of Cerebratulus marginatus. In that through the anterior part of the body five circular vessels at least are transversely cut in the meshes round the cesophageal region, and, moreover, they are connected together by a pink band in the figure, as if from a connecting trunk. I fear the author has been misled by the carmine ~ used in the preparation, for in the British examples of Cerebratulus a true Borlasian arrangement is found. ; Generation and Development.—The sexes are separate, as in Ommatoplea, and the ova and spermatozoa developed in their respective sacs between the inner muscular layer of the body and the digestive cavity. The glandular ele- ments in the walls of the latter indeed undergo a certain amount of atrophy during the period of reproductive perfection, as observed in the transverse — section through a specimen just before spawning (Plate XII. fig. 3). In Borlasia olivacea the spermatozoa (Plate X. fig. 9) have the aspect of slender rods, with a scarcely perceptible enlargement at the end from which the filiform tail proceeds. When a mass is taken from a living animal, they often adhere to a point by one end, and, spreading around this in a radiating manner, lash the surrounding water with their tails. The spermatozoa of B. octoculata (Plate XI. fig. 5) are more minute than the former, and somewhat resemble an awl-handle in shape, with the filament projecting from the butt, which is thus frequently agitated, while the tapered end is comparatively still. In Lineus longissimus the outline of the body of the spermatozoon (Plate XI. fig. 4) is less regular than in Borlasia, and it seems slightly crenated or moniliform. A very long filament proceeds from the body at the larger end. In Micrura fasciolata there is likewise a slight constriction in the middle of the spermatozoon, and the tail proceeds from the — larger extremity. The ova are few and large in B. olivacea, smaller and more numerous in B. octoculata. Both ova and spermatozoa escape by pores on each side a little above the nerve-trunks, these apertures being often indicated by pale specks along the sides of the worm, and occasionally, as in Meckelia annulata, they are boldly marked by white spots. In this species also the rudimentary condi- tion of the generative organs may be seen in transverse section as a series of small globular or pyriform sacs, filled with granules and globules, and situated above the lateral vessel on each side of the body. Thus far there is a certain * Op. cit. pl. ii. fig. 4. + Zeitsch. f w. Zool. xu taf. vii. figs. 3 and 4. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 399 resemblance between Ommatoplea and Borlasia (to take, for example, B. olwvacea), but the moment the ova pass from the animal, and the condition in which they do so, a decided divergence occurs. Instead of being deposited as free circular bodies, the products are here placed within a flask-shaped membrane, with one end narrowed to a fine point, and the whole enclosed in a tough covering of gelatinous mucus, which is fixed either to stone or glass, in the form of a bulky cord, as noticed by GErstepD.* When a female specimen is about to deposit ova, she seeks the water-line, or a space above it, and quietly settles along the vessel. By-and-by a copious exudation of tough translucent mucus takes place, which envelopes the entire animal. In this mucus, which when fresh is crowded with small ovoid granular corpuscles from the cutis, the ova are deposited in the flask- shaped capsules, each of the latter corresponding to an ovary, and containing all its ova, viz., from one to seven. Hence, by the nature of the parts, the ova are arranged in a somewhat irregular double row along each side, the extremities of the cord—corresponding on the one hand to the head and cesophageal portion of the digestive tract, and on the other to the extreme tip of the tail—being free from ova. In some instances, the posterior end of the animal was curiously frilled and grooved on the ventral surface during deposition. When newly depo- posited the mucus is softer and less tenacious than it afterwards becomes, and the same may be said of the membranous flasks. ‘The solidifying of the mucus is analogous to what takes place, under similar circumstances, in the egg-capsules of certain mollusca, e.g., Bucconum undatum and others. If one end of the animal be disturbed from its original site on the glass before the ova are all deposited, four rows will be found there instead of two, for sufficiently obvious reasons. The ova of B. olivacea are of two shades, viz., white and pale- brownish ; and though the dark-greenish examples often lay white eggs, they do not seem to do so always. Each ovum measures from th to ~oth of an inch in diameter. The deposition takes place in January and February in those long confined; but some specimens sent from the St Andrews rocks towards the end of April likewise deposited ova, so that some latitude in regard to date is necessary. The American examples deposited their ova in January, and those from Cuxhaven in March; but the Nemeries communis of M. VAN BENEDEN only did so in September. It is often observed that impurity of the water causes recently captured animals to lay their ova rapidly, as if from a kind of abortion. The development of the ova in Borlasia obscura—a species apparently identi- eal with our B. olivacea—has been described by E. Desor} up to the period of the extrusion of the young from the capsules; and Max ScHu.rze{ and Kroun§ have also investigated the subject, especially the former, so that I shall only dwell on such points as have not been elucidated. Our British forms seem to * Entwurf einer Syst., &c., p. 25. t Boston Jour. Nat. Hist. vol. vi. No. 1, 1850. t Zeitch. fiir wiss. Zool. bd. iv. 1853, § Archiv fiir Anat. 1858. 400 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE offer great facilities for such investigations, and I have had no difficulty in rearing the Borlasiz at a long distance from the sea. The ova on deposition in the flask-shaped capsules are uniformly granular and opaque ; and when broken up, are seen to be composed of a granular oily matter, which forms streaks and rounded masses, and is not cellular, as described by E. Desor. The clear, semi-transparent spot mentioned by the latter as occurring in the ova after deposition is seldom visible, though the germinal vesicle (a) and dot (>) are apparent enough in the centre of a pale oleaginous space, while they are yet in the body of the female (Plate XIII. fig. 8). The cleavage of the vitellus generally commences on the second day, when in some it is found divided into two and in others into four parts. As first pointed out _ by Max Scuutrze, Desor committed an error when he stated that the irregularity of the divisions of the vitellus distinguished this species from other animals. The divisions proceed regularly and somewhat rapidly; for ova which presented four lobes at 9 a.m. were found at 1 p.m. broken up into a number of rounded masses, so that the ovum had a nodulated or mulberry-aspect. No clear spot was observed in the centre of these secondary masses. During the next four or five days the changes which ensue in the ova consist chiefly of sub-divisions of the vitellus, which daily become finer. There is now a pale spot in the ovum, and a few free granules and cells in the flask, as noticed by DEsor. The ova eradually become smoother in the outline from sub-division of the vitellus, and then only a few nodules appear here and there on the otherwise even cir- cumferences. EK. DEsor found the ova ciliated on the twelfth and fourteenth days, Max ScuvuLrTze on the eleventh and twelfth, and I have struck the average amongst the British examples on the latter date. The ova, again, which had been left entirely above the water-line did not develop so quickly. At first the ciliation does not cause the mass to revolve, but subsequently this motion takes place with vigour. They continue in this condition for about a month, and then a further change ensues in the contents of the flasks (Plate XIII. fig. 4); and the latter drawing will explain E. Drsor’s discovery, as well as enable us to correct a slight inaccuracy into which he has fallen. The opaque ciliated mass previously noticed by-and-by shows a double outline under pressure, caused by the develop- ~ ment of the young Borlasian within the ciliated coating; indeed, at an advanced stage, as in the middle of the flask represented in Plate XIII. fig. 4, the embryo seems as if shrouded in a layer of fatty cells and oil-globules (b), within which it distinctly moves. In such a condition the animal readily escapes from its invest- ment, and at the upper part of the same flask a free example (a) is seen. E. DESoR commits an error in his excellent description, when he states that the cells in the interior of the embryo are the “residue of the vitellus destined for the support of the animal ;”’ they are nothing else than the cells in the developing wall of the alimentary canal. The large dark ciliated mass (c) at the lower part of the a BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 401 flask, and the scattered cells and granules, are portions of the discarded external covering of the embryo; and it is to be observed that the cilia on this texture are, if anything, longer than those on the free young animal, though their motion is less vigorous. The “ cells’ of which this rejected covering is made up are entirely of a fatty nature (Plate XI. fig. 10)—in short, an ageregation of fatty granules, with an oil-globule or two, and capable of changing form accordingly. It is a fact that this debris after a time quite disappears from the flask, and therefore it probably acts as nourishment for the young (being swallowed by the mouth, as in the case of the embryo of Purpura lapillus) just as the yolk-sac, by a different mode, does in other animals. In escaping from the flask, the young animals, in many cases, seem to have thrust themselves along the narrow apex, dilating it and bursting through. Fora considerable time afterwards they crawl about in swarms amongst the gelatinous mucus, so that the latter has a curious aspect, being filled, in addition, with the transparent flasks from which they have escaped, and a few undeveloped ova. Moreover, it is a common prac- tice for the adult animals to crawl through these masses, and several are gene- rally coiled in proximity. The number of undeveloped ova is extremely small, showing how easy it is to rear these animals, even with very limited supplies of fresh sea-water. The foregoing development is thus much less complicated than the remark- able evolution of the Nemertean worm, called Alardus caudatus, Buscu., from Pylidium gyrans, as described by J. Mutter.* This form would seem to be allied to Sir J. Datye’s Stylus (Micrura), since it is furnished with a process poste- riorly ; and the author states that most examples are eyeless. Leuckart and PAGENSTECHER} have also recorded another species of Pylidium, and the develop- ment of the Borlasian worm therein; and they remark that the mouth of the worm is in connection with that of the Pylidium—indeed the organ in the latter opens into it—a statement verified in the same volume of the “ Archiv” by KROHN. The young Borlasians, at the stage previously mentioned, are visible to the naked eye as small elongated worms, somewhat tapered at both ends, pale, or rather translucent in front, and opaque-whitish posteriorly (Plate XIII. fig. 5), and in structure now closely approach the adult. The whole surface of the body is richly ciliated, the cilia being especially active in the cephalic fissures, and still more so at the openings of the cephalic sacs. The ganglia are indicated by a paler space (A) on each side, but their actual outline is indistinct. There are in all cases at least two well-marked eyes. The cephalic sacs (m) are large and well defined, indeed very much larger proportionally than they are in the adult: and from their present position with respect to the ganglia, demonstrate the true * Archiv fiir Anat. &c. 1854, p. 75, taf. 4. + Archiv fiir Anat. 1858. VOL. XXV. PART II. dK 402 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE - a form of the latter, as well as the error into which those authors have fallen who have confounded the sacs in the adult animals with posterior ganglionic enlarge- ments. The sacs open by their ducts at the posterior part of the cephalic fissures (b), and the ciliary action can be traced inwards from these points. The cesopha- geal division (7) of the digestive canal is distinguished by its pallor, more evident ciliation, and the well-defined border of the succeeding opaque region (j’). The proboscis (a) is marked by a central streak of papillee, and, after tapering poste- riorly, it curves forwards, and disappears. The proboscidian sheath (0) is observed — to be banded here and there anteriorly by transverse bridles ; and a clear line is occasionally visible on each side of the opaque alimentary tube, as if from circu- latory undulation. An anal papilla (Plate XII. fig. 7), with a ciliated line con- necting it with the digestive cavity, is also apparent. Shortly after reaching the degree of advancement shown in Plate XIII. fig. 5, the young Borlasians leave the gelatinous masses, and congregate at the water- line. Hundreds now perish from want of sufficient food, which in their native haunts is doubtless both abundant and suitable, while in the artificial cir- cumstances and confined vessel it is denied them. Two and a half months after- wards the young animals are found still of the same whitish hue, and possessing only two eyes, rarely with an additional pigmentary fragment. The proboscis has much increased in size; indeed, at this time it has attained a comparatively larger development than the digestive cavity, which is in active use, since the young animal is entirely dependent on its own exertions for a supply of food. The oesophageal region is very distinctly marked, though its dimensions are proportionally small when contrasted with the length of the head; at present it is not a quarter the length of the latter, whereas in the adult it is several times longer. Its space is also considerably encroached on by the large cephalic sacs. At a further stage of development the animal is much elongated, yet still possesses only two eyes. In this condition it has, doubtless, been mistaken for the representative of a different genus, and is probably that referred to by Dr JoHNSTON, under the name of Cephalothria ( Vermiculus lineatus, DALYELL). M. DE QUATREFAGES observes that the reproductive organs are digitate in Borlasia anglie, and figures them after this manner ;* but such is scarcely a cor- rect definition; neither have any cilia been detected in connection with thes structures. Indeed, he has probably mistaken the digestive canal and its saccu- lations for the reproductive system, as he mentions that out of season the ceca are filled with a fluid more or less opaline. M. Van BrENEDEN remarks that the ovisacs contain from one to a hundred ova in his Nemertes communis; bw although deposited in a membranous sheath in September, no change had ensued * Op. cit. p. 182; pli xx. fig: 8. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 403 in November. His figure of the spermatozoa of this species* is not correct, as no tails are present, and he describes them as simple rods. He makes the interest- ing statement,} that in the same animal he found the embryos in some ova covered with vibratile cilia while yet in the body of the parent, while others were only fecundated during or after deposition. The development of the curious form described by Mr Atex. Acassiz,{ which, commencing with an oral and anal circlet of cilia, gradually looses these and two short antennze which subsequently appear, and assumes the form of Nareda (GiRaRp) with two eyes, shows that the type of growth is different from that of any British species yet observed. The opening of the mouth (to all appearance) behind the ganglia points to some affinity with the Borlasians; but the absence of so important an organ as the proboscis, which very soon becomes conspicuous in all the young British forms, again leaves us in doubt as to its actual position. The young Nemertean described by Dr Buscu,§ under the name Alardus caudatus, would seem to have some relation to Stylus (Micrura), since_it possesses a very distinct tail. The apparent segmen- tation of the latter, however, is characteristic. In Cephalothria (Astemma) the ova and spermatozoa are developed in a dense series of sacs (that give the animal a transversely barred aspect), which com- mence a short distance behind the mouth and continue nearly to the tip of the tail. The males are distinguished by their somewhat paler aspect when their reproduc- tive organs are fully developed, viz., towards the end of January and during the subsequent spring months. The spermatozoa (Plate XI. fig. 3) consist of short flattened spindles with rounded instead of pointed ends, that to which the tail is attached being somewhat smaller than the other. In swimming about the two ends appear as clear dots. Though the animal is extremely elongated, the bodies or “heads” of the spermatozoa are comparatively short. The body of the female, with matured ova, presents a duskier or slightly fawn-coloured aspect, the ova, under slight pressure in the living animal, being arranged in dense transverse rows in each ovary. The total number of ova produced by a single female must be very great. In transverse sections they are seen to occupy a large ovoid space on each side of the alimentary canal, upwards of twenty ova—very prettily arranged in a concentric manner—occurring in a single thin slice. The space of the digestive canal in these preparations had thus assumed the form of the letter x, the walls approaching each other in the middle, but diverging superiorly and inferiorly ; while a wedge-shaped fold from the dorsum below the proboscis, and another from the ventral surface, completed the resemblance. This was the more marked, if the * Op. cit. pl. i. fig. 18. + Op. cit. p. 138.—* La vésicule germinative ayant disparu, le vitellus s’organise, et, avant la ponte, nous avons trouvé des embryons couverts de cils vibratiles.” t Ann. Nat. Hist., 3d Ser. vol. xix. 1867, pp. 208-214, pl. v. figs. 3-17. 5 § Beobacht. iiber Anat. u. Entwickelung einiger Wirbellos. Seeth. Berlin, 1851, p, 111, taf. xi. g. 8. 404 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE proboscis had been ejected. The ova are deposited from the beginning of February till June; sometimes adhering together in irregular masses by their edges ora _ little accidental mucus, at others scattered about the vessel in detached groups. In several instances, however, they were deposited in a translucent sheath of mucus. On deposition they have the aspect shown in Plate XIII. fig. 3, being of a granular structure throughout, with a clear spot and globule, and measuring about ;i,th of an inch in diameter. The ova pass rapidly through the usual stages, and on the 11th of February the embryos were revolving rapidly in the egg by aid of their cilia, and in some cases hatched. The extruded animal (Plate XIV. fig. 3), under moderate pressure, has a globular form, but assumes various shapes when freed—the ordinary one being that of an apple—the long ciliary process representing the stalk, while the body slightly tapers towards the posterior end. It revolves rapidly between the glasses. The body is opaque and granular, with the exception of the margin, which is somewhat paler, from the slight differentiation of the cutaneous textures. lxternally, it is coated with long cilia, by aid of which it executes rapid motions, and a tuft anteriorly had the form of a long whip-like process, as during the progress of the animal it appeared like a single mobile thread. The body is sometimes pitted at the origin of the latter, while a slight papilla projects at the posterior end. When fixed between the glasses the cilia were soon pitched off, and the animal resolved itself into a number of cells and granules (Plate XII. fig. 11). In two days the animal is found somewhat elongated (Plate XIV. fig. 4), and the mouth (a) becomes more evident as a strongly ciliated slit placed nearly in the centre of the body, which, — with the above-mentioned exception, is still uniformly granular. A longer tuft of cilia at the anus is now more distinctly seen. Two days later considerable increase has occurred in the length of the body (Plate XIV. fig. 5), and from the — more anterior position of the mouth, it is apparent that the chief increment has — taken place in the posterior region. The outline is now pear-shaped, the snout being much less tapered than the tail. The cutaneous textures are more distinctly marked, and the cells, with their refracting contents, very apparent; there is also — a corresponding advance in the growth of the granules of the alimentary canal, its ciliation, and the posterior sacculations. The whip-like tuft of cilia on the snout is somewhat shorter, and there now exist a few longer cilia on the side of the head, the posterior group of which (c) are evidently the precursors of the long ciliary tuft, which by-and-by appears. ‘There is as yet no trace of eye-specks. A few cylindrical papillze are observed on the snout and tail, and one or two along the sides, which processes do not seem to result from pressure. In a day or two afterwards some are furnished with one and others with two eye-specks. More- over, the tuft of cilia on the snout is gradually diminishing in length, while the lateral cilia (c) before-mentioned are becoming longer. During a period stretch- ing from March to the beginning of June, the various vessels swarmed with BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 405 successive broods of young (from different individuals), which as minute white specks darted about most actively. They did not crawl along the bottom, but, like the young of Phyllodoce and other Annelids, swam freely throughout the water after the manner of Infusorize, or danced to and fro Jike Ephemeree in the air. Externally at this further stage of advancement they have still a coating of very long cilia (Plate XIV. fig. 7), which serve as natatory organs, the tuft (c) on each side being about thrice as long as the rest, while the long anterior whip has disappeared. There are two large well-defined black eyes, no doubt provided by nature for the exigencies of the youthful state, just as the young of certain molluscs and Balani are similarly furnished. The mouth (a), the cesophageal, and succeeding region of the digestive cavity are all richly ciliated. The whole animal is soft and delicate, and none of my specimens survived this stage. We have thus in Cephalothriz a certain resemblance to the development of M. Van BENEDEN’S Polia involuta, already described (see p. 369), and the phases of the growth of the present species likewise corroborate everything that has been advanced in contradistinction to the interpretations of the Belgian author. His views in regard to the scolex and proglottis receive no support from the foregoing observations, for all the changes that occur are only the gradual and very per- ceptible shedding of certain cilia, and the general advance of organisation as shown by the differentiation of tissues and the appearance of pigment in the eye- specks. The shedding of the long anterior tuft of cilia by the young Cephalothrix has its analogue in the loss of the ciliated ring by the young Phyllodoce and others, in the casting of the temporary bristles noticed by Buscu and LeucKkart* in the young of a Nerine, and by M. DE QuaTREFAGES in the young stages of Hermella.} I think there can be no doubt that the remarkable tuft of cilia which occurs in the young Cephalothrix on each side of the snout, and which attains its full development after the long anterior tuft has ceased to be conspicuous, is con- nected homologically with the entrance to the cephalic sacs in the Ommatopleans and the fissures in the Borlasians, as well as with the ciliated ring of Phyllodoce above-mentioned. It is an embryonic type of a structure which disappears entirely in the adult form. The delicacy of the young at the period of the full development of the eye-specks is an interesting feature; but it prevented my observing their growth into perfect animals. Thus, so far as development goes, Cephalothriz is nearly allied to the Omma- topleans, especially to Tetrastemma variegatum, Polia involuta, and probably to others of the group not yet investigated; while, in the structure of its digestive system, circulatory apparatus, and the unarmed proboscis with its bridled sheath, it leans rather towards the Borlasians. Prof. KEFrEeRsTEIN in his proposed classi- * Ann. Nat. Hist. 2d ser. vol. xvi. p. 259, pl. vii. + Annales des Sc. Nat. 3d ser. tom. x. 1848. VOL. XXV. PART II. 5 L 406 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE fication of the Order* rightly places the genus in a special Family, called Gymno- cephalide, whose chief characteristics as described by him are:—Absence of cephalic fissures; brain like that of Polia, but the superior ganglion covers the inferior much less, and is advanced in front of it. He bases his statement of the relationship to the Ommatopleans, as it appears to me, on somewhat questionable grounds, for the ganglia are by no means closely allied in form and structure to those of that group. ANNELIDA. In the following part of the paper I purpose making a few remarks on the structure of some recent additions to the Annelidan fauna of Britain, as well as of a few species believed to be new to science. Many of them have been known to me for years, and, indeed, were figured and described in my MS. long before the appearance of M. pe QuaTReFacEs’s “ Annelés” and Dr A. J. MALMGREN’s ‘Catalogue of Northern Annelids;’’ but the publication of these and other recent works on the subject has occasionally anticipated me in nomenclature—a kind of loss, however, which I esteem rather lightly, since so much yet remains to be done in the minute structure of the entire class. Amphinome vagans, Lnacu(?)—Two genera have hitherto represented the British Amphinomea, viz., Huphrosyne and Spinther, and this species introduces with certainty a third. Two very minute specimens (4th of an inch in length), from St Magnus Bay, occurred in an extensive collection made last year (1867) by Mr Gwyn Jerrreys, while dredging in the Shetland seas. The segments numbered in the one twenty-three, and in the other twenty-seven. The head agrees with that of Hipponde, Aup. and Ep.,} with which genus I at first thought it most closely allied, but the feet are biramous. In these specimens also no caruncle can be observed, the head forming a smooth rounded eminence, from which a subulate antenna projects. No eyes are present. There are two antennee in front of the median at the anterior border of the snout, and two others at a distance behind. The bristles (Plate XV. fig. 1) of the superior and inferior lobes of the feet agree in structure, and consist (1) of a somewhat stout kind (6, c), which has serrations on one side, and thus not observable in all positions ; and (2) of various modifications of a peculiar bifid bristle, some of which (a), especially towards the posterior end of the body, show a swollen part below the bifurcation, with a short and simple limb, and a longer process serrated on one side, while others have the serrated limb extremely elongated and tapered to a fine point, and with little or no swelling at the bifurcation. — The inferior cirrus is very small. A large specimen from the Channel Islands — ‘seems to belong to the same or a closely allied species, but there are sixty-seven * Zeitsch. fiir wiss. Zool. xii. 1863. + Hist. Nat. du litt., &c. tom. ii. p. 128, pl. 11 B. fig. 10. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 407 segments and four distinct eyes. The head in the latter is pale, somewhat horse- shoe-shaped, with two short conical tentacles in front, and two longer ones a little behind—opposite the swollen part of the snout. A curved line separates the anterior from the posterior region of the head, the former being flattened, the latter more elevated, and furnished with four reddish eyes, the anterior pair of which are about twice the size of the posterior. A little behind the anterior pair a filiform tentacle projects upwards in the middle line, and close behind this a wrinkled ridge (caruncle) extends to the anterior border of the third bristled segment. The sulci between the first three bristled segments are somewhat less marked, and the slope of the bristles more oblique, but the rest are very distinctly separated; indeed, the body has a somewhat moniliform aspect. The branchial tuft springs from a point behind, and rather below the dorsal fascicle, and consists of about four pale finger-like processes, which arise from a common basis ; they commence on the second segment, and continue almost to the tip of the tail. In this example, the swelling below the tip of the bristles, corresponding to fig. 1, a, was not very evident, and the serrations of the extremely elongated distal por- tion widely separated ; and, indeed, I was at one time disposed to regard the animal as specifically different. The bristles of these animals are extremely fragile, and the majority are broken during the efforts to decipher their structure. The crop commences at the posterior third of the fourth bristled segment, and extends to the posterior border of the sixth; it is truncated anteriorly and pos- teriorly, and swollen in the middle. The commencement is marked by two brownish specks. The published descriptions of the species of Amphinome make it somewhat difficult to determine them with accuracy, and I am by no means certain at present that Savicny refers to this form under the above-mentioned name. I had provisionally termed the two minute eyeless specimens from the _ Shetlands Hipponoe jefreysu,* but I think they may more correctly be grouped with the example last described. The Hurythoe borealis of Sars} is a very closely allied form. Letmonice jilicornis, Kinsere.{—Three British species of the family Aphro- ditaceze are recorded in the Catalogue of the British Museum, and one since the publication of the latter by Dr Batrp; but I agree with Dr MALMGREN in con- sidering A. borealis, JounsTon, only the young of A. aculeata, and the Lwtma- tonice kinbergt, described by Dr Batrp,§ as L. filicornis of KinBERG,|| a species which abounds on our north-western and northern shores, just as Hermione hystrix does on our southern coasts. KrinpereG does not show the recurved fang towards the extremity of the ventral bristles—an error probably due to the inaccuracy of his artist. The dorsal bristles are very large and powerful, and * Ann. Nat. Hist. Oct. 1868. + Christ, vid. Selsk. Forh. 1861, p. 56. ¢ Kongliga svenska Fregatten Eugen., &c,, 1851-1853, p. 7, taf. iii. fig. 7. § Dr Bairp is now of the same opinion. || Proc. Linnean Soe. vol. viii. p. 180. 408 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE taper towards both ends, especially the terminal. The recurved fangs of the latter are not always readily seen until the bristle is turned round. Lepidonotus pellucidus, Euters.*—Amongst the Lepidonoti dredged in Loch- — maddy, North Uist, in 1865, this peculiar species occurred. The head has two rounded and prominent lobes in front, that do not form the acute angles seen in the common species. The eyes of each side are placed close together, while the pairs are widely separated, and situated far back. Exuers’s description and figures of the bristles need improvement. These structures throughout are pale and translucent, the superior fascicle of the foot having a series of slightly curved bristles (Plate XV. fig. 2, a), whose rows of secondary spines (about eight in number) are very wide apart inferiorly, while the tip of the bristle is notched, as if from a minute claw. Those of the ventral bundle are equally peculiar (0, same figure), having a short but well-marked claw at the tip, with a small spike adjoin- ing. The terminal portion is somewhat flattened, and marked by oblique rows of secondary spikes, while it gradually widens inferiorly, and terminates in an abruptly dilated shoulder, furnished with a projecting series of secondary pro- cesses. The latter appeared to be similar to the spikes of the dorsal bristles, and the intervening angle was filled with debris. Dr Ex ters does not discriminate the bifid nature of the inferior bristles.+ Polynée longisetis, GRuBE,{ a species described as British by Mr E. Ray LANKESTER,§ under the name of Harmothée malmgreni, though unfortunately, owing to the engraver, its bristles have not been figured with anything like recognisable accuracy, has been found after storms at St Andrews. It is distinguished at once from ZL. cirratus (Harmothée imbricata) by the paler and more resplendent bristles which flank its sides, by the structure and ereater pellucidity of its scales, and by the structure of its dorsal cirri. The dorsal bristles are almost identical, except in length, with those of H. imbricata ; while the ventral, though formed on the same plan, characteris- — tically exceed those of the latter in the length of the terminal spiked portion (Plate XV. fig. 3). The dorsal cirri (Plate XV. fig. 3, a) present scarcely any swelling below the tip, are pale throughout, and have only a few pale warts, so that the entire organ is much smoother than in the common species. P. longisetis exhibits a very close affinity with Lenilla glabra, MALMGREN. || Halosydna gelatinosa, Sars, a species first found on the shores of Norway by — this celebrated naturalist, and afterwards by Kinsere** and Loven,}+ is abundant * Die Borstenwiirmer, &c, p. 105, taf. ii. fig. 5, 7-13, and taf. iv. fig. 1-3. + M. Craparnps probably refers 1o this species (in his recent work ‘‘ Les Annélides Chétopodes — du Golfe de Naples”), under the name of Hermadion fragile. § Archiv fiir Naturges. xxix. 1863. t Linnean Trans. vol. xxv. p. 375, tab, 51, fig, 28. || Nordiska Hafs-Annulater, 1865, p. 73, tab. 9, fig. 5. { Beskrivelser og Jattagelser, &c. p. 62, pl. ix. fig. 25. ** Kongliga svenska Fregatten Eugenies, &c. p. 19, taf. v. fig. 26. tt} Cited by Matmeren, op. cit. p. 82. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 409 in the stomachs of cod captured off St Andrews Bay, and a few specimens also occur at low water under stones. In the scale of the living animal a series of radiating lines are observed to stretch outwards from the point of attachment. The dorsal tuft of bristles is not conspicuous, and consists of a series of delicate translucent bristles, with faint serrations at the tip. The bristles of the ventral bundle are characteristic (Plate XV. fig. 6, 6a, 66), being pale, elongated, and flattened out at the tip in varying degrees. The claw at the extremity of the broad examples is short and strong, while the inferior division is slender. The oblique transverse lines from the rows of spines are also very distinctly marked. Sthenelais dendrolepis, Cuar.* was dredged in 90 fathoms, off North Unst, Shetland, by Mr Jerrreys.—It has rather the aspect of S. boa, Jounston, than Sigalion mathilde, Aup. and Ep., but it can at once be observed that its bristles are more elongated than in either of these species. The form of the anterior scales also approaches that in S. boa, being somewhat quadrate, with one end ‘rounded; but instead of having the simple papillee which characterise the margin of the scales in the latter, the new species has peculiar pinnate processes (Plate XII. fig. 12); the whole having a tree-like figure, while the shape of the pinnze and the contour of the process in general readily distinguish it again from the pinnate appendages on the scales of S. mathilde. The process in the latter has aless robust form, its pinnee are hyaline cylindrical processes; whereas in the present species they are lanceolate and granular lamellz, with a narrowed papillary tip. The specific differences are likewise very apparent in the form of the feet and their appendages, the superior lobe being somewhat leaf-shaped or ovate, with a simple terminal process superiorly, and shorter than in S. mathilde; the inferior lobe again has the spine-papilla much more prominent than in the last-mentioned species. While the bristles of S. mathilde are proportionally more slender than in S. boa, here they exceed both in length, especially as regards the terminal process. There is a general resemblance in all the three species as regards the superior fascicle, but the inferior groups differ very characteristically. In the new species the superior bristles of the series with the jointed tips (which adjoin the short tapering-spiked forms) have the terminal portion of the shaft covered with whorls of somewhat sparse spikes (Plate XV. fig. 5), which (spikes) are much more numerous than in either of the others before mentioned; while the stouter series next these (Plate XV. fig. 4) have the same portion of the shaft closely and transversely rowed with minute spikes. The spikes on the terminal portion of the shaft of the inferior bristles are likewise more distinct, and the terminal clawed portion longer. * Les Annélides Chétopodes du Golfe de Naples, p. 99, pl. iv. fig. 4, and pl. v. fig. 1. I had described this new species under the name of 8. buskii, but the unavoidable delay in the publication of the present paper gives M. CrapareEpe’s title the priority, if, as I am inclined to think, it refers to the same species. VOL. XXV. PART Il. 5M 410 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Sthenelais limicola, EnHuters.*—Another species of Sthenelais, brought in numbers by Mr Jerrreys from the Shetland seas, seems to be identical with Dr — EHLERS’s species from Quarnero, in the Adriatic. The anterior scales are furnished, towards the outer margin, with peculiar processes, which, so far as regards our examples, are uncharacteristically represented by the German naturalist. The — processes are irregular, either simple, bifid, or divided into several pieces, and the margin of the scale is generally folded back under examination, so as to render them indistinct. In the first scale the processes are papillary and undivided. -The dorsal lobe of the foot has four or five elongated papillary processes superiorly, and a peculiar broad and curved lobule projects upwards from the inferior lobe. — The inferior bristles have their terminal clawed portions shorter than in S. mathilde, and those corresponding to figs. 4 and 5, Plate XV. (\S. dendrolepis), have only two or three spines at the terminal portion of the shaft. Dr EuLErs’s figures of the bristles are not good, whether as applied to this or any other species of Sthenelais—no compound claw, for instance, appearing on the terminal process: The animal also possesses four eyes, instead of the two mentioned by the foregoing author, the anterior pair being hidden from ordinary observation in two sulci under the squamous processes at the base of the median tentacle. This may be the Aphrodita arcta of Sir J. DaLyELL,} a species likewise brought from Shetland. Notophyllum polynoides, HirstED.—A specimen was procured from the deep- sea fishing, off St Andrews Bay. The feet are described by Dr Matmeren,{ as having the dorsal lamellz of an elliptico-subrectangular or unequally reniform shape; and in this the new or regenerated plates were somewhat reniform, espe- cially posteriorly, while the older inclined to an elliptico-subrectangular form. The new lobes are even at the edges, but the older are slightly frilled or waved— an appearance intensified by the coloured border of rich blackish-brown, which glistens in the play of light with a purplish-red iridescence. They are also characteristically marked with small groups of white grains. The structure of the bristles is represented in (Plate XV. fig. 9), and consists of a long smooth — shaft, which terminates in the swollen end and jointed tip, seen laterally in 9a, and in profilein 9. The terminal portion is finely serrated, and on each side of its base the shaft of the bristle sends off a series of short spikes, which are inclined — towards the serrated edge of the terminal division. Ophiodr omus vittatus, Sars.§—Dredged rather abundantly on a bottom of tenacious grey clay and mud in Lochmaddy, in from four to eight fathoms, and — rarely met with there under immersed stones at extreme low-water. Length, 27 inches; head small, distinct, furnished with five tentacles—two lateral on each side, and a median; the inferior or external lateral being furnished with a thick * Die Borstenwiirmer, &c. 1864, p. 120, taf. iv. fig. 4—7, and taf. v. + Pow. Creat. vol. ii. p. 170, pl. xxiv. fig. 14. t Nord. Hafs-Annulater, p. 93. § Forhandlinger i Videnskabs-Selskabet, 1861, pp, 87, 88. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 411 basal joint, anda more slender distal portion. Eyes four, the anterior pair being larger as well as more distant from each other than the posterior pair. The colour need not be referred to further here, than by simply mentioning that the dorsum is of various shades of lustrous brown, banded at intervals with belts of pale iridescent blue; while the under surface is of a deep, dark madder-brown. The body dilates behind the head, attains its maximum about the anterior third, and then tapers towards the tail. It is proportionally thicker than in its allies (such as Castalia and Psamathe), and garnished at each side with long resplendent bristle-tufts, that glance with the varied hues of the rainbow, the effect being heightened by the two long hair-like cirri that stretch beyond them. The tail terminates in two long slender styles, which are shorter, however, than the cirri of the fourth foot from behind. Through the mouth is protruded a large pro- boscis, which is unfurnished with jaws or tentacular processes; and this assumes various forms after immersion of the living animal in spirit, or when killed by the salt water being impure in any degree,—sometimes being cylindrical, or pre- senting a constriction between the swollen base and distal rim. The first four segments after the head bear modified limbs, each consisting of two long cirri. As soon as the foot attains its perfect condition, it is found to be distinctly biramous, thus at once demonstrating its distinction from all the Hesionea except Scumarna’s Cirrosyllis (Pseudosyllis, QuaTREF.) and GirsrEp’s Castalia. The superior lobe, as observed in a fine spirit-preparation, consists of the long superior cirrus, which has 4 soft articulation at its base; an inferior cirriform branch, from the upper and basal part of which spring a series of elon- gated, slender, and tapering bristles, simple throughout. After attaining some thickness, the shaft (Plate XV. fig. 8) is observed to be striated longitudinally, and to have minute transverse touches, which, however, attain a larger develop- ment in the next series. The inferior branch of the foot also consists of two por- tions, a ventral cirrus, and a bristle-bearing process, from the posterior suface of which the somewhat stiff fan of jointed bristles emerges. In such forms the bristles of the anterior feet have shorter tips, while those of the posterior feet have more elongated terminal processes. Besides, in each foot in this species the terminal pieces vary in length, the shorter occurring superiorly and inferiorly, or at the edges of the fan. When highly magnified (Plate XV. fig. 7), the claw at the tip of the terminal piece is seen to be somewhat faintly marked, from the blocking of its curvature by a process beneath, and the serratures of the edge of the process very fine, indeed scarcely distinguishable near the end. The shaft of the bristle is obliquely striated towards the articulation, longitudinally throughout the rest of its extent, except as usual at the pale diminished base (where the striz become indistinct), and marked by a close series of transverse Specks or touches. The tip of this division of the foot ends in a cirriform pro- longation. The jointed bristles of the inferior branch of the foot differ, as we 412 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE might expect, from any other allied British form, such as Psamathe fusca, Joust., and Castalia punctata, MiLu., each of which possesses similarly jointed bristles, and has the serrated terminal portion peculiarly clawed. In Psamathe the larger size, the structure of the shaft, and the coarser serratures of the terminal portion (Plate XVI. fig. 2), distinguish it from Castalia; while the latter again (Plate — XVI. fig. 1) has a much broader and proportionally longer terminal process than the present form. The distinction in this respect between the Periboea and Podarke of Dr Exters* and the latter is very apparent. Dr Gruse’s genus Oxydromus,+ with which the foregoing has certain affinities, has also an unarmed proboscis, but the feet are uniramous. I may also remark that two very distinct species, or rather genera, have been included—on the one hand, by Dr Jounsron in Britain, and on the other, by several continental authors—under the name of Psamathe punctata. Some of — the most recent foreign publications—such as the work of Dr Enuers and that of Dr Matmcren—do not sufficiently recognise the distinctions between the two. M. DE QUATREFAGES,| however, correctly separates them into genera, yet he places the synonym Castalia punctata, “ Girst.” under both. Dr Maumeren,§ while correctly including the Halimede venusta of RatTuKE || under Castalia punctata, MUutt., falls into the error of comprising Dr JonHNnsTon’s species under the same head—a slip which would not have happened if this excellent observer had seen a specimen. Dr JouHnston’s species, for which, notwithstanding Dr EnLErs’s views, the original name of Psamathe fusca4 may be retained, has a uniramous foot, with the terminal portion of the bristles characteristically marked shortly after its com-— mencement by a series of larger serrations, which gradually rise toa maximum, and similarly diminish, before arriving at the middle of the process, into fine serrations . that disappear before the clawed tip is reached (Plate XVI. fig. 2). All the bristles of the foot are not so boldly marked as this example, but in each there is a ten- dency to have ashorter terminal piece, with coarser serrations, than in those of its immediate allies, and the clawed portion at the tip is very distinctly seen, so that the bristle can be distinguished specifically at aglance. Theshaft has also coarser : transverse markings, and its distal end is somewhat less clavate than in C. punctata. The Psamathe cirrata of Prof. Kurerstern,** also described by M. CLaPaREDE,}} seems to me to be allied in the closest manner to P. fusca, if, indeed, it is not identical therewith. M. pE QuaTREFAGcEs, however,{{ considers the annelids * Die Borstenwiirmer, &c. pp. 190 and 199, taf. viii. } Troscuet’s Archiv fiir Naturges. 1855, p. 98. t Annelés, vol. ii. 1865, pp. 100-102 and 106. § Annulata Polycheta Spetsbergie, &c. 1867, p. 31. || Beitrige zur Fauna Norwegens, &c. (Nov. Act. Acad. C. L. C. Nat. Cur. &c.), p. 168, tab. vii. fig. 1-4. { Loud. Mag. Nat, Hist. vol. ix. p, 15, 1836. ** Zeitsch. fiir wiss. Zool. bd. xii. p. 107, taf. ix. figs, 32-86. tt Beobach. iiber Anat. &c. p. 55, taf. xiv. figs. 1-7. tf Op. cit. vol. ii. p. 41; BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 413 described by the two foregoing authors as distinct species (which I hardly think is the case), and classes them under the genus Kefersteimia. They also appear to me to be in all respects much more nearly allied to the Hesionea than the Syllidea. The Castalia punctata, MULL., again, has a biramous foot, whose compound bristles (Plate XVI. fig. 1) have on the whole a longer terminal portion, with finer serrations than in P. fusca. I have found it on various parts of the British coast. Autolytus pictus, KuLERS.*—I agree with Dr R. Greerr,t} who, in his remarks on Autolytus prolifer, observes that the above species (the Procerwa picia of EHLERS) is, in truth, an Autolytus. It was first found in Britain under a stone in a rock-pool at Paible, North Uist, and again, in greater numbers, at St Andrews. Its length is about an inch. The dorsum is very prettily marked by a pale central band, with numerous and rather regular transverse branches, which, uniting with a pale lateral belt on each side, cut the sepia-brown pigment- masses into oblong spaces. The latter are minutely striated under the lens by fine pale lines, and the intervals dotted by almost microscopic pale grains. The first twelve or thirteen segments are darker in hue dorsally, and the intersecting lines paler; and in some the oblongs are decidedly paler in this region. Below the pale lateral belt, and just above the feet, a dark-brown band runs from end to end, intersected only here and there opposite the pale transverse belts by narrow pale lines. A dark patch of brown is placed behind the median tentacle, and from the latter two characteristic diverging pale lines proceed backwards. The under surface is of a pale whitish or flesh colour. These markings were well seen in specimens preserved for upwards of a year in spirit. The head is rather small, and appears at first sight to be supplied with two eyes only, which are situated laterally, and somewhat in front of the great median tentacle, but a careful examination shows two clear lens-like structures on each side, the larger towards the front of the pigment-mass, and the smaller behind. There is thus some difference between our description and that of Dr Eu ers, since he shows a posterior pair of eyes considerably behind the median tentacle, and quite separated from the compound group in front. This ocular region is richly ciliated, and so is the dark pigmentary portion on the sides immediately behind. The median tentacle had its place supplied in a few instances by two of equal length, but this is simply an abnormality. The segments (upwards of 100 in number) behind the three or four anterior rings are furnished with a rather short dorsal cirrus, a few simple spines, and a fascicle of bristles (Plate XV. fig. 11), which possess a short terminal piece, with a bidentate apex. I have not seen any with a tridentate terminal portion, as shown by Dr Enters. Towards the tail there is only a single conspicuous spine in each bundle of bristles, and, finally, a larger and smaller spine form the sole appendages to the feet. Here, * Die Borstenwiirmer, &c. p. 256, taf. xi. + Archiv fiir Naturges, 1866, and Annals N. Hist. March, 1868. VOL. XXV. PART Il, ON 414 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE also, aS in many of the Syllidea, the terminal joint of the bristles undergoes various changes throughout the course of the body, being very short anteriorly, then lengthening, and again diminishing in size towards the tail. The latter is terminated by two short curved styles. Dr Enters found his specimens at Martinsica. M. pE QuaTREFAGES groups this species under his Myrianida, as M, picta.* Pionosyllis malmgreni, n. 8.—This species, dredged in the Minch, off Loch- maddy, and also procured at the latter under a littoral stone, seems to belong to Dr MALMGREN’s genus Pionosyllis,} but is distinct from the species described by — him. The elongated terminal portion of the bristles (Plate XVI. fig. 10) is pecu- liar, from the somewhat rapid widening below the bidentate apex. Faint serra- tions are observed on the terminal or articulating end of the shaft. The present is distinguished from Matmeren’s species, P. compacta, by the following par- ticulars:—A shorter terminal portion to the bristles; the absence of the elon- gated simple bristles in the non-budding animal; the greater length of the palpi; and in the much more elongated condition of the tentacula and cirri, which, moreover, are distinctly moniliform. In a specimen having a two-eyed bud posteriorly, the latter had, besides the ordinary kind, a tuft of slender — simple bristles, which did not reach beyond the others. Under the title Syl/is armillaris, Dr JouNsTON seems to have included two very distinct species, the S. armillaris, Mitu—a form occurring very abun- dantly between tide-marks, and having a single claw to the tip of the terminal piece of the bristle, and another annelid equally common in the laminarian region and deep water, whose membranous tubes occur in hundreds on the blades ~ of Laminaria saccharina, tossed on shore by storms. The latter is probably the species referred to by Mr Gosse} under the name of Syllis tubifex, though various characteristics, such as the single tooth of the proboscis, and the exact structure of the bristles, are omitted. The palpi are of considerable length, joined at the base in front of the snout, and richly ciliated, besides having in front some motionless microscopic spinules. The processes of the head and the two next segments are most distinctly moniliform, as well as longest, and the succeeding cirri show the crenations in a diminishing degree. All have the microscopic spinules. ‘The proboscis has a denticulated edge, though a third of the circum- ference is only minutely crenated, and it is furnished with a single pyramidal tooth. This region is usually thrown into prominent wrinkles. Several elon- gated papilla are present in front of the anterior edge of the proboscis—some apparently directed forwards, others backwards. The proventriculus is studded with minutely granular glands. Segments about fifty-six in number. Th bristles, which are similar to those represented in Plate XV. fig. 21, have a short: * Annelés, vol. 1. p. 63. t Annulata Polycheta, &. p. 39. + Ann, Nat. Hist. 2d ser. vol. xvi. p. 31. y BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 415 bidentate apicial portion. The colours of this species are very beautiful, and it is brilliantly phosphorescent. It appears to fall under Dr MatmcGren’s genus Eusyllis, and to be most nearly allied to, though not identical with, his #. moni- licornis. Another new British species, characterised by indistinctly articulated tentacles and cirri, four very large and unusually distinct eyes, very short bidentate apicial portions to the compound bristles, and the presence of long simple hairs, seems to be the #. blomstrandi of the same author. It was dredged in the Minch in 1865. Syllis krohnit, HALERS,* var.?—Found under a stone in a rock-pool at Paible, North Uist, in a tube of sand. In this animal every alternate dorsal cirrus is a third larger, more opaque, speckled with white dots, and, instead of passing transversely outwards like the others, curves upwards in a very graceful fashion, and is often coiled at the tip. The others are smaller, paler, also speckled with white dots, and longer than the diameter of the body. The ventral cirrus is very small. The bristles (Plate XVI. fig. 14) have a stout terminal portion, with an entire claw at the apex, and the edge is serrated. The curves of the terminal portion of the shaft are peculiar, and, in this respect, allied to MALMGREN’s Syllis borealis,} from which, however, the animal is readily distinguished by the charac- ters of the dorsal cirri, and the more elongated condition of the cephalic lobes. Unless we are to mistrust the descriptions and figures of the dorsal cirri given by Dr Enters, the British form varies very considerably from the typical one. In no state were the alternate cirri club-shaped, and those of the third and fourth segments were small and nearly equal; whereas he shows them furnished with a clavated pair, and all much more distinctly annulated than in the British example. Syllis cornuta, RatHKe.{—A Syllis, dredged off the Hebrides by Mr Jerrreys, presents certain characteristics which point to its identity with the above-men- tioned species of H. Ratuxe; and since it is doubtful (from the description at least) whether Dr Jonnston’s remarks§ apply to this animal or not, I shall briefiy allude to its structure. The body, composed of fully 100 segments, is about an inch in length, and of a highly iridescent aspect, from the close plaiting of the fine muscular fibres. All the tentacles and cirri are moniliform. Each foot has a dorsal cirrus, divided usually into twelve segments, a bristle-papilla, and a short lingulate inferior lobe. The bristle-bundle is chiefly composed of the form 0 (Plate XVI. fig 15), which at first sight resemble simple bristles, as their articu- lating processes are usually hidden amongst the others. They have, however, a most minute bidentate tip. Some (a) again have an extremely elongated ter- minal process. Dr MatmGRen’s figure|| represents the dorsal cirrus as furnished * Die Borstenwiirner, p. 234, taf. x. { Annulat. Polycheta Spetzbergie, &c. 1867. { Beitrage zur Fauna Norwegens, p. 164, taf. vii. fig. 12. § Catalogue, &. p. 192. || Annulat. Polycheta, &. p. 43, taf. vil. fig. 46 c. 416 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE with at least double the number of annulations described above, and the bristles are not characterised by the minute bidentate apex; moreover, only a linear or profile view of the elongated kind is exhibited, so that the characters required some further elucidation. A species allied to the Syllis macrocera, GruBE,* was found under a littoral stone at Lochmaddy. It had about the same number of segments as the fore- going, smooth cirri, and a very short apicial piece to the bristles. It was of a — dull orange-yellow colour, with the head about as long as broad, the central tentacle longer than the lateral, and all extending beyond the lobes. The bristles — (Plate XV. fig. 12) of the several fascicles do not vary to the same degree as in such as S. armillaris, MULL., and each has a blunt claw at the apex, with a rough edge, for the notches are irregular. The articular portion of the shaft ends bluntly. 7 Spherosyllis hystrix, CLAPAREDE.}|—Two forms of this species were found at North Uist in 1865, the one in the littoral region at Lochmaddy, and the other in the Minch. The littoral form (apparently that described by M. CLAPAREDE) was marked down the centre of its pale body by a moniliform yellow band (intestine). The body tapered anteriorly, and ended in a small snout formed by the united palpi. Eyes four, placed close together in pairs, the anterior only furnished with lenses. Segments thirty-two. The tuberculated dorsal cirri with their swollen bases were well marked. At the eleventh segment a series of flask- shaped bodies (buds)—two in each segment—commenced, and continued almost to the tail. These bodies were of a pale rose-pink hue, with a reddish spot in the centre, where the oil-globules were massed. They were nearly equal in size throughout, had the usual processes at the ends, and were all thrown off when the animal was placed in spirit. The tail terminated in two swollen cirri. The bristle-bearing papillee were distinctly tuberculated, and furnished throughout — with compound bristles (Plate XV. fig. 10, 0), which had a delicate and rather elongated apicial portion with a simple claw at the tip, and a stout simple bristle (fig. 10, a) slightly bent towards the attenuated extremity. In addition, from the ninth segment backwards nearly to the tail, each foot was provided with a tuft of long filiform bristles, which stretched far beyond the others. It seemed an inactive animal, and lay rolling on the bottom of the vessel; and the numerous — parasitic organisms on the bristles would likewise indicate a sluggish habit. In the other form (from the Minch) there were none of the last-mentioned filiform bristles, and the compound series, moreover, had a more elongated apicial piece (Plate XVI. fig. 9). The eyes also were in one specimen six, two larger ones posteriorly on each side, quite separated from each other, and two small round : * Quatrer. Annelés, vol. ii. p. 28. + Beobach, &c. p, 45, taf. xiii. figs. 36, 37, and Glanures Zootomiques, &c. p. 86, pl. vi. fig. 1. “a BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 417 specks in front. In the second specimen the two anterior eyes were absent. Segments about thirty ee ocophiilus kefersteint, n. s.—On both the eastern and western shores of North Uist a species of Prof. Gruse’s genus Staurocephalus* occurred under stones near low-water mark. Body of an orange hue, paler towards head and tail; length about an inch. Eyes two, black, situated near the posterior border of the head. The latter conical, the snout forming a somewhat blunt apex. Tentacles four, the anterior, arising from the infero-lateral region of the head, by much the largest, and having a short jointed process at the tip; the posterior pair, springing from the outer side of each eye, are annulated and much less. The large anterior pair can be coiled and twisted very prettily. The feet, instead of being furnished with a dorsal and ventral cirrus, as in most of the species, have only a small ovate dorsal and ventral process (Plate XVI. fig. 11, fand g) as their representatives, and they are scarcely more prominent than the bristle- papille ; thus it approaches S. eruceformis, Mcrn.; from which, however, it differs in the structure of the bristles and other respects. The superior fascicle of bristles consists of two series, a stout bifid kind (Plate XVI. fig. 11 6) with the long limb of the fork flattened and slightly clawed at the tip, the shorter trun- cate and rounded. The second series (fig. 11 @) are more slender, elongated, finely tapered, and definitely curved, with a limited number of slight serrations on the distal and convex side of the curve. The bristles of the inferior fascicle again are all compound and of one kind, the terminal portion being somewhat elon- gated, clawed at the tip, and without evident serrations on its edge. In regard to the length of the terminal piece, these bristles present a gradational arrange- ment, the longest terminal portions being superior, the shortest inferior. The extreme bristles of a single foot are shown in figs. 11 ¢ and 11 d; and it will be observed that the swollen terminal portion of the shaft has a few serrations. The tail is terminated by two styles of moderate length, which, like the processes of the feet, are much shorter than in S. ciliatus. Matmeren,} alludes to a drawing of a species of “ Prionognathus,” apparently different from the latter, which had been sent him by A. Borck from Norway; but he gives no description. scoticus, n. s.—At least three species of the Family Lwinbrinereide have been hitherto described as frequenting the British shores, viz., Lysidice ninetta, Aup. and Ep., Lumbrinereis tricolor, Mont., and L. latreillii, Aup. and Ep. The two latter, however, have in all probability been sometimes confounded with the L. fragilis of MULLER, a species abounding on our northern and southern coasts. A fourth and very well-marked form, which I have designated by the above name, was dredged amongst tenacious grey clay in 6 to 9 fathoms in Lochmaddy, and subsequently in several parts of the Hebridean seas by Mr Gwyn Jerrreys. The * Prionognathus, Kererstein, Zeitsch. fiir wiss. Zool. vol. xii. p. 99, taf. viii. figs. 13-19. } Annulat. Polychet. &c. 1667, p. 62. _ VOL. XXV. PART II. DO 418 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE head is of an acutely conical form, with two distinct eye-specks at its posterior border, close to the first transverse sulcus. Its body is much more slender than that of ZL. fragilis, and at once attracts notice by its characteristically marked segments, which, with the exception of a few anteriorly, assume quite a monili- form appearance. In the structure of its feet it differs from all the foregoing species. Each foot is furnished with a small branchial lobe (Plate XVI. fig. 17 a) in which a single vascular loop is observed; and thus it would appear to fall under the genus Notocirrus, ScuMARDA,* though the possession of the eyes is exceptional. The tip of a stout spine or two (0) projects beyond the foot amongst the bristles. The latter (c) have simple shafts with a broad spear-tip, which tapers to a fine point, and is faintly serrated along part of the edge. Hyalinecia sicula, QUATREF. (?)—This is a small representative of the Onu- phidide, dredged in 90 fathoms off North Unst, Shetland, by Mr Gwyn JErrreys, F.R.S. It is characterised in spirit by two parallel bands of brown which course along the lustrous dorsum from a transverse belt of the same colour immediately behind the head, and by a brown spot between each foot from the fifth backwards. There are three elongated tentacula (a median and two lateral), and two shorter in front, as in 7. tubscola, Mutt. The small black eyes are situated at the outer side of the base of the long lateral. All the tentacles have a crenated base. The antennz are similar to those of H. tubicola, or perhaps slightly longer. In the structure of the bristles of the anterior feet, however, a very diagnostic feature occurs; for instead of the large unjointed winged hooks, which are found in the latter and in Nothria conchilega, Sars, there are peculiar jointed structures (Plate XVI. fig. 3); and the bristles (fig. 3c) are slender, and furnished with a very narrow wing, whereas in both of the other species they are shaped like a Valentin’s knife. Posteriorly the jointed hooks are supplanted by two simple ones (fig. 3 0), which are stouter and slightly curved. Some of these occasionally present no wing at the tip. The bristles in this region are also shorter, and some are characteristically curved at the point. None of the peculiar brush-shaped bristles common in the two species above-mentioned occurred in this animal. No tube accompanied it; but I have since found that this species inhabits a tube com- posed of gravel and shell-fragments, and thus differs very considerably in its habitation from /7. tubicola, while the length and form of the tube also distinguish it at once from that of Nothria conchilega. The foregoing animal has certain close affinities with the Onuphis sicula of M. DE QuATREFAGES,} but differs from the description of that author in so far as the bases of the tentacles do not occupy the whole surface of the head, which in the Sicilian species is very small. The body is rounded in the latter, flattened in the British; and the bristles of the former — are said by M. DE QuATREFAGES to present a great resemblance to those of * Neue wirb. Thiere, &c. tom. 1. i. p. 114. t Annelés, vol. i. p. 352. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 419 O. tubicola, a statement at variance with the characteristics of the present species. The persistent brown stripes and spots also had not been seen by M. pr QUATREFAGES ———- jeffreysii, 0. s—This curious form, which I have been unable to identify with any known species, occurred amongst the annelids dredged by Mr JEFFREYS off the Hebrides in 1866, and again amongst those from Shetland in 1867. The length is about 13 inch, and the outline of the body somewhat fusi- form, the greatest diameter being at the anterior third. The head is small, fur- nished with two short thick tentacles, which give it a bilobed aspect, and is gene- rally retracted within the papillose anterior region in the preparations. The mouth opens on the ventral surface just behind the snout. The structure of the skin and the arrangement of the rugose annulations resemble the same parts in Travisia, Scalibregma, Eumenia, and their allies; but the animal essentially differs from each of the foregoing in having no trace of branchial filament or appendage. The tail has several elongated processes around the anus.. The ventral surface is in some cases marked by an elevated median line. There are about thirty segments, each of which has three rings. A double row of isolated papillze runs along each side from the snout to the tail, the summit of each process giving exit to a fascicle of bristles composed of two kinds, viz., numerous long, simple, hair-like bristles, tapering to a very fine point, and a shorter forked series (Plate XVI. fig. 5). The only other case in which I have up to this time met with such bristles, is in a remarkable fragment of the posterior end of a small yellow annelid from Lochmaddy, which may have some relation to Montacu’s Nereis pinnigera. The foot had an elongated unjointed dorsal, and a shorter ventral lobe, and possessed two fascicles of bristles, each of which consists of long simple bristles, and a few of the forked kind mentioned above. There is much in the foregoing description that agrees with Humenia crassa, (Hrst., but the absence of the branchial filaments is diagnostic. Dr Bartrp had received this species from the same source, and kindly sent it, with other rare and doubtful specimens, for my examination. He likewise recognised the absence of the branchie, and his preparation was labelled ‘‘ &. ebranchiata(?).” The Vermiculus crassus of DALYELL* had no bristles, and cannot easily be recognised from the description or figure. Chloreemide.—Two examples of this family have been recorded as British, viz., Trophonia plumosa and Siphonostoma uncinata, both of which abound in Scot- land. Another species of Trophonia, dredged by Mr Jerrreys in the Hebridean and Zetlandic seas, is recognised specifically by the absence of hooks in the inferior rows, and the substitution of the jointed bristles. It agrees with the T. glauca of MatMGREN ;+ but this author does not specially point out the essen- *Opxcit. p. 8, pl. x. fig. 11. + Annulat. Polychet. &c. p. 82. 420 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE tial change in regard to the inferior appendages of the feet. As contrasted with the common species, the joints or transverse markings of the bristles are much more boldly indicated in this form, especially in those from the inferior fascicles — (Plate XV. fig. 13 6). The latter bristles (inferior) are shorter than the superior, and both, as usual, have larger joints than the anterior series. A second repre- sentative of the family (Siphonostoma buski, n. s.), from the Minch, off Lochmaddy, North Uist, is remarkable for its deep-red colour throughout, a hue so unusual in the group. The two long tentacles or palpi are pale, but the branchial fila- ments are deep red. The surface of the body is furnished with minute papille, — which have the enlarged terminal portion furnished with a knob at the tip. The hooks (Plate XVI. fig. 4) differ very much from those of S. wncinata, in so far as the shaft is much longer and less robust, and the terminal claw more elongated, and abruptly curved. When the latter breaks off, it separates obliquely at a, a little above the articulation, leaving the short spike through which the dotted line passes. A bristle is shown in fig. 4a, and a fragment more highly magnified in Plate XV. fig. 13 a. Maldanide.—Two species of this family (Clymene, QuaTREF.) are mentioned as British by the authors of the Catalogue, both of which are of doubtful identity, and apparently referable to the common Clymene lumbricalis, Fasr.* (Nicomache lumbricalis, Mern.), though this is by no means certain. Mr E. R. LANKESTER, in his list of the Annelids collected at Guernsey} in 1865, notices a third species— viz., the Clymene amphistoma of Savicny. The explorations of the coast line in the Hebrides, and dredging in the surrounding seas by Mr Jerrreys and myself, as well as the cruise to the Shetland Islands last summer by the former experienced © investigator of our seas, have considerably augmented the number of the British representatives. One of the most remarkable species is the ARhodine Lovent, MautMGREN,t which combines an entire anal funnel, with a pointed snout, and has its characteristic hooks (Plate XV. fig. 16) in a double instead of a single row, thus materially differing from the others pertaining to the family. The outlines of the hooks of the British species differ insome details from those represented by Dr — MALMGREN—a discrepancy in all probably due to the inaccuracy of his artist. The Awtothea catenata, Mern.,§ was dredged recently by Mr Jerrreys, off St Magnus Bay, Shetland, in 80 to 100 fathoms. Besides having an infundibuliform anal — funnel, with alternate longer and shorter filaments, the base of the cup is marked exteriorly on the ventral surface by a continuation of the median line. There are about forty processes on the margin of the funnel, a smaller one, and sometimes two, occurring between the longer filiform divisions. The base of the funnel is surrounded © * Faun. Greenland. p. 374. + Annals Nat. Hist. May, 1866. t Nordiska Hafs-Annulater, &c. 1865, p. 189; and Annulat. Polycheta, &c. p. 99, tab. x. fig. 61 § Annulat. Polychet. p. 99, tab. x. fig, 59. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 42] by a distinct cup or fold exteriorly. The anal nipple, moreover, is roughened by small papillz. The bristles are slightly winged below the tip, and under a power of 700 diameters show minute serrations at the margins of the wings. Instead of hooks, the first bristle-bearing segment has three very stout spines gently curved at the tip, and the second and third four of the same character. They have a distinct shoulder, and the chitinous substance is strongly striated longi- tudinally. Only a small portion of the tip is usually seen beyond the skin. The hooks in the segments which immediately follow have the processes above the ereat tooth somewhat fewer (four to five), but the rest have six; and in those of the last row, in front of the anal funnel, the denticles are even more numerous towards the crown. The great tooth comes off somewhat stiffly at the base, and its upper curve is not sinuous. Dr Maumcren does not notice the peculiar spines anteriorly, but simply mentions that the hooks are fewer in those segments, and omits several characteristics described above. There are no hooks on the soft lobulated processes which succeed the last bristle-bearing segment, with its con- spicuous transverse pad. The frontal lobes form two very prominent laminee. Another species, the Praxilla preetermissa, MALMGREN,* is not uncommon on our western and northern coasts, inhabiting sandy mud at a depth varying from four to eight fathoms. Ina large specimen the teeth of the anal funnel are 27 in number. The hooks are characteristic, having about six teeth above the large fang, and a well-marked interval between the latter and the origin of the spinous tufts. The first three segments have simple and strong spines with the apex slightly curved. There are also a few shallow crenations on the margins of the cephalic lobes. A somewhat rarer species is Praxilla gracilis, Sars,+ two specimens of which appeared in the rich collection brought by Mr JEFrrRrys from the Shetlands. The hooks of the first three bristled segments differ from the others, and are spines with the apices more curved than in Axiothea, so as to resemble a hook furnished with the large fang only. A third species of Prazilla from the same region (North Unst, St Magnus Bay, and the Outer Haaf), while agreeing in several particulars with P. pretermissa, has its funnel- teeth much more filiform and distinct—in one instance 14in number. The hooks (Plate XVI. fig. 13) have the large fang short and powerful, with the spinous filaments arising close underneath, and a numerous array (seven to eight) of diminishing teeth superiorly, the whole forming a very elevated crown, indeed it is the most elevated of the series in this respect. The curves of the hook, especially the posterior, are characteristic. The bristles are also peculiar, for instead of the usual winged margin, the whole shaft is flattened out towards the translucent tip, very minutely serrated: at the edges, and tapered to a delicate point. The shaft below the flattened portion is, as usual, finely striated longitudinally. * Nordiska Hafs-Annulater, p. 191. + Fauna litt. Norveg. ii. p. 15, tab. 2, figs. 18-22. VOL. XXV. PART II. DP 422 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE This may be Matmeren’s P. artica,* but as he only says as to its characteristics that it is similar to P. pretermissa, with the exception of having six teeth on the crown of the hook, we are left quite in doubt as to his species. The anterior portion of a specimen of Clymene ebiensis, Aub. and Ep.,+ also came from Shetland. Itis recognised by the pointed snout, the somewhat swollen anterior segments, and the absence of the usual frontal flattening. The shape of the hooks (Plate XVI. fig. 12) is peculiar, the chief fang being short, and the crown somewhat flattened. There are five or six teeth above the former. The curves of the organ and its coarse strize are also characteristic. I could not find in this specimen either spines or hooks in the first three segments. The figure of the hooks given in the “‘Regne Animal” is quite unfit for identification. The species is also allied to Prof. GruBe’s Clymene leiopygos,t from Cherso, though his drawing of the hooks is widely different. The Ammochares ottonis, GRUBE,S has been found searadonslgs at St Andrews, in the stomachs of cod, at Lochmaddy under stones near low water, and dredged by Mr Jerrreys in Shetland and the Minch. The bristles are rendered hirsute by microscopic spines, as shown by Dr Matmaren;|| but the hooks of the rasp- like belts have a much more characteristic shape than represented by this author's artist, since they are figured without any shoulder, and with the curve at the back of the beak too prominent. Their exact condition is shown in Plate XV. fig. 14. There are three tufts of longer and more delicate bristles in the British specimens on the first region, instead of two, as shown by Drs Gruse and MaLMGREN; but one may have been overlooked from its minuteness. I am inclined to believe, judging from MaumGren’s paper, that the A. assimilis of Sars is the same species as the above. Dr Carrinaton of Eccles describes this species4, under the name of Ops digitata. Of the family of the Ampharetea, MALMGREN, several representatives new to Britain have occurred. One species, the A mphicteis gunneri, Sars, though unnoticed in the recent Catalogue of the British Museum, had been found by Mr Gosss at Ilfracombe, and described by him under the name of Crossostoma midus.** Dr -MatmeGrentt mentions another form, the A. swndevalli, which is characterised by — having nineteen hook-bearing processes posteriorly, whereas the former has but — fifteen; the bristles also have the winged portion striate, and the upper part of each hook widest, while in A. gunneri the corresponding region of the bristle is smooth, and the hook widest in the middle. Our common Hebridean and Zet- landic Amphicteis has certain of the characters ascribed to each of these species, * Annulat. Poly. Spetz. &. p. 100. + Cuv. Reg. An. iii. pl. xxii. fig. 4. + Archiv fiir Naturges, 1860, p. 91, taf. iv. fig. 3. § Archiv fiir Naturges. 1846, p. 163, taf. v. fig. 2 a, b, ¢. || Annulat, Polycheta, &c. tab. xi. fig. 65 D. Proc. Lit. & Phil. Soc. Manchester, 1865. ** Ann, Nat. Hist. vol. xvi. 1855, p. 310, pl. vin. figs. 7-12. ++ Nordiska Hafs-Annul. taf. xix. fig. 46 D. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 423 for the bristles agree with those of A. swndevalli in having the winged portion striate, while the hooks are widest in the middle (Plate XIV. fig. 14), and there are but fifteen hook-bearing processes posteriorly. A boreal form, not uncommon in the Scotch seas, is Ampharete artica, MALMGREN, the hooks in this species being furnished with a large number of teeth (Plate XIV. fig. 13). The former examples possess frontal bristles, but two species in Mr Jerrreys’ Hebridean and Zetlandic collections have none. The first is the Sabellides sexcirrata, Sars.* wherein the hooks have for the most part five teeth, though some of the larger have six (Plate XVI. fig. 16 @ and 16 6). Occasionally one occurs in the centre of the row with only four large teeth. The other species was in a very imperfect state, but seems to be an Amage, Marn., having about fourteen bristle-bundles on each side, somewhat club-shaped smooth tentacles, and the ventral bars very distinctly marked. The hooks (Plate XIII. fig. 10 and 10 q@) have four or five teeth, and differ so much from A. euricula, MeRN., that in all probability the animal is distinct. _ The descriptions of the British Terebelle given in the Catalogue of the British Museum stand very much in need of revision, it. being difficult, indeed, in some cases to understand what species is meant. Thus 7. conchilega could not be identified from the characteristics there noted. The 7. nebulosa of Dr Jounston is not that of Montagu, but a very different form, with 24 pairs of bristle-bundles (he says 23), and well-marked hooks, with the chief fang very long and several smaller processes above it. It may be remarked in passing, that in such a profile view all the small hooks on the crown are not seen, and hence the armature is greater than at first sight appears. This species attains a very large size on our western shores. Dr MatmGren} proposes for it the name of Amphitrite John- stont, but Sir J. Datyett had long previously called it 7. jigulus.t The true T. nebulosa is described in the Catalogue under 7. tuberculata, DALYELL, and Montacu’s name, at any rate, must stand instead of Matmcren’s recent title, T. debilis. The hook of this species has two very distinct fangs and a greatly elongated base. In addition to the twelve species mentioned in the Catalogue no less than eight new British forms require notice. In Terebella (Nicolzea) zostericola, GiRst., ‘a very abundant species, the hooks (Plate XV. fig. 15) are furnished with a single fang above the large one, and in some cases with a trace of a second. Pista eristata, MULLER, a species with a single pair of whorled branchive, was first got at Lochmaddy, and since at various parts of the coast; its hooks are characterised by the singular form represented in Plate XV. fig. 20, with three or four prongs above the chief fang, and a powerful process for the ligament at the posterior end * Fauna litt. Norveg, ii. p. 23. + Nord, Hafs-Ann, p. 377. { Pow. Creat. vol. ii. p. 191, pl. xxvii. figs. 1 and 2. 424 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE of the enlarged base. This animal is quite different from the 7. maculata of Sir J. DALYELL, which may be a species having a speckled aspect in spirit, a single pair of branchize, and hooks of the form shown in Plate XIV. fig, 15. The Grymea bairdi, Mern., a form nearly allied to Thelepus circinnatus, Fase. (Venusia punctata, Jounst.), was dredged in 90 fathoms off St Magnus Bay, Shetland, by Mr Jerrreys. It is at once distinguished from the latter by the much greater prominence of the bristle-papillze, and the greater length and lustre of the bristles themselves throughout the entire body. The hooks resemble those of the common species (7. circinnatus) very much, but the process for the liga- ment is not so near the tip of the upper curve as in the latter, and the organs are proportionally smaller. The tube is composed of fine grains of muddy sand, in- stead of the coarser and stronger structure of 7. circinnatus. Amongst the Polycirridea from the same region is a very interesting form, called by Dr Matmcren Lysilla lovenit, and distinguished by the largely dilated cephalic lobe, furnished with numerous clavated grooved tentacles along its margin, and a cluster of tangled filiform processes inferiorly at each side. The whole of the anterior dorsal region is densely tuberculated with papillee, which, from the intervening lines, assume a transverse arrangement. On the ventral surface, which is thrown in contraction into two prominent longitudinal folds with a central depression, the swollen portions are covered with somewhat larger tubercles than the dorsum, but the depressed central region forms a nearly smooth line of demarcation. There are six pairs of foot-papille in front, each — having a short tuft of simple slender bristles, whose tips in the preparation are entirely within the summit. From the same source as the latter there is also the anterior fragment of another curious and new example of the same sub-family. | Polycirrus tribullata, 0. s., which has neither bristles nor hooks. The head and tip have the usual tentacles. The body has no ventral plates, but only a raised central line. There are three pairs of well-marked circular truncated papille — (on the sixth, seventh, and eighth segments), each consisting of a raised ring externally, with an elevation in the centre. Two minute papille were visible in — front of the first flattened process, but only a trace of an elevation occurred on the lateral region of the succeeding segments, which were two-ringed. The cuticle has a minutely granular aspect. The remarkable lateral processes may — act as suckers. ‘'I'wo species, which come under Dr MauMGREN’s recently con-— stituted genus Lreutho, are not uncommon in Britain. They are distinguished from other Polycirridea by having thirteen pairs of bristle-bundles. The first, which seems closely allied to £. smitti, Mern., has hooks (Plate XV. fig. 17), — which possess only two fangs, and a very much produced and characteristically — striated basal process. The hooks of the other species (Plate XV. figs. 18 and 19) are much smaller than the foregoing, and so exactly resemble the figure by MauMGRrEN from a specimen of P. aurantiacus, GRUBE—forwarded by Prof. GRUBE- BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 425 himself—that one may be allowed to have some doubt as to the correctness of pre- vious descriptions with regard to the number of the bristle-bundles. The last of the group is T’richobranchus glacialis, a species which Dr MatMGREN has only described from aspirit-preparation.* This form was dredged in six to eight fathoms in Loch- maddy, in 1865, as well as got under a stone amongst sandy mud at low water. Length about 3ths of an inch when moderately extended. Of a general blood-red hue, or dark-red anteriorly, paler posteriorly. In shape the body is irregularly fusiform, ending anteriorly in rich red lips, with a translucent projecting collar at each side, leaving the dorsal and ventral edges free. From the dorsum, slightly posterior to the fissure thus left, spring a tangled series of tentacles, which are easily differentiated into three groups, even in the spirit-preparation. The most conspicuous, long, thick cylindrical processes, varying from four to six in number, arise distinctly behind the others, from the dorsal edge posterior to the cephalic frill, and are distinguished by a bright-red central vessel, as well as by the frequency with which they are thrown into spiral curves. They are capable of great exten- sion, and seem more especially homologous with the branchie of the Terebellee. In front of the latter series is a dense mass of short, pale-pink, thread-like ten- tacles, while a number of larger, clavated, red-streaked ones, arising from the border of the lip, are in the centre of these. The latter become grooved in con- traction. In fine specimens, the varying habit of these three groups of tentacles is very marked. Four annulations occurred on the ventral, and three on the dorsal aspect (the first not being visible after immersion in spirit), before the bristles appeared. These are ranged on fifteen prominent papille, and during life are frequently directed forwards. The arrangement of the bristles in the fascicles is peculiar, for they are grouped in pairs—a large and small one alter- | nately—to the number of six (twelve bristles). The latter (Plate XVI. fig. 8) are proportionally strong, and taper from a little above the base to a slightly bent apex. For about a third of the distal portion, there is a very narrow wing or border at each side, which has minute strie directed forwards and outwards. A row of hooks runs in a transverse manner on the ventral surface from each bristle-papilla, the anterior rows being closer to the papilla than the posterior. These hooks (Plate XVI. figs. 6 and 7) have an elongated and slightly-curved form like those of Terebellides, the head possessing a strong beak, behind which are a series of small processes or fangs. There is a distinct narrowing or neck below the head, and the hook gradually tapers from the succeeding shoulder backwards. This form of hook is confined to the somewhat prominent pads of the bristle-bearing segments. A series of elevated mamillee succeed the latter, each being furnished with a row of short hooks, which differ entirely from the foregoing (Plate XVI. fig. 7a). Each has a short and wide basal process, a * Nord. Hafs-Annulat. p. 395, tab. xxiv. fig. 65. VOL. XXV. PART II. 5Q 426 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE characteristic notch between this and the large beak, and numerous curved fangs of smaller size above the latter. The fangs above the larger beak are not simply arranged in a linear manner, but, as it were, form a spined knob, with the points curved obliquely downwards. The ventral surface of the annelid is marked by a central blood-vessel, and in spirit thrown into prominent transverse ruge. In my specimens the posterior part of the body tapered to a blunt tail, terminated by two soft papillee; but these represented the ordinary processes, and probably the tail was absent. The peritoneal bodies are of a pale-red colour, and, as usual in such animals, very large. Dr Matmeren describes the posterior hooks as bidentate, but does not figure them. If this remark is accurate, then the foregoing differs specifically. EXPLANATION OF THE PLATES. The following letters have been employed as far as possible in designating similar organs in Ommatoplea and allies. a. Proboscis A. First region of proboscis. ac. Reflection of proboscis in front of ganglia, B. Second do. do. b, Epidermis. C. Third do. do. ab, Channel in snout for proboscis, €. Globule in lateral stylet-sac. c. Cutis. 8. Stylets in do. d. Circular muscular coat. 6. Duct of lateral stylet-sac. e. Longitudinal muscular coat. «. Muscular chamber behind the floor of the jf. Superior commissure of ganglia. anterior region of proboscis. g. Inferior commissure of ganglia. n- Floor of anterior chamber of proboscis. => h. Superior lobe of ganglion. Muscular setting of granular basal appara- Inferior lobe of do. tus. j- Esophageal apparatus. a. Granular basal sac. j. Digestive canal-proper. #&. Hyjaculatory duct. k. General stroma of snout. “. Aperture of ejaculatory duct into chamber «. 1. Cephalic vessel. m. External granular glands, m. Cephalic sac. e- Reservoir. m’. Duct of do. o. Glands of reservoir. n. Great lateral nerve-trunk. ry. Looping muscular fibres of the walls of re- o. Proboscidian sheath. servoir, p- Dorsal blood-vessel. vo. Longitudinal muscular fibres of the walls of gq. Anastomotic branch. reservoir. r. Lateral blood-vessel. g. Duct of communication with the posterior ov. Ova in situ. chamber, v. Lateral stylet-sacs. %X, Wall of posterior chamber. z. Anus. a). Muscular ribbons. Letters used to designate similar parts in Borlasia and Cephalothria. a. Proboscis. d’. Basement-layer. ao. Tube for proboscis in snout. d’, Pigment-layer in B. olivacea. b. Cephalic fissures. e. External (longitudinal) layer. c. Ciliated epidermis. é. Circular muscular layer. d. External layer of cutis. e”. Inner (longitudinal) muscular layer. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 427 jf. Superior ganglionic commissure. r. Lateral blood-vessel. g. Inferior do. do. s. Lacunz behind ganglia. h. Ganglia. u. Vascular meshes around the cesophageal h’. Superior lobe of ganglion. region. h’. Inferior lobe of do. v. Larger vascular cavity at each side of the j. Csophageal region. sheath for the proboscis in front. j. Alimentary cavity-proper. w. Mouth. k, General stroma of cephalic region. y. Constriction marking the junction of the ceso- m. Cephalic sacs. phageal region with the digestive cavity- m’, Ducts of cephalic sacs. proper. n. Great lateral nerves. z. Anus. o. Proboscidian sheath. : ov. Ovaries and their remains. p. Dorsal blood-vessel. a}. Muscular ribbons of proboscis. Puate IV. Fig. 1. Transverse section, a short distance behind the tip of the snout of Ommatoplea alba, in front Fig. 1. of the ganglia, somewhat flattened from pressure. 1, 2, 3, 4, 5, 6, the various bands of fibres described in the text; ¢, longitudinal muscular fibres ; /, section of cephalic blood- vessel; m, section of cephalic sac. x 210 diameters. . Transverse section of the body-wall of .O. alba, after hardening in spirit and mounting in chloride of calcium; a, cutis, with its cells and areolee, somewhat compressed; 2, struc- tureless basement-layer; c, circular muscular coat; d, longitudinal muscular coat; e, delicate fibres proceeding from the latter to the viscera. x 700 diameters. . View of a portion of skin snipped from a living specimen, and submitted to moderate pres- sure. x 350 diameters. . Longitudinal section of the anterior region of the proboscis of O. alba. The same letters are used as in fig. 4, Pl. V. x 90 diameters, . Transverse section through the anterior part of the cephalic ganglia, in a specimen which had been chloroformed and then immersed in strong alcohol, so as to protrude a small portion of the proboscis. The inferior commissure (g) is not much stretched, but the superior (/) is almost imperceptible ; j, esophagus. x 55 diameters. In this and other drawings, accuracy has been preferred to symmetry. . Section of the snout in front of fig. 1, showing the channel for the proboscis (a), and the cephalic blood-vessels (7), just before they complete the arch. x 210 diameters. . Elements as they escape from the fresh skin of the same animal; a, granular cells; , mu- cous or gelatinous masses, having the appearance of oil-globules. x 350 diameters. . Skin of O. alba, as seen near the tail of a small living specimen, under slight compression. x 350 diameters. . Corpuscles of the proboscidian fluid; a, minute nucleated cells and granules; 0, spindle- shaped corpuscles. x 500 diameters. . Stylet, from a lateral sac of the same species, showing a ‘“‘ wing” at base (from remains of globule), and an abnormal point. x 210 diameters. . Dises of proboscidian fluid, from a specimen of Tetrastemma varicolor. x 850 diameters. . Small gregariniform parasite, from the digestive cavity of Tetrastemma variegatum. x 210 diameters. . Proboscidian aperture in snout of O, alba. x 210 diameters. . Discs of proboscidian fluid from Tetrastemma variegatum. x 350 diameters. PuatTEe V. Transverse section through the cephalic ganglia of O. alba, in the line of the commissures, the superior of which, from the flattening of the preparation, is shown very plainly ; a, proboscis; d, circular muscular fibres of the body-wall; %, muscular and glandular stroma of the region. x 90 diameters, Fig. 2) ae . Isolated gland-cells from the posterior chamber of the proboscis. x 350 diameters. . Transverse section through the anterior region of the proboscis in a large O. alba, after . Transverse section through the stylet-region of the proboscis of the same species, in the . Glandular papillz from the proboscis of Tetrastemmua vermiculus, seen on the free edge of . Glandular papille in the anterior region of the proboscis of O. alba, seen in the ordinary . Portion of the everted inner surface of the posterior chamber of the proboscis of the same . Portion of the glandular surface of the posterior chamber of the proboscis in its normal . Portion of the inner surface of the same chamber, viewed in situ under pressure. The . Lanceolate and pedicled papillee from the anterior part of the proboscis of 7. vermiculus. . Central stylet of Ommatoplea purpurea. x 700 diameters. : . Central stylet and basal apparatus of the same species. x 350 diameters. . Developing or recently repaired central stylet-apparatus in 7. alge. x 700 diameters. . Stylet from a lateral sac of the same animal. x 700 diameters. . Head of O. alba. x 210 diameters. . Proboscis of the same species, gently but completely extruded under chloroform, so as to . View of the nervous and circulatory systems in the anterior end of O. alba. . Abnormal stylet-region in the same species ; a, perfect stylet-sac of the left side; }, shrivelled . Stylet-region of the proboscis of 7. varicolor, with the reservoir somewhat contracted. x 210 . Extremity of the posterior chamber of the proboscis in 7. variegatum, apparently after . Stylet-region in Ommatoplea melanocephala. x 90 diameters. . Circulation, &c., in the posterior end of O, alba; a fragment of the same drawing from which . Isolated lateral stylet-sac of O. alba ; a, a few fibres which probably act as constrictors of . Tip of the snout of Borlasia olivacea, with proboscis partly protruded. x 210 diameters. . Central stylet-apparatus in Ommatoplea pulchra ; a, central stylet; b, reserve-stylet im situ. DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Transverse section through the body of the same animal some distance behind the ganglia. The sheath for the proboscis now separates the latter from the esophagus, which has — attained a considerable size. The lateral nerve-trunks have nearly reached their proper position, viz., to the inner side of the internal muscular layer of the body-wall; s, granular — masses at the sides of the esophagus. x 55 diameters. hardening in spirit and mounting in chloride of calcium; «, central cavity; b, the papillary glandular layer; c, internal circular muscular coat; d, inner longitudinal layer; e¢, pecu- liar reticulated or beaded layer; /, external longitudinal muscular layer; g, external layer; h, basement-layer. x90 diameters. line of the lateral sacs. x 350 diameters. the everted organ. x 700 diameters. condition of the organ under pressure. x 210 diameters. species. The glands have for the most part burst and become minutely hirsute. x 350 diameters, condition. x 350 diameters. papille are hirsute, and their contents scattered over the surface of the organ. x 350 diameters, x 800 diameters. Puate VI. render the central stylet prominent. x 55 diameters. sac of the right side. x 210 diameters. diameters. rupture of the muscular ribands from the sheath of the organ. x 350 diameters. fig. 3 was cut. the aperture of the duct. The laminated arrangement of the calcareous layers of the stylets is indicated in this figure. x 850 diameters. x 210 diameters. d Central stylet and its basal granular apparatus in O. gracilis, turned round so as to demon-— strate the curvature of both. x 100 diameters. Isolated central stylet of the foregomg. x 420 diameters. Fig. earl: a 12: Fig. Fig. mo Ne BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 429 Prate VII. . Stylet-region of the proboscis of O. gracilis. |x 210 diameters. . Stylet-region of the proboscis of O. purpurea. x 210 diameters. . Stylet-region of the proboscis of O pulchra. x 90 diameters. . Extremity of the posterior region of the proboscis of O. alba distended with fluid; a, a group of the peculiar dancing granules. x 90 diameters. . Stylet-region of the proboscis of Polia involuta, VAN BENEDEN. x ‘700 diameters. . Stylet-region of the proboscis of a young O. alba, illustrating the first appearance of the stylets, and the development of the parts. The organ is drawn as it bulged from a wound in the body-wall of the animal. x 700 diameters. . Fragment of the esophagus from a living animal; a, mner edge of ciliated fold; J, sulcus between two folds. x 350 diameters. . Eye of Ommatoplea pulchra. x 210 diameters. . Central stylet and portion of basal apparatus in a large O. gracilis. x 850 diameters. . Transverse section of an everted proboscis in a small specimen of O. pulchra. The papillose mucous surface has been injured in the manipulation. x 90 diameters. Nerve-cells from a cephalic ganglion of O. alba. x 400 diameters. Portion of a sperm-sac in Yetrastemma varicolor, showing a streaked and granular aspect, from the varying nature of the contents. x 350 diameters. Pirate VIII. . Aspect of the developing proboscis in O. melanocephala, about the fifth day after the removal of the original organ. x 55 diameters. . Stylet-region of a developing proboscis in the same species; /, canal, which by-and-by is occupied by the central stylet. The organ is contracted. x 350 diameters. . Anterior region of Tetrastemma alge, showing the arrangement of the digestive system. Enlarged. . Termination of the posterior chamber of the proboscis (C) in O. alba, with muscular ribands. x 210 diameters. . Head and anterior portion of Polia involuta, V. Bren.; f, powerful transverse band of fibres which retains the posterior part of the esophagus in situ. x 180 diameters, . The central (a) and lateral stylets (b) from a young O. albu, on the first appearance of the former. x 700 diameters. . Cephalic ganglia of Tetrastemma varicolor. x 210 diameters. . Unimpregnated ovum of O. alba ; a, outer coat; b, inner coat; c, vitellus; d, “ micropyle,” or cicatrix-like arrangement. x 90 diameters. . Ovum of O. gracilis after impregnation; a, outer coat; /, mner coat; ¢, vitellus. x 90 diameters. . The inner coat and vitellus of an ovum (of O. gracilis) at the same stage of development, with the relations of the spermatozoa. x 210 diameters. . Ovum of O. alba, just before the extrusion of the embryo, x 90 diameters. . Spermatozoa of Tetrastemma vermiculus. x 1000 diameters. . Spermatozoa of O. alba. x 800 diameters. . Spermatozoa of 7. variegatum. x 400 diameters. Puate IX, . Young OQ. alba, on extrusion from the egg, somewhat compressed, x 55 diameters. . Young O. alba eight days older than the preceding; 0, stylet-region; c, point where the posterior chamber of the proboscis becomes lost, after curving forwards. x 90 diameters. . Structure of the stylet- and reservoir-regions in 0. alba. Considerably magnified, . View of the cutis in a living specimen of Borlasia olivacea as a transparent object. x 210 diameters. . Streaked arrangement of the cutis of B. olivacea, from the dorsum, x 210 diameters. . Pigment-cells from the anterior part of the dorsum of the same species. x 350 diameters. . View of the skin of a living Meckelia annulata. x 350 diameters. . Spermatozoa of Ommatoplea gracilis. x 700 diameters. . Spermatozoa of Polia involuta. x 950 diameters. VOL. XXV. PART II. DR 430 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Fig, 10. Transverse section through the contracted reservoir-region of O. alba, showing the complex _ Salas Be oal3y . 14, 2) ar Gs Fig. Fig. ile spiral arrangement of the fibres. x 55 diameters. Superficial structure of the reservoir- and stylet-regions in the same species. Central stylet and basal apparatus with radiating fibres in Tetrastemma vermiculus. x 360 diameters. Stylet-region of a young QO. alba, some weeks older than that represented in fig. 2. x 350 diameters. Transverse section through the posterior chamber of the proboscis in a large example of O. alba. The circular and longitudinal muscular and the mucous coats are well shown. x 90 diameters. Young Tetrastemma variegatum, shortly after extrusion from the egg, and somewhat com- pressed, so as to show its cellulo-granular structure. x 350 diameters. Portion of the long posterior chamber of the proboscis of O. purpurea, showing the charac- teristic plaits of the mucous surface. x 90 diameters. Pruate X. Enlarged view of the anterior end of B. olivacea as a transparent object. 2, Transverse section through the curious example (probably a variety of Meckelia) from © OnaTIo GS Om co © Balta; d, external layer of cutis ; d’, basement-layer; ¢, longitudinal muscular layer ; ea, dorsal sub-divisions of the latter coat in the central line; ¢’, circular muscular coat ; j, section of the cesophageal region of the digestive tract ; ja, distinct band of muscular fibres enclosing the latter ;. x, lateral nerve ; 0, sheath for proboscis; 7, vascular spaces. x 55 diameters, ' . Transverse section through the body of Cephalothriz filiformis. The proboscis is coiled in its sheath. x 90 diameters. . Transverse section just behind the tip of the snout of Borlasia olivacea. The grouping of the pigment (3) readily enables the observer to distinguish the dorsal from the ventral surface ; 2, powerful series of fibres arching over the channel leading to proboscis, and which radiate into the surrounding stroma (x). x 56 diameters. . Portions of the inner surface of the proboscis of the same species, showing the glandular papillz, slightly compressed. x 700 diameters. . Gland-cells from the wall of the digestive cavity of Ommatoplea alba. x 400 diameters. . One of the same slightly compressed glands. x 700 diameters. . Contents of the same gland-cells, with oil-globules. x 700 diameters. . Spermatozoa of Borlasia olivacea. x 700 diameters. Pruate XI. . Transverse section through Borlasia olivacea, just at the commencement of the cesophageal region; 2, radiated or slightly arborescent arrangement of the external longitudinal muscular coat at the sides of the mouth. The thick folds of the cesophagus are seen almost at the termination of the anterior cul-de-sac. x 90 diameters. . Arrangement of the ova in the ovisacs of Tetrastemma vermiculus ; a, proboscis ; 0, probos- cidian sheath. Only a fragment of the body is represented. x 24 diameters. . Spermatozoa of Cephalothrix filiformis. x 900 diameters. . Spermatozoa of Lineus longissimus. x 900 diameters. . Spermatozoa of Borlasia octoculata. x 800 diameters. . Transverse section through the body-wall of Lineus longissimus at a somewhat narrow por- tion ; d, external cuticular layer ; d’, pigmentary layer divided into two strata by a defi- nite black band (2); 8, curious translucent stratum, cut into somewhat regular spaces. Other letters as usual. x 210 diameters. . Longitudinal section of the tissues of the body-wall in the same species; 4, 4, sections of the transverse connecting trunks between the lateral and dorsal vessels ; 5, granular stroma within the inner longitudinal muscular coat, supporting the former and various other tissues. x 90 diameters. . Transverse section of the body-wall of Borlasia olivacea. x 350 diameters. . Proboscis of Cephalothrix filiformis, slightly everted, so as to exhibit the acicular papille. x 850 diameters. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 431 Fig. 10. Aggregations of fatty granules from the discarded coating of the embryo of B. olivacea. x 210 diameters. Pruate XII. . Transverse section through the proboscis of a Borlasian (Micrura) from St Andrews; a, external coat; }, great longitudinal muscular layer; c¢, belt of circular muscular fibres ; d, basement-layer ; e, incomplete series of longitudinal fibres which do not occur in the common species; /, glandular mucous coat; g, peculiar lozenge-shaped portion of longi- tudinal fibres, formed by the splitting and crossing of two bands from the circular muscu- lar coat; g, separated segment at the other pole of the circle. x 90 diameters. . Transverse section of the snout of Borlasia olivaceu, somewhat behind that shown in fig. 4. Pl. X., and through the anterior part of the cephalic fissures. The channel for the proboscis has become more central in position. ‘he superior pigmentary belt (3) is somewhat narrower, and an inferior (4) has now appeared. The central channel has a layer of longitudinal muscular fibres internally, and a powerful series of oblique and circular fibres (2, 2) form a very efficient exterior investment. x 55 diameters. . Transverse section of a specimen of B. olivacea, in which the ova are well developed. The shrunken condition of the walls of the digestive cavity (j’), with the numerous array of gregariniform parasites, is in strong contrast with the state of the animal after spawn- ing. The specimen had been in spirit for a considerable time before dissection, x 55 diameters. . Parasitic ciliated animal from the tissues of the same species. The letters, a, b, c, and d, correspond with the groups of segments described in the text. x 350 diameters. . The foregoing parasite in an earlier state of development. x 350 diameters. . The last-mentioned specimen subjected to slight pressure, so as to exhibit the seyments. x 350 diameters. Posterior end of a young B. olivacea, showing the anal papilla. x 210 diameters. . Transverse section through the post-ganglionic region of Lineus lactea, Mont. MS., show- ing the long vascular lacune (s, s) in front of the esophageal region. The slice of the proboscis has fallen out of its sheath (0). x 90 diameters. . Stylet-region in Tetrastemma varicgatum, somewhat contracted, and with the floor of the anterior chamber pouted forwards. The latter condition is more easily seen in Zetras- temma than in O. alba. x 210 diameters. . Fragment of the wall of the digestive chamber-proper, from the living Borlasia olivacea. The cilia mark the inner surface. x 850 diameters. . Cells from the digestive cavity of a young Cephalothriz filiformis. x 700 diameters. . One of the pinnate processes of the scale of Sthenelais dendrolepis, Cuar. x 90 diameters. PuatE XIII. . Highly magnified view of the anterior end of Cephalothrix filiformis (Astemma) ; 6, b, bridles of sheath for proboscis. . Arrangement of the vessels at the posterior extremity of Borlasia olivacea. Magnified. . Ovum of Cephalothrix filiformis immediately after deposition, x 350 diameters. . Flask from the mucous cord of B. olivacea, with two young animals somewhat compressed; «, embryo forced from its ciliated cellulo-granular fatty coating, the bulk of which lies at « ; b, embryo still within the ciliated coating. x 55 diameters. . Young B. olivacea immediately after leaving the flask-shaped capsule; 4, opening of the cephalic sac of the right side. The other letters as in the adult. x 90 diameters. . Transverse section through the middle of B. olivacea after the second or great region of the digestive cavity has attained its full size. ‘The difference between such a view and the indistinct mass formed by the Ommatoplean digestive cavity, after section, is character- istic. x 56 diameters. . Cellular elements of the wall of the digestive chamber of the same species. x 700 diameters. Pale oily region with germinal vesicle (a), and germinal dot (}), in an ovum removed from the body of the female B. olivacea. x 3650 diameters. . Elements of the glandular papille of the proboscis of B. olivacea, after their escape into the surrounding water. x 700 diameters. 432 DR W. CARMICHAEL M‘INTOSH ON THE STRUCTURE OF THE Seba . Fig. 10. iB eeai en di ee ooks of Amaye. x 700 diameters, ‘ Puate XIV. Fig. 1. Ovum of Polia involuta, Van Bzn., immediately after deposition. x 350 diameters. ... 2, Ovum of the same species about the 10th day, showing the ciliated embryo revolving therein, x 350 diameters. 3. Young of Cephalothrix filiformis shortly after extrusion from the egg. x 350 diameters. 4, A young specimen of Cephalothrix, two days older than that shown in fig. 3; a, mouth; 4, granules of digestive cavity. x 2i0 diameters. 5. A specimen about three days older than the foregoing (fig. 4). x 210 diameters. 6. Young Polia involutd, extruded from the body of the adult under pressure. It has the same appearance when originating in a free ovum. x 350 diameters. 7. Young (©. filiformis, after shedding the long anterior whip of cilia, but having the lateral tufts (c) and eyes; a, mouth; 0, granules of digestive cavity. x 210 diameters. 8. Transverse section through the proboscis of Lineus longissimus. x 55 diameters. 9. Magnified view of the ganglionic region of a large Ommatoplea alba, in which a parasitic ovum (7) lay imbedded in a granular lobulated mass (7). . 10. Parasite extruded from capsule; a, opaque cellular and granular mass ; }, ventral disc; ¢, oral disc; d, cesophageal bulb; e, alimentary ceca; f and g, large circular granular bodies. ... 11. Transverse section through the body of a large Meckelia annulata. x 55 diameters. . 12. Head and proboscis (a) of a remarkable variety of Meckelia, brought from Shetland (Balta) by Mr Gwyn Jeffreys; b, curiously frilled arrangement of the enlarged homologue of the superior lip of the cephalic fissure; w, prolapsus of textures from mouth. Magnified under a lens, ... 18. Hook of Ampharete artica, Mern. x 700 diameters. > ... 14. Hook of Amphicteis gunneri. x '700 diameters. . 15, Hook of Terebella, from the Hebrides. x '700 diameters. Piate XV. Fig. 1. Bristles of Amphinome vagans ; a, bristle from the inferior lobe of foot; }, c, bristles of the © superior lobe. x 700 diameters. 2 a. Dorsal bristle of Lepidonotus pellucidus, Haters. x 700 diameters. 2 b. Ventral bristle of the same species. x 700 diameters. 3. Ventral bristle of Polynée longisetis, GRuBE. x 350 diameters. 3 a. Tip of the dorsal cirrus of the same species. x 55 diameters. | Two of the characteristic bristles (with jointed tips) of Sthenelais dendrolepis, Cur. }. x 350 diameters, 6. 6 a. } Ventral bristles of Halosydna gelatinosa, Sars. x 180 diameters. 6 b. 7. Ventral bristle of Ophiodromus vittatus, Sars., with short terminal process. x 700 _ diameters. 8. Fragment of a bristle from the dorsal lobe of the same animal. x 700 diameters. 9. Bristle of Notophyllum polynoides, CErst. x 420 diameters, 9 a. Lateral view of the end of the shaft and its processes in the same bristle. x 700 diameters. 9. Profile view of the same. x 700 diameters. ~_ . 10. Bristles of the littoral form of Spherosyllis hystrix, CLAPAREDE ; a, simple spine ; /, jointed bristle. x 700 diameters. . LL, Jointed bristles of Autolytus pictus, Enters. x 700 diameters. ... 12. Bristle of Syllis, resembling S. macrocera, GRuBE. x 7U0 diameters. . 13a. Fragment of the frontal bristle (of Siphonostoma buskii) represented in fig. 4 a, Pl. XVI. x 360 diameters. . 13. Piece of a corresponding bristle from Trophonia glauca, MALMGREN. x 300 diameters, — ... 14. Hook from the rasp-like surface of Ammochares ottonis, GRuBE. x 900 diameters. . 15. Hook of Terebella zostericola, rst. x 700 diameters. zo. BRITISH NEMERTEANS, AND SOME NEW BRITISH ANNELIDS. 433 16. Hook of Rhodine loveni, Mern. x 700 diameters. . 17. Hook of a species allied to Hreutho smitti, Mern. x 900 diameters. : : Hooks of a form closely resembling Polycirrus aurantiacus, GRUBE. x 900 diameters. . 20. Hook of Pista cristata, Mttuer. x 700 diameters. . 21. Bristles of Syllis tubifex (%), GossE ; a, a, from middle of body; 6, spine; c, bristle from Fig. the third foot. x 280 diameters. Puate XVI. 1. Ventral bristle of Castalia punctata, Mitt. x 700 diameters. 2. Bristle of Psamathe fusca, Jounst. x 700 diameters. 3. Jointed hook from the anterior segments of Hyalinecia sicula, QuatREF. x 700 diameters. 3 6. Simple hook from the posterior region of the same. x 700 diameters. 3c. Bristle of the foregoing species. x 700 diameters. 4. Hook of Siphonostoma buskii, n.sp. x 3850 diameters, 4 «. Bristle from the frontal series of the same species. x 90 diameters. 5. Forked bristle of Ewmenia jefireysii, n. sp. x 700 diameters. 6. Hook from the bristle-bearing segments of Trichobranchus glacialis, Mern. x 90 diameters. 7. The same. x 700 diameters. 7 a. Hooks from the posterior segments of the same annelid. x 700 diameters, 8. Bristle of 7. glacialis. x 350 diameters. _ 9. Bristle of Spherosyllis from the Minch. x 700 diameters. ... 10. Bristle of Pionosyllis malmgreni, n. sp. x 700 diameters. ... 11. Foot of Staurocephalus kefersteini, n. sp.; f, superior cirrus ; g, inferior cirrus. x 210 diameters. eek a: ... 11. { The varieties of the bristles in the same species, as described in the text. x 700 Beil ¢. _ diameters. fee Lila. . 12. Hook of Clymene ebiensis, Aup. & Ep. x 350 diameters. ... 13. Hook of Prazilla (artica? Mern). x 350 diameters. . 14. Bristle of Syilis krohnii, Huters. x 700 diameters. ong HOMee soe EGR } Bristles of Syilis cornuta, Ravuxe, x 700 diameters. oot ss fe \ Hooks of Sabellides sexcirrata, Sars. x 700 diameters. . 17. Foot of Notocirrus scoticus, nu. sp.; a, branchial lobe; 6, spine; c, bristles. x 350 diameters. Or ™M VOL. XXV. PART II. . 5 v gh! a bd ’ bl | 7) . a me De ~ i Ate 7) a ; ; a 7 ta oe \ 4 , > = "Ae $* S724 BERTI? DINO PEA IG 7 an : bee dl Bi, ay Pot PA ‘ ; Sie awASA ee xx hs Prive viral wD WAU Wie ; bas, fi Ad GO IOS & ae t oa ‘ 7 } = et re s st 6085 wei » ieee ce ‘Cu te tee . F oa m8 a7n 4 y ' yy SLAP ri ~ ' “sr i hy > ia ; iA \ te { sewer wienl! tin 2 ea! - = ae ee . . h... a | - ; rt =—- eee fars OF » aT) eres j Lhe isicy ion > gle boa ht Ae A/a " oo el, i. e1 7 ee ).. vin ieee’ \). lie at ierdge, tra Caliae oeds ase er be . CRE OE J , BLS |! SEIS PER ead wid. at 4i'ti pute ae ant : wa ‘ ‘4 ) : mens VT tbe 004 Uy ae } . *eDiMLL AL " "6 "a “at vt : ‘@ Pb va 7 a » TT So eT ps , : é id \ é ( - iF 2 ia UPL eae eit . ) \ ' i oe O Mio ae y eligi ate ‘ seu, DP inn a : > ¥ 2 } g OTATIED Phd aoa | fa crn ag noe i 3 we (go Ar, wD % . ~ ~ ioral wes te ‘ 2 : fe ar phat | \ Ww Pi ke | +t & us Hd deel GAS et A oe j ay ie ’ P ee oe 4 ie af, nee ane tn : ’ Plat i - els : ‘ ty 1 ” 1 TR45V hie * “p . ™ As ; ’ icy it a) Mr Tua: ; ‘ ’ 4 rs ‘ Vien ~~ a ately 7 Ai, . IV. Pee VOL: XXV. TRANS. ROY. SOC. EDIN. Y Les H. Ford, sc. males TRANS. ROY. SOC. EDIN. VOL: XXV. PL: V. | W. West, imp. G.H. Ford, se. G.H. Ford, se. VOL: XX¥V. PL: Vik. TRANS. ROY. SOC. EDIN. W. West, imp. eee eee A en AOA ME AS VOL: XXV. PL: Vil. ~ TRANS. ROY. SOC. EDIN. ARMA LEIS Ey! Se Rea ISR IT 5 ‘f a a Cel ia] S aa ae o j ' PL: VIII. TRANS. ROY. SOC. EDIN. VOL: XXxv. . West, amp G.H. Ford, sc. (be VOL: XXV. PL: TRANS. ROY. SOC. EDIN. ord Wesrr Stare aes Raat oe RO eS fo TRANS. ROY. SOC. EDIN. VOL: XXV. , PL: X. © G.H. Ford, ec. = tT nero ay wy - 1 he e- . oe ee ae eaya Ne . a } - f . . ~ / \ ‘ , * : TRANS. ROY. SOC. EDIN. VOL: XXV. PL: XI. W. West, imp, : j = G.H. Ford, sc, L! Skee sannrens tte twegte TRANS. ROY. SOC. EDIN. VOL: XXV. PL: XII. W. West. imp. ee GH. Ford. se i i wb. dao TRANS, ROY. SOC. EDIN. VOL: XXV. PL: W. West, imp : G.E. Ford, se. TRANS. ROY. SOC, EDIN. VOL: XXY. PL: XIV. G.H, Ford, se. G.H. Ford, se. XXV. PL: XV. EDIN. VOL: RANS ROX. SOc. Pee SSS TECCEC EET = ASS SSS SASS ban SoS) Ss aa .~ a REE << eee ots Th ¢. , Pies XVI VOL: XXV. a Cl ) A z a wi 2) ie) Cp) > fo} jaz a) z ea (va = X.—Observations on the Temperature of Newly-Born Children. By T. J. Maciacan, M.D., Dundee. Communicated by Dr J. MatrHews Duncan. (Read 5th April 1869.) The observations which form the basis of this paper were made on newly- born children with the object of determining whether their temperature differed from that of the adult, and if so, how and to what extent. They were made during a recent residence in the Edinburgh Maternity Hospital, with the full sanction of the attending physician, Dr Cuarues Bett. The thermometers* used _ were CASELLA’s straight self-registering. The rectum was the part chosen for the insertion of the instrument. The utmost expedition was used in ligaturing the cord, and separating the child from its mother. This being effected, the bulb of the thermometer was at once introduced into the rectum, and the child was wrapped in flannel, and committed to the charge of a nurse, who held the instru- ment steadily 7m situ. In five minutes it was removed, and the temperature noted. The observations were repeated every fifteen minutes during the first hour, every thirty minutes during the second and third hours, and then every hour up till the sixth hour after birth ; after that at wider intervals up to twenty- four hours; and then only twice a day between ten and eleven in the morning, and between six and seven in the evening. By the adoption of the above method, the first observation was made whilst the child yet retained the temperature imparted by the mother, whilst any subse- quent change could not fail to be noted in consequence of the frequency with which the observations were repeated. In order that the peculiarities of the child’s temperature may be made as clear as possible, the facts observed shall be treated of under three different heads. We will consider (a) the temperature at the time of birth; (0), the range noted . during the first twenty-four hours of extra-uterine life; (c), that of the next five days. (a). The temperature of the child at birth is the same as that of the mother. If hers be high during the second stage of labour, that of the infant at birth will show a corresponding elevation; if normal, so also will the child’s be. The mean range of the maternal temperature at the time of delivery was found to be * The instruments were verified by the maker by a standard which is in perfect accordance with that of the Royal Kew Observatory. VOL. XXV. PART II. 57 436 DR T. J. MACLAGAN ON THE 99°'154; that of the child at birth, 99°872, The highest was 103°5 for the mother, and 104° for the child; the lowest 97° and 98°:1. As the former case was altogether abnormal, it ought perhaps to be excluded in striking the average. By doing so, we get a mean range for the mother of 98°6, and for the child of 99°-3—a difference of “7 in favour of the child. This slightly higher range on the part of the child is fully accounted for by the fact that the infant’s tempera- ture was taken in the rectum, whilst the mother’s was taken in the axilla. From observations made on the adult with the object of determining the point in question, I found the temperature of the former locality to be from half a degree to a degree above that of the latter. Making allowance for this, the range of the mother and child may be regarded as the same. The case with the high range, in virtue of its abormality, serves well to illustrate the close con- nection which exists between the two. In it the mother’s temperature towards the end of labour rose five degrees above the normal standard; the child’s at birth was found to have undergone a similar elevation. (b.) The range of the first few hours after birth is altogether peculiar. When the child is separated from the parent, and commences its new mode of existence, a marked change takes place. The temperature acquired from the mother is no longer sustained. The thermometer introduced into the rectum shows a fall which varies in different cases both in rapidity and extent, but which is never altogether awanting. In children born at the full time, the average period after birth at which the temperature reached its lowest point was two hours. The average extent of the fall was five degrees below the normal standard of the adult; the greatest was to 90°'8, the least to 96°—-the average being to 93°4. The mean time which elapsed before the temperature again rose to what might be regarded as its normal range was 22-25 hours after birth; the shortest was two hours; the longest forty- four. In one sickly child it was four days before the depression was recovered from. Ina seven months’ child the temperature fell to 90°:2, more than eight degrees below the adult standard of health; and during the thirteen days on which it was under observation the highest point reached was 94°:6, the mean range being 92°°3. (c.) So much for the first twenty-four hours. The observations made after that time were made only morning and evening. I have selected sixteen cases, in which no disturbing element intervened at all likely to affect the normal range, and find that the mean range for the first five days immediately succeed- ing the time at which the normal standard was attained was in the morning 97°43, and in the evening 98°06, the average being 97°74—that is, more than half a degree below the normal standard of the adult. As the temperature of these cases was invariably taken in the rectum (in which we have seen that the range is higher than in the axilla), it may be inferred that the child’s tempera-— + TEMPERATURE OF NEWLY-BORN CHILDREN. 437 ture during the first few days of its existence is a degree lower than that of the adult. It must also be mentioned, however, that all these observations were made during the winter, and that possibly the external atmosphere may have a ereater effect on the temperature of the child than on that of the adult. I have never had the opportunity to repeat them during the warm weather of summer. How are these pecularities to be accounted for? Why should the child’s temperature fall so rapidly, and to such an extent, immediately after birth ? And why should it, on recovering from this temporary depression, still be lower than that of the adult? (a.) That the child at birth should have the same temperature as the mother is what would naturally be expected. Considering the close connection which exists between them, and the manner in which the child is nourished by the mother, it could not well be otherwise. The circumstance calls for no explana- tion whatever. (b.) With regard to the peculiar range of the first few hours of the child’s sepa- rate existence, it is quite different ; and we have now to inquire why it is that the child’s temperature should fall so rapidly, and to such an extent, immediately after birth. It is probable that the sudden change from the high temperature of the womb to the low temperature of the external air exercises to some extent a chilling influence on the child—an influence which it can the less resist, and with the more difficulty recover from, in consequence of the peculiarities of its circulatory system allowing of the passage of so much venous blood into the arterial circu- lation. That, however, is not of itself sufficient to account for a fall so sudden, so great, and of so short duration; for assuredly, if that were the sole cause, recovery from a very low range so produced would be a much slower process than itis. There must be some other and more powerful agent at work; and this we have in the first necessary act of the child’s independent existence— respiration. I believe that the passage of air into the lungs has at first a refrigerating influence, and is the chief, if not the sole, agent in producing the _ great and sudden fall which takes place immediately after birth. This explana- tion is to a certain extent borne out by what was observed in one case in which the child was apparently still-born, and in which considerable difficulty was experienced in inducing the respiratory act. The temperature in the rectum half an hour after birth (immediately after respiration was established) was 98°3 ; in the next half-hour it fell to 92°-6. The state of the child at birth was such that attention was directed solely to the respiration, and until that was right the temperature wasnot taken. Just before delivery, however, the mother’s stood at 100°, so that the child’s may with propriety be supposed to have been 100°-7 in the rectum. In ordinary cases, in which breathing commenced at once, the mean fall during the first half hour was in full-grown healthy children 5°-2, and during the second half hour 1°4. In this case it was during the first half x 438 . DR T. J. MACLAGAN ON THE hour 2°-4, and during the second half hour (after respiration was established) 5°-7. In all other cases in which a comparison could be made the fall was much greater during the first half hour than during the second; in this one the reverse was the case; and the only explanation of this circumstance is to be found in the tardy establishment of the respiratory act. So far as one case can do so, this one shows that it is not until the child breathes that the temperature falls to any great extent; though the diminished range may also be partly explained by the cooling influence of the external air on the blood in the very active cutaneous circulation. But the question naturally arises, Why should the respiratory act, which in the adult has a heat-producing effect, have an opposite result in the infant? The answer involves a brief consideration of the whole question of the production of animal heat. To the various theories which have at different times been advanced to account for this I shall not allude further than to say, that all have given — place to that which ascribes it to chemical action—to the changes which are con- stantly going on in the blood in all parts of the capillary system—general and pulmonic. As these changes take place in organs and parts which are dependent __ for the proper performance of their functions on the integrity of the nervous system, it follows that the amount of heat produced is apt to be modified by the | operation of that system. Medicine abounds in illustrative cases in which a part of the body, a limb for instance, in consequence of being deprived of its nervous supply by disease or accident, has a lower temperature than it had when that _ supply remained intact. : Sir B. C. Bropre (I quote from Kirxss’ “ Physiology’) “found that if artificial respiration was kept up in animals killed by decapitation, division of the medulla oblongata, destruction of the brain, or poisoning with worara poison, | the action of the heart continued, and the blood underwent the usual changes in the lungs, as shown by the analysis of the air respired, but that the heat of the body was not maintained; on the contrary, being cooled by the air forced into the lungs, it became cold more rapidly than the body of an animal in which artificial respiration was not kept up.” Absence of the due nervous influence is, I believe, the true explanation of the rapid and transient lowering of the child’s temperature during the first few hours of extra-uterine life. It is, indeed, unlikely that the child should have its con- nection with the mother severed, and commence its new and independent existence with patent foramen ovale, unclosed ductus arteriosus, and lungs hitherto untried, and from the first maintain the temperature imparted to it by the parent; but, as already explained, the existence of this peculiar state of the organs of circulation is inadequate to account for a fall so very rapid and of so short duration. Closure of the foramen ovale and ductus arteriosus cannot explain the speedy return to the normal range, for these passages are not — EO TEMPERATURE OF NEWLY-BORN CHILDREN. 439 obliterated for some considerable time after birth; respiration goes on as from the beginning, and why should it after a few hours cease to exert the same lowering influence which it exercised at first? It seems to me that the only feasible explanation is to suppose that the hitherto unexercised influence of the nervous system over the respiratory function is not at once called into vigorous and efficient action— that though the influence required for inducing the muscles of respiration to act is in full force from the beginning, there is still awanting, or only partially supplied, that more delicate and less easily explained agency without which, even though the blood may undergo the usual changes, the due amount of heat is not generated; and that coincidently with the estab- lishment of this influence does the temperature of the child rise to its normal range. This explanation is quite in harmony with the fact that in delicate and premature children the fall is greater than in vigorous ones and those born at the full time, in whom also the normal standard is more rapidly reached, in conse- quence probably of the more speedy establishment of the due nervous influence. (c). During the five days immediately succeeding that on which the tempera- ture rose to a height which might be regarded as normal, we have seen that the range was one degree below that of the adult, after due allowance had been made for the difference resulting from the manner in which the thermometer was applied. This lower range of the early period of extra-uterine life admits, I think, of a very ready explanation. As a general rule, the degree of heat produced bears adefinite relation to the activity of the respiration: in birds, in which respiration is very active, the temperature is high; in reptiles, with a sluggish respiration, there is a low temperature. Anything which interferes with the proper oxygenation of the venous blood. or with the due supply of the purified fluid to the tissues, has a lowering effect on the temperature. Such agencies are constantly at work in the newly-born child. The patent condition of the foramen ovale and ductus arteriosus permit of so free a commingling of the venous and arterial blood, that a lower temperature than exists after the closure of these passages must result; for, in the first place, less blood goes to the lungs at each contraction of the right ventricle, and so less heat is produced there; and, in the second place, the blood which goes to the tissues is less pure, and consequently less of an interchange takes place in the capillaries of the systemic circulation. How long the child’s temperature continues lower than that of the adult I am not prepared to say, as my observations were limited to the first week of extra- uterine life, but should think it probable that the adult standard of health is not maintained till the foramen ovale and ductus arteriosus are closed, or nearly so. This, however, is a mere hypothesis, and must remain so, as the time of closure of VOL. XXV. PART II. aU 440 DR MACLAGAN ON THE TEMPERATURE OF NEW-BORN CHILDREN. these orifices cannot be accurately ascertained. Their obliteration is extremely rare before the completion of the first week of separate existence; but cases are on record in which the foramen ovale, and others in which the ductus arteriosus has been found obliterated before birth; whilst there are recorded several in which the foramen ovale was patulous for many years. The natural vigour of the child seems to exercise some influence on the extent and duration of the fall which takes place after birth. I made some calculations with the object of finding out whether the weight of the child at birth or the weight of the placenta bore any fixed relationship to the child’s range of temperature, but failed to establish any necessary connection. The only conclusion to which I came was, that those children which gave the most decided indications of being in a vigorous healthy state were also those in whom the temperature fell least, and in whom it soonest again rose to the normal standard. In a feeble seven months’ child the range fell to 90°:2, and only once rose as high as 94°-6, during the thirteen days that it was under observation. In another case, a vigorous healthy child, born at the full time, the lowest point was 96°, and in two hours after birth the standard of health was reached. It is very probable that the vigour of a healthy child, and the higher range which it shows, are both merely evidences of a better developed state of the organs generally, and especially of the nervous and circulatory systems, on the integrity of which the production of a due amount of heat is dependent. TPMT UMNO AVM Plate XVII s. Roy. Soc.Edin. Vol XXV. ¥ dr Sp bry \ ‘¢ aul zo uobhoz | a Cd 182 OL 0) Your afeog T UPL ~f Pi 3) q 2 ‘SU0} OE 0} Your ¥epecs “9229 OL 01 Your ¥ epeog T awupig ¢ bry ~~ \ a] SmO}NE = TUL Z sprog \ |Z i CAs can . al Joos OL = YUL e seg ‘~ owns 7 tig suoyO¢ = PUL Zereog Taumy wy big x [ aug [by Veer Ol = yout Zetec ange y waeMpP TY FM [ oo gles i lanai 5 m 2 a ae /4 wy a QQ2S PYG2L oon ced | Ze usohiod apis abs we J |b ge uobhoaz = a | BLZUID == === $= — a) ae Uwcb joa Js i We ——— — = fa = Sl xo mobsjor ape 22) SINIO? WOLLOE pe br ~ | 2 nob hod ( — apis 427 _ i Qo uobQoz “eo pg bur eee. ; apis gyb11 | Cae SINIOF WOLLOG ze = Si 20 UOOKj og — Cee IL I gw uobsjod GY ae IN wis yb ze ve | 7 mobhey apie 42) (Se eeepc gaa ea eis 20 UOO\0d = XK SINTOP dol SOO i | 2 woehpar Sg Ou (bose Se aS se eS at i Poy tee Ys Lb oat , i. on tee \ ‘ f : LAS ] ae ‘ d 7. ri ) Me a 4 < . rele CH ae j oe , i = Ss * } : { | 1 , \ Plate XXII ie COU G cae Fig 14 Scale inch to 15 feet ia” (14411) XI.—On the Practical Application of Reciprocal Figures to the Calculation of Strains on Framework. By Professor FLEEMING JENKIN. (Plates XVII. to XXIL) (Read 15th March 1869.) The theory of reciprocal figures used as diagrams of forces was first com- _ pletely stated by Professor T. CLerK MAxweE LL, in a paper published in the “ Philosophical Magazine,” April 1864. The following definition of reciprocal plane figures, and their application to statics, are there given as follows :— “Two plane figures are reciprocal when they consist of an equal number of lines, so that corresponding lines in the two figures are parallel, and correspond- ing lines which converge to a point in one figure form a closed polygon in the other.” “Tf forces represented in magnitude by two lines of a ee be made to act between the extremities of the corresponding lines of the reciprocal figure, then the points of the reciprocal figure will all be in equilibrium under the action of these forces.” . The demonstration of this statement is given. The conditions under which stresses are determinate, and some examples of reciprocal figures, are also given in the pave which leaves nothing to be desired by the mathe- matician. Few engineers would, however, suspect that the two paragraphs quoted put at their disposal a remarkably simple and accurate method of calculating the stresses in framework; and the author’s attention was drawn to the method chiefly by the circumstance that it was independently discovered by a practical draughtsman, Mr Taytor, working in the office of the well-known contractor, Mr J. B. Cocurane. The object of the present paper is to explain how the principles above enunciated are to be applied to the calculation of the stresses in roofs and bridges of the usual forms. The construction of a reciprocal figure for any frame requires the exercise of a little discrimination, and the method employed can be best explained by examples; those frames only being considered which are so braced as to be stiff, but have not more members than is sufficient for this purpose. The simplest example is that of a triangle loaded in the middle, and supported at the two ends. At each point three forces are acting. Thus we have at point 1 the upward VOL. XXV. PART II. OX 442 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL reaction of the support, the push due to the compressed member A, and the pull due to the extended member ©. The directions of the three triplets of forces are shown by arrows. In the reciprocal figure lines parallel to each triplet of forces must make a triangle, and the Fig. 1. whole figure must consist of six lines. Begin with the joint 1, and draw one triangle mnqg with the sides _ S P, A, C, such that they are parallel to P, A, C in fig. 1; while the line P is equal on any convenient scale to the known force due to ; ; ! the upward reaction at the point of support. Then PAC, fig. 2, is the simple polygon of forces acting at 1. i eae / Next beginning at point m, and using the line A to express “ the upward push at 2 (fig. 1) draw the triangle mno, which re- i presents the polygon of forces at joint 2. We next find that mqgo 0 represents the polygon of forces at joint 3, and that the fig. 2. iG is the reciprocal of fig. 1. The reciprocal figure is thus built up of a series of the well-known polygons of forces acting at each joint, but so arranged that the line representing the elas- tic force exerted by each member does not require to be drawn twice, but forms part of two polygons, in which, however, it represents forces acting in opposite directions. Thus the line mg in fig. 2 forms part of the triangle gnm, in which it repre- sents a pull from m to q, acting at point 1, and it also forms part of the triangle mgo, in which it represents a pull from g to m, acting at joint 3. It is in choosing the form of the component polygons, and in their arrangement, that a certain discrimination is required. To aid in the construction of the figures, we may observe that the lines repre- senting the external forces acting on a rigid frame in equilibrium must in the reciprocal figure form a closed polygon, and when these lines are parallel, as when weights only are applied, this polygon becomes infinitely thin, and is represented by a single straight line, subdivided into parts proportional to the forces. Thus, in figs. 1 and 2, the three vertical forces are represented by the lines no, og, and gn, which represent respectively the solid weight, acting from x to 0, the up- ward reaction P acting from o to g and P from qg tom. This line (on), subdivided in the ratio of the loads, may be conveniently termed the line of loads, and reappears in all reciprocal figures of framework under parallel forces. The reciprocal figures corresponding to the ordinary Warren girder will now — be described in Plate XVII. fig. 1. The load is supposed to be applied at the — bottom joints, and will just be assumed as equal to 10 tons at each of the eight joints. These weights are represented by short vertical lines in fig. 1. FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 443 Fig. la is the reciprocal figure of Frame I., thus uniformly loaded and sup- ported at Xand Y. The line zy is the vertical line of loads, equal to 80 tons in all, and equally subdivided, because the load at each joint is equal. From each of these subdivisions horizontal lines are ruled, and the lines IJKLMNO in the reciprocal figure are drawn parallel to the lines similarly lettered in the frame. The lengths of each of the lines in the reciprocal figure measure the stresses on the members in the frame. The figure can be drawn in five minutes ; whereas the algebraic computation of the stresses, though offering no mathe- matical difficulty, is singularly apt, from mere complexity of notation, to result in error. The figure and the direction of each stress will be easily understood when decomposed into its component polygons. The triangle PIA corresponds to the polygon of forces at X, in which the direction of all the forces is that in which the pen moves, starting from Z towards z. The polygon of forces acting on joint 1, beginning with the forces determined by the previous poly- gon, and proceeding in the direction-in which the forces act on the joint 1. esa, J. | The polygon at joint 2 is shown separately at fig. 16, being AIJB; the polygon at joint 3 is also shown separately, the directions of the forces being in- dicated by arrows. The complete fig. 1a is built up of separate polygons similar to these two; the origin or starting-point on each being indicated by a small circle in fig. 1. Each line in fig. 1a serves as a part of two component polygons, but it _ would be passed over in opposite directions in the two polygons by a pencil fol- lowing the directions of the forces in the two polygons. This fact is of assistance in drawing the reciprocal figures, making it easy to find the starting-point or origin of each new polygon, since the lines representing forces already known must be traversed in the opposite direction to those forces; thus the polygon at joint 4 will include the force due to Band L. These have already formed part of polygons 2 and 3; but in these the direction of the forces was from the joint 4, and hence in the new polygon the direction will be to the joint 4, and the polygon will begin at Z, running BLMC. It must be observed that the lines ABCD all begin at Z, ending at the inter- section of I and J, K and L, M and N respectively. The stress on the two centre diagonals is nil, and with the uniform load the second half of the reciprocal figure is exactly symmetrical with the first half. The stress on d is equal to that on D. When the load is not uniform (fig. 2), the weights supported on the two piers are not equal; in other words, the forces P and P, are not equal, and the line of loads must be subdivided at Z into two portions, P and P, (fig. 2a), equal to the loads borne by the piers. The divisions 1, 3, 5, 7, 9, 11, 18, 15, are made equal 444 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL to the various loads on the several joints, these unequal loads being, as before, - indicated by vertical lines in fig. 2. The two halves of the reciprocal figures are now no longer symmetrical, but it is as easily drawn as the simpler case. Two of the component polygons are shown, as in the previous case. The direction of the stress on each member is found by going round each separate polygon, beginning with some strain the direction of which is known. Thus at joint 7 the polygon is ¢,7, d, P,, O, and knowing that the direction of the weight 7 is down, we find at once that P, and O must both be pulled upwards. Care must be taken as before to measure ABCDEFGH from the origin Z in each case. As soon as the values of P and P, have been determined, the most complicated arrangement of loads presents no more difficulty than the very simplest, the typical form being identical in all cases, and easily remembered. In figs. 3 and 3a the reciprocal figure for the same frame with a single load at the centre is shown. The strains on a, b, c are represented by the lines wa, xb, xe ; the strains on A, B,C by the lines zA, zB, zC. This will be clear from an inspection of the component polygons. In figs. 4 and 4a the reciprocal figure for a single weight hung at any joint is shown, and will readily be understood from the explanations already given. If the frame were inverted, and the loads applied at the top, the strains would remain the same in amount, but be altered in direction in the diagonals; the reciprocal figures would be identical in form with those already given, but would lie on the other side of the line of loads, as if simply turned over through 180° on that line as a hinge. Yeah by. A : If the loads in Frame I. were applied at the 7 <= 7. top joints instead of along the bottom, the ; ae Ms strains and the reciprocal figure would be modi- ; fied, the component polygons for the bottom joints being of the annexed type, fig. 3, and the component polygons for the top joint of the annexed type, fig. 4. P, is also placed above P, so that the upper and lower halves of the figure change places. It is not, however, necessary to recollect these Fig. 3, —« 8 Y changes of arrangement, since the known reaction | ead * at one pier and the first polygon of forces deter- oe mine at once the general arrangement of the Prine figure. In the example just given the members of the frame are simply sufficient in number to make the frame stiff; such a frame is incapable of being self-strained, that is to say, any member might be lengthened or shortened without throwing a strain on the other members. When this condition is fulfilled the stresses on a frame under the action of known external pressure determinate; but when more members are used than suffice to render the frame stiff, the stresses are indeter- FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 445 minate, and the frame may be self-strained. In these cases, therefore, the reciprocal figure is useless to determine the stresses. Such a frame as this shown in Plate XVIII. fig. 5; in which, if the diagonals and verticals were all adapted to resist tension and compression, the stresses could not be determined by the use of reciprocal figures or any ordinary method of computation. If, however, the verticals be alone suited to resist the compression, the diagonals being fit to sustain tension only, the stresses become determinate, half the diagonals being with any given load wholly inoperative. The reciprocal figure can be used to discover which are the active members, as they may be called, and what are the strains upon them. Fig. 5a shows the reciprocal figure for a uniform load. The inactive members in Frame IJ. are not numbered. The component poly- gons of fig. 5a are shown in figs. 5@,506. These figures require no explanation beyond that already given for frame }. Fig. 6 shows the active and inactive members of Frame II. partially loaded. The active members have arrows on them, showing the direction of the stresses. Fig. 6a is the reciprocal of fig. 6, and figs. 6a and 6@ show the component polygons as before. It must be remembered that in fig. 6a, as in fig. 5a, that the lines represent- ing the stresses on B, C, D, E, F, G, H, I, all start from Z. In fig. 7 we have a third frame not unfrequently used in roof work. Fig. 7a is the reciprocal of fig. 7, and is thus constructed. XY is the line of loads subdivided at Zin the ratio of the loads borne by the two piers. It is further subdivided into the parts 1,2,5,4,5,6,7, the loads directly borne by each joint. The lines A, B, C, D and F are in fig. 7a all drawn parallel to the top members of the same name in fig. 7, and start from points in the line of loads determined by the subdivision into partial loads. The lines a, b, ¢, d, ¢, fall radiate from Z, and these two sets of lines are joined by the zigzag line g, h, 7,7, &, 1, m,n, 0, each of course parallel to the corresponding member in fig. 7. The figure, although a little complex at first sight, is extremely easily and rapidly constructed. In building it up out of successive polygons we should as usual begin with the reaction of one pier; start- ing at Z we draw the line ZX, return along load 1 directly borne by the pier, and complete the first polygon by drawing Aa. The second polygon is A, 2, 6, H, g, and the remaining component polygons corresponding to each joint can easily be traced in like manner. It will be observed that all the members except A, B, C, D, E, F are in tension. Fig. 8 and fig. 8a (Plate XIX.) show a slightly different frame with the corre- sponding reciprocal figure when uniformly loaded. 4h, 7,/,% are in compression instead of in tension, as in Frame III. VOL. XXV. PART II. Dat 446 PROF. F. JENKIN ON THE PRACTICAL APPLICATION OF RECIPROCAL Figs. 9 and 9a show Frame IV. and its reciprocal figure when not uniformly loaded. The reciprocal figure now begins to appear very complicated, but it is drawn on precisely the same plan as fig. 8a; but the lines of loads being no longer equally subdivided, the reciprocal figure no longer presents two symmetrical parts. Figs. 10 and 10a with 11 and lla show frames commonly used as roofs, with reciprocal figures. They are only simplified cases of the roof already described. Fig. ila may be compared with fig. 76 in Ranxrne’s “ Applied Mechanics.”’ The series of figures 75 in the same work are true elementary reciprocal figures. Figs. 12 and 12a show a simple roof uniformly loaded, which is drawn in order to render more intelligible the comparatively complex case in figs. 13 and 13a. Fig. 13 shows the roof under a series of external forces which are no longer parallel, but represented by the inclined lines 1, 2, 3, which have been some- what arbitrarily chosen as corresponding to a possible distribution of stresses produced by the lateral and vertical pressure of wind. These external forces are met by the two reactions P and P, at the piers, calculated on the hypothesis that each pier or wall takes half of the horizontal strain. Fig. 13a is the curiously distorted reciprocal figure which results from these assumptions. It is drawn by precisely the same rule as the comparatively simple figs. 12a and 7a. In each the lines a, b, ¢, Jd radiate from a centre Z, which divides the lines P and P, representing the reactions on the piers. In each the members A, B, C, D diverge from points separating the successive loads on the joints 1, 2,3; but in fig. 13a the line of loads 1, 2,3 with the lines P and P, representing the reactions at the piers, build up a polygon enclosing a space, whereas in figs. 7a and 12a this polygon was represented by two straight lines superimposed. Again, if the zig-zag line corresponding to the diagonals be traced, it will be found to run in an essentially similar manner in figs. 12 aand 13a; thus I joins d and ¢ in both, the end of the line d having been determined by its intersection with D, both starting from Z and X. Looked at by the light of fig. 12 a, fig. 13 a becomes readily intelligible, and serves to show how the theory of reciprocal figures can be applied to the most complex conditions of stress which are con- ceivable, without any greater essential complication than occurs in the simplest examples. As a final example, the reciprocal figure is given of a braced suspension bridge or arch uniformly loaded, figs. 14 and 14a. The strains are drawn on the hypo- thesis that the direction and magnitude of the resultant thrust are known. This — thrust can be determined by Professor J. CLERK MaxweEtw’s method for calcu- lating the equilibrium of Frames, published at the same time as his account of reciprocal figures. In conclusion, a few words may be said of the advantage of the diagrams of FIGURES TO THE CALCULATION OF STRAINS ON FRAMEWORK. 447 forces, now explained as reciprocal figures, over the ordinary methods of calcula- tion used by engineers. The graphic method of calculation hitherto employed has been to draw a separate polygon of forces for each joint. To do this it was necessary at each joint to start afresh, setting out the known forces, and from them determining the unknown forces. In thus continually measuring and setting out new lines considerably greater accumulations of error, and more frequent errors, are pro- bable, than when each line when determined by an intersection is used where it lies, and if the successive polygons are drawn to any considerable scale, they lap over one another on the drawing in an awkward and complex manner. Moreover, it is impossible to complete the diagram of the reciprocal figure without taking every line into account; and the closing of the diagram by the final line is an almost perfect check on the accuracy of the delineation. When compared with algebraic methods, the simplicity and rapidity of exe- cution of the graphic method is very striking ; and algebraic methods applied to frames such as the Warren girders, in which there are numerous similar pieces. are found to result in frequent clerical errors, owing to the cumbrous notation which is necessary, and especially owing to the necessary distinction between odd and even diagonals. If this is the case when the loads are uniform or symmetrical, the advantage is much more strikingly in favour of the graphic method when the loads are not symmetrical, and when they are inclined, as in fig. 13, or in such cases as the framed arch and suspension bridge. In fine, the diagram once drawn acts as a sort of graphic formula for the strain on every part of the bridge or roof, and it is a formula which can hardly be misapplied. In conclusion, the author begs to acknowledge with thanks the assistance of his students, Mr T. H. Cunnincuam and Mr A. M‘CuLtocn, in preparing the diagrams; and takes the opportunity of repeating, that the merit of discovering the method is entirely due to Professor MaxweLt and Mr Taytor, the object of the present paper being to put the theory in such a form as should be intelligible to the engineer and mechanician. be i a) 2 as « 4 ry) , x i : a4, “a o + 5 ‘i t re me 2 : ’ a ; “ us 4 ‘ , : ag ; =a : matt vt ae he 7 Ae - ee | f = ¥ \ 7 \ iM 6+" « 7 ‘ .¢ » MU yt ( ie » ss s ; , avis - ' ers elie yo leg a? Oe F fs g ts TyT4 @il Al) T4tV0 AD AMT! edt iy j / P . —~ oF ; *. ’ hy 4 j jf iy Si) AJ 2eftagh [np eres ae 7a nm ¥ } vet yo isk, i" eres bY | Matta Fa 3 Bia) huvix 5 AS | atthe Oye ; Ss a i i gilt oat culo, dees toluetawl to nee ; : ' ple? (bas Tet aecombeigine: whiter cileevi eee ey? hue ufos itanees avis at [Sea & P - a <3 Sat apie DIL Srey oe APOE Ibe. 4 wie vite sh J Ate vit giah velo guel Wage weve 4) lads ' mide Oo , , 2 SY OT ie yin he ee we iL Pi ae : . ' ; ri . i =~ et tee ay ‘| Ten AES RE iets WOT Bl eee ie land. 7 inet oft lo. mange ont Geis Oa 4 : “ \ un pA f yor OILY Diba Srey ee ae Ad No > le dey he : °C Pinca (i¥ur 2 Ty quer ‘ 7 grey Write.) on, pe ( 449 ) XIl.—An Investigation into some previously undescribed Tetanic Symptoms produced by Atropia in Cold-Blooded Animals, with a Comparison of the Action of Atropia on Cold-Blooded Animals and on Mammals. By Tuomas R. Fraser, M.D. (Read 21st December 1868.) Authorities on the action of medicinal substances agree in including convul- sions among the effects on man of belladonna, and of its active principle, atropia.* Similar effects are described as occurring when large doses of these substances are administered to dogs, rabbits, and other mammals, and to various birds. The recent remarkable progress of our knowledge of the exact and ulti- mate physiological action of many medicinal substances is greatly due to investi- gations that have been made on animals of a lower type of organisation ; and, accordingly, numerous observers have instituted experiments with atropia on such animals, and especially on frogs. Hitherto, however, convulsions and tetanus have not been described among the effects of atropia-poisoning in cold- blooded animals. + While making a series of experiments, in April 1868, to determine the minimum fatal dose of atropia for frogs, I was somewhat surprised to find that symptoms of greatly increased reflex excitability occasionally occurred at a certain stage in the poisoning. Believing that a careful examination of these symptoms might probably serve to throw some light on the causation of several of the complicated effects of a substance that has long occupied an important position as a therapeutic agent, I have made a number of experiments (A), to determine accurately the character of these convulsive effects; (B), to ascertain the dose necessary for their production; (C), to differentiate, as far as possible, * Curistison, “A Treatise on Poisons,” 1845, p. 836; Trousszav and Pipoux, “ Traité de Thérapeutique et de Matiére Médicale,” tome ii. 1862, p, 55; Pereira, “ The Elements of Materia Medica and Therapeutics,” vol. ii. part i. 1855, p. 549; Srizxu#, “Therapeutics and Materia Medica,” vol, i. 1868, p.770; GusBieER, “ Commentaires Thérapeutiques du Codex Médicamentarius,” 1868, p. 602; Tu. and A. Husemann, “ Handbuch der Toxikologie,” Erste Halfte, 1862, p. 465 ; Tarpizv, “ Etude Médico-Légale et Clinique sur ’Empoisonnement,” 1867, p. 750; Tayzor, “The Principles and Practice of Medical Jurisprudence,” 1865, p. 358; Scurorr, “ Lehrbuch der Pharmacologie,” 1868, p. 508. { Since this was written, I have communicated with Dr Jouw Hartey, of London (the author of several important papers on the physiological action and therapeutical employment of bella- donna), and have had the satisfaction of learning that he also has observed tetanus, and other symptoms of abnormal reflex activity, in frogs during protracted atropia-poisoning. 2d March 1869.—I quote the following reference to these symptoms from a work which Dr Hartey has published since this paper was communicated :—“ The action of atropia leaves the frog in an excessively nervous state; the least disturbance causes great agitation, with increase of the respiratory movements, and a touch often throws the animal into a tetanic convulsion,”—7he Old Vegetable Neurotics, 1869, p. 240. VOL. XXV. PART IIL. DZ 450 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS the structures on whose affection they depend; and (D), to harmonise these effects with analogous ones in warm-blooded animals, and explain their appearance in certain special circumstances only, in both frogs and mammals. This investigation is limited to the consideration of these objects. Only those effects of atropia that are directly connected with the convulsive symptoms will, therefore, be considered. SECTION A. Soon after a small fatal dose, or one rather Jess than fatal, of a salt of atropia is administered to a frog, a slight degree of weakness occurs in the anterior extremities; the respiratory movements of the chest cease, those of the throat continuing; and the motor power becomes gradually more and more impaired, until at length no voluntary or respiratory movements occur, and the animal lies on the abdomen and chest in a perfectly flaccid state. If the condi- tion of the heart be now examined, it will be observed that the cardiac impulse is scarcely perceptible, and that the contractions are reduced to a very few in the minute. At this time, the application of various stimuli shows that the func- tions of the afferent and efferent nerves and of the spinal cord are retained, though in a greatly impaired condition. Several hours afterwards—it may be not until the following day—the action of the poison is still further advanced; for the afferent and efferent nerves are completely paralysed, while but an occasional and scarcely perceptible cardiac impulse can be discovered, the only signs of vitality being this imperfect cardiac action, and the retained irritability of the striped muscles. This condition may last for many hours, or for several days. Previous observers have apparently mistaken it for one of death, and have therefore failed to observe the symptoms that subsequently appear, and to which, more particularly, I wish to draw attention. The first of these symptoms is usually caused by a change that occurs in the flaccid condition of the animal; the anterior extremities becoming gradually more and more flexed, until they assume a state of rigid and continuous contraction, with the webs pressed either against each other, or against the opposite elbows—-tonic spasm of the muscles of the chest helping to keep the anterior extremities in this position. At this time, a touch of any portion of the skin increases the spasm of the anterior extremities and of the chest muscles, and causes some slight spasmodic movements in the posterior extremities. After a varying interval, the respiratory movements reappear, the cardiac action improves greatly in strength and in frequency, and the posterior extremities assume an extended position, with the webs more or less stretched. I1f the skin be now touched, a violent attack of tetanus occurs (at this time usually opistho- tonic), which may last for from two to ten seconds, and which is succeeded by a PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 451 series of clonic spasms. During the first attacks of tetanus the posterior ex- tremities are often more or less abducted, and immediately after each attack they become flaccid; but the anterior extremities almost always remain rigidly flexed. Ata somewhat later period tetanus of a still more violent character, and of longer duration, may be excited, and the attacks are now almost in- variably emprosthotonic. During them, the posterior extremities are rigidly extended; while at their conclusion, not only do the anterior extremities remain flexed, but the head continues bent downwards by tonic spasm of the muscles of the abdomen, chest, and neck. A series of such attacks may be produced by repeated touches of the skin; but when a number are excited in quick succession, the convulsions become shorter, and rather less violent, though they reacquire all their former violence after a period of rest. During the convulsive stage, and especially at its latter portion, the animal may execute various movements; but from the difficulty with which these are performed, even when they do not themselves excite spasms and convulsions, it is apparent that the power of voluntary movement is still considerably impaired. The period during which this tetanic condition remains was found to vary greatly in different experiments; and, as might have been anticipated, the larger, within certain limits, the dose of atropia administered, the longer the continuance of this condition. It has been observed to continue in some experiments for only a few hours; in others, for several days; and, in one experiment, for even so long as seventeen days. This great protraction of the stage of tetanus occurred in an experiment in which a small fatal dose of the sulphate was administered, and this experiment will now be described, as it admirably illustrates the usual sequence of the phenomena. Experiment XIX.*—A solution of 0°45 grain of sulphate of atropia, in eight minims of distilled water, was injected, by means of a Woop’s hypodermic syringe,+ into the abdominal cavity of a healthy male frog, weighing 455 grains. For some minutes afterwards, the frog jumped about very actively; but in about eight minutes its movements were slow and sluggish, and some weakness occurred in the anterior extremities, and in ten minutes it was unable to jump with normal activity, and when undisturbed lay quietly on the abdomen and chest. A few minutes later, the respiratory movements of the abdominal and chest muscles ceased, those of the throat muscles, however, continuing, and the head rested on the lower jaw. In twenty-one minutes, the frog was placed on the back, and it then made some feeble voluntary movements of the limbs, which * The numbers of the experiments of which detailed descriptions are given in this section have reference to the arrangement in Table I. at the end of the section. + This instrument was employed in all the experiments in this investigation. 452 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS were insufficient to change its condition, though apparently designed to do so. There were now no respiratory movements whatever, and the heart’s action, as ascertained by its impulse, was reduced to twenty-four feeble beats in the minute. In thirty-one minutes, the frog was in a perfectly flaccid condition ; it was obviously unable to perform any voluntary movements, and merely feeble reflex twitches could be excited by strong stimulation. In two hours, reflex movements could still be excited, but the rate of the cardiac contractions had diminished to nineteen per minute. In six hours, however, the nerve-paralysis was more complete; stimulation did not excite any reflex movement; and even direct galvanic excitation of an exposed sciatic nerve failed to produce any mus- cular contraction, although the muscles themselves readily contracted when the poles were applied to their surfaces. The colour of the frog’s skin was now much darker than before the exhibition of atropia. At the earlier portion of the following day—eighteen hours after the adminis- tration of the poison—the frog was in the same state as last noted, except that the heart’s action was still more feeble, the contractions being distinctly vermi- cular, and at the rate of only fifteen beats per minute. Twenty-four hours after the administration, however, an extremely faint twitch of the foot could be excited by galvanism of a sciatic nerve; though a strong current passed through the cord caused no movement beyond that resulting from direct stimulation of several of the muscles of the back, and it was impossible to excite any reflex contraction. On the third day—forty-four hours after the administration—the frog was lying in the same flaccid condition. The heart’s impulse was extremely feeble, and the beats occurred only ten times in the minute. | On the fourth day—sixty-eight hours after the administration—a change of position had occurred, for the anterior extremities were flexed, and formed an arch- like prop on which the raised head and thorax were supported. Reflex movements were now more easily excited, though still very sluggish and feeble; and when such movements occurred the muscles continued in a contracted state for several seconds before they again slowly relaxed. This peculiarity in the contractions was most marked in the muscles of the thorax, anterior extremities, and head. A respiratory movement of the throat occasionally took place; and the rate of the heart’s beats was increased to twelve in the minute. On the fifth day—ninety-two hours after the administration—the frog was lying on the side with the anterior extremities strongly flexed, the webs being m close contact with the opposite elbows, while the posterior extremities were normally flexed. At frequent intervals, the contraction of the muscles of the anterior extremities and of the front of the thorax relaxed somewhat, and, apparently taking advantage of the intervals, the frog made slight voluntary movements, which always excited short attacks of emprosthotonic tetanus. These — PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 458 attacks ceased first in the posterior extremities, continuing for several seconds longer in the anterior extremities and thorax. During the intervals the anterior extremities were constantly flexed by tonic spasm in their muscles, and in those passing to them from the thorax (especially in the pectoralis major). If the skin were touched, or if the frog were otherwise gently stimulated, an attack of empros- thotonic tetanus followed, during which the flexion of the anterior extremities was rendered more rigid, and the posterior extremities were extended and consider- ably abducted. These attacks of tetanus lasted for about five seconds, when the posterior extremities became flaccid; but the increased spasm of the anterior extremities and of the chest muscles continued for about sixty seconds longer. When the frog was not suffering from general tetanus there were occasional respiratory movements of the throat and chest. It was now impossible to observe any cardiac impulse, because of the constant spasm of the chest muscles. On the sixth day—one hundred and sixteen hours after the administration— the frog was lying on the back with the anterior extremities rigidly retained in the position already described; but the head was bent forwards (downwards) by spasm of the anterior abdominal and chest muscles, and the posterior extremities were loosely extended, with the webs slightly stretched. The respiratory move- ments of the throat were frequent, but those of the thorax but rarely occurred. If a posterior web were now touched, a pretty powerful attack of tetanus followed, during which the body was curved in the form of an arch, with the head bent for- wards, while the anterior extremities were strongly clasped against the chest, and the posterior rigidly extended in a straight line. This was general for about six seconds, when the posterior extremities became flaccid; but the increased spasm of the muscles of the anterior extremities and of the anterior surfaces of the abdomen, chest, and throat continued for twelve seconds longer. Still more powerful and prolonged tetanus could be excited by stimulating the skin of the head; and these attacks lasted for eight seconds in the posterior extremities, and for two minutes in the anterior extremities and in the muscles of the anterior surface of the chest. So powerful was the tetanus at this stage that it was possible to lift the frog by the feet and hold it horizontally for eight seconds, with either the back or front of the animal uppermost. The faintest voluntary movements almost invariably excited a tetanic convulsion, and, indeed, such attacks could be produced even by excitations through the organs of vision, as by the sudden approach of any object. The frog remained in this remarkable condition, without any notable change, until the fourteenth day. At this time—three hundred and ten hours after the administration—it still continued in the position last described, but, although violent tetanus could still be excited, this did not occur so invariably as before. Frequently, indeed, excitation produced only slow and stiff movements of the posterior extremities, VOL. XXV. PART II. OA 454 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS with violent convulsive spasms of the anterior extremities and of the trunk. Moreover, to excite general tetanus, stimuli of a rather more severe, though still slight, character were now required. With this modification in the constancy and readiness with which tetanus could be excited, and with a slight diminution in the period during which an attack lasted, the condition of the frog remained unchanged until the twentieth day. At this time—four hundred and fifty hours after the administration—the frog had assumed a most extraordinary and ungainly attitude. It lay on the right side, with the head bent downwards, by strong tonic spasm of the muscles of the front of the abdomen, chest, and neck; with the anterior extremities rigidly clasped against the thorax (the webs being, as before, pressed against the oppo- site elbows) ; and with the right posterior extremity extended, and the left drawn forwards and slightly flexed. The disagreeable appearance resulting from this attitude was greatly increased by the emaciation of the frog, which had gradually increased for several days, until it had so far advanced that the frog now weighed only 385 grains—its weight before the sulphate of atropia was given having been 455 grains. At this time, excitation usually produced merely stiff and slow movements of the posterior extremities, and increase of the tonic spasm of the muscles in the other regions. Occasionally, however, a short attack of empros- thotonic tetanus could still be excited. For other two days the frog remained in this condition; but on the twenty-third day—five hundred and twenty-six hours after the administration—general tetanus could not be excited by any stimulus, however strong. Stimulation only slightly increased the tonic spasm of the muscles of the throat, anterior extremities, chest, and abdomen, and caused slow and feeble movements of the posterior extremities. On the following day—the twenty-fourth of the experiment—the frog was found dead and in rigor; the emprosthotonic curve of the body and the rigid flexion of the anterior extremities being retained in death. In this experiment the tetanic stage lasted for seventeen days, which in this investigation is the longest period during which it has been observed to continue. During eight days the attacks were extremely violent and prolonged; during six days neither could they be invariably excited, nor did they continue for quite so long a period as before; and during the three days that immediately preceded the death of the animal they could but rarely be produced. Loss of weight is by no means an invariable occurrence after a long continu- ance of the tetanic stage. Indeed, Iam inclined to think that an opposite effect, namely, augmentation of weight, more commonly occurs. The latter is caused by general anasarca, and is sometimes very considerable. : Allusion has been made in the general description of these remarkable phenomena to the stage of complete paralysis having continued for several days. In the following experiment its duration was five days. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 455 Experiment XXXIII—I injected into the abdomen of an active male frog, weighing 251 grains, a solution of 0:3 grain of sulphate of atropia, in five minims of distilled water. Flaccidity and motionlessness occurred rather more rapidly than in the previous experiment; and eight hours after the injection it was found that the conductivity of the sciatic nerves was completely suspended —the muscles, however, freely contracting when directly galvanised—and that the heart’s action was extremely feeble, and at the rate of only nineteen beats in the minute. On the following day—twenty-two hours after the administration—the heart’s impulse was even less apparent, and contractions occurred only seven times in the minute; while galvanism of the sciatic and brachial nerves was not followed by any muscular contraction, although idio-muscular contractility was apparently unaffected. The frog remained in this state of complete nerve-paralysis for other four days. The cardiac action, however, improved during the latter portion of this period, and on the sixth and seventh days the contractions occurred sixteen and nineteen times respectively in the minute. On the seventh day—at about one hundred and forty-six hours after the administration—a change occurred. ‘The frog still lay on the abdomen and chest, with the posterior extremities flaccidly extended; but the anterior extremities were now slightly arched, there were infrequent respiratory movements of the throat, and a slight touch of the skin excited a feeble, momentary, and sudden movement of the whole body. On the eighth day—one hundred and sixty-eight hours after the adminis- tration—excitation produced a violent attack of tetanus, which was slightly opisthotonic in character, and was succeeded, after lasting for eight seconds, by a series of quivering movements of the posterior extremities. It was not neces- sary, however, to apply excitation, in order to produce tetanic convulsions, for they also frequently occurred when voluntary movements were attempted. At one hundred and seventy hours, the tetanus was emprosthotonic. On the ninth day—one hundred and ninety hours after the administration—the tetanic condition was exactly the same as at the latter part of the previous day, and the frog remained extended horizontally for five seconds when lifted in that position by the ankles. The heart was now contracting at the rate of twenty- two beats in the minute. On the tenth day—two hundred and sixteen hours after the administration— the frog was lying on the lower jaw, chest, and abdomen, the anterior extremities being extended at right angles to the body, while the posterior were stretched backwards. Excitation now caused a feebler and stiffer movement of the limbs; and however powerful the excitation, it was impossible to cause tetanic convulsions. On the eleventh day—two hundred and thirty-eight hours after the adminis- 456 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS tration—only feeble movements could be excited, and there was now a slight degree of continuous general stiffness. The heart’s action was at the rate of twenty-two beats in the minute, but the respiratory movements were feeble and very infrequent. - On the twelfth day—two hundred and sixty hours after the administration— the stiffness was more marked, no reflex movements whatever could be excited, and it was found that the sciatic nerves were completely paralysed, and that the muscles responded but faintly to direct galvanic stimulation. The heart’s action was at the rate of only eleven beats in the minute. On the thirteenth day, the frog was dead, and in rigor. The dose of atropia administered in this experiment was exceptionally large, when compared with the weight of the frog; but the frog was a small one, and had been kept in the laboratory for many months—conditions which appear to favour a certain amount of tolerance. With a frog recently obtained from its natural habitat so large a dose, however, would most probably have proved fatal before tetanus occurred. The stage of complete paralysis of motor nerves lasted altogether about five days and ten hours. Each of these two experiments has been distinguished by an exceptional cir- cumstance: Experiment XIX. by the long continuance of the stage of tetanus, and Experiment XXXIII. by the long continuance of the stage of complete para- lysis of the motor nerves. In the experiment which will now be described the duration of the phenomena was such as more frequently occurred. Eaperiment XXIU.—A solution of 0:4 grain of sulphate of atropia, in four minims of distilled water, was injected under the skin at the left flank of a frog, weighing 386 grains. As usual, after such a dose, in the course of an hour the frog was flaccid, and unable to perform any voluntary movements. On the following day—eighteen hours after the administration—the frog was lying motionless on the abdomen and lower jaw. It was ascertained by galvanic stimulation that the conductivity of the sciatic nerves was suspended, while the contractility of the voluntary muscles was apparently unaffected. At twenty- two hours after the administration, however, a weak stimulus produced feeble reflex movements. The heart’s impulse was now barely perceptible, and con- tractions occurred but eight times in the minute. On the third day—fifty hours after the administration—the frog was still lying on the abdomen, but the chest and head were slightly raised by continuous flexion of the anterior extremities. The reflex function was in a more active state, for a slight stimulus applied to the skin of the head caused an increase in the flexion of the anterior extremities, by which the head was still further raised, and a sudden extreme abduction of the two posterior extremities. Irregu- lar respiratory movements of the throat were now observed. On the fourth day—seventy-three hours after the administration—a faint ee aes eS ee Se ——<— PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 457 touch of the skin of the head was followed by an attack of opisthotonic tetanus, lasting for four seconds; and during it the anterior extremities were rigidly arched, while the posterior were extended straight backwards. When the stimulus was applied to any other region, the only effect was an increase in the tonic spasm of the anterior extremities, and a sudden somewhat spasmodic flexion of the posterior. On the fifth day—ninety-five hours after the administration—the frog was lying on the back with the anterior extremities rigidly flexed, the webs being pressed against each other, and with the posterior extremities stiffly extended. A slight touch of the skin of any region was immediately followed by a sudden and violent attack of emprosthotonic tetanus. These convulsions were usually general for ten seconds; but the tetanic spasm continued in the anterior extre- mities for several seconds longer than elsewhere. The respiratory movements had now become more frequent and regular. During the two following days the frog remained in this condition. On the eighth day—one hundred and sixty-four hours after the administra- tion—it was more difficult to excite general tetanus, somewhat irregular convul- sions most commonly occurring. When the skin of an ankle was touched, tetanus occurred in that limb and in the two anterior extremities for five seconds; but merely spasms, without extension, occurred in the opposite posterior extremity. General tetanus could be excited only when the irritation was applied to the head. The cardiac impulse had now greatly improved in character, while the rate of contraction had increased to twenty-two beats in the minute. After this a daily improvement was apparent. On the twelfth day the frog had resumed a normal sitting posture, the anterior extremities being, however, still slightly arched; and on the sixteenth day the tonic spasm of the chest muscles and of the anterior extremities had completely disappeared, while slow, voluntary movements could be cautiously performed: but during all this time it was possible to excite a short attack of general tetanus, though severe or frequently repeated stimulation had to be employed. On the seventeenth day—three hundred and eighty-two hours after the administration—stimulation, even when severe, excited mere stiff reflex move- ments of the two posterior extremities, and comparatively slight and short tetanus of the two anterior. The complete disappearance, however, of the exaggerated activity of the reflex function was but slowly effected, and did not occur until about the twenty- fourth day, or five hundred and fifty hours after the administration. For several days after this, the frog was in a somewhat torpid state, moving about very sluggishly, and obviously preferring to remain quiet; but ultimately it recovered perfectly. WOL, XXV. PART Ir. 6B 458 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS The total duration of the symptoms was considerably shorter in a few of the experiments, of which the following is an example :— Experiment XV11.—Three-twentieths of a grain of sulphate of atropia was dissolved in four minims of distilled water, and injected under the skin at the left flank of a male frog, weighing 156 grains; but during some vigorous move- ments of the frog, which succeeded this injection, a small quantity of the solution escaped from the subcutaneous tissue. In a few minutes, the frog was lying on the abdomen ; chest, and lower jaw in a flaccid state; but even in three hours the conductivity of the motor nerves was found to be retained. The observations were now interrupted until the following day. At this time—twenty-four hours after the administration—the frog was lying as last described; but the conductivity of the motor nerves was found to be com- pletely suspended, while idio-muscular contractility was apparently unaffected. The heart’s contractions were very feeble, and occurred twenty-six times in the minute. On the third day—fifty hours after the administration—the state of flaccid paralysis had disappeared, and the frog was sitting in a nearly normal posture, except that the anterior extremities were unnaturally and somewhat rigidly flexed. On touching any part of the body, a violent attack of opisthotonic tetanus occurred, during which the animal was turned on the back. Such attacks could be excited at any time, at short intervals, during the next three hours, at the end of which period the observations were interrupted. They were general for five seconds; but the tetanic contraction continued in the anterior extremities for five seconds longer than elsewhere. In the intervals between them the frog turned itself from the back, and executed feeble and slow voluntary movements. The heart’s contractions were of fair strength, and at the rate of forty-six in the minute; and the respiratory movements of the chest and throat were of nearly normal frequency. On the fourth day—seventy-four hours after the administration—the frog seemed to have perfectly recovered: it moved and jumped about freely, and no trace of exaggerated activity of the reflex function could be discovered. The description that has been given, and the illustrative experiments that have been narrated, are sufficient to indicate the usual characters and sequence of the phenomena with such a dose of atropia as produces tetanus. Experiments have, however, been made in which the functions of the cerebro-spinal nervous system were not observed to be completely suspended in the stage of the poisoning, antecedent to the appearance of tetanus. Only impairment of these functions was observed ; but, as the state of flaccidity often lasts for several days, it is obviously impossible to make observations so continuously during its existence, as to authorise the assertion that total suspension did not occur. At the same time, there is no reason for supposing that complete paralysis is a necessary antecedent to tetanus. 7 PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 459 It has also happened that in one or two experiments symptoms of exaggerated activity of the reflex function occurred, without being observed to assume the violence of tetanus. The following is an example of such an experiment :— Laperiment X.—I\ injected under the skin, at the left flank of a male frog, weighing 231 grains, one-fifth of a grain of sulphate of atropia, dissolved in four minims of distilled water. In ten minutes, the frog was resting flaccidly on the abdomen and chest. In two hours, all voluntary and respiratory movements had ceased, but stimulation still excited feeble reflex contractions; and the heart was contracting at the rate of twenty beats in the minute. On the second day—twenty hours after the administration—the frog had resumed a natural position, the thorax and head being supported by the anterior extremities, while the posterior extremities were normally flexed; and the throat and chest respirations were frequent. When the skin was touched, or when any object was rapidly approached to the eyes, a sudden, spasmodic, and momentary contraction occurred simultaneously in the four extremities ; but it was impossible to excite a tetanic convulsion even by severe stimulation. These spasmodic starts —for they were only such—were often preceded by a “‘ croak,” and when suddenly and unexpectedly excited, were sufficiently strong \to raise the body upwards for about a second. During the following day, these symptoms continued ; but on the fourth day the only symptom was a slight degree of stiffness when the frog jumped. On the fifth day the frog was perfectly well. It is almost superfluous to allude to the resemblance in frogs between the tetanic symptoms of atropia and those of strychnia. There are, however, certain peculiarities connected with the tetanus caused by atropia—altogether apart from the remarkable circumstance of this tetanus being preceded by more or less com- plete paralysis—that distinguish it from the tetanus caused by strychnia. After poisoning by atropia, the symptoms of exaggerated excitability of the reflex func- tion, as has been shown, are extremely slight on their first appearance, and they acquire their greatest violence only after some considerable time. When these con- vulsant effects have become fully developed, the state of the animal is one of nearly constant tonic spasm—this tonic spasm being rarely general, but almost always restricted to certain regions,—so that the attacks of tetanus are of the nature rather of exacerbations of existing spasm than of successive and independent convulsions. Strychnia tetanus, on the other hand, becomes fully developed with great rapidity; and, during the stage of remission, the animal is usually in a perfectly flaccid state.* * Although this is ‘‘ usually” the case, continuous tonic spasm of the anterior extremities may be produced by strychnia also, if an extremely small dose be given. I have found that a dose equivalent to about the 7;;,,;th of the weight of a male frog (or of a female in whom the abdomen is not greatly enlarged by distended oviducts) will almost invariably cause continuous spasm and arch-like flexion of the anterior extremities; and Tarprev (op. cif. p. 983) describes the same effect in an experiment with a minute dose of strychnia. 460 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS Further, in atropia-poisoning, the attacks of tetanus can seldom be excited by the very slight stimuli that are sufficient to do so in strychnia-poisoning. The tetanus of atropia, also, is characterised by various irregularities. Some of these have already been described; such as the continuous spasm of the muscles of the throat, of the front of the thorax and abdomen, and of the anterior extre- mities, either only accompanying a condition in which tetanus in the posterior extremities may be excited, or also persisting after this condition has ceased: and of the others, it is sufficient to mention the occurrence of tonic spasm of one group of muscles in one limb, and of another group in another; of contractions of unequal force in the muscles at the opposite sides of the thorax and neck, causing lateral curvature during a tetanic convulsion; and of tetanus in the posterior extremities, with only slight increase of reflex excitability in the anterior. The last of these irregularities was observed in the following among other experiments :— Experiment XXIX.—A solution of four-tenths of a grain of sulphate of atropia, in four minims of distilled water, was injected under the skin, at the right flank _ of a female frog, weighing 361 grains, whose oviducts were greatly distended. On the following day, the frog was lying on the abdomen, chest, and lower jaw, with the posterior extremities flexed, and the anterior extended at right angles to the body. When the skin was stimulated, some feeble movements followed in the toes of both posterior extremities; but no reflex contraction could elsewhere be excited. On the third day—fifty-two hours after the administration—the posture of the frog was the same as on the previous day; but the paralysis was now more complete, for no reflex movement whatever could be excited, and it was found, on examination, that the motor conductivity of the sciatic nerves had dis- appeared. On the fourth day—seventy-two hours after the administration—the condi- tion of flaccidity was no longer present. The anterior extremities were now | slightly flexed, so as to raise the head and chest; and now and then a feeble __ voluntary movement, and a barely perceptible respiration, occurred. These movements generally excited an attack of violent tetanus in the posterior extremities, and a comparatively feeble spasmodic extension of the anterior, during which the latter assumed a more perpendicular direction than before. Feeble irritation caused similar attacks. They usually lasted for eight seconds in the posterior extremities, and for only three in the anterior. During the fifth and sixth days, the frog continued to suffer from tetanus, . and the character of the symptoms was exactly the same as on the fourth day. Neither abnormal flexion nor tonic spasm occurred in the anterior extremities, and such convulsive movements as appeared in them were always much less violent, and of shorter duration, than in the posterior extremities. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 461 On the seventh day, the posture of the frog was quite normal; voluntary movements took place with considerable activity; and although some exaggera- tion of the reflex function was still present, it was exhibited principally by stiff spasmodic movements of the posterior extremities, and general tetanus could not be excited. The frog recovered completely in a few days. The absence of rigid and continuous flexion of the anterior extremities, which is illustrated by this experiment, has been an invariable occurrence in frogs with distended oviducts. With this exception alone, so far as my experience has shown, rigid and continuous flexion of the anterior extremities is a con- stant, prominent, and early symptom of the motor-stimulant action of atropia. When the dose of atropia exhibited is not a fatal one, the animal usually recovers completely and rapidly. In one experiment, however, this was not the case. The symmetrical tonic spasm of the two anterior extremities passed into unsymmetrical tonic spasm, which persisted for several months after the disap- pearance of every other symptom. This sequela will be best described by a short narration of the experiment. Experiment XX VIII.—I injected three-tenths of a grain of sulphate of atropia, dissolved in four minims of distilled water, into the abdominal cavity of an active and perfectly healthy male frog, weighing 275 grains. The usual paralytic effects followed. During the second and third days, the motor-nerve conductivity was completely suspended; but on the fourth day it reappeared, though in an extremely imperfect form, galvanism of a nerve trunk producing only faint twitches. On the fifth day, the frog was lying on the abdomen with the head and chest raised on the anterior extremities, which had become symmetrically flexed, the webs being rigidly and continuously pressed against the opposite elbows. Slight irritation now excited a short attack of opisthotonic tetanus. On the sixth day, the attacks of tetanus were somewhat more violent, but they were still opisthotonic. On the seventh, eighth, ninth, and tenth days, the attacks of tetanus were very violent, and emprosthotonic in character. On the eleventh day, the violence and duration of the tetanic convulsions had somewhat diminished. On the twelfth, thirteenth, and fourteenth days, the frog still retained the strongly flexed symmetrical posture of the anterior extremities; but irritation now excited merely a sudden momentary extension of the posterior extremities, and an increase of the tonic spasm of the anterior. On the fifteenth day, the frog had assumed a nearly normal sitting posture. The anterior extremities were, however, still rigidly flexed, and the frog could move about only by a vigorous use of the posterior extremities. Irritation now VOL. XXV. PART II. 6 Cc 462 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS caused merely a slight increase of the flexion of the anterior extremities, and perfectly normal movements in the posterior. On the sixteenth day, it was observed that the posture of the anterior extremities was somewhat unsymmetrical; the right being rather more flexed than before, while the left was extended backwards so as to be nearly parallel with the left side of the body. For several days afterwards, the only change was an increase in the rigidity and tonic spasm of the anterior extremities; until, on the twenty-first day, they had assumed the following positions:—The right anterior extremity was in extreme flexion, the upper-arm being at a right angle to the body, with the fore- arm below it, while the hand was everted at the wrist, and had its dorsal surface closely pressed against the anterior surface of the shoulder; the left anterior extremity was extended backwards (towards the posterior extremities), the arm being in close contact with the left side of the thorax, with the fore-arm slightly flexed, inverted, and pressed against the abdomen, while the web was firmly applied, by its palmar surface, against the lower part of the anterior surface of the abdomen. JEoth anterior extremities were rigidly maintained in these postures, and the frog had no control over them. Changes of position were effected by the use of the posterior extremities alone; and, while irritation produced normal reflex contractions in the posterior extremities, it produced only extremely faint movements in the anterior without changing their unsymmetrical postures. When the frog was placed in water, vigorous swimming movements of the posterior extremities occurred, but the anterior remained motionless. This sequela first appeared seventy-four days before this description was written; and at this time, there is neither the slightest abatement in the rigidity, nor any other change in the character of the distortion. Although the physiological action of atropia has been frequently and elabor- ately studied, these very striking and remarkable convulsive phenomena have hitherto escaped attention. I have, therefore, thought it necessary to enter with considerable detail into the description of these effects, so as to indicate with accuracy their usual character, and to point out the principal irregularities that have been observed. I have likewise shown their relations to some of the other effects that are produced by this substance. The following Table contains a succinct account of a number of experiments on frogs with sulphate of atropia, in which the progress of the symptoms was not interfered with, either by ligature of blood-vessels before the administration or by division of nerve-structures before or after the atropia-effects were initiated. The latter classes of experiments will be described in a subsequent portion of this paper. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 463 TABLE I.—SuMMARY OF EXPERIMENTS ON FROGS WITH SULPHATE OF ATROPIA, IN WHICH THE EFFECTS WERE NOT MATERIALLY INTERFERED WITH BY OPERATIONS OR OTHERWISE, : Relation Number Ea Grate, of Dose Region of Weicht to of Effect. | Experiment.| \» Fe Dose. | Weight Injection. On enee of Frog. i, 413 | 0:05 | go> | Under skin of | No obvious effect. left flank. ie 275 | 0:05 | s3y> | Into abdomi-| None observed in 6 hours. nal cavity. III. 333 | O11 | ga3, | Under skin of | No obvious effect. left thigh. IV. 294 | O1 | sgia Do. Slight incomplete paralysis 1st day; and per- fect recovery 2d day. V. 298 | 0:2 | roa Do. Incomplete paralysis 1st day; exaggerated reflex movements 2d day ; tetanus 3d day; and re- covery 4th day. VIi.* 275 | 02 | zA,— | Into abdomi-| Incomplete paralysis 1st day; tetanus 2d to nal cavity. oth days; stiff spasmodic reflex movements 6th to 8th days; and perfect recovery 10th day. VII. 273 | 02 | ass5 Do. Incomplete paralysis 1st day ; exaggerated re- flex movements 2d to 5th days ; and recovery 6th day. WATT. 376 | 03 | rss Do. Incomplete paralysis Ist to 3d days; tonic spasm and tetanus of anterior extremities and chest muscles, with only slightly exaggerated reflex movements of posterior extremities 4th to 10th days ; and perfect recovery 12th day. 1X. 250 | 02 | seh5 Do. Incomplete paralysis lst day; tetanus 2d to 6th days; stiff spasmodic reflex movements 7th and 8th days; and perfect recovery 9th day. Xx. 231 | 0-2 | y¥s5 | Under skin of} Incomplete paralysis 1st day; exaggerated re- left flank. flex movements 2d and 3d days; and perfect | recovery 5th day. XI. 346 | 0°3 | zys3 | Into abdomi-| Incomplete paralysis 1st to 8th days; and nal cavity. death, with commencing rigor, 9th day. | XII. 230 | 02 | ass Do. Incomplete paralysis 1st and 2d days; slight tetunus 3d day; stiff spasmodic reflex move- ments 4th to 6th days; and recovery 7th day. XIII. 340 | 03 gies Under skin of | Incomplete paralysis 1st day ; tetanus 2d day ; right flank. stiff spasmodic reflex movements 3d day; and perfect recovery 5th day. incomplete paralysis 3d day; tetanus 4th to 6th days ; stiff reflex movements 7th day ; | | XIV. 447 | 04 | svar Do. Incomplete paralysis 1st day ; spasms 2d day ; | | and recovery 8th day. * The same frog was used in this experiment as in Experiment II. The second dose (0:2 gr.) was administered 21 hours after the first, and when the frog appeared to be in normal health. The influence of the first dose might, however, have been still partially present; and the exceptional severity of the symptoms described as being caused by a dose equivalent to only the ;,;th of the weight of the frog may thus be accounted for. If this view be correct, the dose of Experiment VI. should be about 0°25 grain, or the ;~5,th of the weight of the frog. 464 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS TABLE I.—SuMMARY oF EXPERIMENTS ON FroGsS—continued. In Grains. Relation Number of Dose Region of Weicht to of Effect. Experiment. of Pog Dose. | Weight Injection. as of Frog XV. 432 | 0-4 | zosz | Under skin of| Complete paralysis Ist and 2d days; tetanus right flank, 3d to 8th days; stiff spasmodic movements 9th day; and perfect recovery 10th day. XVI. 372 | 0°35 | rss Do. Complete paralysis 1st and 2d days; tetanus 3d to 6th days; stiff spasmodic movements 7th to 9th days; and recovery 10th day. xVIL 156 | 0:15 | yj45 | Under skin of| Incomplete paralysis 1st day; complete par- left flank. alysis 2d day; tetanus 3d day; and perfect recovery 4th day. XVIII. | 508 | 0°5 | yj; | Into abdomi-} Complete paralysis 1st to 4th days ; incomplete nal cavity. paralysis 5th day; tetanus 6th to 8th days; stiff reflex movements 9th to 11th days; and perfect recovery 12th day. XIX, 4556 0°48 | a4 Do. Complete paralysis in 6 hours and at earlier part of 2d day; incomplete paralysis, 2d to 4th days ; tetanus 5th to 22d days ; stiff spas- modic movements 23d day; and death, with | commencing rigor, 24th day. |i ¢ pecan 404 | 0-4 | goka | Under skin of | Complete paralysis, 1st and 2d days; tetanus left flank, 3d to 9th days; stiff spasmodic movements 10th and 11th days; and recovery 12th day. XX, 3800 | 0:3 | ror Do. Incomplete paralysis 1st day; slightly exagger- ated reflex movements 2d day; and death 3d day. XXII. 400 | 04 | asb0 Do. Incomplete paralysis 1st day; complete par- alysis 2d day ; tetanus 3d to 6th days ; irregu- lar tetanus, with twisting of body to left, 7th and 8th days; stiff spasmodic movements, also with twisting of body to left, 9th to 13th days; dead, with rigor, 14th day, Do Complete paralysis 1st and earlier part of 2d day ; exaggerated reflex movements 3d day ; | tetanus 4th to 16th days; stiff spasmodic movements 17th to 21st day; stiffmovements 22d to 24th days; and perfect recovery 27th day. XXIV. | 482 | 05 sia | Under skin of iasera hed paralysis lst and 2d days; com- both flanks. | plete paralysis 3d day; exaggerated reflex movements 4th day; tetanus 5th to 7th days ; stiff spasmodic movements 8th and 9th days ; and death, with rigor, 10th day. XXV. | 337 | 0:85 | 52, | Under skin of| Incomplete paralysis 1st to 5th days; and death, left flank. with commencing rigor, 6th day. XXXVI. | 234 | 0:25 | 53; Do. Incomplete paralysis 1st to 3d days; tetanus 4th to 12th days; stiff spasmodic movements 13th and 14th days; and perfect recovery 15th) day. : XXVII. | 465 | 0°5 pat Do. Incomplete paralysis 1st day; tetanus 2d to 4th days; and death, with commencing rigor, } 5th day. Ia XXIII. | 3886 | 0-4 ©| a oy PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 465 TABLE I.—SumMMARyY or EXPERIMENTS oN FRoGS—continued. Number of Experiment. XXVIII. XXIX. XXX. XXXI. XXXII, XXXII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. | | ox XTX. | ih, XLI, XLII. XLII. In Grains. Weight of rae Dose. 275 0:3 361 0°4 270 0:3 305 0:4 340 0-4 251 0:3 410 0°5 403 0:5 638 0-8 396 0-5 147 0:2 214 0°3 322 0-5 254 0-4 259 0-5 340 1: Relation of Dose to Weight of Frog. dx. 917 Region of Injection. Into abdomi- nal cavity. Under skin of Into abdomi- nal cavity. Under skin of right flank. Under skin of both flanks. Into abdomi- nal cavity. Under skin of both flanks. Do. Under skin of left flank. Under skin of left thigh. Into abdomi- nal cavity. Do. Under skin of both flanks. Into abdomi- nal cavity. Under skin of left flank. Do. Effect. right flank, | Incomplete paralysis 1st day ; complete paraly- sis 2d and 8d days; incomplete paralysis again on 4th day; tetanus 5th to 11th days; stiff spasmodic reflex movements 12th to 14th days ; stiff reflex movements 15th day; and unsymmetrical continuous rigidity of the an- terior extremities 16th day, remaining for more than 74 days afterwards, Incomplete paralysis 1st and 2d days ; complete paralysis 3d day; tetanus 4th to 6th days; stiff spasmodic movements 7th and 8th days; and perfect recovery 10th day. Incomplete paralysis 1st to 5th days; and death, with commencing rigor, 6th day. Incomplete paralysis Ist day; slightly exagger- ated reflex movements 2d day; and death 3d day. Incomplete paralysis 1st day; exaggerated re- flex movements 2d day; tetanus 3d and 4th days ; stiff spasmodic movements 5th day; and perfect recovery 7th day. Complete paralysis 1st to 6th days; slightly ex- aggerated reflex movements 7th day ; tetanus 8th and 9th days; stiff reflex movements 10th and 11th days; complete paralysis 12th day ; and, death, with commencing rigor, 13th day. Complete paralysis 1st day; and death, with rigor, 2d day. Do. do. Incomplete paralysis 1st day and earlier part of 2d; exaggerated reflex movement latter part of 2d day ; tetanus 3d day ; stiff reflex move- ments 4th day ; and death 5th day. Complete paralysis 1st and 2d days; incom- plete paralysis 3d day; tetanus 4th to 6th days ; exaggerated reflex movements 7th day ; and death 8th day. Incomplete paralysis 1st day; exaggerated re- flex movements 2d day; fetanus 3d to 10th days ; stiff spasmodic movements 11th to 13th days; and perfect recovery, 15th day. Complete paralysis, lst and 2d days; and death, with commencing rigor, 3d day. Complete paralysis 1st day; and death, with rigor, 2d day. Complete paralysis 1st to 3d days; incomplete paralysis 4th and 5th days; and death, with commencing rigor, 6th day. Complete paralysis lst day; and death, with commencing rigor, 2d day. Do. do. VOL. XXYV. PART II. 6D 466 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS Some experiments were made with acetate of atropia also. I have not con- sidered it necessary to describe these in detail, or to include them in the above Table, as the symptoms were the same as those observed with corresponding doses of the sulphate. It appeared of interest to examine if analogous symptoms were produced in other cold-blooded animals, and, with this view, a number of experiments were made with 77zton cristatus—a species of water-newt, which abounds in many of the lochs in the neighbourhood of Edinburgh. It was found that sulphate of atropia produces in this animal the same general paralytic and convulsant effects as in the frog. After the subcutaneous administration of doses that were somewhat smaller than the minimum fatal, a condition of partial but marked paralysis was, in the first place, produced; and this was succeeded, in less than twenty-four hours, by a condition of slight impair- ment of the power of voluntary movement with decided increase of refiex excitability, which condition persisted, in many of the experiments, for more than fourteen days. The reflex excitability manifested itself by sudden starts, when the skin was gently touched; and by tetanic spasm, lasting for from fifteen to forty seconds, when the irritation was more prolonged and powerful, as when produced by a series of taps with the handle of a scalpel. The appearance of this tetanus was somewhat peculiar, and its characters varied considerably. Fre- quently, the trunk of the body was curved laterally, with the tail curled in three or four coils, and the head twisted round to such an extent that the snout was in contact with the outside coil of the tail; at other times, the body was curved in an opisthotonic spasm, with the tail elevated either in a straight oblique line or in coils, and with the head raised; while, not unfrequently, the trunk of the body was irregularly contorted, with the head and tail in one or other of the above positions. SECTION B. The experiments that have been made are sufficiently numerous to show what dose is required to produce these extraordinary convulsive phenomena. Tetanus, or, at least, a state of greatly exaggerated reflex excitability, may be looked for with great confidence, when a dose of the sulphate or acetate of atropia, equiva- lent to about the ;,4,5th of the weight of the frog, is administered by injection, either under the skin or into the abdominal cavity. If the latter region be selected, it is necessary to puncture the abdominal parietes at a point as far removed from the heart as possible, in order to prevent a powerful local action on that organ; at the same time, taking care to avoid injuring the lungs. It is also important to dissolve the atropia-salt in only a few minims of water—from four to eight is quite a sufficient quantity. Not only is the danger of affecting the heart by local contact thereby diminished when the exhibition is by the - : 4 Pp PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 467 abdominal cavity, but the small bulk of such a solution is also an advantage when atropia is exhibited by injection under the skin. In the latter case, the energetic movements that nearly invariably occur when the frog is set free, are very apt to press some of the solution out of the subcutaneous tissue; and even with this precaution I have found it difficult to prevent all loss. It appears from the experiments contained in Table I. that tetanus is also pretty constantly produced by doses somewhat greater or less than the z,)yoth of the weight of the frog; indeed, by the majority of the doses included between the -4,th and the ;,);jth. The larger doses usually produce the most violent tetanic symptoms, and they may be given with considerable confidence to very small animals, and to such as have been kept in a laboratory for several months. The smaller doses seem best adapted for large frogs, and for such as have been recently obtained from their natural habitats. If a dose be employed smaller than those above indicated, impairment of the functions of the cerebro-spinal nervous system and of the heart may be caused, but general tetanus will seldom follow, although spasms, generally restricted to certain regions, may occasionally appear. The tetanic state resulting from the largest doses usually terminates in death, that from the smallest in recovery. In the above Table, the smallest dose of sulphate of atropia that produced tetanus is equivalent to the ;,,th of the weight of a frog of 298 grains (Experi- ment v.), the largest to the -4;th of the weight of a frog of 147 grains (Experi- ment xxxviil.) Without attaching undue weight to an experience which is insufficient to justify generalisation on such a subject, it may be mentioned that tetanic symp- toms were usually produced most readily, and continued for longest periods, in the experiments that were made in winter, when the temperature of the laboratory was low. SECTION C. It is by no means an easy matter to ascertain what structures are concerned in the production of the convulsant effects of atropia, for the protracted intervals that often elapse between the administration of the poison and the appearance of tetanus, and the difference in the duration and severity of the tetanic symptoms that follow even the most carefully calculated doses, render the inquiry an unusually difficult one, and frequently necessitate a patient repetition of the experiments. It is obvious, at the outset, that experimental investigation is required. It cannot be maintained that these remarkable convulsant and tetanic effects are merely secondary results of certain degrees of the primary paralysing action of atropia on the cerebro-spinal system and on the heart. Against such a supposition it were easy to bring a mass of opposing evidence, derived from the physiological effects of other active substances. It is well known that after the administration 468 DR T. R. FRASER ON SOME UNDECSRIBED TETANIC SYMPTOMS of curara (wourali) frogs may remain for lengthened periods in a state of absolute motor paralysis, with the cardiac action greatly impaired, and nevertheless per- fectly recover without the occurrence of the slightest degree of abnormal activity of the reflex function. Professor VuLPIAN has recently shown that iodide of phos- phethylamine may likewise produce in frogs complete temporary paralysis, yet this is not succeeded by any spasmodic symptoms.* In many experiments, also, which I have made with physostigma—one of which is described in a paper com- municated to this Society|—complete motor paralysis and great diminution of the cardiac action were produced, yet the animal gradually recovered therefrom, with- out any symptom of exaggeration in the reflex activity having been observed. Similar evidence may be accumulated from many other sources; but it is sufficient to mention an interesting experiment by VuLPian, which has a direct bearing on the question. That eminent physiologist ligatured the aorta at its origin from the heart ofa frog, so as completely to stop the arterial circulation. In the course of a few hours, the excitability of the spinal cord was suspended, and, soon after, the conductivity of the motor nerves was considerably impaired. The frog pre- sented all the phenomena of death ; for although the heart still continued to con- tract, it was unable to propel any blood. The ligature was then removed, and the circulation became re-established. By-and-by, respiratory movements reappeared; in one or two hours, reflex contractions could be readily excited, while voluntary movements were freely executed; and, soon after, the animal regained all its suspended functions. Yet, although the recovery was established by gradual stages, no symptoms of exaggerated activity of the reflex function were observed. | It is unnecessary to discuss this hypothesis further, especially as sufficient evidence will be adduced, in this and the following Section, to demonstrate that the convulsant effects of atropia are caused by a direct action on the nervous system. In the attempt to differentiate the structures on whose affection these effects depend, I have considered the possibilities of their being dependent on the muscles, on the efferent (motor) nerves, on the afferent (sensory) nerves, on the spinal cord, or on the encephalon. In the first series of experiments, the atropia was prevented from reaching certain limited regions of the body, while it had access to all other regions. Experiment XLIV.—The blood-vessels were ligatured at the upper third of the right thigh of an active male frog, weighing 272 grains; and immediately afterwards a solution containing one-fourth of a grain of sulphate of atropia, in four minims of distilled water, was injected under the skin of the left flank. In the course of two hours voluntary movements had ceased, and a state of motionless flaccidity was produced. * Archives de Physiologie Normale et Pathologique, 1868, p. 472. + Transactions of the Royal Society of Edinburgh, vol. xxiv. part iii. p. 743. { Legons sur la Physiologie Générale et Comparée du Systéme Nerveux. Paris, 1866, p. 457. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 469 On the following day—twenty-two hours after the administration—this state of flaccidity was present everywhere, except in the right (non-poisoned) leg, which was extended somewhat stiffly. The skin of this leg, below its upper third, was also paler than that of any other part of the body, and, occasionally, spasmodic contractions occurred spontaneously in the right foot, the rest of the body remain- ing motionless. When the skin of any region—poisoned or non-poisoned—was touched, a sudden and violent tetanic convulsion occurred in the right (non- poisoned) leg, continuing in it sometimes for four seconds, and at others for from six to eight seconds; while at the same time merely feeble twitches occurred in the left leg and in the two anterior extremities. After several such attacks had been excited in rapid succession, a repetition of the excitation still caused well- marked tetanus of the right leg, but it did not cause any movement whatever in the poisoned regions. The heart was now contracting only twelve times in the minute, and the respirations were very infrequent. On the third day—fifty hours after the administration—the anterior extre- mities had become flexed, so as slightly to raise the head; there was some improvement in the character of the respiratory movements; and tetanic con- vulsions, which frequently lasted for ten seconds, could be excited in the right (non-poisoned) leg, while merely clonic spasms appeared in the other extremities. On the fourth day—seventy-two hours after the administration—a slight irritation of the skin was followed by a general tetanic convulsion, during which, however, the right (non-poisoned) leg was very slightly affected. A weak inter- rupted galvanic current applied to the right sciatic nerve, below the ligatures, excited only some faint movements in that limb, while it excited a violent attack of tetanus in the rest of the body (poisoned regions). For several days afterwards, tetanic convulsions could still be excited; but now the right posterior extremity took no part whatever in these—the stoppage of the circulation having obviously destroyed the vitality of its structures. Experiment XLV.—Immediately after ligaturing the right sciatic artery and veins of a frog, weighing 322 grains, I injected a solution of three-tenths of a grain of sulphate of atropia, in four minims of distilled water, under the skin of the left flank. On the second day—at forty-five hours after the administration—faint reflex movements could everywhere be excited by gentle stimulation of the skin; but these movements were most marked in the right (non-poisoned) posterior extremity. On the third day—at forty-five hours after the administration—the reflex movements rarely occurred anywhere but in the right posterior extremity. On the same day, at fifty-one hours, the right (non-poisoned) posterior extremity became extended in violent tetanus when stimulation was applied to any portion of the skin, while everywhere else only feeble reflex movements occurred. On the fourth day—seventy-three hours after the administration—stimulation VOL. XXV. PART IL. 6E 470 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS excited severe and prolonged general tetanus, which affected both posterior extre- mities equally. ; On the fifth day, the right posterior extremity was continuously rigid; but for other three days tetanic convulsions could be excited, in which the whole of the body except the right (non-poisoned) posterior extremity was involved. Experiment XLVI.—The right sciatic artery and veins were ligatured in a frog, weighing 315 grains, and immediately afterwards three-tenths of a grain of | sulphate of atropia, dissolved in four minims of distilled water, was injected under ; the skin of the left flank. : On the third day, rigid incurvation of the anterior extremities, and stiff exten- sion of the right posterior extremity, had occurred. A faint touch of the skin of any region caused a violent attack of tetanus; in which the right (non-poisoned) posterior extremity was rigidly extended with the web stretched, for five seconds, while the left was almost unaffected, merely becoming momentarily extended at the commencement of the attack. On the fourth day, some rigor had appeared in the right posterior extremity ; but general tetanus could be excited in all the other regions of the body. Haperiment XLVII.—I tied the left sciatic artery and veins of a frog, weighing 211 grains, and then injected a solution of one-fifth of a grain of sulphate of atropia, in six minims of distilled water, under the skin of the right flank. On the second day—twenty-two hours after the administration—general tetanic convulsions could readily be excited by touching the skin in any region; and both posterior extremities—poisoned as well as non-poisoned—were equally involved in the convulsions. On the third’ day —forty-seven hours after the administration—the left (non- poisoned) posterior extremity was somewhat rigid, and took no part in the convulsions. In the next experiment both the posterior extremities were protected from the direct influence of the sulphate of atropia. Experiment XLVIII.—By excising the sacrum, I exposed the sacral nerves and blood-vessels within the abdomen of a male frog, weighing 210 grains, and then by passing a strong thread below these nerves, I firmly ligatured the abdomen, including all its blood-vessels, but excluding the sacral nerves. After this operative procedure, the frog retained an apparently normal control over the movements of the posterior extremities. Three minutes afterwards, I injected eleven-hundredths of a grain of sulphate of atropia, dissolved in four minims of distilled water, under the skin at the left side of the thorax. On the following day—at twenty-one hours after the administration—the frog was lying on the abdomen, with the anterior extremities flexed inwards and supporting the head and chest, and with the posterior extremities normally flexed. A slight touch of any portion of the skin was followed by ordinary reflex move- eee ee ee ee ee ere PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 471 ments of all the extremities; but a somewhat severe excitation of the head, as by a smart tap, was followed by pretty strong spasm of the anterior extremities, and of the chest muscles, and by violent tetanus of the two posterior extremities, the latter lasting for four seconds. On the same day—at twenty-five hours after the administration—stimulation caused increase of the tonic spasm of the muscles anterior to the ligature, and, simultaneously, sudden and rigid contraction of the muscles posterior to it—in fact, a general tetanic convulsion—the latter lasting for seven seconds. These convulsions could readily be excited by moderate stimulation of the skin of any region—below the ligature (non-poisoned regions) as well as above it. On the third day—at forty-four hours after the administration—it was impos- - sible to excite tetanic spasm in the non-poisoned regions. At forty-six hours, the posterior extremities were slightly rigid, and soon afterwards stimulation of the sacral nerves did not produce in them any movement whatever; but violent spasm could still be excited in the anterior extremities, and in the other poisoned regions. * The evidence contained in these experiments is sufficient to exclude the muscles and the afferent and the efferent nerves from being held to be directly concerned in the production of the spasmodic and convulsive symptoms of atropia. In each experiment, certain regions of considerable extent were protected from the direct influence of the poison, and yet freely participated in the spasmodic and tetanic effects, thereby proving that these effects were not caused by a direct action of atropia on either muscles or efferent nerves. The evidence that excludes the afferent nerves is quite as satisfactory ; for in each experiment an excitation of the skin of the non-poisoned region readily produced spasms and general tetanus, thereby proving that a direct action on the afferent nerves is not required for the production of these symptoms. We are now obliged to look for the cause of these effects to a direct action of atropia on the central nerve-organs. The predominance of cerebral symptoms during atropia-poisoning in animals of a higher development, suggested the possibility of the tetanic symptoms being caused in frogs by an influence origi- nating in the cerebral lobes, or, more probably, in the ganglia at the summit of the medulla. Accordingly, on several occasions, the spinal cord of a frog in the stage of tetanus was divided immediately below the brachial enlargement, with results such as are described in the following experiment. Eaperiment XLIX.—A solution of fifteen-hundredths of a grain of sulphate of atropia, in four minims of distilled water, was injected under the skin at the left flank of a frog, weighing 152 grains. The stage of paralysis continued until * The experiments in this series were all performed in winter, when the low temperature of the laboratory was favourable to a long-continued retention of nerve-irritability in parts cut off from the circulation. 472 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS the end of the third day ; and on the fourth day the frog had entered the tetanic stage—a slight touch of the skin being followed by opisthotonic tetanus lasting for four seconds. On the sixth day, at 1.50 p.m.,a touch of the left ankle caused a violent attack of emprosthotonic tetanus, during which both posterior extremities were rigidly extended for three seconds. At 1.51, a touch of the right ankle caused a similar tetanic convulsion, which lasted in both posterior extemities for three seconds. On the same day (sixth), at 2.10 p.w., the spinal cord was divided imme- diately below the brachial enlargement; and, it is important to note, extremely little blood was lost by this operation (about a drop only). At 2.21 p.m, a touch of the right ankle caused rigid tetanic extension of both posterior extremities for two seconds.. At 2.22, a touch of the left ankle caused similar extension for three seconds. The anterior portion of the body took no part whatever in these convulsions; but when the skin at the head or anywhere anterior to the section of the cord was touched, the regions supplied by the anterior segment of the divided cord were at once thrown into a state of tetanus. These latter attacks lasted for about four seconds; and during them the regions supplied by the posterior segment of the divided cord were unaffected. On the seventh day, a touch of either ankle caused violent tetanus of both posterior extremities and of the muscles at the lower part of the flanks, lasting for five seconds; and immediately after the tetanic contraction had ceased, a series of clonic spasms occurred in these regions for other fifteen seconds. A touch of the skin anterior to the position of the section of the cord was followed by violent tetanus of the anterior portion of the frog, lasting for about eight seconds. This condition of independently excitable tetanus of the anterior and posterior secments continued, with but little change in the character of the excited attacks, until the nineteenth day of the experiment. There were, however, in this pro- longed period, some differences in the duration of the tetanic convulsions: for, on the eighth day, after slight stimulation, the posterior extremities were rigidly extended for six seconds, and were then affected with clonic spasms for seventy seconds; on the eleventh day, the rigid extension lasted for four seconds, and the succeeding clonic spasms for twelve; on the fourteenth day, the rigid extension lasted for four seconds, and the clonic spasms for only two; and on the eighteenth day, the rigid extension lasted for four seconds, but in place of a series of clonic spasms, it was succeeded by merely two or three faint twitches. On the nineteenth day, tetanus of the posterior extremities was caused only — when the stimulation was severe; and there was now no evidence of increased reflex excitability in the anterior part of the frog. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 473 The observations were now stopped. In performing this experiment, care must be taken to avoid injuring important blood-vessels, as any considerable loss of blood would completely vitiate the results. This is at once apparent, if we compare the experiments contained in Table IJ. with those in Table III. TABLE Il—Summary or EXPERIMENTS IN WHICH THE SPINAL CORD WAS DIVIDED DURING ATROPIA-TETANUS, without any material loss of blood. Tn Grains. Relation i oe ; of Pees Effects before the Division oe Effects after the Division Experiment. vy oe Dose. ite of the Cord. IDenetloyi. of the Cord. XLIX. | 152 | 0:15 | ,3,,; | Incomplete paralysis 1st | 6th day. | Tetanus in both seg- to 3d days; tetanus 4th ments 6th to 17th days, to 6th days, and in posterior segment alone 17th to 19th days. L. 294 | 0:3 siz | Incomplete paralysis 1st | 4th day. | Tetanus in both seg- and 2d days; tetanus 3d ments 4th to 7th days. and 4th days. Frog was killed on 7th day. LI. 358 | 0-4 giz | Complete paralysis 1st | 5th day.| Tetanus in ~ both seg- and 2d days; incom- ments 5th and 6th days. plete paralysis 3d day; Frog was killed on 6th tetanus 4th and dth day. days. TABLE ITI.—Summary or EXprrIMENTS IN WHICH THE SPINAL CORD WAS DIVIDED DURING ATROPIA-TETANUS, with considerable loss of blood. In Grains. Relation : paber Wei se we Effects before the Division ne Effects after the Division of Bxperimont.| of a Dose. | Weight of the Cord. Wii aa the Cord, and oss Lof Blood. Ps of Frog LIl. 272 | 0-25 | ,A,, | Incomplete paralysis 1st | 7th day. | Tetanus ceased in 15 to 3d days; tetanus 4th minutes, and rigor mor- to 7th days. tis was present on 8th day. LITT. 288 | 0:3 zéy | Complete paralysis 1st | 5th day. eae of posterior seg- and 2d days; incomplete ment ceased in 10 min., paralysis 3d day; teta- but tonic spasm con- nus 4th and dth days. tinued in the anterior segment for 24 hours longer. LIV. 310 | 0:35 | gt, | Incomplete paralysis 1st | 6th day.| Tetanus ceased in both to 4th days; tetanus segments in 5 minutes.” 4th to 6th days. _ * In this experiment a large quantity of blood was rapidly lost, as the apex of the heart.was excised immediately after the cord had been divided, VOL. XXY. PART II. OF 474 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS I performed the following experiment to ascertain how far the mere division of the cord affects reflex excitability. Experiment LV.—In a healthy male frog the reflex excitability was tested in various ways, and found to be normal. The spinal cord was then divided imme- diately below the brachial enlargement, with the loss of only one or two drops of blood. Except that some general quivering occurred at the time of the division, and for a few minutes afterwards, the frog remained quietly in a normal posture, and showed no symptoms of exaggerated reflex activity until the second day. On the second day—at twenty-one hours after the division of the cord— slight stimulation of an ankle was followed by a series of feeble twitches of various muscles in both legs, lasting for three seconds. These twitches were so slight that they caused no movements of either posterior extremity, and during their occurrence both posterior extremities remained normally flexed. Similar series of twitches were produced other three times by stimulating each ankle alternately at intervals of a minute; but when the same stimulation was repeated for the fifth time, no effect whatever followed. On the third day, the posture of the frog was still perfectly normal; but stimu- lation of an ankle excited merely a feeble twitch in both posterior extremities. On the fourth and fifth days, stimulation of a more energetic character was required to excite similar feeble twitches in the posterior extremities; but such _ series of twitches as appeared on the second day could not be caused by even powerful excitation. The experiment was now terminated. It is therefore apparent that, in Experiments XLIX., L., and LI., the tetanic symptoms that were present in the posterior extremities after division of the spinal cord were not caused by the division. 3 We have thus obtained most satisfactory evidence in favour of the con- clusion that these convulsive symptoms are due to a direct action of atropia on the spinal cord. Moreover, the results of some further experiments made to test this conclusion are entirely confirmatory thereof. Two of these may be briefly described. Experiment LV1.—Immediately after dividing the left sciatic nerve in the thigh of a frog, weighing 360 grains, I injected a solution of seven-twentieths of a grain of sulphate of atropia, in four minims of distilled water, under the skin of the right flank. On the third day, the frog was lying on the abdomen, with the anterior extremities rigidly arched, with the right posterior extremity stiffly extended, and with the left posterior extremity flexed and somewhat flaccid. A touch anywhere, except in the left posterior extremity below the middle of the thigh, excited a violent tetanic convulsion, in which the left leg took no part. Galvanic — stimulation, when applied to the cut end of the distal portion of the left sciatic — PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 475 nerve, caused normal contractions of the left leg ; but when applied to the cut end of its central portion, excited a violent tetanic paroxysm in which the left leg took no part. Experiment LVII. differed from Experiment LVI. mainly in the nerve divi- sion having been postponed until the tetanic stage was entered into. Before the right sciatic nerve was divided, excitation caused a violent attack of tetanus. during which the right posterior extremity was rigidly extended for eight seconds. After the right sciatic nerve was divided, the right leg took no part in the tetanic convulsions. Galvanic stimulation also of the cut end of the distal portion of the nerve caused merely normal movements of the right leg. The symptoms of increased reflex excitability that occur so prominently in frogs after the exhibition of certain pretty well-defined doses of atropia, are therefore caused by a direct action of this poison on the spinal cord. Having reached this stage in the investigation, we are naturally tempted to proceed a step farther, and to inquire what is the nature of the action on the spinal cord, by which atropia produces convulsive and tetanic symptoms’? At first sight, the solution of this question might appear to be an easy one. Inves- tigation has shown that atropia is a powerful agent in influencing the condition of at least certain portions of the vascular system, although there is a difference of opinion among investigators as to the nature of the influence. The probabi- lities are, however, in favour of the view of Mruriot, that when large doses are given, atropia first diminishes the calibre, and increases the vermicular contrac- tion, of the blood-vessels; and, subsequently, increases their calibre by para- lysing the contractile walls.* It may be supposed that the latter effect— dilatation of blood-vessels—is the cause of the tetanic symptoms; for such dilatation might operate either by permitting the augmented blood-supply that many suppose to be essential for abnormal activity, or by causing irritation of the cord directly, by congestion, or even rupture of its blood-vessels.+ The plausibility of this view is strengthened by the opinion of so eminent a physiologist as Brown-S£quarp, who maintains that vascular dilatation is one of the primary causes of the tetanic effects of strychnia;{ and by the post mortem appearances of engorgement of the vessels of the spinal cord, after poison- ing by atropia, which several observers have drawn attention to in mammals,§ and which I have frequently observed in frogs also. There are, however, several grave objections to the adoption of a theory of the * De la Méthode Physiologique en Thérapeutique et de ses applications a ]’étude de la Belladone. Paris, 1868, p. 51, &e. t Mevriot, op. cit. p. 98. { Lectures on the Diagnosis and Treatment of the Principal Forms of Paralysis of the Lower Extremities. Philadelphia, 1861, pp. 51 and 112. § RosenBEerGeR, quoted by Tarpiev, op. cit. p.'752; Scurorr, Lehrbuch der Pharmacologie. Wien, 1868, p. 508. 476 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS vascular causation of atropia-tetanus, founded on the above arguments. It is true that the demonstration appears to be perfect of great dilatation of the blood-vessels of the skin, muscles, abdominal and thoracic viscera, and several other structures occurring at an advanced stage of atropia poisoning—probably, indeed, this dilatation is contemporaneous with the tetanus—but we have yet to wait for the demonstration of a dilatation of the blood-vessels of the spinal cord during the life of the animal. It is even difficult to believe that the analogous tetanic symptoms of strychnia are due to vascular engorgement, for a frog may be bled as perfectly as possible, and still the subsequent direct application of strychnia to the spinal cord will cause tetanus.* Farther, the discovery of vascular engorge- ment after death from tetanus is insufficient to prove that the production of the tetanus is in any way dependent on that engorgement. It might be urged, with equal reason, that the tetanus is the cause of the spinal engorgement, the mechanical effect of the muscular contractions tending to force the blood into those regions where this effect cannot operate. Besides, there are no good grounds for assuming that an engorged state of the vessels of the cord will necessarily increase reflex excitability or originate tetanic convulsions. It is obvious that this question can be solved by direct proof only. An apparent approach to such a solution might appear to be contained in the results of the Experiments in Table III. Tetanus and convulsions rapidly disappeared after copious bleeding. If, however, the blood be freely and abundantly abstracted from a frog in a normal condition, the reflex excitability will be quickly impaired, and, very soon afterwards, it will altogether disappear. While, however, we cannot at present accept the view that the tetanic effects of atropia are produced by dilatation of the blood-vessels of the spinal cord, such a method of production is not disproved by any known fact. The question of the exact nature of the causation of atropia-tetanus—in common with similar questions in relation, probably, to every active substance—is, therefore, still open for future research. Meanwhile, by restricting actions to certain organs and struc-_ tures, we gain an essential advance towards the solution of such problems. SECTION D. In this section an attempt will be made to show that the convulsive and tetanic symptoms that have been described in frogs are represented among the symptoms of atropia-poisoning in rabbits, dogs, and other mammals; and that, in both cases, the causation and special characters of these symptoms, as well as the peculiarities of their occurrence, are the results of exactly the same actions. * MM. Martin-Macron et Buisson, “ Action Comparée de l’Extrait de Noix Vomique et du Carare,’” Journal de la Physiologie de ’Homme et des Animaux, 1859, p. 487; Dr A. J. Spence, “On the Mode of Action of Strychnia,” Edinburgh Medical Journal, July 1866, p. 50. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 477 There can be little doubt that, in many cases, the convulsions that appear during poisoning by atropia in man, dogs, rabbits, and other mammals, are due chiefly to asphyxia, caused by impairment of the functions of the cerebro- spinal nervous system. These convulsions are, however, due also to a special and primary stimulant action of atropia on the spinal cord. ‘The latter method of production has been recognised by observers who were fully alive to the possi- bility of such symptoms being produced by asphyxia alone.* Several experiments in dogs have satisfied me—so far as evidence short of direct demonstration can do so—that this is the case; for, after the administration of doses that were about the minimum fatal, I have, on several occasions, observed a condition of combined unconsciousness, partial paralysis, and exaggerated reflex activity con- tinue for more than twenty-four hours, while, during a considerable portion of this time, the respirations were of fair character. The remarkable position that the convulsive symptoms occupy in frogs— occurring subsequently to either a partial and short, or a complete and protracted paralysis of the cerebro-spinal nervous system—at first sight appears to lend but little support to the assertions that atropia has a primary spinal-stimulant action in mammals, and that atropia-convulsions are caused by the same action in both frogs and mammals. It is, however, necessary to remember, that in atropia the amount of spinal-stimulant is in all animals less than the amount of paralysing action, and that paralysis, compared with spinal-stimulation, is more rapidly pro- duced by atropia in frogs than in mammals. The first of these propositions—that the amount of spinal-stimulant is in all animals less than the amount of paralysing action—is founded on the fact, that the principal symptoms produced by an aggregate of various doses are those of paralysis. Thus, in frogs, the smallest doses that affect motricity cause slight paralysis without any obvious symptom of spinal-stimulation (Experiment IV. Table 1.); somewhat larger doses cause more decided paralysis, with slight symp- toms of spinal-stimulation (Experiments V. and VII. Table I.); still larger doses cause complete paralysis, and violent symptoms of spinal-stimulation (Experi- ments XV. XVI. XVIT. XVIII. XIX. XX. XXI., &c. Table I.); and doses so large as to produce death rapidly, cause complete paralysis without any manifestation of a spinal-stimulant action (Experiments XLII. XLIII., &c. Table I.) In mammals, the symptoms are in like manner confirmatory of the proposition. We may safely refer to almost every investigation in which different doses of atropia have been administered to animals of the same species; but the following short account of two experiments, which are described with minute detail in an inge- * Mevrior, loc. cit. p.98,&c. Brown-Séauarp, “ Lectures on the Diagnosis and Treatment of Functional Nervous Affections,” 1868, p.66. Both authors account for the increased excitability of the spinal cord by dilatation of blood-vessels—a method of causation which, I believe, cannot be established by any evidence that we at present possess. VOL. XXV. PART II. 6 & 478 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS nious and elaborate paper by Dr LemMaTTRE, contains ample evidence in support of the proposition. Both experiments were performed on dogs, and in both a solution of sulphate of atropia was injected into a jugular vein. In the first experiment, the dose was one decigramme (= 1°54 grain). In six minutes, para- lytic symptoms occurred, which gradually became well-marked and severe; and in two hours and forty minutes, “une convulsion réflexe”’ followed pinching of the skin. This is the only synuptom of a spinal-stimulant action that is mentioned, although the details of the experiment are described with great minuteness. This dog recovered.* In the second experiment, the dose was five decigrammes (=7°'7 grains). In about five minutes, paralytic symptoms were observed; and in about one hour and ten minutes, some spasms occurred. The paralytic symp- toms became very obvious soon after their first appearance, while the spinal- stimulant reached more gradually such an intensity as to cause frequent tetanic convulsions. This dog died six hours after the administration.+ The second proposition—that the paralysis, compared with the spinal-stimu- lation, is produced in frogs more rapidly than it is in mammals—may likewise be established by an appeal to observation. The experiments described in Table I. show that in frogs complete paralysis (and, therefore, absolute suspension of reflex activity) may be caused by doses of atropia considerably below the minimum fatal. On the other hand, it is well known that in mammals even fatal doses do not completely suspend reflex activity before death. Indeed, it is not to be expected that they should do so, for an amount of paralysis considerably short of complete suspension of reflex activity would undoubtedly cause such an embar- rassment of respiration as to produce death by asphyxia.{ Hence, it is neces- sary to employ artificial respiration, in order to produce complete paralysis of motor nerves with even so powerful a paralysing agent as curara (wourali).§ It has been amply demonstrated in Section C. that large doses of atropia com- pletely suspend the conductivity of motor nerves.|| This one method, among seve- * “Recherches Expérimentales et Cliniques sur les Alcaloides de la famille des Solanées.” Archives Générales de Médicine, 1865, vol. ii. p. 175. + Op. cit. p. 177. I have in my possession notes of many experiments supporting this proposition, but have preferred to quote evidence obtained from an investigation in which this marked difference between the effects of different doses is not specially alluded to. t That this difficulty in causing complete paralysis does not occur with frogs, is due to their endowment with the function of cutaneous respiration. In this animal, reflex activity may be so far impaired by the action of a poison, that pulmonary respiration is rendered impossible, and yet asphyxia may not take place to such an extent as to bring the circulation to a stand-still, and the poison may thus be allowed sufficient time to produce on the living nerve-structures its complete physiological effects. § Vutrran, op. cit. p. 196. || This action has already been demonstrated by Botkin, Vircnow’s Archiv, Bd. 24, 1862, p. 84; by Vow Bzzozp and Brorsaum, Untersuchungen aus dem Physiologischen Laboratorium in Wiirzburg, 1*s Heft, 1867, p. 13; and by Mzurior, op. cit. p. 90. The last author attempted to prove that it is the result of a local action on the nerves by imbibition, and not of poisoning through the blood; but his arguments seem insufficient to establish this view. I hope to refer more fully to this objection on some future opportunity. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. A79 ral, by which it produces paralysis, is, therefore, sufficient to account for the greater readiness with which complete paralysis is produced in frogs than in mammals. It is thus seen why atropia produces paralysis so much more rapidly and completely in frogs than in mammals, and also why in both frogs and mammals spinal-stimulant effects are obviously manifested only when atropia is adminis- tered in doses that are near the minimum fatal—that is, in doses containing the largest amount of spinal-stimulant action consistent with the production of a prolonged duration of symptoms. When a dose of atropia near the minimum fatal is given to a frog, paralysis is caused with such rapidity and completeness, that the spinal-stimulant action is at first prevented from exhibiting itself; but when a similar dose is given to a mammal, paralysis is caused so slowly and incompletely that a sufficient amount of reflex activity remains to allow the spinal-stimulation to manifest itself by exaggerated reflex movements and convulsive spasms. In the frog, the spinal-stimulation is, in the first stage, concealed by the impossibility of its effects being manifested, and the first symptoms are, therefore, those of paralysis; but, as this paralysis is being recovered from, the spinal-stimulation becomes appa- rent. In the mammal, the spinal-stimulation is merely impaired by the partial paralysis; and during the whole course of the poisoning, the symptoms are, therefore, those of a paralysing combined with a spinal-stimulant action, the former merely lessening the violence, without concealing the effects of the latter. This combined action, and the variety produced by it on the symptoms in frogs and mammals, may be graphically illustrated by two curves, one of which represents the paralysing, and the other the spinal-stimulant action. The forms of these curves are to a great extent arbitrary, and they must of necessity be so until we possess some exact method of estimating degrees of action, and thereby obtaining ordinates that may have some pretension to accuracy. Thus, in the curve op,p, &c., of Diagram 1, the motor nerve paralysis is complete, so far as our methods of examination can show, at pc; but between pe and p, there is aconsiderable interval, during which the degree of action may or may not have been constant. What is termed complete paralysis does not represent the maximum of action, for we know that the paralysis may go on to permanent suspension of motility, or death, as well as return to normal activity. As, therefore, the ordinates are but roughly determined, these curves are in no sense accurate delineations of the paralytic and spinal-stimulant actions. They may, however, serve the useful purpose of exhibiting clearly the relations between the effects of these two actions. For the sake of simplicity, the best marked paralytic action of large doses of atropia—that on the motor nerves —will alone be considered. Diagram | is a delineation, on this plan, of Experiment XVI. of Table I. In 480 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS this experiment, seven-twentieths of a grain of sulphate of atropia, administered to a frog, weighing 372 grains, produced complete paralysis of the motor nerves on the first and second days; tetanus on the third (slight), fourth, fifth, and sixth days; and stiff spasmodic movements on the seventh and eighth days. Complete recovery had taken place on the tenth day. Diagram 1.* In the diagram, the curve of paralysis, op,p,p,, &c., rises abruptly from the line of normality, AB. The symptoms are those of paralysis only, until the curve of spinal-stimulation, os,s,s,, &c., cuts that of paralysis between ¢, and ¢,, after the descent of the latter from the line of complete paralysis, CD. Tetanus then becomes the predominant symptom. At first, its violence is considerably checked by the coexisting paralysis; but as the ordinates of the paralytic curve diminish in length, while those of the tetanic curve increase, the tetanic symp- toms gradually acquire greater prominence and force, until they reach their maximum intensity between 7, and ¢,. They then, in their turn, also diminish. This diagram further shows how a paralytic and a spinal-stimulant (tetanic) action may be coexistent, while the effects of only one of these are apparent. Between o and ¢,, the symptoms are those of paralysis alone, because the spinal- stimulant action is altogether masked by the complete paralysis ; between 7, and t,, tetanic symptoms appear, because the paralysis is incomplete, and reflex movements are therefore permitted to occur; and between ¢, and ¢,, the spinal- stimulant action, being but slightly checked by paralysis, manifests itself by violent tetanic convulsions. The effects of this combined action on a mammal are graphically repre- sented in Diagram 2. The experiment (Experiment LVIII.) I have selected — is one in which eight grains of sulphate of atropia in solution was injected under the skin of a dog, weighing fifteen pounds. Slight paralysis was observed at twenty minutes, and feeble spasms occurred at forty minutes; they together reached their maximum intensities at about seventy minutes; and the * AB, line of normality, each division of which, of,, t,t,, t,f,, &¢., represents a period of twenty-four hours; CD, line of complete paralysis ; op,p,p,, &¢., curve of paralysis ; 05,5983, &¢., curve of spinal-stimulation (tetanus, &c.); ¢,p,, t,, &c., ordinates whose length roughly represents the amount of the paralytic action ; ¢,s,, ¢,s,, &e., ordinates whose length roughly represents the amount of spinal-stimulant action. PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 481 spasms ceased at one hundred minutes, while the paralysis continued until about one hundred and twenty minutes. The dog recovered perfectly. Diagram 2.* In this diagram, the curve of paralysis, op,p,, &c., leaves the line of normality, AB, before the curve of spinal-stimulation, the first symptoms being those of paralysis. As the curve op,p,, &c., never attains the level of the line of com- plete paralysis, CD, the paralytic action is never sufficiently great to prevent the manifestation of the considerable spinal-stimulant action present. Although the ordinates ¢,s,, ¢,s,, and ¢,s,, are considerably longer than the ordinates ¢,s, and t,s,, the effects of spinal-stimulation are not proportionally greater at ¢,,¢,, and t, than at ¢, and ¢,, for the ordinates of the paralytic curves also are longer at the former than at the latter times, reaching their highest point at about the same time as those of the spinal-stimulant curve, and the spinal-stimulant action is, accordingly, more masked about the time of its greatest intensity than at times somewhat anterior and subsequent thereto. These curves, therefore, admirably represent the effects that were observed, the convulsive symptoms having been of nearly uniform intensity throughout the whole time of their occurrence. It has been taken for granted that the paralytic and spinal-stimulant actions coexist in frogs after the administration of large doses of atropia. Some evidence in support of this view may with propriety be given at this place. Experiment LIX.—In a frog, weighing 270 grains, the abdominal aorta was ligatured immediately above its bifurcation into the two iliacs, and one-fifth of a grain of sulphate of atropia, dissolved in four minims of distilled water, was then injected under the skin at the right side of the thorax. Great impairment of motility and other symptoms of atropia action had occurred in one hour, when the observations were interrupted. On the following day—twenty-three hours after the administration—the frog was lying on the abdomen, chest, and lower jaw, the anterior extremities being perfectly flaccid, while the posterior were extended with the webs stretched. A slight touch of the head caused a sudden attack of tetanus in the two pos- terior extremities, which lasted for three seconds; but it was impossible to * AB, line of normality, each division of which, ot,, t,t,, t)t,, &c., represents a period of ten minutes ; CD, line of complete paralysis; op,p.p,, &c., curve of paralysis ; 0s,s,s,, &¢., curve of spinal-stimulation (tetanus, &c.); #,9,, t,p,, &ec., ordinates whose length roughly represents the amount of the paralytic action ; ¢,s,, t,s,, &e., ordinates whose length roughly represents the amount of the spinal-stimulant action. VOL. XXV. PART II. 6H 482 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS excite any movement whatever in the anterior extremities, or in any other part of the poisoned region. At twenty-eight hours, the position of the frog was the same as that last described, there being perfect fiaccidity and complete motionlessness in the poisoned region, while the posterior extremities (non- poisoned region) were rigidly extended. A touch of the skin anywhere now excited violent tetanus of the posterior extremities, lasting for five seconds; but no movement occurred elsewhere, and the anterior extremities were perfectly flaccid. To test the condition of motor conductivity in the poisoned region, the right brachial nerve was exposed, and subjected to galvanic stimulation; no movement of the right anterior extremity was thereby produced, but tetanus of the two posterior extremities invariably followed each stimulation. On the third day, the frog was lying on the abdomen, but the chest and head were now raised by the anterior extremities, which had become rigidly flexed. On stimulating the skin, an attack of general opisthotonic tetanus occurred, involving the poisoned as well as the non-poisoned regions. In this experiment, the spinal-stimulant action would have been completely masked by the paralytic, if the posterior extremities had not been protected from the direct influence of the poison. Yet even when this is done, evidence of the spinal-stimulant action will only exceptionally be obtained at so early a stage. Atropia causes paralysis by an action not only on the motor nerves, but also on the sensory (afferent) and on some portion of the reflex apparatus in the spinal cord. In this experiment, two of these causes of paralysis (suspension of the function of the sensory nerves, and suspension of that of some portion of the reflex apparatus in the spinal cord) ceased before the third (suspension of the function of motor nerves); for the conductivity of the poisoned motor nerves was still completely suspended when the poisoned spinal cord and sensory nerves had regained their functions. Usually the return to normality occurs much more simultaneously in these different structures. It is still more difficult to obtain evidence in frogs of a spinal-stimulant action occurring soon after the adminis- tration of large fatal doses. Complete paralysis is so rapidly produced that no opportunity is given to the spinal-stimulant action to manifest itself. The evi- dence in support of an early stimulation of the cord is, however, readily obtained in mammals; for the paralytic effects are never so great as to prevent the mani- festation of the spinal-stimulant action. The two already mentioned propositions—namely, that in atropia the amount of paralysing is, in all mammals, greater than the amount of spinal-stimulant action, and that atropia-paralysis is more readily produced in frogs than im mammals—are also sufficient to explain why different effects are produced in frogs and mammals by different doses of atropia. When a large fatal dose of atropia is administered to a frog, the predominating PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 483 paralysis is so rapidly and completely produced that no spinal-stimulant symptom can be exhibited. Death results either from an extreme degree of the paralytic action, or, possibly, from some other effect of atropia. In neither case, however, does the paralytic action diminish sufficiently (if it diminish at all) to permit any effects of spinal-stimulation to appear, for death occurs during a high intensity of the paralytic action. Diagram 3 represents an experiment (XLII. of Table L) in which a large fatal dose of sulphate of atropia was administered to a frog. The reflex activity was destroyed in a few minutes, and the conductivity of the -motor nerves was completely suspended in one hour and forty minutes. Death occurred during the complete paralysis. Diagram 3.* As the curve of paralysis, op,p,, &c., rises rapidly to the line of complete paralysis, CD, and crossing, terminates above it (at the time of the occurrence of death), while the curve of spinal-stimulation, os,s,, &c., rises with comparative slowness, it is obvious that no spinal-stimulant effect can possibly be manifested. In frogs, the only symptoms of a fatal dose of atropia are, accordingly, those of paralysis, notwithstanding that such a dose exerts a large amount of spinal-stimu- lant action, which is represented in the diagram by the curve 0s,s,s,,, &c. In mammals, fatal doses of atropia invariably produce spasms and convulsions. We at once see why this should be so, if we bear in mind that mammals are less susceptible than frogs to a paralytic action. I have delineated in Diagram 4 the symptoms that were observed in an experiment (Experiment LX.) in which a solution, containing fifteen grains of sulphate of atropia, was injected under the skin of a dog, weighing nine pounds. Partial, but distinct, paralysis was first observed in eleven minutes, and spasms, with increased reflex excitability, in sixteen minutes. They both gradually increased in severity—the paralytic action causing inability to stand in twenty-two minutes, and the spinal-stimulant pro- ducing the first of a series of frequently recurring tetanic convulsions in nineteen minutes; and death took place one hour and eighteen minutes after the adminis- tration. * AB, line of normality, each division of which, of,, t,f,, tgt,,, &ic., represents a period of forty minutes ; CD, line of complete paralysis; op,p,p,,, &c., curve of paralysis ; 0s,s,8,., &c., curve of spinal-stimulation (tetanus, &c.) 484 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS In this diagram (Diagram 4), the curve of paralysis, op,p,p,, &c., does not at any time rise to the level of the line of complete paralysis, CD; whereas in the Diagram 4.* diagram representing the effects of a fatal dose in a frog (Diagram 3), the curve of paralysis very quickly reaches this line.+ Accordingly, in this experiment, the spinal-stimulant action, which was considerable, was not prevented from manifesting itself, and spasms and tetanus coexisted with paralysis up to the time at which death occurred. When a dose of atropia considerably below the minimum fatal, and just suffi- ciently large to produce obvious effects on motility, is administered to a frog, the effects are such as have been roughly delineated in the next diagram. Diagram 5.f In a mammal the effect of such a dose would be represented by a diagram, in which the differences between the ordinates of the paralytic and spinal- stimulant curves are less than in the above. The symptoms being but slight in both cases, the ordinates of the curves are very short; and as the amount of paralytic action in atropia is greater than the amount of spinal-stimulant, the area enclosed by the curve op,ps, &c., and the * AB, line of normality, each division of which, ot,, ¢,t,, tof,, &c., represents a period of ten minutes ; CD, line of complete paralysis; op,pop3, &¢., curve of paralysis; os,s,8,, &c., curve of spinal-stimulation (tetanus, &c.); ¢,,, t)P>, &e., ordinates whose length roughly represents the amount of the paralytic action; f,s,, 1583, &c., ordinates whose length roughly represents the amount of the spinal-stimulant action. + It is probable that a stage of tetanus occurring subsequently to a stage of paralysis has never been observed in mammals, after the administration of atropia, because a sufficiently large dose can- not be administered without causing death while the paralytic effects are being developed. It is, however, possible that separate paralytic and tetanic stages might be produced in mammals, if artificial respiration were employed after the administration of a very large dose. + hours; CD, line of complete paralysis; op,p.P19, &¢., curve of paralysis; s,5,5;,, &e., curve of spinal-stimulation (tetanus, &c.); t,p,, tgp, wve., ordinates whose length roughly represents the amount of the paralytic action; ¢,s,, t,S, &c., ordinates whose length roughly represents the amount of the spinal-stimulant action. + AB, line of normality, each division of which, of,, t,t,, tgtj,, &¢., represents a period of four 4 PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 485 abscissa o¢,, is greater than the area enclosed by the curve s,s,, &c., and the abscissa ¢,t,,. The symptoms are, accordingly, those of paralysis; the spinal- stimulant action being so slight that its effects are not perceived. With small doses of atropia, spinal-stimulant effects are more likely to be observed in mammals than in frogs. Ifthe minimum dose that produces paralytic effects be determined, and then a series of doses gradually increasing from this be ad- ministered, it will be found that in frogs a considerable increase may be effected before any spinal-stimulant symptom is produced; but that in mammals an extremely slight increase will cause spasmodic symptoms to make their appear- ance. The explanation of this also is to be found in the propositions. It has thus been shown that the tetanic symptoms produced by atropia in frogs are represented, though in a somewhat diferent form, in animals of a higher development. Atropia, therefore, forms no exception to the general Jaw that poisons affect the same structures in the same way, in whatever animals these structures occur. It has also been shown that the differences in the symptoms that are produced by different doses in animals of the same species may be explained by the paralysing action of atropia being greater than the spinal-stimulant. Paralysis, combined with spinal-stimulation, forms, therefore, the leading characteristic of the action of large doses of atropia on the cerebro-spinal nervous system, and unless this combination be taken into account, which it has not hitherto been, the symptoms that are produced by such doses cannot be rationally explained. In the antecedent portion of this paper, and especially in section C, this combined action on the nervous system has been demonstrated by a process of physiological analysis. I now propose to add to this some further proof, derived from what may be termed a process of physiological synthesis. So long as we are unable to separate from one another those elements or groups of elements in atropia that produce its different effects—allowing that it is legitimate to suppose that such elements or groups of elements exist—a strict synthetical method cannot be applied to the investigation of its effects; but an imperfect synthetical method may be applied, in which we imitate these effects by combining various substances of clearly defined action. For this purpose I have selected strychnia, as the best known and most typical of the spinal-stimulants, and sulphate of methyl-strychnium, as one of the simplest and, for such pur- poses, certainly one of the most convenient of the paralysers of motor nerves.* It was found that a dose of strychnia, in the form of a salt, equivalent to * This action of sulphate of methyl-strychnium has been demonstrated by Dr A. Crum Brown and the author in a paper read before this Society, and published in the Transactions, vol. xxv. part 1. pp. 151-203. I prefer this substance to curara, because of its strength being constant; and on this ground I would recommend it to physiologists and physicians. VOL. XXY. PART II. 61 486 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS about the z5g/55ath of the weight of the frog, was sufficient to produce in it violent tetanic symptoms, which lasted for many hours, and terminated in recovery. When such a dose is given to a male frog, or to a female whose abdomen is not greatly enlarged by distended oviducts, it is of interest to note that the anterior extremities become incurved at the commencement of the tetanic symptoms, and continue so until these disappear; thus imitating a symptom produced by atropia that has been fully describedin this paper (Section A.) It was also found that doses of sulphate of methyl-strychnium, varying from the so/goth to the z,dooth of the weight of the frog, were sufficient to produce complete and prolonged paralysis of the motor nerves, without causing death. Guided by these results, I then administered to frogs combined doses of strychnia and sulphate of methyl-strychnium. After making several experi- ments, I at length discovered that the remarkable combination of paralytic and tetanic symptoms that has been described in Section A. of this paper could be exactly imitated by administering to frogs a mixture of strychnia with sulphate of methyl-strychnium in a certain proportion. The following experiment is sufficient to confirm this statement :— Experiment LXI.—One minim of a mixture of two minims of liquor strychnize (B.P.) in eighteen minims of distilled water (equivalent to ~983 ths of a grain of strychnia), was added to three minims of a solution of one-tenth of a grain of sulphate of methyl-strychnium, in ten minims of distilled water (equivalent to three-hundredths of a grain of sulphate of methyl-strychnium), and the four minims of solution thus obtained was injected under the skin at the right flank of a male frog, weighing 355 grains. In two minutes, some sprawling was observed; in three minutes, the frog was unable to jump, and the respiratory movements of the chest had ceased; in twelve minutes, only extremely feeble and sluggish reflex movements could be excited by pinching the skin ; in fourteen minutes, the lower jaw rested on the table, the respiratory movements of the throat ceased, and the frog was perfectly flaccid; and in thirty-five minutes, it was impossible to cause any reflex movement whatever even by severe excitation of the skin. During all this time, there was not the faintest strychnic symptom. The reflex activity was frequently tested. At the com- mencement of the experiment, it was perfectly normal; and as the symptoms advanced, the only change observed was a gradually increasing feebleness. At forty minutes, it was found, by exposing a sciatic nerve, and subjecting it to galvanic stimulation, that motor-nerve conductivity was completely suspended. At this time, the cardiac impulse was good, and the heart’s contractions occurred twenty-eight times in the minute. On the second day—twenty hours after the administration—the frog was lying on the abdomen with the thorax raised and supported by the anterior ex- tremities, which were rigidly incurved, and there were infrequent respiratory PRODUCED BY ATROPIA IN COLD-BLOODED ANIMALS. 487 movements. A slight touch of the skin caused a violent attack of emprostho- tonic tetanus, which lasted for seven seconds, and was succeeded by a series of clonic spasms in the posterior extremities and the abdominal muscles. During the tetanus, the posterior extremities were stiffly extended, with their webs stretched, while the anterior were rigidly incurved. Tetanic convulsions could be excited at any time by repetitions of the excitation, and they sometimes occurred spontaneously. In the intervals between them, the anterior extremi- ties continued rigidly flexed. During the third; fourth, and fifth days, the frog remained in this state, except that, on the fifth day, the convulsions were less powerful and prolonged. On the sixth, seventh, and eighth days, excitation caused merely sudden spas- modic movements; but the anterior extremities were still rigidly flexed inwards. On the ninth and tenth days, the frog was in a normal position; voluntary movements were freely executed ; but there was still a slight increase in the activity of the reflex function. On the twelfth day, the symptoms had completely disappeared. This experiment, therefore, proves that combined doses of strychnia and sulphate of methyl-strychnium may produce symptoms that in every detail imitate the most obvious of the effects of atropia on the cerebro-spinal nervous system of frogs. By comparing the diagramatic representation of this experi- ment with that of Experiment XVI. (p. 480), it will be seen how close are the resemblances. Diagram 6.* It is therefore possible, by combining a paralysing with a convulsant sub- stance, to produce in frogs paralytic and tetanic effects, which in their relative and general characters are undistinguishable from the paralytic and tetanic effects of atropia. The next step was to administer these substances simultaneously to a mammal. It has been shown in a paper communicated to this Society by Dr A. Crum * AB, line of normality, each division of which, ot,,t,t,,tots, &c., represents a period of twenty-four hours ; CD, line of complete paralysis ; op,p,p,, &c., curve of paralysis ; 03,5), &c., curve of spinal-stimulation ; ¢,p,,t,p,, &¢., ordinates whose length roughly represents the amount of the paralytic action ; ¢,s,,,s,, &c., ordinates whose length roughly represents the amount of the spinal- stimulant action. 488 DR T. R. FRASER ON SOME UNDESCRIBED TETANIC SYMPTOMS Brown and myself, that four-fifths of a grain of sulphate of methyl-strychnium is about the minimum fatal dose for a full-grown rabbit* The amount of strychnia that should be combined with this dose, in conformity with the ratio of the last experiment, is about two-hundredths of a grain (or 2°66 minims of liquor strychnie). Experiment LXII.—2°66 minims of liquor strychnice (containing 0°02 grain of strychnia) was mixed with a solution of four-fifths of a grain of sulphate of methyl- strychnia, in twenty-five minims of distilled water, and this solution was injected under the skin at the right flank of a rabbit, weighing three pounds and four ounces. The first symptoms occurred in seven minutes, and consisted of a slight degree of exaggeration in the starts that were caused by irritating the nostrils of the animal. In nine minutes, a series of spontaneous spasms occurred in the ante- rior extremities; and it was now obvious that the motor power of the posterior extremities was slightly diminished. In nine minutes and thirty seconds, a further series of spontaneous spasms occurred, but the spasms now involved the whole body. In ten minutes, the rabbit lay down on the abdomen and chest; and after remaining quietly in this position for a minute, it was again affected with spasms, during which it fell over on the side. In twelve minutes and ten seconds, there was an attack of opisthotonic tetanus, which lasted for only ten seconds, and was immediately succeeded by a second attack, and, on its termina- tion, by a third, both also of short continuance. The rabbit was still lying on the side, and appeared unable to change its position. At frequent intervals, a series of feeble spasms now succeeded each other; and at the termination of one of these death occurred, fourteen minutes after the administration. The symptoms of paralysis and of spinal-stimulation observed in this experi- ment do not, in their relation to each other, exactly resemble those of atropia. Indeed, it was not anticipated that they would do so; but it was anticipated rather that the paralytic phenomena would be less marked, and that the spinal- stimulant would, consequently, acquire a greater prominence than with atropia. In the mixture of strychnia and sulphate of methyl-strychnium, the paralysis is produced by an action on the motor nerves alone, which action affects frogs much more rapidly and powerfully than mammals; whereas in atropia, it is produced not only by an action on the motor nerves, but also by actions on the sensory nerves, and, probably, on a portion of the spinal cord, and the additional actions seem to affect frogs and mammals nearly equally. Therefore, while frogs are more readily and completely paralysed than mammals by both atropia and sulphate of methyl-strychnium, mammals are less readily paralysed by the latter than by the former substance. Accordingly, the effects of the combination of sulphate of methyl-strychnium and of strychnia more closely resemble those of atropia in frogs than in mammals. * Loc. cit. pp. 160 and 196. PRODUCED BY ATROPIA IN COLD BLOODED-ANIMALS. 489 At the same time, the last experiment is in all respects a satisfactory one, for it clearly demonstrates that such a combination of a paralysing with a spinal- stimulant substance as produces in frogs paralysis followed by convulsions, will produce in mammals paralysis coexisting with convulsions, and impeding their manifestation. So that by a process of what may be termed physiological synthesis, further evidence has been obtained in support of the conclusions, that the effects of large doses of atropia on the cerebro-spinal nervous system (mental phenomena excluded) are due to combined spinal-stimulant and paralysing actions of that substance, and that the differences in the relations of these effects to each other, which are seen in different species of animals, may be explained by this com- bination acting on special varieties of organisation. It is generally admitted that atropia produces both paralytic and convulsive symptoms in mammals, but no satisfactory attempt has hitherto been made to define the relations of these symptoms to each other. This investigation has shown in what manner the paralysing is related to the convulsant action both in mammals and in frogs; and it has also accounted for the differences in the mani- festation of these actions after different doses of atropia. It may, without pre- - sumption, be asserted, that it throws a new light on the causation of some of the symptoms of atropia, and also of many other substances, whose action, like that of atropia, produces a combination of paralytic and convulsive symptoms. The principal results that have been obtained may be thus summarised :— 1. Atropia produces in frogs well-marked convulsive and tetanic symptoms, which, when present in an extreme degree, form a separate stage in the poisoning, succeeding that of paralysis. 2. Tetanic symptoms follow the subcutaneous administration of a dose of sulphate of atropia, equivalent to the ;,oth of the weight of the frog, and of doses a little greater or less than this. 3. These symptoms are due to a direct action of atropia on the medulla (oblongata and spinalis). 4. The differences between the paralytic and convulsive synptoms that occur in frogs and those that occur in mammals may be explained by the greater sus- ceptibility of the former to the action of a paralysing agent, and by the amount of paralysing being greater in atropia than the amount of convulsant action. 5. The different symptoms that are produced by different doses of atropia in animals of the same species may be explained by its paralysing being greater than its convulsant action. 6. The paralysing and convulsant actions of atropia can be imitated in both frogs and mammals by a combination of a paralysing with a convulsant sub- stance. VOL. XXV. PART II. 6k ( 491 ) XIII.— Hegel and the Metaphysics of the Fluxional Calculus. By W. RoBertson SmiTH, M.A., Assistant to the Professor of Natural Philosophy in the University of Edinburgh. Communicated by Professor Tarr. (Read 17th May 1869.) It is now many years since Dr WHEwELL drew the attention of the Cambridge Philosophical Society to the courageous, if somewhat Quixotic, attempts of HEGEL to cast discredit on Newron’s law of gravitation, and on the mathematical demonstrations of KEPLEr’s laws given in the “ Principia.” At the time when WHEWELL wrote, it would probably have been difficult to find in Britain any one ready to maintain the cause of HEGEL in this matter, or even to hint that the astounding arguments of the Naturphilosophie flowed from any deeper source than self-complacent ignorance. The present state of matters is different. The philosophy of Hecrt is now for the first time beginning to have a direct and powerful influence on British specula- tion. Men are beginning to study HeceL; and an author whose works con- fessedly demand the labour of years, if they are to be fully understood, can hardly be studied at all except by devoted disciples. A man whose determination to master HecEL’s philosophy survives the repelling impression which the obscurity and arrogance of the philosopher are sure to produce at first, is very likely to be carried away by the calm assumption of omniscience which runs through HrcE.’s writings. It isnot, therefore, surprising that Dr Stirtine extends his admira- tion to HecEw’s physical positions; and if he does not venture to say that HzcEL’s proof of KePier’s laws is right, at least feels sure that it would repay the attention of mathematicians. It would not, perhaps, be impossible to rob Dr Srrruine of even this sorry consolation; but there is the less occasion for retracing any part of the ground gone over by WHEWELL, in so much as “The Secret of Hegel” calls attention to another point, in which Hees. criticises Newton, and in which Dr StirLING has no hesitation in pronouncing HeceEt’s findings “ perfectly safe from assault,” and Newton guilty of an obvious mathematical blunder. Such a statement, proceeding from the most powerful of our living metaphy- sicians, and recently reiterated in the newspaper press, as a sort of challenge to mathematicians, seems to call for some remark from a mathematical point of view. Itis true that a confirmed Hegelian is not likely to be influenced by any reasoning that we can offer. “The judgment of a pure mathematician,” we are VOL. XXV. PART II. 61L 492 MR W. ROBERTSON SMITH ON HEGEL told, “‘has really been so peculiarly trained that, perhaps, any such will never prove decisive as regards any Hegelian element.” We are told, too, that HEGEL’s ‘‘most important note” on the mathematical infinite “‘ has remained hitherto absolutely sealed,” for C. Franrz, who does take up the subject ‘as in opposition to, is to be assumed ignorant of, the views of Heget, which plainly, so far as they go, are inexpugnable”’ (!) Now I do not profess to be able to treat this question from the stand-point of Hecet’s own philosophy. I have no desire to criticise Hraex’s doctrine of the Infinite, in so far as it forms an integral part of his system. But the note to which Dr StTiRL1NG calls attention is itself a critical note, in which HEGEL proposes ‘to consider in detail the most remarkable attempts to justify the use of the mathematical notion of the Infinite, and get rid of the difficulties by which the method feels itself burdened” (HEGEL’s Werke, iii. 286).* What HEGEL seeks to show is, ‘‘ that the mathematical Infinite is at bottom the true Infinite” (p. 283); imperfectly conceived, however, by the mathematicians, who have therefore never been able to put the higher calculus on a basis thoroughly free from con- fusion, or evenerror. Thus, not to speak of Fermat, Lerpnirz, EuLER, and others, whose views HeceL takes up more or less fully, we are told that Newron © himself, although his fundamental thought was quite in harmony with HEGEL’s views, was not so far master of his own thought as to be able fairly to deduce the practical rules of his method. In the actual application of the new instru- ment, NewTon clung “‘ to the formal and superficial principle of omission because of relative smallness.”’ He thus fell into real errors; and even so fundamental : a problem as the determination of the fluxion of a product was solved in a manner analytically unsound. Now these, I maintain, are assertions that can fairly be examined by one who does not profess to have mastered HEGEL’s system. They even afford a fair test whether that system is really so complete in all its parts, and so light-giving in its applications, as we are told to believe. If NewrTon is really confused and in error, it must be possible to make this clear by an argument based on NEwron’s own principles. For if to the mathematician NewrTon’s method is perfectly clear and self-contained, and if its errors can only be observed from an entirely different point of view, we have not one truth, but two truths, mutually destructive. And this surely Dr StirL1ne will not assert. It is possible, however, to go further than this. To the subject of the calculus HEGEL devotes two notes. The first of these alone is taken up by Dr Srir.ine. And in this note Hrecet adds to the destructive criticism of which we have been speaking only a very general account of the principles on which he would base the calculus. These general principles are, as HEGEL says, “‘ abstract’’ (we would rather say vague), “and therefore in themselves also easy” (p. 327). The real * Here and elsewhere I adopt, as far as possible, the language of Dr Stirxine’s own translations from Heaet, which may be viewed as authoritative. AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 493 difficulty lies ‘‘in the concrete side,” in the deduction from these generalities of the practical rules of the method. To this subject Heart devotes his second note, professing to point out a purely analytical method whereby, without any application of the doctrine of limits, everything necessary for practice can be deduced. If we can demonstrate that the analytical method is radically unsound, producing results mathematically false, it will surely be vain to appeal in defence to any “deficiency in the judgment of a pure mathematician.” The plan that suggests itself is therefore the following :—/irst, to consider the real character of NewrTon’s method, and to show what may, I think, be made quite clear to an unprejudiced mind, that that great man really did know what he was doing; and, in the second place, to show that Hecrt having refused to be instructed by NeEwTon’s real knowledge, but having acutely enough caught sight of something like the ghost of an idea, which he could not for want of solid knowledge really make his own, was first ensnared by the plausible but fallacious method of Lacranceg, and then, in attempting to improve that method, lost any elimpse of the truth that he had before, and was swamped in hopeless absurdity. The ingenuity of a great deal that Hrcet has said on this subject I do not wish to dispute. No doubt he, “ with as delicate a hand, Could twist as tough a rope of sand” as any man that ever lived. But the question is, after all, one of plain truth and error; and however much we may admire the chivalry with which HEGEL rushes into an unequal encounter with so gigantic an antagonist as NEwrTon, it will never do to “ Coin a formal lie on’t To make the knight o’ercome the giant.” We must begin, then, by examining the principles on which NewrTon based his doctrine of Fluxions. In doing this, it is not necessary to inquire how far NEWTON’S own views varied during his life. Hrcrt knows Newron’s method from the Principia only, and a quotation from the second Lemma of the Second Book (Werke, iii. 305) shows that it was the current text of the Principia (that of the second edition) which he had before him. In fact, HncEt’s acquaintance with Newton’s writings was clearly of the most superficial character, embracing apparently little if anything beyond the section on Prime and Ultimate Ratios, and the Lemma just referred to. These facts make all merely bibliographical inquiries superfluous in dealing with HEGEt’s objections. I may refer, however, to a paper by Professor p—E Morea, in the “ Philosophical Magazine” for 1852, on the “ Karly History of Infinitesimals in England,” in which it is shown “ that NEwTon never varied in his meaning of #;” or, in other words, that Newron “held to the conception of the velocity or fluxion,” although he at first ‘‘ used the infinitely small increment” (only of the first order, however), “as a means of 494 MR W. ROBERTSON SMITH ON HEGEL determining it.” What follows will, I hope, serve to show that these facts imply that Newton had all along a firm grasp of the principle of his method, and that his frequent employment of abbreviated practical processes was really based on a consciousness of the strength of his method, according to the general principle of mathematicians, who never hesitate to apply the boldest symbolical methods in detail, when they feel confident of the starting-point in the use of these symbols. This, in fact, is a point that metaphysicians have never properly attended to. One is disposed to cap Dr Stiruine’s wish that some great analyst would study Hece, by expressing a hope that some metaphysician of real ability may pay sufficient attention to what are technically called the ‘‘ Symbolical Methods” of mathematics, to enable him to appreciate BooLr’s profound preface to his treatise on “ Differential Equations.” This exercise would at least make it clear that metaphysical criticism on mathematics is still—I speak without any desire to be disrespectful—in the circle-squaring stage, 7.e., still treats as the real questions for discussion points that mathematicians have long seen to be merely special cases of general principles, and therefore to be no longer possessed of independent interest. To return from this digression. NEwTon saw that there were two ways in which quantities might be conceived as generated. The first of these is that which the usual processes of arithmetic have made familiar to everybody, viz., the addition of discrete units. The theory of numbers thus viewed is contained in the arithmetic of integers, to which may be added the doctrine of arithmetical fractions as an extension of the method, reached by supposing the unit itself to change in value. NEwrTon was especially attentive to the importance of the doctrine of decimal fractions, in which the change of unit is so regulated as to give the greatest possible increase of power that the arithmetical conception of quantity admits of; and the opening pages of his “‘ Geometria Analytica” are expressly directed to show that these advantages may be made available in literal as well as in numerical calculations. [See also the treatise ‘‘ De Analysi per Equationes Numero Terminorum Infinitas.” ] NEWTON saw, however, that arithmetic in its most perfect form could give full mastery over quantity, only on the supposition that quantity, as it comes before us in the universe, is always produced by the synthesis of ultimate units, or, in other words, of indivisibles. And this, says NEwTon, is contrary to what Evciip has proved concerning incommensurables in the tenth book of the Elements (Prine. lib. i. sec. i. schol.) Instead, therefore, of endeavouring to eke out this view of quantity by arbi- trary assumptions, NewTon resolved to turn to Nature herself, and inquire how quantity is really generated in the objective universe. ‘‘ Lineae,” he writes ‘‘ describuntur ac describendo generantur non per appositiones partium sed per motum continuum punctorum; superficies per motum linearum; solida per AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 495 motum superficierum; anguli per rotationenem laterum; tempora per fluxum continuum et sic in ceteris. Hae Geneses in rerum natura locum vere habent et in motu corporum quotidie cernuntur.” (Introd. ad Quad. Curv.) In a word, NewrTon’s fundamental position is, that the arithmetical concep- tion of quantity is not that with which nature herself presents us, and is not, therefore, universally applicable. On the other hand, every quantity that has objective reality [.¢., is an object of real intuition] is generated by continuous motion, with definite (constant or variable) velocity within definite limits of time. The metaphysical nature of time and motion NeEwron has nothing to do with. Itis enough for him that mathematical time, conceived as an independent variable flowing uniformly, is clearly the ¢rwe time made known to us in nature (Principia; Schol. to the Defs.), and that the existence of a definite velocity at each point of a motion is in like manner an undoubted physical fact. By means of these profound yet simple considerations, NEwron is at once able to revolutionise the whole theory of quantity, and to substitute for the relation of unit and sum that of velocity and quantity generated, or, in NEwTon’s own language, of fluxion and fluent. It must be remembered that we have said nothing of space, so that fluent is not limited to extensive quantity, while velocity, or as we should rather say rate, has a correspondingly wide application. Thus, any fluxion may itself be treated as a fluent quantity, and its fluxion sought, the only independent variable being time, which is thus a fluent which has no variable fluxion. This conception of time, as the one absolute and independent variable, is undoubtedly one of the most splendid and fruitful in the history of human thought, and well deserves the attention of metaphysicians. Only let it be said that no criticism of NrEwron’s time, which starts from the arithmetical view of quantity, and urges the old objections about infinite divisibility, and so forth, is competent ; for the arithmetical theory is a product of abstract reflection, and so stands on a lower platform than the pure objective notion of NrewTon. There is no difficulty in comprehending the mathematical power which the conception of fluxions at once puts in Nrewron’s hands, if we remember that it is not in any sense an extension of the theory of numbers that he is seeking. It is true that the calculus has revolutionised algebra as well as geometry; but it has done so by transforming algebra from the abstract science of numbers to a physical science—the science of pure time. In Newron’s own mind, however, this conception was probably not explicitly present. What he did see was, that all difficulties in geometry (and to Newmov, as to the old geometers, geometrical magnitude is the type and exponent of all magnitude whatsoever, when viewed with respect to its generation) are reducible to the general form :—‘‘ Given the fluent as a function of time to determine the fluxion and vice versd.” The one class of problems that can be thoroughly treated without explicit VOL. XXV. PART II. 6M 496 MR W. ROBERTSON SMITH ON HEGEL reference to a generation by flux, is that which has for its geometrical type systems of straight lines; and thus geometers were tempted to introduce the fiction of indivisibles, in order to reduce higher problems to this type. But these higher problems are not simply complicated cases of the rectilineal type; on the contrary, that type is produced -by one of the two essentially distinct elements (generated and generating quantity), which usually appear side by side, ceasing to be explicitly manifest. Take, for example, NEwron’s own instance at the beginning of the “De Quadratura.” Suppose the abscissa AB of a curve to flow uniformly, in which case it may be taken as the graphic representation of the independent variable, i.e., of time, while the ordinate BC is of course a func- tion of the abscissa. Then NewrTon shows that the reason why the determination of the tangent at C is a difficult problem, is that the ratio of the ordinate BC to the sub-tangent VB is the graphical represen- tation of the fluxion of the ordinate. In fact, the meaning of the tangent is, that it is the direction in which the curve is flowing at the point C; and all attempts to give it another explanation without reference to motion simply ignore the real gist of the problem, and of course end in diffi- culties that can be escaped only by violent assumptions. It is only in the straight line where the fluxion of the ordinate is constant, or the tangent sinks into the curve, that the conception of vate can be dispensed with. Before we go farther, it is proper to remark that in criticising NEwron, HEGEL coolly ignores the whole foundation of the doctrine of fluxions as here developed. ‘The thought,” says he (Werke, ili. 302; Sriruine, ii. 354), “cannot be more correctly determined than NewrTon has given it; that is, the conceptions of move- ment and velocity (whence fluxion) being withdrawn as burdening the thought with inessential forms and interfering with due abstraction” —~.¢., because HEGEL thought that the calculus should be based, after the manner of LAGRANGE, on purely analytical considerations, it never enters his head that if NewTon thought otherwise there might be some deeper ground for this course than a want of insight into his own method. On the contrary, HEGEL comments in the most edifying manner on the “early still naive period of the calculus” in which ‘‘mathematicians sought to express, in words and propositions, results of the newly invented calculus, and to present them in geometrical delineations,” assigning to the “ definitions and propositions so presented a real sense per sé,” in which sense they were “‘applied in proof of the main positions concerned.” If there is any meaning at all in these statements, which are the gist of a somewhat lengthy discussion (Werke, iii. 324; Srrrurne, ii. 375), that meaning must be that NrewTon and others first differentiated a function, then sought a geometrical construction to suit, and finally invented a physical proposition to correspond. AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 497 Purely analytical considerations without any physical basis were held, HEGEL thinks, to furnish in this way physical laws. In support of this view, Hrece, triumphantly refers to “the Newtonian proof of his fundamental proposition in the theory of gravitation compared with ScuubErt’s ‘ Astronomy,’ where it is admitted that .. . in the point, which is the nerve of the proof, the truth is not as NEwTon assumes it’’[!] And so upheld by the dictum of this forgotten astronomer, HEGEL goes on to inveigh against the mere jugglery by which NewTon, already knowing KepeEr’s results, avails himself of the “‘ mist of the infinitely little” to bring out apparent mathematical proofs of these results. One does not know whether the singular perversity of this accusation against NEwTon’s moral character, or the incredible ignorance of the argument by which it is supported, is most to be wondered at; for, not only do the reasonings of the ‘« Principia” rest throughout on the experimental laws of motion on which NeEwrTon’s first proposition is expressly based, but the proof itself depends not on the interpretation of an analytical process, but on the essentially physical or, more definitely, kinematical considerations above developed. Nay, so little is it the case, that the “mist of the infinitely little” is needed to give a show of plausibility to NEwron’s process, that the whole gist of the proof lies in the one conception of quantity generated at a definite though variable rate, and that thus, without any change in the spirit of the proof, by simply introducing explicitly a theorem about moments of velocity which the demonstration in the “ Principia”’ implies, the law of equal areas can be deduced without even that apparent use of the infinitely little which, as NewTon himself warns his readers, is always merely apparent (THomson and Tarv’s “ Natural Philosophy,” § 234). In one word, NEwrTon’s proofs are always physical throughout, and really belong to the essence of the thing to be proved; while Hecet first shuts his eyes to the real import of the fluxional method, insisting that it mus tbe made purely analytical, and then rails at Newron for using the method to do work for which, if it had been purely algebraic, it would not have been fit. A Hegelian calculus, as we shall see, would certainly have been of little service to physics; but the doctrine of fluxions is itself a part of physics, and absolutely indispensable in some form or other to the right understanding of physical problems. We have still, however, to see how it is that Newron’s system comes to have anything at all to do with the infinitely little which, as he himself says (Introd. ad Quad. Curv. § 11), it is the peculiar merit of that system to render unessential. The reason is simply, as we are told in the scholium at the end of the first section of the “ Principia,”’ that he was anxious to provide for ease of conception, and also to introduce all legitimate abbreviations in his arguments. When Newton is called upon to justify his method, he always refers to the simple fact that a velocity definite, yet never for the shortest space of time uniform, is a notion really furnished by nature, and that the true measure of that velocity is to be 498 MR W. ROBERTSON SMITH ON HEGEL got by allowing the motion at any point to become uniform for a unit of time. But if one wishes, as HEGEL would say, to substitute for this notion a convenient “Vorstellung” to assist the imagination, NEwron is ready, by means of the doctrine of prime and ultimate ratios, to point out a way in which we may avail ourselves of the method of indivisibles, always remembering that this method shall have merely a symbolic value, and so must be used with caution. If two quantities have the same fluxion at any moment, they begin at that moment to increase at the same rate. It does not follow from this that the two quantities shall receive equal increments in any space of time however small, unless during that time the rates of flow remain constant. But NewrTon shows that in a very large class of cases, which he takes up one by one in the first section of the ‘‘ Principia,” not only may we, by taking the time of flow small enough, make the difference of the increments generated in that time as small as we please, but if we enlarge both increments on the same scale up to any given size, we may make the differences of the increased increments as small as we please, while the time of flow has still a definite value. Since, then, the ratio of the increments is always nearer to unity the less the time of flow, and may be brought as near to unity as we please by taking the time short enough, but still finite, the ratio must ultimately be unity—ze., that quantity which, varying according to a definite rule, always represents at any given time the ratio of the increments, may still be constructed when the time is made zero, and is now equal to unity, or is equal to the ratio at which the increments start, which Newton calls their prime or ultimate ratio. The practical application of this reasoning is, of course, that in virtue of it, we may in certain cases with strict accuracy treat the increments of two variables (of a curve, for example, and its tangent) as equal, if, before closing our reason- ing, we proceed to take the limit. Thus, if any one finds that it assists his imagination to deal with magnitudes as if they were composed of indivisibles, instead of confining himself to fluxions, NEwTon provides in the method of prime ratios a criterion by which the applicability of the process may be judged. ‘The details by which it is shown in the “ Principia,” that the limit of the ratio of the increments is equal to the ratio of the fluxions whenever the fluents may be geometrically represented as curves of continuous curvature, involve no new principle in geometry. Everything is as plainly and undeniably reduced to ordinary geometrical intuition as anything in Evciip, when we once bring with us the fundamental kinematical ideas of velocity and acceleration. It is obvious, : 0 , , moreover, that to Newron the fraction o? as above explained, means simply the ratio of the rates at which two quantities are flowing at the moment at which they pass together through the point from which we have agreed to reckon their magnitude backwards and forwards. Except where such rates can be assigned AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 499 ‘ ; 5 22, 20 possessing a definite ratio, NewTon does not pretend to recognise o as a mathe- matical reality. This outline of NEwron’s principles is, of course, very meagre. It will probably, however, suffice to enable us to estimate the real value of HEGEL's criticisms. Hrcet highly approves of NeEwron’s statement of what he means by prime and ultimate ratios, viz., that he always deals not with indivisible but with vanishing divisibles. This is very satisfactory so far, but the next paragraph makes one doubt whether HreceL knew what he was ap- proving. “Newton,” we are told, “‘ only explained what he means by his terms, with- out showing that such a notion has internal truth.” * This is an accusation constantly recurring in various forms. Its source is, of course, that determination which we have already noticed in HEGEL to pay no regard to considerations of velocity and motion. Now it is quite true that Newton does not condescend to offer any explanation of his ‘‘ notion” to the man who has failed to familiarise himself by actual intuition with the nature of velocity, and acceleration, and the genesis of quantities by flux. But these notions are just as truly capable of being constructed by pure intuition as those of ordinary geometry, and so NEwron’s definitions enjoy fully the advantage which Kant ascribes to mathematical definitions in general. They cannot err, because they simply unfold a construction by means of which the notion is actually produced. If HEGEL, however, shut his eyes to Newron’s notion, he has got one of his own, which he is sure is just what Newron wanted. I do not intend to attempt to take up anything but the concrete applications of this notion; but perhaps it may be well to give here part of HEGEL’s abstract statement of what he con- ceives to be the mathematical infinite. ‘“ Das unendliche Quantum. . . ist nicht mehr irgend ein endliches Quantum, nicht eine Grossebestimmtheit, die ein Daseyn als Quantum hatte sondern es ist einfach, und daher nur als Moment; es ist eine Grossebestimmtheit in qualitativer Form; seine Unendlichkeit ist als eine qualitative Bestimmtheit zu seyn” (iii. 289; Srrruine, ii. 341). Now, says HEGEL, this is clearly what Newron needs. His vanishing magnitudes have ceased to exist as quanta, and exist only as sides of a relation; but farther, the relation itself, in so far as itis a quantum, vanishes. “ The limit of a quantitative rela- tion is that in which it both is and is not, or, more accurately, that in which the quantum has disappeared, and there remains the relation only * Dr Srirnuine (ii. 355) seems to have read “ Nach dem damaligen Stande der wissenschaft- lichen Methode wurde nun erklart.” In the collected edition of the “ Werke,” ii, 303, I read *‘ wurde nur erklart,” which seems to give a more intelligible sense. VOL. XXV. PART II. 6N 500 MR W. ROBERTSON SMITH ON HEGEL as qualitative relation of quantity.” This sentence must mean that in the equation oy _¥ Lt 5 3 the left hand side vanishes as quantum in the same sense in which dz and dy vanish, or, as Hrce often puts it, es is “infinite,” just as truly as dy and dz. Now, we are told again and again that the ‘‘ infinity” of the dx and dy does not lie in their being infinitely small, but in their having ceased to be any determinate magnitude, and only representing the qualitative principle of a magnitude. To this statement NEwron would probably not have objected, as his whole use of infinitely small quantities is, as we have seen, merely to help the imagination, and scientific strictness is given to his method from another side. But certainly he would never have dreamed of admitting that y is also indeterminate ; for both numerator and denominator of this fraction are in their nature definite quantities. That the fraction can be expressed as : is to NEwTOoN by no means the essential point. On the contrary, he argues distinctly that : must have a definite value, just because this is the form in which certain processes present to us a quantity which, from kinematical grounds, we know to be definite. To Hxrcrt, however, the fascinating element is just this 5 which for his ends would be quite spoiled by being evaluated. That would reduce it to a mere quantum; but, in the meantime, it is “‘a qualitative relation of quantity,” which is a far finer thing. Not unnaturally, however, Hecex has now to ask himself, what is to be the practical use of this Lt a , Which certainly “ expresses a certain value which lies in the function of variable magnitude.” In asking this question, he still supposes himself to be criticising Newron and the mathematicians, and accordingly proceeds, with much severity of manner, to knock down the indeterminate oH which he has just set up (p. 318). To apply the conception of limit in the concrete we must determine the limit. This is done by TAyLor’s theorem, from which if y = /(z) we get by __ ap PT geet, &e., and then letting dv and dy vanish “es p;—not as it should have been = a This, of course, is sadly inconsistent; for instead of our fine qualitative deter- mination, here is a stubborn quantum turning up. Now, says HxcsEx, the —— re ae SS Ce a oe e) eee / = = « AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 501 mathematicians try to get over this by saying that pis not really = HE but is only a definite value, to which ; comes as near as you please. Of course, if this is so, it is as evident as anything can be that the difference between p and O is not a quantitative one. But, adds the philosopher, naively enough, that d. d doesn’t help one over = = 4. Suppose now that we were to say = really = p (a definite quantity), as, in fact, mathematicians do say, then it is obvious that dx couldn’t have been = 0. Or if, finally, it is conceded that = = 0 (which Heeger seems to think most likely, since dy and dz vanish together), then what can p be? Now, can any one say that the man who devised this argument knew what he was doing? When did any mathematician suppose that after evaluation Oe. 2 - Sm ase 9 is indeterminate? Or had HrceL never read NewrTon’s first lemma, with its “fiunt ultimo equales”? Or, again, if Hecrn allows that there is no quantita- tive difference between p and oe why does he assume a qualitative one? Or, above all, why try to explain Newron’s doctrine without ever deigning more than a contemptuous glance at the one central point of the whole? Hxcet boasts that half an hour would suffice to learn the calculus. Certainly he might have employed a good many hours in unlearning his false conceptions of it. HEGEL has next something to say about the way in which mathematicians have developed the details of the calculus. Since none of them had a clear notion of the matter in hand, their proofs, we are told, are very weak. They always fall back into methods merely approximate, subjecting infinitely small quantities to the laws of finite quanta, and yet rejecting them as relatively unim- portant, in despite of these laws. Of course, adds HEGEL, we need not look for the rigour of demonstration of the old geometry, for the analysis of the infinite is of a nature essentially higher than that geometry. However, mathema- ticians have sought this rigour, and they have all failed.—Of course, it would be easy for any one to point out numerous mathematicians who have failed; but let us simply ask whether Newton has done so. HeceEt unhesitatingly affirms that he has, and Dr Srirtive is jubilant at the discovery. The error is supposed to lie in the deduction in Prin. ii. Lem. 2, of the fluxion of a product. The statement of Newton is as follows:—If A,B be two quantities increasing continuously, and their moments or rates of change a and 8, the moment or change of the rectangle ABis aB + JA. By moment Newron does not mean the increment actually received in any time, however short, but the 502 MR W. ROBERTSON SMITH ON HEGEL nascent principle of the fluent quantity—a notion, of course, made clear by the pre- vious discussion of prime and ultimate ratios. The moments, in fact, are any quan- tities proportional to the rates at which A and B are flowing—the products of the fluxions of A and B by an arbitrary increment of time. If moments, then, are called increments, the meaning is increments which would be received if the rate of flow remained constant, and the ratio of two moments is simply the ratio of the fluxions, and therefore equal to the limit of the ratio of the actual incre- ments, while it is quite independent of the magnitude of the separate moments. Now, says Newton, when A and B are diminished by half their moments, the rectangle is AB — 4 aB —36A + 446; and when A and B are increased by half their moments, it is AB + }¢B + 406A + 4a; and so to the increments @ and } in the sides corresponds an increment @B + 0A in the rectangle. This demon- stration is certainly very curt, and intended only for those who have mastered Nrewton’s fundamental notions, and may therefore be saved the tedium of a long reductio ad absurdum. More at length, the proof would be of this kind. The fluxion of the rectangle must, since the flow is continuous, be a definite quantity, depending only on the magnitudes and fluxions of the sides at each moment. Thus the fluxion of AB will be unchanged, if we suppose that from the values A —4a, B —40 the sides flow with uniform velocity, equal to A and B, until they attain the values A+ 4a, B +40. In this case the increments a and 6 will represent exactly upon the same scale the fluxions A and B. Meantime, the rectangle has been flowing with a constantly increasing velocity, which at the moment when the value AB was reached, was the velocity Newton is seeking to determine. The whole increment of the rectangle is a@B + 0A, which therefore represents the, average velocity of the rectangle on the same scale as a,b repre- sent the uniform velocities of the sides. Clearly the average velocity with which the increment is described is greater than the velocity at the beginning of the motion, and less than that at the end, and therefore, since the velocity is continuous, is strictly the velocity at some intermediate point. But this point can be none other than that at which the rectangle = AB, for were it any other point, we could take a and } small enough to throw this point out, and there would still be another point at which the fluxion of the rectangle must = aB + 0A. But thisis contrary to the intuitive fact that the velocity is continuously increasing. To the mathematician, however, this round-about process is unnecessary. He sees at once that if the average velocity is independent of the duration of flow, and depends solely on a certain point being included within the flow considered, the velocity at that point must be strictly the average velocity, for in the limit the two coincide. Now, Hece., of course, did not see this, because he would not admit the kinematical reality of fluxions. He, therefore, supposes that NEwron wants to find the diferential of AB—a way of stating the problem which Newton would AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 503 have rejected as misleading. The differential can be nothing else than (A + dA) (B +dB)— AB. But Newton writes instead of this (A + 4dA) (B + 3dB) — (B— 4dA) (B — 4. dB), thereby making an error in so elementary a process as the multiplication of two binomials !—But where is HeceEw’s justification for saying that what Newvon is seeking is (A+ dA) (B + dB) — AB? NeEwron says nothing about differentials at all; his a is, as we have seen, not the infinitely small increment of A, but an arbitrary multiple of the fluxion of A, which need aB + bA a not be infinitely small. NerwrTon’s is, if you please, ? _ pp AA) B+ aB)— AB = lt an but even this, which is very different from what Hrcet writes, is simply a different, by no means a more fundamental, view of the problem than NEwrTon’s. Dr Sririine tells us that HEGEL’s expression 7s what NewrTon’s says his is, “ the excess of the increase by a whole dA and dB.” But what NEwTon says is only that when the sides are increased from A — 4a and B — } 4, through incre- ments @ and 0 the rectangle increases by aB + DA. That this is true surely cannot be denied. In fact (A + a) (B + 6)— AB would have represented not the velocity at value AB, but the average velocity of the rectangle during the interval between values AB and (A + @) (B + 0), and therefore the real velocity at a point between these limits which NEwTon was not wanting. We know, in fact, that it would have been the velocity when the sides are = A + 5 and B + ss Instead, therefore, of NEwron rejecting a quantity on the ground of relative smallness, we find that Hrcet has gratuitously introduced such a quantity. Of course, the Hegelian will reply to all this, that our method is “ rendered impure by the concrete adjunct of motion.” And here, of course, we can say nothing, except that the fluxional calculus is essentially kinematical, and that to ~ construct it apart from motion is as likely a task as to make a geometry without lines. To make bricks without straw is a light task compared with that which HEGEL has set himself. Happily unconscious of these difficulties, HrGEL goes on to moralise with much satisfaction upon NewrTon’s melancholy self-deception, in palming on him- self such a proof. After this specimen of HecGeEL’s analytical subtilty, it is perhaps sufficient to confront the assertion which immediately follows (Werke, ili. 313; STIRLING, ii. 364), that NewTon, in finding fluxions by the method of expansions, uses a process analogous to his method of solving approximately numerical equations, con- stantly ‘‘ neglecting what is relatively unimportant,” with the explicit words of the De Quadratura (Introd. § 5)—“‘ Errores quam minimi in rebus mathematicis non sunt contemnendi.” Theterms omitted are, of course, always terms which we VOL. XXV. PART II. 6 0 504 MR W. ROBERTSON SMITH ON HEGEL know to become not relatively but absolutely zero in proceeding to the limit. The motive for using such expressions as ‘‘ minuatur quantitas o in infinitum,” instead of simply saying, let o = zero, is merely to show that o becomes zero not by a discontinuous process, as subtraction, but by a continuous flow. Nay, cries HecEeL, for in the 3d Problem of Book ii. of the “‘ Principia,”” Newton fell into an error, by “ throwing out, as LAGRANGE has shown, the very term which—for the problem in hand—was wanted. Newtown had erred from adhering to the formal and superficial principle of omission from relative smallness.” This error, by the way, is only in the first edition of the “ Principia,” which HEGEL, one may safely affirm, had never seen. The whole statement here is taken from LAGRANGE, and applies much better to LAGRANGE’s analytical way of putting NewTon’s argument, than to that argument in its geometrical form. NEwTOov, in fact, investigating the law of resistance, that a body under gravity may describe a given path, seeks a geometrical expression for the moment of the sagitta—a small quantity of the third order. It is clear, therefore, that no such expression can be exact unless account is taken of every small quantity of an order not higher than the third in the geometrical construction involved, for such quantities will not vanish in the limit, or are not “relatively small,” in a mathe- matical sense. The principle of the problem, then, presents no difficulty on Newton’s method; and the true account of the error is, that by a mere slip in the details of a complicated process, NeEwTon failed to see that he was omitting a term (or better, a line) not small relatively to the moment of the sagitta. HeGeEL, however, conceives that so far as this goes Newton was all right. The error, according to him, lies in neglecting a term which, though “relatively small,” ‘« possessed the qualitative value sought.” ‘In mechanic, a particular import is attached to the terms of the series in which the function of a motion is developed, so that the first term, or the first function, relates to the moment of velocity, the second to the accelerating force, and the third to the resistance of forces.” The terms are thus to be regarded as ‘“‘ qualitative moments of a whole of the notion ;”” and, of course, in a problem about resistances Newron needed the third term.—Now here we have, jivstly, a laxness in the use of terms so gross, as to make it hardly possible to criticise our author fairly. Luckily, we can see that HrGex is leaning entirely on Lacranee, and that “ the series in which the function of a motion is developed,” must therefore mean the series which expresses space in ascending powers of time. And this enables us to ask, secondly, What reason HxrceEu has for supposing that it is in this series that we are to find the basis for a truly philosophical view of kinetics? It was HEGEL’s misfortune to live at a time when, among other fruits of the “ Aufklirung,” Lagrance’s “ formal and superficial” method of treating physics was in great repute; and surely it was a cruel fate that the great enemy of the Aufklirung should, through a defective mathematical education, be made a willing captive to a mathematical SS Beh Val ais, ei dl he 2 pk thd Sa EA Sebi AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 505 ‘ Aufklarung,” which has, from its intrinsic weakness, fallen as fast as it rose. In details, it is true, HEGEL is keen enough in detecting the unsatisfactory character of LAGRANGE’s stand-point [see, for example, a note at this very point]; but that the whole method was artificial he could not see, not for want of mental power, but because, having never studied the subject, he knew nothing whatever about it— had not even mastered its technicalities. Then, again, if it is true that successive differential coefficients have a qualitative difference, how can that be brought out except in virtue of the relations established in mathematics between quantity and quality, relations which are not reached by pure analysis, but only in NEWTON’S way, 7.¢., by intuition? And would not these relations be violated, and all mathematics rendered absurd, if the term that is qualitatively important could be quantitatively negligible? And, last of all, let me challenge HzcEL to bring forward any proof on his own principles, that the third term relates to the resistance of forces; or for that matter, to show that this statement has any real meaning whatever. But most men, I imagine, have now had enough of Heeet’s criticisms— criticisms which simply show that the “ half hour” which he had devoted to the calculus had not sufficed to give him any just idea of that great method. It is certainly much to be regretted that so ableaman did not study mathematics thoroughly, for such a course might have proved useful to the theory of mathe- matics, and could not have failed to be profitable to himself. As it is, he has only given us criticisms such as we have seen, and an attempt to which we now proceed to establish the calculus on a new and very inadequate basis. The point which we have always found HrGet urging is, that mathematical functions, when they become quantitatively indefinite or ‘“ infinite,” may still have areal qualitative value. Passing over the fact that this is not the technical sense of infinite in mathematics, we may grant that there is a kind of meaning, however vague, that may be attached to the view. Thus an incommensurable is infinite in the Hegelian sense, not because it can be expressed arithmetically only by an infinite series, but because it is essentially not a sum of units, but, as HEGEL vaguely says, a “relation.” For relation we should say function, and then we should be able to read in HerceEL’s words some meaning like this. Algebraic and geometrical functions are qualitatively different from mere arith- metical functions. ‘They imply an entirely different way of looking at quantity, expressing, in fact, steps in time or space [or in kinematics, both in time and space]. So, again, the differential coefficient which takes the form : ceases to be intelligible on the mere arithmetical view, but gives us a real result of a different quality, when we understand it as equivalent to a proposition about the rates of the vanishing quantities. But then Hecer does not seem to have seen that 3 has areal quantitative value, expressing accurately a definite quantity of a different 506 MR W. ROBERTSON SMITH ON HEGEL quality. And further, there was in HEGEL a rigid determination not to see the real qualitative difference between the continuous quantity of the higher analysis and of actual nature, and the discrete quantity of arithmetical abstraction.* He thus fell into the delusion, that a writer like LAGRANGE who, from the extreme nominalistic stand-point of the eighteenth century, seeks to make analysis a merely formal instrument, in no way expressing the essence of things, and who, for example, boasts that in his Mécanique Analytique one will find no such unnecessary incumbrances as figures—HEGEL, I say, imagined that such a writer had really reached a higher generality than Newron, when he had only reached an untenable extremity of one-sided abstraction, and hence, without a moment’s hesitation, resolved that by simply treating the successive differential coefficients as the successive derived functions obtained by explanding y in terms of a, we shall be quit “ of the formal categories of the infinite, and of infinite approxima- tion, and of the equally empty category of continuous magnitude”? (iil. 320). The differential calculus, then, is a special branch of mathematics which has to deal (by purely arithmetical methods) with qualitative forms of quantity, 7 é., says HEGEL, with relations of powers. A power, it should be said, means with HEGEL a quantity raised to a higher power than the first, and the link between the clauses of the foregoing sentence is as follows :—“In the equation = a the relation of y to z is an ordinary quantity, and a common fraction, just like 5 so that the function is only formally one of variable magnitudes. On 2 ; the contrary, if a — oe has no determinate quotient, and, in fact, 2 has no ratio to y, but only toy’. Now the relation of a magnitude to a power is not a quantum, but qualitative.” It is needless to say that the man who could make “no con- stant ratio” identical with “no ratio,’ and who did not see that ,/px has a definite value for each value of 2, or who did not see that p is a quantum, though not of the same dimensions as y’ (which probably was what confused HEGEL), is hardly fit to construct a new theory of the calculus. But let us pass on. The subject matter of the calculus is then, we are to believe, equations in which one variable appears as a function of a second, one of these at least occur- ring in a power higher than the first. In such a case the variation of the variables is qualitatively determined, and therefore continuous. It would be vain to ask why; but since we are told that in the equation s = ct there is no scope for differ- entiation, 5 not being qualitative, we may at least conclude that Hzce does not regard uniform motion as continuous! So far as the principle goes it is quite sufficient, continues HEGEL, to consider * Heeger absolutely identifies analysis with arithmetical process—“ Auf analytische d. i. ganz arithmetische Weise” (iii, 328). Had Hrexzn ever studied the treatment of incommensurables in ordinary algebra? If algebra is “ ganz arithmetisch,” the whole doctrine of indices is false. AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 507 the equation x = y”; the advance to more complicated functions is quite mechanical. Now both y and 2 are really numbers, and so may be expressed as sums. _[This, of course, is a very bold assumption, as HEGEL says nothing of the possible case of incommensurables.] The simple and yet comprehensive way of representing « as a sum is to write it as binomial. Now expand 2” as a binomial function, and we have a series of terms which are ‘‘ wholly functions of the potentiation and the power.” The differential calculus seeks the relation between these terms and the original components of z. As we are not concerned with the sum, but merely with the relation of the terms of the expansion, it would be best simply to expand (# +7)", and to define the particular “ Potenzenbestimmung” got by con- sidering the second term of this series as the first derived potence-function of y. In short, the true mathematical commencement in this part of analysis is no more than the discovery of the functions determined by the expansion of a power. We see at once that this is simply an excessively clumsy adaptation of the method of Lagrange, which is based on the proposition that f (x + 72) can always be expanded in a series of ascending integral powers of 7, and then defines the successive fluxions [or derived functions] of 7x with reference to the series. HEGEL adds to LAGRANGE nothing but confusion, and a degree of vagueness which is quite pitiable; and, of course, his method has the same fundamental fallacy as that of LAGRANGE, in so much as /(# +7) cannot always be expanded as LAGRANGE proposes, or what comes to the same thing, the details of the calculus cannot be deduced by processes purely arithmetical from the definition (for it is no more) n n—1 = =nx . Ido not, therefore, think it needful to go into details on this part of Hecret’s method. The really important point is the use to be made of these magical “ Potenzenbestimmungen,” which, according to HeceEt, depends on the discovery of concrete relations which can be referred to these abstract analytical forms. HeceEt proceeds as follows :— There is always a fall of one dimension in passing to the first derived function. Hence the calculus is useful in cases where we have a similar fall in the powers. We are also to remember that, by differentiating an equation, we get not an equation but a relation. Whenever, then, we wish to investigate relations con- nected with any equation, but of a lower dimension, we have room for the cal- culus. A case in point is the investigation of the relations between the tangent, subtangent, and ordinate, for example, in a curve of the second degree. These relations are linear, while the equation contains squares. They depend, there- fore, on the first derived function (pp. 341, 342, 344). That such a statement is mere guess work is clear, if we observe that by a linear relation HrGreL means indifferently the ratio of two straight lines, or a ratio involving only first powers of w andy. Or, again, since the value of the radius of curvature is also on HeGeEL’s principles linear, why does VOL. XXV. PART II. 6 P 508 MR W. ROBERTSON SMITH ON HEGEL it involve the second derived function? Let us, however, follow our philo- sopher further. ‘Suppose we have 2az — a” = y’, and take the derived function, we get a ratio a— ax: y,—a linear ratio representing the proportion of two lines. The real point is to show that these two lines are the ordinate and sub- tangent.” This is very plausible, no doubt; but let us try a cubic equation, say 2ax—a2’=y’. Now the resulting ratio, to put it in HEGEL’s way, is 2(a — 2): 3y’. Is this a linear ratio? Yet it still represents the ratio of the ordinate and sub- tangent. Clearly Hecren does not know that when 2 and y become definite ; ; E) . "heg ’ : co-ordinates of a point on the curve the ratio a ceases to be a linear function of variables in any proper sense, and is simply a determinate fraction. This mistake augurs ill for the validity of Hrcet’s proof, that the two lines, whose ratio is the ratio of the derived functions, are really ordinate and subtangent. But he has Lacrance luckily to help him, who, he says, has entered on the truly scientific way. We get, therefore, a wordy and loose description, which would be utterly unintelligible to any one who did not know the thing before, of the way in which LaGRANGE proves that the line g = fv — af’x + pf lies nearer to the curve y = fz in the neighbourhood of the point (z, y) than any other straight line through that point. HrceEw’s confusion is not diminished by the fact, that LAGRANGE deduces this proposition from a general theorem about the contact of curves, and originally writes the straight line as g= Fp. This piece of tactics so puzzles the philosopher that, after all his invective against the differentiation of linear functions, he allows Lacrance, without rebuke, to write fv = F’a. In other respects, however, we have great improvements on LaGRaNcE. It is absurd to write g = a@ + bp* as the equation of the line to be compared with the tangent, g = pb being quite general. That the line g = dp would not neces- sarily pass through the given point of the curve at all is, of course, a trifling consideration ! A still greater improvement regards the process by which LacrancE shows that we can always find a point (with abscissa 2 + 7), at which g=fx—afax + pf« shall be nearer the curve than any other assigned straight line. At this point Hece begins to dread (not unjustly) that the conception of limit, or rather “ das beriichtigte Increment,” is to be employed. However “this apparently only relative smallness contains absolutely nothing empirical, z.¢., dependent on the quantum as such; it is qualitatively determined through the nature of the formula, when the difference of the moment on which the magnitude to be compared depends, is a difference of powers. Since this difference depends on 2 and 2”, and i, as a proper fraction, is necessarily greater than 2’, it is really not in place to say anything about taking 7 of any size we please, and any such statement is quite * HEGEL uses p = ag + b, but I keep Lacrancr’s own letters throughout, AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 509 superfluous” (p. 347). One word in explanation of these. LaGrange takes an abscissa (2 + 2), and gets fleri=ferife+ Sf @+)), and F+t) = Fot+ilo + i FE’ (x@+J); or for the straight line given above, == fot @ . Thus the difference of the ordinates of the curve and straight line with abscissa 2 a+tis > f’'(@+ 7). For any other straight line the difference may be written mz. Now, the ratio of these increments is it ee J) , which may always be made less 12 than unity by taking 7< Peas . HEGEL, however, asserts that - fF (@+j) < mt, whenever 7 is a proper fraction, which is an obvious analytical absurdity, and, in fact, is equivalent to saying that it is impossible to draw a chord to a curve, the difference of the abscissze of whose points of section is less than unity, since for the chord through (za, y) cutting the curve again at (v+7),mi=0. In the face of this absurdity, it is scarcely necessary to add, that Hecen having resolved to simplify matters, as we saw, by getting his derived functions from the expansion of (# + 7)", has no right even to form for every curve the expan- sions on which LaGrance’s proof depends. I shall, in passing from the subject of geometry, merely enunciate a simple deduction from HEGEL’s result in an intelligible form. ‘‘ At any point of a curve there are an infinite number of tangents, which may be got by uniting that point with any other point on the curve whose abscissa is not different by a quantity greater than unity.” I present this proposition, which is entirely due to HEGEL, and in the development of which my share has been “ purely mechanical,”’ for the admiration of all Hegelians whatsoever. HEGEL’s account of the application of the calculus to mechanic is much briefer, and presents less interest after what WHEWELL has written on a connected point. I cull only one or two illustrative points. For the purposes of the calculus, HecEL classes motion as uniform, uniformly accelerated, and motion returning into itself, alternately uniformly accelerated and retarded. Variable acceleration, which in the form of harmonic motion is by far the most common in nature, is quite ignored. Again, criticising the assertion that = represents the velocity at any point of a course, he tells us that it is “ schiefe Metaphysik” to speak of the velocity at the end of a part of time. ‘‘ This end must still be a part of time; if it were not, 5210 MR W. ROBERTSON SMITH ON HEGEL there would be rest, and no motion; velocity can be measured only by the space passed through in a definite time” (p. 352).—An appeal to Atrwoov’s machine would probably be too ‘‘empirical” for our philosopher, but the law of energy might surely convince HEGEL of the reality of a variable velocity dependent on potential energy lost or gained. It is clear, at least, that HecxEt lacked the first elements of physical notions, and these were not likely to be supplied by the method of LacrancEe to which he adheres, beginning with s=/¢, and deducing every other consideration by differentiation. The following criticism on a remark of LAGRANGE is splendid :—“ We find, _ says LAGRANGE, the motion represented by s=a?@’ in the actual fall of bodies. The next simplest motion would be s=cé’, but nature shows no such motion, and we do not know what ccould mean.”’ [The ground of this is, of course, to be found in the law of the conservation of energy.| “If so, we have at least a motion whose equation is s’=at’,—KeEpLer’s law of planetary motion; and here the : . Lat ; ; investigation of the first derived function sa , &c., the direct treatment of this equation by differentiation, the development of the laws of that absolute move- ment from this starting point, must certainly be a most interesting task, in which analysis would appear in the brightest splendour ”[!]. That ¢ and s in KEpLer’s law are not variables, but constants determined for each planet ; that the equation has no analogy whatsoever with the equation of motion; that its differentiation would be meaningless unless space were filled with planets; and that then it would have nothing to do with “the determinations of that absolute motion,” are considerations that never entered HEGEL’s head. It is rather hard that, from a metaphysical stand-point, a man is still allowed to write about things he has not studied; and more than this, that men so able as Dr SrirLine should be found imploring great mathematicians to come and read such utter nonsense as naturally results from the attempt. Certainly Hecrn’s fame is not likely to rise higher the more his notes on the calculus are studied ; for these notes show quite clearly—irst, substantial ignorance of the subject in hand, bolstered up by some hasty glances at the “literature of the subject;” secondly, great disingenuousness in criticising NEwTon, without having ever given his views a careful study; thirdly, almost incredible confusion of mind, in so far as he seems to have thought that he knew his own meaning when he really had no meaning at all; and dastly, to add nothing more, such a degree of self-compla- cent arrogance as led him to fancy the results of his “ half-hour” more valuable than the fruit of the whole life of men like NEwron. This paper has already grown to such a length that it seems better to say nothing of HEGEL’s remarks on integration in the closing pages of his second note on the calculus, or of the third note, in which he treats “some other forms con- nected with the qualitative determination of quantity.” The subject, in fact, has AND THE METAPHYSICS OF THE FLUXIONAL CALCULUS. 511 a purely adventitious interest, and no one will care to linger longer over such a mass of confusion, both as to language and thought, than is absolutely necessary in self-defence. And the preceding pages may perhaps suffice to show that he who would exchange Newton’s clear ideas, based on nature’s own showings, and alike removed from shallow empiricism and self-conceited dogmatism, for the vague pomposities of a HEGEL, exchanges xpicea XaAkelwy, ExaTouBor évveaBolar. VOL. XXV. PART IT. ( 513°) XIV.— Observations on New Lichenicolous Micro-Fungi. By W.LAupER Linpsay, M.D., F.L.S., &c. (Plates XXIII.—XXIV.) (Read 19th April 1869.) In the course of my studies on the Microscopic Anatomy of Lichens, during the last fifteen years, I have frequently met with various more or less minute Parasites—mostly black and punctiform or papilleeform—sometimes disciform or maculeeform—affecting either the thallus or apothecia of lichens, or both thallus and apothecia. They grow equally on foliaceous and crustaceous lichens, especially of the following genera:—Parmeiia; Physcia; Umbilicaria; Solorina; Peltidea ; Nephromium; Sticta ; Stereocaulon; Usnea; Neuropogon; Cladonia; Beomyces; Squamaria; Placodium; Lecanora; Pertusaria; Thelotrema ; Lecidea ; Graphis ; Endocarpon ; Verrucaria. Most of these Parasites occur on lichens in my own Herbarium, collected by myself in 1856; or on lichens sent me for examination and determination by various British lichenologists between 1856 and 1858. They were examined, and described with figures in my Herbarium Note-books, between 1856 and 1859; in most cases without the assignation of names. I have not hitherto published their descriptions, or assigned names, for a variety of reasons, and especially on account of the difficulties which appear to me* to surround the determination of what, to any single observer, seem to be (so-called) ‘new species.”” Hence the parasites in question have been accumulating in my Herbarium, and their descrip- tions in my Note-books, for twelve years or upwards; and they now form a large and interesting, though obscure and puzzling, group of microscopic plants. I cannot, however, quote them in a Memoir I have in preparation on the Spermo- gonia and Pycnidia of the lower lichens (with which Spermogonia and Pycnidia the said parasites are frequently apt to be confounded) without placing their description—and, in certain cases at least, their names—on record in a form con- venient for future reference. Nor can I otherwise contrast with them various groups of Lichenicolous Micro-Lichens,} Micro-Fungi, or Micro-Algze, which have been described by other authors, or having been observed are yet to be described by myself. Inasmuch, moreover, as the said descriptions and names have not been, so far as I am aware, published by other authors—-whether fungologists or * Vide Author’s ‘ Contributions to New Zealand Botany,” 1868, p. 22; “ Otago Lichens and Fungi,” Transactions of Royal Society of Edinburgh, vol. xxiv, p. 407; “Parasitic (lichenicolous) Micro- Lichens,” Quart. Jour. of Micro. Science, January 1869; “ Polymorphism in Fructification of Lichens,” Quart. Jour. of Micro. Science, January 1868, { E.g. “Enumeration of Micro-Lichens parasitic on other Lichens,’’ Quart. Jour. of Micro. Science, January 1869. VOL. XXV. PART II. OR 514 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. lichenologists—I can no longer hesitate in contributing to botanical science the following observations on the structure and place in classification of the Micro- Parasites referred to. In the earlier years of my lichenological studies, I examined microscopically, with the greatest minuteness, large numbers of lichens for different collectors, from various parts of Britain and Ireland. I gave much more attention to the con- tents of other Herbaria than to those of my own; and to this circumstance, along with my reluctance to describe and name “ new species”—a hesitancy to ‘“‘ rush into print” with accounts of mere novelties, real or supposed—I owe the fact that many of my own gatherings in different parts of the world—many of the original observations recorded in my MSS.—have been published to science, with the stamp and éclat of novelty, by other—mostly continental—lichenologists. This, however, I do not regard as subject for regret. Much more important than the mere discovery and nomenclature of so-called ‘‘ new species” —only a small proportion of which has any claim to permanent rank as species—is, I think, the proper classification of existing material, so as to render additions to our know- ledge capable at once of estimation at their proper value, and of absorption and assimilation in their proper place. So far as regards descriptive or systematic lichenology, my own aim has always been and still is to arrange on a simple plan of classification the data already accumulated, so that they may be readily accessible and intelligible to the student. My own studies in lichenology are and have been preferentially biological; regarding as I do questions affecting (¢.g.) the physiology and anatomy, affinities and uses, of lichens as of higher interest than the mere collection and nomenclature of varieties or species’! The lichenicolous parasites above-mentioned are partly of the character of true lichens, partly of true fungi; while many partake of, or possess, the characters both of lichens and fungi, and can be appropriately referred only to the inter- mediate group of fungo-lichens.* In the present communication I confine myself to the two last-named groups—to Parasites which are either true fungi or fungo- lichens. All of them require for proper examination the microscope, and most — of them are distinguishable only under the lens. Very few, such as Coniothectum — sometimes, are sufficiently large to be visible to the naked eye. All are rendered more conspicuous by moisture, which frequently converts punctiform into papille- form perithecia, and flat surfaces into convex ones. In determining the genera under which to arrange the parasites hereinafter. to be described, I have availed myself of the opinion, kindly accorded, of two of the most competent British Fungologists, who have at various times examined certain of the said parasites at my request, viz., Rev. M. J. BerKevey, F.L.S., and FRep. Currey, F.R.S. While agreeing with these distinguished fungologists * Vide Author’s “ Otago Lichens and Fungi,” p. 434, and Arthonia melaspermella, Journal of Linnean Society (Botany), vol. ix. p. 269. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 515 in many, I do not profess to agree with them in all, respects. When they claim parasites as indubitable fwngz, I have no hesitation in accepting their determina- tions, as I have done (e.y.) in the case of various organisms referred by Mr CurREY to Torula, Conivthecium, and Spheria. While agreeing with Mr BERKELEY as to the close alliance between the fungi and lichens,* I cannot subscribe to his views of the place in classification to be assigned to various members of the group of fungo-lichens.+ Many of the lichenicolous parasites hereinafter described belong to the Torw- lacei—to the genera Torula and Coniothectum. The majority of the remainder, which are confessedly most heterogeneous, I arrange provisionally under the genus Microthelia, adopting this genus only in the sense elsewhere and already explained.{ The parasites in question are, in a manner at least, hereinafter systematically described in detail, their variations especially being made the subject of exposition. But here it is desirable to make certain preliminary general observations regarding the more prominent of their features 1. Genus Torula. § What I hereinafter describe as 7’. lichenicola varies considerably in its internal characters. In particular the spores are not always simple. Nevertheless all the forms described appear to me to be referable to asingle type or species. Externally, 7. lichenicola shows little diversity of form. It is black, punctiform, and superficial, resembling in this respect, and apt to be confounded with, (a). Spermogonia and of many lichens, especially when intermixed (6). Pycnidia therewith. (c). Many minute parasitic lichens belonging to such genera as Verrucaria and Endoccocus. || (d). Many minute parasitic fungo-lichens belonging to the provisional genus Microthelia. * In various letters Mr Berxerey has expressed himself as follows :—“ So convinced am I of the near relation of lichens and fungi that in the portion of my ‘ Introduction to Cryptogamic Botany,’ which is printed, I make one division, Mycetales, to include Fungales and Lichenales” (July 1856). . . . “One or two Verrucarie are so near Spheri@ that it is almost impossible to draw the line” (Dec. 1856). . . . “It is quite impossible to distinguish some lichens from fungi, and I consider the whole series as a division of fungals” (Feb. 1869). I hold quite as decided an opinion as to the impossibility of distinguishing many lichens from many fungi; or, in other words, of referring members of the group of fungo-lichens to the group of fungi rather than to the lichens! But I regard any classification, which arranges lichens as a co-division with fungi of a group of Jungals, as imperfect, artificial, and arbitrary, excluding as it does the equally close alliance that subsists between lichens and Alga. + His views and my objections are fully given in a subsequent part of the present memoir (pp. 528-580). ¢ “Otago Lich. and Fungi,” p. 436; Arthonia melaspermella, p. 279. § As determined by Mr Currey, who wrote me in February 1866 as to “a curious species of Torula” (contained in my Herbarium) “ which I do not recognise as having seen before. It is ramose, with bluish or greenish-black joints, the cells of which measure from 00003 to 0 0005 inch.” || £.g. those described in Korper’s “ Parerga,” p. 452, et seq. 516 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. (e). Many minute parasitic fungi, belonging especially to the genus Spheria. (f). Certain members of the pseudo-genus (of lichens) Pyrenothea. (g). Granules of coal dust, or other morganic foreign bodies. From all of these the Toruwia is readily distinguished on microscopical examination, more especially by the presence of its peculiar spore-chains or filaments. There is no complete perithecium; but the basa] cellular tissue, from which spring the spore- filaments, and which is generally sub-immersed in the host, is indistinguishable from that which constitutes the envelope or perithecium in many lichens, fungi,* or fungo-lichens, and their spermogonia or pycnidia. The cellular tissue in question is most frequently of an indigo colour, or bluish or bluish-black, though sometimes also it is brownish; not varying, however, in colour to so great an extent as do the spores. The free surface, which is granular or powdery, consists of spores separated from their filaments, and of the apices of the spore-filaments, which are closely aggregated, just as are the sterigmata or basidia in lichen or fungus-spermogonia, and pycnidia. In the young state, these filaments are simple hyaline tubes, resembling the simple paraphyses of many lichens, broader or thicker at the distal or free end, tapering into a thread-like pedicle at the lower, basal or proximal extremity. Gradually, however, articulations appear, beginning first at the distal end; and colour is added, the filament increasing in volume. The filaments then resemble the articulated paraphyses of many lichens, e@y., Lecidea lenticularis, Fr. Usually in maturity four or six articulations are formed, and gradually thrown off one after another from the distal end as free spores. Sometimes only one or two articulations are developed. The spore-filaments necessarily vary considerably in length, but less so in breadth. Some filaments appear to be abortive, and maintain throughout the simple or non-articulated, colourless character; not even increasing in length. These sterile filaments are intermixed with the fertile ones—just as sterile sterigmata—in this case gene- rally elongated and ramose, and exceptionally articulated or pseudo-articulated, frequently accompany the fertile ones in the spermogonia of many lichens.t Occasionally there is atrophy of certain articulations, which then assume the character of threads connecting the normal spores. The distal half of the spore- filament is generally coloured, though the colour is sometimes faint or excep- tionally absent. Where colour exists, it is always deepest at the distal or free end—in the terminal articulation. This colour is most frequently bluish (indigo or with a blackish shade); but sometimes it consists of various shades of olive or brown. The colour of the spore-filament is that also of the articulations of which it is composed. The colour of the spores is much more variable than their * E.g. Dichena rugosa, Fr. + Vide author’s “Memoir on Spermogones and Pyenides,” Trans. Royal Society of Edinburgh, vol. xxil, plates iv. v. vi. vii. vill. Xi. xii, DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 517 dimensions or form. The proximal articulation is frequently colourless, while the terminal one is deeply coloured. In size the articulations always vary on the same filament—the oldest or terminal one being the largest—the younger being at least narrower in proportion to their youth. Thus the terminal spore is frequently twice as large as the proximal one, the increase in dimension relating to breadth rather than length. In maturity, and when free—thrown off from their filaments—there is much less difference in the form and size of the spores. In form they are generally oblong, with flattened ends, unless in the terminal spore, which has its free or upper end rounded, even while attached to the filament. Occasionally the corners of all the free articulations or spores are similarly rounded. Sometimes the spores are oval or ellipsoid. Their length is generally ‘ about 00025”. In structure they are usually simple, with or without double con- tour; sometimes, though rarely, granular; occasionally also having a central sep- tum, or faint indications of the existence of one or more septa; more frequently containing one or more (two to three) spherical nuclei. Where there are two nuclei, they are generally arranged near the poles or extremities of the spores, to which they sometimes then give a sub-physcioid aspect, that which occupies the distal end of a spore being always the larger. This bi-nuclear character may attach to all the spores in a given specimen; and then, as well as in other cases, the spores in question resemble many lichen-sporidia. Sometimes chains or groups of spores of equal size and uniform character occur in numbers of four to eight, apparently the result of agglutination after maturity, and gaining the free state. In some cases the concatenate condition might be supposed to arise from simple absorp- tion or disappearance of the pedicle of the filament; but in such a case the constituent articulations would probably retain, even in age, their differences in size. The site of Torula lichenicola is the thallus or apothecia (or both) of various lichens, mostly crustaceous, and belonging to the Lecanorw or Lecidew. It is much more common in Lecanora subfusca than in any other species in my own experience; and it is so markedly more common on Jrish specimens of that Lecanora—mostly from the vicinity of Cork—as to give rise to the supposition that there may be some connection between the greater frequency of the parasite in Ireland and the (alleged) greater moistness of the climate of that country. There is, moreover, a frequent connection between the growth of the parasite and degeneration of the thallus or apothecia of the host; sometimes at least, obviously as productive of degeneration, ¢.g., when the Torula overspreads the disk of L. subfusca, rendering it as black as that of Z. atra. On the thallus of lichens it may be scattered generally over the surface; or only over particular parts thereof, é.g., the periphery, or it may occupy only the areole or verrucee. On the apothecia it may occur only on the disk, or both on the exciple and disk. The apothecia affected by the parasite are frequently degenerate or deformed; the disk has sometimes disappeared, and the whole apothecium has acquired an irregularly VOL. XXV. PART II. 6s ~ 518 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. verruceeform character. But in this case the degeneration appears to be quite unconnected with the growth of the parasite, which equally affects the thallus and apothecia, whether healthy or diseased, normal or deformed. The parasite may be scattered ; or closely aggregated, becoming confluent and maculeform; or it may be copiously studded over the apothecia, and sparingly on the thallus of the same species, or vice versa, though the former arrangement is the more common. Generally there is a marked contrast of colour between the parasite and the whitish or greyish thallus, brownish or reddish disk of the apothecia, which it so frequently affects. Necessarily the Torula is most conspicuous by reason of this contrast, where the thallus and disk of the host are pale—whitish in the one case, and brownish in the other. Its structure is essentially the same on whatever lichen it be parasitic. In one case I found it occupying the cavity of spermogonia (in Lecanora varia).* 2. Genus Coniothecium. There are various points of resemblance between Coniothecium lichenicolum and Yorula lichenicola. In both cases the parasite is black, and is conspicuous from contrast of its colour to that of the pale (or whitish) thallus on which it so frequently occurs. In the Coniothecowm the basal cellular tissue is the same. There is no complete perithecium; the granular or powdery surface consists of the free spores, which possess deep and dirty colours, mostly brown, though some- times blackish or olive. In the young state only is the Coniothecium papilleeform or verrucarioid, in which condition it may be confounded externally with Torwla, or with the various organisms with which the Zorula may itself be confounded. But there is a greater number of points of difference between these two common lichenicolous parasites. While Torula mostly affects corticolous lichens in the fertile state, Coniothecium affects only saxicolous Lecanore in the sterile, and frequently isidioid or other degenerate or hypertrophic, condition. In maturity, moreover, Conzothecitum is much larger, and more conspicuous—visible for the most part to the naked eye. It is largish and flattish, discoid or lecidioid, resembling some forms of the pseudo-genus (of lichens) Spz/oma, as well as the parasitic Spilomatic fungi—Spilomium Graphideorum, and Gassicurtia silacea. It varies considerably in size, surface, and outline; in the old state frequently resembling soot-spots. It is apt to be confounded witli the apothecia, especially when they are sub-degenerate, of various saxicolous Lecidew; and the character of the spores is sometimes such as to assist in this confusion. These spores are typically, in the young state, spherical and single; but they gradually acquire a sub-cubical form, and are associated in groups—sometimes most irregular in out- line—of two, three, or four, the form of the constituent spores then undergoing * Vide p. 520, and foot note ft. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 519 change from mutual pressure. Their colour is usually in maturity and age a deep blackish-brown ; but in the young state they may be pale, or even colourless; while in older conditions they may be olive, with a blackish tinge. When aggre- gated in groups of two, if the form of the constituent spores remains compara- tively regular, they may be indistinguishable from some figure-8-shaped lichen or fungus-sporidia. Hence, in one case, among the parasites hereinafter described (the Mangerton plant),* it is difficult to determine whether it is Coniothecium lichenicolum or a separate parasite. Sometimes the spores are concatenate, as in Torula ; but they are at once distinguished from those of Torula by their breadth being greater than their length, as well as by their sub-cubical form. When in aggregates of four, the spore-groups resemble wool-pack-like or Sarcina- like cubes. When in threes, as well as sometimes in twos or fours, they are very unlike spores, and are apt to be mistaken for fragments of cellular tissue, such as that which constitutes the perithecium of many of the lower lichens and fungi Whether simple or aggregate, the spores always exhibit double contour, presenting the aspect of being thick-walled. The Coniothecituwm may be scattered, as it generally is, or grouped; very rarely it is closely aggregated or even con- fluent. The thallus, which it affects, is frequently so altered—apart, however, from the growth of the parasite—that, in the absence of apothecia, it is impossible to determine the species to which it is referable. It appears generally, if not always, to belong to Lecanora, and, at least frequently, to the species ¢artarea, parella, and glaucoma. 3. Genus Microthelia. The parasites, which I have provisionally grouped in this pseudo-genus,{ are confessedly most diverse in character, though they possess certain characters in common. For the reasons elsewhere set forth,§ I think there is an advantage in considering them as a group until their characters are more fully known and understood. Their common or general characters are the following :— Most of them are microscopic, like Torula; black, papillzeform or punctiform. The papillzeform or verrucarioid condition is always rendered more distinct by moisture. Sometimes they are flattened and discoid, lecidioid or arthonioid (e¢.g., the parasites on Lichen dactylinus, Lecidea pachycarpa, and L. albo-atra). Some- times they are maculeeform ad initio (e.g., the parasites affecting Squamaria crassa and S. saxicola); at other times the macule are produced by the confluence or aggregation of minute papillz (as in the parasite affecting Parmelia perlata). * (b) P. 540, t I have seen true Lichen-sporidia by cohesion acquiring characters closely resembling those concatenate and woolpack-like forms of the spores of Coniotheciwm lichenicolum (pl. xxiii. fig. 28), ¢.g., in Lecidea dubia, T. and B., Leight. Exs. No. 88. In several other cases, I have met with Lichen- sporidia cohering in such manner as to resemble cellular tissue, ¢.g., in Verrucaria subalbicans, Leight, Exs, No. 200. t Vide p. 515, and foot note +. § “ Otago Lich. and Fungi,” p. 436. 520 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. Their size varies in the same species, but mostly with age. As to site, they affect the thallus or apothecia, or both; sometimes the under as well as upper surface of the apothecia. They are, like Torwla, more frequent on fertile than sterile lichens. As in Torula and Coniothecium, they are conspicuous where the colour of their host is pale. As in these parasites also, they may be few or numerous, scattered or aggregated, discrete or confluent; in the latter case becoming maculeform. Externally, they frequently resemble Torula and Coniothecium, or the organisms with which they are apt to be confounded; as well as certain young lichen- apothecia, belonging to the Lecidew, e.g., Abrothallus Smithit and oxysporus. Generally only the base is immersed in the host, but sometimes the body of the perithecium is immersed, only the apex or ostiole projecting above, or being visible on, the surface of the host. The envelope or perithecium is in all cases the same, consisting of brown cellular tissue; frequently, if not generally, the cells being sub- hexagonal. The Microthelic are sometimes associated with, if not productive of, deformities or degenerations of the thallus or apothecia of the lichens on which they grow (¢.g., M. Stereocaulicola, M. Beeomycearia, and the parasite which affects Sguamaria saxicola as Torula does Lecanora subfusca). Their internal structure varies considerably. Some of them are verrucarioid, in so far as they possess sporidiiferous asci, with or without paraphyses. Where paraphyses exist, they are either very delicate, filiform, more or less indistinct, without thickened or coloured tips; or they appear as a mere striated jelly. The asci are frequently saccate, as in Arthonia; short and broad, not tapering below into a pedicle. | In another group, no asci, paraphyses, sterigmata, nor basidia, were visible, so that it was impossible to determine whether the contained reproductive corpuscles are to be considered sporidia, spores, stylospores, or conidio-spores. Probably in the majority of cases they are really sporidia contained in asci. In a third series, the perithecia are quite sterile, containing no reproductive structure. Some of these parasites may prove to be mere pycnidia analogous to Phoma, Septoria, Diplodia, and Spheropsis. At least one of the parasites grouped under Microthelia possesses pycnidia in addition to sporidiiferous perithecia, viz., that affecting Thelotrema lepadinum. In certain exceptional cases, the same perithecium contained not only sporidiiferous asci, but stylospores and basidia; and in one instance ramose filaments, resembling the hypertrophied sterigmata of many lichen-spermogonia* (eg. the parasites accompanying Verrucaria epidermidis v. analepta, and Lecanora pyracea). Parallel phenomena are the occurrence of sporidia and spermatia in the same perithecia in Verrucaria atomaria and Spheria Lindsay- ana, as seen by myself, and in a certain section of the Verrucarie as described * Vide p. 516, and foot note +. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 521 by GrpeLui.* This observation is one obviously of much interest in regard to the physiology of reproduction, and of the reproductive organs, in lichens. I doubt not that careful observation will yet multiply the number of instances in which different forms of reproductive corpuscles exist in the same peritheciwm or organ. It may be provisionally convenient to classify the parasites grouped under Microthelia, according to the character of their contained reproductive corpuscles, as follows (omitting any specific mention of those whose reproductive structure is imperfect, and which are, therefore, for the present indeterminable) :— Sporidia, or reproductive corpuscles— 1. Simple. For the most part spherical and brown. Microthelia atricola. Parasites on (c.) Graphis scripta, Spilomium Graphideorum. (d.) Pertusaria. Gassicurtia silacea. Parasites accompanying Parasites on (a.) Opegrapha atra. (a.) Lecidea rupestris. (b.) Abrothallus Smithi. (0.) L. sanguinaria v. affinis. (c.) Pyrenothea verrucosa. 2. 1-septate (=bilocular). A. Brown, in maturity; frequently or generally soleaforim. Microthelia Stereocaulicola. Parasites on rugulosaria. (c.) Squamaria crassa. Stictaria. (d.) Endocarpon microsticticum. parietinaria. (e.) Usnea barbata v. florida. Parasites on (f.) Lecanora pyracea. (a.) Lecidea pachycarpa. Parasite accompanying (b.) Thelotrema lepadinum. Verrucaria fusiformis. B. Colourless or yellowish; sometimes szmple. Microthelia Cookei. Parasites on Parasites on (c.) Lecidea Hookeri; colourless. (a.) Lecanora cenisia; brownish- (d.) Verrucaria Garovaglii; colourless. yellow. Parasites accompanying (b.) L. polytropa v. intricata; Verrucaria epidermidis v. analepta; sometimes simple; colourless colourless. or yellowish. * So long ago as July 1856, Mr Berxetey wrote me—‘ You are aware, probably, that in a species of Tympanis, Mr Broome and myself have seen on the same hymenium the spores of a Diplodiu and true asc. TuLasne doubts Mr Broome and myself having seen stylospores on the paraphyses of a lichen. Nothing, however, was more clear and free from illusion. Almost in the same breath TuLAsveE calls in question the correctness of Hooker and Bazineton’s observation. He should not do this. I sent Turasnz the very section we had seen the stylospores of the lichen in, but he could see nothing. Unfortunately, there were but two or three scattered apothecia on the roots of Ammophila, sent for a fungus by Gaxpiner. I have in vain tried to get more from the same locality.” (Vide also my “ Monogr. Abrothallus,” p. 55; Ny tanper’s “ Prodromus,” p. 55; BerKexey’s “ Brit. Fungology,” p. &7, plate i. fig. 18.) In December of the same year Mr BerkeLEy again wrote me (in regard probably to Abro thallus Smithii)—“ In American specimens of your plant I sometimes find asci, sometimes naked spores, which have the same relation to the asci that the stylospores of Diplodia to the asci of the Spheria to which they belong. Whether the production in question is a lichen or fungus is a knotty point. It grows on living burk, and therefore should be a lichen !” VOL. XXV. PART II. 6T 522 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 3. 1 to 3-septate, mostly 3-septate and brown; sometime colourless. Microthelia vesicularia; 1—3 septate. Parasites on Umbilicariz; 1- sometimes (a.) Physcia ciliaris. 2-septate. (b.) Lecidea lurida. Nepromiaria; colourless. Parasites accompanying Beomycearia, (a.) Lecidea ferruginea v. sinapisperma., (b.) Verrucaria Taylori, Any such classification, however, is obviously artificial and defective; for not only in the same species, but in the same individual, the sporidia frequently vary much in character—in size, form, colour, and structure. In particular, they are frequently both simple and compound, colourless or coloured, of regular or irregular outline—according to the stage of growth. The “character” selected as the basis of classification must, therefore, be that which is presumed to prevail in maturity, and in normal conditions of growth. But what is prevalent or normal in one district or set of circumstances is not so in another, especially if the district or circumstances in or under which one systematist works are very diverse from those of others. There is, therefore, in such cases no precise or permanent basis of classification; whence it follows that the classification itself must be faulty. These remarks apply to too many modern “ classifications” of lichens, based on the characters of the sporidia alone, or on any single ‘‘ characters” or combination thereof ! In the group of parasites hereinafter described under Microthelia, the Iodine- reaction, which by fungologists is considered /ichenoid, denoting the presence of lichenine in the lichen-tissues, is generally absent. In the parasite accompany- ing Verrucaria epidermidis v. analepta, however, the asci give a blue reaction with iodine; in Microthelia Stictaria they become deep violet; in M. Umbilicaric the asci and hymenial gelatine assume various shades of violet; while in J. Nephronuaria the hymenial gelatine becomes violet. These exceptional reactions, however, neither prove nor disprove in themselves that the parasites, in which they occur, are lichens or fungi ; for, as I have elsewhere* sufficiently shown, this so-called lichenoid reaction occurs in indubitable fungi ; while there are many true lichens destitute of any colour-reaction—indicative of the presence of starch, or its varieties or allies—with iodine. Lodine-reaction is a subject of so great (supposed) importance in relation to the differential diagnosis between lichens and fungi: and as a “character” it bears so intimately on the place in classification to be assigned to the group of fungo-lichens, and to the members of the provisional genus M/icrothelia, as adopted or established by me, that it requires here some additional consideration. Asa ground for regarding it as a diagnostic ‘‘ character,” it appears to me necessary, * Arthonia melaspermella, p. 283; “Otago Lich, and Fungi,” p. 423; “Parasitic Micro- lichens.” : 4 ! q DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. a23 in the first place, that we should possess some trustworthy information as to the chemstry of the reaction, and as to the nature of those substances which, in lichens and fungi respectively, yield colour-reactions with iodine. As regards the lichens, I have carefully studied the most recent and approved standard works in chemistry; and the result is, that I find a discrepancy and confusion of asser- tion and opinion among chemists, nearly as great as that which exists between lichenologists and fungologists in regard to the application of the test, or of its colour-reaction, as a botanical ‘“ character.” So far as I have been able to ascertain, the substances occurring in lichens, which give colour-reactions with iodine, of the class which is now under review, are the following :— I. Starch or its modifications. A. Lichenine, Syn. Lichen starch, Lichenic acid. Formule, C,H,,0,. C,,H,,0,, (GrEecory).* Has been examined by chemists as it occurs in Cetraria Islandica and aculeata, Sticta pulmonaria, Ramalina fraxinea, Usnea barbata, Physcia parietina. Chemical characters.—Isomeric with starch. In C. Jslandica does not occur in granules; but is uniformly distributed through the tissues in a soluble con- dition. Pure lichenine is merely coloured yellow by iodine; but a green or blue is often produced from admixture of starch (Wart).+ A colourles jelly ‘‘ some- times assumes a dlue, and sometimes a greenish tint,” with iodine (Gorup BESsANEZ).{ Gives with iodine a greenish-brown colour (KaNne).§ ‘Its solu- tion is not coloured by iodine; but the jelly is rendered blue by that test” (GreGoRY). Other authors describe the reaction with iodine as blue, and this is the reaction (generally) assumed by lichenologists as the basis of theirlodine- testings. B. Jnuline, Syn. Dahline, Alantine, Menyanthine, Datiscine|| (GrEGoRy). Formule, C,,H,,0,, (GREGoRY), C,,H,,0,, (PARNELL). Has been examined as it oceurs in Cetraria Islandica in association with lichenine. Chemical Characters.—Also isomeric with starch. Occurs in white, crystal- line grains. Sparingly soluble in cold, very soluble in hot, water. Iodine colours it slightly brown (GreEGoRY). Insoluble in alcohol. Not blue, but yellow, with iodine (MILLER). C. Starch. Formula, C,,H,,0,,. Has been examined as it occurs in Rama- hina fastigiata (in large quantity); and Cladonia macilenta, digitata, and uncialis (Watt). It does not quite clearly appear whether this is ordinary starch in its * « Handbook of Organic Chemistry,” 4th edition (1856). + “Dictionary of Chemistry,” 5 vols. (1860-68). ¢ Quoted in ‘‘ Chambers’s Encyclopedia,’ 10 vols. (1860-68). § “Elements of Chemistry,” 2d. ed. (1849). || Mrzxer (‘‘ Elements of Chemistry,” 2d ed., 1862, p. 597”) gives Datiscine (=C,,H,,0,,), as the colorific principle of Datisca cannabina—not as a starch ! 524 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. ordinary form. ‘There is asubstance in lichens that gives a beautiful and deep blue reaction with iodine; and if chemists are correct in asserting that such a reaction is indicative of the presence of free starch in its ordinary form, while lichenine and inuline give yellow or brown colours to the reagent, we must admit that common starch not only occurs in the lichen-tissues, but that it is sometimes associated with, and at other times substituted for, lichenine and inuline. Il. Gum, or its modifications. Gum has been examined as it exists in Lecanora parella. Gives a greenish- blue with iodine (ScHuNcK). Ordinary gum (= Arabin) is not altered in colour by iodine; but the modification thereof known as Bassorin gives blue and red reactions (MILLER, p. 109). Were we to accept as a trustworthy basis for our conclusions the foregoing assertions of chemists, we would deduce that in lichens occur several forms or modifications of starch and gum that give reactions with iodine, variously blue, red, or brown, or admixtures of these shades, especially green. But it is impos- sible to accept as proper bases, on which to found diagnostic characters, state- ments so contradictory. The conclusion to be drawn is rather that chemists are yet ignorant in great measure of the composition and character of the muci- laginous and other components of lichens; and that at present they probably confound substances of somewhat dissimilar character. Thus the character of the iodine-reaction leads to the suspicion that what ScuuncK describes as a gum, may be in reality a starch! It by no means follows that the same reagent should produce the same colour- reaction in the same species of lichen, whether it is applied by the chemist in the laboratory to the separated amylaceous or mucilaginous principles, or by the lichenologist in his library to microscopical sections or preparations of the hymenium or other tissues. On the contrary, what we know of other colour- developments in lichens would lead us here to expect a certain difference in result; and, in point of fact, there 7s such a difference. And, further, differences of result in the same species, when iodine is applied as a test in microscopico- botanical diagnosis, arise in the hands of different experimenters from circum- — stances sometimes apparently most trivial, ¢.g., the strength or character of the iodine solution, the age or other conditions of development of the specimen operated on. I need not, however, further pursue or illustrate the subject here, having pointed out in detail elsewhere the sources of fallacy and the causes of difference in the colour-reactions of lichens as supposed botanical characters.* The substances or tissues in lichens, which yield colour-reactions with iodine, are chiefly—(i.) The hymenial gelatine or mucilage, which has hitherto been * “On Chemical Reaction as a Specific Character in Lichens,” Journ. of Linn. Soc. vol. xi. (Botany), p. 86; and “ Experiments on Colour-reaction as a Specific Character in Lichens,” Trans. Botanical Society of Edinburgh, vol. x. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 525 generally assumed to be, but on insufficient grounds, lichenine; (2.) The asci; (3.) The sporidia; (4.) The medullary or other tissues of the thallus. Excep- tionally colour-reaction may occur in other tissues. I have, for instance, met with a blue reaction from iodine in the interior structure of the spermogonia of Abrothallus oxysporus (Birnam, June 1856). The commonest iodine-reaction, that with which lichenologists have to do as a botanical character, is that of the hymenial gelatine,* in which are imbedded the asci and paraphyses; and of the asci themselves, on which the reaction is generally the most intense. Typically this reaction is a beautiful Prusszan-blue; that is to say, it has been generally regarded by continental lichenologists as what NyLanpER calls a “ Nota lichenosa,”—a diagnostic “character” of lichens as contra-distinguished from fungi. But this blue is not always exhibited in different specimens of the same species, nor even in the same specimen at different times; it may, moreover, be faintt or fugacious. Ina large number of lichens, instead of blue, the colour- reaction with iodine is violet, red, brown, or yellow; while in another large group there is no colour-reaction! Thus, in the genus Verrucaria, as defined by NYLANDER (in his “Lich. Scand.” p. 266), iodine developes in the hymenial gelatine of (a.) One section—the supposed typical or lichenic reaction. (6.) In another section—a wine red. (¢.) In a third section—a faint bluish or reddish tinge. (d.) In a fourth section—no reaction. t To which it may be here added, that some Verrucarie have no paraphyses, while in others they are distinct; but, are always (where they exist) more or less graceful, delicate, and filiform. Further, different tissue-constituents of the same lichen, or different parts of the same organ, give frequently different colour- results with the same reagent. These irregularities in colour-reaction may be conveniently and sufficiently illustrated by the following selection of quotations from the record of my micro- scopical examination of the lichens contained in the published Fasciculi of Sco =RER (Switzerland), NyLanper (France), and LeicuTon (England). The advantage of using published Fasciculi is, that a standard of comparison is secured accessible * The term, “ gelatine” or “ mucilage,” is here used, and by lichenologists generally, in a popular, not in a strictly chemical, sense; for it has already been shown that the so-called “gelatine” may really be a form of starch or gum, ora mixture of forms of either or both! Compare Arthoniu melaspermella, p. 283. + It is faint or obscure in the following, and in many other, true lichens :— Collema turgidum, Scher. Exs. 433. Asci. Stereocaulon condensatum, Scher. Exs. 509. Asci. Calicium stigonellum, Leight. Exs. 226. Asci. Lecidea Wahlenbergiana v. truncigena, Ach., Leight. Exs. 123. Hymenium, mere trace. t In his “ Prodromus” he describes some species as possessing a yellow reaction, e.g. V. xylina (p. 191). Ole XOX Ve PART 11. 6uU 526 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. to other lichenologists ; and I doubt not that, if they take the trouble to make similar microscopico-botanical testings, they will meet with many marked instances in which their own results will differ both from mine and from those recorded by authors, like NyLANnDER, who have given prominence in their works to chemical reaction as a botanical character.* This arises from the circum- stance, already mentioned, that the same species, under different circumstances, yields different colour-results with the same reagent. The following list could have been largely extended had I introduced quotations from similar records relating to the contents of my own Herbarium or of that at Kew. But such plenitude of illustration is, for present purposes at least, quite unnecessary. Omitting all instances of b/we-reaction with iodine, whether’ distinct or faint, the other results of iodine-testing may be roughly classified as follows :— I. No reaction. Thelopsis rubella, Nyl. Exs. 96. According to Nytanper (Prod. 196), its hymenial gelatine becomes red. Nephromium cellulosum, Ach, Hermite Island, Cape Horn. According to NYLANDER (Syn. 318), hymenial gelatine becomes blue. Urceolaria actinostoma, Scher, Exs. 578. Strigula Babingtonti, Leight. Exs, 35. Lecidea spheroides, Smrf., accompanying Opegrapha atra in my copy of LetcHrTon’s Exs. 245. According to NyLanper (Scand. 204), hymenial gelatine gives in different forms of the plant various shades of violet, or wine-red. L. foveolaris, Scher, Exs. 293. LL, Lightfootii, Ach. v. commutata, Scher. Exs. 581. Apothecia here degenerate. Calicium turbinatum, Scher. Exs. 6. Verrucaria chlorotica, Ach., Nyl. Exs. 96. V. eleina, Scher. Exs, 590. V. biformis, Scher. Exs. 109 (= V. chlorotiea, Ach.) V. levata, Leight. Exs. 198. V. rupestris, accompanying V. pyrenophora in my copy of Letcuton’s Exs. 245. Melaspilea arthonioides, Nyl. Exs. According to Nytanper (Prod. 159), hymenial gelatine becomes wine-red or bluish. Il. Reaction violet, red, or brown. Lecidea luteola, Leight, Exs. 150. Hymenium deep violet, with reddish tinge. LL. Wahlenbergiana, Ach., Leight. Exs. 123. Hymenium very faint purple. Li. cupularis, Ach., Leight. Exs. 122. Hymenial gelatine and asci deep brownish-red ; hypothecium (only) blue. L. abietina, Ach., Leight. Exs. 124. Same reactions as in L. cupuluris. L. lurida, Nyl. Exs. 131. Some tissues rose-red, others purple. Scher. Exs. 157, asci pale blue or wine-red; Hepp Exs. 121, asci wine-red. L. exilis, Hepp Exs. 473. Asci violet. LL. premnea, Ach. (saxicolous), Leight. Exs. 185. Asci lilac or lake-coloured. L, atro-alba v. concentrica, Leight. Exs. 17. Hymenial gelatine violet. According to Nyanper (Scand. 283), it becomes deep blue. L. expansa, Nyl., Leight. Exs. 186. Hymenium indistinct blue, with a lilac tinge. L. coarctata, Leight. Exs. 177. sci faint blue; contained protoplasm orange-red. * The majority of lichenological systematists give no attention to chemico-botanical characters, — e.g., Massatoneo, Kérzer, Tu. M. Fries and Mupp; while Nyzanper, on the contrary, gives them decided prominence, e.g., in his “ Lich. Scand.” DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. O24 Lvcanora aivra v. verrucoso-areolata, Scher. Exs. 538. Hymenium pale rose-coloured. Asci give no blue. According to Nytanper (Scand. 192), the hymenial gelatine of Verrucaria verrucoso-arcolata becomes yellowish-red. Physcia stellaris v. ambigua, Scher. Exs. 351. Asci-tips pale brown. Squamaria crassa, Ach., Leight. Exs. 5. Hymenium dirty palish blue or violet. Opegrapha dendritica, Scher, Exs, 585. Hymenial gelatine pale lilac. O. vulgata, Ach. v. vulgata, Leight. Exs. 194. Asci violet. Arthonia cinnabarina, Wallr., accompanying Opegrapha atra in my copy of Leiguton’s Exs. 245. Some asci very pale purple. Verrucaria rimosicola, Leight. Exs, 253. Hymenial gelatine violet ; asei not blue. V. subalbicans, Leight. Exs. 200. Hymenium violet or lilac; hypothecium pale blue. V. epigwa, Ach. (apparently), accompanying Sguamaria saxicola, in my copy of Leicu- ton’s Exs.145. Hymenial gelatine palish purple or violet; asci not blue. Accord- ing to NyLanper (Scand, 276), hymenial gelatine becomes blue. V. gemmifera, Tayl. Glenfarg, April 1858. Hymenium pale rose-red; no blue tinge. On the other hand, I found a very marked Uichenic reaction—a beautiful and more or less deep blue—with iodine in certain plants, generally regarded by fungologists as fungi; but now classed by lichenologists as lichens, on the sole ground apparently of this supposed diagnostic reaction. In Xylographa parallelu v. pallens, Ny. Exs., the asci and hymenial gelatine gave a beautiful blue. In X. flexella, Ny\. Exs., they gave a deep blue; and in Agyriwin rufum, Nyl. Exs., the hymenium became blue.* Ihave elsewhere} cited instances of what are still regarded, alike by lichenologists and fungologists, as fung?, giving so-called lichenic reactions with iodine. Sphweria ventosaria, which Mr Currey considers “a true Spheria,” gave me in its hymenium a violet or carmine with iodine; while ina plant lately submitted to Mr Berxe ey, and by him regarded as a “ Peziza of the tribe Patellea,” the asci sometimes give a b/we, sometimes no reaction with iodine. This Peziza (which appears to be new, and for which, if it is so, I propose the specific name lichenotdes), is associated with Lecidea parasema and disciforimis on the bark of fir trees, Morchone, Braemar, collected by myself in August 1856. The apothecia are apparently sub-stipitate; this appearance being produced by the dis- integration of the fibres of the bark on which they are seated. They vary greatly in form and size, being variously angular or oblong, or irregularly subspherical. The margins are involute to various degrees. ‘They are always black ; frequently wavy both in surface and outline, and generally thin. The paraphyses are very delicate, filiform, wavy, without coloured tips. The asci are long and sublinear or clavate, springing in groups or tufts from the hypothecium. The sporidia are innumerable in each ascus; atomic, subellipsoid or subspherical. The protoplasm, which is gradually developed into sporidia, closely occupies the cavity of the asci, separated only by a very narrow margin or double contour. Externally the Peziza has much of the character of a Patellaria, e.g., P. atrata (as described in * In BerKeey’s “ British Fungology” (1860) p. 375, both Agyrium and Xylographa tigure among fungi, the latter having rank as a subgenus under Stictis. A. rufum aud X. parallelu are mentioned; but not X. flexella (unless it be as Peziza flewella, Fr., p. 871), which, however, appears associated with X. parallela in NytanpeEr’s “ Prodromus,” p. 148, as a lichen. } ‘Parasitic Micro-lichens;” Arthonia melaspermella, p. 284. o28 - DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. my ‘Otago Lich. and Fungi,” p. 427). It has also certain resemblances to a Hysterium, e.g., H. pulicare, P. The asci and sporidia are similar to those of what, now regarded as a lichen, was by Fries the elder considered a Peziza, viz., Lecidea (Peziza) resine, Fr. (= Biatorella, Mudd, p. 191).* From that Lecidea or Peziza, P. lichenoides differs only in the colour of its apothecium. The asci of Abrothallus Smithi, which NyLanvER regards as a fungus, and BERKELEY} as a lichen, though they generally give no colour-reaction with iodine, + have, in one instance at least, yielded in my hands the lichenic blue, less distinct, however, than in A. oxysporus. In the latter species, on the other hand, which is equally by fungologists and lichenologists admitted to be a lichen, while iodine generally developes a vivid and beautiful blue in the asci, this reaction is some- times either obscure or absent; and the same remark applies to many true lichens, which generally exhibit the typical iodine-reaction: Spheria (Stereocaulicola), Th. Fries, and Leptosphwria (Lopadiicola), Th. Fries (Lich. Spitsb. p. 34), give in their hymenium a yellow iodine-reaction. But, accord- ing to the same careful observer, F'r1Es the younger (in his ‘‘ Lich. Spitsbergenses,”’ where he has recorded the iodine-reactions of most or many of the lichens therein described), the same reaction§ is exhibited by the following true lichens :— Leptogium \acerum and tenuissimum ; ) Lecothecium asperellum; protoplasm of asci. Collema pulposum ; Pannaria arctophila ; sporidia. hymenium, except the sporidia; i Lecidea pezizoidea ; sporidia and paraphyses. L. scotinum ; sporidia. Endocarpon pulvinatum ; protoplasm of asc. Sphcerophoron fragile; medullary tissue (of Microglena sphinctrinoides ; sporidia. thallus.) Staurothele clopima; sporidia and protoplasm of Gyrophora cylindrica; sporidia, asc. Leeanora flavida; sporidia and protoplasm of Thelidium pyrenophorum ; sporidia. the asci. Verrucaria extrema; do. L. mastrucata ; hymenium. Arthapyrenia couspurcans ; protoplasm of asci. L. ealcarea; do. Some of the parasites, which I have grouped meanwhile under M/zcrothelia, were lately submitted to Mr BerKELey, in the hope that he might claim a portion at least as fungi proper. But only one of them, what I have described as MW. Nephromiaria, he refers to Sphwria and the fungi. The remainder he considers lichens belonging to the genera Verrucaria, Celidium, and Abrothallus. To Verru- caria he refers M. Umbilicarie and M. Beomycearia; to Abrothallus the parasite * Quoad the asci and sporidia it also resembles Lecanora cervina, Pers., Lecidea morio, Sch., L. fossarum, Duf. of Nytanver’s Exs., and LZ. pruinosa, Sm. + “I think,” writes Mr Berxezey, in Feb. 1869, “TuLasne is quite right in making Phacopsis, Abrothallus, Celidium, and Scutula lichens.” + Vide my “Monograph of Abrothallus,” Quart. Journ, of Micro. Science, Jany. 1857. Nyan- DER (Prod, 55) remarks, ‘* Nullam enim mihi obtulit notam lichenosam.” But what constitutes a “ Nota lichenosa?” What diagnostic is there characteristic of a lichen as contradistinguished from a Fungus 2? For my own part, I know of none / § I have never myself met with in lichens a yellow iodine-reaction, which I did or could not regard as the natural (unchanged) colour of the reagent itself. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 529 which affects Lecanora polytropa v. intricata ; to Celidium, M. Stereocaulicola and the parasites on Sguamaria crassa and S. saxicola. Some of the parasites formerly grouped by me under Microthelia and the fungo-lichens have been transferred to the fungi proper, ¢.g., Spheria ventosaria, by Mr Currey. And it is most likely that other members of that provisional genus or group will from time to time be claimed as true fungi. But I find it impossible to perceive the validity of the claim, or the grounds of distinction. To me it appears that Sphwria is quite as nondescript or heterogeneous a genus as Microthelia, and that it passes into Verrucaria by connecting links that defy differential definitions! In the “‘ Treasury of Botany,” Mr Brerxeey says that the only distinction between Verrucaria and Spheria consists in the presence of thalline gonidia ; but, as | have elsewhere* shown, no gonidia can be present in the large group of parasitic athalline lichens, in which the apothecia—with or without spermogonia or pycnidia—constitute the plant. In the same work he describes Endothia as distinguished from Verrucaria by its ‘naked spores.” He also apparently regards it as consisting merely of the pycnidia or spermogonia of different lichens (Treasury, p. 1211); but he elsewhere describes “ asci’’ (Brit. Fungology, p. 384)! I am utterly at a loss to reconcile or understand these diverse and puzzling statements. Moreover, if we may judge from NyLanpEr’s description of S. homostegia (Prod. 56), which is flat and maculeform, the Spheeric are not necessarily papilleeform or verrucarioid. Some of them are thus arthonioid; and there are a few parasitic athalline Arthonie which have quite the facies of Sphweria homostegia, e.g., A. varians, Dav. (Nyx. Scand. 260). Mr Berxerey regards M. Umbilicaric and M. Beeomycearia (in my specimens) as having a “distinct crust;” or, in other words, a proper thallus. This I quite fail to discover, on repeated examination; the perithecia appearing to me to be indubitably seated directly on an alien (lichen) thallus. No doubt, AZ. Umbili- caricee and M. Beomycearia may be referred to the Verrucarie ; but only in the same sense in which the whole group of the Microthelie may be so transferred, constituting, with Lndococcus or other pseudo-genera, an athalline (parasitic) sec- tion. We have already seen that the botanical ‘‘ characters” of Verrucaria are in great measure negative; while there can be no doubt, as a genus, it is already much too (confusingly) large and heterogeneous. None of my Microthelie have the essential characters of TULASNE’s genus Celi- diwmn (as defined in his Mémoire, p. 120, pl. xiv. figs. 9-13, or in my ‘‘ Otago Lich. and Fungi,” p. 448). According to TuLasnz, the perithecia are aggregated so as to form maculee, in the centre of which are seated spermogonia, the spermatia being linear and very slender. In the typical species C. Stictarwm, Tul.(Mém. p. 122), the iodine-reaction is lichenic; the hymenium becoming bluish, reddish, * Arthonia melaspermella, p. 282. VOL. XXV. PART II. ; 6 Xx 530 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. brownish, or yellowish; but there is no such reaction in the Microtheliw, which Mr Berxexey refers to Celidium. Nor can I conceive any proper ground for assigning the parasite of Lecanora polytropa v. intricata to Abrothallus, which is itself a provisional and pseudo-genus. Indeed, I am utterly at a loss to comprehend the principles of Mr BERKELEY’s classification in the parasites above referred to; and I am led to regard his opinion as another of the many illustrations that may be cited of the diversity between lichenologists and fungologists regarding the nature and affinities of a large and important group of parasites, which have been fully studied by neither class of observers, and are yet, therefore, most imperfectly known. And further, his (quite recent) opinion I accept, as strongly confirmatory of the propriety of estab- lishing a provisional group of Fungo-lichens, and of resting contented with placing therein such doubtful organisms as the Microthelic, which I have hereinafter and elsewhere described,* instead of engaging in fruitless and interminable dis- cussion as to whether they are /wngz or lichens. When they become more generally studied and more thoroughly known, it may prove that some of the A/icrothelie in question are not parasitic or athalline, really possessing a proper thallus; or they may occur—as not a few true lichens do—both in the thalline and athalline state. . Only in certain cases, in describing the parasites, which form the subject of the present communication, have I ventured to assign names, viz., in the cases of those which may be considered typical or representative. In other cases—by reason of their resemblances to certain types or to each other, of the imperfec- tions of their structure, or for other causes—I have deemed it preferable for the present not to assign names, either generic or specific, though all these doubtful parasites are grouped provisionally, for convenience in future study and reference, under the pseudo-genus Aicrothelia. I have little doubt that when the parasites in question, as well as the parasitic Micro-lichens and Micro-fungi that have been described by other authors, are more thoroughly studied and known, the same type or species will be held to include several of those which at present appear distinct. There will be not only a certain reduction, but abolition, of genera and species, of which there is at present a most confusing redundancy.f Description of Illustrative Specvmens. I. Torula lichenicola. A. Parasitic on thallus or apothecia (or both) of Lecanora subfusca, Ach. 1. Scotch forms. (a) Corticolous ; Craig Choinich, Braemar, Aug. 1856, W. L. L.—Parasitic both on thallus and apothecia in one specimen of ordinary form of the Lecanora. The * « Otago Lich, and Fungi,” pp. 436-442. ++ An excellent illustration is to be found in the group of * Parasitie Micro-lichens,” (antea citat.) DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 531 disk of the apothecium is, however, chiefly affected. Here the parasite is so abundant and so closely aggregated, that it renders the usually smooth disk quite black, and rough-granular or warted; the apothecia then resembling, especially in colour, those of LZ. atra. The spores are sometimes 1-septate or 3-nuclear, resembling many lichen-sporidia. (>) Corticolous: on birch bark, Corramulzie Linn, Braemar, Aug. 16856, W. L. L. —Parasitic on both thallus and apothecia. As in the last case, the disk of the apothecia is frequently quite black and roughened from the growth of the Torula. . (c) Corticolous: Morchone, Braemar, Aug. 1856, W. L. L.—On thallus only. (d) Corticolous: on firs, base of Ben Lawers, on banks of Loch Tay, June 1856, W. L. L.—Equally on thallus and apothecia. Sometimes, as in cases « and }, the disk is blackened with the parasite, and resembles that of Z. atra. Spores bluish. (e) Corticolous: on ash, roadside, Loch Tay, June 1856, W. L. L.—Copiously and generally studded over thallus; much more abundant than the spermo- gonia of the Lecanora ; very distinct, black, punctiform bodies; spores generally 2-nuclear, brown. (f) Both corticolous and saxicolous: Kyles of Bute, Aug. 1852, W. L. L._—On thallus; spores indigo-blue; simple (no contained nuclei); narrow, and fre- quently longer than usual. (g) Corticolous: on firs and other trees, Caerlaverock road, Dumfries, Aug. 1856, . L. L.—Seattered on thallus of var. albella, Pers. Spores large and more numerous than usual; frequently exhibit 2 polar nuclei; that which occupies the upper and broader end of each spore in the spore-chain being generally the larger ; or there is only one nucleus at the superior or distal end of the spore. (h) Corticolous: near Dunglass, Cockburnspath, June 1856, Dr Murray Lindsay. —Variety of the Lecanora. Torula intermixed on thallus with spermogonia, which have not the usual characters of those of L. swbfusca. Spores bluish. Terminal articulation of the spore-chain, as usual, darkest in colour, with a rounded apex. The other spores, when separated, have squarish or truncated ends, and an oblong form. Occasionally the mature spore contains one or two nuclei. Sometimes the spore-filament developes only one (terminal) articula- tion; at other times there is no articulation at all—the filament being sterile or abortive—then resembling the paraphysis of a lichen, (i) Corticolous: woods of Blackhall, Strichen, Aberdeenshire, July 1865, Layton. —Copiously scattered over the warts or areole of the subverrucose and areolate thallus, but sparingly studding the apothecia. (k) Corticolous: on alder; Pease Dean, Berwickshire, 1856, James Hardy.— Thallus sub-tartareous ; many apothecia degenerate; disks eroded. Parasite abundant, both on disk and exciple'of apothecia, and on thalline areole. Spores with polar nuclei, somewhat resembling certain physcioid sporidia in lichens. (2) Corticolous: Penmanshiel, Berwickshire, February 1857, Hardy. 2. Irish forms. (a) Corticolous: near Cork, March 1858, Isaac Carroll. Associated with Physciu candelaria, Ach.—Thallus subtartareous, made up of numerous closely-aggre- gated verruceform areole ; apothecia mostly degenerate ; disk has disappeared, and the apothecia have assumed the appearance of irregular warts. Parasite is copiously studded over both thallus and apothecia, which have alike a black- punctate character. The Torula has its usual black, punctiform character. The basal cellular tissue is bluish, bluish-black, or brownish, resembling in this respect the varying colour of the spores. Lach spore-filament usually developes four or five articulations, which are oblong and simple, broader above than below. The terminal ones, the largest, are about *00025” long, and ‘000111” broad. (b) Corticolous: on old keeches, Castle Bernard, Cork, Carroll, Associated with Stigmatidium crassum, Dub.—On both thallus and apothecia (disk and exciple 532 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. alike). Parasite very minute, punctiform, black; basal cellular tissue deep indigo-blue. Spore-filaments about :001” long, and -000111” broad. Spores pale olive to bluish-black—about 00025” long, and -000111” broad. (c) Corticolous: Rathconnac, Co. Cork, Mar. 1858, Carroll.—On thalline areol and apothecia. Parasite resembles granules of a black powder dusted over thallus, its blackness contrasting strongly with the brown disk of the apo- thecium and white thallus of the ZLecanora. Basal cellular tissue, like the spores, bluish-black or indigo colour. Spore-filament, before separation of the spores, ‘00066” long. It frequently throws off only two articulations from its tip; the lower or basal—that is, the longer—portion showing no division. Sometimes there are three articulations or spores; rarely more. The mature spores are 00025” long, and -00014” broad. (2) Corticolous: Great Island, Cork, Mar. 1858, Carroll.—On periphery of thallus. Spores pale olive or brown; oval, ellipsoid, or oblong; 00016” long, and 000090” broad. (ec) Corticolous: Carrigaloe, Cork Harbour, Mar. 1858, Carroll. Associated with Physcia pulverulenta, Schreb.—Both on apothecia and thallus, on the latter somewhat inconspicuous; apothecia degenerate; margin eroded; disk black- punctate with the parasite, which is very numerous and crowded. The Torula is here larger than is usual, Basal cellular tissue indigo-blue. Spores brown ; 00025” to -00033” long, and 00016” broad—usually simple. Asso- ciated with the sporiferous filaments are numerous sterile or non-articulated— probably abortive—colourless, very delicate and linear filaments, which re- semble the paraphyses of many lichens. Sometimes they exhibit a faint appear- ance of septa, A parallel to these sterile filaments is to be found in the sterile _ hypertrophied sterigmata in the spermogonia of many lichens.* (f) Corticolous: Upper Lakes, Killarney, Mar. 1858, Carroll. —Disk of apo- thecia destroyed, and the apothecia converted into an uniform dark purple, sterile, degenerate mass. (g) Corticolous: Ardrum, Carroll.—Basal cellular tissue deep indigo. Spore- filaments 001338” long, ‘000111” broad; spores -00025” long, ‘000111” broad; olive or bluish-brown ; oblong, with rounded ends; simple, or frequently with two polar spherical nuclei; sometimes with double contour. (2) Kerry: Taylor in Herb. Mackay.—On apothecia ; disks of which become syb- convex and deformed, and frequently as black as those of LZ. atra, from growth of the parasite. 3. English or other forms. Betton, 1805,in Herb. Kew. All disks of the Lecanora entirely blackened by growth of the parasite, so that the lichen is apt to be mistaken for L. atra. Korzer (“ Parerga,” p. 470) describes his Pharcidia congesta as very frequently para- sitic on the apothecia of Z. subfusca and L. intumescens, Rebent., in Germany. It possesses 8-spored asci; the sporidia clavate-oblong, sub-baccillar, 1-3-septate, hyaline. Lecidea parasitica, Flk., and Arthonia varians, Dav., are also occasionally parasitic either on the thallus or apothecia (or both) of LZ. subfusca.t B. Parasitic on thallus of Lecidea canescens, Ach. Corticolous: Aghada, Cork Harbour, Carroll_—On portions of thallus free of apothecia. Basal cellular tissue bluish-black. Spores pale indigo-blue or olive ; terminal or larger ones 00041” long; ‘00016” broad ; others 00025” long, and 00011” to -00016” broad. C. Parasitic on thallus of Lecidea parasema, Ach. On a specimen in Herb, Kew, from Ireland (sub nom. Opegrapha gemmata, Ach.) Apothecia of the Zecidea confluent and somewhat irregular in form and surface ; colour bluish or greenish ; sporidia normal. The parasite presents very numerous individuals, closely aggregated, occupying the site of, and otherwise externally resembling, spermogonia ; very minute (microscopic), black, punctiform, superficial on, or more or less immersed in, thallus of the Lecidea. Spore-filaments about 0025” long, and -00016” broad, * Vide ‘‘ Mem. Spermog.” Plates IV. V. VI. VIII. XI. XII. t+ Vide Paper on “ Parasitic Micro-Lichens.” DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. D990 varying, however, both in length and breadth. Spores also variable in dimension ; simple; oblong, with rounded ends when mature; colourless in the young state, gradually acquiring an olive tint with maturescence ; terminal articulation, as usual, deepest in colour. Spore-filaments consist frequently of six articulations—some of which, however, are sometimes atrophied, assuming the aspect of linear threads or ribbons connecting the normal spores. D. Parasitic on the apothecia of Lecidea ferruginea, Huds. (a) Corticolous: Craig Rossie, Dunning, Perthshire, April 1858, W. L. L. (b) Corticolous: on silver fir: Ardrum, near Cork, Mar. 1858, Carroll. E. Parasitic on thallus of Lecidea anomala, Ach. (a) On ash and other trees, associated with Lecanora subfusca and Pertusaria com- munis; near Dunglass, Cockburnspath, Berwickshire, Dr Murray Lindsay, June 1856.- The parasite here is associated with, and apt to be mistaken for, spermogonia. Terminal spores blackish; rounded at upper end; sometimes containing enclosed nuclei. (b) Dunglass; thallus of the Zecidea white and granulate. Torula intermixed with spermogonia, F. Parasitic on thallus of Lecanora varia, Ach. Sub Parmelia in Lziguton’s Exs. No, 176; on fir bark, Twyford Churchyard, Shropshire. Intermixed with spermogonia, with which the parasitic perithecia are apt to be con- founded. In the same perithecia, moreover, the spore-filaments of the Torula are associated with the sterigmata of the Zecanora, taking here the place of the sterile hypertrophied sterigmata of lichen-spermogonia,* G. Closely associated with, but not parasitic on, various corticolous Lichens. (a) On or with Arthonia melaspermella, Nyl.; corticolous; Weybridge, Surrey, Currey. In the “Journal of the Linnean Society” (Botany, vol. ix. pp, 271 and 286, tab. 6, figs. 2 c, 3 c, and 6), I have erroneously described and figured the parasite as the Pycnides of the Arthonia. Mere the articulations of the spore- filament are bluish. It is impossible to determine whether or not there is a proper thallus of the Arthonia, on which the Torula occurs. (6) With Opegrapha atra, Pers.; in Scu#rer’s Exs. No. 634; right hand specimen in my copy. Spores brown ; smaller than is usual. (ce) With Verrucaria epidermidis, Ach., Malham, Yorkshire, Oct. 1857, Dr Carrington. —Spore-filaments of two or three articulations only. Terminal spores :00025” long, very narrow and granular. In the foregoing cases (6 to G) the parasite has the same essential characters that it exhibits when frequenting its much commoner host—especially in Ireland —Lecanora subfusca. It is probable that the Torula, which is described as destroying the apothecia of Biatorina fraudans, Helb., in Spitzbergen (TH. Fries in “ Lichenes Spitsber- genses,”’ p. 35), as well as that referred to in NyYLANDER’s “Synopsis” (p. 58), is Torula lichenicola. But of neither Fries’ nor NyLanpEr’s plants have I seen specimens. 7’ lichenicola has a suspiciously close resemblance to what NYLANDER describes in his “ Prodromus” (p. 86), as the Pycnides of Spheria epicymatia— a parasite, which, he says, is common on Lecanora subfusca, but which I have never found. In the same work (and same page) he mentions Torula moni- lioides, Bon. ; but I have no means of knowing whether this is 7. monilioides, Cd., or Bispora monilioides, Cd., of BrrKELEy’s “ British Fungology” (pp. 326 and 327); or 7. lichenicola ; or some plant—fungus or lichen—different from either. * Vide p. 532 and foot note.* VOL. XXV. PART II. 6 Y 534 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. IL. Coniothecium lichenicoluin. A, Parasitic on thallus of Lecanora tartarea, L. (a) Morchone, Braemar, Aug. 1856, W. L. L.—On isidioid, sterile states of the thallus of the Lecanora. Spores deep brown; sometimes spherical and simple ; frequently 8-shaped (didymous) ; frequently also in moniliform chains, as in Torula lichenicola, or in groups of four or three, B, Parasitic on thallus of LZ. parella, Ach. (a) Blackeairn Hill, near Newburgh, Fifeshire, May 1858, W. L. L.—On sterile forms of thallus of the Lecanora. Parasite more irregular in surface and out- line, more crowded, and more frequently confluent than is usual. Occurs in groups on different parts of the thallus of the host. Spores sometimes 8-shaped (didymous), 00025” broad, 0005” long; more generally single or simple and spherical, about -00016” in diameter, (b) Morchone, Braemar, Aug. 1856, W. L. L.—On sterile states of thallus, spar- ingly scattered, sometimes only about periphery of thallus. Parasite has sometimes an apothecioid aspect, its black mass being girt with an obscure thalline ring. Occasionally it appears as if seated in thalline verruce, and is so small as to resemble spermogonia. At other times it resembles the smaller urceolate apothecia of Lecanora cinerea ; and if the thallus of L. parella were more generally covered with the parasite, it might, at first sight, be confounded with a form of L. cinerea, (c) Glen Dee, Braemar, Aug. 1856, W. L. L.—On isidioid states of thallus. Parasite mostly large and flattish, with very ragged outline in the old state, resembling spots of soot; in young state, is regularly papillar. Has a close resemblance to Spilomium Graphideorum, Nyl., in size and irregularity of out- line and surface. C. Parasitic on Isidiwm corallinum, Ach. (a) Old Wall, Craigie Hill, Perth, May 1856, W. L. L.—The surface of the thallus shows little distinction between the constituent isidia, which are so closely aggregated as to form a general white subcretaceous mass, sometimes obscurely divided into areole. Parasite occupies generally the centre of these areole where they occur, or is studded generally over surface of thallus, as black, round, convex masses, varying in size. Spores in all cases show double contour; in age acquire an irregular or corrugate outline; colour generally brown, or blackish-brown, graduating into olive; sometimes very pale or almost colourless in young state. It appears to be the same parasite which occurs on Isidium corallinum im Moveror and Nestter’s Exsic. No. 74; which Jsidiwm is there probably refer- able to Lecanora parella. The parasite resembles black apothecia, which have been doubtless by lichenologists of the pre-microscope era mistaken for the “fruit” of the Lsidiwm or Lecanora. The columns of [sidium corallinum have apices that are frequently coloured more darkly than the body of the isidia; which coloured apices were often mistaken by the earlier lichenologists for apothecia or “ fruit” of different kinds, and which often have aclose resemblance to some forms of spermogonia. The plant consists, when typically developed, of a series of minute, round, perpen- dicular columns, which become by close appression sometimes subangulose, and may even lose their individuality, coalescing into a general subcretaceous mass, }” to 1” thick. Where such coalescence does not take place, there is seen on cross section, either natural or artificial—a honeycomb-like arrangement of columns—similar to the basaltic columns of Staffa or the Giant’s Causeway on a microscopic scale. Where the apices are not cut off by natural cross section or erosion, they are discrete and papilleform, resembling, on a small scale, the young ramuscles of Sphcrophoron, as these are figured in my “Observations — on New Zealand Lichens” (PI. Ixii. fig. 5).* The colour of the isidia varies considerably ; sometimes, especially in specimens long preserved in the * Transactions of Linnean Society of London, vol. xxv. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 535 Herbarium, they are flesh-coloured; more generally they are grey. The colour is always deepest at the apex, gradually disappearing below, where the bodies of the columns coalesce into a chalky mass. The tips of the papille, which form the upper or free extremities of the columns, are generally brown; but this tint varies in depth or distinctness, being frequently very obscure. D. Parasitic on thallus of Lecanora atra, Ach. Saxicolous: Pentland Hills, Edinburgh, Aug. 1855, W. L L.—No part of this parasite gives a blue reaction with iodine. E. Parasitic on thallus of Diplotomma caleareum, Weis. Clapham, Yorkshire, Dr Carrington, Oct. 1857.— What appears to be the Coniothecium is seated on the thalline areol, where they are at all distinct. It is black, generally round, sometimes irregular in form, e.., becoming sub-arthonioid; generally flat; seldom, and only in young state, verrucarioid or papilleform; sometimes confluent ; superficial, the base only immersed. The parasite is sometimes indistinguishable from the apothecia of its host, save as to the inferior size of the Coniothecium; its size, how- ever, is variable; it generally wants the thalline margin—which is, however, sometimes comparatively distinct, girding the apothecia. Here the Coniotheciwm exhibits no reproductive structure. The same Diplotomma is in England the seat of the parasitic Microthelia rimosicola, Leight. (Munpp, “‘ Brit. Lich.,” p. 308, plate v. fig. 129), which has 8-spored asci, and oblong, 3-septate, brown sporidia, My note-book records, on the Yorkshire plant, the presence of Pycnidia, containing stylospores. F. Parasitic on thallus of Lecanora cinerea, UL. Kerry, Taylor (in Fl. Hibern., sub-nom, Spiloma spherale).—Thallus of Lecanora sterile. The parasite is scattered about the periphery of the alien thallus, much more abundantly than the spermogonia of the Zecanora usually are. In the young state the Coniothecium is immersed, and then frequently resembles closely some forms of the spermogonia of LL. cinerea ; but gradually it becomes emergent and epithalline, resembling, according to its size and form—whether flattish or sub-globose—the black apothecial disks of a sessile Calicium or a Lecidea. It contains no reproductive structure, exhibiting under the microscope only its deep-brown, basal, cellular tissue. G. Parasitic on sterile conditions (which are variously isidioid or variolarioid) of the thallus of several Lecanore. It is in general impossible to determine in these cases what is the species of Lecanora. Sometimes only it appears to be Z. glaucoma, L. parella, or L. tartarea. In no case is the isidioid condition so marked as to bring the thallus under the category (C) of Isidium corallinum.* (a) Scuir-na-gillean, Skye, Aug. 1856, W. L. L.—Black papille of parasite very variable in size; generally very distinct. Spores of a sooty-brown colour. (b) Saxicolous: Moors east of Reykjavik, Iceland, June 1860, W. L. L.—Here, again, no distinct reproductive structure is visible. The parasite is large, black, and conspicuous by contrast of colour on the whitish or grey thallus, having somewhat the characters of the apothecia of a Lecidea of the parasema or contiguiu group; much more irregular in form, however, and variable in size; consist- ing, moreover, apparently of aggregations, or glomeruli, of irregular papille ; semi-immersed in the thalline areolx, but projecting by an irregular, rough, granular surface above their level. (ec) Morchone, Braemar, Aug. 1856, W. L. L.—Abundant and in fine condition. (d) North Wales, Rev. H. Davies (sub-nom, I[sidiwm microsticticum, E. B. and Lich, Brit.) in Herb. Kew.—Parasite seated on, and partly in, small thalline papillz ; in which latter case it possesses a pale thalline border; small, black, * IT have recently (August 1869) found Coniothecium frequent on the sterile saxicolous thalli of Lecanore, both in the northern and southern Highlands, ¢.g., Helmsdale, Sutherlandshire, and St Mary’s Loch district, Selkirkshire. In these districts the thalli in question are most probably referable to Lecanora parella or glaucoma, or both. On similar sterile thalli the parasite is common throughout Scotland, and probably throughout Britain. 536 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. lecidioid, convex, scabrous—studded over the thallus of the host. Spores brown; very irregular; concatenate, or Sarcinate, in groups of 4-woolpack- like masses, similar to those of Surcina ventriculi, Goodsir. (c) Kinnoull Hill, Perth, May 1856, W. L. L.— Associated with Sguwamaria gelida, . Parasite occurs on an areolate, white, crustaceous thallus, sterile of apothecia, referable, doubtless, to some Lecanora. The Coniothecium has quite the aspect of some species of Microthelia, e.g., M. rimosicola, Leight. Spores chestnut-brown; have the appearance of portions of cellular tissue,* composed of irregular, subcubical cellules, (7) Barmouth, N. Wales, June 1836, Leighton (sub-nom. Spiloma).—Referred by Mr Cooke to “ Sporidesmium sp.” in my Herbarium. H. Not parasitic on, though closely associated with, various saxicolous lichens. Roadside between Sligachan and Portree, Skye, Aug. 1856, W. L. L. Some at least of the parasites which I have referred to Coniotheciwm licheni- colum have apparently been mentioned, if not also described, by various of the earlier lichenologists, under most diverse names. Specimen (d) has the characters of /sidiwm nucrosticticum of ** English Botany” and the “ Lichenographia Britannica ;” (+) has quite the appearance externally of Spiloma nigrum, Leight. and “English Botany,”+ and of Spilomium Graphideorum, Nyl.t A plant from Clapham, Yorkshire, Dr Carrington, is apparently—partly at least—Sclerococcum sphorale, Fr.; § and Cyphelium (or Acolium) corallinum, Herp Exs. No. 531, and Korser’s “ Parerga,” pp. 299 and 465. Coniothecium lichenicolum agrees also with Variolaria conspurcata, Eng). Bot., tab. 1993 (at least) with the char- acters of the plate. Coniothecium lichenicolum has a close resemblance to some forms of Sporides- muum; and it is quite likely that there is a lichenicolous Sporidesmium, hitherto undescribed, for which the specific name Jlichenicolum would be appropriate. — I have not, however, at present sufficient data for determining this. What appears to me to be Con. lichenicolum, occurring on the white, crustaceous, sterile thallus of a Lecanora from Barmouth, N. Wales, Leighton, June 1856—in my Herbarium—was (as already stated) labelled by Mr Cooks “ Sporidesmium sp.” Two of the lichens of the earlier lichenologists have been transferred by fungo- logists to the genus Sporidesmium, viz , 1. Lepraria nigra, Engl. Bot., t. 2409, of Ist edition, which is the Coniothecium effusum, Cd., and the Sporidesmium * Vide p. 519 and foot note.* + P. 45, tab. 1984, 2d ed., 1843. t The specimen of S. Graphideorum, Nyl., contained in my copy of his ‘ Herb. Lich. Paris,” No. 72 (from Fontainebleau, on a white, mealy thallus—of some Graphis—coating a very rugged bark, and associated with a Hysteriwm), has the external characters, on a large scale, of a Spiloma. Spiloma nigrum, var. variolosum, Turn. & Borr. in Leieuton’s Exsic. No. 259, closely resembles it, though LeicHTon’s plant is more crowded and more irregular in outline. The French Spilomium is quite visible to the naked eye; variable in size; very black; irregular in outline, though generally round; sometimes confluent; surface usually more or less convex and rough, as in Coniothecium, from the projecting powdery or granular spore-masses. The spores are spherical or oval; generally with double contour; simple; deep brown; about -00025” in diameter ; sometimes slightly irregular in outline; cohering frequently in rouleaux like blood-corpuscles. § = Spiloma spherale, Ach., but not Buellia saxatilis, Scher. (NyLaNpDER, ‘“ Prod.” p. 140), ac- cording to Tu. Frigs (“L. Aret.” p. 116). DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. Dot Lepraria, Berk. and Broome, of BERKELEY’s “ Brit. Fungology,” p. 327; and 2. Spiloma melanopum, Eng). Bot. t. 2358 of Ist edition, which is the Sporidesmium melanopum, Berk. and Broome, of BERKELEY’s “ Brit. Fungol.” p. 327. IIL. Spheria ventosaria, Linds. “ Obs. on Otago Lichens and Fungi,” p. 439 ;* “ Obs. on Greenland Lichens.’+ Parasitic on the thallus of what appears to be Lecidea grossa, Ach., Ingleby, Cleveland, Yorkshire, Mudd; inmy Herbarium. Occurs as minute, black papille, intermixed with the apothecia of the Lecidea. Externally the parasite has the character, as it has the position, of certain verrucarioid spermogonia, ¢.g., in the genus Lecidea; and it has also the facies of Endococcus or Microthelia. No distinct asci are visible; but the hymenial gelatine showed a beautiful carmine or violet colour with rodine, just as many true lichens do. Sporidia minute, pale brown, oblong, with rounded ends, with or without double contour, according to age; l-septate—septum indistinct in young state. Mr Currey regards it as “a true Spheria. ... There are certainly thece filled with very numerous, brown, 1-septate sporidia, 0:0003”. . . . The perithecia are so minute and so scattered, that it is extremely difficult to detach them for examination.” He refers the parasite to S. ventosaria; but the perithecia are very different from those common in the same parasite on Lecanora ventosa. IV. Microthelia. 1. M. Cookei. Parasitic on thallus of Lecanora crenulata, Dicks., Barrack wall, Chichester, W. C. Cooke, March 1866. The parasite occurs on the thicker, whiter portions of the thallus, as black, papilleeform, scattered conceptacles. The hymenium gives no blue with iodine; its constituents are very indistinct, unless under the action of iodine or other colouring matter. Hypothecium is colourless. Paraphyses appear rather like a mass of striated jelly than as distinct, filiform threads—resembling in this respect those of Pertusaria. Apices not coloured. Asci polysporous, saccate, bulging irregularly, 0018” long, 00045” broad. Sporidia very small, 00022” long, 00009” broad; colourless; oblong-ellipsoid ; 1-septate, sometimes simple. M. Cookei externally resembles MM. rimosicola of Mupn’s Exsic. No. 301; but the asci in the latter are 8-spored. It differs from all the MZccrotheliw men- tioned in Mupp’s “ Manual of British Lichens,” in having colourless sporidia; but in other points it resembles JZ. pygmea, Korb., which is also polysporous. 2. M. Stereocaulicola. Parasitic on thallus of Stereocaulon paschale, L., Glen Derrie, Braemar, Croall, July 1854. The free ends of some of the podetia of the Stereocaulon are the seat of bullose-looking deformities or expansions, which are compound solid verruce, made up of an aggregation of minute wartlets, of the same colour as the normal * Transactions of the Royal Society of Edinburgh, vol. xxiv. + Transactions of the Linnean Society, vol. xxvii. (1869). VOL. XXV. PART II. 6 Z 538 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. podetium and its squamules. These thalline deformities closely resemble those which are occupied by spermogonia in the same Séereocaulon and in S. denudatum, Flk., as they are figured in my ‘‘ Memoir on Spermogones” (plate v. figs. 33 and 36). Moreover, the parasite closely resembles the spermogonia in question in its conceptacles forming brown or black verrucarioid papilla; sometimes visible as mere points, the body immersed in the wartlets of the thalline deformities of the Stereocaulon—one or two in each wartlet—the apex alone projecting. Asci not blue with iodine, ‘0023” long, -00066” broad. No distinct paraphyses. Sporidia, 0005” long, ‘00033” broad; obovate; colourless when young, becoming olive or brown with age; 1-septate. Tu. Frres* has described, without naming, a Spheria as parasitic on the thallus of S. alpinum, Laur., in Spitzbergen ; whose sporidia, however, distinguish it from | the Microthelia. The hymenium of the Spheria—which may appropriately bear the specific name Stereocaulicola—becomes yellow with iodine. The sporidia are blackish, four in each ascus, oblong-elongate, 3-5-septate, becoming submuri- form by longitudinal division of the loculi. Korser (in his “ Parerga,” p. 455), describes Scutula Stereocaulorum, Anzi, as parasitic on Stereocaulon alpinum and S. fastigiatum in the Alps of Northern Italy. But its sporidia are smallish, narrowly ellipsoid, subcymbiform, 1-septate, and colourless. Also his Polycoccum Sauteri (“ Parerga,” p. 470) as occurring on the protothallus and thallus of S. con- densatum, Hffm. Sporidia small, dacryoid, 1-septate, brownish. One or more species of Sirosiphon (an alga belonging to the family Siro- siphoniacee, of the Palmellacec or Protophyta, according to RasENHorsT (FI. Europ. Algar. Aq. dulcis, &c. p. 289), are parasitic on some species of Stereocaulon. Thus Sirosiphon saxicola, Neg. (perhaps the SS. crustacea, Ag., of RABENHORST, op. cit. p. 289), is parasitic on Stereocaulon denudatum in Scandinavia (Ny. ‘ Scand.” p. 65); while a Szvosiphon, not named, and which may be also S. sazicola, grows on the podetia of Stereocaulon vulcani, Bor., and was mistaken for cephalodia by Fries (Nyt. “ Lich. Exotic.” p. 252). The parasite occurs as blackish pulvinuli, which are quite different in anatomical constitution from cephalodia; the latter always exhibiting on section the structure of—1. The cortical; 2. Gonimic; and 3. Medullary, tissues of the lichen-thallus. 3. M. Umbilicarie. Parasitic on the sterile thallus of Umbilicaria pustulata, Hiffm.; collected in Norway as commercial ‘‘ Pustulatous moss.” The parasite is copiously studded over both the bullae and interspaces of the thallus, as black, papilleeform conceptacles, varying somewhat in size and form; semi-immersed ; comparatively conspicuous on the gray, cracked thallus of the host. Paraphyses very delicate and indistinct, as in Verrucaria. Asci very faint violet with iodine; while the hymenial gelatine shows more distinctly the same tint with the same * ‘“* Lichenes Spitsbergenses,” p. 386. Vide also author’s ‘“ Observations on Greenland Lichens.” DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 539 reagent. Large quantity of oil globules intermixed with the hymenial consti- tuents. Contents of young asci colourless, gradually assuming a brown tint as the protoplasm becomes distinctly partitioned into sporidia. Latter are, in maturity and when free, deep brown, generally 1- sometimes 2-septate; oval or broadly ellipsoid. It is possible the parasite on U. pustulata may prove referable to what KorBeEr describes in his “ Parerga’”’ (pp. 40 and 469) as Ticho- thecium grossum, which affects the thallus of U. arctica, Ach. The latter species of Umbilicaria is the seat also of Dothidea lichenum, Smrf., which Tu. Frtes (Lich. Arct. p. 166) suggests may be KorBer’s 7. grossum. I have not met with any description of SomMERFELT’s plant. Its name, D. lichenum, is apt to be con- founded with that of MassaLoneo’s D. lichenicola (‘ Richerche,” p. 45, fig. 81), which affects the apothecia of Pachyspora viridescens, Mass.; has 1-septate sporidia, that, however, are colourless, elliptic-oblong, and slightly curved; and is apparently, therefore, a different plant. 4. M. Nephromiaria. Parasitic on thallus, and (back or under side of old) apothecia of Nephromium cellulosum, Ach.; Hermite Island, Cape Horn, Dr Hooker, Antarctic Expedition, 1839-48. Parasite occurs as very minute, black, punctiform or papilleform, semi- immersed conceptacles, dotted over the thalline ruge, or on the back of the old apothecia. It is sparingly scattered about the centre of the thallus, more plentifully on the thalline underside of the apothecia. The black apex is the cnly part that is superficial, the body being immersed. According to their size, and the form of the ostioles, the perithecia resemble those of many lichen-spermogonia, or of some of the smaller Verrucarie. They vary in size, and are sometimes con- fluent, though generally scattered. The asci are sac-shaped like those of Arthonia, bulging broadly, not blue with iodine. Hymenial gelatine wzolet under iodine. Paraphyses indistinct, and as in Verrucaria. Sporidia 3-septate, colourless, fusiform; eight in each ascus. The asci and sporidia agree with those of what I described in my ‘“ Memoir on Spermogones” (p. 135) as Lecidea Alectorie; and as the plants otherwise appear essentially the same, I merge the two in a single type, and abolish both the generic and specific* designations as inappropriate. MM. Nephromiaria also resembles externally M. Cargilliana ;+ but the simple, spherical, brown sporidia of the latter sufficiently distinguish it. Also having 3-septate sporidia in sac-shaped asci is a parasite which covers copiously, with its punctiform perithecia, some of the lacinize of Physcia ciliaris, L., in ScH2ZRER’s Exs. No. 388 (sub-nom. Parmelia ciliaris: the lower of two Specimens in my copy =ed. alt. immut., 1840). The body of the perithecium is * What was originally designated Alecforia, is now known as Newropogon, Taylori (Nyt. ey, p. 273). Tt ‘‘ Otago Lichens and Fungi,” p. 441, pl xxx. figs. 31-34. 540 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. immersed in the thallus of the host, only the black apex being visible on the surface. The whole length of some laciniz is dotted over with the parasite, while others are unaffected. My notes, made in 1857, do not record, unfortunately, the colour, size, or form of the sporidia. 5. M. rugulosaria. Parasitic on apothecia of Placodium rugulosum, Ny). (“ Chil.” p. 193 ;) Tasmania, Stuart, in Herb. Kew; saxicolous. The apothecia, which are of a deep orange-red, are abundantly studded over with the very minute, black, punctiform, or papilleeform conceptacles of the parasite. The latter are prominent under the lens, especially when the apothecia are moistened, from the striking contrast of colour. They are semi-immersed in the epithecium of the Placodium. Paraphyses very delicate and _ filiform. Asci as long as the paraphyses; ‘0016’ long, -0005" broad; 8-spored. Sporidia 0004" long, ‘00016" broad; 1-septate; soleaform ;* brown. Both asci and sporidia resemble those of tlhe microspermous and microsporous forms of Abrothallus Smithit. (a) Having similar sporidia—brown, soleaform, -0005" long, -00016" broad—is a similar parasite (which may prove referable to MW. rugulosaria, or to the same type to which it may hereafter itself be referred) that affects the thallus of Thelotrema lepadinum, Ach.; on Holly, Ireland, Carroll. Its perithecia are black and sub-verrucarioid, resembling those of Verrucaria fusiformis or epider- midis. These sporidiiferous perithecia are accompanied by others containing stylospores, like some of those of Lecidea abietina ; narrowly ellipsoid; -00033’ long, ‘000111" broad; pale yellow, Both forms of perithecia are probably refer- able to the same parasite. The thallus of 7. lepadinum is also affected by Nesolechia Nitschkit, Korb. (Par. p. 462), which has minute, oblong-sub-bacillar, simple, hyaline sporidia; and by Stenocbye eusporum, Nyl. (b) Another Irish specimen, sent me as a Spheria, by CaRRo.t, in August 1856, from Mangerton, County Kerry, on a tartareous, white, much areolate, sterile thallus (which cannot be referred to its proper species), has figure-8- shaped, l-septate, deep brown or olive sporidia or spores; ‘00033’ long, and 00025" broad. The perithecia are largish and verrucarioid; very black; vary- ing greatly in size and form; in the young state papilleform, in age flattened and lecidioid ; they are scattered on the thalline areola, and are very conspicuous on the whitish or cream-coloured thallus. The plant has externally the facies of Coniothectwm lichenicolum, to which it may really belong.+ Mr Cooxe, who examined it, describes the contained repro- ductive corpuscles, which may be either sporidia or spores, as ‘‘ Toruloid spores.” * Frequently erroneously written soleform. Soleaform sporidia are necessarily 1-septate. Vide definition of the term in “ Otago Lich. and Fungi,” foot note, p. 447. t Vide p. 519. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 541 Both thallus (of the host) and disks of the parasite closely resemble those of Barmouth (North Wales) specimens of C. lichenicolwm. (c) Lecanora cenisia, Ach. (which = var. atrynea, Ach., of Lecanora subfusca, Ach. according to NyLANDER) from Ayton, Cleveland, Yorkshire, Mudd, in my Herbarium, bears on its apothecia a minute punctiform parasite, containing solea- form sporidia; here, however, of a pale, brownish-yellow hue. (d) On thallus of Lecidea pachycarpa, Duf., Ireland, Admiral Jones, June 1858. Parasite is small, black, and Lecidioid, resembling certain lichen-spermo- gonia of the flat, discoid type. Hymenium gives no blue with iodine. Paraphyses filiform, indistinct, wavy, not coloured at tips; asci -0040" long, :00083" broad ; sporidia colourless when young, gradually acquiring an olive or brown tint with age; soleaform; 00066" to 0010" long, -00033" broad. It is impossible to confound the perithecia or sporidia of the parasite with the apothecia or sporidia of the Lecidea. The apothecia in question are very large and conspicuous; while the sporidia of the Lecidea are also very large—-0040" long, and -00133" broad; 7-septate, colourless, oval-oblong. The asci of the Lecidea are, moreover, 1-spored, 0050" long, :0014" broad, becoming pale blue with iodine. Its paraphyses are indistinct ; obscured about their irregular tips by much granular, greenish pigment-matter, and throughout the length of their bodies by the same colouring matter (in quantity), and by oil globules. 6. M. Stictaria. Parasitic on thallus of Sticta Freycinetiz, Dél., Campbell's Island, Dr Hooker, Antarctic Expedition (sub-nom. S. scrobiculata). The con- ceptacles of the parasite are small, black, and superficial, easily detached. Asci 8-spored, small, subsaccate, deep violet with iodine. This is, at least, an unusual reaction if the plant is a fungus; while it does not appear to possess other characters of a lichen! Sporidia brown, soleaform (1-septate),* resembling those of M. rugulosaria, but much smaller. 7. M. parietinaria. Parasitic on thallus of Physcia parietina, L., Cottishall, in Herb. Kew; on a single fragment of the Physcia. Parasite occurs as minute, black perithecia, variously punctiform or papilleeform according very much to size; partly immersed; much crowded on the thallus of the host; variously resembling lichen-spermogonia (¢.g. of some Leczdec), or the smaller Verrucarie. Asci not seen; sporidia brown, 1-septate, -0005” long, 00016" broad; soleaform as in M. Stictaria and M. rugulosaria ; nearly of same size as those of latter, but larger considerably than those of former. JZ. purietinaria must not be con- founded with Phacopsis varia, Tul. (Mém., p. 125, tab. 14, figs. 1-3; Celidium, Korb., Parerga, p. 456), which has 3-septate, ellipsoid, colourless sporidia, according to TULASNE; but oblong and becoming brown, according to Korper. 8. M. Beomycearia. Parasitic on sterile thallus of Beomyces rufus, DC., Bal- * Frequently erroneously written soleform. Soleaform sporidia are necessarily 1-septate. Vide definition of the term in “ Otago Lich. and Fungi,” foot note, p. 447. VOL. XXV. PART II. (ee 542 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. thayock Woods, Perth, June 1856, W. L.L. Thallus consists of a series of minute, irregular pulvinuli, of a buff colour, on which the black perithecia of the parasite are conspicuous by contrast. This contrast is rendered greater, however, by the circumstance that the patches of thallus occupied by the parasite are lighter in colour than the rest of its surface. The parasitic perithecia are extremely minute and punctiform, so closely scattered as to give the thallus the appearance of being covered with granules of coal-dust. Sometimes they are so numerous and so closely aggregated as to become confluent in very irregular patches. Under moisture, the single perithecia assume a papilleeform character. The Microthelia cannot be confounded with the young apothecia of the Beomyces, which are brown, and much larger in almost all stages of growth. Sporidia of the Microthelia dark brown, oval; 3-septate; frequently or generally con- stricted at or opposite the septa. The thallus of the same Bwomyces, as well as that of B. roseus, Pers., is affected by Nesolechia ericetorum, Fw. (Kors., Parerga, p. 461), whose sporidia are minute, ellipsoid, sub-bacillar, simple, and hyaline. On B. rufus also occur Lecidea parasitica, Flk., L. scabrosa. Ach., ZL. inquinans, Tul., and LZ. arenicola, Nyl., as well as Thelocarpon epithal- linum, Leight. * 9. MW. atricola. Parasitic on thallus of Lecanora atra, Ach., on red sandstone, Derriquin, County Kerry, Taylor in Herb. Moore, Dublin; associated with Lecanora periclea, Ach. (= var. of ZL. sophodes, Ach.). The parasite has the facies of a Verrucaria or Endococcus ; its perithecia being minute, distinct, black cones, with sometimes a flattish or depressed apex; becoming occasionally irregular in form; seated on, scarcely 7m, the thallus of the host. Asci -0020° long, ‘00066’ broad ; crowded with innumerable sporidia. Sporidia spherical, simple, deep brown, about -000083" in diameter; resembling those of many Calicia. L. atra, on the Continent,+ is occasionally the seat of another parasitic fungus, Gassicurtia silacea, Fée (NYLANDER, Prod. p. 91; Lich. Parisienses, No. 150), which either affects the thallus or apothecia, sometimes occupying the place of the latter. The parasite consists of black filaments, forming in the aggregate brush-like masses, similar to the apothecium of Sphwrophoron in some of its old stages of growth; it has a Spilomatic or glomeruliform facies. In the only authentic specimen I have examined (in NYLANDER’s Herb. Lich. Paris., No. 150; on stones in Forest of Fontainebleau), the thallus is sterile, consisting of a series of cushion- like areole, more or less scattered, seldom closely aggregated. Some of these white tartareous verrucee are occupied by the parasite, which is very black, irregular in form, and easily distinguishable under the lens from the apothecia of the — Lecanora ; surface generally more or lesssubgranular. The spores are deep brown; * Vide Paper on ‘ Parasitic Micro-Lichens”’ (antea citat.). + And in New Zealand ; Linpsay, ‘* Obs. on N. Z. Lichens,” p. 540. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 343 spherical, ‘00033’ in diameter, generally with double contour—rough or granulate - externally—resembling, in some respects, those of Sphwrophoron ; than which, however, they are much larger. Sometimes in age they become oval and unequally figure-8-shaped, as if in process of fission. What appear to be the nuclei of the spores also occur abundantly, as much smaller spherical corpuscles, 00016’ to 00020’ in diameter, pale yellow, gradually becoming olive and brown, exhibiting like the spores themselves double contour. NyLANpER describes (Prod. 91) its spores as black and spherical, and thinks the plant should be referred to the genus Spilomium * (Uredinee). 10. M. vesicularia. Parasitic on thallus of Lecidea vesicularis, Ach., Switzer- land; in Herb. Kew. Occurs as small but distinct black papillee, closely aggregated; superficial; scarcely immersed ; externally resembling those of M. pygmea. It resembles that species further in its asci being polysporous; but the sporidia are 1-3-septate, according to age; most usually the latter in maturity. The smaller ones, when 1-septate, resemble those of M/. pygmwa. Hymenium gives no blue with iodine. Asci -0027" long, and -00083" broad. Sporidia :00033’ to :00050" long, 00016" broad, but variable in size ; fusiform or oval; brown. ~ Also having brown, minute sporidia, which are here, however, oval or ellipsoid, and are sometimes concatenate, is a parasite that affects the sterile thallus of what appears to be a Pertusaria, in Balthayock Woods, Perth, June 1856, W. L. L. No part of the hymenium gives blue reaction with iodine. The thallus of Pertusaria communis is the seat of a parasitic fungus, Spilomiwm Pertusariicolum, Nyl. (Enum. Génér. p. 91, and Synopsis, p. 144), which is conidio- sporous, the spores being oblong and blackish. The same thallus is affected by Lecidea parasitica, Flk., Sphinctrina turbinata, Pers., and var. microcephala, Ny}., Trachylia stigonella, Ach., Pseudographis elatina, Ach., and Opegrapha anomea, Nyl.+ My Herbarium contains a number of other lichenicolous parasites, having (more or less) characters resembling those of the Microthelice above described. But I cannot at present venture to assign names, or a specific place in classification, on account of the imperfections of their reproductive structure, the doubtful nature of their habitats, or other difficulties as regards their determination or description. The following are illustrations of this heterogeneous group of parasites :— 1. Associated with Verrucaria epidermidis, Ach., var. analepta, Ach. ; banks of Crinan Canal, Argyleshire; on birch; Aug. 1856, W. L. L.—It has quite the thallus and aspect of a Verrucaria (e.g. gemmata); and it is impossible to determine whether the thallus is that of V. epidermidis or other Verrucaria, or belongs to the plant now to be described. Intermixed with the apothecia of * A genus not mentioned in Berxsxey’s “ British Fungology” (1860), t Vide Paper on * Parasitic Micro-Lichens” (untea citat.), 544 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. V. epidermidis are certain other perithecia—scattered, round, minute, punctiform —somewhat prominent. Instead of paraphyses of ordinary character, the para- site possesses long, delicate, branching filaments, like those of many lichen-sper- mogonia. Asci are frequently grouped and ribbon-shaped; giving a faint blue- reaction with iodine; 8-spored. Sporidia ellipsoid, colourless, 1-septate, exactly like those of Verrucaria gemmata. The same hymenium, which contains spori- diiferous asci and ramose paraphyses, contains also stylospores, oval or ellipsoid, ‘00066’ long; borne on long filiform basidia, resembling paraphyses; sometimes l1-septate; occasionally exhibiting 3 nuclei, central largest. 2. Associated with Physcia obscura, Fr., var. leprosa, Hepp; Morchone, Brae- mar; corticolous; Aug. 1856, W. L. L. (Mem. Spermog. p. 247.)—Black and punctiform, but exhibiting no reproductive structure. 3. Associated with Lecidea ferruginea, Huds., var. sinapisperma, DC.; on dead mosses, grasses, twigs of shrubs, &c.; Hepp Exsic. No. 200 (sub-nom. Placodium sinapispermum, DC.)—Scattered over the decayed vegetation on which the apothecia of the Lecidea occur, and apparently partly intermixed with them, are very minute, black specks, which are perithecia, containing brown, 3-septate, ellipsoid, largish sporidia or spores. 4. On thallus of Lecanora polytropa, Ehrh., var. intricata, Schrad., Penman- shiel, Berwickshire; Hardy, Novem. 1856; saxicolous.—Parasite occurs on thalline areolee as punctiform and black conceptacles, very minute, sometimes papille- form and Verrucarioid, varying in size; full of corpuscles, which may be either sporidia or stylospores (for neither asci nor basidia were observed), these re- productive corpuscles being very variable in size and shape—spherical to figure-8-shaped, simple to l-septate, and colourless. The parasite is certainly not the Thelidium epipolytropum of Muvp (Brit. Lich. p. 298). I have also met with what appears to be the latter, externally resembling Verrucarioid spermo- gonia, and containing ellipsoid, 1-septate sporidia, with pale yellow loculi, but having no distinct paraphyses; while Mupp describes the paraphyses as distinct in his plant. 5. On apothecia (disk) of Physcia chrysophthalma, L., var. Dickieana, Linds. (Nyl. and Mudd, Brit. Lich. p. 112; sub-nom. var. of Physcia villosa, Dub., in Linds. Mem. Spermog., plate xiii. fig. 14); Belfast, Prof. Dickie Parasite consists of small, round, brown, quite superficial papillae or points, easily removable. Its envelope is composed of dark brown or bluish-brown cellular tissue, but the conceptacle contains no sporidia, stylospores, nor spermatia. 6. On thallus of Zecidea albo-atra, Fr.; shore of Great Island, Cork, Carroll, Sept. 1858.—Parasite is studded over areolate thallus as black papillee, generally crowded; varying in size; frequently flattened and irregular in form; semi- immersed ; sometimes confluent, and then very difform. 7. With Verrucaria fusiformis, Leight.; Douglas, near Cork; on ash; Carroll, DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 545 Mar. 1858.—Perithecia are black and punctiform, containing in great numbers corpuscles that are ‘00025’ long, and 000066" broad; simple, or sometimes faintly l-septate, brown, linear or ellipsoid-oblong, frequently somewhat constricted centrally. Neither asci nor basidia were visible, and the corpuscles above described may therefore be either sporidia or stylospores. 8. The horizontal squamules (and, to a less extent, the scales of the podetia from base to apex) of a specimen of Cladonia bellidijiora, Ach., collected on Kelly's Green, Ireland, by Dr Moorz, Aug. 1853, in Herb. Carrol), (Linds. Mem. Spermog. p. 163), bear, copiously scattered, a parasite, which has certain of the characters of NyLanpeEr’s Lecidea Cladoniaria* (Enum. Génér., Suppl. p. 339). His description, however, is imperfect, ¢.g., as regards the sporidia, which, he hints, may some- times be normally d7own. In the Irish plant, the sporidia are eight in each ascus, arranged in one series; ellipsoid, simple, and colourless, 00033" long, -000111’ broad; asci elongated, 00166” long, 00033” broad; paraphyses with discrete tips, but colourless, and not thickened. With apothecia, having externally the characters partly of those of Abrothallus Smithi, partly of A. oxysporus, are associated Pycnidia, containing stylospores precisely of the characters of the sporidia as respects size, form, colour, and structure, ‘00033” long, ‘00014’ broad. Externally, however, these pycnidia are always brown. In my “Memoir on Spermogones and Pycnides,” I have described them as spermogones ; but their con- tained corpuscles have rather the characters of stylospores.+_ The apothecia have a convex surface in maturity; seldom sessile, and equally seldom altogether immersed; the body or bulk being generally immersed, and the surface nearly on the same level as the thallus of the host. They are discoid; black throughout ; and their section resembles that of a double convex lens. In the young state they appear as minute, black papillee, emergent from the thallus; in which condition they are apt to be confounded with the pycnidia. In my “Memoir on Spermogones,” I have mentioned this parasite under the head of NyLANDER’s Lecidea Cladoniaria; to which I have also provisionally referred a commoner parasite on Cladonia uncialis, Hffm. (p. 285, plate vii. figs. 14-16). But the stylospores of the latter parasite are not the same as those of the para- site on C. bellidiflora; and, indeed, the two parasites seem distinct in several essential respects. Nor does NYLANDER mention either spermogonia or pycnidia as possessed by his plant. While, then, it is possible that one or other of the parasites in question is referable to NYLANDER’s plant, it is equally likely they are hitherto undescribed. Should this prove to be the case, I propose for that which affects * It may also be compared with his Lecidea oxysporella (Prod. 145), which grows on the thallus of C. digituta on the Spliigen; and with Lecidea Cetraricola, Linds. (“ Lichenicolous Micro-Lichens,” Quart. Journal of Microscopical Science, Jan. 1869). t I have pointed out the anatomical or morphological distinction between stylospores and sj er- matia in my paper on “ Polymorphism in the Fructification of Lichens ” (antea citat.). VOL. XXV. PART II. Ly ( B 546 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. C. bellidiflora—as an appropriate name—A brothallus Moorei,* in honour of the distinguished Director of the Botanic Garden of Glasnevin, Dublin, who has made so many important contributions to the Irish flora—cryptogamic as well as phenogamic. The protothallus of various Cladonie is affected by Nesolechia punctum, Mass. (Korper, Parerga, p. 461), the sporidia of which are minute, linear-fusiform, simple, and hyaline. 9. On thallus of Squamaria crassa, Huds.; Crosshaven, Cork Harbour, Sullivan. Parasite occurs as deep bluish-black round macul, surrounded frequently by a black ring; both conspicuous on the buff-coloured thallus of the host; seated on a sort of thalline papillze; body immersed. Paraphyses Verrucarioid—very delicate, wavy, filiform, indistinct—not knobbed nor coloured at tips; asci :0028" long, and 00066" broad. Sporidia brown, soleaform, ‘00050" to 00066" long, :00025” broad ; while in the asci always have the broadest and shortest end upwards. This parasite is obviously different from the Spheria squamarioides and S. gelidaria of Mupp. (Brit. Lich. p. 130), which affect the thallus of Squamaria gelida, L. Nor does it appear to be any of these parasites which copiously affects the apothecia of 8. saxicola, Poll., in a specimen which I collected near Jerkin, Nor- way (4600 feet), in August 1857. I have not in this case, however, been able to detect reproductive structure. In its young state the parasite appears as black spots on the epithecium. These gradually increase in number, and at length coalesce till they cover the whole disk; which covering leads apparently to the degeneration and consequent shrivelling of the whole apothecium. Its outline becomes most irregular; both exciple and disk acquire a very black granular surface, while the whole apothecium decreases in thickness. At a later stage it appears as a very black shapeless granular mass, frequently crowded or confluent, conspicuous on the pale stramineous thallus. NyYLANDER (Scand. p. 133), describes a parasitic Sphwria as affecting, in some parts of Scandinavia, Squamaria saxicola and S.chrysoleuca, Sm. Itis black, puncti- form, immersed in the thallus; spores fusiform, colourless; possessed of spermo- gonia, which are also black and punctiform, containing minute straight spermatia. Korper (Parerga, p. 458) deseribes Conida clemens, Tul. (Mém. p. 124, sub Phacopsis) as parasitic on the apothecia of Sqguwamaria chrysoleuca and saxicola ; the sporidia being small, irregularly oblong, l-septate, and hyaline. Also Cerei- dospora Ulothii (Parerga, p. 466), as affecting the thallus of S. saxicola ; sporidia fusiform or cymbiform, 1-septate, and hyaline. S. sazicola is also affected with Lecidea micraspis, Smrf., and Thelidium epipolytropum, Mudd.+ * In my MS. Notes on Moore's Irish Lichens—made in 1858—I named this parasite pro- visionally Abroth. Cladoniarum, but any such specific designation is apt to lead to confusion with Nyvanpver’s Lecidea Ciadoniaria. + Vide Paper on “ Parasitic Micro-Lichens” (anteu citat.). DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 547 10. On or with Lecanora varia, Ach., var. symmicta, Ach. ; on rotten stumps of Pinus sylvestris, Blaeberry Hill, Perth, April 1858, W. L. L. Conceptacles, ex- ternally resembling spermogonia, contain deep brown, oval or ellipsoid, apparently simple, sporidia, 0005" long, 00033" broad. 11. On Lecidea rupestris, Scop. (sub-nom. Biatora rupestris, var. calva, Dicks.), on limestone rocks, in Hepp’s Exsic. No. 134. Parasite consists of very small, black, punctiform perithecia, scattered among the apothecia of the Lecidea, ex- ternally resembling spermogonia, but containing very deep brown, oval sporidia ; simple, or 1-septate, or both; the colour rendering it impossible to determine their structure. NYLANDER arranges LZ. rupestris as a variety under Lecanora cerina ; a classification to which I cannot subscribe. 12. Accompanying Pyrenothea verrucosa ; on old oak, Castle Bernard, near Cork, Carroll. Parasite is seated on some of the thalline verruce, associated and apt to be confounded with spermogonia; sporidia spherical, brown, -00025" in diameter. 13. On thallus of Endocarpon microsticticum, Leight. (which appears to be only a var. of Lecanora cervina, Pers.; having quite the aspect of the common var. smaragdula, Whinb.); Barmouth, North Wales, Leighton, 1856. Hymenium gives no blue with iodine. Asci sublinear, -00020” to 000233” long, -00033” to 0005” broad. Sporidia deep brown or olive according to age, 1-septate, oval, 0005” long, 00025” broad, arranged either in a single row, or in a double series, in each ascus. Endocarpon rufescens, Ach. is the seat of Spharia Hookeri, Ny. (Prod. p. 139 and 175; Linps. Otago Lich. and Fungi, p. 438), which has broadly fusiform, 3-septate sporidia (NyL. Prod. 139), becoming sometimes 5-septate or polysep- tate and muriform (Mupp, Brit. Lich. p. 271, plate v. fig. 112), in all cases brown —sometimes constricted centrally or opposite each septum. Lecidea Endocarpicola. On the thallus of Endocarpon hepaticum, Ach.—on walls, Lower Glanmire Road, Cork, Carroll—there is a parasitic Lecidea associated with the apothecia and spermogonia of the Hndocarpon, having many of the cha- racters of Z. aromatica, Turn. (which, however, is not known to occur in the athalline condition). The paraphyses have deep brown or bluish-black apices, which are irregularly knobbed; their bodies constitute, however, a mere striated indistinct mass. Hymenial gelatine and asci become deep indigo-blue under iodine; latter are 00233" long, and -00050" broad. Sporidia very variable in size, length from 00033" to -00083", and in breadth from :000083’ to -000133’; ellipsoid-oblong or linear-oblong; simple in young state, normally 3-septate in maturity. 14. On thallus of Usnea barbata, Fr., var. florida, L.; Rio Janeiro, Henry Paul, 1851. Parasite is seated on some of the thalline tubercles usually occupied by the spermogonia. Sporidia brown, l-septate; very different from the simple, colour- 048 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. less, oval sporidia of the Usnea. No hymenial tissue, asci, nor paraphyses can be made out, even under iodine; which, however, produces in some places only a blue reaction in the medullary tissue of the Usnea. The structure of the spermo- gones of the Usnea is described and figured in my “‘ Memoir on Spermogones” (p. 122, plate iv. figs. 2-5). This parasite has certain points of resemblance, espe- cially as regards the sporidia, to Phymatopsis dubia, Linds., and Abrothallus Usnee, Rabenh., as I have described and figured them in my ‘ Otago Lichens and Fungi” (p. 442, et seq., plate xxx. figs. 36-41). 15. Onsterile thallus of Parmelia perlata, L.; India, M. C. Cooke, 1866; ordinary a-ciliate form of the Parmelia as it occurs, from Britain, Norway, New Zealand, and the Canary Islands, in my Herbarium. In what appears to be its highest stage of growth, the parasite occurs as sub-rotund or sub-difform, raised, sub- convex, black maculze, with a granulate irregular surface. In the young state it is developed as punctiform or papilleeform bodies, sometimes girt with a ragged thalline margin. In the young state the body is wholly immersed in the thallus of the host or nearly so, while in age it emerges and becomes epithalline. In none of its stages of growth does the parasite show sporidia or other reproductive structure. 16. Associated with Verrucaria Taylori, Carr., and Opegrapha vulgata, Ach.; corticolous; Dunscombes Wood, Cork, Carroll. Perithecia contain sporidia that are brown, 3-septate, bulging opposite each septum; 00083” long, and -00033" broad. 17. On thallus of Lecidea Hookeri, Scheer. (sub-nom. L. spherica, Scheer.) in his Exsic. No. 526. The thalline squamules are dotted over with small, black, prominent papille, externally resembling spermogonia, but containing sac-shaped asci, and 1l-septate, colourless, ellipsoid sporidia, somewhat resembling those of some forms of Verrucaria epidermidis. The same thallus bears the parasitic Spheeria Hookert, Nyl. (Prod. 175 and 139; Linps. “Otago Lich. and Fungi,” p. 438)* with verrucarioid perithecia, and deep brown, 3-septate sporidia, ‘001’ * Two specimens of §. Hookeri (sub-nom, Verrucaria), which I examined in the Kew Herbarium, had the following characters :— 1. Summit of Ben Lawers, Thallus Parmelioid, pale yellowish-white. Perithecia are quit those of a Verrucaria ; seldom, however, forming regular cones or papillze; more usually flattened and irregular as to form and size. None of the hymenial elements give blue with iodine. Sporidia broadly ellipsoid, tapering suddenly at the tips ; 3-septate; becoming by longitudinal sub-division of the loculi sub-muriform ; deep brown; ‘001” long, 0005” broad. 2. Gemmi, Switzerland. Perithecia much larger and ostioles more distinct; immersed or semi- immersed ; bursting through the cortical layer of thallus, with—at least usually at first, in their young state—stellate fissuring. Thallus here again Parmelioid and simple; usually buff-coloured, sometimes pale green. The plant has an Endocarpoid facies. In both cases the perithecia occur by themselves on a thallus, which appears to belong to them. It seems to me that it is the same plant that occurs sometimes with a proper thallus (Verrucaria), and at other times as an athalline parasite (Sphewria); that it has equal claims to rank as a Spheria or Verrucaria ; and that it matters little whether it is classed among the Spherie or Verrucarie— fungi or lichens—provided only fungologists and lichenologists would come to some common under- standing regarding it ! DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 549 long, and :0004" broad. The Zecidea itself (in my copy, original edition, 1847) has simple, ellipsoid, colourless sporidia; while those of the true L. Hooker, according to NYLANDER (Prod. p. 139), are brown and 1-septate. 18. On thallus of Lecidea sangunaria, Ach., var. affinis, Scher. (Exsic. No. 629, on left hand specimen in my copy, orig. ed. 1852). Intermixed with the spermogonia, and indistinguishable therefrom ; but the parasitic perithecia con- tain round, brown spores. 19. On thalline scales of Lecanora coarctata, Ach., var. involuta, Tayl. (sub- nom. LZ. znvoluta, Tayl., Fl. Hibern., p. 134); Dunkerron, Taylor in Herb. Moore. ; on grey sandstone; associated with Z. varia. Parasite occurs as minute black cones, externally resembling spermogonia, but exhibiting no reproductive structure. 20. On thallus of an isidioid form of Lecanora parella, Ach. (sub-nom. Lichen dactylinus, Ach.), collected by Dr Scorr, 1802; in Herb. Kew, where it was ex- amined by Dawson TurNER. Associated with spermogonia, and externally resembling them. Parasite is black and discoid; immersed, and bursting through cortical layer of thallus of host. 21. On thallus of Verrucaria Garovaglii, Mont. (sub-nom. Thelotrema Scheereri) Hepp, Exsic. No. 100; which I regard as a mere form of V. pallida, Ach. Parasite may be externally confounded either with the sporidiiferous perithecia or spermo- gonia of the Verrucaria; but its sporidia are oblong-ovoid, colourless, and 1- septate. 22. On thallus of Graphis scripta, Ach., var. horizontalis, Leight. Exsic. No. 244 (sub-nom. G. serpentina, var.); Abdon, Shropshire. Intermixed with apo- thecia and pycnidia, and externally resembling the latter; occurring here and there as minute black cones, full of minute brown spherical sporidia. 23. Associated with Opegrapha atra, Pers., var., and Lecidea canescens. Aghada: corticolous ; Carroll. Possesses no distinct paaicplnyses Sporidia simple, pale brown, -00066" long, :00033” broad—contained in asci. 24. Associated with Lecanora pyracea, Ach. (sub-nom. Beatora rupestiis, var. irrubata) in Leighton’s Exsic. No. 213, are conceptacles externally resembling pycnidia or spermogonia, which contain not only stylospores but sporidiiferous asci; in which, further, the stylospores and sporidia have the same characters. The perithecia occur as small, brown, punctiform bodies seated on the thalline scales of the Lecanora. Stylospores are oblong-ellipsoid—normally 1-septate; granular or occupied by two or more nuclear globules or cellules in the young and older States; borne on long, filiform basidia. Sporidia also 1-septate, and having otherwise precisely the characters of the stylospores; asci 8-spored. There is no possibility of confounding the internal structure of what appears to be a fungus with that of the ordinary spermogonia of the Lecanora, which possess arthro- sterigmata, and very short rod-shaped spermatia. The existence in this fungus of stylospores and sporidia within the same perithecium—springing from the same VOL. XXV. PART II. Tc 550 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. hymenium—is most interesting in both an anatomical and physiological point of view. Ihave met with the same phenomenon in several other fungi, ¢.g., that described in this paper as associated with Verrucaria epidermidis. Parallel phenomena are the co-existence of sporidia and spermatia or stylospores in the same perithecia in Spheria Inndsayana, Curr. (Linps. “‘ Otago Lich. and Fungi,” p. 425, plate xxx. fig. 7); of sporidia and spermatia in Verrucaria atomaria, Ach. (Linps. ‘‘On Polymorphism in the Fructification of Lichens,” in Quart. Journal of Microscopical Science, Jan. 1868); and of spermatia in the ordinary sporidii- ferous perithecia of Verrucaria, by GipeLLi (Annals of Nat. History, April 1866, p. 270). 25. Associated with Lecidea luwrida, Ach., in Herb. Kew; “sea rocks near Bangor, July 1802.” Thallus exhibits a number of spermogonia scattered about the margins of its lobes as deep brown points, the body of the conceptacle be- ing immersed in the thallus. Intermixed are the externally similar, but more conoid, perithecia of the parasite, whose hymenium gives no blue with iodine. Asci apparently polysporous; -0020" long, ‘00066’ broad. Sporidia fusiform or ellipsoid, dark bottle-green or brown, irregularly 3-septate in maturity ; -0005" to 00066" long, 00014" broad. On the same sheet, and associated with ZL. /urida, are fastened specimens of what appears to be the same lichen, labelled “No. 19, on rocks by the sea, Miss Hutchins,” from Ireland doubtless. In both, the apothecia are distinctly Lecan- orine in the young state, possessing a thalline margin, and thus differing alto- gether from the Lecidea. But their apothecia resemble those of L. luwrida in the old state, when the disk becomes sub-convex, and the thalline border dis- appears, or is covered by the swollen disk. The disk in the Lecanorine apothecia is usually of a lighter red than in LZ. Jurida. In Miss Hurcuins’ plant the thallus is much paler than in Bangor specimens. The colour of the thallus obviously varies, just as it does in Physcia aquila, with its degree of exposure to light; being palest when the plant grows in the shaded crevices of rocks. In the Irish plant the paryphyses are subdiscrete, with brown tips; the asci 8-spored, -00166" long, 0005" broad; the sporidia ellipsoid, colourless, apparently 1-septate, -00033° long, 00014" broad. Probably the lichen in both the Bangor and Irish speci- mens is Lecidea sublurida, Nyl. (Mupp. Brit. Lich. p. 172), which Mupp places in the genus Thalloidima, Mass. 26. Several parasitic fungi, or fungoid growths of the most diverse character, — affect the apothecia of Abrothallus Siithii, Tul. or are associated with its pycnidia. But their apparent frequency in that lichen probably depends simply on the greater amount of attention I gave to the examination of the pseudo- genus Abrothallus while preparing my ‘‘ Monograph” thereof* in 1856. * Quarterly Journal of Microscopical Science, vol. v. 1857. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. ODL (a) Ben Lawers. Intermixed with the pycnidia of the Adrothallus, and externally indistinguishable therefrom, is a minute papilleeform parasite, which consists of an envelope of dark-brown, hexagonal, cellular tissue, enclosing myriads of dark-brown spherical spores, which are frequently irregular or jagged in outline, like blood-corpuscles in a condition of shrivelling from exosmosis. (0) Var. Welwitzschit, Tul.; Amulree Road, Dunkeld. Black perithecia— exter- nally resembling pycnidia, with which they are associated—contain nothing but spherical oil globules, or corpuscles closely resembling them. (c) Craigie Hill, Perth As in (a) and (6), intermixed with pycnidia, and like them papilleeform or punctiform. They contain— 1. Largish, spherical corpuscles, with pale brownish-yellow subgranular proto- plasm, resembling the sporidia of certain lichens, ¢.g. some forms of Lecanora cinerea. Sometimes the protoplasm becomes distinctly circumscribed and separated from the cell-wall by a varying hyaline interspace. This protoplasm gradually acquires a nuclear character and a central position, and then divides into two or four (sometimes three) equal subspherical segments, after the manner of some of the larger forms of gonidia. In age, both cell-wall and outline of nucleus, or its segments, become irregular, as if from shrivelling. 2. Corpuscles resembling shrivelled sporidia; most irregular in form, colour- less, generally with double contour, and containing one or more largish, distinct subspherical nuclei, and frequently also fine granular protoplasm. These cor- puscles are often found attached to each other in groups of two or more. 3. Most irregular, ribbon-like tubules, marked by subspherical nuclei, which are sometimes of an iodine colour. In some cases these would appear to be mere chains of degenerate sporidia. Sometimes only two or three constitute the pseudo-tubule, whose septa (the walls of the sporidia) have disappeared. But at other times the outline of the sporidia remains; there isa pedicle formed by the base of the shrivelled ascus; the nuclei are polar and distinct, sometimes yellowish; or they are connected by a central canal, as in the sporidia of Physcia parietina. A solitary black conceptacle, externally resembling an apothecium of the Abrothallus, picked off the bluish, curled squamules of the host (Parmelia saxa- tis), consists of an envelope of dark-brown, honeycomb-like cellular tissue ; rootlets being sent downwards into the tissues of the thallus of the Parmelia, penetrating through its cortical and gonidic layers to the medullary tissue. It contains—(1.) A parenchymaof colourless hexagonal cells, associated with mycelioid tubes—also hyaline, but short and thickish, and intermixed with much oily matter in the form of globules; (2.) Largish, spherical, colourless, sporoid corpuscles, full of a nucleiform, cellular, or granular protoplasm. On one of the true apothecia of A. Smzthiz, from Craigie, I found a large, dark- brown, 3-septate sporidium, with bulgings opposite the loculi. Its size and form Dd2 DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. are so different from those of the sporidia of the Abrothallus (as figured in my ‘‘ Monograph,” pl. iv.) that it is more probably referable to some Sphwria or fungus—not necessarily immediately associated with the Abrothallus, for in the course of microscopic studies on lichens, I have frequently met with alien spori- dia—sporidia belonging to other and topographically distant lichens or fungi. Thus, in a specimen of var. Welmitzschu in Leicuron’s Exsic. No. 191, 1 found a number of dark-brown figure-8-shaped sporidia on and among the thalline rhizinee of Parmelia saxatilis. They had not the usual soleaform character of the sporidia of A. Smthuv and its varieties; nevertheless they probably belonged, in this case, to the parasitic Abrothallus. (dq) Var. Welwitzschii (LEIicHTon’s Exsic. No. 191). A specimen of the deformed thallus of P. saxatilis, without apothecia of the Abrothallus, bears bodies externally similar—like some degenerate forms of the apothecia of A. Smithu. Their envelope is of hexagonal cellular tissue, containing bodies like some forms of gonidia in process of segmentation—large spherical cells with delicate hyaline wall, enclosing centrally four bluish corpuscles, evidently resulting from segmentation into four of a central spherical nucleus. (e) A specimen of A. Smitha (from Glen Dee, Braemar; on boulders, August 1856, W. L. L.), bears a Spheerioid parasite on its apothecia. In another specimen of the same Abrothallus, from Glenbeg, between Spittal of Glenshee and Braemar (on a roadside wall), August 1856, a similar parasite, occurring on the thallus of P. saxatilis, resembles externally the apothecia of the Abrothallus, and is apt to be confounded therewith. It contains a mass of minute globular brown spores, intermixed with a few partially disintegrated sporidia of the Abrothallus. (f) Associated with A. oxysporus, Tul., and with the pycnidia of A. Smithii (on an old wall, top of Craig-y-Barns, Dunkeld, June 1856, W. L. L.), on thallus of P. saxatilis. Parasite punctiform, black, containing masses of hyaline Toruloid spore-filaments, with myriads of very minute, also colourless, globular cells, generally aggregated in irregular masses; associated with a few sporidia, partially degenerate, both of A. oxysporus and A. Smithit. Those parasitic fungi, accompanying Abrothallus Smithii, that are Verrucarioid externally, are apt to be confounded not only with the pycnidia of the Abro- thallus, but with young states of the apothecia of both A. Smith and A. oxysporus. 27. In my copy of ScH#rRER’s Exsic. No 503, Calicium disseminatum, Fr., patelleforme, Sch., has not the sporidia of the Caliciwm, which are, according to NYLANDER (Syn. 146), blackish, oblong, and sometimes subspherical; but ellip- soid, colourless ones, ‘00033’ long, 00013” broad, contained in asci ‘00133’ long, — 00033” broad. There are no distinct paraphyses, and the plant may be regarded as either Verrucaria or Microthelia—lichen or fungus. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. 553 EXPLANATION OF PLATES XXIII, XXIV. PuatTE Figs. 1 to 18. Torula lichenicola. 1 to 12. On Lecanora subfusca. 1. Craig Choinich, Braemar, (a) Portion of thallus, with apo- thecia, of the Lecanora. (b) Sections of said thallus and apothecia—magnified. (c) One of its apothecia—magnified. (d) Spore-filaments and spores of Torula.* . Ben Lawers. Spore-filaments and spores of Torula. Loch Tay. Do. Kyles of Bute. Do. Caerlaverock road, Dumfries. Spores. Dunglass, Berwickshire. Spore-fila- ments and spores. Pease Dean, Berwickshire. Near Cork. (a) Portion of thallus of the Leca- nora with apothecia. (b) Section of said thallus and apo- thecia. (c) Spore-filaments and spores of Torula. Castle Bernard, Co. Cork. Spore-fila- ments and spores. Rathconnae, Co. Cork. (a) Portion of thallus, with apo- thecia, of the Lecanora. (b) Section of said thallus and an apothecium. Great Island, Cork. (a) Portion of thallus of the Leca- nora with apothecia. (b) Spores. Carrigaloe, Cork. (a) Portion of thallus of Leca- Spores. OT Arp ww so 10. jibe 12. nora. (b) Section of do. 13. On Lecidea canescens. Aghada, Cork. (a) Portion of thallus of the Lecidea with apothecia. (bc) Sections of said thallus and an apothecium. 14. On Lecidea parasema. Ireland. Spore- filaments and spores of the Torula. 15. Accompanying Opegrapha atra, Scherer’s Exsic. No. 634. Spore-filaments and spores. 16. Accompanying Verrucaria epidermidis, var.; Malham, Yorkshire. Spore-fila- ments and spores. XXIII. 17. In spermogonia of Lecanora varia, Leighton’s Exsie. No. 176. (a) Portion of thalline scales bearing spermogonia. (b) Section of said spermogonia. (c) Normal spermatia and sterigmata of the Lecanora. (d) Associated Torula. (e) Spore-filaments and spores of do. 18. Torula lichenicola on Lecanora subfusca. Ardrum, Co. Cork. Spore-filaments and spores. Coniothectwm lichenicolum. On Lecanora parella. Morchone, Braemar. (a) Portion of thallus of Lecanora, showing the parasite on its areolee. (6) The Coniothecitum, magnified and sectioned. Isidium corallinum. Craigie, Perth. (a) Section, logitudinal. (b) Portions (terminal) of some of the Isidia, variously magnified. (c) Portion of the plant viewed from above, showing the brown-tipped apices of the Isidia. Fig. 21. Parasite on I. corallinwm (sub-nom. Lichen dactylinus, Ach.), in Herb. Kew. (a) Section of disk. (b) Sporidia. Figs. 22 to 28. Coniotheciwm lichenicolum. 22. On I. corallinwm. Oraigie, Perth. (a) Portion of thallus of the Isidiwm. (b) Do. magnified. (c) Sections of parasite. 23. Diplotomma calcareum. Clapham, York- shire. (a) Portion of thallus of the Diplo- tomma. (b) Do. magnified. (c) Sections of the parasite. Coniothectum lichenicolum. Perth. Spores. Do. Scuir-na-gillean, Skye. Spores. Do. Sligachan, Skye. Spores. Do. Mangerton, Co. Kerry. (a) Portion of thallus of host. Fig. 19. Fig. 20. 24. Kinnoull, 25. 26. 27. (b) Sections of the parasite, variously magnified. (c) Spores. Do. NorthWales; Davies, in Herb. Kew. (a) Sections of the parasite. (b) Spores. 28. * The magnifying power is that which I have uniformly adopted in my drawings of microscopical structure in Lichens, viz., 425 diameters linear (under Objective No. 8, and Eye-piece No. 3) of a Nachet’s microscope made for me in 1851 (vide ‘‘ Otago Lich. and Fungi,” foot note, p. 410). VOL. XXV. PART Ii. rey) 554 Fig. 29, Microthelia Cookei, on Lecanora crenulata. Chichester. (a) Section of hymenium, showing asci and paraphyses. (6) Sporidia. Fig. 30. M. Stereocaulicola, on Stereocaulon paschale. Glen Derrie, Braemar. (a) Portions of the podetia of Stereocaulon paschale, showing the deformities occu- pied by the parasite; variously mag- nified. (6) One of the conglomerate wartlets iso- lated. (c) Sections of the parasite. (ad) Ascus, with young sporidia. (e) Mature sporidium. Fig. 31. M. Umbilicarie, on Umbilicaria pustulata. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. Fig. 32. Fig. 33. Fig. 34. Fig. 35. Piate XXIV. Fig. 1. Microthelia Nephromiaria, on Nephromiwm cellulosum. Hermite Island. (a) Old apothecium of the Nephromium ; under side—bearing the parasite. (b) Sections of the parasite. (c) Section of hymenium, showing an ascus and paraphyses. (d) Sporidium, mature. M. Nephromiaria, on Neuropogon Taylori. Kerguelen’s Land. (a) Ascus. (b) Mature sporidia. M. Umbilicarie. Norway. (a) Section of hymenium, showing asci and paraphyses. (b) Young, and (c) Mature, ascus. (d) Oil globules. (e) Reaction of iodine on hymenial gelatine. (f) Mature sporidia. (Vide Plate xxiii. fig. 31.) MM. Stictaria, on Sticta Freycinetii. Campbell’s Island. (a) Ascus, showing reaction with iodine. (b) Sporidia, mature and young. Parasite on Lecidea pachycarpa. Sporidia, young and mature. Microthelia Beomycearia, on Beomyces rufus. Balthayock. (a) Portion of thallus of the Beomyces, showing—(1) its own young apothecia ; and (2) the parasite. (b) Portion of same thallus, further mag- nified, showing young apothecia. (c) Sections of said apothecia. (d) Sections of parasite, (e) Sporidia. M. atricola, on Lecanora atra. Co. Kerry, (a) Perithecia, magnified ; one sectioned. (b) Sporidia. Parasite on Pertusaria. Sporidia. Gassicurtia silacea. Exsic. No. 150. (a) Portion of thallus of Lecanora atra, showing the parasite on its areole. (b) Two of said areole, further magnified. (c) Sections of the said areole and of their parasite. d) Spores. Fig.10. Microthelia vesicularia, on Lecidea vesicu- laris. Switzerland. Sporida. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Treland. Fig. 6. Fig. 7. Derriquin, Fig. 8. Balthayock, Perth. Fig. 9. Fontainebleau, Nyl. Fig. 11. Fig. Fig. Fig. Fig. Fig. Fig. Fig. 12. is St 16. . Parasite on Lecidea albo-atra. Great Island, . Parasite on Sguamaria crassa. Crosshaven, Cork, (a) Thallus bearing apothecia and the para- site. (b) Section of an apothecium and of the parasite. (c) Section of hymenium, showing ascus and paraphyses, . Parasite on Squamaria saxicola. . Lecidea Endocarpicola, on Endocarpon hepa- . Abrothallus Moore, on Cladonia bellidifiora, , Associated with Verrucaria Taylort. Dun Norway. (a) Portion of thallus of the Umbilicaria, magnified. (b) Sections of the parasite. (Vide also Plate xxiv. fig. 3.) M. rugulosaria, on Placodium rugulosum. Tasmania. Sporidia. M. parietinaria, on Physcia parietina. tishall. Sporidia. Parasite on Thelotrema lepadinum. (a) Sporidium. (b) Stylospores. Parasite on Lecanora cenisea. land. Sporidia. Cot- Treland. Ayton, Cleve- Spilomium Graphideorum. Fontainebleau, Nyl. Exsic. No. 72. (a) Portion of thallus of Graphis, bearing the parasite. (6) Sections of the latter. (c) Spores. Parasite on Lecanora polytropa, var. intricata. Penmanshiel. (a) Portion of thallus of the Lecanora, with apothecia and the parasite. (b) Sections of young apothecia. (c) Sections of mature apothecium and of the parasite. (d) Sporida or stylospores. Cork. (a) Portion of the thallus of the Lecidea with apothecia and the parasite. (b) Sections of (1) said apothecia and (2) parasite. (d) Mature sporidia. Jerkin, Norway. (a) Portion of thallus bearing apothecia and the parasite. (b) Sections of said apothecia and para- site. Parasite on Endocarpon microsticticum. Barmouth, N. Wales, . (a) Section of hymenium, showing asci and paraphyses. (6) Mature sporidia. ticum, Glanmire Road, Cork. (a) Ascus under iodine, with young sporidia. — b) Paraphyses, isolated. Sporidia, mature and young. Ach. Kelly’s Green, Ireland. (a) Ascus. (6) Mature sporidia. (c) Stylospores. combes Wood, Cork. Sporidium. DR LAUDER LINDSAY ON NEW LICHENICOLOUS MICRO-FUNGI. Fig. 20. Associated with Verrucaria fusiformis. Dou- glas, Cork. Sporidia. é Fig. 21. Associated with Graphis scripta. Leighton’s Exsic. No. 244. Sporidia. Fig. 22. Microthelia Collemaria, on Collemamuscicolum, Ach. On walls, Ingleby, Cleveland, York- shire, Mupp, 1857. (Compare Parasite (Spheria or Microthelia) on C. melenum, Ach., in Linps. “ Otago Lich. and Fungi,” p. 442; and “Mem. Spermog.” p. 272.) (a) Section of hymenium, showing an ascus and paraphyses ; with the reaction of iodine on the hymenial gelatine. (b) Mature sporidia. Parasite on Usnea barbata, var. florida. Janeiro. Sporidia. Parasite on Urceolaria. Glenarm, Co. Antrim. Spores or stylospores. Associated with Opegrapha atra, Leighton’s Exsic. No. 245. Sporidia. Associated with Opegrapha atra, Scherer’s Exsic. No. 634. Ascus and sporidia. Spheria Hookeri, on Lecidea spherica. Scher. (Exsic. No. 526). Sporidia ; (a) One of them preparing to germinate. S. Hookeri (sub-nom. Verrucaria), in Herb. Kew. (a) Specimen from the summit of Ben Lawers ; perithecia magnified and sec- tioned. Fig. 23. Rio Fig. 24, Fig. 25. Fig. 26. Fig. 27. Fig. 28. Fig. 29. Fig. 30. Fig. 31. Fig. 32. Fig. 33. Fig. 34. Fig. 35. 555 (b) Specimen from the Gemmi, Switzerland ; Sporidia. Accompanying Hndocarpon rufescens, Ach. Scherer’s Exsic. No. 465. Ascus with young sporidia. (Perhaps Hndocarpon cinerewm, Pers. 2) Associated with Physcia astroidea, Fr., var. Clementi, Turn. Sporidia. (Perithecia verrucarioid.) Associated with Umbilicaria hyperborea, Hffm., Scherer’s Exsic. No. 151. Sporidia. Parasite on Lecidea sanguinaria, var. affinis. Scher. Exsic. No. 629. (a) Sporidium, (6) Spores. Associated with Abrothallus Smithi, Tul. Craigie Hill, Perth. (a) Perithecium of dark-brown hexagonien- chyma; parasitic on thallus of Par- melia saxatilis, (6) Mycelium ; (1) spores, and (2) oil globules. (c) Spores, Associated with Abrothallus oxysporus, Tul. Craig-y-Barns, Dunkeld. Toruloid spore- filaments and spores. Associated with Lecidea lurida, Ach. Herb, Kew. Sporidia. (a) On seaside rocks, Ireland, Miss Hutchins. (6) Seaside rocks, Bangor, July 1802. In Prae XXIII | ; ' TRANS. Rox Soc Epi. You. XXV. SP) IN i éS Pel ~ f > oe Kt - JXS) e 3 is : am .. ‘ Z (a Af ‘4 * Sis a ee AGES ine seh RINSED ARIA 8 Nae 2 { / 25 J. N. Fitch imp 8 SS al de. Bye eee % = igen hells Lh , a yay @s + S — Ce Cee CRE eo f Perret . pS) . Se Y a oe Sages’ SS) \ SS = se S@S¥8 ay Prare XXIV. Fe Rox. Soc Evry. Vor. XXV. J.N-Fittch amp PTET SS Rae ; == Cm CoCo , = »\ Lo e SA , / - =) == — = S - 2 \® \ 5 = = = GG), I~ S Noe Gy = Sa = x sf / 1» \ \ \ — Yp © aN Yih ie Ca ees 8 g ys ‘ ndsay del: W Fitch lith. ¥ rs . YY +. si & Te ‘ yA ° i a Ju} i s eee cs Tag Om Car Pal * Rey Sid be Ga ~ : Lon! Ry Ae , ‘é on ‘ f 7 . 4 \ ' | < A XV.—On the Thermal Energy of Molecular Vortices. By W. J. Macquorn RanxIne, C.E., LL.D., F.R.SS. L. & E., &e. (Read 31st May 1869.) § 1. Object of this Paper.—In a paper on the Mechanical Action of Heat, which I sent to the Royal Society of Edinburgh in December 1849, and which was read in February 1850, it was shown, that if sensible or thermometric heat consists in the motion of molecular vortices supposed to be arranged in a par- ticular way, and combined in a particular way with oscillatory movements, the principles of thermodynamics, and various relations between heat and elasticity, are arrived at by applying the laws of dynamics to that hypothesis.* The object of the present paper is to show how the general equation of thermodynamics, and other propositions, are deduced from the hypothesis of molecular vortices, when freed from all special suppositions as to the figure and arrangement of the vor- tices, and the properties of the matter that moves in them, and reduced to the following form :—That thermometric heat consists in a motion of the particles of bodies in circulating streams, with a velocity either constant or fluctuating periodi- cally. This, of course, implies that the forces acting amongst those particles are capable of transmitting that motion. § 2. Steady und Periodical Component Motions.—A vortex, in the most general sense of the word, is a stream or current which circulates within a limited space. Conceive a closed vessel of any figure and volume to be filled with vortices, or circulating streams, the mean velocity of circulation in each such stream being the same; and let the velocities of the moving particles be either constant or periodic. How complex soever those motions may be, they may be resolved into the following component motions ;—a motion of steady circulation with the uniform velocity already mentioned as the mean velocity; and a motion consisting in periodical fluctuations of velocity. Those two component motions may be called respectively the steady circulation and the disturbance. § 3. Mean Pressure due to Centrifugal Force.—Let an elementary circu- lating stream—that is, a circulating stream of indefinitely small sectional area— be supposed to flow round and round in an endless tube with the uniform velocity mw; let p denote the density of the stream ; do the sectional area. Consider two cross sections of the stream at which the directions of motion of the particles are * Transactions of the Royal Society of Edinburgh, 1850, vol. xx. VOL. XXV. PART II. 7E 558 PROFESSOR RANKINE ON THE THERMAL ENERGY contrary; and consider what resultant forces are exerted by the stream on the two parts into which those two cross sections divide the tube. The mass of matter which flows through each cross section of the tube in an unit of time is pwde ; and in each unit of time a mass of matter of that amount has its velocity reversed. The force required in order to produce that reversal of velocity is of the following amount in absolute units, 2 pw de ; and such is the amount of each of the pair of inward pressures which the tube exerts on the stream, and of each of the pair of equal and opposite outward pressures exerted by the stream on the tube, tending to pull it to pieces. It may be called the centrifugal tension of an elementary stream. The velocity of the particles flowing in the stream may undergo periodical fluctuations, positive and negative alternately ; these will cause periodical varia- tions in the centrifugal tension; but the mean value of that tension will continue to be that given by the formula. The mean intensity of the centrifugal tension, in a direction tangential to the stream, is found by dividing the amount given in the preceding expression by the collective area, 2dco, of the two cross sections, giving the following result, pu. Suppose now that the stream is cut by an oblique sectional plane, making the angle 6 with a transverse section. Then the area of that oblique section is ereater than that of a transverse section in the ratio of 1:cos@; and the amount of the component tension in a direction normal to the oblique section is less than that of the total centrifugal tension in the ration of cos 0:1; whence it follows, that the mean intensity of the component centrifugal tension in a direction making an angle @ with a tangent to the stream is pw? cos” 6. Next, suppose a vessel of any invariable volume and figure to be filled with vortices or circulating streams, the velocity of steady circulation being w, and the mean density p. ‘The centrifugal force will cause a pressure to be exerted in all directions against the inside of the vessel. To determine the mean intensity of that pressure, irrespectively of periodical variations, conceive the contents of the vessel to be divided into two parts by an imaginary plane, and consider what will be the mean intensity of the force with which the circulating streams tend to drive asunder the portions of matter at the two sides of that plane. The . ——— : ; 4 : . OF MOLECULAR VORTICES. 559 plane will cut the streams that flow across it, some normally, others obliquely ; and the tangents to those streams will have all possible directions relatively to a normal to the plane, subject to the condition, in the case of isotropic action, that the mean value of cos’@ must be the same for all positions of the plane. But the sum of the mean values of cos’@ for three planes at right angles to each other must be = 1; therefore the mean value of cos’@ is = ta and finally, the mean intensity of the centrifugal pressure is given in absolute units per unit ot area, by the equation, aye ee : 2 : : : : (1.) § 4. Energy of Steady Circulation compared with Centrifugal Pressure.— The actual energy} of the steady circulation in an unit of volume, is expressed in absolute units of work, as follows :— wr oe aOR aa OE Nie. oll pain Q)s which, being compared with equation (1), gives the following result :— as =e 2 ' . , ° . (3); that is to say, the intensity of the centrifugal pressure on the unit of area is tivo- thirds of the energy of the steady circulation in an unit of volume. This is one ot the propositions of the paper of 1849-50, p. 151, eq. v.; but it is now shown to be true, not merely, as in the former paper, for molecular vortices arranged in a particular way, but for molecular vortices arranged in any way whatsoever, provided their action is isotropic, and their mean velocity uniform. A similar proposition has been proved by Warerston, Ciausius, CLERK MAXweELL, and others, for the pressure produced by the impulse of small particles flying about in all directions within a closed vessel, and rebounding from its sides. § 5. Vortices with Heterotropic Action.—It is conceivable that in solid bodies, molecular vortices may be so arranged as to produce centrifugal pressures of different intensities in different directions. In such cases, it is to be recollected that the sum of the mean values of cos’@ for the obliquities of any set of lines to any three planes at right angles to each other is = 1; whence it follows, that if Pp, p’, and p” be the mean intensities of the centrifugal pressures in any three orthogonal directions, we have p+p +p" = pw ; : , : (4); * There is a well-known integration by which it is easily proved, that for a number of ; — ’ deal directions equally distributed round a point, the mean value of cos”@ is 3° + Called by Tomson and Tarr the “ Kinetic Energy.” 560 PROFESSOR RANKINE ON THE THERMAL ENERGY that is to say, the sum of the mean intensities of the three centrifugal pressures in any three orthogonal directions ts equal to twice the energy of the steady circula- tion in an unit of volume. This proposition was not in the paper of 1849-50. which was confined to an isotropic arrangement of vortices. § 6. Energy of the Periodical Disturbances.—In the paper of 1849-50, p. 152, equation x., the energy of the periodical disturbances was taken into account by multiplying the energy of the steady circulation by a factor & greater than unity; thus giving for the total energy in an unit of volume the following expression, vr 2 € 4 xe) kpu? Q > in which v* denotes the mean of the squares of the resultant velocities of the particles with their combined motions. The values of the factor 4, being the ratio which the total energy of the molecular motions bears to the energy of the steady circulation, are to be deduced in each case from the results of experiments on specific heat. Thus the energy of the disturbances in an unit of volume is expressed by (1) °F = 5(e-1)p 5 =, nee It may now be observed, in addition, that the energy of the disturbances may, and indeed must, be at times partly potential as well as actual; in other words, partly due to displacement as well as to fluctuation of velocity. Let + wu be the greatest fluctuation of velocity; then a particle of the mass 2 unity has the energy = due to that fluctuation, in addition to the energy due to the steady circulation. It is only at the instants of greatest disturbance of velocity that the energy is all actual: at every other instant the energy is partly potential. Hence v? = kw? may be taken to denote, not the square of an actual velocity common to all the particles, but the value to which the square of the velocity of the particles would rise, if all the energy of the disturbances, actual and potential, were expended in increasing the velocity of steady circulation. § 7. Total Energy of Thermal Motions.—The total energy of the motion, com- pounded of steady circulation and periodical disturbances, in an unit of volume, is expressed, as in the paper of 1849-50, by the following equation, which also shows its relation to the centrifugal pressure, kpw? 8k a eee in which (to recapitulate the notation) p is the mean density; w the velocity of steady circulation; the centrifugal pressure p is expressed in absolute units of OF MOLECULAR VORTICES. 561 force on the unit of area; and the proportion 4, in which the total energy of thermal motions exceeds the energy of steady circulation, is a quantity whose values and laws are left to be deduced from the results of experiment. §$ 8. Determination of Centrifugal Pressures——The external pressure exerted by any substance, as we find it in nature, is a complex quantity, being com- pounded of the centrifugal pressure already mentioned, and of forces which may be classed together under the name of cohesion. To enable us to distinguish those components of the total pressure from each other, we have the principle, that the centrifugal pressure varies as the density simply; whereas pressure or tension, or siress (to use a general term), arising from cohesive forces, must vary as some function of the density of a higher order than the first power. The perfectly gaseous state is an ideal state in which the substance exerts no external pressure except that which varies as the density simply; that is, centrifugal pressure. It is impossible to obtain a substance absolutely in the state of perfect gas; but the cohesive stress diminishes with increase of tempera- ture and diminution of density in such a manner, that it is possible, as is well known, to obtain substances approaching very nearly to the perfectly gaseous state, such as atmospheric air and various other gases; and the actual pressures of such nearly perfect gases may be used, either as approximate values of the pressures in the ideal state of perfect gas, or as data for calculating the latter kind of pressures by the method of limits. We thus have the means of determin- ing, to a close approximation, the centrifugal pressure of a given substance at a given temperature and density; the well-known formula being ee Og ey Ore!) | kt UCP): p Po To in which 7, is the absolute temperature of melting ice; + the actual absolute temperature; and Fs the value of the quotient 5 at the temperature of melting 0 ice, for the particular substance in question. § 9. Temperature and Specific Heat.—It is shown in the paper of 1849-50, that temperature, according to the hypothesis of molecular vortices, is a function of the quotient found by dividing the energy of the steady circulation in an unit of mass by a constant depending on the nature of the substance; which constant may be defined, as the value which the energy of steady circulation in an unit of mass of the given substance assumes at a standard temperature, such as that of melting ice. The energy of the steady circulation in an unit of mass is whence it appears, that the principle stated as to absolute temperature is VOL. XXV. PART II. 7F 562 PROFESSOR RANKINE ON THE THERMAL ENERGY expressed by equation (7), already given in§ 8. The total energy of the thermal motions in an unit of mass is expressed by dividing equation (6) of § 7 by the density p; hence that quantity of energy (denoted for shortness by Q) is given in terms of the absolute temperature by the following equation, we Shep oR Dye. Q= S. = se = ==> i oh T) . . . - (8). The real specific heat of a substance, as defined in the previous paper, when expressed in units of work per degree, is dQ okp, 3p oT , dk Je = dr 2 oT 20,7) Ot (9). in which ¢ is the real specific heat, in terms of the minimum specific heat of liquid water, and J, JouLe’s equivalent, or the dynamical value of the ordinary thermal unit. There is one part of the specific heat which is necessarily constant for a given substance in all conditions; and that is the part which expresses the rate of increase with the temperature, of the energy of the steady circulation alone in an unit of mass, viZ., Q ii Le: Po AG: )= oan = == 2o5T : (10). The part of the specific heat which depends on periodical disturbances is expressed as follows :— d ((k—1 3(k—1 Op yt . dk dr {! k ey a 25 aa Bs ne dr j ; Op It is only by experiment that it can be ascertained whether this part of the specific heat is constant or variable. Experiment has proved that it is constant for the perfectly gaseous state, and nearly, if not exactly constant, for other con- ditions; but that its values for the same substance in the solid, liquid, and gaseous conditions are often different.* The apparent specific heat contains other terms, depending on the expenditure of energy in performing external and internal work, according to principles of thermodynamics which are now well known. § 10. Examples of the Proportion in which the Total Energy of the Thermal Motions exceeds the Energy of the Steady Circulation.—In the perfectly gaseous * According to the nomenclature used by Crausius, the phrase “ real specific heat” is applied to that part only of the specific heat which is necessarily constant for a given substance in all conditions. Hence, if that nomenclature were adapted to the hypothesis of molecular vortices, the term real specific heat would be applied to the coefficient given in equation (10) only, and that given in equation (11) would be considered as part of the apparent specific heat. OF MOLECULAR VORTICES. 563 state, the coefficient given in equation (9) is the specific heat at constant volume; and as that quantity is known to be constant at all temperatures, the second term of the right hand side of the equation disappears, and it is reduced simply to the following— 3kp Jc = u . 2 . 5 . 5 Wy . 2PoTo ee The specific heat, in dynamical units per degree, of a perfect gas under constant pressure, is expressed as follows :— Jd = Jo+ Pe _ he (#41). PDA aiid PoT. ~~ PoTo \ 2 and the ratio in which the latter coefficient is greater than the former is, therefore, rou Dy Bir array (14); whence we have the following formule for deducing the proportion 4, borne by the total energy of the thermal motions to the energy of the steady circulation, from the ratio — as determined by experiment, 2 eo) (15). is This method is applicable only to substances that are nearly in the perfectly gaseous state. There is another method, applicable to the same class of substances, which is expressed as follows :— 2 = “Peet PES PAE AE UTS OPE ie This second method may be applied to liquids and solids also, under the follow- aN : Poo state; and the specific heat ¢ must be nearly constant. The ratio which the energy of periodical disturbances in an unit of volume bears to the centrifugal pressure may be interesting in connection with hypo- thetical views of the constitution of matter. It is expressed as follows :— ing conditions; the quantity is to be calculated as for the perfectly gaseous ss lea oulkys, kadai aati daa avg 564 PROFESSOR RANKINE ON THE THERMAL ENERGY The following are some examples of the results of calculations by for- mulee (15) and (17) :— Substance, — k 5(H =) Atmospheric air, .. : 1-408 1634 0-951 Nitrogen, ; ; 1-409 1630 0:945 Oxygen,. . . . 1400 1667 1-000 Hydrogen, ; : : 1-413 1614 0921 Steam-gas, . - : 1:297 2°242 1863 § 11. General Equation of Thermodynamics.—In the paper of 1849-50, pp. 158 to 164, the general equation of thermodynamics (equation 6 of that paper- p. 161) is deduced from the hypothesis of molecular vortices, on the supposition of a special form and arrangement of the vortices. In a subsequent paper, ‘On the Centrifugal Theory of Elasticity,” read to the Royal Society of Edinburgh in December 1851 (‘ Transactions,” vol. xx. pp. 433 to 436), the same general equation (being equation 25 of the latter paper, p. 436) is deduced from the hypothesis of molecular vortices, without any special supposition as to the form and arrangement of the vortices, but with certain assumptions as to the laws of the elasticity of the matter which moves in them. In a paper read to the British Association in 1865, and published in the “ Philosophical Magazine” for October of that year, a further generalisation is effected; and it is shown that the general equation of thermodynamics follows from the supposition, that sensible heat con- sists in any kind of steady molecular motion within limited spaces, without any assumption either as to the figures of vortices, or as to the special properties of the matter that moves in them. The object of this section of the present paper is to show how the same general equation is deducible from the hypothesis of molecular vortices, as stated at the commencement of the paper; that is, freed from all special suppositions except that of a steady circulation, combined with periodical disturbances of speed, whose energy may bear any proportion, constant or variable, to that of the steady circulation. The forces by which an elementary circulating stream, whether flowing with a steady or with a fluctuating speed, is kept in a given state of motion, and of a definite figure and dimensions, are equivalent in their action to a tension exerted at each cross-section of the stream, of an amount which, at a given cross-section, and at a given instant, is expressed in absolute units of force by the product of the mass which flows along the stream in a second into the velocity of flow at that cross-section and instant. The mean value of the tension is the product of the same mass into the mean velocity; that is, into the velocity of steady circu- lation. Hence the mean centrifugal tension, as this force may be called, is pro- portional to the square of the velocity of steady circulation, and therefore to the absolute temperature; and the work done by the forces to which the virtual OF MOLECULAR VORTICES. 565 tension is equivalent, during a change of the figure and dimensions of all the elementary circulating streams in a given body, may therefore be expressed by multiplying the absolute temperature by the change in the value of a function, to be afterwards determined, of the dimensions, figure, and temperature. If to that function be added a function which is the integral of the increment of the energy of steady circulation divided by the absolute temperature, the sum is what I have elsewhere called the thermodynamic function. Let it be denoted by ¢; and let dQ denote the quantity of energy which must be communicated to the body, in order to produce the increment d. ¢ in the thermodynamic function at the mean absolute temperature 7 ; then we have PE ENS” ae een a ei and this, when the proper value has been assigned to the thermodynamic function, is the general equation of thermodynamics. The process of finding the value of the thermodynamic function is well known; but a summary of it will be given here for the sake of completeness :— Let dx, dy, dz, &c., denote changes in the dimensions of unity of mass of the body, of the nature of strain, such as dilatations and distortions; and let X, Y, Z, &c., denote the forces, of the nature of elastic stress, which the body exerts in the respective directions of such changes; so that while the thermodynamic function undergoes the change d¢, the external work done by unity of mass of the body is Xda+Ydy + Zda+ &e.; Then, by the principle of the conservation of energy, it is necessary that the following expression should be a complete differential :— tdh — Xda — &e.; whence it follows, that the thermodynamic function ¢ is the integral of the following set of partial differential equations :* Eee ee es Oe, Ge dr dy de> de de? that is to say, the thermodynamic function has the following value :-— dX 9= Wr) + “dat f O dy + &e.; dr in which all the integrals are taken at constant temperature. For a perfect gas at constant volume, we have dQ, = Je dr, in which Jc is the * See Philos. Mag. for December 1865. VOL. XXV. PART II. 7G 566 PROF. RANKINE ON THE THERMAL ENERGY OF MOLECULAR VORTICES. dynamical value of the specific heat of the gas at constant volume; and conse- quently, (7) = Jc hyp. log. 7; and the same is the value for any substance which, at the temperature 7, is capable of approaching indefinitely near to the perfectly gaseous condition. There is some reason for believing that all substances may have that property;* but to provide for the possibility, pointed out by Cuausius (“PoacenporFr’s Annalen,” vol. xcvi. p. 73), of the existence of substances which at certain temperatures are incapable of approaching indefinitely near to the perfectly gaseous condition, we may make (as that author does), (7) = Jc hyp. log. t — x(7); where x (r) is a function of the temperature, which becomes = 0 at all tempe- ratures at which an indefinitely close approximation to the perfectly gaseous state is possible; thus giving, for the complete value of the thermodynamic function, gh = Jc hyp. log. t + x(7) +f[S da + [2 dy + &ce. : (19). That expression may be abbreviated as follows :—Let U be the potential energy of the elastic stress of unity of mass of the body at constant temperature; then g = Jchyp. log. 7 + y(r) + _ - . : (20); and the corresponding form of the general equation of thermodynamics is as follows :— dQ = Je+7xX (th dr+rd . = ee § 12. Conclusion—In conclusion, then, it appears that the special supposi- tions as to matters of detail, introduced into the hypothesis of molecular vortices in the paper of 1849-50, are not essential to the deduction from that hypothesis of the principles of thermodynamics, but that such matters of detail may be left open to be determined by future investigations. * See Phil. Mag. December 1865. © S67)" ) XVI.—On the Alkaloids contained in the Wood of the Bebeeruor Greenheart Tree (Nectandra Rodici, Schomb.). By Dovatas Mactagan, M.D., F.R.S.E., Professor of Medical Jurisprudence in the University of Edinburgh, and ARTHUR GAMGEE, M.D., F.R.S.E., Lecturer on Physiology in Surgeon’s Hall, Edinburgh. (Read 8d May 1869.) In a paper read before the Royal Society of Edinburgh in April 1848,* Dr MacuaGan described the general properties of the alkaloid, whose presence had been indicated in the bark of the bebeeru or greenheart tree, by Dr Rope of Demerara, and described the mode cf. preparation of its sulphate for medicinal use. The fact that bebeerine appeared to possess marked antiperiodic pro- perties,} rendered its careful chemical study desirable, and accordingly the alka- loid, purified as far as possible, was subjected to analysis by Drs Maciacan and Trmuey.{ It resulted from this research that bebeerine is an uncrystallisable base, very soluble in alcohol, less so in ether, and very sparingly so in water. It forms with acids salts which are all uncrystallisable. With perchloride of gold, mercury, copper, and platinum, it gives precipitates which are soluble to a certain extent in water and alcohol, but which are deposited in a non-crystalline form when the solution cools. To this base the author assigned the formula C,,H,,N,0,(C=6). Von Pianta* subsequently attempts to purify further the alkaloid, and assigned to it the formula C,,H,,0,N(C=6) or C,,H,,0,N(C=12.) In consequence of the apparent impossibility to obtain bebeerine in a crystal- line form, it is impossible to state whether the substances examined by Maciacan and TILLEY, or by Von Puanta, were absolutely pure; and there is no evidence to show that the product obtained by the latter chemist was purer than that examined by the former investigators. Since the time when these papers were published, sulphate of bebeerine has found its way into medical practice, and the experience of many appears to show that it is possessed of no insignificant tonic and antiperiodic properties. The sulphate of bebeerine, as it occurs in the market, has been, we believe, almost entirely manufactured by Messrs MAcFARLANE & Co. of Edinburgh. Experimenting with various portions of the bebeeru tree, one of the members * Transactions of the Royal Society of Edinburgh, vol. xv. part. ii. + Mactaean, Edinburgh Medical and Surgical Journal, April 1845. + London and Edinburgh Philosophical Magazine, series ni. vol. xxvil. p. 253. VOL. XXV. PART II. 7H 568 DRS MACLAGAN AND A. GAMGEE ON THE. ALKALOIDS CONTAINED of that firm discovered that, on subjecting the wood to a process similar to that which had been used in the separation of bebeerine from the bark, a product was obtained which did not apparently differ from bebeerine in its physical properties. He requested us to undertake for ourselves the examination of the product which he had obtained from the wood. , The substance handed to us for examination had been prepared by subjecting the wood of the bebeeru tree to a process substantially identical with that recom- ' mended in the “ British Pharmacopceia” for the extraction of the sulphate of bebeerine from the bark. The product did not differ in appearance from the latter substance as it occurs in commerce, 7.é., it was in the form of shining yellowish-brown scales, soluble in water, and possessed of an intensely bitter taste, not differing perceptibly from that of sulphate of bebeerine. In the first place, a portion of this substance was dried in the water-bath, and : then the amount of sulphuric acid determined. (1.) 2°001 grms. of substance yielded 0:5300 grms. of cnigliate of barium. ] (2) 2.001 germs. of substance yielded 0:483 grms. of sulphate of barium. | The mean of these two results gives to amount of sulphuric acid (calculated as H,SO,) as 10°69 per cent. This would indicate that the substance examined consisted of sulphate of bebeerine, mixed with other substances; or that it was composed of the sulphate of one or more alkaloids, having a higher molecular weight than bebeerine. One hundred grammes of the powdered but undried sulphate were dissolved in two litres and a half of distilled water. An insignificant quantity of a brownish powder was left undissolved. The fluid was filtered through calico, and precipi- tated carefully with solution of ammonia. The bulky precipitate was collected on calico, carefully washed, and dried on the water-bath. When dry, it was boiled for some time with chloroform. The latter fluid soon acquired a deep brownish-yellow colour. The residue was treated three successive times with chloroform. At the end of that time, the chloroform appeared to exert no action upon the tolerably abundant residue. When dried, the chloroform extract weighed 60°55 grammes; it had a brownish-yellow colour, and broke witha resinoid fracture. When powdered, it possessed a very pretty yellow colour. We shall, in the first place, state the result of our examination of this sub- stance before proceeding to that of the bodies which were left undissolved by the chloroform. I. Examination of Nectandria, a new Base soluble in Chloroform. The chloroformic extract, to which we have referred, left no ash when ignited on platinum. It was very freely soluble in rectified spirit; less soluble in absolute alcohol. It was not perceptibly dissolved by cold distilled water. When boiled with water, it very readily fused at a temperature below 100°C.; and the boiling IN THE WOOD OF THE BEBEERU OR GREENHEART TREE. 569 solution, when filtered, deposited a small quantity of yellow powder, which was found to be amorphous when examined under the microscope. 49 grammes of the solution in boiling water yielded 0:07 grammes of dry residue; or 100 parts yielded 0-142 parts of solid residue. The powder was found to be entirely soluble in dilute acid; the solution possessed a yellow colour, and an intensely bitter taste. The residue, dissolved in water, and treated with solution of ammonia, or of any of the fixed alkalies, yielded a bulky yellowish precipitate. When evapo- rated to dryness, and redissolved in water, a perfectly neutral solution was obtained. This was abundantly precipitated by tetrachloride of platinum, the precipitate being quite amorphous, and not fusible when heated to 100°C. 0°709 grammes of this hydrochlorate yielded 0-268 grammes of chloride of silver; 100 parts, therefore, contained 9:361 per cent. of chlorine. Oil of vitriol added to the base did not blacken it, but merely caused it to assume a faint rose tint. When binoxide of manganese was added to the acid solution thus obtained, a most splendid rich green colour was developed, which, on exposure to the air, passed into a violet of great beauty, scarcely distinguishable from that procured when strychnia is similarly treated.. This reaction is one of very great delicacy. On adding sulphuric acid and binoxide of manganese to a fragment of the alkaloid placed in a tube, and afterwards diluting the fluid sufficiently by means of oil of vitriol, we observed its effects on the spectrum. In the case of the green fluid first spoken of, the violet end of the spectrum was cut off, and when a sufficiently thick stratum was examined none but the red rays passed. No definite absorption band was, however, present. After assuming the violet tint, besides a cutting off of the violet end of the spectrum, a very well-marked absorption band, situated between C and D, is noticed, as is shown in the annexed diagram. A Br c D E | 1 2 3 : ip | Pee tvsoluntbushnn mili i WA) EE ee AIRE nial Hil HM hit fe byididdt I| The reaction above described was possessed equally by all compounds of the alkaloid under examination. On heating the alkaloid on a platinum spoon, it first melts, and then burns with the evolution of fumes which are both pungent and fragrant. ‘These are identical with the fumes evolved under the same circumstances by bebeerine. A comparison of the properties which we have described with those of pure bebeerine, established in the clearest manner the difference between the two. The chief of these differences are— ene Ig a pean 570 DRS MACLAGAN AND A. GAMGEE ON THE ALKALOIDS CONTAINED lst, The ready fusibility in hot water of the base from the wood. 2d, The beautiful and most delicate reaction with binoxide of manganese and sulphuric acid, which is not possessed by bebeerine. 3d, The much smaller solubility of the new base in ether. With regard to this point it may be stated, that, in a paper previously quoted, one of us had stated the solubility of bebeerine in ether to be 1 in 13. The ether used had a specific gravity of 730. On repeating, however, our observations with perfectly pure ether, of density 0-715, and pure bebeerine, which had been prepared from the bark exhibited by the firm of MacrarLaANnE & Co. in the Great Exhibition, we ascertained the solubility to be smaller. 100 parts of this ether dissolved, at 14° C., 0:96 parts of pure bebeerine. Under the same circumstances, 100 parts of this ether dissolved 0:201 parts of the base from the wood. After being boiled in contact with the base for ten minutes, being filtered and evaporated, 100 parts of ether was found to have dissolved 07188 parts of our new base. These numbers are, however, higher than the truth. After the two latter determinations, it was found that the substance which had been used retained chloroform with great tenacity, and could only be freed from it by very prolonged heating and exhaustion im vacuo. The base, when purified by a process to be mentioned below, and thoroughly dried, was again treated with ether. 1. After standing for many days in contact with it, ether of density 715 had dissolved only 0:04 parts of alkaloid. 2. After standing for twenty-four hours only, in contact with the same sample of base, 100 parts of the same ether had dissolved only 0-021 parts of the base. We have mentioned that the base which we obtained from the wood possessed a fine yellow colour. This colour is not, however, essential to it. On treating the yellow solution of the hydrochlorate of the base with animal charcoal, the solution is almost completely decolorised ; and when treated with solution of ammonia a precipitate is obtained, which, after being drained and allowed to dry (without the application of heat), either in the air or zn vacuo, occurs in the form ofan almost purely white powder. When heated in the water- bath, it soon acquires the fawn colour which it possessed before the treatment with charcoal. On dissolving the white powder in alcohol, and evaporating the solution, a translucent residue of yellowish tint is obtained. All-attempts to obtain this base in a crystalline form have failed. Obtained by evaporation from alcohol, chloroform, or ether, like bebeerine, it never presents the slightest crystalline form. We have ascertained the composition of this base, to which we now assign the name of Nectandria, by the analysis of two different samples, one of which IN THE WOOD OF THE BEBEERU OR GREENHEART TREE. 571 was quite white, the other possessed of a light fawn colour. We must remark, that this alkaloid is excessively difficult to burn. In the two first analyses quoted, the substance was burned in the manner now usual with oxide of copper and oxygen gas, taking great care to have a sufficient quantity of copper turnings in the anterior part of the tube. In the third analysis, we used the method proposed by GrnrL, one of RocunepErR’s pupils, and which consists in mixing the substance intimately with fused and powdered bichromate of potash and powdered oxide of copper, and filling up the tube as usual with granulated oxide of copper. Operating with the greatest precaution, the combination was, however, not completed until a very considerable quantity of oxygen gas had been passed through the tube. I. 0:225 germs. of substance gave 0:139 germs. of water and 0°583 grms. of carbonic acid. If. 0:317 grms. of substance gave 0:194 grms. of water and 0°816 grms of carbonic acid. III. 0272 grms. of substance gave 0158 grms. of water and 0°6945 grms. of carbonic acid. Nitrogen was determined by Witt and VaRRENPTRAPP’S method. The ammonia evolved was collected in standard sulphuric acid. 04015 grms. of substance yielded ammonia, which required for neutralisation 13 cubic cents. of normal sulphuric acid (1 C.C. corresponded to 0°0177 ammonia, or 0°014 grms. of nitrogen). These numbers lead to the following per-centage composition :— I. Il. Ill. Mean. Carbon, ‘ : - (0:26 70°19 69°63 70:02 Hydrogen, : ; 6:86 6°81 6°43 6°73 Nitrogen, : : 4:53 4:53 4°53 4:53 Oxygen, : : 18°35 18:47 19°31 18-72 The double compound, with tetrachloride of platinum, was employed in the determination of the atomic weight of the base. (1.) 0:2985 grms. of the salt gave 0-053 grms, of platinum = 17-72 per cent. of platinum. (2.) 0:259 9 ) 0046 39 29 = lag fev ” 93 (3.) 0°1735 “ 33 00295 __,, m = 17:0 i a (4.) 0:288 ¥ es 0-052 BS a — 18:05 - , (5.) 0°329 ‘, =f 0:06 9 a = 18:23 = 99 The mean of these five determinations gives the per-centage composition of platinum in the double salt as 17°72, from which we deduce 348-08 as the atomic weight of the alkaloid. From the above numbers, we deduce for our new alkaloid, Nectandria, the formula— C,oH,3NO,(C=6.) Crile N O (C=12') VOL. XXV. PART II. (ey 572 DRS MACLAGAN AND A. GAMGEE ON THE ALKALOIDS CONTAINED This gives by calculation— Found. Carbon, . : : 70°38 70:02 Hydrogen, : : 6-74 6:70 Nitrogen, . ; ' 4:10 4:53 Oxygen, - : : 18-79 18°71 100:00 100-00 According to this formula, the compound with tetrachloride of platinum should contain ; é } : : : 18°07 per cent. of platinum, Mean of five determinations, . Lt-F2 2 a According to this formula, the hydrochlorate of the base should contain é : : 9°60 _ per cent of chlorine. Actually found, y : ' : 9°361 Me Below the formula of bebeerine, as ascertained by Von PLANTA, is placed side by side with that of nectandria, as ascertained by ourselves— Bebeerine, : E : C,H Oe Nectandria, : 3 : Cts, aN. II. ELxamination of a new Base insoluble in Chloroform. In a previous part of this paper it has been stated, that the precipitate pro- duced by ammonia in a solution of the mixed sulphates obtained from the wood of the bebeeru tree, was by treatment with chloroform subdivided into two portions, of which one, Nectandria, has been already examined. After the treatment with chloroform, 16:7 grammes of a greyish solid matter remained. This matter was nitrogenous, soluble in dilute acids; its alcoholic solution had a very marked alkaline reaction; its solution in hydrochloric acid was abundantly precipitated by tetrachloride of platinum. On boiling the base with water, the latter soon acquired a rich yellow colour, and possessed a very bitter taste; the solution had a strongly alkaline reaction. On allowing the hot solution to cool, a yellow powder subsided. When examined with a power of 300 diameters, this powder was seen to be uniformly composed of nodules, and clustres of nodules. On repeatedly dissolving the powder in boiling water, and examining the deposit which subsided on cooling, the same forms were visible. From the portion of residue insoluble in chloroform, we obtained 5°65 grammes of this yellow sub- stance, which our observations prove to be a powerful base. It was entirely soluble in water. 1. 100 grammes of the boiling solution, on being evaporated, gave 2:11 grammes _ of solid. residue. 2. 100 grammes of the solution which had cooled, and had deposited the yellow nodules, yielded 1:77 grammes of solid residue. P From these determinations, it would appear that one part of this yellow base IN THE WOOD OF THE BEBEERU OR GREENHEART TREE, 573 is soluble in 56°81 parts of cold water, and in 473 parts of boiling water. The aqueous solution possessed a powerfully alkaline reaction. When boiled with a solution of chloride of ammonium, ammonia was evolved abundantly ; when treated with solution of nitrate of silver, a white precipitate fell, which became black on boiling. Sulphuric acid dissolved the yellow base with the production of a dirty brownish-yellow colour. When binoxide of manganese was added to the acid solution, a magnificent green colour was produced, which, on exposure to air, changed to a rich purple, and ultimately assumed a dirty red tint. This reaction was compared with, and found to be identical with that manifested by nec- tandria, although, from the very remarkable differences in the action of solvents upon them, the one alkaloid could not be contaminated with the other. The yellow base is rich in nitrogen; and when heated on platinum it melts, and evolves the same fumes as bebeerine and nectandria. When dissolved in hydrochloric acid, and treated with tetrachloride of platinum, a yellow precipitate falls, which on the fluid being heated to boiling point fuses, and is then perceptibly dissolved. i tle E; . pe CESS Seon CHARTS SHEWING (1) BY ISOBARIC LINES THE MEAN PRESSURE oF THEATMOSPHERE AND (2) BY ARROWS THE PREVAILING WINDS over THE GLOBE cach MONTH From JUNE To NOVEMBER. Calms marled thits 0 Variahle Winds this * - —n 4 29:9 t Saas maeal) | | id rear 20 ° 20 cr) 160 is TO Lmginda 100 Eat of 120 Orme 140 ee BO Defies 100 Bers of 120 Orme 30 SEPTEMBER j ai | | aa anee J ove 160 180, 120 Lm gma 100 Wert of BO Greareich 6O = 27m DI Wom oh Ui comm wo 20 20 Defeats 100 Bart of 120 Germ 40 W. & A.K, JOHNSTON, EDINBURGH es ae A Ce 5 Mee Sik oe ae A aes _ -_ — - opr id lee et ee eae i as —— tet? + ee atin ae ian ae Ty Sa are re | a ‘4 ; a a, bs wv? ’ } ' CHART SHEWING (I) BY ISOBARIC LINES THE MEAN PRESSURE oF THEATMOSPHERE AnD (2) BY ARROWS THE PREVAILING WINDS ror THE YEAR. Trans. Roy: Soc.Edin. YolXXV. Calins marked thus O Variable Winds this * PLATE XXVIL | {YEAR et To WOLeapesie100 Wer af 80 Grearics 60 CHARTS SHEWING BY ARROWS THE LEAST FREQUENT WINDS wick PREVAIL IN JANUARY AND JULY. THE ISOBARIC LINES ARE ALSO GIVEN FOR THESE MONTHS. a0 100 8 eo 40 20 0 00 120 140 180 160 x 1 — 00 80 x0 o ‘0 | SS) esl Sees eee 3 = Le] =e Alea JANUARY a BY ates ee eel eI 100 20 Lafemsie 100 Wert of 80 Greed = 1D 60 (BO Lempiels 100 Burt of 120 Gren 140) (80 Longin 100 Bart of 180 Genera 140) W. & A.K. JOHNSTON. EDINBURGH — QEsBA XVII.— The Mean Pressure of the Atmosphere and the Prevailing Winds over the Globe, for the Months and for the Year. Part Il. By ALEXANDER Bucuay, M.A., Secretary of the Scottish Meteorological Society. (Plates XXV. to XXVIL) (Read 19th April 1869.) Cuarts, showing by Jsobaric Lines the mean pressure of the atmosphere over the globe during the months of the year, may be justly regarded as furnishing the key to all questions of meteorological inquiry; for without the information conveyed by such charts it is impossible to discuss satisfactorily those questions which relate to prevailing winds, the varying temperature, and the rainfall throughout the year in the different countries of the world. It is to meet this desideratum that the Charts of Mean Atmospheric Pressure of the globe which are given with this paper are offered as the first approximate solution of this great physical problem. Since Part I.* was read in March 1868, valuable additional information has been obtained from Australia, New Zealand, Tasmania, Africa, South America, the west coast of North America, Iceland, Norway, and Sweden, and from several isolated stations in different parts of Europe and Asia. The period for the British Islands and a large portion of Europe has been extended so as to include the eleven years from 1857 to 1867. In this Part the complete set of Charts for the twelve months and for the year are given, together with the data from which the Charts have been con- structed. As regards Pressure, the stations were selected with the view of representing as well as possible the geographical distribution of the pressure. The first place was assigned to those stations at which the barometric observations were known to be, or presumably were, of the best quality; and in drawing the isobaric curves, the greatest weight was given to means deduced from these observations. Since it is the mean pressure at sea-level which is here inquired into, and since the manner of the geographical distribution of the pressure doubtless varies at different heights, stations at low elevations were preferred to those at greater heights. The pressures at a few elevated places, such as Great St Bernard and Dodabetta, are given in the Tables; but they were not made use of in drawing the curves,—their value consisting in the light they tend to throw on the _ movements of the upper currents of the atmosphere. In an inquiry into the comparative distribution of atmospheric pressure, it i: * Proceedings of the Society, vol. vi. p. 303. VOL. XXV. PART II. 7 576 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE evident that the first requisite, as regards time, is, that the means be deduced from observations made in the same years. In the tropics, where there is great regularity in the mean pressure of the same month from year to year, observa- tions in the same years are of less importance; but in extra-tropical regions, where the mean pressure of the same month varies considerably frem year to year, it is of the utmost importance to obtain observations for the same years. This has been the guiding principle in selecting the years from which the means of the different places in Table I. have been calculated. Thus, in the British Islands, the means are uniformly given for the eleven years from 1857 to 1867, and the means of many European stations are given for the same years; and in the United States of America the means are for the six years from 1854 to 1859. It will be observed, that the means for two or more series of years are given for several places, such as Christiania, Upsal, Toronto, Hobart Town, Algiers, &c. At Christiania, the average for 1861-68 is that for most other Norwegian stations, and that for 1857-67 is the average adopted for the British Islands. For Upsala, the average for 1857-67 is given together with the average for 1859-66, the average of the other stations in Sweden. By the comparisons which may be instituted between these means, a closer approximation to the course of the isobaric curves over this portion of north-western Europe is ob- tained. Similar comparisons may be made from the data given in Table I. for different regions of the world, and thus the disadvantages, arising from the necessary use of averages of different terms of years, for different places in the same or in neighbouring regions, may, to some extent, be obviated. In addition to these two classes of averages, the averages deduced from long series of years are given for many places, such as London, 89 years; Turin, 74 years ; Bologna, 45 years ; Brussels, 38 years; Christiania, 31 years; Toronto, 27 years; Stykkisholm, 23 years; Hobart Town, 28 years, &c. A comparison of these with the other averages will give some indication of the true mean pressure of the atmosphere for different regions of the globe. But for a general survey of the geographical distribution of the mass of the earth’s atmosphere through the months of the year, the data, from which the isobaric lines of the charts have been drawn, may be regarded as sufficient. The closer approximations to the true mean pressure of the atmosphere, to be obtained from the accumulated observations of future years, will give the data for more detailed representations of the pressure of the atmosphere over different regions of the earth. Ifthe isobaric curves could be drawn true for every 0:025 inch, the disturbing influence of the Mediterranean, Black and Caspian Seas, and American Lakes; and of the Pyrenees, Alps, Dovrefeld, Himalayas, and other mountain ranges, would be more apparent. In every case, where possible, the means in the Table are the arithmetic means of the observations, reduced to-32° Fahr. only,—no corrections being AND THE PREVAILING WINDS OVER THE GLOBE. 577 applied for daily range or for height. For places, for which the means were obtained corrected for daily range, “red.” (meaning reduced to mean daily pressure), is entered in Table I. in the column of Houwrs of Observation. Those stations for which the means are reduced to sea-level are printed in ztalics. The next step was to apply to the figures in Table I. corrections (1) for daily range and (2) for height. So far as possible, that hour, or those hours, of observation were selected when the pressure of the atmosphere is nearly the mean of the day. For places for which this could not be done, a collection of Mean Hourly Variations of the Barometer was made from a considerable number of stations in different parts of the world. From these, approximate corrections for daily range were deduced, and applied to the monthly means of the stations. For reducing to sea-level, a table was prepared from the Formula and Table XVL, given in Guyor’s Meteorological and Physical Tables, D, p. 89. This table, calculated for each 5° Fahr. of the temperature of the air, from — 40° to 90°, was used in all cases where the height did not exceed 800 feet. For higher situations, the reduction was made by means of Dippr’s method, as detailed in Guyot’s Tables, D, p. 60. , The means,* so corrected, were then entered on large polar projections of the northern hemisphere, from which the dsobars were drawn for every tenth of an English inch of pressure. The isobars for the southern hemisphere were drawn on charts of MERcarTor’s Projection. The whole was ultimately transferred to charts of the projection on Plates XXV. to XXVII. The isobars, indicating a pressure of 30 inches, which is nearly the average pressure, and upwards, are represented on the charts by heavy lines, and lower pressures are represented by light lines. For many of the means I have been indebted to the labours and writings of Dove, Buys Batiot, Seccur, Cart JeLtinck, Moun, JAMES, QUETELET, and Kuprrer. For the means of single stations and groups of stations, I have received most valuable assistance from Meteorologists in all parts of the world, for which I beg to return them my grateful thanks. DISTRIBUTION OF ATMOSPHERIC PreEssuRE, in December, January, and February. —In these months, the highest pressures are grouped over the land portions of the northern hemisphere, and the larger the extent of the land the greater is the pressure. The area of high barometer (30 inches and upwards) embraces nearly all Asia; all Europe, south of the North and Baltic Seas; the North Atlantic, between 15° and 45° lat.; the West Indies; North America, except the north and north-west; and the North Pacific, between 8° and 24° lat. There are also two regions of high pressure of comparatively small extent—the one in the South Atlantic, and the other in the South Pacific. * The original observations are given in Table I. in preference to the corrected means deduced from them. 578 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE The regions of low pressure are the northern portions of the North Atlantic and of the North Pacific, including portions of the continents adjoining; the belt of low pressure in the equatorial regions, towards which the trade winds blow; and the remarkable depression in the Antarctic regions, which probably is subject to little variation throughout the year. In March, pressure diminishes over Asia, the middle and south of Europe, and the United States of America. Everywhere else, except in the tropics, it is rising. ‘This rise of pressure is most apparent in the temperate regions of the southern hemisphere. In the north of the Atlantic it is rapidly rising, the average pressure in Iceland now being 29°609 inches, thus showing an increase of 0-34 inch as compared with January. In April, the heavy lines showing a pressure above the average have now all but left Asia, Europe, and the United States, and the isobars of 30 inches bound a belt of high pressure which completely encircles the globe in the south tem- perate zone. Pressure continues to rise in the north of the Atlantic, and to the north of North America, and it is probable that a space of high pressure (at least 30 inches) surrounds the North Pole. In this month pressure is more equally dis- tributed over the globe than in any other month; for, excepting the Antarctic Ocean, it scarcely rises anywhere above 30:1 inches, or falls below 29°8 inches. In May, in the north of Europe, in Greenland, and in the north of America, atmospheric pressure attains the maximum of the year. Pressure continues to increase over the south temperate zone, and the zsobar of 30:1 inches now nearly extends round the globe. At this time the highest pressure in the southern hemisphere occurs in the south-east of Australia, where, at Deniliquin, it is 30°185 inches. Pressure is rapidly falling over Asia and the United States. In June, July, and August, pressure falls in the central regions of Asia to about 295 inches. In this season this great diminution of pressure, which may be regarded as absolutely determining the summer climates of Asia, reaches its lowest point. Pressure falls also in the interior of North America, where at Utah, Great Salt Lake, it is only about 29:7 inches. The annual maximum of the south temperate zone is attained in these months. The isobar of 30:1 inches goes completely round the globe, and a still higher pressure prevails over the south of Africa, and over those parts of the ocean immediately to the west and east of it. In these months the arrangement of the isobars may be regarded as being, generally speaking, reversed from that of December, January, and February, and on this account a comparison of these two groups of months is very instructive. From this period, pressures increase over the continents of the northern hemisphere, and diminish over the south temperate zone, till the distribution of pressure is regained, which has been already shown to prevail during the winter months. Jn September and October, an interesting feature of these lines is a very “ee ————— == —*" AND THE FREVAILING WINDS OVER THE GLOBE. O79 rapid diminution of the pressure indicated as taking place in the north of the Atlantic and adjoining regions. This is the season of the year when the first great decrease of temperature takes place, which is accompanied by heavy rains and furious storms. The increase of pressure in Sweden in October, taken in con- nection with the simultaneous decrease in Greenland, Iceland, north of Norway, and the British Islands, is interesting, as bearing on the transference of masses of the atmosphere from one region to another. In November, pressure rises considerably over the continents of the northern hemisphere, and falls in the south temperate zone; and the belt of low pressure in the equatorial regions may be regarded as now passing completely round the elobe. This belt, towards which the trades on each side of the equator blow, does not occur in the summer months in the Indian Ocean; but, on the contrary, there is a continuous diminution of pressure northwards, from Australia and Mauritius to the interior of Asia. It will be seen that in November, as compared with October, the isobars have advanced a little northwards from the British Isles to Iceland, and eastwards from Baffin’s Bay to Iceland, thus indicating a general increase of pressure over the north of the Atlantic and regions adjoining. Coincident with this increase of pressure, there occurs a diminution of pressure to the south-east of it, including Austria, Italy, and countries adjoining the Mediterranean; and in the Atlantic to the south of it, from about latitude 45° to 15° N. Probably these extensive oscillations of the pressure are parts of one general movement of the atmosphere, which in one of its manifestations has been long known to meteorologists under the name of the great November wave, but of which no very satisfactory account has yet been given. In addition to these changes in the monthly distribution of the pressure, it is probable that a system of low pressures traverses the continent of Africa, follow- ing the sun’s course ; but since the grounds of this supposition have been recently laid before the Society, in a paper on ‘‘ The Determination of Heights, chiefly in the Interior of Continents, by Observations of Atmospheric Pressure,” * it is not necessary to reproduce them here. The probable pressure for the months is shown on the separate charts. PrevalLinc Winps.—It will be seen that every one of the charts shows con- siderable disturbance of the equilibrium of the atmosphere at the surface of the earth. If the pressure was equal in all parts of the globe, we should have the physical conditions of a stagnant atmosphere. But such is not the case. From the different pressures which the charts show in different regions, it might be expected, from the laws of aérial fluids, that movements of the atmosphere would set in, giving rise to the prevailing winds of these regions. * Proceedings of the Roy. Soc, Edin. vol. vi. p. 465. VOL. XXV. PART I, 7L 580 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE To ascertain what relation may subsist between mean atmospheric pressure and prevailing winds, Table II. has beemprepared, which shows the mean number of days in each month winds from N., N.E., E., 8.E., 8., S.W., W., and N.W. have been observed to blow. In tropical and subtropical regions, a period of one or two years is sufficient to indicate the average direction, or the prevailing winds of the locality, owing to the steadiness with which the wind blows in these regions; but in temperate and polar regions a considerable number of years is indispensable. The direction of the winds has been generally obtained, or calculated, for the same years as the atmospheric pressure; but where such obser- vations could not be obtained, care was taken to include in the list only those places for which a sufficient number of years was available, so as to give a good average. As regards the stations in British North America, the shortness of the time during which, in each case, the observations were made, is to a great extent compensated for by the number of places at which observations have been made, and the comparative steadiness of the winds in these high latitudes of America. Valuable assistance was obtained from Professor Corrin’s elaborate “ Treatise on the Winds of the Northern Hemisphere,” though many averages given in this work could not be adopted, being based on an insufficient number of years,—a remark which applies extensively to averages of observations of the wind hitherto published. In selecting stations, a preference was given to those which are situated in comparatively level localities, with the view of obtaining as close an approxima- tion as possible to the true direction of the wind. To this there are, however, several exceptions, such as the stations in Norway and in Greenland, these places being given to illustrate the effect of mountain ranges in changing the mean direction of the wind. Stations at no great elevation above the sea were selected in different regions, it being evident that winds observed at great elevations are not suited to an inquiry into the movements of the atmosphere in relation to sea-level pressures. It will be observed that the time, or the duration of the prevalence of each wind (N., N.E., E., &c.), is the only element taken into account in this inquiry. The element of force has, for several reasons, been neglected :—(1.) The force of the wind has been less generally observed than the direction; and at very many places where the force has been observed, the observations, from the manner in which they have been made, do not give the materials for arriving at absolute results. (2.) It is well known that the velocity of the wind is retarded by the land as it passes across it; thus, for example, an anemometer on the west coast of the British Islés registers considerably more wind than one erected at an inland or eastern situation. Also, more wind is registered in rising above the surface of the earth. The effect of local situation on the velocity of the different winds is very great. Hence, whilst the amount of these disturbing influences are AND THE PREVAILING WINDS OVER THE GLOBE. 581 unknown, to attempt to determine the velocity of any general movement of the atmosphere from the observed velocity of the wind at Observatories could lead to no satisfactory result as regards the present inquiry. In the broad results aimed at in this comparison of atmospheric pressure and prevailing winds, it cannot affect the conclusions arrived at to assume, as is here done, that the mean velocities of winds from different directions are equal to each other. From the figures given in Table II. the mean direction of the wind has been calculated in the usual way. This direction is represented in the charts by arrows flying in the direction of the wind. In cases where the winds do not pre- ponderate from one quarter, but are nearly equally distributed over different points of the compass, an asterisk (*) is entered on the charts, which thus repre- sents variable winds ; when calms preponderate, a circle with a dot in the centre (©) is used. When two maximum directions are strongly indicated, or when the smaller one is very decidedly marked, instead of resolving the two into one intermediate, which would in many cases represent a wind which scarcely ever occurs at the time, the greater of the two is represented by the ordinary arrow, and the smaller in the more marked cases by a less arrow placed beside it. By this means an important feature in climate is represented. Thus two distinct sets of facts are exhibited on the charts, viz., lines showing the mean pressure of the atmosphere, and arrows showing the prevailing winds at the earth’s surface, each being independently arrived at by the summing and averag- ing of observed facts. What relation is there between these two classes of facts ? I Winbs within, or near, a space of Low Pressure.—Of this class, the best example is the low pressure which prevails in the north of the Atlantic and adjoining regions in the winter months. This region of low pressure is bounded to the S.W. by the high pressure of North America; to the S. by the high pressure in the Atlantic, about 30° lat. N.; to the S.E. by the high pressure in the interior of Asia. In January, the difference between the average pressure of Iceland and the interior of Asia is fully an inch. It is seen from the charts, that in Baffin’s Bay and east of the Rocky Moun- tains, as far south as 40° lat., the winds are N.N.W., N.W., and W.N.W. Cross- ing the Atlantic, winds in the British Islands, in France, and the north of Germany, are from W.S.W. to S.W.; in Denmark, 8.8S.W.; near Bergen, in Norway, S.; and at Christiansund and Hammerfest, S.S.E. The relation of these winds to the isobaric lines is the same as that which is illustrated by the winds in storms, in their relation to the isobaric lines of these storms. This has been already stated in a Paper by the author, published in the ‘“‘ Transactions of the Society,” vol. xxiv. Part i. p. 201, in the following words :—‘‘ The wind in storms neither blows round the centre of least pressure in circles, or as tangents to the concentric isobaric curves, nor does it blow directly towards that centre. It 582 MR ALEX BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE takes a direction intermediate, approaching, however, more nearly to the direc- tion and course of the circular curves than of the radii to the centre.” Or, according to Dr Buys Ba tor, the angle is not a right angle, but from about 60° to 80°. This relation is usually called “ Buys Batiot’s Law or THE WINDs.” Another well-marked depression is the low summer pressure in the interior of Asia; with reference to which, it is seen from the charts that the winds of Eastern Europe and Western Asia are from N.W. to W.N.W. and W.; at Ceylon, S.W.; at Shanghai, 8.E.; and on the Sea of Okotsk, N.E.; whilst in the interior, calms generally prevail. The behaviour of the winds, as regards the low pressure of North America, is exactly similar to that of the winds in Asia at this season. In all these cases the wind appears to flow round and in upon the space where pressures are low. Even in those instances where the depression over a limited space is com- paratively small, such as in Australia during the summer months, the winds observe the same course with respect to it. A well-known and remarkable diminution of pressure is that of the Antarctic regions; and though, except in Tasmania and the south of New Zealand, obser- vations are wanting at particular points for a sufficiently long time to give good averages, yet the concurrent testimony of sailors and the inhabitants of these regions all go to show that, at least on the outskirts of the region, winds are chiefly N.W. or W.N.W.—that is, they appear to flow in upon the space of low pressure. The low pressure in the equatorial regions, towards which the trades blow, is an illustration of the same principle. Winns within. or near, a space of High Pressure—The most prominent illus- tration of this is the high pressure in the interior of Asia in winter. It is seen from a single glance at the charts that the winds flow owt of this space in every direction. The same outflow is seen with respect to the less strongly marked, but still very distinct space of high pressure in North America; owing to the large number of stations available here, this principle is amply illustrated. The next most noteworthy area of high pressure occurs in summer between Africa and North America, out of which also the charts show the winds blowing in all directions towards and round upon the surrounding low pressures. The following mean pressures, in inches, at 32° and sea-level, occur in Australia in June :—At Brisbane, Queensland, 30:062 ; Sydney, 30°116; Melbourne, 30:173; Adelaide, 30°132; Freemantle, 30:121; and at Deniliquin, in the interior, on a branch of the Murray River, 30:217. Hence a higher pressure occurs at this season (winter) in the interior, and it may be inferred that it is greatest in the southern portion of the interior. The prevailing winds are these :—At Brisbane, 8.S.W.; Sydney, W. by N.W.; Melbourne, N.; Adelaide, N.E. by N.; Freemantle, N.E. by E.; in other words, the winds blow out from this space of high pressure. ‘Lhis behaviour of the winds with respect to spaces of high pressure differs in AND THE PREVAILING WINDS OVER THE GLOBE. 083 no respect from what occurs on particular days on which the isobaric lines present the same conditions of pressure. Mr Francis GAuTon first drew attention to this peculiarity, under the name of Anticyclones, by which name he intended to convey the idea that in cases of high pressure occurring over a limited area, the course of the winds is exactly the reverse of what is seen to prevail in cyclones in which the winds blow round and in upon a space of low pressure. The outflow of the air from a region of high pressure, and the zzflow upon a region of low pressure, appears to be reducible to a single principle, viz., the principle of gravitation. Given as observed facts the differences of pressure, it might almost be predicted, before calculating the averages, what the prevailing winds are. Indeed, so predominating is the influence of gravitation that it may be regarded as the sole force immediately concerned in determining the movements of the atmosphere. If there be any other force or forces which set the winds in mo- tion, their influence must be altogether insignificant as compared with gravitation. The effect of a mountain range interposed in the course of one of these great atmospheric currents is interesting. Of this, the best example is furnished by the mountain range of the Scandinavian peninsula, in its effect on the prevailing winds in winter. It will be observed that this mountain range lies between the low pressure about Iceland, and the high pressure in the interior of Asia. The following are the mean directions of the wind at different places in Norway in January, deduced from Table II., to which are added the winds at other points, courteously sent by Professor Moun :—Christiania, N.E.; Sandosund, N.N.E.; Lindesnes, N.E.; Mandal, N.E. by E. ; Lister, E.; Skudesnes, 8.S.E. ; Udsire and Bergen, S.; Christiansund, 8.8.E.; Villa, S.E.; Hammerfest, 8.E. by S.; and Vardo,S.W. Thus at Christiania, Sandosund, and Lindesnes, which lie on the east side of the south spur of the mountain range, the prevailing winds are N.E. or N.N.E.; at Mandal, at the extreme south point of Norway, the wind is N.E. by E., and calms also largely prevail; and at Lister, a little to the west, the wind is E.; along the whole west coast from Skudesnes to Hammerfest, near the North Cape, winds are chiefly S., 8.S.E., or S.E.; while at Vardo, to the east of the north spur of the mountain range, the prevailing winds are S.W. These directions are very much the directions water should take in flowing past and round a rock lying in the bed of the current; the Scandinavian mountains being in this case the obstacle which diverts the winds from what may called their normal course in flowing towards and round the low pressure in the north of the Atlantic. On the other hand, in July it is seen from the Chart (Plate XXVI.) that the lowest pressures occur in the interior of Asia, towards which there is an extensive aérial current from W.S.W., W., and N.W. over Europe and Western Asia. Here also the influence of the mountain system of Norway is very perceptible. The following are the prevailing winds in July:—Christiansund, N.W. by N.; Bergen, N.; Skudesnes, N.W.; Lindesnes, W.; Mandal, W. by S.W.; Sandosund, S.W. ; VOL. XXV. PART II. 7M 584 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE Christiania, S. Thus, this part of the great atmospheric current flows round the southern region of Norway, being N. at Bergen, thence in succession N.W. and W., and on rounding the coast becomes diverted intoa SW. and S. wind. The extraordinary deflection of the isothermal lines in the different months, as they cross Norway and Sweden, is doubtless to no inconsiderable extent occasioned by the opposite prevailing winds, which arise from the obstruction presented by the mountain range to the prevailing atmospheric currents of the seasons. The prevailing winds at Upernivik, Jacobshavn, and Godthaab, in the west of Greenland, appear to point to another principle. It will be seen from the Charts and the Table that the prevailing winds in the winter months at these stations are N.E. and E. instead of N. and N.N.W., which, from the analogy of the winds at other places, they might have been supposed to be. They are thus diverted a few points from their proper course in the direction of E., or, roughly speaking, into a direction which is perpendicular to the line of the coast; in other words, they follow the course of the ravines. The daily observations at the Greenland stations have been published by the Danish Academy of Sciences, from which the averages have been calculated. A large proportion of these winds are very light, being frequently marked 0 by the observers ; that is, they were too light to be represented by the scale for wind force in use (0 to 4.) Since the west coast of Greenland is bounded immediately to the east by a steep high mountain range covered with snow, it is probable that the direction of these winds is still further modified by the same causes which give rise to the well-known class of breezes peculiar to mountain districts, of which the Vent du Mont Blanc is an example. These breezes are caused by the cooling of the air in immediate contact with the high ground, which, thus acquiring greater density, flows down their slopes, and thence diffuses itself over the low ground as a surface wind of inconsiderable depth. The Greenland stations are in those very situations which expose them to this wind. It is in favour of this supposition that these easterly winds occur oftenest, and blow with greatest force in the afternoon, it being at this time of the day that the difference is greatest between the temperature of the low grounds and that of the snow-covered mountains; just as sea and land breezes are strongest at those hours of the day, when the difference of temperature is greatest between the sea and land. It will be observed that at St Helena the mean direction of the wind varies little from month to month,—being almost uniformly from S.E. or §.; and it will also be observed that the relative distribution of the pressure in neighbouring regions varies little from month to month. The result is one mean annual direction of nearly S.E. by S. At Mauritius there occurs a little variation from month to month. Thus, whilst in June, July, and August, the mean direction is about S.E. by E., in December, January, and February, it is nearly due E.; in other words, during the summer season the wind shifts a few points from S.E. by E. in AND THE PREVAILING WINDS OVER THE GLOBE. 585 the direction of N. This northing of the winds at Mauritius is exactly what should be expected to result from the proximity to the low pressures which prevail in South Africa at this season. This change in the mean direction of the wind being small, the mean annual direction may be regarded as E.S.H. Such slight variation, however, is limited to very few regions, for on examin- ing the number of days each wind (N., N.E., E., &c.) has on the mean of the year prevailed at the different stations in Table II., it will be observed that in almost every instance there are two maximum directions, the one being con- siderably greater than the other. These maximum directions may arise in two ways— 1st, At places such as Colombo, Ceylon, where the wind during summer is S.W., and during winter chiefly N.E., the two annual maximum directions are S.W. and N.E.; in like manner the maximum directions at all places in monsoon regions are occasioned. 2d, At Greenwich two maximum directions, from about S.W. and N.E., appear in the means of every month, from which it is evident that the wind at this place blows oftener, and remains longer, in these two directions than in any other. In cases where the less maximum arises from the prevalence of winds from that direction during a few months of the year, the isobaric charts of the separate months give a ready explanation of both maxima in the annual means. But at places where both maxima appear in the same months, it is evident that the isobaric charts can only furnish data towards the explanation of the greater maximum direction ; and it may be assumed as equally evident that the smaller maximum, of which the east wind of the British Islands is an illustration, can alone be legitimately discussed by daily synoptic charts of the weather. Towards the discussion of this and other questions of meteorology, the value of the Daily Synoptic Charts prepared and issued under the superintendence of M. LEVERRIER cannot be overrated.* There are 115 stations in Table II. situated in the north temperate zone. I have tabulated the two maximum directions at these stations where they occur according to sixteen points of the compass—viz., N., N.N.E., N.E., E.N.E., E., &c. of which the following Table shows the maximum directions most frequently observed :— Greater Max. Smaller Max. Maximum directions of wind are— S.W. N.E. at 16. stations. 99 bh) 9? N, 8 39 8 by) B. 4 B N.E. S.W, my Loan -, +h] ” 9 N.W. Ss E 39 6 +B > ?> 99 8. N. 9° as) 9° ) 99 ? W. N.E 3° 5 99 9° th) 39 N.W. S. 3° 4 39 bP} 9° 99 W. E. 9? 3 99 9 bb) 29 E. W. te) 3 99 3) 93 33 W.S.W. EK. be) 3 ” a 7 Fe W.S.W. S.E. eee * Atlas des Mouvements Généraux de l’Atmosphére pour 1864-5. 586 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE Thus the number of stations, at which the greater maximum direction of the wind is S.W., and the smaller, N.E., is 15. Further, if the whole 115 stations be examined, and those picked out at which the greater maximum direction is from any point between S.S.W. and W., and the smaller maximum from any point between N.N.E. and E., the number is found to amount only to 34, or less than 30 per cent. of the whole. Now, since these are the directions in which truly equatorial and truly polar atmospheric currents should blow, it is evident that these two currents, as often represented, are not the two prevailing winds generally observed over the north temperate zone. For if the two great currents of the atmosphere were, one flowing from subtropical regions towards the poles, and the other flowing from the poles towards the tropics, it is plain that a much larger percentage of the stations than 30 would follow the course of these currents in the north temperate zone. If to these 34 stations, at which the maximum directions are in the course of the equatorial and polar currents respectively, we add 17 stations, at which the greater maximum direction is from N.N.E. to E., and the smaller from 8.S.W. to W., the number of stations at which the two prevailing winds follow the course of these two currents is only 51, or about 44 per cent. of the whole—a proportion, it need scarcely be said, . which could not obtain, if it be the case that there is a general flow of the atmo- sphere at the surface of the earth in the northern hemisphere from the tropics towards the north pole, and from the north pole towards the tropics. Further, if the two maximum directions be separately examined, it is seen that the greater maximum direction being from any point of the compass from S.S.W. to W. occurs at 47 stations. WNW to Ne eas NN to 24 deme ESE. toS. nat DGiet, and the Jesser maximum direction being from any point from S.S.W. to W. occurs at 20 stations. W.N.W. to W. 99 22 bb] N.N.E. to 1D, ” 38 ”? E.S.E. to S. # eas Thus the chief prevailing winds in the north temperate zone blow from some point from S.S.W. to W. at 41 per cent. of the stations, leaving 59 per cent of the stations at which the prevailing winds are from other points of the compass; and the secondary prevailing winds come from some point from N.N.E. to E. at 34 per cent. of the stations, or only a third of the whole. Hence, as in the for- mer case, while the largest percentages of prevailing winds are in the directions in which truly equatorial and polar currents should blow, the percentages from other directions are so large as to preclude the supposition of a general flow of AND THE PREVAILING WINDS OVER THE GLOBE. 587 the surface winds of north temperate regions towards and from the polar regions. An examination of the isobaric and wind charts for the months shows, as has been already pointed out, that where there is a mean low pressure, such as occurs in the north of the Atlantic in the winter months, and in the centre of Asia in the summer months, thitherward the winds tend in all directions in an inmoving spiral course; and where there occurs a mean high pressure, as in the centre of Asia in winter, and in the Atlantic between Africa and the United States in summer, out of this space the winds flow in all directions, or they appear to be thrown out from the space of high pressure in a manner exactly the reverse from that by which they are drawn inward upon a space of low pressure. These spaces of low and high pressures may therefore be regarded as the true poles of the winds, which blow at the surface of the earth, towards which, and from which, the great movements of the atmosphere proceed. From the unequal distribution of land and water, it results that the poles of the pressure and movements of the atmosphere are, as in the case of the poles of temperature, very far from being coincident with the north pole. The causes which bring about an unequal distribution of the mass of the earth’s atmosphere may be considered to be chiefly two, viz., the temperature primarily ; and, secondarily, the moisture of the atmosphere, in their relations to the geographical distribution of land and water. From the relations of land and water to temperature, the summer temperature of continents greatly exceeds that of the ocean in the same latitudes. Hence the abnormally high temperatures which prevail in Asia, Africa, and North America during summer, in conse- quence of which the air becomes specifically lighter, and ascends, as from a furnace, in vast columns thousands of miles in diameter. In this way the summer pressure of continents is diminished, the amount of the decrease being greatest in Asia, the largest continent, and least in Australia, the smallest. At Barnaul, in Asia, the pressure in July is 0-418 inch below the annual average ;* whereas at Deniliquin, in Australia, the pressure in January is only 0:154 inch below the annual average: at Great Salt Lake, in North America, it is inter- mediate, being 0°333 inch. In the remarks which follow on the vapour of the atmosphere, the principles laid down in the two following extracts are assumed :—1. “ Air charged with vapour, or vaporised air, is specifically lighter than when without the vapour; or, in other words, the more vapour any given quantity of atmospheric air has in it, the less is its specific gravity.”}+ 2. “It appears, therefore, that the explanation suggested by Dr Jouz is correct; and that the condensation of vapour in ascend- * Some part of this diminished pressure in Asia is doubtless due to the condensation of the vapour of the south-west monsoon. ft Daxton’s Meteorological Observations and Essays, 2d ed. Memncliester 1834, p. 100. VOL. XXV. PART II. 7N 588 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE ing air is the chief cause of the cooling effect being so much less than that which would be experienced by the dry air.”* The influence of vapour in lowering the pressure is well illustrated by the low pressure in the tropics towards which the trades blow, this belt being characterised by a highly saturated atmosphere and heavy rains. Again, much more vapour is observed in the air at places near the shores of the north of the Atlantic in winter than at places in the same latitudes in the interior of continents. In Great Britain, as compared with the interior of Asia, the excess is great; and in the former case the skies are generally cloudy, and in the latter clear. Also, over the same region, the atmosphere of which abounds in vapour, the mean winter temperature is much higher than it is on the continent; and from the conclusion arrived at by Sir Witt1am Tuomson regarding the temperature of an ascending column of saturated air, the relatively higher temperature over such regions must continue to prevail up to very great heights. Hence, owing to the presence of a larger amount of vapour, and to a higher temperature, the air resting on the north of the Atlantic and regions adjoining is specifically lighter than in the continents which surround it; consequently the charts show an enormous diminution of pressure over this region, as compared with the continents. Similar depressions from like causes occur in the north of the Pacific and in the Antarctic regions. Since dry and cold air is, on the other hand, specifically heavy, we should expect that in the interior of continents, where temperatures are low and the air is dry in winter, that pressures would be high; and observations show (see the Charts) that the highest mean pressures occur in Asia and North America at this season. For the same reason, pressures are also highest in Australia, South Africa, and the south of South America in the winter months. There is another source from which atmospheric pressure is increased. It has been shown from the Charts that the tendency of the prevailing winds on the surface of the earth is to blow round and in upon the space where pressures are low, and out of the space where pressures are high. Now, since in this way vast volumes of air are poured into the space where pressure is low without increasing that pressure, and vast volumes flow out of the space of high pressure without diminishing that pressure, it follows that the air poured in is not allowed to accumulate over this space, but must escape into other regions; and that the air which flows out from the place of high pressure must have its place supplied by fresh accessions from above. The exchange indicated here is probably brought about in this way :—Since in winter, over the north of the Atlantic, the atmosphere is specifically lighter than in surrounding regions, there are here the conditions of an ascending current ; and it may be inferred that the ascent will continue until * Sir Wittram Tuomson in Mem. Lit. and Phil. Soc. Manchester, vol. ii. 3d series, p. 131. AND THE PREVAILING WINDS OVER THE GLOBE. 589 a height is attained at which pressures at that level are equal; thence the air will flow over, as an upper current, towards those regions which offer the least resistance to its course,—in other words, where the tension at that height is least: Over what part of the earth’s surface is the pressure of the air least at great heights? Evidently, that region over which the air is coldest and driest near the surface of the earth; because, being thereby densest, the great mass of the air is condensed or gathered together in the lower beds of the atmosphere, thus leaving less air, or a diminished pressure, in the upper regions. Thus the extra- ordinarily high pressure in Asia in winter will be due both to the low temperature and great dryness of the atmosphere, and to proximity to the regions of low pressure in the north of the Atlantic, the north of the Pacific, and in the, equatorial regions to the south; from which it may be inferred that upper cur- rents flow towards the centre of Asia, and that these upper currents compensate for the drain arising from the surface currents, which flow out of this space in all directions. In corroboration of this view, it is seen that while in winter the winds in India at low levels blow from some northerly point, at Dodabetta, on the Neilgherry Hills, 8640 feet high, the mean direction of the wind during winter is from about E.S.E.; and, on the other hand, while in summer winds blow from some southerly point at low levels, at Dodabetta they are almost wholly N.W. But by far the most striking illustration of this principle, is the high pressure in summer which prevails in the Atlantic, between Africa and North America. If the principle here suggested, as regulating the movements of the atmosphere, be correct, the following will be the explanation of this singularly high pressure :—Since, at this season, the temperature of the air resting on this part of the ocean is much lower than that of the land, it follows that the ascend- ing currents which rise from the heated plains of Africa, South America, North America, and Europe, and from the tropical belt of calms to the south, will, on reaching the upper regions of the atmosphere, flow over upon this part of the Atlantic, because the temperature being comparatively low in the lower beds, the air is condensed there, thus leaving less pressure in the upper regions. It may also be added, that since the surface winds of this region are constantly drawing away the air poured down upon it by the upper currents, extreme saturation of the atmosphere cannot take place; and hence the atmosphere is relatively cool and dry. The high pressure maintained in the South Atlantic, between Africa and South America in the summer of the southern hemisphere, corroborates this view. From these considerations, it may be concluded that the winds on the sur- face of the earth are approximately known from the isobaric lines,—the direc- tion being from regions of high towards those of low pressure, subject to the changes in the direction of the currents produced by the earth’s rotation; and that the upper currents of the atmosphere may be inferred from the isobaric lines 590 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE | taken reversely, together with the isothermal lines taken directly. In other words, the regionsof lowest pressure, by giving the ascending currents, point out the sources or fountains whence the upper currents flow; and the isothermals, by showing where, on account of the low temperature, the greater portion of the air is con- densed in the lower beds, and so diminishing the pressure in the upper beds, point out the regions towards and over which the upper currents diffuse themselves. 1. To travellers in the interior of continents and regions at a great distance from places where Meteorological Observations are made, the Charts will be of use in showing the approximate sea-level pressures for each month of the year. They show at a glance the ze70 points from which the heights of places may be calcu- lated, at which observations of the pressure of the atmosphere have been made.* 2. To sailors, the Charts will be useful as showing the prevailing winds at many places in each of the twelve months, and still further as suggesting, from the connection which is here pointed out between mean atmospheric pressure and prevailing winds, the winds which are most likely to be met with in regions where little is known of the general course of the winds from actual observations. The charts of least prevailing winds in January and July (Plate XXVIL.), will also be useful in this respect. The following illustration will show the method of using the Charts in apply- ing Buys Batuot’s Law or THE Winps. This law has been stated at the foot of page 581, but it may be more popularly expressed thus,—Stand with your back to the wind, and the low barometer will be to your left in the northern hemi- sphere; or, reversing it, stand with the high barometer to your right, and the Jow barometer to your left, and the wind will blow on your back. Suppose, during the summer months, a person at Lisbon to stand so, with reference to the high pressure in the Atlantic, and the low pressure in Africa, he should have a N.N_E. wind; and as he proceeded southward along the coast of Africa, the wind would wear more to eastward. On the north coast of South America, being between the high pressure of the Atlantic and the low pressure of South America, the winds should be about easterly; and on the north coast of Central America, the low pressure in the Pacific being now to his left, the winds should be about N.N.E. On passing through the West Indies towards Florida and the south-eastern States, as the influence of the low pressure in North America in its relations to the high ~ pressure in the Atlantic comes into play, the prevailing winds should gradually become E., E.S.E., 8., S.S.W., and S.W., and from this region to England to about W.S.W. These are, it need scarcely be said, the prevailing winds of these regions. * Note of the Determination of Heights, chiefly in the interior of Continents, from Observations — of Atmospheric Pressure.—‘ Proceedings of the Society,’’ vol. vi. p. 465. t In the southern hemisphere the low barometer will be to the right. AND THE PREVAILING WINDS OVER THE GLOBE. 599 Further, the Table of Winds shows a total absence of westerly winds on the north coast of South America, the winds there being almost always from N.E. to E. or occasionally S.E.; whereas, at Bermuda, the winds, while mostly S.W., are more distributed over the other points of the compass. The daily pressures charted in LEvERRIER’s ‘‘Atlas des Mouvements Généraux de l Atmosphére,” give a ready explanation of the winds of these two regions—pressures in the one case being comparatively steady, whilst in the other they are fluctuating. 3. Since winds bring with them the temperature and vapour of the regions they have traversed, it follows that the data mapped on the Charts may be considered as furnishing the key to the climates of the different parts of the globe, since the approximate temperature and rainfall of the different seasons may thereby be known. Between the monthly isobars and the rainy seasons of portions of Asia, Africa, America, and Australia, there is an obvious connection. The distribution of the pressure also explains the greater rainfall which occurs in Russia and other places in the interior of Europe in summer, as compared with the other seasons. For, if the winds of July in Table II. be compared with those in January at British, French. German, Russian, and other European stations, they will be found uniformly to show a shifting of the prevailing winds farther to the west and north,—a change, doubtless, arising from the low pressures in Asia in summer. The effect of this is, to draw over these parts of Europe, during the summer months, air-currents more directly from the ocean than in the other seasons, from which result a larger rainfall and greater fertility to these regions. The political importance even of such information will be seen when it is con- sidered, that if there had been two or more years’ Meteorological Observations, especially of atmospheric pressure and winds, at Aden, Massuah, and Suez, at the beginning of the Abyssinian war, the time of the commencement of the rainy season in Abyssinia could have been stated. The Charts of monthly isobars, the monthly isothermals, and the information tabulated in Table II., furnish materials from which more exact information regarding the climate of a particular place may be obtained. Thus, suppose it were required to know something of the climate of Shanghai, China. The mean temperature in January is about 40°, being nearly that of the west coast of Scotland; the isobaric lines show an increase of pressure from Shanghai in the direction of the interior of the continent; the winds for January are these :— Days each wind has prevailed Re Ee, Si SSW. WW. NW. Calm (January) at Shanghai, } 2 3 2 2 3 610 0 Thus the mean direction of the wind is nearly N.N.W.; and, since this wind comes from the continent, it may be concluded that it is dry, and, consequently, that very low temperatures are of certain occurrence. Again, since in nine days winds blow from N.E., E., §.E., and 8., or from the ocean, and these winds, especially VOL. XXV. PART II. ° 7 0 592 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE. from the §.E. and S., may be expected to be warm and moist, it may further be inferred, that the winter climate, so far as regards the two important elements of heat and moisture, is subject to great fluctuation. On the other hand, since the July mean temperature is about 80°, and in the same month the wind blows ten days from S.E. and fourteen from S., it may be concluded that the summer climate will be hot, stifling, and relaxing. These are shown, by observation, to be the peculiar characteristics of the climate of Shanghai in winter and in summer. 4. An inquiry of still greater interest is suggested by the isobaric lines of the Charts. Their position appears to be altogether determined by the geographical distribution of land and water on the surface of the earth; and since the isobaric lines determine the prevailing winds, and these in their turn the peculiar distri- bution of temperature and rainfall,—in other words, the climates of the globe,— it is evident that we have here a principle applicable not merely to the present state of the earth, but also to different distributions of land and water in past time. In other words, there is here a principle which the geologist will require to apply in attempting to account for glacial and warm epochs, through which the climates of great Britain and other countries have passed. In this way it is possible to arrive at an approximate numerical statement, as regards tempera- ture and rainfall, of Sir Cartes LYELL’s idea of the changes of climate brought about through the displacements of continents. The following instances will serve to illustrate the effect of the partial dis- placements of continents in changing climate. On examining the chart for July (Plate XXVLI.), it is seen that the fine summer climates of Western Europe, and of the Eastern States of America, are caused by south-westerly prevailing winds, which, having their origin in the region of high pressure in the Atlantic, possess, in admirable proportions, the genial qualities of warmth and moisture. Since these winds depend on the high pressure in the Atlantic between Africa and the United States, whatever would alter this arrangement of the pressure may be expected to change the character of the climates. Suppose, then, a displacement of the con- tinents, either of Africa or South America, so that land would occupy the place of the part of the ocean lying between Africa and the United States. With this new disposition of the land, it is plain that the high pressure in the Atlantic would disappear, and the spaces of low pressure in Asia, Africa, and North America would unite into one region of low pressure, stretching from the west of North America to the east of Asia. Simultaneously with this change in the pressure, the winds of the United States and Western Europe, including Great Britain, would become northerly, and, as a consequence, the summer climates of large portions of these regions would be so seriously deteriorated that the cultivation of cereals could not be attempted. Observations show that the lowest pressures which accompany the storms which traverse Europe, or the centres of these storms, pass eastward for the most ee SY. 2 ee AND THE PREVAILING WINDS OVER THE GLOBE 593 part, in a course lying somewhere between Iceland and Faro; as a consequence of this, and of the mean low pressure in the north of the Atlantic in the winter months, the prevailing winds in Great Britain at this season are south-westerly, and even in stormy weather the wind seldom veers further towards the north than N.W., and continues only for a short time in this quarter. To these con- siderations we owe the mildness and equableness of the winter climate of Great Britain. At Stykkisholm, in the north-west of Iceland, which lies on the north side of the storms’ path, the great preponderance of winds in the six stormy months, from October to March, are N.E. and E., as will appear from the follow- ing Table, which gives the number of days on an average of the three years, 1866-69, winds from the different points have blown during these six months :— Number of days the wind has blown N. N.E. E. S.E. Ne S.W. We N.W. Calm. eee Be Be BT years, viz., 1866-69, Suppose a change in the distribution of land and water took place in this part of the globe; on the one hand, land taking the place of sea to the west of a line drawn through Spitzbergen, the north of Norway, Faro, and the east of Newfoundland ; and, on the other hand, sea taking the place of land over part of the north of Africa, and over the comparatively low plains of Europe and Siberia, the following changes would take place in the distribution of atmo- spheric pressure in winter:—The high pressure over Asia would be reduced and contracted; the high pressure in North America would be increased and extended, so as to include Greenland ; and the low pressure round Iceland would be transferred to the south-east, so that the central space of least mean pressure would probably stretch from the north of France to the Gulf of Finland. Under these new conditions, mean pressure would increase greatly from the south of Great Britain towards the north-west, and thus northerly and easterly winds would become the prevailing winds in winter; and as the mean central track of storms would lie in a line from the north of France to St Petersburg, the winds accom- panying storms, particularly those in the rear of the storms, would be dry and intensely cold. Further, suppose the Gulf Stream, or any oceanic current from equatorial regions, to flow past Great Britain on its way to the Arctic Ocean, through the Baltic and White Seas, from the lower mean temperature which would be brought about by the now prevailing northerly winds, the vapour brought by the Gulf Stream would be precipitated no longer in the form of rain » but of snow, and frost would be of frequent occurrence. Since the heat of summer would be insufficient to melt this snow, it would accumulate from year to year; and thus the Gulf Stream, instead of ameliorating the climate, as at present, would only the sooner and more effectually, by accumulations of snow and ice, bring back to the British Islands the climate of the glacial epoch. 594 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE 1.—SHowine THE MEAN MONTHLY AND ANNUAL HEIGHT OF THE BAROMETER Note.—Under column of “ Hours of Observation” “red.” signifies that a correction has been applied for Daily Range, the p.m. after it. A Minus Sign before Latitudes signifies Latitude South, and before Longitudes, it Autho- ER Number Hours of Height Places. Country. ae ™ Specified, Observa- | Latitude. |Longitude.| in Ts 635. ears. tion. Feet. Stykkisholm, ‘ : Iceland 1 23 | 1846-68} noon | 65 4 |—22 43 37 Do., : ; do. 1 11 | 1857-67} noon | 65 4 |—22 43 37 Reykjavik, . ; 5 do. 2 13 | 1823-35| 8 or 9: | 64 40 |-22 0 36 Dor Soi) “athe do. 3 3 |1866-69| 9: 64 40|-22 0} 10 Eyafiord, . , : do. 4 2 | 1811-13 ? 66 0j—18 20 2 Thorshavn, . ‘ : Far6é 3 3 | 1866-69 9:9 G24 2 ie < 12 Armagh, . ; ; Treland 5 11 | 1857-67| 10:10] 54 21] -6 49] 210 Belfast, . do. 6 11 do, 9: 54 36] -—5 56 66 Dublin, : ; do. 7 22 |1831-52| noon | 53 22] —6 21} 162 Do., : : ; do. 8 11 1857-67| 92:31 | 53 22] —6 21 159 Monkstown, . : : do. 9 8 | 1859-66} 83:83 | 53 18] -6 8] 110 Cork, . : ; : do. 10 11 | 1857-67| 9:3 | 51 53} —8 38 25 Sandwick, . : : Scotland 3 11 do. 929 (59)? 25| Bais 94 Stornoway, . ' do. a 11 do. do. | 58 12] -6 21 a Tongwe,.- , j A do. 3 11 do. do. 58 30 - ee Culloden, . : s do. 3 11 do. do. 57 30] —4 104, Elgin, . : , , do. 3 11 do. do. 57 38 | —3 19 40 Aberdeen, . : , do. 5 11 do. do. 57 9| -2 7} 110 Braemar, . : : do. 3 11 do. do. 57, 0} —3 24) uaa Kettins, : ) : do. 3 11 do. do. 56 32] -3 16] 228 Barry, . : i do. 3 11 do. do. 56 31 | —2 44 38 Callion Mor, . do. 3 11 do. do. | 56 8| -5 30] 65 Glasgow, -. ~. : do. 3 11 do. do. 55 53| -4 18] 180 Nookton, . ; : do. 3 11 do. do. 56 11} -3 3 80 Smeaton, . : do. 3 11 do. do. 56 Oj] —2 40] 100 Thirlestane Castle, : do. 3 11 do. do. 55 43 | -2 45] 558 Milne-Graden, . ; do. 3 11 do. do. 55 Oj] —2 12] 103 Durham, . ; : England 11 11 do. 10:10) 54 46] —1 35] 352 Silloth, ‘ ; ; do. 12 11 do. 9:9 | 54 52| —3 23 28 Stonyhurst, ; do. 13 2 | 1848-68) ‘red. | 53° 51 | —2°28") gem Do., : : : do. 14 11 | 1857-67| 7:1,9 | 53 51] —2 28| 381 orks <<) 35 acca oak do. 15 11 do. red. |.53 58 | —1 i 50 Manchester, é , do. 15 11 do. 8:11] 53 39] -2 14] 123 Liverpool, . é do. 16 11 do. 71 | 53 25 | —2 &9 3a Derby, j ; : wkdge {7 11 do. 9:3 | 52 56] —1 28| 174 Holkham, . : ‘ do. 18 11 do. 9n3.. | 52.5 ay 0 48 39 Norwich, . : : do. 19 7 do. 10:3 -| 32- 3S 1 18 50 Cardington, gti do. 20 11 do. 9:3°°| 52 7 | +0 (2) eae Oxford, ; ; ; do. Si 515) 1d do. biho. | 51 46{ -—1 16] 210 Greenwich, . 3 fc do. 2 ia, elt do. red. 51 28 0 O| 159 London, ; ; : do. 23 89 Ries do. various | various |various Clifton, : : : Sac: 15 11 | 1857-67 do. ol 28 | —2 36 228 Worthing, . : : do. 15 11 do. do. 50 49 | —0O 22 34 Helston, ; : : do. 24 20 |1849-68|} 9:3,9 | 50 7) —5 16 106 | Do. ‘ ‘ : do. 24 11 1857-67| 9: 3,9 | 50 7) —5 16 106 Guernsey, . : : Channel Isles | 25,15] 11 do. 9:3 49 98'|} —2 32) |\seoge Hammerfest, ; : Norway 26 13 | 1848-60} 8: 2,8 | 70 40| 23 46 21 | AND THE PREVAILING WINDS OVER THE GLOBE. 595 REDUCED TO 32° Faur., IN ENGLISH INCHES, AT DIFFERENT PLACES OVER THE GLOBE. in all other cases no such correction has been applied; the Hours of the A.m. Observations are placed before the Colon [:], signifies Longitude West. The Observations are reduced to sea-level at all places which are printed in Italics. January.| Feb. | March.|. April. | May. | June. | July. | August.) Sept. |October.} Noy. Dec. Year. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. } Inches. 29-303 | 29-457 | 29-634 | 29-747 | 29-806 | 29-730 | 29-700 | 29-688 | 29-615 | 29-554 | 29-600 | 29-388 | 29.602 29-308 | 29-400 | 29-648 | 29-723 | 29-845 | 29-747 | 29-701 | 29-669 | 29-549 | 29-550 | 29-628 | 29-360 | 29.593 29-467 | 29-307 | 29-449 | 29-663 | 29-724 | 29-717 | 29-687 | 29-660 | 29-514 | 29-457 | 29-482 | 29-274 | 29.534 29-431 | 29-228 | 29-719 | 29-608 | 29-877 | 29-836 | 29-792 | 29-723 | 29-718 | 29-395 | 29-772 | 29-328 | 29.619 29-433 | 29-246 | 29-602 | 29.904 | 29-948 | 29-717 | 29-753 | 29-699 | 29-566 | 29-468 | 29-619 | 29-797 | 29-646 29-571 | 29-394 | 29-746 | 29-691 | 29-913 | 29.896 | 29-872 | 29-782 | 29.757 | 29-485 | 29-827 | 29-485 | 29-702 29-541 | 29-623 | 29-539 | 29-673 | 29-691 | 29-692 | 29-690 | 29-639 | 29-623 | 29-581 | 29-650 | 29-650 | 29-633 29-807 | 29-901 | 29-787 | 29-927 | 29-949 | 29.932 | 29-922 | 29-887 | 29-865 | 29-834 | 29-870 | 29-9Q0 | 29-882 29-684 | 29-693 | 29-752 | 29-747 | 29-796 | 29-732 | 29-772 | 29-751 | 29-754 | 29-688 | 29-600 | 29-747 | 29.726 29-678 | 29-759 | 29-640 | 29-777 | 29-789 | 29-796 | 29-795 | 29-740 | 29-734 | 29-681 | 29-757 | 29-775 | 29-743 29-761 | 29-873 | 29-730 | 29-955 | 29-915 | 29-899 | 29-944 | 29-857 | 29-847 | 29-798 | 29-814 | 29-882 | 29-856 29-813 | 29-934 | 29-823 | 29.894 | 29.932 | 29-998 | 29-959 | 29-929 | 29-909 | 29-833 | 29-881 | 29-933 | 29-903 29-535 | 29-661 | 29-574 | 29-774 | 29-820 | 29-786 | 29-753 | 29°697 | 29-658 | 29-642 | 29-716 | 29-620 | 29.686 29-523 | 29-660 | 29-580 | 29-743 | 29-788 | 29-776 | 29-748 | 29-688 | 29-634 | 29-628 | 29-700 | 29-628 | 29-676 29-586 | 29-690 | 29-639 | 29-809 | 29-840 | 29-820 | 29-808 | 29-739 | 29-698 | 29-697 | 29-798 | 29-704 | 29-736 29-534 | 29-665 | 29-564 | 29-758 | 29-788 | 29-764 | 29-732 | 29-673 | 29.631 | 29-617 | 29-705 | 29-636 | 29-672 29-627 | 29-752 | 29-652 | 29-836 | 29-867 | 29-840 | 29-803 | 29-750 | 29-732 | 29-697 | 29-779 | 29-718 | 29-754 29-598 | 29.730 | 29-614 | 29-793 | 29-830 | 29-802 | 29-759 | 29-715 | 29-692 | 29.663 | 29-747 | 29-704 | 29-721 28-494 | 28-607 | 28-495 | 28-678 | 28-709 | 28-703 | 28-684 | 28-628 | 28-611 | 28-589 | 28-647 | 28-592 | 28-620 29-495 | 29-610 | 29-494 | 29.668 | 29-688 | 29-665 | 29-632 | 29-584 | 29-571 | 29-548 | 29-635 | 29-600 | 29-599 29-700 | 29-828 | 29-708 | 29-883 | 29-905 | 29-885 | 29-839 | 29-795 | 29-776 | 29-763 | 29-847 | 29-832 | 29-813 29-617 | 29-730 | 29-624 | 29-786 | 29-803 | 29-777 | 29-778 | 29-722 | 29-704 | 29-676 | 29-771 | 29-721 | 29-726 29-534 | 29-641 | 29-515 | 29-694 29.712 | 29-694 | 29-677 | 29-622 | 29-606 | 29-581 | 29-668 | 29-615 | 29-630 29-682 | 29-803 | 29-674 | 29-853 | 29-876 | 29-853 | 29-825 | 29-780 | 29-770 | 29-749 | 29-820 | 29-788 | 29-789 29-651 | 29-769 | 29-646 | 29-835 29-850 | 29-826 | 29-803 | 29-750 | 29-744 | 29.717 | 29-786 | 29-765 | 29.762 29-171 | 29-288 | 29-157 | 29-328 | 29-365 | 29-34] | 29-314 | 29-261 | 29.249 | 29.228 | 29-293 | 29-269 | 29.274 29-675 | 29-793 | 29-650 | 29-823 | 29-846 | 29-811 | 29-793 | 29-747 | 29.736 | 29-712 | 29-778 | 29-768 | 29-761 29-415 | 29-530 | 29-379 | 29-560 | 29-555 | 29-559 | 29-510 | 29-500 | 29-500 | 29-460 | 29.523 | 29-524 | 29-501 29-739 | 29-860 | 29-714 | 29-880 | 29-895 | 29-896 | 29-868 | 29-818 | 29-823 | 29.772 | 29-850 | 29-858 | 29-831 29-457 | 29-499 '| 29-438 | 29-486 | 29-513 | 29-520 | 29-510 | 29.478 | 29.523 | 29-408 | 29-481 | 29-453 | 29-481 29-411 | 29.497 | 29-341 | 29-491 | 29-516 | 29-514 | 29-503 | 29-466 | 29.459 | 29-403 | 29-487 | 29.496 | 29-465 29-770 | 29-865 | 29-701 | 29-866 | 29-868 | 29-867 | 29-842 | 29-806 | 29-830 | 29-773 | 29-847 | 29-886 | 29-827 29-736 | 29-832 | 29-671 | 29-822 | 29-836 | 29-830 | 29-813 | 29.781 | 29-781 | 29-733 | 29-805 | 29-839 | 29-790 29-834 | 29-922 | 29-776 | 29-927 | 29-939 | 29-938 | 29-931 | 29-881 | 29-889 | 29-827 | 29-867 | 29-932 | 29-889 29-688 | 29-769 | 29-589 | 29-750 | 29-758 | 29-770 | 29-756 | 29-716 | 29-723 | 29-662 | 29-734 | 29-788 | 29.725 29-870 | 29-950 | 29-763 | 29-908 | 29-922 | 29.914 | 29-905 | 29-870 | 29-882 | 29-840 | 29.914 | 29-984 | 29.894 29-906 | 29-975 | 29-807 | 29-979 | 29-973 | 29.971 | 29-958 | 29-904 | 29-950 | 29-894 | 29-955 | 30-008 | 29-940 29-806 | 29-880 | 29.705 | 29-852 | 29-860 | 29.863 | 29-858 | 29-824 | 29-844 | 29-777 | 29-858 | 29-905 | 29.836 29-699 | 29-779 | 29-598 | 29-745 | 29-749 | 29.761 | 29-753 | 29-721 | 29-733 | 29-666 | 29-737 } 29-800 | 29-728 29-760 | 29.829 | 29-650 | 29-792 | 29-793 | 29-810 | 29-814 | 29.778 | 29-794 | 29-721 | 29-790 | 29-853 | 29-782 29-947 | 29-962 | 29-959 | 29-941 | 29-965 | 30-001 | 29-967 | 29-982 | 29-975 | 29-909 | 29-904 | 29-943 | 29.955 29-668 | 29-744 | 29-572 | 29-709 | 29-716 | 29-730 | 29-731 | 29-696 | 29-704 | 29-628 | 29-7035 | 29-764 | 29-697 29-926 | 29-967 | 29-797 | 29-933 | 29-934 | 29.947 | 29.965 | 29-925 | 29.931 | 29-869 | 29-937 | 29-988 | 29-926 29-810 | 29-986 | 29-857 | 29-863 | 29-866 | 29-929 | 29-924 | 29-900 | 29-903 | 29-796 | 29-856 | 29-893 | 29-882 29-849 | 29-919 | 29-772 | 29.886 | 29-888 | 29-930 | 29-932 | 29-899 | 29-893 | 29-796 | 29-867 | 29-947 | 29-882 29-777 | 29-789 | 29-651 | 29-766 | 29-759 | 29-811 | 29-819 | 29-788 | 29-780 | 29-695 | 29-737 | 29-836 | 29-767 29-515 | 29-366 | 29-614 | 29-726 | 29-798 | 29-728 | 29-726 | 29-682 | 29-651 | 29-568 | 29-594 | 29-478 | 29-620 VOL. XXV. PART II. 7P 596 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE MEAN MonTHLY AND ANNUAL HEIGHT Autho- Number a Hours of Heigh Places. Country. ae, Years | Observa- Latitude. |Longitude. in Hag pisces Years. | 5P eeified. tion. _ Feet. Alten (at 32°?) . - Norway 27 12) SHS37=48') 9.309% 69) 58) |eecoeee 2 Christiansund, . ‘ do. 28 8 |1861-68| 8: 2,8 | 63 7 7 45 65 Alesund, . ; : do. 28 8 do. do. 62 29 6°59 32 Bergen, ; : : do. 28 8 do. do. 60 24 5 20 50 Skudesnes, : ; do. 28 8 do. do. 59 9 5 16 37 Mandal, . ; : do. 28 8 do. do. 58 2 7 27 54 Sandésund, . ; : do. 28 8 do. do. DU AEeO 10 27 41 Christiania, . . . do. 29 31 | 1837-67 |7,9:2,4,10} 59 55 10 44 74 « Do.sthye : ; do. 29 11 | 1857-67] do. do. do. 74 Do., 3 : . do. 28 8 |1861-68| do. do. do. 74 Haparanda, . : : Sweden 30 7% | 1859-66 Bi: 65 50] 24 11 0 Umea, ‘ ‘ ; do. 30 8 do. do. 63 50] 20 17 0 Hernésund, . ‘ : do. 30 8 do. do. 62° 438% 27ase 0 Goteborg, . ; a do. 30 7% do. do. 57. 42) 1168 0 Wishy helknt pLade do. 30 74| do. do. | 57 39| 1819] 39 Jénk6éping, : do. 30 8 do. do. 57 47 | 14 11 | 292 Kalmar, : ; ; do. 30 8 do do 56 40 16 21 0 Carlshamm, . ; : do. 30 8 do do 56 10] 14 52 0 Orebro, -do. 30 8 do do 59 _ 16 15 13 97 Upsala, : ; do. 31,30| 11 |1857-67| 7 or 8: | 55 52) 17 38 77 Do. 5 d : do. 31, 30 8 | 1859-66 8 55 52 17 32 77 Copenhagen, d : Denmark 32 11 | 1857-67] noo 55 41) 12 35 12 Biyjehes,. & loF8 +426, do. 33 11 do. 6: |54 19] 10 20 7 Groningen, . ; ; Netherlands 33 11 do. S: 2 NVR" “as 6 34 49 Leeuwarden, . : do. 33 25 | 1843-67) 8: 2,8 | 53 12 5 47 24 Do., e : 5 do. 33 11 1857-67 8:2 53. 12 5 47 24 Utrecht, . Z do. 33 20 | 1849-68 Bie 52 5 anes 44 Do., : < : do. 33 11 1857-67 8:2 52 5 Dein 44 Flushing, . . : do. 33 11 do. do. 51 26 3 35 0 Luxemburg, : ; do. 33 11 - do. do, 49 37 6 8 | 1020 | Maestricht, : ! do. 33 11 do. do. 50 52 5 37 | 174 Brussels, . : 5 Belgium 34 35 |1833-67| noon | 50 51 4 22] 186 Do., : : ; do. 34 11 | 1857-67 do. 50 51 4 22 186 Liege, Sat Pras gies do. 34 | 20 |1847-66| do. | 50 41| 5 23] 199 Namur, : : : do. 34 13 | 1849-63 do. 50 28 4 51 491 Metz, . : ‘ : France 35 22 | 1825-46] do. AD cod 6 10] 595 Paris, : F : do. 35 30 | 1816-45 do. 48 50 2 20 216 Dor. ¢ 5 é do. 36,37), 11 1857-67 do. 48 50 2 20 216 Strasburg, . : : do. 4 15 2 at 48 36 7 42| 460 Dijon, : ‘ . do. 38 23 | 1845-67) noon | 47 19 5 2] 806 Do., : ; : do. 38 11 | 1857-67 do. do. do. 806 Ahun, : : : do. 39 38 | 1828-65 2. 46. 210 2 0 | 147 Lyon, : 3 : do. 39 6 | 1861-66 oe 45 46 4 49 636 Toulouse, . : : do. 40 22 | 1839-60 |9.12:3,6,9| 43 37 1 28 | 650 St Rambert, : . ~ do. 41 G 11838-43075 lf toed, 5 26 | 1017 Alais, ; i : do. 35 35 |1802-36| noon | 44 7 4 4 2 Orange, 4 ¢ 5 do. 35 36 | 1813-48] 9:3 44 8 4 48 149 Montpellier, : . do. 42 7 |1857-63| noon | 43 36 3 54 | 193 Bordeaux, . . . do 93 | 10 |1847-56| :2 |44 50|-035| 75] Oviedo, ; ; . [Spain & Portugal] “40 11 | 1852-62 |9, 12: 3,9| 43 24 |-10 29) 718 | AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 29-712 29-544 29-630 29-634 29-717 29-733 29-741 29-753 29-732 29-693 29-663 29-659 29-675 29-787 29-801 29-497 29-863 29-900 29-716 29-713 29-680 29-875 29-888 29-882 29-887 29-894 29-896 29-918 29-977 28-926 29-819 29-766 | 29-773 oe Lid 29-567 29-400 29-808 29-800 29-587 29-179 29-201 28-430 29-413 29-402 28-983 29-673 29-867 29-878 29-937 29-229 Feb. Inches. 29-653 29-595 29-686 29-693 29-788 29-788 29-772 29-729 29-790 29-682 29-811 29-775 29-758 29-836 29-818 29-508 29-835 29-882 29-741 29-766 29-716 29-936 29-954 29-926 29-909 29-963 29-971 29-969 30-032 28-953 29-863 29-778 29-835 29-764 29-650 29-370 29-762 29-840 29-615 29-194 29-221 28-436 29-362 29-359 28-881 29-623 29-825 29-878 30-007 29-217 Mar. Inches. 29-754 29-619 29-694 29-674 29-745 29-725 29-745 29-770 29-676 29-697 29-774 29-702 29-678 29-733 29-740 29-410 29-738 29-732 29-670 29-676 29-652 29-776 29-761 29-747 29-886 29-780 29-886 29-780 29-843 28-768 29-666 29-746 29-641 29-690 29-575 29-367 29-762 29-650 29-567 29-115 29-025 28-416 29-158 29-341 28-968 29-619 29-823 29-756 29-956 29-215 April. Inches. 29-856 29-764 29-843 29-823 29-894 29-855 29-856 29-813 29-796 29-788 29-850 29-828 29-836 29-938 29-925 29-589 29-912 29-948 29-834 29-792 29-833, 29-909 29-922 29-910 29-909 29-934 29-916 29-930 29-985 28-894 29-812 29-743 29-770 29-685 29-520 29-286 29-708 29-753 29-526 29-100 29-135 28-388 29-362 29-278 28-882 29.553 29-762 29-741 29-870 29-185 May. Inches. 29-892 29-843 29-902 29-859 29-934 29-898 29-897 29-831 29-835 29-812 29-838 29-850 29-850 29-892 29-872 29-613 29-922 29-966 29-848 29-855 29-842 29-947 29-959 29-914 29-933 29-941 29-915 29-934 29-993 28-886 29-796 29-758 29-763 29-697 29-532 29-310 29-723 29.735 29-533 29-108 29-113 28-435 29-316 29-290 28-904 29-548 29-788 29-735 29-901 29-175 June. Inches. 29-802 29-788 29-855 29-832 29-890 29-843 29-827 29-734 29-777 29-756 29-832 29-822 29-513 29-848 29-863 29-560 29-869 29-903 29-791 29-816 29-790 29-914 29-927 29-914 29-940 29-941 29-951 29-945 30-020 28-938 29-819 29-786 29-791 29-733 29-540 29-366 29-780 29-786 29-612 29-172 29-173 28-522 29-355 29-366 28-976 29-601 29-840 29-787 29-980 29-261 VOL. XXV. PART II. July. Inches. 29-781 29-710 29-780 29-752 29-792 29-764 29-730 29-691 29-696 29-670 29-694 29-693 29-697 29-781 29-772 29-511 29-810 29-872 29-704 29.692 29-695 29-857 29-848 29-894 29-932 29-922 29-954 29-934 30-009 28-953 29-815 29-795 29-794 29-745 29-575 29-376 29-771 29-796 29-590 29-192 August. Inches. 29-808 29-686 29-749 29-721 29-772 29-756 29-745 29-726 29-718 29-686 29-740 29-700 29-680 29-756 29-750 29-470 29-780 29-844 29-681 29-734 29-684 29-873 29-906 29-878 29-913 29-898 29-925 29-914 29-981 28-928 29-800 29-779 29-767 29-725 29-567 29-359 29-767 29-768 29-606 29-179 29-164 28-5395 29-366 29-381 29-022 29-602 29-870 29-792 29-993 29-287 Sept. Inches. 29-771 29-701 29-768 29-749 29-800 29-795 29-800 29-797 29-765 29-753 29-778 29-748 29-749 29-842 29-870 29-564 29-865 29-874 29-767 29-792 29-772 29-937 29.949 29-918 29-979 29-938 29-970 29-949 30-005 28-965 29-843 29-794 29-802 29-761 29-603 29-352 29-754 29-800 29-631 29-201 29221 28-509 29-395 29.355 28-965 29-621 29-829 29-812 29-973 29.281 | October. Inches. 29-698 29-666 29-737 29-737 29-796 29-812 29-831 29-736 29.772 29-776 29-792 29-778 29-795 29-894 29-906 29-599 29-921 29-961 29-818 29-805 29-817 29-921 29.919 29-871 29-867 29-894 29-886 29-894 29-941 28-902 29-776 29-728 29-739 29-686 29-524 29-383 29-757 29-728 29-573 29-157 29-158 28-464 29-316 29-329 28-949 29-544 29-862 29-807 29-919 29-208 Nov. Inches. 29-668 29-630 29-713 29-705 29-776 29-764 29-772 29-756 29-806 29-717 29-771 29-776 29-745 29-841 29-865 29-548 29-870 29-907 29-793 29-795 29-786 29-918 29-937 29-910 29-911 29-930 29-928 29-938 29-989 28-910 29-815 29-741 29-781 29-705 29-560 29-315 29-721 29-775 29-563 29-156 29-146 28-414 29-339 29-321 28-875 29-611 29-827 79-772 29-978 29-153 Dec. Inches. 29-662 29-583 29-678 29-701 29-788 29-800 29-799 29-789 29-803 29-745 29-725 29-740 29-725 29-886 29-886 29-594 29-917 29-943 29-797 29-787 29-785 29-947 29-907 29-973 29-969 29-985 29-981 29.989 30-052 28-989 29-897 29-835 29-860 29-776 29-611 29-409 29-804 29-869 29-548 29-227 29-218 28-494 29-366 29-421 29-085 29-597 29-884 29-886 30-024 29-239 597 Year. Inches. 29-755 29-677 29-753 29-740 29-808 29-794 29-793 29-760 29-764 29-731 29:772 29-756 29-750 29-836 29-839 29-539 29-858 29-894 29-763 29-769 29-754 29-901 29-906 29-894 29-919 29-918 29-928 29-925 29-985 28-918 29-810 29-771 29-776 29-724 29-567 29-357 29-759 29-775 29-580 29-165 29-164 28-467 29-342 29-353 28-958 29-600 29-836 29-805 29-970 29-231 7Q 598 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE Mean MontTHLY AND ANNUAL HEIGHT Autho- é -,. _ \Number Hours of Height Places. Country. 2 a ee Observa- | Latitude. |Longitude.]in Eng. z nee Years. eect tion. Rese arte Barcelona, Spain &Portugal] 33 4 | 1864-67; 7or8: | 41 22 2 9 ? Oporto, do. 43 5, | R863-67))- 9:3 41 9 | —8 27 278 Madrid, do. 40 9 | 1853-62 ic 40 24) —3 52 | 2149 Lisbon, do. 43 11- | 1857-67 |9, 12:3,9| 38 43] -—9 8 336 Alicante, do. 33 4 | 1864-67] 7 or8 38 21 | —O 25 ? San Fernando, do. 33 9 | 1859-67 do. 36 27) -—6 13 ? Gibraltar, do. 44 6 | 1853-59) 93:32 | 36 6) —5 21 46 Gibraltar, do. 45 3 |1864-66| 9:3 36 6| —5 21 50 Zurich, Switzerland 46 10 | 1837—46 |9,12:3,9| 47 22 § 32 | 1432 Geneva, do. 40 25 |1836-60| biho. | 46 12 6 9 | 1335 Do., F : do. 47 11 |1857-67| noon | 46 12 6 9 | 1335 Great St Bernard, do. 47 11 do. do. 45 51 7 11 | 8174 Trient, : Italy 48 11 | 1856-66| various | 46 4/{ 11 4] 622 Udine, do. 40 40 | 1803-42 92: AO. ei 13 14 393 6, 12: Milan, ‘ do. 48 16 | 1848-53 \° | 45 28 9. 9| 482 6, 12:3 Verona, do. 40 7 |1854-60| 8: 2,8 | 45 27/].1059) 186 sr: 2:9 Venice, do. 48 10} | 1853-63 or 45° 26% T1217 66 6: 2, 10 Turin, do. 40 74 | 1787-1860 ? 45 4 741 /] 915 Brescia, do. 40 27 | 1818-44} sr: 12:ss| 45 32 | 10 13 |) ag2 Bologna, do. 40 45 | 1814-58 e 44 30/ 11 21] 244 Genoa, do. 4 10 “4 ? 44 25 8 55 | 157 Do., do. 40 2 |1860-61/9,12:3,9| do. do. 157 Rome, do. 40 10 | 1852-61 73 41 54 12 28 163 Rome, . do. 40 15 | 1852-66 74 do. do. 163 Naples, do. 40 28 | 1833-60 93: 40 52 14 15 482 Palermo, do. 55 78 | 1791-1868 | various | 38 7 13 21 237 Do. do. 55 11 | 1857-67 do. do. do. 237 1853-55,|),, g Malta, do. 44 6 { 1858-59 lox 34 | 35 54 14 31 232 Malta, do. 45 2 |1865-66| 9: 3 35 «54 14 30 111 Bodenbach, . Austria 48 19 | 1848-66] 6:2,10/ 50 46] 1410] 466 Prague, do. 48 19 do. do. 50) 5 | 14-23 4668 Do., do. 48 11 | 1857-67 do do. do. 660 Krakau, do. 48 19 | 1848-66) do 50 49) 19.55 | e7G8 Do., do. 48 11 | 1857-67 do. do. do. 708 Troppau, do. 48 7% | 1858-65| do 49 56| 17 52| 847 _pe |f 60r7:2, Lemberg, do. 48 17 | 1850-66 19 or 10 49 50] 24- 0 | ' 928 Do., do. 48 | 11 | 1857-67 peat ay do. | do. | 998 Brunn, do. 48 19 | 1848-66) 6: 2,10} 49 I1 16 35 697 Vienna, do. 48 19 do. do. 48 12 16 20 638 Do., : do. 48 11 | 1857-67 do. do. do. 638 Kremsminster, do. 48 19 |1848-66| do. 48 3 14 6 | 1258 Debreczin, . do. as | 11 |1857-67 se ee 47 32] 2139] 417 \ . | Ofen (Buda), do. 48 10. | 1856-66] 6:2,10 | 47-31] 19 1] 420mm Klagenfurt, do. 48 19 | 1848-66) 7:2;9 | 46 37] 14 16 | 1438] Szegedin, do. 48 12 |1853-66| 6:2,10| 46 15] 20 6] 276) AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 30-024 29-748 27-835 29-828 30-138 30-170 30-082 30-138 28-504 28-630 28-660 22-062 29-434 29-629 29-523 29-756 29-975 29-077 29-487 29-776 29-863 29-857 29-849 30-040 29-545 29-720 29-735 30-096 29-883 29-515 29-327 29-325 29-282 29-295 29-166 29-014 29-011 29-298 29-378 29-384 28-702 29-602 29-647 28-491 29-757 Feb. Inches. 30-056 29-825 27-836 29-773 30-134 30-111 30-018 30-002 28-434 28-584 28-670 22-112 29-407 29-655 29-504 29-760) 29-970 29-068 29-441 29-764 29-813 29-787 29-798 29-989 29-503 29-718 29-734 29-915 29-825 29-472 29-288 29-355 29-208 29-297 29-120 28-952 29-027 29-235 29-320 29-388 28-664 29-592 29.604 28-427 29-709 May. Inches. 29-985 29-634 27-739 29-665 30-020 30-000 30-017 29-965 28-430 28-538 28-565 22-227 29-289 29-569 29-392 29-634 29-872 29-112 29-406 29-666 29-774 29-796 29-760 29-961 29-519 29-693 29-680 29-973 29-854 29-428 29-221 29-240 29-189 29-120 29-053 28-917 28-939 29-170 29-241 29-265 28-602 29-430 29-476 28-371 29-593 June. Inches. 30-016 29-747 27-816 29-735 30-091 30-091 30-075 30-015 28-520 28-626 28-630 22-337 29-311 29-590 29-438 29-749 29-890 29-166 29-424 29-705 29-804 29-800 29-817 29-993 29-582 29-729 29-705 30-016 29-846 29-449 29-253 29-265 29-211 29-219 29-053 28-943 28-932 29-202 29-281 29-290 28-661 29-415 29-491 28-424 29-644 July. Inches. 30-004 29-754 27-830 29-747 30-064 30-044 30-050 29-998 28-536 28-650 28-658 22-394 29.322 29:576 29-445 29-741 29-915 29-176 29-415 29-701 29-779 29-751 29-813 29-989 29-572 29-714 29-718 30-031 29-808 29-471 29:267 29.258 29-220 29-219 29-061 28-936 28-937 29-211 29-297 29-297 28-683 29-427 29-508 28-440 29-625 Sept. October. Nov. 599 Year. Inches. 30-071 29-762 27-741 29-745 30-123 30-056 30-080 30-042 28-516 28-634 28-676 22-377 29-387 29-630 29-496 29-815 29-972 29-176 29-450 29-760 29:786 29-823 29-850 30-032 29-589 29-743 29-753 30-060 29-903 29-526 29-332 29-337 29-300 29-322 29-094 29-043 29-047 29-287 29-360 29.376 28-715 29-558 29-570 28-496 29:745 Inches. 29-941 29-622 27-825 29-672 30-012 30-013 30-076 29-928 28-504 28-605 28-613 22-254 29-356 29-631 29-481 29-733 29-944 29-117 29-450 29-756 29-798 29-933 29-845 30-016 29-567 29-728 29-715 30-045 29-839 29-479 29-290 29-305 29-282 29-307 29-133 29-040 29-054 29-251 29-330 29-349 28-667 29.544 29-609 28-456 29-780 Inches. 30-024 29-741 27-752 29-678 30-127 30-079 29-995 30-047 28-434 28-570 28-618 22-146 29-362 29-624 29-446 29-686 29-928 29-068 29-441 29-756 29-753 29-774 29-766 29-949 29-520 29-713 29-695 29-996 29-896 29-489 29-286 29-323 29-246 29-298 29-111 29-023 29-036 29-240 29-320 29-364 28-652 29-568 29-606 28-431 29-735 Inches. 30-015 29-723 27-834 29-731 30-077 30-068 30-056 30-010 28-489 28-601 28-629 22-218 29-350 29-604 29-458 29-729 29-928 29-109 29-435 29-729 29-800 29-806 29-808 29.989 29-539 29-709 29-703 30-019 29-856 29-474 29-278 29-285 29-235 29-246 29-083 28-972 28-979 29-231 29-311 29-325 28-663 29-502 29-555 28-431 29-686 600 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT ~ Autho- oe Number Hours of Height Places, . Country. se pate et ete FL pitas Latitude. |Longitude. a an: ° / cme Agram, : : ; Austria 48 8 \ saris i fie 45 49 | 15 53] 448 Hermanstadt, . : do. 48 16 |1851-66| 6:2,10 | 45 47 | 24 7 | 1354 Do., ’ : do. 48 11 | 1857-67| do. do. do. 1354 Trieste, A ° - do. 48 -19 | 1848-66] 7:2,9 | 45 39 13 44 79 Do., ; ; s do. 48 11 | 1857-67) do. do. do. 79 6 or7 Pancsova, . : ; do. 48 7 | 1860-66 f or | 44 50] 20 35| 224 8 or 9 6 or 7: | Lesina, : : do. 48 9 | 1858-67 (2 9 at 430c11)| , 06325 63 10 Munich, . ; 4 Bavaria 49 10 |1857-66| hourly | 48 9] 11 34 | 1676 Memel, : ; Prussia, &c. 50 7 | 1861-67 | 622,10 (959344) Obes ? Kénigsberg, : ; do. 50 10 |1858-67| do. 54 43] 20 29 72 Dopey ee : : do. 50, 33 7 |1861-67| do. do. do. 72 Danizig, . ; . do. 4 32 ? do. a4 21 18 41 30 Do., : . : do. 50 7 |1861-67| do. do. do. 30 Putbus, : : : do. 50233) Ll }) 1857-67 do. 54 22 1335 173 Coslin, a : . do. 50 7 | 1861-67 do. 54 12 16 15 128 Stettin, . ’ , do. 50 if do. do. 53 25 | 12.30 49 Bromberg, . 4 do. 50 7 do. do. 53. 8| 18 0 | “246 Berlin, ; ‘ : do. 502331 lel 1857-67 do. 52 30 13. 3 153 Do., : : do. 50 7 |1861-67| do. do. do. 153 Posen, ‘ ; : do. 50 7 do. do. 52 25 | 17 5 | 28% Halle, : : ; do. 50 Z do. do. 51 30] 11 57 | 372 Weipsig; cay aut | a; : do. 51 33 | 1835-67| do. 51, 20 | 12 21 |) sa86 Miilhausen, ; : do. 50, 33 105 1857-67| do. 51. -13-| 10 27 | S68Gam Breslau, , . do. 50,33| 103 |1857-67| do. 51. 7 |. 1-2 Erfurt, é : ‘ do. 50 7 | 1861-67 do. 50 59 1] 4 682 Bucharest, . ' . |Turkey &Greece| 52 6 |1863-68| do. 44 26| 26 8] 700 Janina, : : : do. 3 5 |1864-69| various | 39 47 | 20 55 | 1570 Corfu, Be Ove do. 44 6 |1853-59] 93:32 |39 39| 1955| 74} Constantinople, . : do. 52 11 |1858-68| 9: 41 0} 28.59 jee Athens, ‘ ‘ : do. 52 11 do. 8: 37 58 | 23 439Rzae Archangel, . : : Russia 4 18 ? ? 64 33 | 40 33 ? Helsinfors, . ‘ ~ do. 26 10 | 1852-62) hourly | 60 14 | 24 57 50 St Petersburg, . i do. 26 19 | 1846-64] do. 59 56] 30 18 10 | Do., 5 ; - do. 26,33) 11 | 1857-67 Se do. do. 10 | Baltischport, . . do. 26 | 10 |1855-64/8,12:3,10} 59 21| 24 3 0 | Dorpat, ; : : do. 33,53| 11 |1857-67| a.m. 58 17 | 26 47 | doGe Kostroma, . : ; do. 26 7 |1850-56!7:2,2x9| 57 46! 40 56] 640° Mittaa, C202 OSp-08, do. 26 | 12 |1852-63|6:2,10|56 35| 2343] 13) 1847-48, Riga, . Swab, be : do. 26 10 seca do. | 56 57| 24 6| 20% 1863-64 |) Moscow, ; , E do, 33 10 | 1858-67 A.M. 55 442 37, 39 400 | Zlalouste, . : : do. 26 28 | 1837-64] various | 55 10] 59 40 | 1444 | Gorki, 9 ; ; do. 26 4 | 1851-54) 6:2,10 | 54 15 30 35 690 | ‘Walnas.) TVS OOS-05, do. 26 | 9 { ty 2 | ba 41 | 25 17 Kaluga, . : ; do. 26 13 | 1851-6317, 2:29] 54 30] 36.15 | 57 AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 29-556 28-597 28-602 29-939 29-956 29-898 29-968 28-220 29-844 29-913 29-875 29-980 29-894 29-706 29-829 29-862 29-789 29-818 29-774 29-758 29-668 29-610 29-283 29-550 29-303 29-308 28-323 30-036 30-081 29-730 29-743 29-820 29-915 29-850 29-857 29-690 29-336 29-910 29-901 29-483 28-634 29-305 29-473 29-470 VOL. XXV. PART II. Feb, Inches. 29-495 28-518 28-592 29-902 29-970 29-835 29-901 28-201 29-904 29-912 29.922 29-949 29-943 29-723 29-880 29-883 29-830 29-867 29-846 29-774 29-707 29-577 29-305 29-544 29-325 29-239 28-371 29-981 30-058 29-734 29-765 29-829 29-801 29-943 29-891 29-776 29-157 29-905 29-968 29-495 28-556 29-023 29-493 March. Inches. 29-295 28-437 28-410 29-825 29-774 29-589 29-772 28-040 29-768 29-749 29-783 29-917 29-792 29-576 29-714 29-703 29-650 29-679 29-641 29-586 29-492 29-600 29-198 29-359 29-114 29:092 28-135 29-981 29-898 29-605 29-703 29-775 29-841 29-819 29-754 29-658 29-230 29-854 29-807 29-482 28-547 29-188 29-450 29-397 29-378 April. Inches. 29-423 28-470 28-480 29-804 29-871 29-766 29-884 28-151 29-890 29-857 29-907 29-912 \ 29-893 29-696 29-873 29-885 29-801 29-786 29-800 29-769 29-705 29-535 29-257 29-478 29-318 29-174 28-326 29-955 29.924 29-669 29-782 29-786 29-877 29-834 29-843 29-713 29-273 29-882 29-846 29-474 28-525 29-143 29-492 29-354 May. Inches. 29-299 28-477 28-493 29-840 29-860 29-733 29-864 28-148 29-904 29-900 29-922 29-952 29-943 29-744 29-910 29-873 29-819 29-813 29-820 29-763 29-676 29-568 29-253 29-464 29.290 29-269 28-361 29-954 29-878 29-651 29-798 29-860 29-898 29-896 29-882 29-729 29-293 29-901 29-859 29-473 28-475 29-142 29-584 29-375 June, Inches. 29.414 28-500 28-493 29-870 29-870 29-702 29-859 28-203 29-871 29-882 29-882 29.927 29-908 29-744 29-848 29-837 29-799 29-812 29-795 29-739 29-674 29-602 29-286 29-467 29-308 29-174 28-330 29-972 29-877 29-607 29-734 29-820 29-827 29-847 29-881 29-741 29-208 29-880 29-864 29-457 28-344 29-078 29-534 29-314 July. Inches. 29-428 28-503 28-500 29-861 29-868 29-724 29-856 | 28-228 29-790 29-817 29-830 29-892 29-846 29-686 29-822 29-798 29-756 29-786 29-770 29-664 29-656 29-624 29-277 29-436 29-306 29-146 28-283 29-940 29-839 29-571 29-698 29-764 29-798 29-780 29-801 29-619 29-148 29-845 29-794 29-447 28-341 29-093 29-519 29.284 August. Inches. 29-400 28-533 28-535 29-863 29-859 29-739 29-866 28-211 29-811 29-847 29-845 29-908 29-877 29-683 29-837 29-830 29-789 29-814 29-795 29-741 29-675 29-613 29-270 29.457 29-309 29-172 28-311 29-953 29-877 29-611 29-685 29:777 29-836 29-806 29-808 29-642 29.235 29-870 29-842 29-455 28-411 29-187 29-599 29-346 Sept. Inches. 29-540 28-620 28-620 29-922 29-944 29-809 29-937 28-249 29-924 29-848 29-953 29-967 29-981 29-768 29-905 29-894 29-859 29-875 29-870 29-824 29-736 29-623 29-316 29-553 29-358 29-314 28-414 30-040 29-979 29-673 29-798 29-814 29-891 29-897 29-880 29-729 29.284 29-914 29-893 29-483 28-527 29-198 29-673 29-410 October. Inches. 29-453 28-621 28-617 29-898 29-917 29-819 29-930 28-190 29-958 29-954 29-978 29-961 29-992 29-714 29-900 29-915 29-863 29-843 29-835 29-806 29-695 29-597 29-270 29-550 29-309 29-334 28-365 30-080 30-055 29-750 29-725 29-844 29-904 29-926 29-888 29-772 29-328 29-949 29-908 29-504 28-559 29-224 29-649 29-499 Noy. Inches. 29-476 28-565 28-602 29-850 29-902 29-811 29-870 28-171 29-775 29-916 29-890 29-912 29-910 29-747 29-848 29-879 29-790 29-816 29-800 29-763 29-682 29-560 29-291 29-521 29-298 29-296 28-333 30-002 30-038 29-728 29-696 29-852 29-916 29-888 29-942 29-745 29-351 30-104 29-980 29-499 28-615 29.205 29-522 29-447 Dec. Inches. 29-653 28-621 28-621 29-945 29-944 29-887 29-907 28-267 29-928 29-937 29-914 29-919 29-977 29-766 29-930 29.974 29-889 29-866 29-898 29-825 29-806 29-626 29-328 29-592 29-410 29-396 28-364 30-040 30-055 29-728 29-694 29-728 29-833 29-885 29-800 29-725 29-126 29-909 29-761 29-498 28-550 29-092 29-522 29-401 ce 601 Year. Inches. 29-452 28-538 28-547 29-876 29-895 29-776 29-885 28-189 29-864 29-878 29-892 29-933 29-913 29-710 29-858 29-861 29-803 29-815 29-804 29-751 29-681 29-596 29-278 29-598 29-304 29-242 28-326 29-995 29-963 29-671 29-735 29-806 29-861 29-864 29-852 29-712 29-247 29-910 29-869 29-479 28-507 29-158 29-542 29-390 602 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE MEAN MontTHLY AND ANNUAL HEIGHT Autho- 2 Places Country. Bune, nee — he oo Latitude. aed in Bop 1 ee Ye, | tion. Feet. ° / ° / ifs Tamboyv, . ‘ : Russia 26 13 { peer \s:sor10 52 41 | 41 30] 580 Warsaw, : 5 : do. 33 10 | 1858-67 6: 52 14 21 7 | 460 ., |) 10:2,10 Orenburg, . ; : do. 26 21 | 1844-64 h aniciiy 51 49] 35 6] 280 Asiracan (at 32°?), do. 4 1 ? ? 46 15] 48 4 40 Kursk, 5 : : do. 26 27 =| 1835-59 |9, 12: 3,9) 51 44 36 14 700 Morshansk,. . . do. 2 | 4 \ peed | 8:8 |52 27| 41 53| 520 Woltchansk, : do. 26 13 | 1852-64|6: 2,10} 50 17 36 56 370 Lugan, : : do. 26 23 | 1842-64] various | 48 35 39 20 330 Nicholaieff, . f do. 26 6 | 1859-64] 10: 10 | 46 58 31 58 85 Otlessa, ee qc a anne do. 2 | 9 | tees O| 9:9 | 46 28| 30 43 | aay Kiew, . : , 3 do. 52 10} | 1858-68 Gr 50 27 30 34 578 Alagir, : : . do. 26 16 | 1848-63] 7:2,9 | 43 2] 43 53 | 2060 Derbent, . : : do. 26 4 |1852-55| do. 42 12) 48°15 | ie Jakutsk, . ; . | Asiatic Russia d 12 ? ? 62 2] 129 14] 285 Bogoslovsk, t 3 do. 26 26 | 1839-64] various | 59 45] 60 2)| 593 6: 2, 10 Tobolsk, 0 0 : do. 26 11 1852-62 and 58 912 68 16 355 Piece) (| Nijni-Tagilsk, . . do. 54 | 21 |1845-65| 8:3,8 |57 59| 6019| 7302 Catherinenburg, . : do. 26 19 | 1846-64} hourly | 56 49] 60 35] 997 Tomsk, His Dae ¢ do. 26 2 1852-53 8:8 56 30 85 10 300 gins aaa cone! peas ayee do. 26 2 |1847-49| 7:2,9 | 56 27] 138 96| ? | Krasnoyarsk, - , do. 26 10. | 1838-47 |'9: or. 10:/ 56, “. 1.) 92.54 ? Udskoi, : , ; do. 4 1 ? ? 54 30 | 134 28 ? Bamaul 5. ; : do. 26 19 | 1846-64] hourly | 53 20] 83 57] 400 Peterpaulshavn, . ; do. 4 1 ? ? 53 °10.| 158 32°\ame Irkutsh, : ; : do. 26 £50 || 1830 —44as fe 2e 0 oon ln 122 11 | 1253 Nertchinsk,. . . do. 26 | 18 |1847-64| hourly | 51 19] 119 36 | 2130 Fort No. 1, 2 ; do. 26 1 1865 6: 2,10) 45 465 64 27 170 Novo Petrovsk, . : do. 26 6 |1852-57| do. 44 27 | 50 8} 100 Kutais, - * 3 do. 26 3 1850-52) 7:2,9 | 42 31 42 27 470 Redut Kale, ; : do. 26 8 |1847-54| do. 42 16 | (41°36 20, SRLS Bae ae (deers, do. 26 14 |1850-63} hourly | 41 42] 44 50 | 1500 Alexandropol, . 5 do. 26 I2 |1854-65| 7: 2,9 | 40 48] 43 49 | 5010 Baku, . c : S do. 26 17 ‘| 1848-64 do. 40 22 49 50] —53 ; 7: 12 or Aralikh, ; = - do. 26 , 3 | 1851-53 heetan 39 53 44 33 | 2600 Lencoran, . ¢ : do. 26 5 |1852-56| 7:2,9 | 388 44 | 48 52 | —65] Wernoie (132 obs.), do. 26 1 1859 noon | 43 16| 77 0 | 2430 | Chusan (at 32°?), ~. China 4 1 2 ? 30-30 | 122 6 jim ; Bs a9: Pe = &ce., to | =e Pekin, : 4 : do. 26 14 | 1842-55|) og og 39 54 | 116 26 ? te hourly} “ti Tien Tsin, . : : do. 105 1 | 1860-61] (9:3 39. 9) Tiww6 29 | Shanghai, . : : do. 56 2 |1867-68| various | 30 4] 85 33 0} Canton, : : : do. 4 10 3 ? 23 12 | 113 17 < AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 29-587 29-587 29-870 30-206 29-303 29-462 29-672 29-835 30-010 29-876 29-432 27-888 30-187 29-895 29-280 30-002 29-386 29-127 30-092 29-786 30-078 30-003 29-807 29-409 28-777 27-963 29-986 30-080 29-624 30-094 28-547 24-938 30-215 27-458 30-292 27-597 30-412 30-244 30-313 30-254 30-175 Feb. Inches. 29-419 29-548 29-820 30-402 29-263 29-435 29-672 29-736 29-990 29-714 29-430 27-873 30-076 29-957 29-245 29-926 29-347 28-990 30-215 29-874 30-043 29-866 29-739 29-547 28-719 27-922 29-938 30-017 29-510 29-977 28-502 24-895 30-179 27-294 30-171 27-409 30-426 30-170 30-336 30-186 30-099 March. Inches. 29-426 29-426 29-827 30-099 29-198 29-404 29-611 29-686 29-840 29-806 29-343 27-877 30-059 29-748 29-255 29-917 29-372 29-002 29-934 29-910 29-952 29-766 29-689 29-700 28-624 27-876 29-986 29.982 29-490 29-994. 28-460 24-905 30-132 27-200 30-152 27-579 30-009 30-132 30-108 30-018 April. Inches. 29-397 29-497 29.742 30-000 29-236 29-418 29-538 29-622 29-825 29-732 29-337 27-827 30-020 29-620 29-216 29-802 29-303 28-999 29-822 29-806 29-813 29-766 29-521 29.921 28-590 27-662 29-804 29-901 29.439 29-911 28-397 24-874 30-023 27-164 30-099 27-419 29-826 29-950 29-944 29-849 May. Inches. 29-397 29-520 29-618 29-899 29-230 29-456 29-549 29-626 29-788 29-720 29-378 27-844 30-001 29-472 29-185 29-681 29-241 28-922 29-600 29-751 29-662 29-590 29-375 29-805 28:353 27-604 29-736 29-866 29-458 29-936 28-398 24-925 29-988 27-202 30-065 27-294 29-668 Inches. 29-299 29-489 29-481 29-600 29-163 29-389 29-468 29-523 29-732 29-677 29-314 27-801 29-886 29-366 29-016 29-504 29-107 28-777 29-483 29-688 29-550 29-550 29-186 29-732 28-261 27-566 29-635 29-772 29-388 29-866 28-322 24-908 29.884 27-080 29-958 27-222 29-517 29-642 29-707 29-731 Inches. 29-265 29-445 29-439 29-600 29-148 29-322 29-437 29-480 29-740 29-667 29-291 27-781 29-834 29-383 29-055 29-462 29-103 28-778 29-350 29-633 29-536 29-463 29-104 29-685 28-192 27-566 29-512 29-724 29-328 29-819 28-291 24-871 29°815 27:022 29-904 27-182 29-470 29-571 29-719 29-656 August. Inches. 29-381 29-504 29-534 29-899 29-224 29-379 29-499 29-595 29-822 29-691 29-348 27-831 29-936 29-435 29-104 29-498 29-165 28-843 29-561 29-754 29-672 29-412 29.228 29-714 28-264 27-649 29-624 29-794 29-365 29-829 28-362 24.912 29.907 27-061 29-962 27-270 29-586 Sept. Inches. 29-413 29-611 29-688 29-899 29-309 29-465 29-620 29-690 29-884 29-768 29-425 27-912 30-016 29-711 29-188 29-571 29-282 28-963 29-601 29-766 29-818 29.568 29.409 29-709 28-443 27-752 29-756 29-923 29-484 29-945 28-473 24-982 30-025 27-214 30-095 27-425 30-027 29-813 29-927 29-903 29-685 October. Inches. 29-432 29-603 29-761 30-201 29-343 29-441 29.729 29-800 29-963 29-838 29-498 28-018 30-162 29-670 29-205 29-719 29-300 29-000 29-819 29-855 29-907 29-655 29-556 29-626 28-588 27-834 29-945 30-120 29-595 30-037 28-589 25-060 30-183 27-339 30-246 27-578 30-176 30-008 30-076 30-062 29-912 Nov. Inches. 29-483 29-556 29-908 30-300 29-352 29-442 29-754 29-864 30-047 29-937 29-479 28-013 30-134 29-829 29-261 29-816 29-384 29-058 29-852 29-743 30-041 29-788 29-667 29-600 28-657 27-856 30-120 30-137 29-572 30-055 28-608 25-049 30-219 27-376 30-262 27-665 30-193 30-154 Dec. Inches. 29-455 29-670 29-844 30-300 29-277 29-515 29-608 29-785 29-907 29-709 29-461 27-941 30-153 30-060 29-253 29-803 29-317 28-957 29-835 29-752 30-112 29-860 29-703 29-720 28-677 27-848 29-986 30-034 29-598 30-076 28-561 24-976 30-166 27-364 30-243 27-700 30-344 30-217 30-245 30-205 30-123 603 Year. Inches. 29-413 29-538 29-711 30-034 29-254 29-427 29-596 29-685 29-879 29-761 29-395 27-884 30-039 29-679 29-191 29-725 29-276 28-951 29-763 29-776 29-850 29-691 29-499 29-679 28-512 27-758 29-836 29-946 29-484 29-962 28-459 24-941 30-061 27-232 30-121 27-445 29-890 29-985 29-990 29-895 604 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHowincG THE MEAN MonTHLY AND ANNUAL HEIGHT Autho- : Number Hours of Height Places, Country. es, aes Observa- | Latitude. |Longitude.|in Eng. ee Years. sat tion. Feet. a wstnell | cate Macao, ‘ " : China 4 1 ? ? 22.15 | 113 36 ? Hong Kong, 3 5 do. 44 6 |1853-59| 93:34 | 22 16 | 114 10 35 Nafa, . : : . | Pelew Islands 4 1 ? 4 26 14 | 127 46 ? Chacodate, . ‘ : Japan 26 4,5;| 1859-63 | 7,9:2,9]| 41 48 | 140 47 | 150 Decima (Nangasaki) do 33 7, {| 1845-48, 6,9: 32,1] 35 44 | 109 42) 96 ‘= pd : * (| 1852-55 10 Erzroum, . . . |Turkeyin Asia| 3 1 | 1836-38 daily } 39 57 | 41 13a Scutari, ‘i : do. 45 2 | 1865-66; 9:3 Ail: 0s) 29in 8 60 Larnaka, Cyprus, : Syria 3° 3 |1866-69| 9:9 34 55] 33 39 25 Beyrout, . : . do. 4 1 ? ? 33.54) 25, 29 ? Dore : : : do. 3 1 1868-69} 9:10 33 54 39 29 160 Jerusalem, . ; : do. 3 8 | 1861-68 9: 31 47 | 35°13 | 2500 jeHds,) eee ‘Creer, do. 57 1 \ aa 9:3 |21 28| 3913| 25 LSA Se ar do. 57 |. 3, |..1831..| 82:31 | 28..13'| 33 Some Aden, . ‘ : ‘ do. 4 2 4 ? 12 46} 45 5} 199 Mooltan, . : ; Hindostan 58 6 | 1862-67; 10:4. |.31. 11,| -71 333 Roorkee, . : : do. 59 4 |1865-68| do. 29.52 | 77 57 | 8388 Nynee Tal, . ; , do. 59 4 do. do. 29 23) 79 31 | 6433 Agyra,-. : A é do. ~ 59 4 do. do. 27 +10 73,5 551 Nazirabad, . ‘ 4 do. 4 4 ? ? 26 18 | 74 45 | 1585 Benares, . 5 : do. 59 3 | 1865-68, 10:4-|25 2) 83 5 | 9269 Calcutta, . ; ; do. 60 12 |1856-67| hourly | 22 33] 88 21 19 Kurrachee, . : F do. 45 1 1864 9:3 24 ol) BT ae ? Bombay. to. : do. 61 14 |1847-60| hourly | 18 54] 72 48 35 9, 10 Poonah, : : . do. 98 1 1830 is, | 1S ol 74 6 | 1823 10-11 Secunderabad, . : do. 62 1 1864 |4,10:4,10) 17 25 | 78 40 | 1700 Dodabetta, . : : do. 63 5 | 1851-55 9:3 11 32 76 50 | 8640 Madras, ‘ : : do. 64 5 |1846-50| hourly | 13 4] 80 19 27 Do, *. : : : do. 64 22 | 1822-43] red. do. do. 25 Merkera, . : d do. 27 3 | 1838-40 Oro 12 46 75 44 | 4500 Trivandrum, : A do. 4 83 ? ? 8 31) ‘77 “0))aaae Colombo, . ; : do. 44 6 | 1853-59} 93:33 6 56 79 50 18 Gangaroowa, : ; do. 60 13 | 1863-64| do. 7 #17-| 80 37 | Tone Ava, . ‘ j : do. 4 1 is ? 2t 50| 96 5 ? Saigon, . . . | Cochin China | 51 14 | 1867-68 6,10: 4,10, 10 33 | 106 33| ? East India Honolulu, . : 5 Islands and 4 1 ? ? 21 16 |-157 59] ? Pacific Manilla, . , : do. 4 1 ? ? 14 36 | 129 0) 95am Stncapore, . do. 66 1 1866 9: 1 17 103 51) age Shales (Sin- it, do 66 2 |1866-67) noon | 1 9| 103 44) 65 | Padang, . 3 : do. 33 34 | 1850-53 6,9:3,10,\-0 56| 100 2| ? Batavia, . : : do. 4 1 2 ? —6 9 106 53/58 Buitenzorg: 5 sae: do. 33 | 12 | 1841-54 { Hee ah —6 37) 106 49| 889 | Samarang, . } 3 do. 4 1 ? ? -6 50}| 110 33) ? AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 30-232 30-179 30-087 29-743 30-173 23-974 29-975 30-084 29-897 29-890 27-432 eee 29-823 29-653 29-153 23-873 29-496 28-475 29-882 30-022 30-092 29,935 28-087 28-267 22-176 29-986 30-019 26-130 29-739 29-909 28-359 29-801 29-985 30-027 29-992 30-017 | 29.951 29-686 29-747 28-983 29-953 VOL. XXV. PART II. Feb. Inches. 30:197 30-126 30-080 29-769 30-123 23-898 29-852 30-068 29-836 29-932 27-432 29-844 29-566 29-069 23-825 29-409 28-387 29-782 29.944 30-058 29-908 28-002 28-226 22-183 29-971 30-008 26-154 29-721 29-906 28-334 29-688 29-992 30-018 29-936 29-980 29-943 29-696 29-746 28-985 29-978 March. April. May. Inches. 30-161 30-014 30-063 29-870 30-099 23°953 29-793 29-885 29-737 29-721 27-374 29-776 29-492 29-018 23-882 29-345 28-317 29-697 29-859 30-004 29-856 27-952 28-193 22-187 29-909 29-923 26-105 29-688 29-885 28-335 29-624 29-989 30-095 29-896 30-017 29-940 29-696 29-739 28-975 29-973 Inches. 29-997 29-951 29-991 29-799 29-983 23-869 30-032 29-932 29-772 29-830 27-341 29-701 29-342 28-876 23-823 29-210 28-224 29-557 29.754 29-914 29-794 27-908 28-113 22-171 29-816 29-848 26-080 29-653 29-841 28-280 29-546 29-961 30-122 29-854 29-970 29-875 29-662 29-707 28-969 29-983 Inches. 29-987 29-864 29-996 29-721 29-886 23-954 29-942 29-879 29-689 29-749 27-376 29-891 29-610 29-179 28-762 23-745 29-061 28-109 29-415 29-645 29-827 29-745 27-846 28-097 22-146 29-730 29-740 26-065 29-631 29-839 28-287 29-468 29-953 30-130 29-797 29-934 29-916 29-646 29-730 28-964 30-004 June. Inches. 29-815 29-764 29-802 29-610 29-783 24-004 29-868 29-890 29-604 29-704 27-330 29-528 29-013 28-625 23-697 28-940 27-997 29-289 29-542 29-634 29-648 27-768 27-986 22-088 29-693 29-698 26-086 29-650 29-835 28-275 29-417 29-910 30-078 29-764 29-972 29-945 29-662 29-769 28-973 30-014 July. Inches. 29-840 29-713 29-780 29-603 29-790 24-037 29-791 29-535 29-639 27-263 29-714 29-482 29-017 28-638 23-703 28-954 27-973 29-299 29-538 29-550 29-644 27-767 27-993 22-064 29-714 29-721 26:019 29-680 29-846 28-278 29-396 29-938 30-105 29-763 29-972 29-923 29-670 29-757 28-971 30-042 August. Inches. 29-840 29-702 29-677 29-628 29-748 24-049 29-800 29-563 29-638 27-278 29-733 29-512 29-106 28-696 23-726 28-983 28-025 29-365 29-592 29-672 69-718 27-840 28-053 22-092 29-746 29-748 25-998 29-678 29-854 28-287 29-447 29-922 30-077 29-750 30-000 29-930 29-689 29-765 28-980 30-045 Sept. Inches. 30-009 29-790 29-783 29-732 29-871 24-126 29-966 29-697 29-714 27-361 eee 29-632 29-273 28-779 23-784 29-099 28-137 29.446 29-676 29-826 29.772 27-925 28-105 22-128 29-763 29-772 26-030 29-694 29-880 28-304 29-472 29.922 30-084 29-759 30-000 29-922 29-698 29-769 28-983 30-041 605 October. Inches. 30-055 29-981 29-918 29-840 30-033 24-052 29-972 30-004 29-723 27-443 29-778 29-437 28-969 23-884 29-301 28-305 29-670 29-827 29-993 29-829 27-924 28-192 22-149 29-827 29-846 26-045 29-707 29-881 28-308 29-583 29-922 30-105 29-820 29.974 29.922 29.704 29.782 28-993 30-041 Noy. Inches. 30-165 30-104 30-065 29-838 30-143 24-027 30-002 30-040 29-792 27-446 29-876 29-604 29-109 23-904 29-429 28-431 29-808 29-968 30-094 29-897 28-018 28-230 22-155 29-918 29-932 26-098 29-708 29-886 28-328 29-684 30-040 30-058 29-888 29-967 29-934 29-666 29-757 28-964 30-010 Dec. Inches. 30-263 30-143 30-115 29-715 30-170 23-978 30-124 30-002 29-818 29-922 27-431 28-247 22-171 29-957 29-995 26-120 29-730 29-909 28-350 29-774 30-064 30-105 30-005 30-000 29-904 29-691 29-730 28-973 29-911 va) 606 Places. Tahiti (said to be red. to sea-level), Port de ge N. Cale- “| donia, Suez, . Ismailia, Port Said, Alexandria, Cairo, . Gondar, Massuah, Tripolis, La Calle, Dellys, Algiers, Do., 7 ; : Djidjilly, . . + Medeah, ; é Aumale, Orleansville, Oran, Wor. Laghouat, Casa Blanca, : St George d’Elmina, Christiansburg, Gondokoro, . Lagos, Cape Town, Do., Worcester, Simon’s Town, Mossel Bay, Somerset West, Graham’s Town, Graff Reinet, Pieter Maritzburg, Zambesi Delta, Tamatave, St Louis, St Denis, Socotra, Somerset, Cape York, Brisbane, Brisbane, TABLE I.—SHowi1ne THE MEAN MontTHLY AND ANNUAL HEIGHT Country. East India Islands and Pacific do. Abyssinia do. Tripoli Algeria Moroceo Ashantee do. Benin Slave Coast Cape Colony do. do. Mozambique Madagascar Mauritius Bourbon Queensland 0. 65 Autho- ar Number see page 635. | Years. on ee Oe bo Years | Ghoorre: Specified. tion, 1855-60 ‘< ay } obs. 6,10: 1, 1863-64 | nes } 1866-68 |! ®9 aa | 3, 6,9 do. do. do. do. 1858-60 ene ? & 1832-33] 9:3 1831-32| 9:32 2 ? 1865-68 ? do. ? 1857-67 ? 1865-68 ? do ? do. if do. i do. ? 1841-53 10: 4 1866-68 2 do. ? 1867-68} various 1860-62] 6:2,9 1829-40])__. 1833-34 | |vatious ? ? 1863 ? hourly; 1842-55 |2 5,9: 1, 5,9 1862-65 |5,9: 1,5,9 do. 9:1,5 do. do 1862-63 do 1861-64 do. 1864-69| 93: 33 1863-65 | 9: 1, 5 1858-65 9:3 1858 mean 1863 9:4 34, 94: 1853-65 \ 32, a ? im ? 2 1865-67 9:3 1859-61 9:3 1867-69) 9:3 Height |. Latitude. |Longitude.|in Eng. Feet. ° 3 ° / 17 32 |—149 34) ? —22 16 166 26 22 29 57 32: 32 20 30 38 32 13 25 31-18 32 18 10 31 11 29 50 50 30 6 31 26 ? 15 50 37 32 | 7422 15 36 39 21 5 32 54 13 19 is 36 52 8 23 30 |: 36 49 3 50 75 36 43 2 03 66 do. do. 66 36 17 5 42 49 36 13 2 43 | 3150 oGmag, 3 40 | 2933 36),..6 1 19 459 35 40 | -—0O 38 164 do. do. 164 33 47 2 54 | 2461 30 0} —-7 30 te 5 5| —1 20 75 5 24 0 10 60 4 30 31 40 | 1800 6 12 3°25 0 = oD OOF) “LS 7 37 do. do. Sif —33 38 19 23 776 —34 12 18 24 50 —34 12 22 5 429 —34 2 18 46 124 —33 13 26 32 | 1750 —32 18 24 51 | 2517 —29 30 30 2 | 2096 —18 24 35 30 OF -18 3 49 11 0 -— 20 10 57 30 (30 —20 51 55 30 142 | —12 30 54 10 ie —10 44 | 142 36 70 | = 27 “b | lose 0 70 | —27 28 | 153 6 140 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 29-868 29-913 30-095 30-062 30-080 29-998 30-000 23-338 30-097 30-138 29-977 29-953 30-073 29-985 29-982 26-977 26-956 29-686 29-984 29-941 27-512 30-268 29-877 29-862 28-356 29-940 29-937 29-162 29-947 29-576 29-845 29-919 27-395 27-786 Feb. Inches. 29-846 29-946 30-127 30-079 30-103 29.929 30-036 23-302 30-010 29-993 30-024 30-004 30-061 30-083 30-028 27-000 27-067 29-784 29-956 30-024 27-665 30-335 29-857 29-838 28-300 29-966 29-911 29-146 29-911 29-557 29-821 29-955 27-416 27-802 29-854 29-687 29-399 29-785 29-837 29-875 March. Inches. 29-856 30-008 29-938 29-906 29-934 29-993 29-900 23-268 29-955 29.928 29-831 29-867 29-934 29-863 29-775 26-812 26-890 29-520 29-924 29-819 27-391 30-001 29-844 29-829 28-317 29-968 29-954 29-184 29-961 29-576 29-878 29-966 27-414 27-844 29-925 29-679 29-380 29-847 29-916 30-015 April. Inches. 29-864 30-008 29-939 29-920 29-950 29-919 29-821 23-267 29-926 29-956 29-985 29-902 29-944 29-934 29-886 26-890 26-981 29-611 29-858 29-886 27-441 30-154 29-849 29-837 28-349 29-984 30-002 29-232 30-000 29.598 29-915 30-050 27-480 27-914 May, Inches. 29-910 30-107 29-902 29.896 29-906 29-827 29-842 29-946 29-953 29-902 29-930 29-914 29-867 26-886 26-986 29:585 29-836 29-874 27-500 30-048 29-882 29-874 28-425 30-087 30-065 29-298 30-066 29-680 29-982 Inches. 29-921 30-119 29-865 29-821 29-853 29-792 29-834 30-044 29-944 29-878 29-961 29-906 29-875 26-936 27-016 29-603 29-870 29-914 27-469 30-060 29-942 29-939 28-474 29-974 30-085 30-110 29-330 30-087 29-642 29-984 30-078 27-616 27-994 30-126 29-901 29-086 29-914 29-987 30-093 July. Inches. 29-943 30-131 29-786 29-731 29-772 29-738 29-730 30-019 29-958 29-858 29-993 29-948 29-878 26-981 27-060 29-699 29-861 29-827 27-452 30-134 29-985 29.971 28-469 30-011 August, Inches. 29-966 30-079 29-812 29-750 29-798 29-732 29-756 30-035 29-931 29-839 29-958 29-914 29-846 26-966 27-028 29-620 29-845 29-804 27-465 30-095 29-981 29-958 28-439 30-047 30-112 30-129 29-376 30-118 29-713 30-055 30-085 27-572 27-981 30-077 30-171 29-935 29-933 30-109 30-117 Sept. Inches. 29-968 30-119 29-894 29.847 29-896 29-840 29-923 29-859 30-034 29-971 29-879 29-996 29-973 29-904 26-945 27-099 29-579 29-861 29-855 27-472 30-123 29-953 29-920 28-433 30-001 30-072 30-090 29-309 30-098 29-681 30-000 30-075 27-524 27-905 30-016 30-158 29-894 29-907 30-033 30-020 October. Inches. 29-946 30-032 29-999 29-963 29-985 29-966 29-938 23-312 29-956 30-013 29-930 29-840 29-960 29.934 29-871 26-908 27-004 29-548 29.857 29-823 27-461 30-119 29-901 29-882 28-413 29-950 30-080 30-006 29-227 30-011 29-615 29-928 30-037 27-422 27-864 30-024 30-111 29-859 29-898 30-001 29-991 Nov. Inches. 29-913 30-008 30:079 30-042 30-052 29-978 29-998 23-312 30-028 30-000 30-025 29-875 29-981 30-073 29-963 26-956 27-083 29-693 29-935 29-934 27-469 30-103 29-870 29-862 28-392 29-925 29-975 30-019 29-234 30-023 29-583 29.915 29-984 27-409 27-822 29-977 30-031 29-811 29-868 29-918 29-966 Dec. Inches. 29-887 29-934 30-071 30-024 30-046 29-977 30-080 23-315 30-055 30-068 30-036 29-985 30-097 30-073 29.991 26-974 27-063 29-750 30-002 29-952 27-477 30-099 29.887 29-849 28-394 29-955 29-974 29-932 29-152 29-942 29-531 29-835 29-938 27-353 27-795 29-963 29-740 29-780 29-850 29-888 607 Year. Inches. 29-907 30-034 29-959 29-920 29-947 29-891 29-904 30-014 29-960 29-900 29-986 29-967 29-906 26:936 27-020 29-640 29-895 29-888 27-481 30-128 29-901 29-885 608 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE J.—SHOWING THE MEAN MoNTHLY AND ANNUAL HEIGHT Autho- Number Hours of Height rities, Years § Places. . Country. see page - s Specified. cpr ae Latitude. |Longitude. a wires a e J ° a Casino & Richmond River,| Queensland 76 5 1858-62), 9:3) |—28.50) | h15s0 00 139 Armidale, . . |N. South Wales} 76 31 | 1860-63 9: -30 33 | 151 46 | 3195 Newcastle, 5 i : do. 76 9 |1858-66| do. |-32 57 | 151 47 18 Windsor, . : 5 do. 77 4 | 1863-66 9:3 —33 36 | 150 50 53 Paramatta, . ‘ é do. 76 33 |1858-61|} do. |-33 49] 151 1 60 Bathurst, . ‘ : do. 76 5 | 1859-63 9; —33 24 | 149 37 | 2333 Goulburn, . : : do. 76 8 | 1858-65 |9: 3,9,&9:|-34 45 | 149 45 | 2129 Sydney, 4 , : do. 76 11 | 1858-68 do. —33 52 | 151 11 155 Do., any pre, do. 76 9 |1858-66|9:3,&9:| do. do. 155 Deniliquin, . : : do. 76 9 doi” 79: 3,9,&9: +35 32 | 145 2 [> 416 Albury, ; ‘ : do. 76 8h do. do. |-36 6| 147 0 572 Cooma, ‘ : A, do. 76 7 | 1858-64| 9:3, & 9:|—36 13 | 149 9 | 2637 Sandhurst, . s : Victoria 78 5 | 1863-67] 9:3,9 |—36 43 | 144 21 778 Ararat, : ' ; do. 78 5 do. 9:3 —37 18 | 142 58 | 1072 Ballartts nye tae On: do. 78 5 do 93:33, 93-37 34 | 143 53 | 1438 Melbourne, . ; ‘ do. 78 10 | 1858-67 | 6, 9: 3,9|-—37 50 | 144 59] 121 Do., ; , : do. 78 5 | 1863-67] do. do do. 12] Portland, . ‘ : do. 78 5 do. do. |—38 21 | 141 32 37 Cape Otway, ; ‘ do. 73 5 do. do. |—38 54] 143 37 | 300 Kupunda, . ; . |South Australia} 79 4 |1861-64| 9:6 |-—34 20] 139 0} 730 Adelaidenah s. + san yes do. yo hell { oa do. |-34 53] 138 39] 140 Strathalbyn, ; : do. 79 4 |1861-64} do. |-35 8 | 138 57} 220 Guichen Bay, : ‘ do. 79 4 do. do. —37 3] 139 42 19 Mount Gambier, . : do. 79 4 do. do. |-—37 51] 140 53 | 133 Freemantle, : . | West Australia| 44 3 | 1853-85] 93:32 |-—33 2] 115 45 16 Kent’s Group, . : Tasmania 80 5 | 1861-66] 6,12: 6 |—39 29 | 147 35 | 280 Swan Island, 5 : do. 80 23 | 1864-66 do. —40 45 | 148 10 14 Swansea, ; : do. 80 3 do. do. |—42 8] 148 5 18 Hobart Town, . : do. 80 28 | 1841-68 do. |—42 52] 147 21 37 Do. : ‘ : Poasley 80 5 1861-66 do. do do. 37 Port Arthur, ; : do. 80 5 |1861-66| do. |-43 9 | 147 54 55 Auckland, . . . | New Zealand Meo ak 11 { eee on: 33 |-36 50| 174 51| 140 Taranaki, . : : do. 81 5 |1864-68} 10:4 |—39 4] 174 5 70 Wellington, , : do. 81 5 do. do. |—41 16} 174 47 90 Nelson, : : . do. 81 3 do. 9:3 —41 16] 173 19 18 Hokitika, . . c do. 81 3 | 1866-68} 10:4 |—42 42 | 170 59 8 Christchurch, ; : do. 81 5 | 1864-68 )92: 34, 93/-—42 33 | 172 39 21 Do., : ; : do. 81 3 | 1866-68 do. do do. 21 Dunedin, . .. do. 81 52 |1862-68| 93:42 |-45 52] 170 31] 550 Southland, . : A do. 81 10 | 1859-68; 9:3,9 |—46 17 | 168 20 79 Upernivik, . i ; Greenland 2 5 | 1833-38] noon 72 48 |—55 53 15 Jacobshavn, ; ; Je | G0; 2 93 | 1842-51 do. 69 12 |-d1 0 10 | Godthaab, . : : do. 2 5 1841-46 do. 64 10 |—51 53 15 | Baffin Bay, ; : Arctic 82 1 | 1857-58/ various | °°" 722°) various “On Van Rensselaer, . : do. 82 2 |1853-4-5) do. 78 37: |-73 O 07 Port Foulke, i , do. 82 1 | 1860-61 do. 78 18 |-73 0 Rep | Port Kennedy . : do. 82 1 | 1858-59} do. 72 1|-94 0 0; Boothia Felix, . ‘ do. 4 2 tee tee 70 3/-95 0 0] AND THE PREVAILING WINDS OVER THE GLOBE. OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. 29-776 26-631 29-912 29-847 29-846 27-655 27-766 29-773 29-774 29-506 29-238 27-241 29-109 28-783 28-464 29-811 29-827 29-931 29-701 29-062 29-805 29-676 29-878 29-792 29-936 29-620 29-933 29-677 29-744 29-807 29-791 29-968 29-906 29.838 29.874 29-903 29-783 29-812 29-859 29-789 29-580 29-634 29-582 29-532 29-778 29-834 29-979 29-823 Feb. Inches. 29-780 26-617 29-936 29-869 29-888 27-668 27-796 29-792 29-795 29-554. 29-318 27-290 29-143 28-826 28-484 29-839 29-843 29-942 29-708 29-090 29-825 29-705 29.914 29-816 29-930 29-650 30-023 29-748 29-837 29-849 29-829 29-999 29-946 29-876 29-923 29.861 29-840 29-808 29-855 29-843 29-458 29-681 29-713 29-649 29-848 29-747 29-933 29-975 March. Inches. 29-849 26-733 30-037 30-012 29-972 27-766 27-911 29-906 29-903 29-660 29-449 27-379 29-257 28-902 28-589 29-940 29-966 30-050 29-819 29-187 29-915 29-787 30-010 29-922 29-987 29-766 30-090 29-854 29-867 29:973 29-865 30-067 30-040 29-963 29.974 30-007 29-947 29.957 30-011 29-867 29-699 29-786 29-824 29-893 29-750 29-816 30-173 29-962 April. Inches. 29-911 26-752 30-100 30-061 30-022 27-832 27-934 29-948 w 29-950 29-728 29-478 27-393 29-308 28-957 28-620 29-987 30-000 30-075 29-840 29-240 29-975 29-843 30-063 29.960 30-072 29-764 30-060 29-855 29-903 29-996 29-835 30-098 30-058 30-007 30-058 30-026 29-953 29-926 29-968 29-897 29-774 29-830 29-833 29-940 29-903 30-085 30-179 29-993 May. Inches. 29-961 26-741 30-103 30-057 29-999 27-822 27-896 29-959 29-939 29-741 29-482 27-342 29-310 28-952 28-593 29-958 29-994 30-049 29-757 29-146 30-008 29.825 30-018 29-903 30-122 29-686 30-010 29-781 29-871 29.927 29-747 29-990 29-974 29-895 29-959 30-082 29-910 30-040 30-023 29-889 29-803 29-867 29-963 30-014 29-942 29-985 30-010 30-141 June. Inches. 29-909 26-717 30-117 30-086 30-029 27-816 27-889 29-949 29-949 29-767 29-540 27-340 29-357 28-977 28-630 30-000 30-045 30-121 29-848 29-210 29-980 29-817 30-032 29-921 30-121 29-776 30-060 29-827 29-892 30-002 29-823 29-954 29-930 29-902 29-984 29-971 29-892 29-952 30-023 29-866 29-703 29-815 29-897 29-817 29-719 29-678 29-913 30-023 July. Inches. 29-962 26-671 30-087 29-980 30-084 27-825 27-884 29-916 29-907 29-716 29-468 27-292 29-223 28-880 28-509 29-950 29-911 29-971 29-719 29.203 29-942 29-751 29-951 29-814 30-010 29-588 29-955 29-734 29-856 29-855 29-654 29-968 29-898 29-886 30-000 29-975 29-880 29-870 29-912 29-826 29.694 29-766 29-869 29-753 29-741 29.691 29-704 29-891 August. Inches. 30-032 26-716 30-112 30-045 30-047 27-868 27-885 29-950 29-951 29-735 29-518 27-323 29-304 28-936 28-576 29-985 29-988 30-033 29-795 29-262 30-013 29-859 30-056 29-926 30-066 29-652 30-030 29-704 29-822 29-912 29-700 29-941 29-839 29-822 29-903 29-885 29-835 29-838 29-882 29-770 29-671 29.744 29-763 29-736 29-694 29-662 29.741 29-857 Sept. Inches. 29-958 26-690 30-025 29-916 29-956 27-807 27-796 29-858 29-866 29-670 29-473 27-275 29-168 28-812 28-458 29-852 29-837 29-893 29-657 29-188 29-866 29-761 29-975 29-854 30-080 29-600 29-875 29-665 29-758 29-789 29-647 29-930 29-814 29-866 29-898 29-910 29-848 29-902 29-871 29-788 29.620 29-777 29.824 29-735 29-658 29-684 29-899 29-826 October. Inches. 29-905 26-681 29-994 29-854 29-972 27-747 27-818 29-828 29-852 29-577 29-365 27-280 29-074 28-760 28-394 29-833 29-768 29-851 29-594 29-130 29-844 29-741 29-928 29-812 30-023 29-610 30-020 29-681 29-772 29-824 29-727 29-950 29-832 29-781 29-670 29-778 29-716 29-682 29-773 29-665 29.576 29.722 29-818 29-756 29-755 29-618 29-798 29-957 609 Year. Inches. 29-886 26-682 30-024 29-949 29-966 27-767 27-842 29-874. 29-871 29-646 29-412 27-303 29-207 28-867 28:517 29-899 29-900 29-977 29-722 29-159 29-902 29-761 29-970 29-860 30-027 29-656 29-987 29-734 29-816 29-873 29-752 29-980 29-915 29-871 29-906 29-922 29-841 29-851 29.898 29-803 29-640 29-749 | 29-786 29-755 29-775 29-824 29-938 29-943 VOL. XXV. PART II. 610 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHowine THE MEAN MonTHLY AND ANNUAL HEIGHT ac Number Hours of Height rities, Years & Places. Country an pase fe Specified. pee Latitude. |Longitude. i Eng. . AY i Le TL ickatd Bo oats Melville Island, Arctic 4 1 | 1819-20 ? 75 40 |-112 3 0 Port Bowen, do. 4 1 | 1824-25 ? 73 13 |-88 54 ) 1807-12, 66 to about E. of Greenland, . do. 83 7 \ 1822 } noon 30 34 | —7 of 0 . : ; , | hourly : Sitka, . Russian America| 26 17 | 1848-64) 04g &o } 56 50 |—135 0] 20 2=9 * New Westminster, British Columbia) 84 2 |1860-61| 93: 33 | 49 13 |—122 53) 54 Esquimault Harbour, Vancouver 85 1 do. ¢ 48 25 |—123 27 0 : ; 1859-60 Astoria, Oregon 86 2) 1866 ? 46 8 |-123 48} ? Sacramento, California 86 9 | 1858-66] 7:2,9 | 38 35 |-121 28) 81 San Francisco, do. 86 9 do. do. 37 48 |—122 23) 86 Great Salt Lake City, : Utah 87 2 | 1858-59|6,9:3,9] 40 45 |—111 26] 4260 St John’s, . Newfoundland 44 6 | 1853-59] 94: 32 47 35 | —52 42) 130 Halifax, . Nova Scotia 44 4 \ econ do. 44 39 | —63 37 8 Do., do. 45 2 | 1864-65) 9: 3 44 39 | —63 36] 137 Albion Mines, do. 27 10 | 1843-52] noon 45 34 | —62 42) 128 1853-55, Quebec, Canada Hast | 44, 45 | 1858, |/93: 34 | 46 48 | —71 12] 230 1866 St Martin’s, do. 87 6 | 1854-59] 6:2, 10 45 32 | —73 36) 118 Kingston, : ; Canada West 44 4} do. 93: 33 | 44 14] —76 31} 294 Toronto, : : : do. 88,71| 28 | 1840-67] 6: 2,10 43 39 | —79 2| 342 Do., do. 88 11 | 1857-67] do. do. do. 342 Do., do. 88 6 | 1854-59 do. do. do. 342 Hamilton, do. Si oo mel 1849-59} 9:9 43.15 | —79 57)2290 Gardiner, Maine, U.S. 87 5 | 1855-59] 7:2,9 | 44 11 | —69 46} 90 Steuben, do. 87 6 1854-59 do. 44 28 | —67 50 50 Amherst, Massachusetts | 87 6 ao. do. 42 22 | —72 34| 267 New Bedford, do. 87 6 do. do. 41 39 | —70 56) 90° Nantucket, do. 87 6 do. do. 41 16 | —70 6) 30 1854-56, Burlington, . Vermont 87 5 \ 1858-59 } do. 44 29 | -73 11} 346 Providence, Rhode Is. 89 29 | 1832-60 |sr: 2,10) 41 50] --71 23) 170 Do., do. 89 6 |1854-59| do. do. do. 170 Rochester, New York 87 4 | 1856-59| 7:2,9 43 8 | -—77 51) 516 Bedford, Pennsylvania | 87 4 \ tie do. 40 1 | —78 30) 900 Harrisburg, do. 87 6 | 1854-59} do. 40 16 | —76 50) 280 Pittsburg, do. 87 6 do. various | 40 30 | —80 00) 960 Lambertville, New Jersey 87 6 do. 7: 2,9 40 23 | —74 56) ? Washington { Pere OF kaa? do do 38 56 | —76 58| 40 S000; Columbia f ; : 0, 3, 6, Do., do. 90 5 | 1862-66 |< 9, ah 38 56 | —76 58) 103° 3, 6, 9 i Portsmouth, Virginia 87 3 |1857-59| 7:29 | 3650] -76 19] 34] Chapel Hill, N. Carolina 87 6 | 1854-59 do. 35 54 | —79 17| 500 | All Saints, 8. Carolina 87 5 | 1855-59| do. 33 40 | —79 17) 20 | Athens, =). Georgia 87 2 | 1857-59] do. 33 58 | —83 30 730 | Savannah, (at sea ‘level 2) do. 87 6 | 1854-59} do. 32 5| -—81 7) ae AND THE PREVAILING WINDS OVER THE GLOBE. 611 OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January. Inches. | Inches. 30:077 29-717 29-551 30-074 30-110 29-985 30-106 30-070 25:880 29-924 29-985 29-744 29-696 30-104 29-842 30-062 29-647 29-650 29-670 29.693 29-874 29-988 29-813 29-972 30-043 29-668 29-807 29-857 29-508 29-145 29-820 29-043 30-058 30-145 30-031 30-140 29-602 30-090 29-410 30-135 pe A ny pn Sn et Feb. 29-769 29-886 29-644 30-042 30-030 30-138 30-074 30-043 25-780 29-781 29-797 29-681 29-687 30-055 29-753 30-014 29-624 29-654 29-643 29-648 29-782 29-895 29-730 29-915 29-970 29-572 29-779 29-773 29-420 29-045 29.765 28-952 29-982 30-047 30-030 30-083 29-525 30-006 29-275 30-087 March. Inches. 29-803 30-107 29-648 30-022 30-090 29-957 30-060 30-040 25-670 29-690 29-685 29-748 29-672 29-901 29-639 29-941 29-596 29-577 29-538 29-608 29-702 29-773 29-788 29-788 29-873 29-488 29-743 29-674 29-358 29-005 29-678 28-923 29-933 29-963 29-921 29-967 29-468 29-962 29-270 30-038 April. Inches. 29-979 30-068 29-852 29-711 30-000 30-030 30-094 30-011 30-004 25-685 29-942 29-931 29-842 29-702 30-010 29-693 29-970 29-597 29-583 29-572 29-606 29-750 29-848 29-648 29-827 29-900 29-558 29-740 29-718 29-348 29-110 29-675 28-914 29-920 29-952 29-956 29-887 29-448 29-942 29-210 30-015 May. Inches. 30-109 30-051 29-870 29-836 29-984 30-030 29-996 29-938 29-938 25-640 29-943 29-959 29-780 29-746 29-864 29-770 29-965 29-574 29.564 29-593 29-663 29-824 29-918 29-687 29-878 29-963 29-612 29-722 29-773 29-385 29-048 29-695 28-912 29-953 29-967 29-844 29-963 29-453 29-920 29-233 29-985 June. Inches. 29-823 29-888 29-852 29-814 29-962 30-060 30-067 29-888 29-897 25-655 29-934 29-976 29-823 29-674 29-934 29-719 29-917 29-572 29-577 29-542 29-650 29-746 29-862 29-717 29-853 29-928 29-555 29-725 29.722 29-338 29-060 29-670 28-910 29-945 29-938 29-912 29-927 29-463 29-960 29-293 30-010 July. Inches. 29-668 29-817 29-870 29-877 30-032 30-100 30-067 29-869 29-891 25-645 29-993 29-974 29-778 29-710 29-955 29-796 29-999 29-599 29-593 29-613 29-707 29-792 29-923 29-673 29-925 29-973 29-618 29-722 29-797 29-405 29-112 29-733 28-968 30-025 29-990 29-914 29-977 29-478 29-968 29.273 30-037 August. Inches. 29-726 29-683 29-850 30-012 30-040 30-023 29-867 29-890 25-675 29-964 29-950 29-810 29-770 29-947 29-773 29-977 29-622 29-606 29-608 29-700: 29-786 29-928 29-723 29-925 29-985 29-625 29-788 29-789 29-350 29-105 29-728 28-953 30-010 29-988 29-932 29-980 29-483 29-946 29-285 30-018 Sept. Inches. 29-748 29-689 29-766 30-029 30-080 30-032 29-880 29-894 25-727 29-971 30-024 29-848 29-767 30-022 29-820 30-054 29-662 29-671 29-675 29-745 29-860 29-985 29-720 29-985 30-053 29-682 29-823 29-856 29-418 29-160 29-815 29-035 30-100 30-055 30-000 30-043 29-552 30-006 29-315 30-053 October. Inches. 29-811 29-962 29-623 30-008 30-010 30-021 29-946 29-943 25-760 29-986 29-962 29-674 29-766 30-045 29-846 30-078 29-645 29-645 29-655 29-684 29-810 29-928 29-788 29-928 29-988 29-612 29-808 29-808 29-432 29-180 29-785 28-995 30-023 30-047 29-967 30-010 29-540 29-998 29-348 30-058 Nov. Dec. Year. Inches. | Inches. | Inches. 29-945 | 29-865/| 29-860 29-899 | 29-869| 29-886 29-615] 29-630} 29-714 29-937 | 29-928] 30-002 30-100} 29-960} 30-053 29-992) 29-958 30-028 30-049] 30-080} 29-981 30-024 | 30-041] 29-973 25-705 (25-800)| 25-717 29-908| 29-842| 29-906 29-954 | 29-869] 29.922 29-836 | 29-737) 29-776 29-687 | 29-688] 29-714 29-936) 29-982) 29.980 29-800 | 29.852] 29.775 29-946 | 30-044] 29.973 29-612) 29-656| 29-617 29-595 | 29-676] 29-617 29-600) 29-672| 29.615 29-634 | 29-670) 29-666 29-850) 29-854} 29.802 29-920) 29-932| 29.908 29-737 | 29-788 | 29-730 29-900 | 29-925} 29.902 29-960} 30-008} 29-970 29-602 | 29-652) 29-604 29-783 | 29-784| 29-779 29-765 | 29-805 | 29-778 29-365 | 29-435] 29-397 29-102} 29-100} 29-097 29-770 29-803 | 29-745 28-980 | 28-983} 28-964 30-017 | 30-028; 30-000 30-028 | 30-080} 30-017 30-004 | 30-035 | 29-962 30-047 | 30-073) 30-005 29-550 | 29-570) 29-511 30-042 | 30-074} 29-993 29-410 | 29-340)| 29.297 30-085 | 30-118] 30-053 612 MR ALEX. Places. Jacksonsville, Warrington, Auburn, Colum bus, Washington, Sisterdale, Goliad, Memphis, Glenwood, Springdale, . Cincinnati, . Marquette, Ottawa Point, New Harmony, Wheaton, St Louis, Beloit, . Dubuque, Beaver Bay, Lawrence, Leavenworth City, Cordova, . . Vera Cruz, Guatimala, . Port of Saphea4 Belize, Ber muda, : Nassau, Bahama, Havanna, Cuba, . , Up Park: Camp, Jamaica, Barbadoes, ; Do., Port of Spain, Trinidad, Caledonia Bay, Cartagena, Bogota, Caraccas, George Town, Cayenne, Ghitietin Sophia, Ceara, Pernambuco, Rio de Janeiro, Asuncion (and vicinity), Buenos Ayres (& vicinity), Monte Video, Santiago de Chile, BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT Florida do. Alabama Mississippi Texas Tennessee do. Kentucky Ohio Michigan do. Indiania Illinois Missouri Wisconsin Iowa Minnesota Kansas do. Mexico do. Central America do. Brit. Honduras West Indies do. do. do. do. do. do. New Granada do. Venezuela British Guiana French do. Dutch do. Brazil do. do. Paraguay La Plata Uruguay Chili Autho- rities Number Years of : See page] y pars, | Specified Se Set poe crs 87 6 1854-59 1854-57 ea 4g | 1859 87 3 1855-57 87 4 1856-59 87 2 1858-59 87 1 1859 87 1 1858 87 24 | 1857-59 87 6 1854-59 87 6 do. 87 4 1856-59 87 23 | 1857-59 87 14 | 1858-59 if 6 1854-59 $7 2 1858-59 87 6 1854-59 87 6 do. 87 6 do. 87 14 | 1858-59 87 2 1857-59 87 13 | 1858-59 87 2 do. 87 24 | 1857-59 40 2 1860-6! 100 3 1857 71 4 | 1862-63 44 34 | 1855-59 a4 6 1853-59 40 3 1859-61 44 6 | 1853-59 44 6 do. 45 2 1865-66 87 aos | 1856-57 67 1854 67 2 do. 35 1848-50 92 1 1860 91 11 1846-56 35 6 1845-52 87 1858-59 37 1 1860 4 6 1851-56 101 434° | 1854-55 101 24 | 1853-56 102 10 1843-52 4 3 1850-52 Hours of Observa- tion. Height Latitude. |Longitude.| in Eng. Feet. AND THE PREVAILING WINDS OVER THE GLOBE. 613 OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January.| Feb. | March.}| April. | May. | June. | July. | August.} Sept. | October.) Nov. Dee. Year. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. 30-220} 30-143} 30-100) 30-080) 30-023) 30-058 | 30-087| 30-060 | 30-083 | 30-088] 30-127} 30-178) 30-104 30-136} 30-092} 30-088 | 30-037| 29-912) 29-972) 30-004] 29-992) 29-996) 30-034 | 30-054} 30-102] 30-027 29-443] 29-377 | 29-353 | 29-343 | 29-260/ 29-300| 29-320| 29-357| 29-380) 29-383) 29-397 | 29-420) 29-361 29-990| 29-865 | 29-812] 29-768| 29-752) 29-780) 29-800] 29-768] 29-855 | 29-868] 29-880] 29-920} 29-838 29-750} 29-685 | 29-540] 29-575| 29-620] 29-625] 29-660) 29-595) 29-630] 29-675 | 29-705} 29-750) 29-650 28-850| 28-650} 28-560] 28-610] 28-570) 28-670} 28-680| 28-580| 28-660) 28-730| 28-720} 28-760} 28-670 30-060} 30-040) 29-940] 29-870} 29-900) 29-940} 29-970) 29-950} 30-020] 29-920) 30-080] 30-065) 29-980 29-890| 29-775 | 29-685} 29-650} 29-680 | 29-745 | 29-755] 29-720) 29-800} 29-817| 29-790} 29-830) 29-761 29-683| 29-587 | 29-545| 29-507| 29-477 | 29-513| 29-552) 29-543 | 29-593| 29-598| 29-558} 29-630| 29-566 29-500} 29-415) 29-387] 29-365 | 29-320] 29-377 | 29-398) 29-390) 29-448| 29-453 | 29-418] 29-470] 29-412 29-600| 29-513 | 29-488] 29-435] 29-375| 29-455 | 29-430) 29-453 | 29.522) 29-533) 29-500) 29-570) 29-490 29-325 | 29-330 | 29-160| 29-220} 29-330| 29-290/ 29-370] 29-330| 29-330| 29-370] 29-277| 29-320/ 29.304 29-440 | 29-340) 29-150) 29-260) 29-380] 29-400} 29-410] 29.370 | 29-445 | 29-405) 29-385) 29-395] 29-365 29-787| 29-702| 29-665) 29-612) 29-585 | 29-598 | 29-643 | 29-635] 29-688| 29-702] 29-667] 29-723 | 29-667 29-270) 29-215} 29-090} 29-070} 29-165| 29-210) 29-240} 29.215 | 29-235| 29-240] 29-200] 29-240] 29-199 29-632) 29-540] 29-498} 29-437 | 29-428| 29-448) 29-502) 29-512) 29.547 | 29-543 | 29-517) 29-578) 29-515 29-250} 29-188] 29-085] 29-085} 29-117 | 29-105} 29-188| 29-193| 29-215 | 29-220) 29-128] 29-205) 29-167 29-397| 29-338 | 29-293 | 29-238] 29.242 | 29-243 | 29-310] 29-327 | 29-340] 29-345 | 29-300] 29-352) 29-310 29-220) 29-220} 29-020} 29-160} 29-190| 29-160) 29-220) 29-160} 29-190) 29-220] 29-205] 29-200] 29-180 29-120} 29-080} 28-950} 28-945} 29-000} 29-050 | 29-077) 29-095 | 29-130} 29-095 | 29-010} 29-115] 29-055 28-745} 28-750 | 28-660} 28-560} 29-580} 28-550} 28-570) 28-640) 28-640} 28-540] 28-735] 28-720] 28-641 27-200) 27-125) 27-090] 27-070} 27-065) 27-095 | 27-165| 27-135 | 27-120| 27-140} 27-185] 27-180} 27-131 30-100) 29-995] 29-930) 29-920} 29-860) 29-863 | 29-957] 29-980 | 30-020] 30-020) 30-105/ 30-085] 29-986 25-269| 25-264| 25-252] 25-233| 25.922) 25.225 | 25-247) 25-235 | 25.208| 25-208| 25-254] 25-276| 25.241 siete 29-887 | 29-860| 29-893 ado pe Ane son ee 30-100} «+ ooo te tee tee oo 29-970) 29-950] 29-980} 30-080) 30-060) .-.- 30-114] 30-069 | 30-009} 30-049| 30-065) 30-120) 30-156] 30-093} 30-075 | 30-015 | 30-061} 30-155} 30-082 30-146| 30-125] 30-104] 30-079} 30-018) 30-066) 30-080) 30-057 | 30-024} 29-999) 30-033} 30-096} 30-069 30-063) 30-026] 29-998] 29-952] 29-896] 29-943] 29-981] 29-937) 29-915 | 29-885 | 29-982) 30-027) 29.964 30-060} 30-031 | 30-017} 29-998} 29-958 | 29-987 | 30-006} 29-984) 29-960) 29-950} 29-963) 30-015} 29-990 29-955| 29-950) 29-952} 29-935] 29-937) 29-949 | 29-950} 29-934) 29.927 | 29-904] 29-892) 29-914) 29.933 30-009} 30-010} 30-004} 29-985} 29-970) 30-018} 30-005} 29-950) 29-954 | 29-925 | 29.924] 29-942) 29.975 29-940] 29-890] -.. 29-870} 29-850} 29-890 ane 29-922] 29-8585] .. bcc ase g00 de ies Ae dic aa 29-848] 29-856] 29-843] ... aoc ae ae oon ale occ 22-048| 22-060} 22-061} 22-079] 22-060 | 22-060} 22-058) 22-062} 22-076 | 22-068] 22-049 | 22-034) 22-060 26-960) 26-971} 26-954) 26-964] 26-984 | 26-975] 26-980} 26-964) 26-956 | 26-946] 26-938} 26-959} 26-963 29-943} 29-965| 29-957] 29-944] 29-933) 29-962 | 29-966] 29-954] 29-938} 29-913] 29-877) 29-910| 29-939 29-903 | 29-932} 29-924 | 29-925) 29-916 | 29-946] 29-957] 29-961 | 29-944] 29-917| 29-880) 29-889 | 29.924 29-890} 29-900| 29-880] 29-880) 29-870) 29-895 | 29-915} 29-890} 29-890/ 29-855] 29-870) 29-870} 29-884 29-823 | 29-863 | 29-855 | 29-831] 29-851 | 29-875 | 29-898; 29-875) 29-918) 29-871 | 29-823 | 29-819) 29-859 a9 30-181} 30-154} 30-081] 30-042) 30-042 29-745| 29-765| 29-796| 29-822) 29-912] 29-970 | 29-979| 29-917] 29-904 | 29-815 | 29-754| 29-744) 29-844 29-910] --- ooo ooo 30-070} 30-130} 30-172] 30-094| 30-050) 30-037 | 29-860) 29-884 29-824| 29-865 | 29-962] 29-990} 30-068 | 29-954] 29-950| 29-988] 30-015 | 29-925 | 29-849 | 29-860) 29-938 29-841| 29-876| 29-924 | 29-965) 29-959 | 29-990] 29-974] 30-049 | 30-012} 29-940} 29-900} 29-860 | 29-938 28-025 | 28-021 | 28-043 | 28-076| 28-074| 28-114) 28-095] 28-151) 28-117| 28-109 | 28-046) 28.044 | 28-077 Woke OX VePART IT: “0 614 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE TABLE I.—SHOWING THE MEAN MONTHLY AND ANNUAL HEIGHT Autho- ais Number Hours of Height rities, Years ae ; : Places. Country. see page| y cam Specified. wes Latitude. |Longitude. ee 635. Rin | iia Valparaiso, . : . Chili 67 $| 1853 | 93: 323 |—33 25 |—71 40 0 Port Famine, : 3 Patagonia 4 2 ? —53 38 |—70 52 % Port Louis, . : . | E. Falkland Isl.| 104 qve| 1842 ? -51 40 |-59 0 0 St Michael (at 32°?), . Azores 27 10 | 1840-49 ? 37 35 |—25 30 ? Ponta Delgada, . . do. 94 1 | 1868-69] hourly | 37 40 |—25 32 2 Funchal, . . . Madeira An ee \ ee ad en ; 3238 |-16 56| 95 Orotava, . : E Canaries 67 1 | 1856-57 | about 9:| 28 27 |—16 38 70 North Atlantic | 96 40to35 0 do. 96 35 to 30 0 do. 96 30to025 0 do. 96 25 to 20 0 do. 96 20to15 2 0 do. 96 15to10 i 0 do. 96 10to 5 “Bp 0 do. 96 —5to 0 a 0 South Atlantic | 96 -—Oto 5 Sj 0 22] do. 96 —5to10 - 0 do. 96 —10to15) == 0 do. 96 | \—15t020} 3 0 do. 96 | |-20to25) 3 0 do. 96 — 25to30 2 0 do. 96 -—30t035| 5 0 do. 96 -35t040] 0 do. 96 —40t045 0 do. 96 — 45t050 0 do. 96 — 50t055 0 do. 96 — 55t060 0 Ascension, . : F do. 67 2 | 1854-55] 93: 33 | -8 8 |-14 28 0 St Helena, . , : do. 44 5 1854-59 do. -15 55 | -—5 42 40 Do., : c : do. 97 3y7,| 1844-47] biho. |—15 55 | —5 43 | 1763 ADDENDUM. The Atmospheric Pressure of the Atlantic Ocean —The following Pressures are the means of observations made in July and August by Captain ToynBeEz, during five voyages to India, at different points on the Outward Route :— Inches. Inches. Inches. 35° N. Lat. 30-252 10° N. Lat. 30-017 10° S. Lat. 30-082 S02 Gag, 30-166 oF re 30-025 lee FF 30-142 25° 53 30-092 Equator 30-042 20° . 30-245 20° a 30-022 5° S. Lat. 30-050 25° nS 30-236 15° .. 29-996 The results were published in the “ Proceedings of the Royal Society,” June 15, 1865, but not corrected for temperature.* The figures given above Captain ToyNBEE has kindly corrected for temperature and height. * The uncorrected means were used in constructing the charts exhibited in reading Part I. of this paper. AND THE PREVAILING WINDS OVER THE GLOBE. 615 OF THE BAROMETER AT DIFFERENT PLACES OVER THE GLOBE—continued. January.| Feb. | March.| April. | May. | June. | July. | August.| Sept. | October.| Nov. Dec. | Year. Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. | Inches. ose tee tee 30-090 30-079] 30-056] 30-098} = oon 29-405 | 29-646] 29-573 | 29-304) 29-279 | 29.571 | 29-286) --- oo. ase os 580 29-428) 29-304) 29-396} 29-665 | 29-654] 29-576| --- ate 29-349] .-- 30-214] 30-166) 30-255) 30-247 | 30-237 30-253) 30-311] 30-238| 30-210) 30-142] 30-115| 30-201] 30-216 30-020} 30-268) 30-343 | 30-056] 29-961, 30-180) 30-192] 30-243 | 30-052 | 30.241 | 29.989] 30-071] 30-135 30-012] 30-092) 30-016| 29-929] 29-978 30-068] 29-992) 29-997 | 30-025 | 29.941 | 29-898] 30-048 | 29-998 30-290] 30-116} 30-177 | 30-110} 30-100 30-140} 30-094] 30-095 | 30-125) 30-121] 30-119) 30-180) 30-144 30-210} 30-110} 30-150} 30-060} 30-070, 30-200) 30-190] 30-160} 30-110, 30-090) 30-020) 30-060) 30-119 29-293 | 29-539 30-260} 30-180) 30-200) 30-160 30-120. 30-200 | 30-240} 30-190} 30-150, 30-180} 30-030) 30-180} 30-174 30-250] 30-160| 30-130} 30-170 30-220, 30-230) 30-190} 30-160; 30-100 30-140) 30-060) 30-180] 30-166 30-100] 30-110} 30-100} 30-100, 30-140, 30-160) 30-090} 30-070 | 30-030) 30-070) 30-010] 30-000] 30-082 30-010} 30-060} 30-040} 30-000} 30:060) 30-030] 30-000] 30-000} 29-990) 29-990| 29-980} 30-010} 30-014 29-950} 29-970) 29-990] 29-970! 29-990) 29-960) 29-970] 29-930} 29-930) 29-950] 29-960} 29-960} 29-961 29-900] 29-940] 29-910| 29-920} 29-940) 20-940} 29-980} 29-970) 29-950| 29-930] 29-940] 29-910] 29-936 29-880] 29-910] 29-890] 29-900) 29-920) 29-930] 29-980] 29-970 | 29-980 | 29-950) 29-920| 29-910] 29-928 29-890} 29-910} 29-900] 29-920; 29-940} 29-940] 29-990] 30-000) 30-010} 29-960] 29-940| 29-930] 29.944 29-950) 29-940] 29-940) 29-940! 29-990) 30-010] 30-020} 30-030 | 30-030) 30-020] 29-990] 29-960] 29-985 29-970) 29-980) 29-960} 29-990} 30-040 30-050) 30-050; 30-060 | 30-090 30-070) 30-040} 30-000] 30-025 30-020) 30-010) 30-010) 30-030} 30-090, 30-090] 30-090} 30-130 | 30-110) 30-100} 30-050) 30-050} 30-065 30-060} 30-050} 30-070) 30-050} 30-060) 30-140} 30-110| 30-160| 30-170) 30-180} 30-080} 30-080] 30-101 30-070} 30-050} 30-060) 30-030; 30-140, 30-090} 30-130} 30-180 | 30-130 | 30-160] 30-080| 30-080] 30-100 30-050) 30-050) 30-040) 30-030] 30-100] 30-040} 30-120) 30-100] 30-080| 30-080] 30-090] 30-000) 30-065 29-980) 30-040} 30-020} 29-980] 29-900} 29-900} 30-040) 29-940] 29-950} 30-050) 30-050) 29-970] 29-985 29-920} 29-950) 29-990| 29-950) 29-880) 29-890} 29-950) 29-930) 29-960} 30-020] 29-940] 29-950) 29-944 29-710) 29-780| 29-770} 29-760) 29-720) 29-650) 29-820} 29-830] 29-870| 29-770] 29-700) 29-670] 29-754 29-410) 29-440| 29.490) 29-440) 29-410 | 29-480] 29-530) 29-560) 29-570)| 29-480} 29-310} 29-430} 29-462 29-250 | 29-230, 29-250| 29-200) 29-260] 29-280) 29-250} 29-280) 29-290) 29-100] 29-100) 29-210] 29-225 30-018 | 30-049! 30-037 | 30-036) 30-011 | 30-085 | 30-092) 30-086) 30-080) 30-058} 30-091 | 29-977] 30-052 30-048 | 30-043) 30-030) 30-039) 30-079 | 30-126] 30-163) 30-152) 30-137 | 30-107] 30-079} 30-085) 30-091 28-241 | 28-238) 28.228) 28.249 | 28-279) 28-328) 28-351) 28-349 | 28-305 | 28-286} 28.262] 28-247 | 28.280 The Pressures reduced to 32° and sea-level, on the Homeward Passage from the Cape, being the means of five voyages in 1861-62—63-64-65, in the latter part of February, in March, and beginning of April, are as follow :— Inches. Inches. Inches. 35° N. Lat. 30-034 10° N. Lat. 29-986 15° S. Lat. 30-018 30° 0 30-098 aie ee 29-944 20° x 30-040 25 5. 30-202 Equator 29-950 Dig G0 DOgaes 30-122 5° S. Lat. 29-954 30% Us 30-076 T5s sf 30-062 OP 29-978 It may be noted, that if Captain Toynprn’s Chart (Proc. Roy. Soc. vol. xiv. Plate VII.), and the Isobaric Charts for March and July be compared with reference to Buys Battot’s Law oF THE WIND, it will be seen that the Prevailing Wind will blow aft over nearly the whole Outward Tract and the Homeward Tract to India _ or the Cape. MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 616 TABLE II.—SHowING THE AVERAGE NUMBER OF Days EACH MONTH THE WIND HAS PREVAILED FROM Nortu, Nortu-East, East, &c., AT DIFFERENT PLACES OVER THE GLOBE. , x oo j Tee i — ee ——— aneeeeceen | 5 E - a | 3 so a s sninihaiaitecch S ‘ oO pu P Al ce SO OM oe Sees oan |S ‘2 ZB OTN HOY WHO won| 2 B ENN ie) al Cc . ~ . s . a E ANY maw ON aa | Z EMM NBA AAN awa |g a FE OM M ONH HHN HAs |S > 3 ce oe) ra ® =i 5 ae g.| F onw oOo nnw noalgZ Ha | Emon now nan pod bs Py Oe See aor ee eee Sto mares pre | oe | = oe = Soe D : ; = mer |e AE) da Me NAM Aa ao |X aZ| a AVN own owe wae |S 32) 4 HON AMA MAN oven on | & FAS |e a Seer anc arco AS : ase] A z Moanin Horo ats one |Z am 2 AN 20 HHO mM aNM wen oo | S "Sp > el ANN FWHAN aca | a 3s S r 3 HAMANN OMA BAAN aa- | § a qm AN ANN AAA =-o(/8 o Gg tNM OMN BAN aaa] 3 , ee ————— aT [=| = ie =) ce) 3 => oF 7s a er) a4 TNMH HNN Be mt HOA a sae N MMM MAT WAS 3 3 7 OHH ON~D HMM HOMWAN 5 Z a eB z N A Zz SE Se Se eee ee SS xs = S) 2 3 = BAe ANS A -a-|= a ZaAAN MAM HO aaa | 2 & Zommat Hw mot owe | 5 . : l aS WUBRINNAN wees NAN oso | b UR Oe ase OO Aes on-=|S ai UWUtOM aR ae NAR Ae aoa |S BS ; | i k | i Fue wow wn aso | 5 1D Fatt mmm Ham owen |S o3 FM min me wn dH aon. |P eo) ai wl ei eo Zi 4 ; * : q F \ og F mmm OND AAD oon |% B OOM MHO HOD woo |Z a Emoto wtnr OWD now |e a FX is 5 SS] FE aoe ons noe nro |Z Hoe | EF owo noo 00M ane|5 na Fowdt mno non van |S oD nm lee ee) ei = oO mn ao ™ for) Son : Hl Aa MNN ANN ANM aaa | gel au HHN HON NWO vow |S TE8] Gg MON AAA MAN aan |S xe & oO 35 3 he 3H 5 on aA] aM Nn NMA ANN aan |S S| F nan owe aan aan |S a Bo pcre MAG crores or dt | oy 8 S) i 3) é a n : = op ; n pi} ANMH ONnMM ANN woo |S RI H NNO HHO HAN aaa|e 3 ANIM DMHN AND MIDS | w& n 3 = : 3 : Es : 5 on Gn) Eth ont ana | 2 5 A Aen MH MAAN ana | x a atuee' oom ANH vow | 5 2 A a ce 3 x aS i] ZaAANMAAN AN aan |x 2 ZANMD NBA AHA awa |e 'S) BANNAN ADA ADN aon |S a UWL HOA att wen aaa |x = UtANNA ANN AMA aaa |e 5 UuRDANA ANN AMM aaa | 5 I 7 I ine} = ioe NX Foaan AAW ota =--|§ 5 F oven 6 mot own vo | Sy Fon oa ot mae Hoo ooo |S TI & 4 ~ . im : > o) S a gS ee i ee N SLO) aan [2 8 Ewmno HHO OWO avo |S a Fone nan NOM oon |e S + — o o > 10 ar EF moo mmm mam won |S Ao EF ows Hot How wi |S iar FE nom mNno Or NON MW | o': 2 al See n rq = ao ca 10 re Rc ANM MMA aan |S ae Ag to mae ANG avo |S 2 A MOA Me MOOD ooo oo | 22 ¥S + 2 BS 4° : =e) > RSS) 3 1D ee Boeo oa NH Hid od 09 oD 09 aaa |i SH | 2 ooo nor 1H ron | 2 Biel) |. (op 09) 9) 960 HONE GANGS GI 8 99/09 | ce S = 3 D eS n gAwmwmno WOM MOP ono|S wm q Nam MOMNM BAAN aaa | 3 @ Gant WOT MAAN aan | 2 = BY: a 5 : Ss} = ro 5 ie) iy pee ee eR rene woe | F — Se a ae aan | 5 5 i Revenoms ep ees aaa |i = no) = Ep | 4 = ; 19 a yZVwtw OWNM OOO 0 oie | '5 & ZANM MMA ANS ana |S 3 Zann ann ana am | 8 re] ES a ra ei et ms : d Ha a a ro) : : 4 ey SI oO . 6 Pay rs 9 fA D Par Be elesta lines Zz goes Bee Swe Sb o | a e Hoe a eS kes Bs |e das Bee 2Ha 8631/5 a aS Poe es Ses |? 6 ao Sess) Seo SS 25 2 S Sos 255 523 O40 |> a baa aa5 Sdn O40 |H = Beeson Ore mel ae aie se ee 617 Wee TABLE I1.—continued. AND THE PREVAILING WINDS OVER THE GLOBE. a j os ° Us N MHO OAM =aa|S 36 “UFO 00 MOM HHO reo |e s UHI HNN BANA AAM * Cc a TT —_—_—_——. sl E l ® BAAN MW Was aac | 3 = ar Aaa ANN aaa |2 GR Emo aA N moana! S ~ a eo ice) | ° el rH 3 Pe Nore NE SUC 62) 260 et oo cv on | 3 o E MINN OHH SCH wonle & Boome a © mw. i pa Ho | eB NAN AAW NAA ANIM /|A sa | & WAN ten oo” wo | 3 mH EF Ho o9 a no]. Re) 2% oes ea an ODD OWN Hm non |e = n sss see ANON aaa| acd gag ~1oo A BH 2H O65 > to na SS Ean] na = e n x 4D : S : 2 HAMM MDH HHA nan |e a AH WOW Hawt ato wae |B f Bg ANN S < a : a : g SH atlcal ANA ANAS aa-|s 3 E ho wt AH noo|S a ete a 5 5 S a" s ZAND MMM ANN aaa|s = yaaa Ono Con aa | 4 tO 00 S =a WR aa OAH MoS =-=/8 8 WRONANH MAN ANNA ana |S S THTBD of cv) = - OHI HOO OnhKrR NHM © a SH 1 : sH 8 = Ke EA ie HO WH nRinm aon | 3 BZ NAN x Lan . il a ~ na . op | E OO Bee ON aaa |x q SE NHN MMM HHH aon | 5 a ze Ne cu u Ow o . Sol F aMNA OFM BANOO See pO | ee pw | = a5 o ; -| F WMA MHM MNnH OAT ~| F aan Pies a ests) oe Mee! for) co N a st oo ue oD cor : : Ber) 3 oe) 2 Aa NAH AAS aaa ls Ben wh OnD NOM HOO ono|S Bo awit 9 ym . BS eae] 5 e5/ 2 mmm mmo Noo wa |S HS) 2 wmnm ANA ANM wno |Z Bol] A AM =4 Fg ee -— Ae a PAS. na So ~ : ZA HASCmM AMA Mas =aa|e a aHwmW ANN AAN aay | 5 x] a wos eS :S A a j 3 BOF Ne VHA ON om | 5 & NN Aaa aan aca | a ‘S BOO SS 3 “4 > g = 5 zrNam HHH Hoe a--|& za Zz AMM OND O0OMN vor | 2 3) % 12 Hw 8 = [ue : Dit ae rs) MIRO A eD HHO 1919 woo | 19 QB | WIND om ON = ates Sls eS wae a |e 2 B wwe wie nny went | 18 6 BZ TINN MOM WHO aan |o 2 BZ NAS re n Lem! « nN i - (oe) ce 0 eo Z F ONO HHMI WOW nao |s 3 Eto ONnN oNnW 2 oo 0 | 2 g = AN a ee Hod ® oS Ss Re | FE C00 ONK 2HO wveo|e D2 | F wow dit coco wow | 3 Piet) ae Ounce =) mo n LN n aN wm Lama! “Sly manana ann aman | BOE) Me Mealesten Vag entriay Gad es cel eee OB) Gy mma 5 ees r) oF E an n D a ea ua a mH oH es z a5) ° Os |e S Fe) 3 es Eine) Om AAs sete AOA | a Z DOD TNR -~“MO HH W]1o i 7 AAS nN std |_a aw a Aa a A : is] gVwo ROW MOH now|2 5 A HTAM ANA BAM naw |s Z qa —m7aAN < a 7 > qa 5 3 3 BN ey aes |X Sg 2 a Hmm won sa |5 BS 2 eS fe nm n ot rol © a P q ; eo Zmot Ht mons ooo on | 2 3 Zadae ANH WAN =au/3 a Zw Man Mra oot | aq | re | | I & Con = ) $ see | pees a : on r () . u ay =| () : H Fa pb > ap oc ee) : H i Paspr a 3 ES S55 SPE SSS |S 6 | gS8 BES SPR EES) s E d63 B28 SPE SSS s a bee dan 540 OFA | = Rea «aan h4n O40 |H a Bea 4465 14n O4A/H VOL. XXV. PART II. MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 618 TABLE I1.—continued. : ri oO ee} es g nee all Palle) ge a5 = (=) iy EB & n - oa _ g nm 8 Years, 1859-66. Hour 8: Wisby, Sweden. 8 Years, 1855-62. Hours 7: 2, 9. Upsala, Sweden. Monta. ranwg se il a lai Pi] t g [MM m0 = e i Sale ee) Me E ran lie SRO ML Waa ace |S He) AMT OMM OW ana |2 © se ANG Bi CNS OD) OH GNC EIGN EA Ney 2 g al Nineees . oO . ; AMA onNN OOM aan | 2 EAMH MAH WM aoe | 8 a Eno HHnK DOW wie |S SS eed s n nm mM EF anoo noo ma nen |S aa F 0 0 OnA OO roa | e FE ose Hino HNO onn |S wm aie Oe reed E HK ANMM ANN MOH anon | x Fat Pap Mec CPCON AN aX NSS Ls) win o | SE} A DAH HIM aAMw ooo |f es ian] oo . . Aondw ann mtn onn |3 AZM} A wmm ANN Ars owe |Z 3 A MAN AN aA ooo en | & nm i nm | f= SS HANA MMA WAN anal x S| a tH MON ANN tian | 8 RS HANNAN AMA HAN aan | x = al : “ ; : © 2 Ore Hom BAAN wae |S ES aT iy WON OO Oo wen | a Bot et 1d HOD 6D OD SH aad |S om 3 ev . ZANN MMA MAN aca |S 4 ZatN MOHAN ANN ana |Q a ZHtodt ota mma aver cy | 2 WRANN BHNM BAN ~on|2 S “mB |: “weg ae = a rho | oo as E Ole BZ VON MMA Win vo | 8 2 BZ NH MoD AOS aac |S So | FW MM WINN vive | 3 Los] bo ons = ONM MOH OM owe |g a FRM tot ONO van |s Firs = Sem4e COO HHO mano So « « = A el or E (=j | -> i am ww CnW awe |Z Ao Fr COR HOM HMO aao|s £o FE HOO Onn OnN aaalo ow Las! rset at n Tae . . n MOH ANA Mm HW wet |S oo A weno COM ONT =a | 0 36 nan wtoo rROrY- OKnRD ono | 3 . _— me bm : : 3 if Bonnin How AM win | 5 88/8 ono nnn mond non |Z ea | A Onn ANH AHN aan | n fafan| n oH nn ree> % os H e . BH mmr MAM ANN vt oo |B a Rm MHA ANN w von |S Ay | BH COnm COnm OOH =o |s Bann mnt man ana |’ a Bunn Hon ANN AMA 2 ae Anne new mno non|S %, ine) E 7, Ine) D 7 bt . . . N BAMA MON wad aad | 3 & Z mon OSO HOO cool|n Pepa esas ao Shpall Sa ieee ereelis9 “mye : £8 | : Ce ic 0) ee | : oi fueo cae : | : E ae laa raisacih kcha |t-e = ZB Yam ATA moo ote | 38 a) BZ Tam Sin OK vo oo | 3 wel gE AMM HH Woon aan] 3 cy) wo rr 3 ‘ E HOON ANN OOO sien | x oo se SUNG MoCo Ss eos woe | gn bE wnNo miro ONnW wie |S Ho er =) os — Food wo Hod vow |S par F 00 WIN WMO von [5 a Pace Se, Sonia eH otelare, N oy j nh) — E A HHO MOH Hod om | 2 S| A MMM MNM HHO wit | 3 i: nM ANN AMS on | > ad 4 - : = go ; 4 SAAN ANN ANA aaa |S a6 AH oWto WHM ote roo |Z cafe 4 ANN AANA AAN oon | 8 ———— m|@ &o 8 ‘=| on “ HANAN AMM HMM aaa | & 4 HANH AMM BAHN aan |S a Ba ANKTH HHH AANN woo [5 Eas! . nn = no : Aawtnm OKO Hod woe |'5 g se at AN ae vines | 8 $8 Boca en on MHA ANH aaa | 3 Za 2) e 2 7 % ron HNOr- KYO noo | x a ZANN ANN sae mon | 2 Pay Zara N MMA ADA enn | 5 = | ej | S| as Oe =| (0) . : uw eS =| ® 245 : H a oO o . . dace RpE PRR SES ls z cS a BPS Pa 58/5 5 dca ESS cee 5 Ss ao Sees o o rob) Bee dAS6 64n OZ2ZA|H = bee 4565 640 COZ = bees 4ae6 64n O4Aly 619 AND THE PREVAILING WINDS OVER THE GLOBE. TABLE I1.—continued. * e wd EM ieee Eee See Se oa de || OOM Cha free ee ES S anh Gene oe ee nee ale os E CR era Wage Se BE a ey Mattei eA) Mert se he © % z X2OR NA ATS roo|S 69 BAND AHH Waco awa | 3 63 a see ANS ---|3 oak Coca cs ae ga| EE ano non now woo | 2 a E NAM NIH Wao aoe | BE) fo wee eee eee aaa |S 5 | gf oH Pos | FAN aN A nese | 8 se Fonts CON NON ©oo|fh me EFmaso ooo =oN AoA N .. Oo n n = Lon! NN Hy CO 45 , S ‘ , T) an ANN BAN FAM aan |x a5] A NOH HHN NM ten |S gdp] a mann sae ane mae | 5 oom jan ao cS) 3 oD . : 5 us 5 ae A ea 2 te e= |S e BAAN DAT MAN aan |g mo) BR AMS HOO Onn =ova | = HS N 2 ——— & . =) 4 PH 2 an gy COO sexe OFS mea |s cee BE TDONnN HPN HMO AOE pel eas HB Nes On Oo s= OO onalo a : == se] - =— Oy ; 5 Home Ne HOM aHoe/S 7 AH HOD HHO On OWHA|2 rs A yOnR OhwD nHno RoOo|® = z — - & ~~ a 3 4 hand 5 Zi fo) . . . = AmaaAN ANN HHH aaa |R = ZmMoo MAM MOH avo |S 3 py ee Sey Srey Ses — < ‘mED ¢ 2: | : : wyBO : ate | z a “mTeO ' Rete | : N = Phamns) 2 . . ° : ~ Yen) — oD E SY i oo BZ wt ONS nod oan |g a Foo RRO RWO van |g 92 Zhao ACH 00 one | 8 Yen) io) ~= — 7 3 co) 5 a 5 z EF WMnR CHA OMO ova |S a PE We ANH NOR ~a0 |& fF bE wd MMM WHwH am |S S Se gD LS i FHHH mit HH Howl] S goo | & Mae HANA CO = oe ie ee ° ol ee is Cae x mae | a SCS |e DO OMHD NMHM OMM!S rin = 7 S . co . 8 n HOO Saas Be awa | § us AS nnn aA BOO menco | S n NAN See NBO =na | é g om : 2 . dn . g AR aand aan onan aoe |S a3 ZB mON NDS COO aso [x ‘a5 BHAA SH Hoo oon eo | 5 i) 'S ° im : ad 7 n ‘ & HOOD OWN HHO non |S nD H CAN sea oO ood mon[é ee HrRODO MNO BOD ane |Z « oS se 5 5 is) = > = x 3S sH a= 5 2 5 ill. — St aaa |x 3 S ipaaae en Se fe No Score & NOM nHOn ae acc | & Lot i 3 BMA HHO ae ama |S © ZNOn ornwn onwn oa on oo | t S Za-ad oOo Onn =a | m ‘mtg fs : eel ie q eet i9) : D |: WOH OD ONT ANN aac | & & a BB | isi J Th Ea aaa | tt al E ree) e E ol % , ee) oS hs vai EHmnm mon OnNM soo oo | $3 Sl EE HOM AMHR OH waa |S Hal Foto wnat ano soo oo | SF m ~ 7 =| ac o< fos] 3 Faoo oor RRO Oon | En| FE omtb mtn ROO Hnhun |S Hel Fann aanm Onn aman |o Pio n = ce anes n = ao aA os m LS) SE) Aa ttn man aan mt | 2 oi i MOI Wh 1910 oot | =o a ANN HNO NOK aan | 2 qi Ee f.e . ‘. 5 c : aor = 3 et ee oe el acres |S ae a ooo naa oon coo |a BY woos =—=S3S One on |o q § Sip E HMMA HDAN aA H aco | 8 $05 sta N MAN BAAN ona |S a AMON MnnNN aA awe | 8 e : = : on = o : | 2 wo mOwm ONO wow |& q BAN oH NAN ana |k a ceed mrn onwd ona | | 3S o A = ZhMM HMMA AA ano |Z i Zwvwtnm Ono tad vis tt | 23 ‘mya > 3 : : : | : cl [Mkhoeey GoS See anola : wD 3 E aa + E ~ Gk FFE ale ition yew ode Ba re RAW HHO Hawt add | s S ioe) ® : ; a am - NOOO COM HHM Ano |R aa gS Be] FE naw Hi Rim aan | ¥ i F ONH AMA ATH waa |S oS | ot : pre 10% aol ua wHtHo DOK ROW ois | 2 ola Heo HHMm mon can |Z are ——| | de}, mS 2] By No) SM] yg mtdt HMM AAS awe |S = BG Naa OMM ANS ana] 5 > 8 oO . u : g a OHH AND MMO aoa|g 2 cc BACON HAN NAH aaa|s [ext q oOo ZOCOowm nim HON rao] =| ZARA MMH AAN aan | x coli Pic Skea : | : Pere [oc loa aa : : | : ro) = io) | x F OOO MAH WOH 2s | °3 Ko) Re} che Sel Cole eh ighey ones S oO i°.2) ; 00 ot : a Ss 2S fee Sa SE ra | FOO Ant ANA one oy n — ie uw eo) s ® Fann mat Anm ano |g by os F aan HAH 009 moo | is la. wn on n 10 : oO i) : oO st B n =aas NMN KH NN AH = (2 on SION St Se HAN an a a oe 5 a siz) A COHN AAN OMAN a=—|5 Zl A HAM AWN MONA WHAM |B x Gq mAaAd ROO KNO van |Z SH] yg man Hearn ann onma|& Lal a : : : 2» Bo oad AD ANN aanls s Eas monk nMo aam | 15 Lan le} bj ® ZmaAN ADNAN MAN aa | 3 = ZAHN AABN ONM aaa] 3 z F I OS) SS) P : H iS 28 Gro : H 2 doa brs SPs 353) 8 : G38 RES SPS 85S| 8 ° ® S ® 3 Bee da65 65407 O4A|H = BRe 44a6 64n O40 |H 5 Years, 1854-58. Hours 6: 2, 10. Debreczin, Austria. Mont. E Hon Hato a S KH NM ANH esa aa = n nea Nee Botti ON Gy roa om eB OKN HHO Zowmini WOR TmPO In en oD OOO N F. aN ONO = nn Funan AHO mn nNnoro mwnm A Sse SK NN wn Bq Nant OMN R ae ON Se ion ioe a - BON OmMO a — —= Sn Ah oe ee ah SoS O85 bee 4aa5 621 AND THE PREVAILING WINDS OVER THE GLOBE. TABLE I1.—continued. ik “uypey = iyi teyecs oo I~ a Siete Sonat Ss nl be wre Solos ~OWD DAD Sree an | — a is MHD ODO DOH ONNIS Ss ic AHN ANN MOAN Bas |S x) ie NAA DMHM HHAM MAK ou boil re ee) 5 ee : = 3 a FmHToO HTO MmHo Hno]/ ee EMH NOHO HIM Wrw |e g EMO MHD MOH HoH | i) H Ores a E No) By E S He| Ee H S. | Won tHo mon now | © cae , MOOD MMM ATA AN~ |S as - TWN wot ann oon |S HO n xs n o:s vn te! = Ln} = Hy] a OH MAN BHA te | S m5 Bh aAM ANA AnH ANNA ge | 2 AAD Emm ANN mma/|S S : i ; ‘ng F SA | FE Hom Hon tam Ham | 2 A By RUG ee CA eather 0 tia S35) aR N NAN ANN ARWHA!S ae n BA wm td = n Ss | n Pe GID AOH Age Wi = et GZ mtn NOM Ain WOM |S ad Gg CAA NNN AHA ~ao |e es = ap 5 > : - a = HAN THAN mam maw |S ise fe HAM MMA ATA Amo |B 3 : MAM MAD MAN aan |R ) : 3 ‘S) 0 ie BAAN MAN MAN Nam 1A SI Zar N NAN ANNAN HH A/a a ZaNN AMM HON aan |Q . a _ 3 WONO OHH HoH Han |S Z URDR ea eee Aes ae | = COTE) cere) GNU GUS GUNG ST ES ES S ev} I i - —— wD ® Fann Ane MANA man |B 3 Fano aN MOAN aan | 3 ie Foam ANH ANA aan | 2 rt lee) - 1 n ° . a 5 3 FE OnM NOM DMD oN | je ey Ew om WOO RRR DOW | 5 a Fm N OHM mmm Ma |S 3 val - P Sal eS) = ee) 3 = S - WWD MON QDHH OMO ] is rales HOD ses ANN HHH | Q = - ©oCS Baws wes woo |] VJ Sa| hd mann mma mmm WH! S “3] d Hom ata maw maw | 2 “HE ANAND MMM NnMM NMoN | B SEAN) : am | s ‘a gid | ? é |g n n p>) mn - t=] a ey ss B Bi MAN ARN ANN ANN] A a BH POA AHS HHO HH) Da Gq CtdW AMH MMA HHO|F™R 2 a = oS » aI = = ; ad 7 3 Pe AN OHH ONM ANA|S B Bana mam MMN Nam |X g Ee —een ee er | SS ca Z a 5 Z of =| z 4 S| 4 2 2 3 ZAON MAM MAN ANA] SF 8 ZAnW mno KNOW owes | i a ZOon O©Onm OAH WHOA! TOONS HHH MAN Hama | 5 BP [(UROANA ATA HAN ANH || ni UR AH MOO MHN Hi | F ‘ i SS _ 2 a 2 VWOA NOW wm9M aac | 5 re F AMD Mmm MOH HAE | = E ANH ANM MAN AANA|R Soy oI = s ss o . . . AS) FE MNT MAN AHN ao oo | 8 a EWM m CON ROO KRONA of FE mOAN HHO AdWw woo | & “Sa Ee 3 = TS s/ 2 nwo nnn nad oon |i HO | EF HN NM OH want | F Ho} EF aN NOM MMM AAA |A 5 n oN n oN n n ¥ a 2 Ao 2 A Wino mitt oom. ros | 3 ~)| kh On OM MOH won |% “S| yg mon Hit mom amo |S . ~ Q : ao : a8 7 = af 5 a da | F CON HAN AWA eae | 5 ae A wr o DHN ANN awe |% BE! PANN MIN AMA AND | F aN16 =| 2) 5 td n I : 5 : = am Gq moto tam Wor soe |S a GB MON MAN ANN ava | & ms By SERS OO PORES Ta See < 3S ae op O16 7 5 o 5 - Lat 5 SI 48 S sas ANH HHH aaa | 5 S Hon HMH NAS ~ao|s q . OOH NA ANA ANNA a) A e's 3 7) ao Zmonmnanatt Hon =a-=]8 a ZANN AND OWS ama | 2 Si ZMAN HAN ANN nan | a td ra — Bt is a — i = — elon q = SD Pepe é H a BS) acre eae) Sunt es Saar an lai a » 22 Bp eo pass : H z ges BFS SHE SSS) 8 B BS 8 ASS SES 855/85 5 Se BSS SER ESS |S S Re ae R4n O4A/H 3 BRE da45 64n O40] S BRea de6H 4n O4A/H Tae 6 VOL. XXY. PART II. 10 Years, 1855-64. Hour 9: UBD OO ee Barnaul, Siberia. 2 Years, Aug. 1847— Sept. 1849. Hours 7: 2,9. TABLE I1.—continued. Ajansk, Siberia. 10 Years, 1855-64. Hourly. MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE Catherinenburg, Siberia. 622 Monta. s Nn oo fe Nn % ron) a) ~ NAM DHH OMH WH | S & Palos) [a i bila ics 4 Ro) co aor . 1 = | F ANN MAH won ana | & <2) ANS wae HOM aaa | © pA go] - —) an ° eo) g a) Z _ a a — a Mi a yee: et 35 che Co SHH an NN OD soo oo | ay} : ro S ia all Maa | op AwWO RAO HON now |S + “UR - 1 ; 9) > : eet we val Gn Sls ‘i ONS MEESD USAGE OO Be SOR a 10 a E > ANIM WON a iS a B | Boom ame See. |S ~Rbee Aaa Sag See hn io.@) re 4 — re . ~ . B oe = SO CSS coo | a PoHOn wee HOH a= |e =P as isd sO o o ta see ooo coo] a Foeosco ooo ono coo | wt : =p | oD Low m aig ‘no PA ere se sa} 3 2 ag. | pet Stee Saisie ooo 2 ANNO ONO OND how () Go] 2h |— S eo Da yg mmo OSS onrNn | xR A g Wow NAW AIS acl wt | ay : eS ADA ANH 2 £ Boos ooo cocl|o : 2 Hem ao He on | ron) fH » DDS MNO aan | a Fe : Ss SB NO ON Se = me x ay pe Pee a ae or) a Zi aANAN NM TAN AN — : q 5 =| ‘ — fae] Oo z jee] om o 5 J =p OD pp wey u a Cs o H a ey te my ar Be 8 ooo é z S35 kas SS Grae z dos EPa PRR EES 44545 ain S hee das CO4A |H S 5bRe da25 540 O47 55| 1 1 623 22 U1 9 |10 | 0 Ww 8 9 7 10 11 |12 0 0 1 1 1 3 Years, 1840-42. 1 Hours 6, 9: 3, 10. 4 Years, 1865-68. Ss. |S.W 1 22| 26 | 84] 85 1 S.E. Hours 10: 4. . |N.E.| E. Roorkee, India. Chacodate, Japan. 4 Years, 1847-50. Hourly. (or) ley) tre piatess Se tralitce)i¢) EO) Mea) = 60 = e = BOD 11D 1D GIA co aS EAN OMAN HAN x = >) ~ Mas NN ANRN KH BN a nm n Onn ANA Bee = BmMAN HOR WHts wm ee ma rd BANOS HAN ANH SS 2 om AaAN AnH XS) Sa) Ses) eo S) =~: N. 5 Years, 1853-59. UCSHO SBNa TAS Madras, India. 39 | 68 | 14| 22| 85) 76)| 47 | 14}-- ONT HOMO OM Now ONw COT ANH Pha TH se om 1} Year, 1866-67. . |S.W] W. IN. W iS) 0 o) 3 ony Ota Sliema Hours 10: 4. Omyt MHNM OANA Hours, 9.30: 3.80. Mooltan, India. TABLE I1.—continued. Hong-Kong, China. 6 Years, 1861-65. Hour 8: Calcutta, India. 75 | 38| 14 | 28 | 65 | 64 | 22/35/19]| 4 AND THE PREVAILING WINDS OVER THE GLOBE. 2 Years, 1867-69. Hour A.M. and P.M. 51 Years, 1863-69. Hour 9: 54 | 48 | 58/50/18/30/50} 2 || 18/81/97 )63| 9 | 35) 19) 20) 23 18] 1 | 32/75, Shanghai, China. Jerusalem, Syria. 59 1 4 Years, 1865-68. Hours 10: 4. Agra, India. DBNUNN ATO wee 4 HHN OMN COR pH HMO NHN COR : wna Ata sae zm aa N ODMH ANC MontH. MonrtTH. 30 | 28 | 39 | 22 | 22 | 26| 94 | 28 | 76 || 56 | 19| 33 | 32 | 87 | 36 | 27 | 21 Mont. MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 624 TABLE Il.—continued. ~~ — ee a ee ee a f WLINCO AMN ARO =on | 3 UROSOSO FOO HOO ~oo|a ie {ws : : : le © is: a ao [re = pal 2 WO HOW ANA AMA! 2 Sj ERR Fae So Bik st co 60 CY | 45 eas’ [ces US Se ae OL mes Ye ues o : Pe) eo . . 1D oe . > ti “A]| FE OND OMA AMA =o |S 3 ENAN wee aA maa |h a| - LS ee aes ee met : HS . Sinn ‘4 $0} F CON NON HHO wou|3 4 FOODS MAH Ane aw | 2 SOLE noo Hot HOt won |S mS |_2 (is | eet —_ as na ayes e48 uw OOn CON mor -oo0 |& ie A Anh HAN AMO won| es FIN pica aia Gar aps oad Sane = ooh : ; en : A i a yp Boma N Cnw HAM wao|R S AR OM HMA OHH con |z ag | Baa NTA ANOS aaa |= ‘ee S| Ke Bo “A ee q Sal 5 Bae] eH COD DON HON wot |B 3 Aq ANN MOM WHE was | re | te SP ROBES: GO UN CME ORS “ce % Pc} a i 5 Fea] (=) 20 = A “4 a ; - wwe oO aM HOM aan | x zANH DHOR ONO wan |g KM ZANM HHA am mma] sy is “wyeO : : . . oJ URQOom= = ae O Saas ae Oo |o of ete) cei : : nif Es Hie 3 E x re eeera tear 8 EN MAA RRA aaa | 8 . . Sl . ip Ne — YG? cha aan |Z ef cr SH ee = 10 2 oF a . = a x on z aa a BE SOSS O-n ONMM acoo|f Bl Boe Se ae psec Bonn mann anw onw/S | HE ipmo Hom wmOomM Horan |A s REE = c a Zi re 3 Zz = o A Zwmonn Nnma Awnr can | oR Boma BAAN NAN =a] 3 ‘aa ZOOS Onn FHF HOO] os [MOR OO OHH One aaa | 3 _. |(TMOnNtm COS COS eons ® Oma : Va) — omer Loma =e =H oo Pee eee eS ace | 5 = it mo aos oan occa. |S D Fagan ana wan wan | x 3 Z Renye A= Sy a 4 cps fale u - c) = 5 n . ie) o FOmRN HHO AOD oao |x o2|/ EF mMa4 HOS CoS =oa|o a ESE Nic Nac) OT =P On =f 00) sae | & a be Burs i) 3 : oe) (aXe) 5 oo HS e SH 19 hRO OMHO =a-|s Rss) tal aN SF On BO een |S PA E MOD MMs NDOT TOS ! io =) n =O —) a nm for) Le a Oo aed 5 eS n Omn Maen HOw ano |S BS BR Onn BBN ANN =o-|% Bae nan HHH ANN ATA coo | 8 :5 I 2 fy =I) : ea) = 7 4 fefjes) al iS) = | ~ aN A S- eee NAM am a Sat Bas O'S aa | 5 Sela ia gus eee eT SS) Saba g SCS Epon! or) oO rm oS _— ma is Ll =-— ee _— ~_ — Er Q ; 5 5 5 o a ~ El a Se COO occ one |9 lal eae =) ome | a = COR SSC OS MERIC B Be baer — — — + a} fe) RA o 3 ~ ie) a I a SSaea oaSo Coe Sees ES) yt 09 0O0O OOM wt eo.o0 | . fes| [ . ot = fe) é = is Oo = o ee F, ss To 5 . | Oe Oe as ie H : : ee = . : 5 | 3 5 | 22) Big ibe, os ES 8 E aas Beer eats, 8 eo 3 > a26 Bee pee ees ) 3 Ses fae Sao se8\2 S Son fia FE o Seals S See 4qa26 640 OFA | S Be q8365 64n OZAlH S bee 4q4a5 44m OZA|H S ac) AND THE PREVAILING WINDS OVER THE GLOBE, 625 TABLE Il. —continued. Moar Hobart Town, Tasmania. 5} Years, Port Arthur, Tasmania, 5 Years, Auckland, New Zealand. 8 Years, i 1861-67. Hours 6, 12: 6. 1861-66. Hours 6,12: 6. 1853-59, 66-67. Hours 9.380: 3.30. N. |N.E.| E. |S.E.| S. |S.W | W. |N.W E N. |N.E.| E. |S.E.| S. |S.W) W. |N.W c N. |N.E,| E. |S.E.| S. |S.W] W. | NW E iS) Jan. SAD | 21 4 | 3 Mi elllesleale Gal dealt Sell Qui Gils sealeenl cern i ve | Se Der WO) | Bei 2) ike Feb. ae meee Dee Soe ile aieces ee Nea fb mmerl| Dee AL DE 7. iD) ole, al Bi || Se Onin aap On |t-aalire March) 4] 1|2/7/)3/]2)|2/1!10 ipsa eddie spel i eal coe eam eS BW GW Be Be I aa ye sh 8 April So\eeni le | | 2) 4.1) 2 1 1d Dee OM Din) mises al 2'4)2)|41)] 38 }10 | 2) 3 | -- May AS eat te) Qe\-2)) 4.) 2) | 14.) = PIAA (0) a Ses heal) a7 EN Bt |e 1/3;1;)3)4 10/41] 5 damenie4s | Tit) i b | 3) a) 15 ON SP hey) a 2 SW Ga tf, Ly Be By ee a teh eta) 083 July Sele le 2a 3h) oy le! OM eet hl 2 i) eit GING: 4: PB) BB AEN ZB BY Wino Aug. S233) 29) 4) 2) 13 AS EON De ON See lee 7ae| ween || de |) mel Ge (4a le: | Ob QA 4 ics Sept. Seems lelecalee lear | 3) 1512) AS |e 3 | NON a) ||) ob Onl on |no Qa Ge 2a Se 2 We Sp 4s |efealis Oct. Aen le Ga) 24) 42) 2) 110 Dede) IE Gy) 3 Gp eae 14 QA 1s els) TOF Gy |e: Nov. Semone le ior) Na) a oe | 10 Oe} By WW By] ate 4 By Qn ee Ol eer ON Ge ee: Dec. Smonleon i Ol 20) 2. |) 22-8 TE ES) LO || es) >) BN ly GO ee | Ze iB Year | 45 | 22/16) 59| 23|39/30/131 21) 44/11) 59 | 26} 73 | 46 | 85 26 | 59 | 24) 31) 41)99) 41) 44 Monte Christchurch, New Zealand. 4 Years, Dunedin, New Zealand. 44 Years, Southland, New Zealand. 8 Years, : 1864-67. Hours 10: 4. 1862-64,66-67. Hours 9.30:8.30: or 4.30. 1858-6, 1866-67. Hours 9: 3, 9. N. |N.E.| BE. |S.E./ S. [S.w] W. |N.W g WN. |N.E.| E. |S.E.| S. |S.W] W. |N.W 5 N. |N.E.| E. |S.E.] S. |S.W] W. |N.W E iS) Jan. Ste Se Ve OF |) tel Ze) Le) 40 Pa NE 7h ML NDE N83 aN ath est PS OR ton) On| Om el 8] 9]: Feb. A ete eee De eee fee Op 2. Gy By ey ee at OR 2h ese On ls On On ts7, Mien naan eon le eT Oe le Dee De Vs Te Ne 2) Gal 7a!) LT | 6 i lO) 2) 6) oO} Wl 11! 10 April OR NKOM eon) 1) 1s) fel ee 2)| 3 1a eae ee esate Poe Seinen! 7 Lo @ SP aE at OTE) Tea May ee eraeliecsin oe Mey Os | te ee tS Hs IE Oy a EO By Ze Poy) C0) 9/15] Mamewie2e| 5 45) 26) Or12>| Qe) 1 | 2 1 Pom RON On nies iG ile ioe QeeOy eae. 2) OF al 8/12} + July ae essen ee ene Me eee Te Om Oe Se Ons lel vor | Ga 2. Ori Qi tail ve) 451 Onl Oo 6/12 Aug. CO erie elas |e lee eae eel ee Om ee eles Dee ten om loa 2.1 1G i @ |] aE By ee Sept. Na me erie | ten Van Sea) Deel | BN WW Ba et By a eG BO Ge eat ah aT 6] 8] ee Oct. feos Ge) le. teu Se) le sd) ab 2a ee lee see On eae AT Oe ORT Om One 9; 9 Seem mOM Ge se | 2) | Le Fall ele| (Go) On Qe e7e\ 1) Qe) Qa" Ge | 4/2.) 45 i. te) On.) SP] S| Te] 8} 8]- Dec. OR! tS) 1st Leow! as ea PAN YP ES ay EN Syn a es) TON oe OF) tei 9| 7|- Year | 10) 94 | 62) 15 | 12|106) 17 | 27 | 22] 21 | 70} 13 | 16) 20| 59| 76/| 20|70 15] 1 |43/70/ 4 | 8 104/120 Mion Cape Town, Cape Colony. 4 Years, | Graham’s Town, Cape Colony. 43 Years,|| Graff Reinet, Cape Colony. 38 Years, 1 1862-65. Hours 5, 9: 1,5, 9. 1854-59. Hours 9.380: 38.30. 1863-65, Hours 9: 1, 5. N. |N.E.| E. |S.E.| S. |S.W] W. |N.W a N. |N.E.| E, |S.E.| S. |S.W) W. IN. W 5 N. |N.E.| E, |S.E.] 8. |S.W]| W. |N.W Z Memes) 1 0 | O| 2124) 1) 2) 4) 0) 3] 4) 9) 3/9) 2) fle plol i] pii9| 5] 3} 1 Feb. On SOs 2 ON AE a 2s) x PPP Shl nom |e faiect leo Oy it iO) 2) | yp Warch) 1 |-0)| 1+) 2'\17| 1 | 316 SRI ECE Shue SL ede mom ssl Qe de We el T4e) or | 2) leet: April DS On| LOM 3h 142529) 3916 1 28 S20 pa 25 ONS 7 4) ene Ten ets sali Ob) Onl Ol nase May Sr On| LO) S25) 135 a Si 9) - 1) Ne De) ee De | Resin es | SHe Onl 25) 433) Pon es June |5/0/]0)]1 9/3|)4/8]- 1 eles OR ee te (Geom ta 10) | 0) | 2 BYP I 22 July Bi |) ON Pee a ae ay GMail COP Ap ah 7 tay lat ele ele ss GI 2 wy ie Aug. Sl On ROM Peel Wen soni as ON 2 2a 255 is \N9F) 5) LO @ | te) Oe Sih er ep Ss We Sept. DS ROP | LOM eee 2 eZ on 7 1 ee suleoe | See Oe eae ede) eset ll 501 Ol OF] 3) E21) 3) -2) | oj he Oct. Dai SOM On 14s |) 265/16 Wee [Pes ee rh es Ws} AD ON Ono |G) Qe hie | ponte Nov. DOM On 2! Neg lea) Si sa OM 2a eae | Ph E4s 7ele ob ee TOs VOR 2 GH Gre | esi Dec. LOM POs Pan 20))) 4) 35) 3 ee Ronse Por le oels ale? Sole Ob Pot eras |e Ze Year |28/ 0 | 1 | 23 |178/ 19] 43] 73 9 | 25 | 26| 59/31 | 97) 37) 81 61) 7 | 5 | 27/134) 45 | 27 | 59 VOL. XXV. PART II. 7Z 6 Years, 1858-69. Hours 9.30: 3.30. Mauritius. 3 Year. Hour A.M. Tamatave, Madagascar. TABLE II.—continued. 2 Years, Hours 9: 3. 1858-59. MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE Pieter Maritzburg, Natal. 626 Monta. oon rw OC con |o WES ae ae AN HOS con|e ‘wre SOS © 0 ~ Sas wipes 2 ”~ ms _— Ee a 4 = 5 a ANB ANN AHH | { 3 2 OS Sin se ono|e 2 F mo° ooc HOe coo|a H a 3 : 3S : E =e aa N aaa |S oS Een O san NAO waelc a) Ea oS) Sa Ss sooo aso | E jf | a sel Ee r sHe COSC ONO] zs *, SESE OGIO), rN woo | 3 ce eee OOH OHM HOM MH H fr aS 2 &5 Seal Lal : ws = . a OND NHN n = 5H c S fs she) , Gr) : See eee ome iis i le |e Noe ae es heel S| |e | eg CSS eee woe eRe |e 5 e so} n ° = oO Ss z ANH AMS ann | a AMOS ch), Sa oon |S ae yANMO ~OO HON von |Z : As| iso] a = © Fail a sy ss o o 5 ay a Cs=| oO * = q Be Pee ses] s z doe Heo Pws wes | 2 z poe Ere Sha SESS Ss 2 o &F a rs) = el slap 3S o| o e) Ee) SoS > D SiS 425 647 O4A|H S BRe qa5 64m O40 |H = bee 4qe65 542 OZA]H 627 AND THE PREVAILING WINDS OVER THE GLOBE. TABLE I1.—continued. ne Ee eee SS —— ee St nn. a a ae eal. le OP ee, Fe Be lie ° . . . , _ a see . . . e . . . . z . ; WURSoSS COO mA ono|s yey NCL Go Cpl Sayles) SON te ri is (0. Ui) Oe) ee x SOL Set 6d Iylttn ae amen. me eas | : a a Es e : A Ee \ FOotm HNO HANH ONT] = - 2 6 Gece Gio 4) oo 4 ono: 5 - OONMN NWMOH ANN nro | @ : pe : pees ae ches : ; : ra) vs EAR Ont ANO Sore Ee Sey II WNBO SASS Nig ae Ra =o | : eS eno ra t Ols Cora Cle cancun ao |§ y : tm! : Sin ae 4H ouew nee ry = a acy Fomon AND On-O nani ag pect ale Hosa) : oon | ‘a 8 ee eHND OnWO KOLO aan |S ao) 2S So cal isa) : : om wo nN . ANCTD OWMNN NANO ane |S A 2) aia) s con| am COPS 603 es Se van |S Se xt Se a O10 Si |es Seo aoe on |S Be BNCSO Ot AHH HANOI S Sob | oi Anat «© Ne) ae ("5 © 19 2 © A v2) Lo! sH al —S— 2 co . a so = Bq MAO Ons AHH no~|R oot el ees CORE re co aoe ae HE ANN FHOnm OO som | = Fee B | & s Rann OHA AMN roa] os | FR wma an: —a2©o 8 2 Rae Oo Sn ~a | 3 6) Ai es Z = (op) =a! ° H . © eS Zorn ONN NHN co tin | 2 Sat hd eo etelinlt: aan | : ZOnm tAN ANH roo | 8 — _ ; : +H : AN =—CSO WOM NH URaQOMe HMC BOs onn|5 urmoncoe oon S) =) coo | a TOD yo oy a4 = heist [esd mH = 3s m 2 = . o Ee 4 S 19 19 10 me H mmo mewn |B 3 e818 CAN mm OMS! } Ps RES iN Io Mie ooo ao |= . oD for) 5 : : 5 ~| os HMO NOD OrKH OMS “S| Ee mmn cot Nom wan |S SS SF OAN NNN x mo | : yy Nees SaaS ae |= .3 3 iar ; pao | = nN eit} Ee “CO OnmM MH10 van | 5 Ee - On Oo One =—se Noo : an aS | ANDAMAN ANN YA Seas : Be | 25 | aE . 49 ‘ 7) ta g mam att OAS ==0 |% el. COO OO Sa) =o | am A WIM MA ANOS wow |k “e o Leo} Lo} . ale j 2S ER ii Oa H NMOS =on | & aH oe°o ono SS) -o°| gs py mrrce ooo oso coola n = alte. S Sen lige on Bf Mee HAA ANS soo |x aa fH CON OND aN moo | 19 a SoS Soo Seo 22059) 2 ict : — Sey a ; S| j ‘ nN SHO NANS ANH Hor |B yhoo ood mH owe ) yun ABO COON awa |S Z ee = = AN = —_ ass ) . AON ONMM WHOA WOM HHA aA |S URIDOSO ACH HOR coo|# Meo eee oom poner ay |s . nn ——— n,m Sis N n S00] Foto HmMH amt non |e | Eoqont O©OOn OnwM moo |B S| Sa a emai aa=|Q Se a = ! n = SS — — o A o 5 > . © fox) for) Eg ENON DAH ONAAAN a ES EF OnwM Hin AN =+~|3 2 x. EANN ATH HO aaa|8 ° Eee nes 1D a SS SOO OHH NOH|o se F ona MAM Onn aa|& $5 Z aan CD 1D 60 19 OF aa-| 38 5 oO Ro) 8 By a Ro 3 So aa : Aan i) gp CSS COSCO KHAN BOO] | a OSS Vet 1m 166 on0|8 E ZARA ANM AAN 4 |S nn (>) . Paco = wt i ie} Bel] RF ono OOH OM aonw|o ae Ot ING (8 ot wa |k Eg ETS UT. SUNN es aon | ae 2] 5 rag - er n 210 z for) ea qm aaw HANH MDS aaa|s i BH NOS HOt FISH ano|a Aw grrr ofnn MOO aro |Z © tS) a : a Sr BR ame ono ome onm |Z = A NSOn MHA WHM awo|s ce Fo St at O_o eo eet eet ge sow |S NSCS nem ANM OHO |A BROW mot KYM HOH! Peace ie — Pa I oP Ta amy [hc Za NX — eS 00 . - re iss is] ars) — r . = fy ° . o . h a Sites > Z =e peer ee =e, we S 3 S) ) a OW 5 o 2 I a Smee dae5 4m O4A|H Ss St John’s, Newfoundland. 6 Years, rFRMOo HRN OOM HNO 66 | 68 6 Years, 1843-48. Hours 9: 8, 9. 20 117} --- 1809-59. A.m., Noon, p.m. N.E.| E. |S.E.| S. |S.W] W. [N.W mw 61| 36 | 36) 12| 60| 18 | 21 | 27 | 94 Brunswick, Maine, U.S. 50 Years, N. AAS N. |N.E.| E. |S.E.| 8. 1 1 1 TABLE II.—continued. N.W “HUB oO OD 6D ~ws N.W 4 Years, 1854-59. ||York Factory, Hudson B., Brit. America. Hour 9.30: 7 Years, 1841-47. Hour? Norway House, British Ame rica, . N.E.| EB. /g.B.| 8. |S.w] Ww. HL SH N. |N.E.| E. |S.E.] S. |S.W] W. 3 2 2 2 10 CO MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 628 3 og i on |g CSA OHA OM nor] = a x ANNAN ANMANM BANA! GY Bl Rant wat Adm oan |B | QD oO % a a gr On Bane ANA AA = re ic sH OF Aton HANK HAN] BAMA HAR ANN MOMMY wrRpCOoOO FeO ORM NBO] 3 F Amo OM = Bo a on co ad Br | FE AWE Ho x rio 251 =F awnco wwe te eS n NX Ae) Ep AMN NM IE; 0s {=| 5 -2/ A omin mann E 8a m | —- S56] yf ONM Ma on ro | By a To) 1 MNAN ANA | n Zi N yA BMH Fe a |: So 2 Fo aan man is — Za Zo) Food mmo Fe Sod oO Pigs |) Beas oes He a nm = ag ; Nn 8 Ato M00 | aba (2 v BS ; = ie Rmmt HAHN Ba Loiets 7) mM 68 o =e | H OOH HAN | So ica} oO = 1 Ramm NAA | a z ag ei a | =. Orr : H o sR Rs 3s 5 Ao S asa o SI See 485 al 4} Years, 1854-59. || Kingstown, Canada. Hours 7: 2, 9. Montreal, Canada. “WITRD oF 20 19 N.W 13 | 32 | 67 | 62| 70| 24 || 37| 50 | 24/22] 48 | 92 | 47 | 45 4 Years, 1855-59. Hours 7: 2, 9. N. |N.E.| E. |S.E.] S. |S.W)] W. |N.W Red River Settlement, British America. 36) 56] 5 Mont. Monta. N. |N.E.| E. |S.E.| S. |S.W] W. 0 0 1 74/11/15) 13 105) 32 | 33 | 36 | 46 | 59| 47 | 13 | 22| 75 | 26 | 16 | 59| 48 || 16 | 47/13 | 27) 11)114 629 AND THE PREVAILING WINDS OVER THE GLOBE. TABLE I1.—continued. os OTE are : |: — (MOOS Soo See aso|a Es WOAMOnN BOO ae ono |n i = a 8 s ot nN oC i= 3 3 Br OmmN hom mn ra=|3 oe OHH NMID OMAN wow |S ae F 00 © Hoo oN 2oa|2 nl 3 ‘— Sp i 10 x Z Hi * a EF won~N Won OOO oon |i ‘ON E NAR On AHS aaa | > Sie} FANN BO aH eH ==-=|2 oan Er sae ad © ah |e + ae bags moe noo HHH |S el RB ONO NDHR ANH don | st Dn . OHM OND CON Han | & eo Ps = 4 — <) 1S) S| n a id ae : 10 SS) a2) E Seer eines ao |i On nmOnW HAN ANG =a-|% Bm | A aa coe won =ao/Q ae| wa 9 ape |e eo | a Sh a OL SS aye oot HL ea | a Ant HHH RHwD mond | NR ve Amat hnw noe aad |e n ! ! ; - sH Sid . eS a Bato ANN HANH HHH | Bg | HF ANA AMG AAM AHA iS ae BH ANN HAH ANN aa | < e HY COnm nHW ow | g 2 OOh ©Bnt Onn anno/|S 5 Homo mwt Amo oaal* oO Ss) Ai a = re = ~ . Nn . Gq Zsa s BNO CH ANS = RONNN HAs Hem aac |g x MON AwewT Saws aac |X We, ~~ 5 . . wel e HORM O NAN WHHe HOR |S me : : ae moon CGHO OSS cool|a 3 Rigas S o 4 E a 2 E mes ao FAT AAAS 3 BT AAA aA wan | a BO HA ae aaa |g ror) AD res) SO -l te ORS COM ARM CoOn|S - : es N | EF a = iS Od} FF HRD KDR ADD ane |& ane FOFnH ANS Bae aaa |2 Cra a= cs = |e = Da ZB OND AMM DMN Mon |Z oe BZ ODO OFN NH awn |B On a Ssqae ANANH oon |S Te) |e aS ; Ps ao | o NN Hinw OND wn] SH | oa Nm mmm HAN Aan |S te | oh ANH AHA MTA HAN |S tH 2 oc) Hi N a iS a ; a j ES) BVAS OMe NAMM ini | S “ra | Bo AOR AAA Ae =a |% Bet | 2 Sigas ino Sea os most | ay me nM a9 Q — — as = n SR | A ANMA MAG HAAN Amd |h Hig Haas aM ANN Bee] oS) Gg HHH Rim OnRD eno |i dor = Do SO = iS = Paann won Bal a | & N eo | a E : Nmom wan | 2 3 7 HHO WON WH wis |B 5 Fant mom Ano = 00 | ZmanNnmM NOR AHN an ]2 Zmntt ttm Hoo nddH | 2 Zorn Hts AaAm oan|s ~ |me9 : p : |: nn ee ee : Ts 3 oi TE ON 9 i: wos | HRD sos : WURDOCOOSO HOO BHO cnn |o 3 = Kes Zz 3 es a = is S SSS Sas Tx Ss 5 PH os 2 mee kre OF ase /G- s BOO HAA ANS aor | oO we * I . S To. EAMM DHMH HOt tam | ¥ | EF OHH HHO Hoo in ton |B Oy! FE ANNA HHH MHO aaa |S ae - 3 = acer) oy Ro A = iS SH gy 12 ao ZS) =o ooo |g Po Zan Not wt san |x fon a wor~SO OMS HHH wro|s = oi Ps n coal = se dg | AANA AMD mam ana |S ao | 2H DOO COO HOW|D Ho] A ANA MAN AAR AHAN/S eo) oS = BS) a i = mn : ey 5 Fig BR NAM ma teo on on aca | 3 As mB NON no HH MNO marcy | 3 so | BAAN MHR OHM aaa |g oO a a m on . ian 5 To & H MONM HAN NAM maa | A = HAN MAN ANN ana | § FS | oH Onn HHO ANH =ao]o (>) ; 5 aS Ae S aa) <3) a ; on : STN HOD CN CN en oo cacu ce | 33 EO) DR omdt wan ane aac |B “4 PookrR RAND WON enn |e B aa a, 3 a = oo : 3 5 a BANNAN FAA Ha ace | 2 =x ZANM AMM HH sence |B %ONN FAA OAN aaw | x a | a g | j | a alpen Merwe SO ogres sr dl a a 72 = © i ; “f A p= aD 2 , - | 883 BSS See SoS | 8 é gee Bea ohe 2s 3} 3 z Go B ERE Soe wks] Z o S BHA 4qa6 542 O4Q|y S See 4a5 640 64Q/H- S| BoA 4ae46 647 OZA|H SA VOL. XXV. PART II. 1 Year, 1858. Hours 7: 2, 9. Goliad, Texas, U.S. 3 Years, 1857-59. TABLE II.—continued. Hours 7: 2, 9. Austin, Texas, U.S. Ee se OO HOO HOS son | a an rina aan on — o i fe eoeo sec =o Oo coo|- MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 1854-56, 1857. Hours 9, 12: 3. New Orleans, Lous., U.S. 23 Years, 630 Monts. amr RMO NOOO wo N Se NM Ne — [or Ee oe Be Le wo | 2 NS ANN Od onn |g AHO HHH BION eue\é A Se — Sse = WUteaee Ono OCS onn|e Ee a 2) o HMA AMR AR oO 10 on] : ro) Ee Ana Bee SS oven oo | Foto Hho 19 0 one |S B OMnR OhH AAD oon | = _— | sH A AYO HHH 200 wan | : a) Ban O Res BANM ana |< cathy AWA most aan | Zmrmryo NNM ANW ane |x = pine — MUnROoOone Onn AMM ono |S ar MAH ANS naw] & SFANM ANN AND naa|& EF mae ate NAH ana |S AATH ODO NON mio |S Raw moo nen ave |S HWHH ORO NANO coco wt | fs Fionn HANH AMO ron |B An BHM MmM MAM HH ane |s ai ye ist (0) 5 : y Gah Bea Pwe ses] sa SO SSeS Siig Oo, S io bee aAeH Amn O4ZA|H TU SoS SS Sse) sie 1829-50. 29 |136) 2 52 5 3 3 2 1 2 1 2 2 2 2 4 a ‘ 3 3 3 2 3 1 3 1 1 MWr~o CHO OwWW iol fom) Om 390 0 SH 19 | 29 | 64 | 78 =A Ones 1855-59. Hours 7: 2, 9. Mean of day observations. N.E.| E. |S.E.} S. |S.W] W. |N.W Hazelwood, Minn., U.S. 5 Years, Marietta, Ohio, U.S. 22 Years, 20) 15/13 39) 84 | 2 N. N. S.W| W. |N.W 54 | 42 | 23 | 42} 66 || 78 | 12 8.B.| 8. 50 1854-59. Hours 7: 2. 9. N.E.] E. |S8.E.) 8S. |S.W) W. IN. W Glenwood, Tenn., U.S. 6 Years, Greenbay, Wisc., U.S. 9 Years, 1822-30. Hours, sunrise, 9: 3, 9. . |N.E.| E. 31] 38) 19 N. S.W| W. |N.W 55 | 89] 71) 37) 33 1858-59. Hours 7: 2, 9. KR. |8.E.! S. 52 | 34) 32 | 33 |119| 52] 26| --- 29 | 89 10 | 12 | 48 |125) 30 | 22} --- Fort Towson, Indian Territory, U.S. ?Years,1833-42. Hours, sunrise, 9: 3, 9. Detroit, Mich., U.S. 5 Years, 1854-56, 31 | 27 | 22 N. |N.E. Monti. Oct. Nov. Dec. Year | 17 Monta. 631 TABLE II.—continued. AND THE PREVAILING WINDS OVER THE GLOBE. SP ap ReOs be aes Hen OF tr ees: |e ae |. ore Se sh a he Be a Oe chase. |! pe Z A Sa SOs Oats pec Se One A + GNOME ars ens ek, BREN oS UOC 4 2 ® Ee Ly = a ee = prot aan ANH nwo |B SS > Hea HOC COSCO Ooo] xs oD F ) mic, ee ire: les —- | F MIM MHM ONnH Waa |S ice oO SoS onole ae 5 S ois (Te H 3 = Bg - AN TANNA HH a4 18 ae Fane ==—O OOO coo|h HS ie 7) - > 5H 5 OOM ANH Ye) 2 o Ore) || Soe Sea Sh Sus “Hi bd O2MR MOO COS HW |e ke ; = ze = — nel 4 a vw | ea be) a | a) 3 : : ae a SCOn HOH NOH OnH!oo Koa A ado one coo non |8 eter Bi = oo 2 | eg |e a) ee (2 © no ; AANH HM AA nN S ~5 MOMm~ MMO CHE wo SD S : aie i I MOOSE es 2a La St sise eed uS oa A Ne 5 a 5 qi j Z BATA ARS Gon san |S 5 Bo ANM HOw ono] x & fe =I S) =] 3S = ic %FMWNSD SHH DHMH AN 3 S ot 7 : S NAA |S Ss Ze Erm on eS sere te A Zz &@ S [eagey : é S Ww : | Py UMMAH AHI WAM ait |S “mye & ES See ue st OO SS a) od > OMIM HON mad mm | aS S = a, 2) eee M9 6 Z io) aos . a 1 fen] for} . £ os E NaH 10 a OS, oom | os | FE OAT MMM HHH vaio | 3 3 E 4 oD oh wa : ON BHO Dd 7 Vodt mdm ott tam |S vee 2 10 S 3 n ~~ nS val (ee) 2 - ONO moN Six : oo be BS Se 2 Boe Cae | BANN ANA AMA aan | x pa ae S 4 2 5 op mio A mn ic] j 2 j Be. | Belo. (Ole: =o oNO ao | Baan adn oun man |e eon ae D> m . va) foe) 5 Haz ae mR N _6 5 sae qa : 3 q.° | & oo SHO AN AA sfi§ | AB NBRN MAM ATH MAN! S 7 j Xx ox |— eae) ae ee eee = a ; - a pe onS on aan | £3) BF mmt KRHH modo soo | 2 S eI @ = Ao |_% ST Q Zi SH S FORO » £00 10 HH 2 ZwtrtA AMA ANM wwe |S ; HS ‘e) SH A or) = oe USCC CON BAe coo ]o “wR : : | Bs wooo é for) HO | E = a E ae E Se - DMNS OINM NMH Non Ny “OM ROM aA MOO |] LS eo) : BH mo, |e = o> at Zt a | © 19 % -O . for) Es Bo | FANN ANH Hae ann] oa @ > i : 5 ¢ 5 lox] Ch Oe EFmoyrFy ROD Hot HHH 10 on = Sy ae 7 Hina 320010 sH a Ee : Sa) e rE ee © DoH HHH | F Boe BZ NM WAI Hae aac |S ee Here Mid. A AH | 2 ea nas = ba 2 NS : SE uta won onwm Oomnm |S co G | 2 AND MOM ARO aan | 8 Pl eg AMAR NAR ARS HAN /® - a oe SO) FB wmm tw mom wan| os 2 | a > 82] a : a > a d op BANA AWS ROM ATH ag BZ NAIA AAA 2g ES = ® st ; ie | 3°) Ams ANM ANMN cuca | er Bae ae Fee MOH ana | 8 = HANH ARH Sy per) [=] > F oe = OD] mmm wom om wera | 8 iS Anam Man HNM wan |X 5 HAAR ANN © eS ees oa Zi 5 3 Zi a 2 = 5 = S Ziman MAN ANN asia | 3 ZCOn HHA ANOS non|Z io) Z OMI MAM SS = = Sli oe | sw is] re | : a oS lo ; = a a Pape H a) Sr 0) . A oOo mo | dS BFS PES 25 8] 8 | G55 BPE PRR eES/S| | 2 | gee ERE SPR o 6 oO 5 DB o = Bee den 640 OZAlS SI bee 4d465 640 O40 |H a Bes eet ae FaeAN ANN ANA HAN / 2 re 5 S (sz a © a E sf cs =a Coco sek LS a OQ ttdt wwe Nn 7S A See ae ae : * : #a | BG AN ANA a Tm lceres BMAN Fen COO anan| “i = ee le = Ooh acl a aaa a as Ss HHH Amwm mnwnm wad | OS La & OO ss i g =e Se Ee ald wn So Nee oeSy Zi ss = By] Goap Lt BIN) EPA ce Pere uel B z eH ] fi = a |ca} _—-— © a a = Be ors ASS MHA Cho |S a = 4 a — P= Se = a) ie = = a = oon Onn = Zaaeae aN NO aca oo | 2 fa “wre z —— re WoO Fs 3 SOM DHO aMH 00 “uLYR, : = iS BRDDOACOCOo = ea] ve A =. : 3 AN MAN HOH Ana | © 3 ff a : a 1 SR SES o a a2 EmMNN FRR HON an] © 2 A Che == - 5 ides . = A ro | G Pere HAN ame NO nN ane pee aoe zi ar too Ho | 3 “MAO oo°O P| g OnRwW x = ie mA HH oo) 3 6 Now By Po yng HNO COOn Ae a SBN HRA MNH BHO |? # el = = -2 wo a aca Se . = = g A COO was FAAM avai | 33 ge Kae a fe ANMM MMA HAN | 3 i : eS © ie ooo > Ztm1 OOn NOX © ore | $2 : L 4 S Re Bm See Soe 3 2 >) # 5 GSS Res PORES |s z s | See #35 648 644 |h : BRAD O4A|H EI 8 B VOL, XXV, PART If. 634 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE A oN aN A A A A |TNIOMIMJO GN) ON fc AN G |TIOAN| AN AN MN AN | AN a 8 8 8 8 BION] N N |SJON/|NJ0S|] 8 as |G8 10 A) gs as AS AS AS MS as as 8 |MNdos} 8 AS aN A ON aN 8 8 0 I S 0 € € ¢ b Sj Sb € € S 8 9 S ¢ Dp OI LZ 0 I 6 b L S él bl 9 b 13 96 ZI SI PI LI Il él II 41 ON ON | ‘awa | “ava as as as |S Aq a| ‘ava |NAqa obh § |.€68 |.ShS | Shs |.Sh8 fers |.opsS | PbS |.9b8 |.9FS 06S MA | Eh M | 8g M | GTA |.6L85 | 016 4M 18g M | Gb M | 8h A | Pb M oPSN | .9N | FPN |,69 N j.0 & |.8€8 |.6¢8 |.€hS |.Sha |ILN ob A} .O€S |.6¢4 |.812 |,16¢% |.9 | .e8N |.62N |.8EN |.06 M oR Ht | S40 |18H | o2H |.o20 |9L8 |.0Lm |.ooa |19% f,.60% o6$8 | 882 |.48% |,09% |. 692% | 694 |.69 4 |.69 4 | 8h aX |9L8 IN N MSM | AS ASS | ASS 8 ASS | HNN aN 9L4).€6 N |TLM4 {of M]GLS |.698 |.€98 |.01 4 |.66 | 9b M 98 M4 | .98 4 |.6 N | €6N |1€8 | LI 8 |.€98 |.£9 4 | GEM | BL mM bo | 96 bl € S if i b Or €I L b dt 16 62 0€ 96 £6 06 sl 00 AON 190 ae ‘ysnsny| ‘Ainge | ‘oung | “Avy | ‘prady |‘ qoreyzy 12 € ‘aer cé GP ‘opnyrsuoy]| ‘epnzyyey 06- G& bil FIl €ST bor Pil PIT €0I GL 661 OSs Iv PI oul 9T cE €¢ 8I PP GE SI G6 6S :L or‘e :6°9} 2 m0} -CAIOS( jo sImoy{ 89-981 89-€981 89-T981 89-S98T 89-€98T 19-0981 69-1981 ‘op bE-6681 19-681 9S-0S8T1 ZS-OS8T 8S-0S8T L9-9981 09-8SS8T GS-ZS8T ‘8p-SPSI 9P-SPSI *poytoadg S1vO X ‘sousopul'y © ‘104817 ‘ues10g “CITA ‘Lemon ‘souepuy Gog “oq “oq ‘| “ann jo sKep ‘epeumeyeny “Taye 6c STMA 73 Gusg “ ‘sqos,oyadgeomyy[e1} Ue” “og {SvoO pjoxy‘srioqsuerysliq) ‘purjsuoent) ‘eurqslig * “ereung “cuequie[t > Saer ‘orsuemoolueg cs OO k= 7 ao 860 re ‘ooulog ‘suisseumsefueg . * — 9z0deourg 6 ‘gsnoyyysiy = —_ SoEFeyy € ; * ‘erpuy ‘Aequiog: ty : * ‘oede p ‘eumrooq sp, ‘sy'pavg ‘putaanjosfep) !1°FPMA KZ ° “soot g a 2, ‘SHOVIG NUGLXIG LY UVEA AHL AO HINO HOV SANIA\ DNITIVADUY FHL DNIMOHS—(TT QML 07 Aumpuowojddng)—TIT WIAVL \ AND THE PREVAILING WINDS OVER THE GLOBE, 639 LIST OF AUTHORITIES, Showing the sources from which the data in Tables I., II., and III. have been obtained. A, For Barometers (TABLE I.) _ . Letter from A. O. Thorlacius, Stykkisholm. 2. Collectanea Meteorologica sub auspiciis Societatis Scientiarum Danice edita. Fasc. II. Reykjavik; NI. Christiansborg ; 1V. Godthaab, Jacobs- havn, and Upernivik. 3. Journal of the Scottish Meteorological Society. 4, Monatsberichte K. Akad. der Wissen. zu Berlin, 1842, p. 306; 1849, p. 177; 1849, p. 157; 1860, p. 646. (Papers by Dove.) 5. Letter from Dr T. R. Robinson, The Observatory, Armagh. 6. Letter from Alexander Dickey, Bursar, Queen’s College, Belfast. 7. Meteorol. Obs. taken from 1829 to 1852, at Ord. Sur. Office, Phenix Park, Dublin, edited by Captain Cameron, R.E., Dublin, 1856. 8. Abstracts of Meteorol. Obs. made at Ord. Sur. Office, Phenix Park, Dublin, by Capt. Wilkin- son, R.E. 9. Meteorol. Obs. taken at Monkstown, Co. Dublin, by Arthur Pim. 10. Letter from Dr Caulfield, Royal Institution, Cork. 11. Letter from John Plummer, Assistant to Professor Chevallier, Durham Observatory. 12. Letter from the Rev. Francis Redford, The Rectory, Silloth. 13. Abstracts of Meteorol. Obs. taken at Stoneyhurst, 1868. 14. Letter from the Rev. J. S. Perry, Stoneyhurst. 15. Quarterly Tables of Meteorological Society of England. ° 16. Letter from John Hartnup, The Observatory, Bidston, Liverpool. 17. Letter from John Davis, Optician, Derby. 18. Letter from John Davidson, Holkham. 19. Letter from C. M. Gibson, Norwich. 20. Letter from John M‘Laren, Cardington. 21. Astron. and Meteorol. Obs., Radcliffe Observatory, Oxford, 1857-66. 22. Greenwich Magnet. and Meteorol. Observations, 1857-66. 23. Letter from Henry Storks Eaton. Note.—For the details of this long series of observa- tions, see Proceedings Meteorol. Society of England, vol. i. p. 273, which Mr Eaton has kindly extended to 31st December 1868, by adding the Greenwich Observa- tions, 1863-68. 24. Letter and Annual Abstracts from Matthew P. Moyle, M.R.C.S., Helston. 25. Monthly Meteorol. Obs. by Dr Hoskins, Guernsey. 26. 34. 48, Annales de l’Observatoire Physique Central de Russie, 1837-64. ; . Reports of British Association. - Meteorologiske lagttagelser i Norge; and Letter from Professor Mohn, Christiania. . Meteorologische Beobachtungen K. Universitiats- Sternwarte zu Christiania, 1837-67. . Meteorologiska Iakttagelser i Sverige, K. Svensha Vetenskaps-Akademien, af Prof. Er. Edlund, 1859-66. . Obs. Météorol. 4 Upsal 1855-62; and Letter from Prof. Rubensen. . Oversigt, K. danske Videnskabernes Selskabs, &c., Kjobenhavn, 1852-68. . Nederlandsch Meteorologisch Jaarboek 1855-68. Sur la Marche Annuelle du Thermométre et du Barométre, en Neérlande et en divers Lieux de l Europe, par C. H. D. Buys Ballot. Météorologie de la Belgique comparée 4 celle du Globe, par Ad. Quetelet, 1867. Annales Météorol. de Observatoire Royal de Bruxelles, 1863-68. - Annuaire de la Société Météorologique de France, 1849-53. . Annales de l’Observatoire Impérial de Paris, 1857-64. . Bulletin International, Paris, 1862-69. . Letter from Prof. Alexis Perrey, Dijon. . Ann. Com, Hydromet. de Lyon, 1861-66. . Bulletino Meteorologico dell’Osservatorio del Col. Romano dal P. Angelo Secchi, D.C.D.G., Dirrettore, 1862-66. . Ann. Soc. Roy. d’ Agricul. de Lyon, 1852. . Mem. Acad. des Sciences et Lettres de Montpellier. . Letter from Prof. Cavallo, Lisbon. . Abstracts Meteorol. Obs. at Stations of Royal Engineers, 1853-59, edited by Col. Sir Henry James, R.E. London, 1862. . Reports of the Director-General, London, 1864— 66. . Mittheilungen der Naturforschanden Gesellschaft in Zurich, 1837-46, . Résumé Météorol. pour Genéve et Grand St Ber- nard, par Prof. E. Plantamour, 1857-67. Uber den Jahrlichen gang der temperatur und des Luftdruckes in Osterreich, von DrK. Jelinek, Wien, 1866. Jahrbiicher der K. K. Central- Anstalt fiir Meteorol. und Erdmagnet. von C. Jelinek und C. Fritsch, 1864-66. Daily ob- servations from Sixteen Stations in Austria during 1867. 636 MR ALEX. BUCHAN ON THE MEAN PRESSURE OF THE ATMOSPHERE 49, 50. 51. 67. 78. 79. . Reise in Abyssinien. . Annual Reports on Meteorol. Obs. in the Punjab, Resultate der an der K. Sternwarte bei Miinchen von 1857-66. Angestellten Meteorologischen Beobachtungen. Preussische Statistik. Die Witterungserschein- ungen des nérdlichen Deutschlands, von H W. Dove, 1861-67. Berlin, 1864—7-8.* Bul. Hebd. del’ Association Scientifique de France; Atlas Météorol. de l’Obs. Impérial, 1868, D. 4. . Letters from Dr Buys Ballot, Utrecht. . Météorol. Beob. angestellt in Dorpat, 1867. . Obs. Météorol. faites 4 Nijni-Taguilsk, 1845-65. . Bull. Meteorol. del R. Osserv. di Palermo, vol. v. p. 72. . Observations sent by Harbour-Master at Shanghai, and in China Mail. Dr Edward Riippel, 1840. by A. Kiel, M.R.C.S., 1866-67. . Reports on Meteorol. Obs. in the North-Western Provinces of India, by Professor Murray Thom- son, M.D., 1865-68. . Journal of the Asiatic Society of Bengal. . Meteorol. Obs. at the Observatory, Bombay, 1847-60. . Meteorol. Obs. at Secunderabad for 1864, by W. Arnot Smith, M.D. Madras, 1865. . Meteorol. Obs. at Dodabetta in 1851-55, by W. S. Jacob and Major W. K. Worster. Madras,1875. . Meteorol. Obs. at H.E.1.C. Observatory, Madras. Madras, 1844 and 1854. . Zeitschrift der osterreichischen Gesellschaft fiir Metorologie, 1866-69. . Letter from Capt. M‘M. Moyle, Sincapore. Meteorological Papers of the Board of Trade, by Admiral Fitzroy. . Du Climat de l’Kgypt, par M. le Dr B. Schnepp. Paris, 1862. . Gazette Médicale de l Algérie, 1865-69, and Letter from Dr Emile Bertherand. . Bulletin de la Société de Géographie, Paris. . Journal of the Meteorological Society of England. . Results of Meteorol. Obs. at Royal Observatory, Cape of Good Hope, 1842-56. . Results of Meteorol. Obs. at certain Stations in Cape Colony, 1861-65, compiled by a Com- mittee appointed by Government. . Letter from Dr Mann, Pieter Maritzburg. . Proceedings of the Meteorological Society of Mauritius, 1866, page 23. . Meteorol. Tables of New South Wales; and Meteorol. Obs. at the Government Observatory. Sydney, 1858-69. . Meteorol. Obs. by John Tebbutt, at Windsor. Sydney, 1868. Statistics of Victoria. Letter from R. L. J. Hillery, President of Royal Society, Melbourne. Climate of Victoria, by R. L: J. Ellery. Meteorol. Obs. in South Australia, under the direc- tion of Charles Todd, 1861-68. 80. 81. 90. 91 92. 93. 94. 95. 96. 97. 98. 99. Results Meteorol. Obs. for Hobart Town, 1841-65, by Francis Abbott, F.R.A.S.; Meteorol. Ab- stracts and Monthly Notices and Papers of Roy. Soc. Tasmania, 1856-68, do. Statistics of New Zealand, 1866-68. Letters and Annual Meteorol. Reports of Christchurch and Hokitika for 1864-67, from R. L. Holmes, Colonial Museum, Wellington. Meteorol. Report, 1868, by James Hector M.D., F.R.S., Wellington, 1869. Letter from Charles Rous Marten, Martendale, Southland. . Physical Observations in the Arctic Seas, by Isaac Hayes, M.D., Smithsonian Institution, p. 218. . Scoresby’s Voyages to the Arctic Regions, and Transactions Wernerian Society, Edinburgh - 1811-14. . Abs. Meteorol. Obs. at New Westminster, British Columbia, by Col. Sir Henry James, R.E. London, 1861. . Vancouver Island and British Columbia, by Alex- ander Rattray, M.D. london, 1862. . R. S. Williamson on the Use of the Barometer on Surveys and Reconnaissances. 1868, pp. 79-81. New York, . Results of Meteorol. Obs. 1854 to 1859, vol. i., Smithsonian Institution. Washington, 1861, . Canadian Journal of Science. . Meteorol. Obs. made at Providence, R.I., United States, by Prof. Alexis Caswell. Institution. Discussion of Meteorol. Phenomena, U.S. Naval Observatory, App. I. to Washington Astron. and Meteorol. Obs, for 1866. Meteorological Elements, from Obs. at the Ob- servatory, Georgetown, Demerara, British Guiana, 1846-56, by Patrick Sandeman. Greenock, 1857. Smithsonian Report for 1867, p. 473. Letter from Professor M. V. Raulin, Bordeaux. Nouvelles Météorologiques de la Société Meé- téorologique de France. Le Climat de Madére, par F. A. Barral, M.D. Pilot Charts for the Atlantic Ocean, issued by Hydrographic Department of the Admiralty. London, 1868. Magnet. and Meteorol. Obs. at St Helena, vol. ii., edited by General Sabine, P.R.S. London, 1860. Atmospheric Tides and Meteorology of Dukhun, by Lieut.-Col. Sykes, F.R.S., Phil, Trans. Roy. Soc. 1835, part i. Meteorol. Abst. for Hamilton, C.W., 1849-53, sent by the Rev. Charles Clouston, LL.D., Sandwick, Orkney. Smithsonian 100. The States of Central America, by E. G. Squier, p. 763. London, 1858. 3 101. La Plata, the Argentine Confederation and Paraguay, by T. J. Page, U.S.N. New York, 1859. * The Heights of the Prussian Stations are taken from a Paper by Dove in “ Geographisches Jahrbuch,” edited by Behm. Gotha, 1868. AND THE PREVAILING WINDS OVER THE GLOBE. 102. Descrip. Géograph. et Statist. de la Confédéra- tion Argentine, par V. Martin de Moussy. 103. Annual Reports from the Registrar-General, Queensland, Australia, 1866-68. Summa- ries of Meteorol. Obs. taken at Brisbane, Queensland. Sent by Edmund MacDonnell, 637 Government Meteorological Observer, Bris- bane. 104. Voyage to the Southern and Antarctic Regions during 1839-43, by Captain Sir James Clark Ross, R.N. London, 1847. 105. Gordon on China. London, 1863. B, For Winps (Tastss IJ. anp III.) The authorities for Winds are the same as for the Barometers, if not otherwise stated below. Curron.—Dr W. C. Burder’s Meteorology of Clifton. London, 1864. GrEEnwicu.—Proceedings Meteorol. Soc. Eng., vol. i. p. 21. Varpo, 70° 22’ lat., N., 31° 7’ long. E.; Tacanroa, 47° 12’ lat. N., 38° 57’ long. E.; East or Nova ZemBia, 70° 37’ lat. N.—Annales Obs. Phys. Cent. de Russie. Smipstrup, 55° 46’ lat. N., 9° 33’ long. E.; Tarum, 55° 26’ lat. N., 8° 39’ long. E.—Aarsber. K. Landhunsh. Meteorol. Comittee, 1861-67. Bremen, 53° 5’ lat. N., 8° 43’ long. E.—Abhand- lungen vom natur. Vereine zu Bremen, 1867. Lisson.—Meteorol. Journal kept by Walter Ivens, Lisbon. Me tvitze Is., Ienoormx, Winter Is., Narn, 56° 25’ lat. N., 62° 15’ long. W.; Norway Ho., 53° 43’ lat. N., 98° 30’ long. W.; Fort Towson, 34° 0/ lat. N., 95° 33’ long. W.; Fort Jounson, 33° 54/ lat. N., 78° 3’ long. W.; Wazo11.—Professor J. H. Coffin’s Winds of Northern Hemisphere. Smithsonian Institution, Washington, 1853. Fort Conrrpence.—Maen. and Meteorol. Obs. at Fort Confidence, Gt. Bear Lake. By Sir John Richard- son, C.B., M.D. London, 1855. P. 389. San Drrco, 32° 42’ lat. N., 117° 14’ long. W. ; Srerna- coom, 47° 10’ lat. N., 122° 25’ long. W.; Fort Leavenworth, 39° 21’ lat. N., 94° 44’ long. W.; Cantonment Lorine, 43° 4’ lat. N., 112° 27’ long. W. (4800 feet); Fort Yuma, 32° 43/ lat, N., 114° 36’ long. W.; Sanra Fr, 35° 41’ lat. N., 106° 2’ long. W.; Maramoras, 25° 56’ lat. N., 97° 36’ long. W.—Army Meteorol. Register from VOL. XXV. PART II. Obs. made at Military Posts of the United States, 1843-54. Washington, 1855. York Factory, 57° 5’ lat. N., 98° 15’ long. W. —Manuscript Register of Daily Obs., 1843-48, sent by the Rey. Charles Clouston, LL.D., Orkney. Rep River Serrrement, 50° 0’ lat. N.,90° 0’ long. W.; New Orurans, 29° 57’ lat. N., 90° 0’ long. W. ; Key West, 24° 33’ lat. N., 81° 48’ long. W.; Derrorr, 42° 24’ lat. N., 83 °O’ long. W.; Green- Bay, 45° 0’ lat. N., 87° 30’ long. W. ; Hazrnwoop, 45° 0’ lat. N., 95° 0’ long. W.; Oswxao, 43° 25’ lat. N., 76° 35’ long. W.; New Yorn, 40° 43’ lat. N., 74° 5’ long. W.—Results of Meteorol. Obs. made from 1854 to 1859. Smithsonian Institu- tion. Washington, 1861. Brunswick, 43° 52’ lat. N., 70° 1’ long. W.—Results of Meteorol Obs. made at Brunswick, Maine, by Parker Cleveland, LL.D., Smithsonian Institu- tion. Washington, 1867. Marierra, 39° 25’ lat. N., 81° 29’ long. W.—Results of Meteorol. Obs. made at Marietta, Ohio, by S. P. Hildreth, M.D., Smithsonian Institution. Washington, 1868. CocHanamsBa, 17° 20’ lat. S., 65° 45’ long. W.—Ex- ploration of the Valley of the Amazon, by Lieut. Lardner Gibbon. Washington, 1854. Asuncion, 25° 16’ lat. S., 57° 45’ long. W.—Do., and same as for Barometer. Bansermassine, Banyorwaneiz, PatEemBanc.— Nederlandsch Meteorolo. Jaarboek. Awnpenes, VitLA, Berern, Lister, Linprsnes.—Letter from Professor Mohn, Christiania. 4 ‘5 ‘ - s af ra r 4 - | 9 ‘ Siad ¥ et af * j 1 F ‘ 4¥u mato sh ° e t ivi, of ye? rat 2 tae e> S be - ri F ) } . 2 b ‘ YW F ‘ e? a : ob a —_— _ —» " Z ‘ 4 a 4 i “ ~ = ba” —, . . x ’ . a 7 bea a a r ~~ 4 . ‘ s - : “ . ~ 7 OKI hid ws a ait ev ev 3a eo ae ao be . vu n= 6 tau ‘a a tae : on ¥ Met) ak ot: dale 1 eter at i: Opa z a s) net Mi banadvel ee é eat, 7 yt ara . mt 3 Y UO te ; 4 4 a - 5 7% b +a . TY e4x qpc1 . =~ 4 - } } re 5 tae ‘a pero - & ) E lat ei) 4 “5 - 28 re ae "ee-7 ay a s mer 57) oS en ee A | Gas. ms \tee r me “ea t's te nh ° ray ia ‘ : e . 4 > 7 i? ’ ; i 5 fines’ Ao Fi ob hank SOLE | : “ A + : f y eeve . ¥ _ 2 % Plate XXVIIL. ane y be | mr Dickson, M.D. delt WHOM Farlane, Lith? Edin Be eo a i ee | a Plate XXIX. s. Roy. Soc. Edin? Vol. XXV. WH.M Farlane, Lith’ Edin® KXX. Plate ie n= Vol. XX 1 s. Roy. Soc. Ed WHLM Farlane, Lith? Edin®™ ( 639 ) XVIII.—On the Development of the Flower of Pinguicula vulgaris, Z.; with Remarks on the Embryos of P. vulgaris, P. grandiflora, P. lusitanica, P. caudata, and Utricularia minor. By ALExanper Dickson, M.D. Edin. & Dublin. ; Regius Professor of Botany in the University of Glasgow. (Plates XXVHI— XXX.) (Read 19th April 1869.) The order Lentibulariaceze is usually described in systematic works as exhibiting affinities, on the one hand with Scrophulariaceze, which it resembles in the bilabiate corolla, partial suppression of the androecium, bilabiate stigma, and two-valved capsule; and, on the other, with Primulaceze and its allies, with which it agrees in having a truly free central placenta. Linbey places the order in his alliance of Bignoniales, along with Scrophu- lariaceze, apparently following Mr Benrnam, whom he quotes in support of the supposed affinity between the families.* Others, again, more impressed with the importance of the placental character, place the family near Primulaceze, as has been done by PayEr.+ In the hope that the study of the development of the flower in Lentibulari- acese might throw some light on the question of the affinities of the order, I have, from time to time during several years past, taken up the investigation of the organogeny of the flower of Pinguicula vulgaris, according as opportunities occurred for collecting suitable material; and I now venture to lay my results, imperfect as they still are, before this Society. If a plant of Pinguicula vulgaris be examined during the flowering season, it is found to exhibit a short axis, on which are crowded a variable number of leaves, spreading out in a rosette-like manner upon the surface of the soil or turf on which the plant is found. This short axis is terminated by a contracted indefinite inflorescence, consisting of a variable number of ebracteate flowers with long pedicels—an unstalked umbel, in fact, analogous to that in the ordinary form of Primula vulgaris. _ Immediately below the inflorescence, a leaf-bud is found in the axil of the last leaf. As the fruit ripens, the leaves of the main axis gradually wither off, and the main axis itself decays; the original rosette becoming replaced in the autumn by a similar one, resulting from the develop- ment of the axillary bud of its last leaf. On the approach of winter, the * Vegetable Kingdom, p. 686. + Lecons sur les Fam. Nat. des Plantes, p. 14. VOL. XXV. PART II. 8D 640 DR DICKSON ON DEVELOPMENT OF expanded outer leaves of the autumn rosette disappear; the central portion remaining as a firm, bulb-like, winter-resting bud, the outer leaves of which are developed as somewhat fleshy scales. This bulb-like bud remains during the winter sunk in the soil, or among the surrounding moss; and, on the return of warm weather the next season, expands into the summer-rosette, terminated by the inflorescence as above described. Rudiment of the Inflorescence in Winter-Bud. On removing the leaves from the winter-resting bud, the following struc- tures appear :—1s¢, A cushion-like mass in the axil of the last leaf, the rudiment of the bud which developes the autumn-rosette of the next season, and becomes the flowering plant of the summer thereafter. This cushion usually (always?) appears somewhat depressed, in a direction corresponding to the middle line of the supporting leaf, as I have indicated in Plate XXVIII. fig. 1; but as to the significance of this median furrow, I am unable to offer any suggestion. 2d, The termination of the main axis, which appears as an unequally three-sided cushion, nearly flat on the top, and with rounded angles, the largest and thickest of which represents the rudiment of the first flower, the angle next in size representing that of the second flower, and the remaining angle (often very obscure) that of the third flower. These floral rudiments continue, as to position, the spiral succession of the leaves upon the main axis. If a number of plants be examined, the spiral will be found running sometimes to the right, and sometimes to the left, in about equal proportions (see figs. 1, 2, 3,4, 5, and 9). The fraction expressing the leaf- arrangement appears to be ;®; approximately; and the spiral succession of leaves developed upon the axillary shoot of the last leaf is homodromous with that of the main axis. Early Obliquity of the Floral Axis. Almost as soon as the young flower has begun distinctly to project from the axis of inflorescence, and before there is any appearance of sepals or other floral parts, it is seen to be more developed on the anterior aspect (that furthest from the axis of inflorescence) than on the posterior. At this stage the young flower appears as a short cylindrical body, the free extremity of which is flattened ina direction from above anteriorly, downwards posteriorly (see Plate XXVIII. fig. 2). This very early indication of irregularity is noteworthy, from the circumstance that, as a rule, irregularity commences to show itself only with, or shortly after, the appearance of the appendicular organs. Calyx. ; The sepals make their appearance a little below the obliquely flattened FLOWER OF PINGUICULA VULGARIS, ETC. 641 extremity of the floral axis. The two anterior are developed first (Plate XXVIII. fig. 3). Of the lateral sepals and the posterior one, I have not been able satis- factorily to determine the relative time of appearance; but there can be little doubt that the lateral precede the posterior. The sepals soon become connate with each other; but unequally so, the two anterior with each other, and the posterior with the lateral, respectively forming an anterior lip with two lobes, and a posterior with three. These lips are almost free from each other, the antero-lateral connation being very slight. When the sepals are sufficiently developed to cover in the young flower-bud, they are found, in the great majority of cases, so arranged, that the posterior sepal is overlapped by the lateral ones, which are in turn overlapped by the anterior (Plate XXIX. fig. 15). The anterior sepals, as a rule, have not their surfaces in contact.* Corolla. The examination of the earliest appearance of the corolla has been the most unsatisfactory part of my research. Its parts very soon become connate, if, indeed, they are not ‘‘congenitally’ so. Jam inclined to think that, as in the calyx, its anterior portion is developed first ; the anterior petal appearing to me to be a more salient projection than the others in the early condition. In Plate XXVIII. fig. 4, I have represented a young flower, where the corolla is seen as a rim-like, faintly angular edging to the receptacle, just within or above the calyx, its angles alternating with the sepals. Here the stamens have not yet made their appearance, unless the very slight furrow in the middle line anteriorly be held as indicating, indirectly, the presence of the anterior stamens, one on either side of it. At this stage the centre of the receptacle is seen to exhibit a slight con- cavity, chiefly in the antero-posterior direction, a concavity which becomes still more marked in the subsequent stages represented in Plate XXVIII. figs. 5 and 6, and which I shall have further occasion to refer to in connection with the de- velopment of the pistil. The growth of the corolla appears to continue uninter- ruptedly until its full development, not exhibiting the pause which occurs so frequently in its course in other plants. As the calyx does not at all keep pace with the corolla, the latter soon forces its way from between the sepals, which at an early period are folded over it; and, in consequence of this, it is only in comparatively young flower-buds that the eestivation of the sepals can be observed. A little before the sepals are thus pushed aside, the spur of the corolla begins’to appear, as a small dilatation from within of the tube of the corolla at its base, in the middle line anteriorly, indicated externally by a rounded knob- * Exceptions are sometimes met with. I have seen the posterior sepal overlapping only one of the lateral ; or one, or both of the lateral sepals wholly external. A hasty observation of such an exception as the last, probably led Payer (Legons, p. 14) to describe the estivation of the calyx as quincuncial, which I can hardly believe it ever is. 642 DR DICKSON ON DEVELOPMENT OF like projection. The process of dilatation or expansion commenced in this portion of the corolla-tube progresses gradually until the period of flowering, by which time the characteristic spur is fully developed. As in the calyx, the connation of the parts of the corolla is unequal in extent, the anterior and lateral petals forming an anterior lip, and the two posterior a posterior one. The estivation of the corolla is similar to that of the calyx—that is to say, the odd part (here, of course, anterior) is overlapped by the lateral, which are overlapped by the other two parts. Andrecium. In the adult condition, the androecium of Pinguwiculu consists of two stamens placed anteriorly. The examination of the flower in its earlier stages, however, reveals the interesting fact of the presence of two lateral rudiments or staminodes. The two fertile stamens appear first—at least they may be seen as distinctly present when the staminodes are as yet very indistinct, if not quite inappreciable. Their appearance seems to follow that of the corolla in quick succession, from the great difficulty I have experienced in finding flowers having the corolla dis- tinctly visible, with at the same time no trace of the stamens. Indeed, even in the stage represented in Plate XXVIII. fig. 4, although the stamens can scarcely be said to be visible, yet, as I have already said, the slight indentation in the middle line anteriorly may possibly be held as indicating, indirectly, the presence of a staminal elevation on either side of it. : The stamens originate as rather large protuberances, which very soon exhibit an oblong figure, being wider from side to side than deep from without inwards. They alternate with the petals, being superposed to the two anterior sepals. In their further development there is nothing very special to be noted. As usual, the anther is formed first, becoming raised upon the subsequently developed fila- ment. The connective forms the great bulk of the young anther, and broadens upwards in such a way that the four anther-cells lie upon its upper surface, what correspond to lateral furrows forming a single transverse one across the top of the anther. Ultimately the anther becomes one-celled, by the occurrence of absorp- tion in the substance of the connective and consequent fusion of the anther-cells. Dehiscence takes place at the transverse furrow just mentioned. The staminodes originate as mammillze of small size, compared with the staminal rudiments, and are superposed to the lateral sepals. They are repre- sented in different stages in Plate XXVIII. figs. 5-9. As a rule, they do not proceed beyond the stage represented in fig. 7, and usually become wholly obliterated by the disproportionate development of the neighbouring parts. Sometimes, however, they are developed as shorter or longer styloid processes ; and I have met with a good many instances where one or both presented a terminal knob, or were even distinctly antheriferous; in the best developed cases FLOWER OF PINGUICULA VULGARIS, ETC. 643 being scarcely distinguishable from the normal stamens. In Plate XXX. fig. 31, I have represented the essential organs of a flower where a moderate degree of this condition is to be seen, accompanied by an interesting reversion to regularity in the stigma, to which I shall afterwards refer. Pistil. The pistil appears very quickly after the development of the androecium ; it being a matter of some difficulty to find a flower with the staminodes visible that does not, at the same time, exhibit some vestige of the pistil. It makes its first appearance as a semilunar elevation placed anteriorly just within, or (from the downward slope of the receptacle) below the two fertile stamens, with which it alternates. The extremities of this semilunar elevation gradually extend themselves around the organic centre of the receptacle, till they meet in the middle line posteriorly. The ovarian wall, thus completed, grows up as a short tube, which very soon exhibits a tendency to bilabiation, the result of pre- ponderating growth, anteriorly and posteriorly (Plate XXVIII. fig. 9). The orifice of the short tube constituting the young ovarian wall, at first nearly circular, very soon becomes narrowed in the antero-posterior direction. This narrowing, apparently, is mainly caused by the inclination of the anterior and posterior walls towards each other, in consequence of the antero-posterior concavity of the receptacle, to which I have above alluded.* The antero-posterior inclination towards each other of the ovarian walls, is well seen in the sections represented in Plate XXIX. figs. 12 and 13. The anterior and posterior walls thus inclined towards each other, at last come in contact, whereby the cavity of the ovary is closed in above. From this point of contact the lips of the ovarian margin, in their further development, curve away from each other; the one posteriorly as a narrow strap-like body; the other anteriorly as a broadly expanded lamina, which rests upon and ultimately wholly conceals the anthers of the two fertile stamens (Plate XXIX. fig. 11). These lips become covered on their upper surface by papillee, and together constitute an unequally bilabiate stigma. The part where the ovarian walls are in contact becomes somewhat elongated (ap- parently to a variable extent), and constitutes the short style. The basal portion of the pistil becomes dilated, forming the ovary proper. It is to be noted that the ovary is to a certain extent inferior posteriorly—that is to say, its cavity posteriorly extends distinctly below the level of the insertion of the calyx and corolla. Placenta and Ovules. In the earlier stages of the development of the flower, and up to the time when * The slight bilabiation of the ovarian orifice seen in Plate XXVIII. fig. 9, though real, is doubtless in appearance considerably exaggerated by this antero-posterior narrowing. VOL, XXV. PART II. SE 644 DR DICKSON ON DEVELOPMENT OF the ovarian wall is completed posteriorly, by the coalescence of the extremities of the original semilunar elevation, the organic centre of the receptacle is some- what depressed. Almost as soon, however, as the ovarian wall is complete, the receptacular centre enclosed by it begins to be developed as a more or less hemi- spherical protuberance—the young placenta. At no period of its development has it any connection with the ovarian wall: it is as truly ‘‘ free-central” as that in Primulaceze. The ovules make their appearance first on the top of this hemi- spherical placenta, and continue to appear in succession from above downwards, until the surface is covered by them (Plate XXIX. fig. 16). This placenta does not exhibit the slightest trace of the barren apex, which is so characteristically present in that of Primulaceze—not even a bare spot,—but is uniformly and densely crowded with ovules over its whole surface. The ovules originate as small mammille, which become invested with a single integument, and undergo the anatropal curvature, as represented in the series given in Plate XXIX. figs. 17-22. They are placed so that the raphe is superior where the ovules project horizon- tally, internal where they have an upward direction, and external where they have a downward one. Abnormalities. In the course of the examination of numerous flowers, for the purposes of the foregoing investigation, I have met with a considerable number of cases of abnor- mality or monstrosity, some of which I think worthy of being recorded. In Plate XXX. figs. 23 and 24, are represented two cases of remarkable modi- fication inthe symmetry. In fig. 23, the flower is dimerous and regular, with two sepals, two petals, and two stamens, in decussate succession. The ovary here is as yet only faintly indicated.* In fig. 24, there are six sepals, of which one is anterior, one is posterior, and four are lateral, these last being conveniently distinguishable as antero-lateral and postero-lateral. Alternating with the sepals are six petals. There are five parts of the andrcecium, viz., two fertile stamens superposed to the antero-lateral sepals, and three staminodes, of which two are superposed to the postero-lateral sepals, and the third is placed between the two fertile stamens, and thus superposed to the anterior sepal. The other abnormalities I have figured are some very interesting ones affect- ing the pistil. In fig. 25, the posterior wall of the ovary is deficient, the placenta and ovules being exposed; the result, doubtless, of imperfect coal- escence of the extremities of the primitive semilunar elevation, a defect of development analogous to spina bifida, cleft-palate, hypospadias, &c., in the animal subject. In fig. 26, the posterior (small) lip of the stigma is seen to be bipartite. In this, as in the last abnormality, we have impressed upon us * This flower was unfortunately detached before I had ascertained whether the sepals weie antero-posterior or lateral. FLOWER OF PINGUICULA VULGARIS, ETC. 645 the fact that the posterior middle line of the ovarian wall is a line of suture, and in consequence that the small posterior lip of the stigma is potentially a double organ.* In fig. 27, the posterior lip is normal, but the anterior (large) lip is tripartite. Fig. 28 represents a left} antero-lateral view of the same pistil, showing a slightly marked lobule (/i/) at the base of the antero- median lobe; the right antero-lateral fissure, however, was found to be uncom- plicated by any such lobule. Fig. 29 exhibits a nearly anterior view of an ab- normality very similar to the last; but where a lobule occurs on either side of the base of the middle anterior lobe, that on the left side (to the right hand in the figure) being developed to about the same exent as the corresponding lobule in the last abnormality, while the lobule on the right side is considerably more distinct.{ I have represented in fig. 30 a pistil with the posterior lip somewhat broader than usual, though undivided, and the anterior lip cleft down the left side, thus exhibiting one antero-lateral fissure.§ A very small notch is seen on the right side, which possibly may be held as representing a right antero-lateral fissure. In fig. 31 is seen an abnormality of quite another character. Here the stigma is altogether undivided and almost quite regular, resembling a funnel the walls of which are to a great extent turned inside out from reflection of the margin. As I previously mentioned, when treating of the andrcecium, the two staminodes here are well developed, with distinct filaments and anther-like terminal knobs. Morphological Constitution of the Ovary. In connection with the monstrous pistils just described, and of course always keeping in view the normal course of development, I would here make a few observations as to the probable morphological constitution of the ovary. The ordinary view has hitherto been, that the ovary in Lentibulariaceze is bicarpellary, a view supported by the bilabiate stigma, bivalved capsule, and last, not least, by the fact that of the somewhat numerous vascular bundles entering its walls, the two strongest are in the mesial plane, one anteriorly the other posteriorly. This view, however, must be set aside in the face of developmental facts, which show the posterior middle line to bea line of suture. Ifit be objected that the presence of a strong vascular bundle in the posterior middle line constitutes a difficulty, I need only point to the interpetiolar stipules in Cimchona, where we have a well- marked vascular bundle occupying the middle line of the stipule, although that middle line is the line of a suture, and not of a true midrib. There are, it seems * T have met with three instances of this bipartite condition of the posterior lip. + To the left of an observer supposed to stand in the axis of inflorescence. t I have in my possession a third example of an ovary with tripartite anterior lip, but as I have been unwilling to remove the stamens from the specimen, I cannot say what appearance is pre- sented on an anterior view; its posterior aspect, however, is almost identical with that given in Plate XXX. fig. 27. § This antero-lateral fissure is uncomplicated by any lobule. 646 DR DICKSON ON DEVELOPMENT OF to me, only two suppositions possessing any elements of probability and com- patible with the history of development: either the ovary consists of one carpel, embracing the extremities of the receptacle; or it consists of five connate carpels, as in Primulaceee. With regard to the first supposition it will, I think, be admitted that it is, a priori, improbable that a corollifloral plant, like Pingwicula, should have only one carpel; all the orders with which it might possibly be compared having com- pound ovaries. On this ground alone I should be inclined to dismiss the idea. On the other hand, the 5-carpellary hypothesis has the support of the mon- strosities just referred to. In some we have the posterior lip of the stigma bipar- tite, in others the anterior lip tripartite.* Now, if we combine these monstrosities, we obtain five parts, and these placed in the proper position—superposed to the petals. Were we to take the ovary of Primula, which originates as an entire annulus, and so modify its development that its anterior part should appear first (just as the anterior part of the calyx in Pinguicula appears first), we should have a structure originating in semilunar form exactly as in the young ovary of Pinguicula. That five connate carpels should go to form a bilabiate stigma, is just what might be expected in a family where the tendency to bilabiation is so strongly marked. To take an extreme case, I may refer to Utricularia minor, where the corolla, with two vascular bundles going to its upper and three to its lower part, is bilabiate with two perfectly entire lips. General Conclusions. A few words may be said with regard to the probable affinities of the order Lentibulariaceze. In the first place, I shall allude to the opinion of Mr BentHam, as quoted by LinpLEY (Veget. Kingd. p. 686), to the effect that they are very closely related to Scrophulariaceze, in ‘‘ having the same calyx, corolla, stamens, and bivalve capsule, but distinguished solely by their realby unilocular fruit, with a free central placenta, and the minuteness of their embryo. In respect of the former character, they come very near to Limosella, Lindernia, and other Gratiolee, with parallel dissepiments and entire valves; for in these plants the dissepiment is very thin, and usually detaches itself from the valves before maturity, so that being concealed by the seeds, which fill nearly the whole capsule, it often escapes observation, and many of these genera have frequently been described as having a unilocular fruit.” Having, as I think, satisfactorily set aside the idea that the ovary of Lenti- bulariaceze is bicarpellary, it is, perhaps, unnecessary on my part to refer to Mr BENTHAM’s view, that the premature detachment from the valves of the thin * The variable and inconstant lobules at the base of the middle anterior lobe in this form of monstrosity I am, I think, justified in considering of secondary importance. FLOWER OF PINGUICULA VULGARIS, ETC. 547 dissepiments in the Gratioleze is an indication of an approach to the structure of an ovary with free central placenta; I would only suggest that this is an idea of the same character, and quite as fallacious, as the popular one that the pecu- liar splitting of the fruit in Platystemon indicates an approach in that plant to the apocarpous Ranunculaceze. If, then, any affinity with Scrophulariaceze is to be found it must be in the floral envelopes and stamens. In Lentibulariaceze we have, no doubt, irregular bilabiate floral envelopes and partial suppression of the andreecium with a tendency to the didynamous structure; but the value of this combination of bilabiation with didynamy as determining the true affinities of a given plant is seriously open to question. It must, I think, be evident to any one reflecting on the subject, that such a combination of characters occurs in several very different types, by what may be called a parallelism of development or modification. Thus, lst, In Scrophulariacee, with 2-celled ovary and axile placentation; a modification of the Solanaceous type. 2d, In Gesneraceze and Orobanchaceze, with l-celled ovary and parietal placentation ; a modification of the Hydrophyllaceous (?) type. 3d, In Labiate, with gynobasic style and spuriously multiplied loculi; a modification (in spite of the difference in the position of the raphe) of the Boraginaceous type. 4th, In Morina (belonging to the order Dipsacacee), where we have a bilabiate corolla of five petals, and four stamens, two large and two small. On the whole, it seems to me that we have as little right to associate Lenti- bulariaceze with Scrophulariaceze on account of bilabiate floral envelopes and more or less didynamous stamens, as a zoologist would have to associate the Echidna with Hedgehogs or with Porcupines, on account of the remarkable correspondence in their prickly defence. With regard to the supposed affinity with Primulaceze, we have a correspond- ence in what may perhaps be viewed as the most remarkable structure in the Lentibulariaceous flower, viz., the free central placenta; and I have shown at least some plausible grounds for believing the Lentibulariaceous ovary to be com- posed of five carpels, like that of Primulaceee. The important differences between the orders may thus be reduced to the position of the stamens and the albuminous or exalbuminous character of the seeds. PAYER, in his Lecons sur les Fam. Nat. des Plantes, places the order Salvador- acez (consisting of the single genus Salvadora) in juxta-position with Lenti- bulariaceze. Both agree in the superposition of the stamens to the sepals, in having a unilocular ovary with free central or basilar placentation, and in the exalbuminous character of the seed. The question very naturally suggests itself, VOL. XXV. PART II. 8F 648 DR DICKSON ON DEVELOPMENT OF have we not in Salvadora, with oppositi-sepalous stamens and solitary exalbu- minous seed,* a plant bearing the same relation to Lentibulariaceze, with numerous exalbuminous seeds, as Plumbaginacez, with oppositi-petalous stamens and solitary albuminous seed, bears to Primulaceze, with numerous albuminous seeds ? I believe that in Salvadoraceze with Lentibulariacese, on the one hand, and Plumbaginaceze with Primulaceze, on the other, we have two parallel nearly allied series. I shall not, however, pursue this subject further, as my personal knowledge of Salvadora is very limited. Diagram of the flower of Pinguiewla vulgaris, L., showing the estivation of calyx and corolla, the stamens and staminodes superposed to the anterior and lateral sepals, and the one-celled ovary with free central placenta. The wall of the ovary is represented as divided into five parts by two plain and three dotted lines, the two plain lines representing the division of the stigma into two lips or of the capsule into two valves, the three dotted lines representing the abnormal fissures in the above mentioned monstrosities. * Wicut (Icones pl. Ind. Orient. t. 1621), Enpiicuzr (Genera, p. 349), Linpiey (Veget. Kingd. p. 652), and Payer (Legons, p. 14) agree in describing Salvadora as having a unilocular ovary with solitary erect ovule. Professor Oxrver has kindly examined for me flowers of S. persica, L., and S. Wightiana, Pl., from the Kew Herbarium, of which he reports in a letter as follows :— “In each of these I find a 1-celled ovary with a solitary basal ovule.” My own somewhat limited examination of the flowers of S. persica has led me to the same conclusion. On the other hand, Prancuon (Sur les Salvadoracées, Ann. des Sc. Nat. 8° serie x. p. 190), and more recently MM. Maovur and Decaisne (Traité de Botanique, p. 453) describe the ovary here (PLANCHON in the genus Salvadora, Maout and Decaisyz in the order Salvadoracez) as bilocular, with two collateral ascending ovules in each cell. The only explanation I can suggest for the statement in the “ Traité de Botanique,” is that the authors have probably followed Prancuon, for M. Decaisnz had formerly described S. oleoides as having ‘‘ovarium . . . uniloculare, loculo uniovulato”’ (Jacquemont Voyage, p. 140, t. 144); while M. Prancuon’s description is so opposed to the results of other botanists, and so unlike anything I myself have been able to see, that I am constrained to believe that it was some other plant, and not Salvadora, that he examined. I should mention, however, that Decatsne (Jacquemont Voy, t. 144) gives a figure of a fruit of S. Madurensis containing three seeds. FLOWER OF PINGUICULA VULGARIS, ETC. 649 Remarks on the Embryos of Pinguicula vulgaris, P. grandiflora, P. lusitanica, P. caudata,* and Utricularia minor. The remarkable diversity in the structure of the embryo in the Lentibu- lariaceze is, perhaps, one of the most extraordinary circumstances connected with the order. A. DE St Hizarre pointed to the occurrence of a dicotyledonous embryo in P. lusttanica, a monocotyledonous one in P. vulgaris, and an acotyled- onous one in Utricularia vulgaris, as an instance of how the most important characters may vary, even within the limits of a single order.t TREVIRANUS, in 1838,{ was the first to show that the embryo of P. vulgaris has only one cotyledon. In 1848, he published his researches on its germination, which were called forth by a statement of Kiorzscn’s, that this embryo germin- ates with two cotyledons, of which one is much smaller than the other. Here, he showed that KLorzscu’s smaller cotyledon does not appear until germination is considerably advanced, thus proving that it does not legitimately fall under the definition of a cotyledon at all.§ P. vulgaris, L. (Plate XXX. figs. 33-40). The embryo of Pinguicula vulgaris, taken as a whole, is of a cylindrical form, with rounded extremities, and measures about 34,d of an inch inlength. The single cotyledon constitutes about one-half of the entire length of the embryo, and is folded upon itself in a conduplicate manner, its margins being approximate and parallel to each other, except towards the base, where they diverge rather suddenly, leaving a considerable interval, where the termination of the embryonic axis (rudimentary plumule) is to be seen (fig. 33). The apex of the cotyledon is almost constantly entire, or, at least, not sufficiently emarginate to appear dis- tinctly so in a back view, such as is represented in fig. 34. In two, or at most three instances, however, out of the large number of embryos that I have examined, the tip of the cotyledon was somewhat bifid, as is seen in the back view in fig. 35. When sections made in the mesial plane (fig. 38) and at right angles to it (fig. 37) are compared, the rudimentary plumule is seen to be compressed laterally, having a strong convex curvature from side to side, while there is only the slightest possible convexity from before backwards. That there * The observations on the embryo of this species were made after the paper had been sub- mitted to the Society. t Morphologie, pp, 755-6. t In a communication to a meeting of naturalists, at Freyburg in Br., of which I have seen no report, but which is referred to by Treviranus in his subsequent paper in the Bot. Zeitung, 1848. § Botanische Zeitung, 1848, p. 444. 650 DR DICKSON ON DEVELOPMENT OF is no trace of a second cotyledon is quite evident from examination of the mesial sections.* P. grandiflora, Lam. (Plate XXX. figs. 41-42). After examining the embryo of P. vulgaris, I was curious to ascertain whether there was any difference between it and that of this species, which is so nearly allied to P. vulgaris that some botanists are disposed to combine them together ; and I was gratified to find embryonic characters by which they may readily be distinguished from each other. In front view (fig. 41), the embryo of P. grandiflora (which is about the same size as the last) exhibits a single cotyledon having about the same relative length to the whole as that of P. vulgaris. The base of the cotyledon, however, is found almost completely to surround the extremity of the embryonic axis, so that hardly a vestige of the plumule is to be seen from the outside; and on back view (fig. 42), the tip of the cotyledon is seen to be constantly and deeply bifid.+ The first peculiarity is, so far as I have seen, absolutely distinctive between this embryo and that of P. vulgaris; while as to the second one, it is, as I have just mentioned, only in very rare cases that the cotyledon of P. vulgaris is bifid at its extremity. These embryonic characters, combined with some other remarkable differences (such as the number of adven- titious buds produced at the bases of the outer leaves of the autumn-rosette— in P. vulgaris, usually only one in the middle line of each leaf; in P. grandiflora, a considerable number in a single transverse row), go far, in my opinion, to establish the validity of the claim of P. grandijiora to be ranked as a species. P. lusitanica. With regard to the very minute embryo of this species (about 3th of an inch in length), I need not say much, beyond confirming the statements of St Hia1rE as to there being two cotyledons. These are relatively considerably shorter than the single one of P. vulgaris or P. grandifiora. I have to note the presence of a trace of albumen in the seed here. * Treviranus figure of the embryo from the seed is somewhat faulty, from the cotyledon being represented as considerably too short in proportion to the radicle, and from the absence of any indication of the rudimentary plumule. There is also no indication of the plumule in his figures of the earlier stages of germination, the result, doubtless, of imperfect observation (Joc. cit. t. iv.). He also makes a curious blunder in describing the apex of the embryo as pointed towards the hilum of the seed (loc. cit. p. 442), the fact being that in this, as in all anatropal seeds, the apex of the embryo points away from the hilum, the radicle being directed towards it. This mistake is probably due to the circumstance that there is often a projecting portion of the testa at the chalazal extremity, which is apt to be mistaken for the somewhat similar projection at the hilum, + I think it not improbable that back views of this embryo may have had something to do with the statement found in most of the books, that there are two “ cotyledones brevissime” in Pingwicula. { I should mention that a very brief statement, by me, of the differences between the embryos of P. vulgaris and P. grandiflora, has already appeared in the report of a meeting of the Dublin Microscopical Club (‘‘ Quarterly Journal of Microscopical Science,” viii. pp. 121-2). I now take this opportunity of describing them in greater detail, and with figures. CO ———— a a FLOWER OF PINGUICULA VULGARIS, ETC. 651 ‘ P. caudata (Plate XXX. figs. 43-44). Since bringing this paper before the Society, I have succeeded in extracting an embryo, almost entire, from one of a very few seeds of this Mexican species obtained from the University Herbarium in Dublin; and I find that there are two cotyledons, whose length is about one-half of that of the embryo, which measures about 1,th of an inch. The embryo here, like the seed containing it, is very narrow and considerably elongated. I have given two views of this speci- men, so as to show the division between the cotyledons on either side; from which the fact that there are two cotyledons is abundantly manifest. In the specimen figured, one cotyledon is a little shorter than the other; this, however, is accidental, as the cotyledons were of equal length in another embryo which I extracted in a somewhat mutilated condition. Utricularia minor, L. (Plate XXX. fig. 45.) The embryo here is somewhat globular, about ;,th of an inch in diameter, and at first sight appears to have a smooth undivided surface; on careful inspec- tion, however, a remarkable conformation is to be observed of that end of the embryo which is remote from the hilum of the seed, viz., a minute, slightly convex punctum vegetationis surrounded by four slight elevations placed so as to- form the somewhat incurved sides of a square. Iam not exactly prepared to call these elevations cotyledons; but the whole structure is interesting, as show- ing this embryo to be a little in advance of a mere “ embryonal globule,” as are most of the embryos described as ‘“‘ undivided” or “‘ acotyledonous.”’ Explanation of Plates XX VIIT., XXIX., XXX. Prate XXVIII. Pinguicula vulgaris. Fig. 1. Extremity of winter-resting bud, showing rudiment of the inflorescence, and of the axillary bud of the last leaf. 1’, 3d last leaf cut across; 7’, 2d last leaf; 7, last leaf; ad, axillary bud of last leaf; #1, indication of 1st flower; #2, that of 2d flower. Leaf- spiral from right to left of observer supposed to occupy the axis. x 77. Fig. 2. Young inflorescence further advanced. The first flower (1) distinctly projects, and exhibits irregularity, being flattened from above anteriorly, downwards posteriorly, although not even the calyx has appeared. Leaf-spiral from right to left. x 77. Fig. 3. Young inflorescence, in which the anterior sepals of the 1st flower are beginning to appear (sa). Leaf-spiral from left to right. x 77. Fig. 4. Young inflorescence. Here the calyx of the 1st flower is now complete, and the corolla is visible. s/, lateral sepal ; sp, posterior sepal. Leaf-spiral from right to left. x 77. Fig. 5. Young inflorescence. Fertile stamens (st) distinctly present, and staminodes (st’) faintly so in the lst flower. pp, posterior, and pi, lateral petals. Leaf-spiral from left to right. x77. VOL. XXV. PART II. 8G Fig. Fig. Fig. Fig. Fig Fig. Fig. Fig. Fig. Fig. Fig. Fig. DR DICKSON ON DEVELOPMENT OF 6. Young flower. Ovary beginning to appear to the anterior side of receptacular centre as a semilunar elevation alternate with the anterior (fertile) stamens. x 77. 7. Young flower. The extremities of the semilunar ovarian wall are now extending them- selves round the receptacular centre. x 77. 8. Young flower. The ovarian wall is now completed by union of the extremities of the semilunar elevation in the middle line posteriorly. The receptacular centre, hitherto depressed, is becoming slightly elevated; forming the rudiment of the free central placenta, x77. 9. Young inflorescence. In the first flower the ovarian wall is completed, and begins to show a tendency to bilabiation. The fertile anthers now show themselves to be 4-celled. Leaf-spiral from right to left. x 77. Puate X XIX, Pinguicula vulgaris. 10. Young pistil, showing larger or anterior (a) and smaller or posterior (p) lip of the stigma, The disproportion between the lips is not yet very great. x 85. 11.* Young pistil, considerably further advanced, exhibiting nearly its adult form. Anterior lip of stigma broadly expanded, the posterior narrow and strap-shaped. x 15. 12. Longitudinal section of young flower at about the stage represented in fig. 9, pst, pistil. The placental elevation (pc) is now commencing to appear. x 30, 13. Longitudinal section of young flower at a further advanced stage. The ovarian cavity is becoming somewhat “inferior’’ posteriorly. As yet no ovules. x 30. 14, Longitudinal section of half-mature flower-bud. The corolla now extends beyond the sepals, and its spur (c) is of considerable length. The ovarian cavity is now nearly half-inferior posteriorly. x 30. 15. Young flower-bud, showing the zstivation of the sepals, x 15. 16. Young placenta, showing the basipetal succession of the ovules (07), which have as yet appeared only on its upper part. x 100. 17-22. Outline-sections (partly optical) of ovules at different stages of development. Nucleus (n); integument (int), In fig. 22 the embryo-sac (es) appears to have wholly replaced the nucleus. Puate XXX. Pinguicula vulgaris. . 28. Abnormality. Young flower with dimerous symmetry and regular, ; 2 sepals (s), 2 petals (p), 2 stamens (st). The ovary is faintly indicated. x77. . 24, Abnormality. Young flower with hexamerous symmetry. Sepals—1 anterior (sa), 2 antero-lateral (sal), 2 postero-lateral (sp/), and 1 posterior (sp). Petals—2 anterior (pa), 2 lateral (pl), and 2 posterior (pp). Two stamens (sf), here antero-lateral ; and three staminodes (st’), 1 anterior and 2 postero-lateral. x77. . 26, Abnormal young pistil. Ovarian. wall deficient posteriorly, exposing the placenta and ovules, «, lappet of doubtful significance. x 15, 26. Abnormal young pistil, with bipartite posterior lip of the stigma. a, anterior lip of stigma ; p p’, the halves of the posterior lip. x 85. 27, Abnormal young pistil. Anterior lip of stigma tripartite, being divided into an antero- median lobe (am), and two antero-lateral lobes, one right (ral), the other left (/al.) . x 85. 28. Left antero-lateral view of the same pistil, showing a slightly-marked “lobule” (02) at the left side of the base of the antero-median lobe. x 8d. * In this figure, as also in fig. 31, the capitate hairs scattered over the surface of the ovary are not represented. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fic. t—) Fig. > Hig. Fig. Fig. Fig. Fig. Fig. Fig. 29. 30. él. 32. 33. 43. 45. FLOWER OF PINGUICULA VULGARIS, ETC. 653 Nearly anterior view of a monstrous pistil resembling the last; but where there is a “lobule” (dbl) on each side of the base of the antero-median lobe, that on the right side (to left hand in the fig.) being considerably the larger. x 85. Abnormal pistil. Posterior lip of the stigma (») somewhat broader than usual, but undi- vided, Anterior lip with a fissure on the left side, separating off a left antero-lateral lobe (Jal). x 85. Abnormal pistil. Stigma funnel-shaped, and nearly regular, The staminodes (sé’) here are greatly developed, showing distinct filaments terminated by anther-like knobs. x 15. Monstrous pitcher-like leaf. The dotted line indicates where the cavity of the leaf termi- nates below. Natural size. Embryo. Front view. Solitary cotyledon (c); radicle (7); rudimentary plumule or punctum vegetationis (pv). x41, . Embryo. Back view. x 41. . Embryo. Back view, exhibiting an unusual bifid condition of the extremity of the coty- ledon, x4. . Embryo. Side view. x 41. . Embryo. Longitudinal section at right angles to the mesial plane. x 41. . Embryo. Longitudinal section in the mesial plane. x 41. . Embryo. Remarkably curved. x 41. . Mesial section of embryo similar to the last. x 41. Pinguicula grandiflora. . Embryo. Front view. x 41. . Embryo. Back view. x41. Pinguicula caudata. and 44. Views from both sides of one embryo, showing the presence of two cotyledons. x 43. ” Utricularia minor. Embryo, showing punctum vegetationis (pv) surrounded by four very slight elevations (c) forming the somewhat incurved sides of a square. x 43. (Te |ROne A In ag re ne OTs : cfull wide teh; oat wels yale Hiecepainier ease Ian Sire on Sif bewtrin ede canolentte’ siMoae ls 3 ogee ale St y | “a pa soa uiate, cll eal alla yaa, Leda Bagel ut tad Jeane easly wl * intra mmg iNy hy Aad a. nf HABA J Ha pres ene fee ETS Ls alt aes = tix als ; Be “Sil = ty | cole Sequrerdhe dees aad Nantnte ais . js it 2 oti) ed yee ee Diag ‘ar Ped aL auigtt Ohi Sar ps Ti, “Saadaral qh Toe a wren alt= avilte wipaabon. dade ast calc ape ’ : ~— bit ee | oe coe 70 Freionewoy St Parr. hes sata \eenifnas eal gk ; Tia Aw Hue ikeqne ; pete OS eee” ely a ‘do. rhuenles ond We fetinieauy jis terponer isi in mirditne rate tall it = ): ‘he peers A, ‘ » cn oa ees ; ob al 0 dale af ent ey aa i Pe ao ae $).« ¢ why Ai dOd et nd tontaeiae 2) d? ee -hohds aeons } ak RS) 6°34 oA ed say ~orsthh te pte’ ; ot ol aie aan ae ke pla eee iy wnlheant 7 yy out Nt dia apa A, DY an pr ae Oe" Vie plhja’ eR ed omas fea é ee . oe Pe. * seaplane o (% swe \? - nites tia ie zg : arite) ce ais: Plate XXX1 ans. Roy. Soc. Edin? Vol. XXV FROG UIPT STON VY A COZ) LORIN Ag Pern ojsip pin dn pay 22g wy 7 posoddus “PAGS PUBSIUNT Y D wor eucpsrunyT Ty.10 sq yous Funes ‘Op wspynog (PAYOLLYS WPILS YOFUOZLLOY U2 PUOPFULOD EB 43343 SZ LNOGV NOILI9S JO HLONAT = AYHWNO G13aI4SMNIN Q eucpsruny gy) fo peprosip osyp wpo.4s ueppoyy Luahptaag — Pp suoytod ‘suapynog qonsn sy, saprisag Funcampuoo hazy LaTOOT, dn 12019 Pu Pegnnysipy YMULFUPSIUNT Jo Uppys uty I~ J "POVOLGS P PIgGns “DYO.BS TPOUCALOY UL FUQBSULO) ~ "B 1434 08 NOIL93S 40 HLONST AYWYWNO GT13I4SMNIT SOSA TY SG SN Sea een tS S Ge eanee oe te Aceon a a x ik ee .eetesan ty Ye 2, a8 ( 655 ) XIX.—On the Boulder-Clay of Europe. By Davip Minne Home, Esq. (Plate XXXI.) (Read 19th April 1869.) “‘ Boulder-clay” or “till,” abundant in Scotland, and occurring also in Eng- land, Ireland, and in some other parts of North-Western Europe, has long been, and still is, a puzzle to geologists. Sir James Hatt, about fifty years ago, in this Society, was the first to draw attention to the deposit, by describing its composition, and endeavouring to ex- plain its origin. He saw that it could not be included in either of the two great classes into which rocks were then divided. It was a deposit swz generis, bearing no resemblance to anything known, except a heap of rubbish, there being in the arrangement of its ingredients no regard to specific gravity or size. Sir James Hatu ascribed the deposit to diluvial agency, and attempted to show how the transport of the boulders and pebbles in it, their rounded forms, and the abrasion of rocks covered by it, might all be accounted for, by supposing that great waves of the ocean had swept over the country from west to east, scattering debris in all quarters.* This diluvial theory was generally accepted, and relied on as satisfactory, until about the year 1840, when the “ glacier” theory was started, suggested probably by the discovery that many of the shells found, if not in the boulder-clay itself, at all events in other pleistocene beds, alternating with it, bespoke an Arctic climate. | A strong impulse was given to this new theory by the publication of a magnificent work, on the Swiss Glaciers, by AGassiz, and by an account of a visit which was shortly afterwards made by that naturalist to Scotland, in company with the late Dr BuckLanp. -Both of these eminent men affirmed that they had seen unmistakable signs of glaciers in almost every valley they visited. Shortly afterwards, the late Principal Fornes, who had, by frequent visits to the Swiss glaciers, made himself well acquainted with their action, went to Skye, and discovered marks of ice on many of its rocks. He read a paper in this Society, describing these marks; and as the learned Principal was distin- * Sir James Hatu’s theory is explained by him in the following paragraph :—“I imagine that a diluvial wave flowed at some remote period from a westerly or north-west direction, and broke over our island; that its magnitude was such, that a great body of its water crossing the ridge of country which separates the two coasts, overwhelmed the district, discharging itself into the German Ocean.”—(Ed. R. 8. Tr. vol. vii. p. 202. VOL. XXV. PART II. 8H 656 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. guished for accurate observation and cautious deduction, his discovery in Skye added largely to the popularity of the glacier theory. The next quarter from which light came was Wales, where Professor Ramsay recognised signs of ice action. He was followed by Dr CuAmpBers, the late Mr Mactaren, and Mr JAMESON of Ellon, who severally pointed out localities in many of the Scotch counties. But whilst generally adopting and helping to illustrate this theory, almost all of these geologists admitted that there were some phenomena of the boulder-clay which could not be explained by any imaginable local glacier; and they threw out the idea that icebergs or icefloes, which it was discovered carried in the Arctic and Antarctic regions enormous masses of rock and rubbish, might possibly have in former times done similar work in North-Western Europe. By this time Acassiz himself appears to have become satisfied that many of the ascertained facts could not be explained on the theory of glaciers flowing down from isolated mountain ranges. Having gone to reside in America, he obtained there an opportunity of studying the phenomena on a much larger scale than either Switzerland or the whole- of Northern Europe supplied, and was greatly struck by seeing that boulders were scattered over an area of the earth’s surface, extending to nearly 1000 miles in every direction, and that these boulders generally had all been transported from one quarter, viz., the north. Having learnt, from the writings of Murcutson and others, that the great mass of boulders in Russia and Poland had also come from the north, and that in some cases the parent rocks were more than 100 miles distant, he formally renounced the theory of local glaciers, and propounded the notion that gigantic glaciers, more than a mile in thickness, and derived from snow two or three miles deep, had been generated in the Arctic regions, and were by some cause made to move over the earth’s surface towards the south, encasing great continents, filling sea-beds, rising up slopes of land, overtopping mountains, and pushing before them, with a colossal ice-foot, immense heaps of detritus. From his recent work on the Brazils, it appears that this enthusiastic naturalist contends that the huge glacier which passed over North America, reached even to the tropics.* I do not know or believe that this theory of Acassiz, in its full extent, has been adopted by any geologist in either America or Europe; but Iam not sure that it is not, to a modified extent, adopted by some of our Scotch geologists. Mr GEIKIE, in a very valuable paper on the “ Glacial Drift of Scotland,” says, “that the ice existed, not as mere local glaciers descending the chief valleys, but as one wide sheet covering the whole, or nearly the whole, country” (p. 78). * “Visit to the Brazils,” p. 403.—Agassiz in this work contends for the existence of “a sheet of snow 10,000 or 15,000 feet in thickness, extending all over the northern and southern portions of the globe,—which in the end formed a northern and southern cap of ice moving towards the equator !” MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 657 “Down the whole of the west coast, from Cape Wrath to the Mull of Cantyre, one long expanse of ice filled up the fiords, and stretched out into the Atlantic. From the uplands of Wigtown and Galloway, the icy stream swept down into the valley of the Solway, and onward for Ireland. From the hills that border the lonely valley of Liddesdale, far away into the blue Cheviots, the same universal mantle of ice threw its folds athwart the hills and dales of the north of England.” (‘‘ Glacial Drift.” P. 84.) The following passages in a later publication by Mr Gerxie (“Scenery and Geology of Scotland,” 1865) may also be referred to :— ‘‘The massive ice of the great Highland area came down into Strathmore, and kept steadily southward in such force as to mount over the chain of the Sidlaws, and even it would seem over the Ochils, until it went out to sea by the basin of the Forth.” (P. 300). Referring to Scotch boulder-clay or till, Mr Grrxie says, that “land ice has now given us the clue to the history of this remarkable superficial deposit, as will be afterwards pointed out; its internal structure, and its striated stones, show it to be the result of the abrasion carried on by the ice-sheet, as it moved over the land.” (P. 183). “ The high grounds of the interior receive a constant accession of snow; and the accumulated mass, pressing down the valleys, goes out to sea in long wide walls of ice.” ‘The moraine-rubbish of this great ice-sheet gathers into the thick deposit known as boulder-clay.” (P. 345). The Rev. R. B. Watson, in a paper on the “ Drift-beds of Arran,” read in this Society in January 1864, says, that the phenomena indicated the existence not of glaciers merely, but of a massive zce-cake, “‘more universal than even in Southern Greenland now. Beneath this ice-cake the soil, and all of life it sup- ported, would be gradually harried away to the sea; any traces of it left being nests of debris niched into corners, ground over and disturbed in every conceiv- able way by the ice above.” (P. 537 ‘“‘ Roy. Soc. Trans.” vol. xxiii.) ‘This being so, we are entitled to say that the boulder-clay is the result of land glaciation.” (P. 538). . Dr Bryce of Glasgow, shortly after the publication of Mr Watson’s paper, went to Arran to examine the sections described in it; and he concurs in holding that the circumstances proved “ for the boulder-clay an origin on Jand.”’ (“* Lond. Geol. Journal” for 1864, p. 211.) The most recently published paper on boulder-clay, with which I am acquainted, is by the Rev. Dr Tuomas Brown, who read in this Society an account of the “Arctic Shell-clay of Elie and Errol.” In this instructive paper he has a chapter on boulder-clay, which he says, both at Elie and Errol, lies beneath the Arctic shell-clay, and rests immediately on the rock. He states his opinion of its origin thus:—“ It would seem that this lowest deposit, so long an enigma, 658 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. has at last yielded up its secret. It is a Jand deposit, formed at the period when Scotland, like Spitzbergen, lay beneath an immense covering of ice, which wrapped the whole face of the country, hill and dale. Underneath such a covering, possibly thousands of feet in thickness, the rocks would be ground down, and the boulder- clay formed. Thus the absence of fossils is accounted for; inasmuch as none of our usual forms of life could exist beneath such an ice-sheet ; and thus we see also how the clay is so peculiarly hard and untractable.” (P. 630). I have briefly sketched the various theories relating to boulder-clay, to show the difficulty of the subject, and have referred more particularly to the views of the latest writers. whose geological experience and knowledge are held in just repute. It is, therefore, with considerable hesitation that I venture to call in question the soundness of these views, and I would not have done so, had it not been that some observations, bearing on the subject, do not appear to me to have received sufficient consideration. Most of the observations to which I allude are to be found scattered through different publications, and have never yet been brought together, so as to throw a combined light on the question ;—I am able also to adduce some observations of my own, not yet published. I shall advert, first, to the difficulties which beset the theory that our Scotch boulder-clay ‘‘is a dand deposit,” the product of glaciers; and will afterwards state the reasons which lead me to believe that it has been formed at the bottom of the sea—by the action of floating ice. I disavow any originality in presenting the iceberg theory. Moreover, it has this presumption against it, that, having been formerly adopted by Mr Geixig, he has lately intimated that he has had to abandon it, because, as he says, ‘‘ though the iceberg hypothesis is generally the accepted explanation of the phenomena of striated rocks and boulder-clay, its untenableness seems to me completely estab- lished.”’ (‘‘ Glacial Drift,” p. 10.) Notwithstanding this very decided condemnation, I think there are good erounds for upholding the correctness of the iceberg hypothesis. That there are some points not altogether explained by it, I will not deny; but that there are insuperable difficulties with which the glacier hypothesis has to contend, I shall now proceed to show— 1. If the boulder-clay was formed, as is alleged, by the action of glaciers; if it consists of debris derived from the rocks which the ice grinds down in its passage over them, and which are pushed forward by its ice-foot, we would see boulder- clay now forming in those countries where glaciers are in action. But it has never been alleged that in Switzerland, Norway, or Upper India, whose glaciers have been described by competent observers, anything like boulder-clay is seen to be produced. I have been twice in Switzerland; and, being anxious to watch the effects of glaciers on the rocks, made them a subject of study, and penetrated Se ee eee ————— ee ee MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 659 under three glaciers near their lower extremities, without discovering anything like boulder-clay. Great abrasion of rocks there was undoubtedly. Blocks and pebbles under the ice I saw in abundance, all grinding, and many of them scoring the rocks. Much sediment there was, flowing out from under the ice. But what became of this sediment? It was carried off into rivers and lakes, there to form beds of mud or sand—none having any resemblance to boulder-clay. The terminal moraines of glaciers, no doubt, resembled it in one feature—want of stratification ; but the absence from these moraines, of clay, hard, tough, and compact, showed that the deposits were essentially different. It is no small confirmation of my own testimony on this point, that Acassiz, when he visited Scotland to search for the signs of ancient glaciers, avowed that he had never seen boulder-clay before he saw it in Scotland.* 2. The next difficulty with which the glacier theory has to contend is, the prevalence of boulder-clay in districts where it is scarcely possible to suppose that glaciers could have existed, or, if they did exist, a have had to do with the production of the deposit. Thus, in the flat districts of Norfolk, and in the still flatter districts of Denmark and North Holland, boulder-clay is found. But there are no moun- tains in or near these districts, where any glaciers could have been formed. The same remark has been made by Mr Cummine of the boulder-clay in the Isle of Man. + Even in those parts where there are both boulder-clay and mountains, as in the Highlands of Scotland, it appears that the boulder-clay is derived from a quarter the very opposite from that where a glacier may have existed. Along the coasts of Western Ross-shire and Caithness, this deposit abounds, and has been studied by Mr Jameson of Ellon and Dr Roserrt CoAmBers—both of whom at first advocated the theory, that its formation could be accounted for by glacier- action. Mr JAmEson says—* The distribution of this dark grey mud harmonises with the supposition that the transport of it has been from the N.W.; and a movement of ice, from the N.W. to the S.E. across Caithness, is totally at variance with the notion of the scratches having been caused by glacier-action proceeding from the interior of the country towards the present coast.”{ And he adds ina footnote, that the phenomena “ indicate a movement of ice from the N.W., where there is now nothing but open sea for an immense distance,” and ‘all suggestive of marine conditions.” 3. The next difficulty to the glacier theory is suggested by the immense extent of earth’s surface over which the transporting agent has moved in one and the same direction. * See Edin. Phil. Journal for 1842, p. 227; and Geological Researches, by James SuitH of Jordanhall, p. 12. t “Isle of Man,” by Cummine, p. 248. t Proceedings of the Geological Society of London for 1866, p. 269. VOL. XXV. PART II. SI 660 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. If the boulder-clay was produced by glaciers, its transport would be coinci- dent with the direction in which the glaciers moved—that is, in directions parallel with the valleys from which they emerged. We should expect, therefore, to find that the boulder-clay, and the blocks embedded in it, indicated a movement and transport from every conceivable point. The boulder-clay and boulders found on the west coast of Scotland should indicate a movement from the eastward; on the north coast, from the southward; and on the east coast, from the west- ward. But is this the true state of the case, as shown by most recent observation ? The phenomena of the boulder-clay show in all parts, not of Scotland only, but of Ireland, England, and even of the adjoining districts of North-Western Europe, a general movement from the north-westward. That exceptions to the rule exist I admit, and an explanation of these I shall afterwards offer; but I affirm that there is a general and prevailing direction over the wide area just mentioned, and that direction is from W.N.W. or N.N.W. Before, however, giving proofs of this position, let us see what are the signs of transport on which geologists are agreed. (1.) Mr Gerxiz has pointed out a relation between the colour of the boulder- clay and the rocks of the districts adjoining the deposit—as indicating transport. Thus he says—‘“‘ The main mass of the boulder-clay, in the basin of the Forth for instance, consists of the comminuted debris of the carboniferous and other rocks which form the framework of that district. We can also gather that this loose fragmentary material has moved (there?) from west to east. In the upper part of the basin of the Firth of Forth, the coal-fields are covered with ved boulder- clay, abounding in fragments of the rocks that lie towards the N.W., and deriving its prevalent tint from the waste of the Old Red Sandstone which stretches up to the foot of the Highland mountains.” * The late HucH Mier had previously pointed out how the pale oolitic rocks of Brora and Golspie are covered by a yellow boulder-clay, and the flagstones of Caithness are covered by a boulder-clay of a grey leaden colour. So also Mr Cummine showed how, in the Black Isle, the boulder-clay has the colour of the red rocks there; whilst to the westward, the colour changes to a colour in corres- pondence with that of the slaty rocks. The same author points out how, in the Isle of Man, the colour of the boulder-clay is blwe near the limestone rocks, and red near the Old Red Sandstone rocks; and how in each case these rocks are in the same direction from the boulder-clay, as if a current had swept over the rocks to provide materials for the clay. Mr Nico has pointed out the same relationship in Cantyre.t * Glacial Drift, p. 43. + Lond, Geolog. Journal for 1850, vol. vii—Isle of Man, pp. 115, 247. t Lond, Geolog. Journal for 1852, vol. viii. p. 417. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 661 Arguing from this test, the late Dr FLemince showed very clearly that in the neighbourhood of Edinburgh, the boulder-clay “had been in motion from west to east.”* These views are important, as proving also that geologists agree in holding that whatever may be the case with regard to the erratic blocks in the boulder- clay, the boulder-clay itself has been derived chiefly from the rocks over or near which it lies, and (to use Mr Gerrkin’s expression) ‘‘ consists of the comminuted debris of ” these rocks. ; (2.) Another well-established indication of the direction in which the boulder- clay has moved, is afforded by the striations and groovings of the rocks covered by the deposit. Mr Jameson, after stating various facts bearing on this point, says, ‘“‘all this shows that the boulder earth, with its embedded fragments, was pushed along by the same agent that scored the rocky bed on which it lies.” + So also Mr Gertz, after mentioning other examples, says—“ Here it will be seen that the direction of transport of the boulder-clay exactly coincides with the trend of the groovings and striations on the rocks below,” + (3.) Farther evidence bearing on the same point is afforded by the nature of the boulders or erratics embedded in the boulder-clay ; for when an examination of the rocks composing them has led to a discovery of the locality from which they have apparently been transported, the direction in most cases coincides with that of the striations on the rocks, and with the direction of the movement of the boulder-clay as indicated by its colour. Accordingly, AGAssiz does not hesitate to admit, that the striz on the rocks are due to the same cause which transported the blocks.§ This remark applies not merely to blocks in the boulder-clay, but to erratic or transported blocks in other positions, whether on rocky knolls or on beds of gravel. Whenever the quarter from which they have come has been clearly ascertained, it is found that the direction of their transport agrees with that of strize on rocks in the neighbourhood. ; There is another circumstance, not undeserving of consideration, long familiar to geologists, viz., that when erratics are of such a shape that their length greatly exceeds their width, their longer axis generally lies in the direction of their transport. I believe, therefore, in common with other geologists, that the movement of the boulder-clay, whenever that has been ascertained, the transport of boulders, and the striations, groovings, and smoothings of the rocks, are due to one and the same agent; and hence the phenomena to which reference has just been made, * Lithology of Edinburgh. t Lond. Geolog. Journal for 1866, p. 167. Glacial Drift, p. 45. fe + § Edin, Phil. Journ, for 1842, vol. xxxiii. p. 223. 662 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. can be competently relied on to ascertain the quarter from which that agent has come. What, then, is the evidence on this point afforded by these phenomena? Let me enumerate the localities where the direction has been clearly ascertained. Caithness—Mr JAmMEsON, in his instructive paper on this subject, enumerates about twenty localities in this county, where “ the glacial markings on the rocks showed a pretty uniform direction over the whole district from the N.W.” Mr Jameson also examined the directions in which “the dark grey mud”— by which he designates the boulder-clay—derived, as he considered, “from the Caithness flags, had moved,” and he found that it also had moved from the N.W. He found that the Caithness flags—situated in the N.W. of the county—were themselves covered by ‘‘ drift of a reddish-brown colour,” derived probably from the north-westward.* Ross-shire and Argyleshire—Dr CHAMBERS mentions that “‘ near Rhiconish we find striz coming from the coast—.e., from the N.W., and passing across a high moor, with no regard whatever to the inequalities of the ground. A little further north, at Loch Laxford, a fine surface is marked with striation from the N.W., being across the valley in which it occurs. At an opening in the bold gneissic coast, which looks out upon the Pentland Firth, there are strong markings in a direction from N.N.W.”+ In the small Isle of Kerrara, opposite to Oban, and also in the Island of Mull, Dr CuAmbers found striation, pointing in the one case N. 68° W., and in the other N. 60° W.+ Perthshire—tThe lofty mountain of Schehallion has been examined by both Dr Cuampers and Mr Jameson. Dr CHampers§ found striz on it at a height of above 3000 feet, pointing W. 30° N.; and Mr Jameson satisfied himself that the strice he saw on the same mountain must have been made “not by ice flowing down the sides of the hill, but by ice pressing over it from the north.”|| He adds—“ On the Perthshire hills, between Blair-Atholl and Dunkeld, I found ice- worn surfaces of rock at elevations of 2200 feet, as if caused by ice passing over them from the N.W., and transplanted boulders at even greater heights.” Forfarshire—Sir CHar_es LyeL1, in the year 1842, pointed out how the till and its embedded boulders had been transported from the N.W. Dr Howopen, of Montrose, has lately published a paper in the “Transactions of the Edinburgh Geological Society,” in which he observes ‘that the general lie of the range of hills is W.S.W: to E.N.E., while the -direction of the glacial grooy- * Lond. Geolog. Journ. for 1866, p. 268. t Edin. New Phil. Journ, for 1852, vol. liv. + Ibid. § Proceed. Geolog. Soc. of London for January 1865. | Ibid. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE: 663 ings is from W. by N. to E. by S., so that the polishing agency must have crossed the hills at an angle of 30°.” Dumbarton and Renfrew shires—Dr CHAMBERS mentions that on the sand- stone plateau between Campsie and Stirling, the striations on the rocks were W. 20° N. Having myself visited the moors, about three miles N.W. of Milngavie, in the parish of Baldernock, I found the white sandstone rocks ground down and flattened in large patches, with striz and rents on them, indicating a movement from W.N.W. and N.W. (magnetic.) The late Mr Situ of Jordanhall, in his Geological Researches, after enumerat- ing several localities where boulders of various kinds of rock had been examined by him in Clydesdale, observes—‘“‘ In these cases, the bearing of the supposed parent rocks is N.W.; but in all of them the intervening space is intersected by deep arms of the sea and steep mountain ranges (p. 13). One of the boulders was found in the boulder-clay near Airdrie, the nearest granite rock being at Cruachan, about 60 miles N.W. of Airdrie.” Mr SmirH adds—‘‘I never yet saw or heard of an erratic block in the valley of the Clyde, whose course could be traced, that did not come in an opposite direction to the flow of the river. We can trace their course, not from the mountains to the sea, but from the sea to the mountains” (p. 131). Edinburghshire.—The general direction of the movement in this district has been very accurately ascertained by Sir JAmMes Hatz, Mr Macuaren, Dr FLEMING, Rosert CuamsBers, Mr Nicon, Hues Minter, Mr Gernts, and myself. All concur in representing that the movement has been from points varying between W. by S. and N.W., the most prevalent being from W. by N. (magnetic). The evidence of this is well stated by Mr Grrxiz in the following passage in his Memoir of the Geological Survey, No. 32:—“ The parallelism of the striations throughout the district show that the floating ice must have moved in a pretty uniform direction ; and that it was from the west, is clear by the striation of the western face of the hills, the great depth of the drift on their eastern sides, and by the fact that the transported boulders, when traceable to their parent rock, have been carried from west to east.” Mr Gerxiz then specifies several of these boulders on the Pentland Hills, and one in particular of mica slate, first noticed by Mr MacnarEn, weigh- ing eight or ten tons, and at a height of 1060 feet above the sea, which he says -had “undoubtedly been transported from Cantyre or the Grampians.” These boulders Mr Geixiz at that time considered to be “ice-borne blocks dropped on the submarine slopes of the Pentlands.”’ Whether he now thinks that they were brought by the agency of a glacier, I do not know. Stirlingshire and Lanarkshire.—On the west side of Damyat (one of the Ochils) I found, at a height of from 500 to 600 feet, many patches of hard con- glomerate rock, ground down and striated by an agent which had come from the VOL, XXV. PART II. 8K 664 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. N.W. and N.N.W. At these places the general slope of the county is down towards the N.W. Therefore the agent which ground down these hard conglo- merate rocks must have moved up hill. On the trap hill of Croy, near Aisyth, I lately found a conglomerate boulder, which probably came from the hills of that rock, situated between Dumbarton and Callander; and on the felspar hill at Stonebyres, I found pebbles of coal sandstone and clay ironstone, which apparently had come from the west. Sir James Haut describes a sandstone rock in Torwood, near Stirling, smoothed and striated—the direction of the striations being N. 50° W. (Ed. R. S. Tr. vol. vii. p. 200.) Berwickshire.—In the parish of Eyemouth there is a brickwork of boulder- clay, in which lumps of water-worn coal and ironstone are occasionally found. In sinking a well lately on the farm of Blackhill (Coldingham parish) through boulder-clay, lumps of water-worn coal were found. The nearest place from which these erratics could have been transported is East Lothian, situated to the N.W.—the Lammermuir range of hills intervening. In the last-mentioned parish, lumps of hematite have been picked up on the surface of the ground, resembling extremely the hematite worked on the Garlton Hills, in East Lothian, situated about 30 miles to the W.N.W. In the parish of Dunse,* there is a rounded boulder of mica slate, about one ton in weight, which must have come from the Highlands of Scotland. In the parish of Hutton, there is a brickwork situated on a mass of boulder- clay, containing occasionally rounded pebbles and boulders. One of the boulders is amass of blue greenstone, weighing about eleven tons, and angular in shape. The nearest parent rock is on Borthwick Hill, near Dunse, situated about ten miles N.W. from the boulder; and its longer axis points in that direction. In the same brickwork there are smaller boulders of greywacke, old conglomerate, and chert, all of which have most probably come from the Lammermuir Hills, situated to the north and west. An angular block of coal sandstone has also been excavated which adjoined the large greenstone boulder. No such sandstone is known in Berwickshire. I know of no place nearer than Mid-Lothian where this peculiar sandstone occurs in strata. It is of a yellow colour, and rather soft in texture. As the block is of an angular shape, its transportation could have been effected only by drift ice. In Liddesdale, 1 found boulders of granite, which probably came from the granite hills of Dumfries and Ayrshire ;+ and within these few weeks I have found in Northumberland, north of Hexham, several granite boulders, probably from the same quarter. * This boulder was pointed out to me by Mr Stevenson of Dunse, t Geology of Roxburghshire, Roy. Soc. Trans. vol. xv. p. 402. = MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 665 Arran.—Dr Bryce* has pointed out that the rocks on the N.W. sides of many of the hills have been denuded and smoothed, whilst on all other sides they are rough. Kirkeudbright—Mr Hay CunnineHam states that “large rounded frag- ments of granites and syenites are abundantly scattered over the county, and so arranged as to indicate that they have been dispersed by a force proceeding from the N.W.”’+ In Northumberland, the following table compiled from the reports of Mr Tait of Alnwick, Secretary to the Berwickshire Naturalists’ Club, [ shows the quarter from which the transporting agent moved, judging by the striations and groovings :— Locality. Nature of Surface. True Bearings. Ratcheugh, Limestone Rock below Boulder-clay. | N. Do. Blocks in Boulder-clay. N.W. Belsay. Limestone Rock. N.N.W. pogsiores ao} Limestone Rock below Boulder-clay. | W.N.W. stanborough. Swinhoe. Bre ae do. N. 50° E. Belford. Bee Be do. N.W. by W. Sea-shore, Birling. | Sandstone Rock under do. N.E. St Abb’s Head, Porphyry under do. N.W. and W.N.W. Farne Islands. Basalt under do. N.N.W. Alnwick. Limestone under do. N.N.W. The plains of Yorkshire are strewed over with blocks transported from Cum- berland, one of which is the well-known boulder of shap-granite, now standing in one of the streets of the town of Darlington. Near Liverpool, the direction of the striations on the rocks is between N. 15° W. and N. 42° W. In Cheshire, the direction is N. 30° W.§ In Wales and Somersetshire, chalk flints occur in the drift, which must have come from the county of Antrim, Ireland—z.e., from N.W. In Norfolk there are two boulder-clays, separated by a bed of sand containing sea-shells. The upper boulder-clay, as the late Mr Trimmer showed,|| contains fragments of oolite rocks, which must have come from the westward, passing over a ridge of chalk rocks, which, however, do not indicate any abrasion. Mr Trimmer, taking into view the levels of the country, held it impossible to ascribe * Geology of Clydesdale, p. 271. } Highland Society’s Transactions for 1843, + Transactions of Berwickshire Naturalists’ Club, vol. v. pp. 238, 372. § Lond. Geol. Journ. for 1862, vol. xviii. p. 377. || Lond. Geol. Journ. for 1858, vol. xiv. 666 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. the transport of the oolitic blocks to glaciers. Floating ice alone, in his opinion, afforded a solution. In the Jsle of Man, Mr Cummine found chalk flints in the boulder-clay, which he thought must have come from the county of Antrim, in Ireland, situated to the N.W.; and in the drift gravels of the island there were pebbles, which he could only refer to rocks also situated to the N.W.* In Ireland, the general direction of the transported boulders is the same as in Scotland and England. Sir Ricnuarp Grirrira} says—“ If we look to the distri- bution of erratic blocks, as indicative of the direction of the currents by which they were distributed, we find in Ireland generally that they were carried from N.W. to S.E., though the current was often modified by the opposition of moun- tain ridges.” “ The prevailing direction of our mountain ridges is N.E. and S.W., viz., at right angles to the supposed direction of the current; and, as might be expected, we find the gravel banks and detritus distributed on the N.W. declivities of the hills, and intruding into the interior valleys.” A later observer, Du Noyer, has identified the boulders lying on the moun- tains near Cork with the granite rocks of Galway, situated on the N.W. coast of Ireland, and has shown that the striz on the smoothed rocks have the same direction. { In the Shetland Islands, an examination was instituted by Mr Pracu, at the request of Sir Roperick Murcuison, into the drift phenomena. Mr Peacu found on the hard primitive rock of the islands, clear evidence of grinding and polishing. The general inference which he drew was, that the agent, whatever it was, must have passed over the islands from the northward. The only exact bearings stated in his report were taken in the island of Unst, the most northern of the group, containing about 36 square miles, and having one hill on it about 500 feet high. The ruts in the rocks there all pointed W.N.W.; and the side of the hill facing that quarter was (he says) polished to a depth from its top of about 150 feet.§ In the Faroe Islands, on the N.W. coast, the late Mr ALLAN,]|| when he visited them with Sir Gzorce Mackenzig in the year 1812, was struck with a rocky hill, the surface of which appeared ‘‘to have been worn down by the friction of heavy bodies” over it. “The rock was scooped and scratched in a very wonderful degree, not only on the horizontal surface, but also on a vertical one of 30 to 40 feet, which had been opposed to the current, and presented the same scooped and polished appearance with the rest of the rock.” Mr ALLAN says, “it would be * Lond. Geolog. Soc. August 1846, pp. 336 and 342. + British Assoc. Rep. for 1863, vol. xii. p, 51, + Geologist for 1862, p. 246. § British Assoc, Rep. for 1864. || Edin, Roy. Soc. Trans. for 1815, vol. vii. pp. 244-265. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 667 curious to investigate, whether this smoothness could be traced to any external cause such as that observed by Sir James Haut, on Corstorphine Hill.” At an early period geologists were unacquainted with the abrading effects of ice. From Mr Auuan’s description of the markings on the hill at Eide, and from its situation on the N.W. coast of Faroe, it is not difficult to see the agency of icebergs. In Iceland the striz, as Dr CHAMBERS states in his instructive little book,* run N. 30° W. (true). Having endeavoured, through my friend, Mr R. M. Smrru of Leith, who has correspondents in the island, to obtain farther information regarding the markings on the rocks, I have had sent to me by Mr Smiru the following extract from a letter by Dr Hysatre in, of Reykavik, Knight of the Dannebrog, and principal physician in the island :—‘“‘ The diluvial scratches are to be seen everywhere in the south part of our country.. They run in lines parallel to one another, and can scarcely be occasioned by the action of rain or water. Their direction is very much against this view. You see them on the slope of the hills, not following the declivity of the rocks, but everywhere run- ning in the well-known direction from N.W. to S.E., in spite of the declivity. Many of these scratches are very unequal, and seem evidently to have been pro- duced by a hard material gliding over the rocks in the aforesaid direction. It must furthermore be remarked, that these furrows, which are unequal both in depth and diameter, could hardly have such a regular parallel direction, if occasioned by water or rain. ‘* These scratches are all round here in our mountains. In the lower flat lava- fields, some deep and broad irregular scratches may also be seen; but they have no constant direction, and seem to have been produced by pieces ‘ of hard material gliding over the lava when still in a soft condition.’ ” + | In Sweden, the markings on the rocks show a movement generally from the N.N.W., which is also the direction of the osars or elongated gravel ridges, so abundant in that country. In Finland, on the Gulf of Bothnia, and on the Lake of Ladoga, in Russia, the direction is N.W. In Denmark (as ForscHAMMER shows), the markings on the rocks show a move- ment from W. 25° N. (true). The following case mentioned by him at Gothenburg (situated near the southern extremity of Sweden) leaves little doubt regarding the nature of the agent which made the markings. There was a large furrow or rut on a rock, the prolongation of which rut had been arrested or prevented by a boulder lying on the rock and firmly jammed. The boulder was about 3 feet thick vertically; and on its upper surface there was a rut, which being exactly in a line with the rut on the rock, seemed to have been made by the same agent, * Voyage to Iceland and the Faroe Isles. { Letter from Dr Hsatrexiy, Knight of the Dannebrog, and Chief Physician in Iceland. VOL., XXV. PART II. 8 L 668 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. which agent must, therefore, have risen up from the rock about 3 feet, in order to score the boulder.* If the foregoing enumeration of localities correctly represents the general direction of the markings on the rocks, it is impossible to avoid the conclusion that they have been made by one and the same agent, and over a very large area of the earth’s surface. How can it be conceived that glaciers should over that large area have all moved in the same direction? Objections to the glacier theory are suggested even by cases of isolated boulders.+ But the objections become infinitely stronger, when it appears that over an area of North-Western Europe, comprising Iceland, Faroe, Shetland, Scotland, Ireland, a great part of England, and on some of the adjoining continental countries, the agent which affected the boulder-clay, transporting blocks and striating rocks, moved almost everywhere in nearly the same direction, and came chiefly from that quarter where there is only the ocean. The late Principal Forses, much as he was inclined to uphold the agency of glaciers, felt the force of these objections, and makes the following confession in his work on the Glaciers of Norway (p. 241):—“ I hesitate to ascribe everything to glaciers. In fact, there appears to me to be situations along the coast of Norway, where the action of abrasion having been parallel with the coast, the movement of a glacier would be inconceivable. The general parallelism of the strize, observed by Botuuink and others, over a large area of country, not coincident with the general fall of the ground, would seem, if confirmed, to be equally inexplicable on the pure glacier hypothesis. The continuation of the striz across table-lands, and over cols, is of the like ambiguous character. I have never hesitated to express, on similar grounds, doubts as to the universal application of the usual glacier theory to the phenomena of our own islands, which, on a small scale, are the counterpart of those of Norway. For, though perfectly satisfied that our hills were in former times the seat of glaciers which even approached the sea-level, I find the utmost difficulty in explaining, by such an hypothesis alone, the facts which occur even in the immediate vicinity of Edinburgh.” In another part of the same work, Principal Forpes threw out a surmise of the kind of agent which seemed to him probable. Referring to the range of hills on the west coast of Norway (p. 190), he says that these bore “the whole brunt of forces which appear to have come from the north, and not only * Lond. Geolog. Journal for 1845, vol. i. p. 376. t Thus Mr Macraren says—“ I have pointed out a boulder of mica slate in the Pentland Hills, weighing 8 or 10 tons, which must have come 50 miles at least. It lies on a steep acclivity 1000 feet above the sea; and it must have passed over extensive tracts of country from 500 to 800 feet lower than the spot on which it rests. Even were all Scotland converted into a mer de glace, like Greenland, no glacier could carry the boulder (and there are many such) from its parent rock, in Perthshire or Argyleshire, to the Pentlands.’—Select Writings, vol. ii. p. 115. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 669 defended the entire north of Europe from the shock, but probably furnished by their abrasion the materials, of which the low grounds of the Continent of Europe are mainly composed. In this general disposition of the mountains of Norway, we see a strong analogy to the west coasts of our own islands. It appears almost certain, that a common cause has devastated the western shores of nearly every continent.” It is very evident what this “ common cause” alluded to by Principal Forsss, as having left its mark on the western shores of North-Western Europe, must have been nothing less than the ocean itself. Sir Jamms Hatt was, on the limited body of facts known in his day, led to the opinion that a resistless rush of waters over the country from the westward would explain the phenomena; and, down to avery recent period, attempts have been made to show how boulders could be carried by what are called waves of translation. These views have now been generally abandoned; and in place of them, it has been suggested that oceanic currents, with floating ice, and flowing over the submerged land, would afford a better explanation—an explanation strongly supported by the great extent of area over which the transporting agent has moved. But in stating that the agent has moved over this large extent of area in the same direction, let me repeat that there are cases where the direction of the strie and the transport of boulders point to a different quarter than the north- west. The percentage of these cases is so small, as not to affect the argument based on the generality of that direction, and on the extent of area over which it prevails. Moreover, whilst some of these exceptional markings are undoubtedly indicative of local glaciers,—the probable epoch of which will be afterwards referred to,—others are not inconsistent with, but, on the contrary, are corro- borative of the theory of oceanic currents. Thus, in the great glen of Scotland, the lines of strize and the course of the transported boulders show a movement from S.W.* So also in the estuary of the Forth, as well as in the trough which crosses Scotland along the south slopes of the Kilsyth and Campsie hills, the striz and many of the boulders indicate a movement from W. by 8. and W. by N. Now, in each of these cases, the deviation from the general or normal N.W. direction coincides with the range of the valley where it occurs; and it is not unreasonable to suppose that the obstruction, caused by adjoining hills of considerable height and extent, would modify the direction of the current so that it should flow with some approach to parallelism with them. Sir James Hatt, in his paper, brings out this point very clearly, when he says “that the direction in the neighbourhood of Edinburgh may have been occasioned by the local influence of the estuary, since the direction of the stream * Lond. Geolog. Society’s Proceedings for April 1849, p. 13. 670 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE: before entering it, and after quitting it, is nearly from N.W. toS.E.” Whilst he shows from numerous examples, that the direction in the Lothians was from W.35S., he shows that near Stirling it was from N. 50° W., and near St Abb’s Head from N. 35° W.* (true bearings). 4. The next point bearing on this question which I wish to put, is the char- acter of the fauna found in the boulder-clay ; which, being marine, afford strong evidence not only adverse to the theory that it is a land deposit, but favourable to the theory that it is a sea deposit. The following enumeration of localities where boulder-clay has been found containing sea-shells is not complete; but it is sufficiently extensive to establish the fact :— Near Airdrie (Lanarkshire), ‘‘in the till itself,” the late Mr Smirx “ found broken and water-worn fragments of shells irregularly dispersed in it, and amongst them the Cyprina islandica and a large species of Balanus.”’ + In Wigtownshire, “in the genuine till or brown sandy unstratified clay, with blocks of transported rocks interspersed through it,” Mr Moore found “one perfect valve of Astarte compressa.” } In Aberdeenshire, various species of sea-shells have been found in the boulder- clay by both Dr Cuambers and Mr JAmzEson.§ In Caithness, at several places sea-shells and other marine ¢estacea have been found in this deposit by Mr Jameson and Mr Peacz. || This point was seen to be of so much importance that a special examination of the Caithness boulder-clay was undertaken by Mr Pracu and two other gentle- men. They not only discovered in it many species of sea-shells, but by washing it, and examining with the microscope, they discovered no less than ten or twelve genera of Foraminifera, Entomostraca, and other minute marine organisms. In a paper read by Mr Peacu before the British Association in 1864, and published in their Transactions, it is stated that he and Mr ANDERSON had “ washed boulder- clays from many localities extending from near John O’Groat’s to beyond Wick, and all the samples tried yielded more or fewer of these animals, from whatever part of the deposit the clay was taken.” He adds, that “he had not previously found two valves of a shell united in the clay. He had, however, since got an Anomia with both valves in place. It occurred in boulder-clay containing the usual rubbed stones and broken shells. Mr. ANpERsoN has also a piece of shell on which is a cluster of young Balan.’ Mr Pracu gives a list of no less than “eighty-three species of shells, &c., from the boulder-clay of Caithness.” 4 In the same volume of the British Association Reports there is a list of thirteen * Ed. B.S. Tr. vol. vii. p. 200. + Researches, p. 141. t Smirn’s Researches, p. 143. § Proceedings of the Lond, Geolog. Society far 1866, pp. 274-5. || Ibid. p. 267, { Brit. Assoc. Reports for 1864, p. 62. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 671 species of marine shells from boulder-clay at Scarborough and Whitby, on the Yorkshire coast. These shells were discovered by Mr Lackensy and Mr JEFFREYs, both recognised authorities.* The Rev. Mr CrosskEy, Vice-President of the Glasgow Geological Society, well known for his knowledge of drift deposits, states that he found boulder-clay near Sunderland, “ containing fragments of broken shells and many Lntomostraca and Foraminifera.’ + That gentleman adds that he had found shells in boulder-clay on the banks of the Mersey and on the coasts of Jreland. In boulder-clay, near Zynemouth (Northumberland), fragments of Cyprina islandica have been found by two accurate observers, Mr Howse and Mr Binnie of Manchester. f Dr THomas Brown, in the paper recently published in the Transactions of this Society,§ has given a list of above twenty species of sea-shells found at Errol (Perthshire), and at Elie (Fifeshire). Dr Brown mentions (p. 630), that at both places the shells were in a bed resting on the boulder-clay. I had an opportunity lately, in company with Dr Brown, of examining the deposit at Elie containing these shells, and found that it consisted of a hard or tough clay of a dark grey colour, presenting no stratification, and containing abundance of hard pebbles and boulders, all rounded and some of them scratched. It had the usual appear- ance of boulder-clay, and I expressed this opinion to Dr Brown. The Elie deposit I have not seen; but from the account given of it in Dr Brown’s paper, and also by Mr Jameson, I cannot doubt that it also is a true boulder-clay. In the section which Dr Brown gives in his paper, he represents boulders in the deposit ; and he expressly says that the shells “are found cluster- ing around and beneath the enclosed boulders, a fact which seems to show that at the time these shells lived, this part of the sea-bottom must have been swept by a strong current.” Dr Brown adds, that he had obtained from the Errol deposit ‘“ portions of the skeleton of a seal.” Mr Jameson says, that in the deposit at Errol containing Arctic shells—-being the same bed mentioned in Dr Brown’s paper—he found many of the included boulders “glacially scratched—occasionally one may be found with barnacles on it;” and he adds, that “‘ Entomostraca of the genus Cythere also occur.”’ || In Canada, where till or boulder-clay abounds, marine shells have been found in the deposit. (Amer. Journ. of Science for 1866, vol. 1xxxvil. p. 235.) The fact of sea-shells, of various species, having thus been found in great numbers, and at places far distant from each other, in the boulder-clay, seems so conclusive as to the marine origin of the deposit, as to render further evi- * Brit. Assoc. Reports for 1864, p. 58; R.S. E. Tr. vol. xxiv. p. 617. t Trans. Glasg. Geol. Soe. vol. ii. p. 150, t Berwickshire Nat. Club, vol. v. p. 238. § Vol. xxiv. || Proceed. of Lond. Geolog. Society for January 1865, pp. 175 and 196. VOL. XXY. PART II. SM 672 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROFE, dence superfluous. It therefore may simply be mentioned, that confirmatory evidence is afforded by numerous cases of boulder-clay alternating with strata, the marine character of which is indisputable. Localities are mentioned by Mr GEIKIE* as occurring in Roxburghshire, Lanarkshire, and Ayrshire, where beds of unstratified boulder-clay, 30 to 40 feet thick, alternate with beds about the same thickness of stratified clay and stratified sand, the former sometimes con- taining marine shells. In such cases, the boulder-clay virtually forms part of the series. 5. Several observers, who have found marine shells in the boulder-clay, have been struck with their broken or fragmentary condition. This feature is not observable in the stratified or laminated clay beds where the same shells occur. In the brick clays of Lanark, Renfrew, and Ayr shires they are found perfect in form, and apparently in their natural position. But in boulder-clay, the same shells have been mutilated and smashed, so that it is difficult to identify the species.}| Is it not a fair inference from this fact, that the beds in which, at the bottom of the sea, these shells had lived, must have been disturbed and deranged by some intrusive body of great weight and power, which both crushed the shells and obliterated all traces of stratification or lamination in the structure of the beds? It seems to me that such effects would result from the intrusion of ice- * Glacial Drift, pp. 54 to 65. + Thus Dr Watson, in describing the boulder-clay of Arran, says that the shells in it “ are very much broken. The shells may often be found crushed, yet with each fragment in its own place. Some of the large specimens of Cyprina, though unbroken, are indented, as by a sudden violent blow. The whole condition of the shells suggests that heavy stones have been dashed down upon them.” Dr Bryce also notices that the Arctic shells found by him in Arran were “in single valves or in a fragmentary state, yet not so small but that the species can be determined.”—Geology of Arran, p. 168. The shells in the boulder-clay of Caithness have been examined by a great number of com- petent geologists, who all give the same testimony, Mr Pracu describes the shells so “ broken” and “rubbed” he could find only one entire shell. Messrs Crosskey and Rogertson of Glasgow, having gone to Caithness on purpose to examine the boulder-clay there, describe it as ‘‘ a hard and compact mass, with striated and polished boulders, being in appearance similar to that in the west of Scotland, The shells are thinly interspersed from top to bottom, and are of a water-worn and fragmentary character. They appear equally distributed, as if the whole mass had been mixed up and kneaded together.”—Geolog. Society of Glasgow Trans. vol. iii. p. 126. Mr Jameson of Ellon says that the drift-beds of Caithness contain “ remains of sea-shells all through them, and these are broken, rubbed, and scratched, and evidently by the same agency that marked the rocks and boulders.” His theory to account for the facts, is, that “much floating ice seems to have passed over the district from the N.W., which crushed and destroyed these marine beds, broke the shells, and mixed them up with other superficial debris into that mass of rough pebbly mud which now overspreads the surface.”—Proceed. of Lond. Geol. Society for 1865, pp. 176-7. Mr Jameson has also the following statement regarding a deposit of boulder-clay near Paisley which he examined. He says—“I sometimes found, on heaving up a boulder, a number of young crushed mussel-shells beneath it, as if they had been squashed by the fall of the stone. The clay around also occasionally exhibited black stains, as if from the decay of sea-weed that had been attached to the stone.” At the various places where the Rev. Mr Crossxey found sea-shells in boulder-clay, along the coasts of Scotland, England, and Ireland, the shells were “ very fragmentary, and even single valves are seldom found whole.”—Glasg. Geol. Soc. Trans. vol. ui. p. 151, MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE, 673 bergs, the lower portion of which penetrated the sea-bottom, pushing before them boulders and pebbles, and pressing the sediment into-greater compactness. Besides the generally mutilated condition of the sea-shells in the boulder- clay, there is another circumstance, first pointed out by the late E>pwarp ForbEs, which tends in the same direction. On examining the shells found in the drift- beds of Wales, he observed that they belonged to different zones of life. These drift-beds presented “a confused mixture of fragments of species from all depths, both littoral and such as invariably live at a depth of many fathoms; inhabitants some of muddy grounds, some of sandy, some of rocky. Deep and shallow water species could not have lived together, or have been thrown up on one shore.” His conclusion, therefore, was, that this confused and unnatural mixture ‘indicated the action of some disturbing influence, through the agency of icebergs, or a wave of translation, or of both combined.” The beds to which this observation applied was, it is true, not boulder-clay or till, but mud, gravel, and sand, “in the lowest beds of which were small and large boulders of transported rocks polished and scored.” * The position of these drift-beds was 1360 feet above the sea. If icebergs acted on these drift-beds, as Epwarp Forses inferred for the reasons mentioned by him, icebergs could have acted in like manner on the materials of boulder-clay. Those who look upon the boulder-clay as a land deposit, meet the fact of marine shells being found in it thus :—They say that the glaciers which formed the deposit reached the coast, as now in Norway and Greenland, and pushed detrital matter out into the sea, where it became occupied by testacea. This answer is not satisfactory, because the testacea are almost invariably found in a mutilated state. These animals must have been bred and grown in asea-bottom, which, whilst they lived, was undisturbed ; and if the disturbance of their dwell- ings was due to the protrusion of glaciers, this would be admitting the marine origin of the deposit. Moreover, if the climate was so severe as to bring glaciers to the coast, icebergs would also abound in the adjoining seas; so that the question would then be, whether the effects were more likely due to the pro- trusion of glaciers, at the mouths of valleys, or to icebergs drifting in the sea and grating along the bottom. On the former supposition, boulder-clay would be formed only at particular spots, viz., at the mouths of valleys which reached the sea. On the latter supposition, boulder-clay would be formed much more extensively. The great abundance and continuity of the deposit in Northern Britain is there- fore better accounted for by the iceberg than by the glacier hypothesis. The advocates of the glacier theory of boulder-clay have also referred to the fact that terrestrial remains occur in the deposit, from which an inference * Notes of a Ramble through Wales, by W. S. Symonps, 1864, p. 12. 674 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. is drawn, that the deposit must have been formed, not in the sea, but in the land, it being supposed that these remains were drifted into the boulder-clay by rivers.* But rivers flow into the sea, as well as into lakes. It is true that the boulder-clay near Glasgow and near Falkirk, at both of which places elephants’ tusks were found, presented no marine shells. But it is equally true that elephants’ tusks have been found in what are allowed to be sea-beds. At Kilmaurs (Ayrshire), two tusks of an elephant were found in a bed of stratified mud 9 inches thick, which was overlaid by a bed of sand containing sea-shells, these shells being covered by boulder-clay. (Journ. Lond. Geolog. Soc. vol. xx. p. 217). In Dumbartonshire, the bones of a rein-deer were taken out of a bed of laminated clay, associated with sea-shells.+ (Edin. Phil. Journ. new series, vol. vi. p. 105.) Mr GEIKIE, in support of his view, endeavours to explain the association of sea-shells and the bones of terrestrial animals in boulder-clay, by suggesting that the mass of earth and stones may have been pushed forward by a glacier ‘“ close to the sea-shore, and sea-shells might either be thrown up by high tides over the bones previous to their entombment, or be deposited above them during the slow sinking of the land.” He adds—“I mention this as a possibility, in order that no difficulty need be felt in harmonising such a fact with the hypothesis that the boulder-clay is a deposit from land ice, and not from icebergs.” (‘On the Glacial Drift of Scotland,” p. 94.) The possibility of the occurrence here suggested I admit. Its probability is not so clear. But it is quite clear that the occurrence of elephants’ bones at two places in boulder-clay, where no sea-shells were found, is no conclusive proof that the deposit must have been formed on the land, when, at two other places, similar bones were found in pleistocene beds, which must have been at the bottom of the sea when the bones were drifted into them. 6. I now pass to other facts which indicate that the boulder-clay not only has been disturbed and intruded on by some foreign agent, but has, n some cases, been moved en masse by some agent of tremendous power. Thus Mr Cumminc, in his “ Memoir on the Isle of Man” (Proc. Lond. Geol. Soc.” 4th Jan. 1854, p. 213), says—‘ There are appearances, as if the boulder-clay had been forced violently amongst the different beds of limestone. Fragments of the latter are torn up and carried forward, and these remain angular, though much scratched, at no great distance in the mass of clay which now covers the limestone beds.” . The late Dr Fiemine (“Lithology of Edinburgh,” p. 60) pointed out ‘“ near Gilmerton, a sandstone quarry, where the outcrop of the rocks is seen, covered * GEIKIE on Giacial Drift, p. 93. + Bones of elephants, rhinoceros, &c., are found in Siberia very generally associated with Arctic sea-shells. (Lyexz, “ Principles,” i, 183; Quart. Journ. Lond. Geolog. Society, 1st Feb. 1848.) MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 675 by a sandy boulder-clay, which, having been in motion, has squeezed or bent the ends of the sandstone and shale towards the 8.E.” Two other localities are mentioned by this observer, where the outcropping strata of shale had been in like manner broken off and carried towards the 8.H., by some agent pressing down upon them. Dr Howpen, in describing the superficial deposits of Forfarshire (‘‘Edin. Geol. Soc.” vol. i. p. 139), says that “‘in the Brechin Quarry, and in other localities, where the strata are nearly horizontal, especially if they consist of thin lamine, the rock has been broken up into shivers, large detached masses being embedded in the (boulder) clay.” Dr Howpen suggests no explanation, but it is evident that here also some agent must have ploughed up the strata, and disturbed the covering of clay. I might refer also to the curious foldings observed in beds of clay, and even of sand, which both Sir CHartes LyeLtt and Mr GEIKkiz admit cannot be ex- plained in any other way, than by supposing that icebergs or heavy masses of floating ice had pushed them out of their original position.* But the most remarkable case, where boulder-clay is shown to have been pushed and pressed forward en masse, was described some years ago by two most competent observers, Captain BrickENDEN and Mr Marrmins of Elgin, ob- servers who wrote independent reports, the former in the ‘‘ Proceedings of the Geological Society of London,” + the other in the “Edinburgh Philosophical Journal’’| some years afterwards. Being much impressed with the importance of the facts related by both observers, and wishing to obtain further information, I wrote to the only one whose address I could discover, Mr Martins, and received from him a letter, in which the following passages occur :— “The Linksfield strata consist of a series of bands of limestone, shales, and blue clay. These have obtained the name of Wealden, from the fossils in them. Under these bands there lies a great deposit of limestone, called Cornstone. In some places, the Wealden bands are separated from the Cornstone by intercalated boulder-clay, having all the characteristics of boulder-clay met with throughout the country. It has the same tenacity, and the same want of stratification, and contains the usual travelled pebbles and blocks. The only difference observable is, that the clay when intercalated has a purplish tinge, evidently acquired by contact with the blue clay of the Wealden. It also contains fragments of the limestone from the band lying immediately above it. In some instances, large * Ly=tt, “Antiquity of Man,” p. 138. Mr Gers (‘Glacial Drift,” p. 119), after alluding to cases where ‘‘ beds of clay were fairly bent back upon each other,” says, ‘such contortion must he due to powerful pressure. It may have been produced by masses of ice standing here, and pushed onward, partly by their own impetus, partly by the action of winds or currents. The compression to which such a weight of ice would give rise, would probably be quite sufficient to corrugate beds of clay and sand.” + Proceed. of Geol. Society for 1851, vol. vii. p. 289. t E. Ph, J. for 1856, vol. iv. p. 222. VOL. XXV. PART II. SN 676 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. flakes of the laminated blue clay were lying in it. This mass of intruded (boulder) clay always presents great irregularities in a section. At one place it is scarcely a foot thick, allowing the Wealden beds to rest nearly on the Corn- stone. Ata short distance it rises abruptly to the height of ten feet, in the form of a cone, from the apex of which several narrow bands stretch up through the fissures of the overlying mass, looking like veins of red granite among crystalline rocks. At one place the boulder-clay formed a rounded mass, and the super- incumbent bands of limestone were folded neatly over it, so as to present the appearance of a stone arch. By the movement, a number of fissures had been caused in the overlying bands, into which the clay had been forced up. Some of these rents were 6 feet in length.” ‘“‘Tt may be noticed that the surface of the Cornstone, when cleared of the till, is found finely smoothed and polished; any hollows on the rock are also smooth and polished. The Cornstone strata are not in the least disturbed.” Mr Martins had the goodness to send with his letter two or three sections, showing the relative positions of the boulder-clay to the rocks above and below it. These sections, it is right to add, were made by Mr Martins from memory, as the quarry had ceased to be used, and was filled with rubbish. The sections, therefore, can be taken only as giving a pictorial representation of what is described in Mr Martins’ letter.* Both Captain BrickENDEN and Mr Martins express their conviction, produced by a study of the sections when they were exposed, that the boulder-clay had been forced im between the upper Wealden bands and the lower Cornstone rock. Captain BRIcKENDEN notices particularly the polished and striated surface of the Cornstone, caused by the passage and attrition of the overlying boulder-clay. He states that the direction of the striations was N.W. and S.E., and he inferred from the appearances, that the boulder-clay had been thrust in from the N.W. When he visited the quarry, the exposed boulder-clay had “a bright red colour,” which made the embedded fragments of the purple Wealden rocks all the more striking. The explanation suggested by Captain BrickENDEN is precisely the theory which it is the object of the present Memoir to support, viz., that the materials of the boulder-clay “had been subjected. to the action of vast and extensive masses of ice, which by continuing to press onwards the accumulations of clay retained beneath it, had, by a force superior to that which the beds above could offer in resistance, eventually produced the phenomenon.” If it be said that a glacier could have propelled and pushed the boulder-clay between the rocks, quite as well as masses of floating ice, the question would be, whether, in the places referred to, where the boulder-clay has apparently been pushed forward en masse, there was any probability of a glacier having existed. * Two of these sections are given on Plate XXXI. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 677 The low-lying, flat country of Elgin is, to say the least, most unfavourable for the glacier theory; and the Isle of Man is, from the absence of mountains, equally unfavourable. The facts and views set forth in the preceding paragraphs, show that the materials of the boulder-clay have been disturbed, intruded on, pushed forward, and heavily pressed on by some extraneous agent; and if it be allowed that these materials, when so acted on, formed a sea-bottom, very little doubt can exist that floating ice was the agent. 7. But it will be asked, whether similar effects are now observable in the Arctic regions, where there are icebergs and floes drifted about by the winds and currents? Can it be shown that they do work on the sea-bottom or shores at all analogous to the appearances presented by our boulder-clay and drift-beds ? In all the channels and estuaries of the Arctic regions, we know that the sea is constantly covered with floating ice in every variety of form. As icebergs, they often strand in places where the sea is 1200 feet deep. On one occasion, the keeper of the lighthouse at Belle Isle, near the mouth of the St Lawrence, in latitude 50°, counted no less than 496 icebergs, some of them 200 feet high and half-a-mile long. About 100 of them were stranded, or were grating over the submarine banks.* . It is not difficult to conceive what must be the effect on a sea-bottom, what- ever the materials, of icebergs having a size greater than the hill of Arthur Seat. Soft materials would be so disturbed and ploughed through, that any appearance of regular bedding would be obliterated, testacea would be crushed, whilst hard fragments of rock would be pushed forward and rounded by the enormous friction. This inference as to the disturbance and tearing up of the sea-bottom is con- firmed by Dr SUTHERLAND, a surgeon in one of the Arctic expeditions. He says that in Davis’ Straits, the icebergs, by their action on the sea-bottom, produce ‘whole rafts of submarine forests” of sea-weed, which float on the surface of the sea; and when the sea-bottom in these straits is dredged, little else than ‘‘broken shells” are brought up.+ The disturbance and dislocation of the submarine beds where icebergs abound, is further evidenced by the large amount of muddy sediment raised, discolouring the sea not only to the surface, but for many miles round. Messrs DrEAseE and Simpson, in the account they give of their Arctic discoveries in the year 1838, describe a long low spit, composed of gravel and coarse sand, in some places more than a quarter of a mile wide, the formation of which they did not hesitate to attribute to the action of floating ice—judging by what they saw done by ice. * See a short paper on this subject by Principal Dawson, of Montreal, in the ‘ Canadian Naturalist.” + Lond. Geolog. Journal, vol. ix. p. 306. + De La Bicuz, Geolog. Observer, p. 266. 678 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. Dr Hayes, in his account of a visit to the West Coast of Greenland in 1867,* says, “ where the current is swift, and the ice is pressed down upon the land with great force and rapidity, the rocks are worn away until they are as smooth and polished as the surface of a table.” The bearing of this remark on the innumer- able smooth and polished rock surfaces in Scotland and the north of England needs not be pointed out. Dr Hayes mentions another effect of floating ice. He says that “‘a shelf of ice glued to the shore forms a winter girdle of all the Arctic coasts. It is usually broken away towards the close of every summer, when the masses of rock which have been hurled down upon it (during the previous eight months) from the cliffs above are carried away and dropped in the sea. The amount of rock thus transported is immense; and yet it falls far short of what is carried by icebergs” (p. 403). Much to the same effect, on both of these points, Dr Wa.uicu mentions that, when dredging off Labrador at a depth of from 10 to 15 fathoms, he found the sea-bottom to consist “ wholly of uncovered rock or of boulders” —‘‘ owing (as he adds) to the long continued action of drift ice and currents.” + Another effect produced by floating ice has been observed—the formation of ruts and strice on the smooth surfaces of rocks. Many competent observers have given evidence on this point. The foregoing statements refer to what is now seen going on, wherever there are icebergs and icefloes, and they show that these agents, if they existed in Scottish seas, at a former epoch of the world, must have had the power of pro- ducing most of the phenomena connected with our pleistocene deposits. It is not unimportant to remark, in further confirmation of this view, that in the Arctic regions there exist boulder-clay and boulders pretty high above the sea, just as in Scotland, and that all the Arctic travellers who have paid attention to the subject do not doubt that the chief agents in producing them were icebergs and shore ice. Thus Dr SurHERLAND found in Barrow’s Straits, up to a height of about 1000 feet, great numbers of boulders, all (he says) clearly transported by coast- ice previous to the elevation of the land,—just as he saw them being transported in that way along the existing shore of Greenland. Mr Lamont, in his Memoir on Spitzbergen, takes notice of several places where icebergs had evidently left their footprints, when the land was submerged. At one spot, about 20 feet above the present sea-level, he found a trench, about 100 yards long by 3 or 4 feet deep, formed among boulders, and caused, as he believed, by an iceberg drifting through them. At another spot, he found what * The Open Polar Sea. Tt North Atlantic Sea-Bed, p. 40. t Sir Cuarztes Lyetr—(1) Travels in North America, vol, ii. p. 173; (2) Lond. Geolog. Journal fer 1849, Trapolli in Scandinavia ; Lond, Geolog. Journal for 1868, xcviii. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 679 had the appearance of a gigantic causeway of boulders, caused apparently by icebergs sliding over them, and levelling them.* It also deserves notice that true boulder-clay or till exists in the Arctic regions, and in districts where there is much less probability of glaciers than of icebergs having been at work. Sir Jonn Ricuarpson evidently describes this deposit when he mentions “ a denacious and somewhat slaty blue clay, containing many boulder-stones,” on the western shores of Hudson’s Bay,—a country very little elevated above the sea, and possessing no mountains where glaciers could be formed.t Nor is it irrelevant to notice the occurrence of boulder-clay in the Antarctic regions, and the opinion formed by that eminent naturalist, Mr Darwin, as to its origin. After describing “great masses of mud of a dark colour, full of boulders of primitive rocks derived from mountains situated to the W. or S.W. about 60 miles distant,” he says, that “the deposit in all respects resembles the till of Scotland ;” and adds, that “at present the oceanic currents off Cape Horn set from the west; so that if the ancient currents had the same direction, the phenomena would be explained by floating ice.” It thus appears that both in Arctic and in the Antarctic regions, where float- ing ice has abounded, boulder-clay, boulders, and polished rock surfaces exist: These phenomena do not occur in warmer regions of the earth. Wherever they do occur, there are indications of the sea having stood much higher than at present, so that ice could have drifted at the necessary level; whilst, on the other hand, in many districts there is a total want of the conditions necessary for the formation and for the movement of glaciers in the required direction. 8. In the previous part of this Memoir, I have attempted to show—1st, That glaciers were not the agents to which boulder-clay owes its origin. 2d, That an examination of the deposits, containing, in numerous localities, sea-shells generally mutilated, suggests a submarine origin. 3d, That the way in which the deposit has been driven forwards, and pushed between older rocks, indicates pressure by some agent of enormous weight and magnitude. 4th, That icebergs and shore-ice would probably answer these conditions, and are seen now in the Arctic regions producing similar effects. Assuming that the facts adduced at all events establish the probability of the theory, that icebergs and shore-ice would account for most of the drift phenomena in Great Britain, I proceed to offer a few remarks as to the circum- stances and condition of Great Britain at that time. Most geologists are agreed that, at the period of the boulder-clay, the sea must have stood greatly higher upon the land than at present. Beds of sea- * Lond. Geolog. Journal for 1868, vol. xvi. p. 433. + Franxuin’s Journey in 1823, pp. 499, 501, 583. t Phil, Journal for 1841, vol, xix. p, 530. VOL. XXV. PART II, 80 680 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. shells occur in the pleistocene beds of Lanarkshire, at a height of 526 feet above the sea; and as one of these shells is the Cyprina islandica, which requires for healthful existence a depth of at least 30 fathoms, that Lanarkshire deposit implies a submergence of more than 700 feet. But in Wales, sea-shells of a similar character have been found in drift-beds at a height of no less than 1600 feet above the sea. And there are in many parts of England and Scotland beds of clay, sand, and gravel, at a height of nearly 2500 feet above the sea, which, judging from their stratification and materials, must have been marine. If, therefore, the whole of the British Islands were submerged to the depth of 2500 feet lower than they are at present, they must have presented little else than an archipelago of islands,—few of which would, at their highest points, be more than 1500 feet above the sea. As many of the shells found in these pleistocene beds are of an exclusively Arctic type, the sea, during the period of submergence now referred to, was favourable for the presence of drifting ice,—assuming, in the meantime, the existence of some current to bring the ice. But it is not Great Britain only which was submerged. In Sweden, sea-shells of the same Arctic type have been found in drift-beds to the height of 800 feet, there being also beds, apparently marine, which occur at a still greater height. These Swedish shell-beds have furnished one or two instructive facts bearing on the process of submergence, which probably apply to Northern Europe gene- rally. Some of the beds are occupied almost exclusively by shells which lived in shallow water. These are in some places covered by beds containing shells of deep-water habits,—indicative not only of a submergence of the country, but a submergence to a considerable extent. Farther, it has been ascertained that these deep-water shells belong to much more Arctic types than those of shallow water which preceded them,—indicating that as the submergence went on, the cold was increasing. Then, again, other shell-beds have been discovered at a lower level, and evidently, from their geological relations, of a more recent date than those above mentioned, in which the Arctic shells are fewer in number and species,—a fact which suggests that, as the land emerged from beneath the waters, the climate improved.* It is, however, not in Sweden only that these Arctic shells are found on the Continent. Sir RopEr1ck Murcuison, in his great work on the Geology of Russia, has shown that the drift-lands of that country are full of them, implying a general submergence of the whole of Northern Europe under the waters of an Arctic sea, reaching as far south as about latitude 51°. * These interesting and instructive facts will be found stated in a Memoir, by Mr Gywn Jerrreys, in the British Association Reports for 1863; and also in a paper, by Professor Sars of Christiania, in the Edinburgh Phil. Journal for 1863. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 681 Assuming, then, that icebergs and shore-ice prevailed in the sea which covered the British Islands and other parts of Northern Europe, how would these operate as agents in the production of boulder-clay? In some places, boulder-clay lies over stratified beds; in other places, boulder-clay is covered by them. In the former case, it may be supposed that an iceberg pierced through the sea-bottom only to a certain depth, leaving the part next to the rocks untouched. In the latter case, it may be supposed that more sediment was subsequently deposited by currents over the disturbed beds, and remained undisturbed. There are cases where, in one section, there have been found as many as three layers of boulder-clay, each from 20 to 30 feet thick, alternating with laminated beds of clay and sand. In such cases it is only necessary to suppose that icebergs came, drifted by currents, at different periods, some being larger and deeper in the water than others. If the glacier theory be adopted, which assumes that the boulder-clay was formed on the land at the end of a glacier, or under its mass, then to account for these alternations of marine beds with boulder-clay, there must have been as many oscillations of the land below and above the sea as there are layers of boulder-clay—a supposition surely very improbable. 9. But a difficulty here suggests itself. Where did these icebergs come from? They could not have been generated by Scotch or English glaciers, if, when the land was submerged, there were no mountains higher than 1500 feet. . Where, then, was the high land to give birth to glaciers from which these ice- bergs came; and was there a current in the ocean so strong and extensive as to bring these icebergs over North-Western Europe, and in the direction indicated by the transported boulders and rock surface striations ? That the physical geography of the Northern Hemisphere must have been totally different from what it now is, is plain from the circumstance that the climate was so different. Perhaps the colder climate was brought about by the same conditions, which would suit the formation of icebergs, and the existence of a great current from the north-west by which they were drifted. The problem is to ascertain what circumstances would produce an Arctic temperature in North- Western Europe, and so far south as Jatitude 51°. Labrador is in the latitude of Great Britain. What are the circumstances which give to that country a mean annual temperature of 25°, and a mid-winter temperature of—50°? Two causes co-operate—an Arctic current, loaded with ice- bergs, which flows past its shores; and proximity to the high land of Greenland, whose snow and ice chill the atmosphere. From this fact, is it not probable that North-Western Europe, when it pos- sessed a Labrador climate, was indebted for it to similar conditions ? One thing is certain—the Gulf Stream could not then have flowed along its 682 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. present course. But its absence would cause the winter temperature of Scotland to fall only by 28°; and a winter temperature of 10° would not give to us a Labrador climate. Other conditions must therefore be sought for. At present the Arctic current, which flows into the North Atlantic, is strong enough to carry icebergs even farther south than latitude 50°. They have been sometimes seen in latitude 40°. Of course, that Arctic current cannot cross the Atlantic and float icebergs on Great Britain, because the Gulf Stream would intercept it. But suppose the Gulf Stream not to run, as it now does, in a N.E. direction towards Norway. Suppose that, by the Isthmus of Panama being 300 feet lower than at present, the equatorial current, instead of being deflected by the American coast northwards, were to flow into the Pacific, and find its way through Behring’s Straits, where there is now a current running from the Pacific, the Arctic current which now flows into the North Atlantic would not only have no Gulf Stream to interrupt it in its progress towards Europe, but would be immensely augmented in volume and speed. The stream passing through Behring’s Straits would carry with it a tendency to move eastwards, having acquired that tendency in equatorial regions by the earth’s diurnal rotation. If high land nearer than Greenland is thought necessary, evidence is not awanting to justify that supposition. In the first place, it is well ascertained that Greenland at its southern extremity has long been sinking, whilst its northern parts are rising.* Dr Kane and Dr Hayes endeavoured to find where the axis of oscillation is situated. The one gives 76° of latitude, the other 7 7° of latitude. Both observers were struck with the fact, that whilst to the north of this supposed axis, lines of raised beaches were visible, none were visible to the south of it. Dr KANE saw and counted no less than forty-one beach lines, at a part of the coast in latitude 78° 30’, or about 150 miles to the north of the axis; the highest being 480 feet above the sea. Now it is not unreasonable to suppose, that on the south side of the axis of oscilla- tion, the sinking would be at the same rate as the rising on the north; in which case, what is now the southern extremity of the continent, which is in latitude 60°, and therefore about 1000 miles from the axis of oscillation, must, before the sinking began, have been 3200 feet higher than it is at present, and a great deal of what is now sea-bottom to the S. and 8.E. of Greenland must have been dry land. The probability of changes having occurred in the bed of the North Atlantic is all the greater on account of the volcanic convulsions to which it has frequently been subject, of which not only Iceland is a proof, but the igneous * Dr Hoatrerin of Iceland, in his letter to Mr R. M. Smrru, quoted on page 667, mentions— ‘‘ T have seen the secular elevation of the northern shores of this island ; and it is not unlikely that the north coast of Greenland is in a similar state.”” Therefore it is probable that the north extremity of Iceland rose up simultaneously with North Greenland. MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 683 rocks in the Western Hebrides and the north of Ireland, which are certainly more recent than the chalk, and perhaps belong to the glacial period. On the shores of the Baltic, it has been made out that during this period there were great fractures in the earth’s crust. Whilst there are geological reasons for assuming the existence of high land in the North Atlantic Ocean, now submerged, there are physiological reasons in favour both of high land and of a great Arctic current from the north-west. It was the late Professor Epwarp Forses who first drew prominent attention to the light thrown on the past history of the earth, by reference to the migrations of the fauna and flora of a country. His remarks, as applicable to Great Britain, are these—‘‘ There could not always have been such a separating abyss between Northern Europe and Boreal America as now divides them. ‘The sea, through a great part, must have been a shallow sea; and somewhere, probably far to the north, there must have been ezther a connection, or such a proximity, of and as would account for the transmission of a non-migratory terrestrial * and a littoral marine fauna.” + In another passage he says—“ It is strongly impressed on my mind that the close of the glacial period was marked by the gradual swbmergence of some great northern /and, along the coasts of which the littoral mollusks, aided by favouring currents, migrated; whilst a common flora { became diffused over its hills and plains. Although I have made icebergs and icefloes the chief agents in the trans- portation of flora southwards, I cannot but think that so complete a transmission of that flora as we find on the Scottish mountains, was aided perhaps mainly by land to the north now submerged.” (‘‘ Memoirs of the Geological Survey of Great Britain,” vol. i.) 10. In considering the claims of the two. theories which have been proposed for explaining the boulder-clay deposit and other drift phenomena, it is proper to keep in view, that whilst there are many of these phenomena which are sus- ceptible of explanation on either theory, there are others again which, whilst * Allusion is probably here made to the remains of the woolly-haired elephant, rhinoceros, musk ox, rein-deer, black bear,.and polar bear having been found in pleistocene beds in various parts of Great Britain. If, as is believed, these animals belong naturally to North America, how did they reach the small island of Britain ? 7 In a list of sea-shells given by Mr Jameson of Ellon, as found in the boulder-clay and other pleistocene beds of Scotland, amounting altogether to 137, he represents 134 as now living in the Arctic circle, 60 in North-Eastern America, 26 in the North Pacific, and 82 in British seas. The number now living in the Arctic circle, North-Eastern America, and North Pacific, but not in British seas, is 52. { Professor E, Forses mentions, in illustration of this point, the EHriocaulon septangulare, “known in Europe only in the Hebrides, and at Connemara, in the west of Ireland. Elsewhere,’’ he says, “it is an inhabitant of Boreal America, which is its true native country, and from whence, by means of transport, it has in all probability been introduced naturally into the British Isles.” Pro- fessor Batrour has given to me the names of the following additional plants, natives of Labrador and Canada, which are found in Skye and on the west coast of Ireland, but nowhere else in Europe, viz., Neottia gemmipara and Sisyrinchium anceps. VOL. XXV. PART Il. 8P 684 MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. difficult of explanation on the glacier theory, are very intelligible on the other. A few of these difficulties will now be referred to. (1.) It has been mentioned, as a result of the examination of the sea-shells in the ‘pleistocene beds of Sweden, that the period of greatest cold was when the land was most deeply submerged. If this be the case, which of the two theories is most reconcilable with it? When the land was most deeply submerged, the mountains would be elevated above the sea less than at any other period; and therefore circumstances would not be favourable for the formation of glaciers. On the other hand, circumstances would be especially favourable for the drifting of icebergs among the archipelago of the British Islands. (2.) The unequal distribution of boulder-clay over North-Western Europe deserves a passing remark. The deposit is much more abundant in Scotland than in any other country. Whilst it exists in both England and Ireland, it is chiefly in the northern and midland counties. In the southern parts of both England and Ireland it is hardly known. Then in Denmark, the beds which are there called boulder-clay appear not to have been so disturbed as in Scotland. There are beds of clay which contain boulders and pebbles, evidently transported, and which also contain Arctic shells; but these are not described to be in a fragmentary or mutilated condition. These shells are described as belonging to species which are known to inhabit shallow water; and it is added by ForscrtamMer,* that there are extensive beds of sand, containing boulders and pebbles, which seem to belong to the same epoch as the boulder-clay. These beds of sand he also looks on as indications of a shallow sea. Why should there be in the south of England and Ireland a less develop- ment of boulder-clay? May it not be that the icebergs melted before reaching so far south ? Why should there be little or none of the true “ till” in Denmark? May it not be that the icebergs, brought by a north-west Arctic current, were inter- cepted by the Scotch archipelago? and if any drifted towards Denmark, would not the shallowness of the sea prevent them floating over and disturbing the banks of mud and sand forming the sea-bottom there ? Shore ice alone probably floated over these Danish waters, carrying boulders and pebbles, and spreading them on the submarine banks. Whilst some such explanation of the unequal distribution of boulder-clay is suggested by the theory of water-borne ice, it is not easy to draw any explana- tion from the glacier theory. (3.) Many persons have been perplexed at finding a ridge dividing two valleys, forming what is sometimes called in the Highlands a col, consisting of rock smoothed * Journ, of London Geological Society for 1845, vol. i. p. 373, MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 685 and striated by the action of ice. Thus, for example, the late Mr Maciaren points out that the ridge which divides the Gareloch from Loch Long, about 450 feet above the sea, as also two other ridges to the eastward, the one 700 feet, and the other about 1700 feet above the sea, present rocks the surfaces of which are ‘smoothed and rounded off.” Mr MActaren remarks upon this fact— A glacier lodged within the valley would grind off the asperities of the rocks at its bottom ; but what smoothed the very tops of the ridges? Is it not probable that it was icebergs ?”’ * The Duke of ArGyLz was struck with the same appearances on the ridge of hills dividing Loch Fine and Loch Awe, and at a height of about 1800 feet above the sea. In a letter addressed to the late Principal Forzers,} His Grace observes, “Tn this case glacier action is impossible. Even if this hill had been the seat of a glacier, it could only have been snow, so near the summit. The only explana- tion which seems to me possible is, that this peak, when subject to the grinding force, was a rocky islet above the surface of a glacial sea, and that floating ice- bergs drifting from the N.E. were constantly grinding upon its sides.” In Arran, as Dr Booc Watson points out, there are several ridges between adjoining valleys which are smoothed in a like remarkable manner. He has no doubt that they were smoothed by ice; but he leans to the opinion that glaciers may have produced the effect, by overflowing the sides of the valleys in which they were formed. (4.) Another remarkable phenomenon is the position of isolated boulders on narrow ridges of hills, or ledges of rock, from which to all appearance the slightest force could dislodge them. The wonder is how these boulders could have been placed in such precarious positions. The Duke of Arcyte takes notice of a number of these boulders as being on the hills about Loch Fine and Loch Awe, adding, that it is much less difficult to account for their transportation on the supposition of floating ice than of glaciers. Professor Ramsay, in his “ Ancient Glaciers of Wales,” gives a representation of several of these boulders perched on the very edges of cliffs; and I can, from personal observation, as well as sketches made by myself in Wales, confirm Pro- fessor Ramsay’s account of the singular appearance which some of these “blocs percés” present. One of these boulders, of angular shape (being 27 feet long, 15 feet high, and 6 feet broad), and weighing about 180 tons, is stated by Professor Ramsay as being} ‘on the very crest of the slaty ridge of” a mountain, about 2000 feet above the sea. ‘The parent rock is at least a mile distant.” What says Professor Ramsay to the question, how this boulder was transported? “I am aware it has not been customary to consider accumulations at so great an * Edin, New Phil. Journ, for 1846, vol. xl. p. 141. t Proceedings Roy. Soc. Edin. vol. ii, p. 461. t Ancient Glaciers of Wales, p. 80. 686 = MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. elevation as belonging to glacial marine deposits. But when we consider their continuity with the shell-bearing strata,* their regular smoothly sloping outline, and add to this the travelled boulders and masses of rock on the summits of hills and ridges 2300 feet high, it seems impossible to resist the conclusion that the whole is of marine origin, and due to the operation of one set of causes extending over a definite period.” + The conclusion which Professor Ramsay drew from these phenomena was, “that the blocks of stone that now strew our continents and islands were chiefly dropped by the same agency —icebergs—that is now sowing the Western Atlantic with earth and boulders derived from the mountains and coasts of Greenland, where glaciers descend to the sea.” | There is another fact connected with the position of boulders which has often arrested my attention. They are more frequently found in clusters, at or near the tops of hills of moderate height, than anywhere else. On the hill of Croy, near Kilsyth, and on several hills to the west of Dunfermline, examples occur. Almost all the very large boulders, which are known to me, are situated near rising ground, and on the east side of it—as in the case of the Clochodrick stone in Renfrewshire, the great conglomerate boulder near Doune, the Carlin stone in Dunmore Park, and the Auld Wives’ Lift, near Milngavie.§ Floating ice would ground most frequently on islets or shallow places, and discharge its cargo there on melting. Glaciers occupying chiefly the lowest parts of avalley would discharge their cargoes at the bottom. Therefore if boulders, either singly or in clusters, most frequently occupy crests or ridges of hills, they afford evidence more of icebergs than of glaciers. (5.) There is, however, one phenomenon of a perplexing kind, which I admit cannot be easily explained by either of the two theories. I allude to the boulders whose present position has been ascertained to be higher than that of the parent rock. Such cases have been made out in the Isle of Man, Cumberland, and Roxburghshire. If floating ice will not explain these cases, still less will land ice, which, being moved by gravitation, must carry everything to a Jower level. On the other hand, instances are on record of stones and gravel being raised to a higher level by means of floating ice. Sir CHarutes LYELL states, that on the coast of Norway sheets of ice with pebbles and moderately-sized boulders have, during a storm, been known to be driven up fully 50 feet above the sea-level. It * Professor Ramsay mentions (p. 96), that sea-shells were found by him at a height of 1300 feet above the sea, ‘‘ two miles west of Snowdon, on a sloping plain of drift charged with erratic blocks, one of which, of great size, is known as Maen-bras, or the large stone.” t Proceed. Lond. Geolog. Society, vol. vii. p. 373. t Anc. Gl. of Wales, p.-92. § De Luc (as quoted by Sir James Hatt, Ed. R. S. Tr. vol. vii. p. 160) says, “ that the granitic blocks lying in the district between Berlin and the Baltic, occur frequently, and almost constantly, in very numerous assemblages, upon the summits of the sandy hills with which that country is interspersed, whilst none are to be met with in the intervening valleys.” MR DAVID MILNE HOME ON THE BOULDER-CLAY OF EUROPE. 687 is also related that Sir James Ross once saw an iceberg capsize, bringing up mud and stones to a height of more than 100 feet from the sea-bottom. Perhaps, therefore, the anomalous position of some boulders, in respect of being above the level of the parent rock, may, on the iceberg theory, admit of some explanation. On the glacier theory they admit of none. (6.) The chief objection to the views which they have submitted in this Memoir, may be found in the following paragraph :— “ The iceberg hypothesis will not account for the phenomena. We cannot conceive of a set of ice-rafts moving for ages 7z one persistent direction within a given area of the sea. (7°82 to Dose. LXXI. |112 grs.| y#,5th. | 0-1 gr. | Complete paralysis of motor nerves in 1 hour. 3 FA reflex function of spinal cord in 1 ho. 35 min. LXXII. | 200 gers.} scoath. | 0:2 gr. | Complete paralysis of motor nerves in 40 minutes. A BZ reflex function of spinal cord in 1 ho. 10 min. LXXIII. | 256 grs.| yi5d. | 03 gr. | Complete paralysis of motor nerves in 1 hour 25 minutes. a = reflex function of spinal cord in 1 ho. 25 min. LXXIV. | 290 grs.| 535th. | 0°36 gr. | Complete paralysis of motor nerves in 18 minutes. reflex function of spinal cord in from 2 to 18 hours. LXXV. |110 ers.| z3oth. | 0:2 gr. | Complete paralysis of reflew function of spinal cord in 47 minutes. motor nerves in from 1 ho. 20 min. to 22 ho. ” 2) ” »”? LXXVI. | 140 grs.| zsth. | 03 gr. | Complete paralysis of reflew function of spinal cord in 35 minutes. motor nerves in from 1 ho. 20 min. to 21 ho. LXXVII. | 110 grs.| sisth. | 03 gr. | Complete paralysis of motor nerves in 30 minutes. +5 8 reflex function of spinal cord in 1 ho. 30 min. LXXVIII.| 110 grs.| s3sth. | 03 gr. | Complete paralysis of reflew function of spinal cord in 49 minutes. re an motor nerves in | hour 14 minutes. LXXIX. | 115 grs.| 237th. | 0-4 gr. | Complete paralysis of reflew function of spinal cord in 28 minutes. | 3 motor nerves in 35 minutes. ” In the experiments in this Table, in which doses between the oth and the =4;th of the frog’s weight were given, the complete paralysis of the motor nerves occurred before the complete paralysis of the reflex function of the spinal cord; and in the experiments in which doses between the ;4,th and the ,3,th were given (excepting Experiment LX XVII.), the complete paralysis of the métor nerves occurred after that of the reflex function of the spinal cord. As we have already said, these two actions are, however, of nearly equal energy; for, at the time when the one has been completed, the other is usually nearly so. Experi- ment LX XVII., in which a dose equivalent to the ,4,th was administered, con- spicuously illustrates this nearly simultaneous progress, by its occurrence as an exception to the order in which the two actions are usually completed after such a dose. We have accordingly shown that Mr Morson’s conia differs from that of Dr Curistison, both in lethal activity and in mode of action. We shall en- deavour to explain these differences in a subsequent portion of this paper; the explanation of the varieties in the mechanism of the paralysing action of Mr Morson’s conia being dependent on results obtained by our experiments with methyl-conia. Hydrochlorate of methyl-conia (C,H, ,(CH,)NHCl).—Iodide of methyl acts readily upon conia, producing a syrupy or crystalline substance, which is a mixture 720 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN of hydriodate of methyl-conia and iodide of dimethy]-conium—the former pro- duced from the normal conia, and the latter from the methyl-conia. If the conia be free from water, this action is very rapid, and as heat is developed it is necessary that the vessel should be kept cool; if the conia contain water, the chemical change is very slowly effected. Caustic potash is added to the mixture, and it decomposes the hydriodate of methyl-conia, setting the base free as an oil, while it leaves the iodide of dimethyl-conium unacted upon. The methyl-conia was converted, after separation, into a hydrochlorate, which is extremely deli- quescent, and has a brownish, semicrystalline appearance. We found that this substance possesses a poisonous (lethal) activity, consider- ably greater than that of Mr Morson’s conia, but nearly equal to that of Dr CuRISTISON’s conia; for two-tenths of a grain, exhibited by subcutaneous injection, speedily caused death in a rabbit, and a dose, equivalent to the zA;,5th of the weight of the animal, is about the minimum fatal dose for a frog. The general character of the symptoms is likewise similar to that of Dr Curisrison’s conia, and, therefore, to that also of Mr Morson’s; but the causation of these symptoms rather resembles that of the latter than-of the former conia. Paralysis is the main symptom; and a careful examination, by experiments on frogs, of the mechanism by which this symptom is produced, showed that it is a result of actions on the motor nerves and spinal cord, and that with large doses the former action is completed before the latter, while with small doses the latter action is completed before the former. We shall, in the first place, describe the symptoms that appeared in a rabbit, after the administration of a fatal dose. EXPERIMENT LXXXI.—Two-tenths of a grain of hydrochlorate of methyl- conia was dissolved in twenty-five minims of distilled water, and injected under the skin at the right flank of a healthy rabbit, weighing two pounds and ten ounces and-a-half. The rabbit moved about in a normal manner until four minutes after the injection, when the movements became constrained, and it was observed that this was owing to stiff extension of the four limbs. A slight touch of the animal caused a series of rapid tremors, during which, as well as at other times, the body was elevated on the stiffly extended limbs. This somewhat remarkable condition continued without change until ten minutes, when the stiffness of the posterior extremities disappeared; but, in place of assuming a normally flexed position, these extremities became flaccidly abducted ; and, when the animal moved about, they trailed behind it in asomewhat powerless manner. In eighteen minutes, the symptoms of exaggerated reflex activity, and the spasmodic extension of the anterior extremities had disappeared; and, now, there was so great a degree of general paralysis present, that the rabbit was unable to move about, and it lay quietly on the abdomen and chest. In nineteen minutes, the neck muscles could no longer continuously support the head, which, soon after, rested on the table. In twenty CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 121 minutes, the respiratory movements were laboured, and they occurred only twenty-four times in the minute. The rabbit now lay on the side, quite flaccid and powerless; and, at times, a series of slight tremors occurred. The respira- tions gradually became weaker and less frequent, the common sensibility dis- appeared, and death occurred, twenty-two minutes after the administration. Three minutes after death, the exposed heart was contracting in normal rhythm, at the rate of seventy-four beats in the minute; and it was ascertained that the conductivity of the afferent and efferent nerve fibres of the sciatic nerves, the reflex function of the spinal cord, and the contractility of the striped muscles were still retained. This description is sufficient to show that in rabbits hydrochlorate of methyl- conia produces very similar effects to hydrochlorate of conia. That this similarity also occurs in frogs will be seen from the following experiment. ExPERIMENT LXXXVI.—A solution containing six-hundredths of a grain of hydrochlorate of methyl-conia, in five minims of distilled water, was injected under the skin at the right flank of a frog, weighing 185 grains. In ten minutes, a slight degree of stiffness, with rigid elevation of the fingers, was present in the anterior extremities, but the frog still jumped about actively. Gradually the movements became less energetic; some sprawling occurred ; and, soon, the frog lay on the abdomen and chest, quite unable to jump or move about. In twenty minutes, the power of voluntary movement was completely lost, and irritation of the skin caused but feeble reflex twitches in both posterior extremities. The frog remained in this state until forty-seven minutes after the administration ; but in fifty minutes, the most severe stimulation of the skin was unable to excite any reflex movement whatever. The right sciatic nerve was now exposed and galvanised; twitches were thereby excited in the right toes, but these were unaccompanied by any movement in the left posterior extremity or elsewhere. At this time the cardiac impulse was of fair strength, and the contractions of the heart were occurring at the rate of forty in the minute. On the morning of the following day, the frog was dead and in rigor. These symptoms agree closely in their general character with those described after corresponding doses of hydrochlorate of Dr Curistison’s conia (Experiment LXI.), and of Mr Morson’s conia (Experiment LXXVI.); but the slight spasmodic symptoms that appeared in the anterior extremities were not invariably observed in our other experiments with this substance. Paralysis is shown to be the pre- dominant symptom, and the causation of this paralysis, after the small fatal dose exhibited in this experiment, appears to be due to an abolition of the reflex function of the spinal cord, rather than to a suspension of the conductivity of motor nerves. The action of hydrochlorate of methyl-conia, therefore, apparently resembles that of hydrochlorate of Morson’s conia; and we shall see from the following experiments that the special variations pointed out as occurring with VOL. XXYV. PART II. 9B 722 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN different doses of conia obtained from that chemist, occur also with different doses of hydrochlorate of methyl-conia. ; EXPERIMENT LXXXVIII.—Immediately after ligaturing the blood-vessels at the upper part of the right thigh in a frog, weighing 140 grains, we injected a solution, containing one-tenth of a grain of hydrochlorate of methyl-conia, under the skin at the left flank. In thirteen minutes, the frog was flaccid, and no voluntary movements occurred in the poisoned region ; but vigorous movements, consisting of extreme and somewhat spasmodic extensions, occurred at frequent intervals in the right (non-poisoned) posterior extremity. Irritation of the skin in the poisoned region now caused merely feeble twitches in the left (poisoned) posterior extremity, and energetic movements in the right posterior. In fifty minutes, however, no reflex movement could be excited anywhere by irritation of the skin. The left sciatic nerve was exposed and subjected to galvanic stimulation, with the result that, while well-marked movements occurred in the left posterior extremity, no movement occurred in the right (non-poisoned). It was at the same time ascertained that the motor conductivity of the right sciatic nerve was not appreciably impaired, even in that part of the trunk exposed to the direct action of the poison; that the poisoned muscles retained their con- tractility ; and that the heart was contracting, in normal rhythm, at the rate of twenty beats per minute. Several observations were made during the succeeding fifty minutes, but no change had occurred during this time, with the exception of a slight diminution in the rate of the heart’s contractions. On the following morning, the frog was dead. ExPERIMENT XCI.—The blood-vessels were tied at the lowest third of the right thigh of a frog, weighing 200 grains, and two-tenths of a grain of hydro- chlorate of methyl-conia, dissolved in four minims of distilled water, was then injected under the skin at the left flank. The first symptom that was observed occurred in three minutes, and consisted of a stiff extension of the anterior extremities, causing unnatural elevation of the thorax. After a few seconds, this symptom was modified to the extent that the anterior extremities became rigidly incurved, with the fore-paws in contact with each other. Vigorous jump- ing movements were still attempted, but as the anterior extremities took no part in these, they were very imperfect, and frequently resulted in the frog falling on one side. In ten minutes, this spasmodic condition of the anterior extremities disappeared, and now the frog lay flaccid on the lower jaw, chest, and abdomen. The power of voluntary movement seemed to be suspended in the poisoned region, but it was retained in the non-poisoned (right posterior extremity), where vigorous and somewhat spasmodic movements of extreme extension frequently occurred. In thirty-three minutes, irritation of the skin caused energetic reflex movements in the right posterior extremity, but no movement in any part of the poisoned region. In thirty-four minutes, the left sciatic nerve was exposed, and CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 123 it was found that its motor conductivity was completely suspended—galvanism of its trunk causing no contractions in the left posterior extremity; while its sensory conductivity was retained—galvanism causing energetic reflex movements in the right (non-poisoned) posterior extremity. The heart was now contracting twenty-four times in the minute; and the contractility of the striped muscles was apparently unimpaired. It was possible to excite reflex movements in the right posterior extremity by stimulating the skin of the poisoned region, until one hour and forty minutes after the administration. Very soon after this time, the activity of the reflex function was completely suspended. Irritation of the skin in the poisoned and non-poisoned regions, as well as galvanic stimulation of the poisoned (left) sciatic nerve, caused no movement, notwithstanding that the non-poisoned (right) sciatic nerve and muscles, and even the trunk of the right sciatic nerve above the position of the ligatures, retained their functional activity. These two experiments are selected from nine which were made on frogs with different relative doses, and in which distinct evidence was obtained of the primary cause of the paralysis. The conductivity of the motor nerves was suspended before the reflex function was abolished in experiments in which doses were administered, equivalent to the ,1,th, the ,4,th, the 5ioth, the goth, and the ;;5 th of the weight of the frog employed; while the activity of the reflex function was abolished before the motor nerves were paralysed in experi- ments in which doses were administered, equivalent to the ;4,5th, the ;,,;th, the +,15th, and the =,4:4d of the weight of the frog. The details we have narrated of Experiments LXXXVIII. and XCI. demon- strate that paralysis of the motor nerves is due to an action on their peripheral terminations; as well when this paralysis precedes the abolition of the reflex function, as when it occurs subsequently thereto. It would appear that the abolition of the reflex function depends, at least in part, on an action on the spinal cord ; for these experiments show that, after its occurrence, irritation of the skin of a region protected from the direct action of the poison, or galvanic stimulation of the trunk of a mixed nerve likewise protected from the direct action of the poison, does not cause any reflex movement, notwithstanding that the motor nerves and muscles everywhere retain their functional activity. We have accordingly shown that conia and methyl-conia produce very similar symptoms; the more prominent of which are spasms and paralysis. Our analysis of the mode in which the paralysis is produced, has resulted in proving its dependence on an action on the motor nerves and on the spinal cord. The rate at which each of these actions is produced by the substances examined (estimating this by the time of completion) varies in a remarkable, and, at first sight, perplexing manner. In the case of the conia prepared by Dr CuristIson, the former of these actions is the more powerful; while in that prepared by Mr Morson, and in methyl-conia, the two are nearly equally prominent. In a series 724 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN of experiments on frogs with varying doses, it was found that Dr Curistison’s conia invariably produced complete paralysis of the motor nerves before that of the reflex function of the spinal cord; that Mr Morson’s conia usually produced complete paralysis of the motor nerves before that of the reflex function of the spinal cord in those experiments of the series where the dose was small, and complete paralysis of the reflex function of the spinal cord before that of the motor nerves where the dose was large; and that methyl-conia produced com- plete paralysis of the reflex function of the spinal cord before that of the motor nerves in those experiments where the dose was small, and complete paralysis of the motor nerves before that of the reflex function of the spinal cord where the dose was large. As already mentioned, our chemical examination of the two specimens of conia proved that that of Dr Curistison contains a much smaller proportion of methyl- conia than that of Mr Morson. Our physiological examination has confirmed this result; for the action of the latter specimen of conia more closely resembles that of methyl-conia than the former. In other words, the conia containing the smallest proportion of methyl-conia acts most purely as a paralyser of motor nerves. It seems a legitimate deduction from this, that conia altogether free from methyl-conia (7.¢., normal conia) will be free also from all spinal action, and will, accordingly, produce paralysis solely by influencing the motor nerves.* Our experiments have shown that the lethal activity of Dr Curistison’s conia is considerably greater than that of Mr Morson’s. The comparatively feeble potency of the latter cannot be explained by its containing a large proportion of methyl-conia, for the activity of this substance is about the same as that of Dr CHRISTISON’S conia; it may be due to the presence of ammonia. Iodide of dimethyl-conium.—When a moderately dilute solution of caustic potash is added to the mixture of iodide of dimethyl-conium and hydriodate of methyl-conia, the latter salt, as stated above, is decomposed, while the former remains in solution, and may be purified by crystallisation from strong aqueous, caustic potash. It is tolerably soluble in hot solutions of caustic potash, but on cooling the solution, it separates in the form of colourless silky needles. It is readily soluble in water, and its composition may be represented by the formula, C,H,,(CH,)NCH,I. In various experiments, we have administered to rabbits, by subcutaneous injection, doses of half-a-grain, two grains, two grains and-a-half, three, four, and five grains. No obvious effects were produced by half-a-grain, or by two erains; slight temporary paralysis was produced by two grains and-a-half, and death by three, four, and five grains respectively. It is, therefore, obvious that the * We have not as yet succeeded in obtaining a pure specimen of normal conia ; and the quantities of ordinary conia at our disposal have not been sufficient to enable us to attempt a separation of normal conia from methyl-conia. CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 725 lethal activity of iodide of dimethyl-conium is greatly less than that of either conia or methyl-conia. That the character of the symptoms it produces is also different, will be seen from the following experiment. EXPERIMENT XCVIII.—Having dissolved three grains of iodide of dimethyl- conium in forty minims of distilled water, we injected the solution under the skin of a rabbit, weighing four pounds. The animal remained sitting quietly for more _ than half an hour, during which time no symptom was observed. In thirty-two minutes, however, it became restless, and faint tremors occurred. Soon, it had difficulty in moving about; and after some endeavours to maintain a sitting posture, it lay down on the abdomen and chest. In forty-one minutes, the head rested on the table; and at this time the respirations were shallow, and at the increased rate of 144 in the minute. The rabbit remained quietly in this position until one hour and four minutes, when it succeeded, after some efforts, in rising on its limbs, but, being unable to support itself thus, it again lay down on the abdomen and chest, with the head resting on the table. The respirations were now eighty-four in the minute. In one hour and eleven minutes, slight tremors again occurred, and then the rabbit became perfectly fiaccid, and the respirations infrequent and laboured. In one hour and twelve minutes, the respirations were mere gasps, occurring at the rate of about twelve in the minute; and soon after they became so shallow as to be hardly visible. In one hour and fifteen minutes, a few twitches occurred in the muscles of. the face, and in a few seconds the rabbit was dead. In the autopsy, the motor nerves and muscles were found active, twelve minutes after death ; but at this time the exposed heart was found to be contract- ing irregularly and feebly. | In this experiment, we frequently tested the reflex excitability, but never observed the slightest evidence of its being increased. We shall now briefly describe the experiment in which we administered five grains. ExPrErIMEeNnT C.—A solution, containing five grains of iodide of dimethy]- conium, in fifty minims of distilled water, was injected under the skin of a rabbit, which weighed three pounds and six ounces and-a-half. As in the previous experiment, the first effects observed were a number of restless, uneasy move- ments, which occurred in eleven minutes. Soon afterwards, paralytic symptoms appeared ; and in twenty minutes, these had so far advanced that the rabbit lay flaccid on the abdomen, chest, and lower jaw, while irritation of the skin was followed by extremely feeble movements of the head, or one or other of the extremities. In twenty-four minutes, the head fell over on the side, and rested thus on the table; and the respirations were infrequent, shallow, and laboured. After this, the respirations became greatly more infrequent and laboured, until they altogether ceased, thirty-one minutes after the injection of the poison. VOL. XXV. PART IL, I¢ 726 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN In this experiment, likewise, we failed in discovering the slightest evidence of exaggeration in the reflex excitability, or any spasmodic symptom. These descriptions are sufficient to show that iodide of dimethyl-conium acts simply as a paralysing agent, and that it does not produce any spasmodic effects in rabbits. The general symptoms that appear in frogs after the adininsvinltion of a fatal dose are illustrated in the following experiment. EXPERIMENT CVIJ.—Having dissolved one-tenth of a grain of iodide of dimethyl- conium in four minims of distilled water, we injected the solution under the skin at the right flank of a frog, weighing 150 grains. In two minutes and thirty seconds, a slight degree of paralysis was observed in the anterior extremities, which were scarcely able to support the chest; and the jumping movements were now less active than before. Quickly, the paralysis became more decided ; until at six minutes, the frog was lying on the abdomen and the lower jaw. The respiratory movements of the chest had now ceased, while those of the throat continued for several minutes longer. In nine minutes, irritation of the skin produced merely feeble movements in the posterior extremities; and in thirty minutes, it was impossible to excite any reflex movement whatever, even by severe irritation of the skin. The right sciatic nerve was now exposed in the thigh, and stimulated by an interrupted galvanic current, but no muscular con- tractions were thereby produced, although the muscles contracted actively when the electrodes were directly applied to their surfaces. At this time, the heart’s impulse was of fair strength, and the beats occurred twenty-two times in the minute. On the following day, the frog was found to be in the condition last noted ; but on tbe third day, the contractility of the muscles had disappeared, and the heart’s contractions had ceased. In many other experiments on frogs, the same general phenomena were observed. The spasmodic symptoms to which we have drawn attention in our description of the effects of conia and of methyl-conia were entirely absent in our experiments with iodide of dimethyl-conium ; and, accordingly, the symptoms we observed were those of paralysis only. We made several experiments to determine what structures are influenced in the production of this paralysis. Experiment CVIII.—Immediately after ligaturing the blood-vessels at the upper part of the right thigh of a frog, weighing 192 grains, we injected three- twentieths of a grain of iodide of dimethyl-conium, dissolved in four minims of distilled water, under the skin of the left flank. In one minute thereafter, the movements of the frog had become somewhat feeble, the poisoned extremities being obviously weakened. In two minutes and thirty seconds, the frog lay on the abdomen and lower jaw, apparently unable to execute any voluntary move- ments with any part of the body except the right (non-poisoned) posterior CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. 727 extremity, and there were no respiratory movements whatever. In nine minutes, stimulation of the skin in any region was followed by energetic reflex movements in the right posterior extremity, but no movements occurred in the poisoned region. In fourteen minutes, the left sciatic nerve was stimulated by an inter- rupted galvanic current, and, although active reflex movements of the right (non-poisoned) posterior extremity were thereby excited, no movement occurred in the left (poisoned) posterior extremity, or in any other part of the poisoned region. The heart’s impulse was, at this time, found to be of fair strength, and occurring forty-two times in the minute; and the muscles contracted vigorously on direct stimulation. In three hours, the condition of the frog was the same as last noted, excepting that the rate of the heart’s contractions had diminished to thirty-eight in the minute. The observations were now interrupted until the following morning, when the frog was found dead and in rigor. In many other similar experiments with different doses of this substance, the symptoms and mode of action were exactly the same as in the last experi- ment. They show that the paralysis produced by dimethyl-conium is dependent on an action on the motor nerves, primarily restricted to the peripheral termina- tions. Even after the administration of a fatal dose, we have never observed any action on the spinal cord, beyond its necessary implication in the progress towards death. On the other hand, in experiments where doses below the mini- mum fatal, and therefore considerably smaller than in Experiments CVII. and CVIII., were given, the condition of complete paralysis of the peripheral termina- tions of the motor nerves existed along with retained functional activity of the spinal cord and sensory nerves, for periods protracted over many hours. Thus, in an experiment where the dose was equivalent to the =4,th of the frog’s weight (Experiment CIII.), the poisoned motor nerves remained completely paralysed for more than twenty-six hours, while, during this time, the poisoned sensory nerves and the spinal cord retained their functional activity. We conclude from our experiments, that in physiological action iodide of dimethyl-conium differs from conia and methyl-conia in being entirely free from spasmodic and spinal-paralysing actions. It is shown in the following Table of minimum fatal doses, that iodide of dimethyl-conium is much less active than either conia or methyl-conia :— 728 DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN Relation a 0, of Substance Animal and its aaa of Dose to Effect es Employed. Weight. injection Weight of a men J ‘ Animal. LITT. | Hydrochlorate of | Rabbit, 3 Ibs. 01 gr. z7ss7zth. | Slight degree of stiffness in the Dr Curistison’s| 142 oz. ; limbs, followed by recovery. conia. , LIV. Do. Do., 3 lbs. 63 oz. 0:2 gr. xrsrssth. | Death, in 32 minutes. LXVI. | Hydrochlorate of | Do., 2 Ibs. 12 oz. 0:2 gr. persath. | None. Mr Morson’s conia. LXVIII. Do. Do., 4 Ibs, 1 oz. 1 gr. azt7zth. | Death, in 33 minutes, LXXX. | Hydrochlorate of | Do., 3 Ibs. 144 oz. 0-1 gr. u7zs7ath. | None. methyl-conia. LXXXI. Do. Do., 2 lbs. 103 oz. 0:2 gr. szbezth. | Death, in 22 minutes. XCOVII. | Iodideofdimethyl-| Do., 3 Ibs. 63 oz. 2°5 grs. sesxth. | Slight paralysis, followed by re- conium, covery. XCVIII. Do. Do., 4 lbs. 3 grs. past. | Death, in 1 hour and 15 minutes. [This investigation into the physiological action of atropia and its methyl and ethyl derivatives, and of conia and its methyl derivatives, was commenced in July 1867; but, after performing a number of experiments, we considered it advisable to postpone the further examination of these substances until we had finished that portion of our researches which is published in Vol. XXY. Part 1 of the “ Transactions.’’ Although an abstract was read before the Society on the 18th of January 1869, this paper was not delivered to the Secretary for publication until the month of October. | The subjoined Tabular Summary contains the leading facts of all the Experi- ments included in the present part of this investigation. 729 CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION ‘soatyvatsop [Aqyo pue [Ayjour syt pure vidosye YIM syeamument uo syueutredxe on} [[@ Ur peadasqo seam strdnd oy} Jo uotyryepIG » “A Juewried “XQ UL SB yIqqea OUI “AJ Juoutred -X] UI sv ZIG q er ouleg (TIXX yueu -1dedxq) vidosye jo eyeydins jo ‘si3 OT PeATAINS sv Sop outeg "S040 NT ‘OP UL} SsoT “Araaosar fq pomoy pue sanoy -[oy ‘saarou 10j0ur 9% Wey} OL0TT ‘oynuimt T | Jo siskjered ajotdurog | “18 ¢0.9 0d ‘SIs EOP “Od 0g "AIX ‘QT ULYy ssoy “£1eAo0ser Lq pomoy pue sanoy *So]NUTUL -[OF ‘soATou zO}oUT g ueyy e10;y | F ULYyy ssoT | Fo siskjeaed oyofdmoy | a8 ¢Z0.0 0d ‘sis cGy “og 0d ‘THX ‘Kraaooer Aq poor *samoy [oy ‘seartou 10}0Ur @ Uey} O10; ‘oynurut T | Jo stskjvred ojoqdmog | “19 [0-0 ‘od "SIS GOP “Od ‘og ‘TIX “Aqoaooar Lq "ULUL OZ pure peaorpoy ‘stsATered Imoy [ jnoqy ‘soynuImM € | [vreues oyo;duoouT | “1d CQO. ‘0g "sid 6G ‘SOIT 0g TX ssayoqtany Lavy : -[liqy. puv stsATered “‘SOJNUIUL g ‘sojnuimt @ | Aq popessad ‘qyveq ‘sid ‘0d ‘20G Sq[p “oq ‘0g NG *SIOULOT} qyst[s pur stsAyvaed ‘SoU FF | ‘sojnurut QT | Aq popasaad ‘yyroq ‘S13 $ 0d ZOE Sq F “og OYE | XI ‘stsATered “SoqnUIU ZG *SOJNUIUL 9 fq popesord ‘qe9q "S10 ¢ XO ‘ZOOL sq1g “og ‘0g ‘TIIA ‘SoJNULUT (G ‘Araaooar Lq poaoy pue anoy [oy ‘soyoytmy Arey I wey} osoyy | “seynurer gy | -aqy pur sisXfereg | ‘SIS g.g | “A[snoeuejoqng | -zo fez sqrg “og od ‘ITA “A19A0001 Aq pamoypoy ‘sxourer4 ‘UIOA [VIORy @ ‘UIUIGZNoqy | ‘semMUIMZ | 4yYsIs pue siskTearg "sd Z oyur uoroatur Aq | -zog ‘sq, g “og od TA “£rdAover fq “SoM UTUL pemorfoy ‘sisAyvaed OSpuvinoyy, | ‘soynururg | pue szowesy 4YyS1I9 ‘sad ‘A[snoourynoqng | zogrt sqTg “oq 0d "A *£I9A0D9I ‘UTOA [BIORT B Aq pomoyos ‘sisXpeavg | “19 G.9 | oyur uopoluthg | -zog‘sqrg “og 0g “AI ‘op ‘od 13 1.0 ‘od "20 L'sq,G “og ‘od ‘TIT *£10A 0001 Aq paMolpoy ‘soarou Tova oy} Jo stsd[vavq | “13 60.0 "od "Zo ¢ “ST & “HqqQe yy ‘od apt yon ‘stskyered ‘uuntdorye ‘soynurmr 9g | ‘soqnurmg | 4q pepeoord ‘yyvog | ‘sad QT | *ATsnooueynoqng "20 9 ‘sqt g ‘eo | -[Aq}0ur Jo oprpoy T : durk Reis *yuotati1edx seat : pane ee “OOH “eso, “TONFIQI YX “4310 M ‘pokopdung, ; jo a BERGE UIE eh a J? poe S}I pus [eUIny eounjsqug requinyy -Oq [CAIOUT SINANTCAdXad HO ACVWNNS AV TINAVE VOL. XXV. PART II. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN 730 . “(sird -ud uo ydeoxo) ouoy sid 0 ‘(sd -nd uo ydooxe) ouon | ‘813 Og ‘0g ‘(syd -nd uo ydooxo) ouon | ‘su5 07 “‘youmoys Aq ‘pory oroM AytuI0I} x9 “sts{yeavd Lortojsod 9U0 FO STOSsO A *poyou JON *‘SOJNUIUL 8 &q pepesoad “yyeoqd "13 GZ.0 ‘od *‘£aaaooor £q ‘SOJNULU —| paar oT[OF ‘SMOTs_NAUOD ‘skepg ynoqy | GT wey} ssor] | oruvyoy pue sisdqeavg | “a3 ¢.9 od 6 URI} Ssoy *£19A0001 pue sanoy Aq pomoy[of ‘tonsuvy G Uvy} O10 | UIUC TINOQYW | pue‘sisavyyvo‘stsommiq | ‘sid GT od “£19A0001 “PZ WL} Ssoy Aq pomoypoy ‘suorspna *T quoursod pue sanoy -109 9Tme49} JUoN bay “Xq UL sv sop ouvg | g uvyy osoyy | “UI Y JNOGY | pue ‘surseds ‘sisf[vreg | ‘si3 OT od *SdATOU 10}0UL jo stsAyeavdoyazdut09 ‘sup Z jnoqy ‘poyou FON | fq papoooad ‘yyvaqr | 33 ¢.¢ 0d ‘SOATOU I0JOUL jo sts{{ered ojo; ur00 ‘sfep Z Jnoqy ‘peyou JON | Aq popooord ‘yyeoq | 18 ¢.0 og *SoATou 1OOUr jo stsAyeavdoyord moo ‘sep gynoqy | ‘wu ¢g ynoqy | fq popesord ‘yywoq | “18 ¢.0 ‘og ‘SoA TOU *pomnqesiy a10M rojour pouostod oy} apsnur snrardus0I4sevd jostsfeaed ojo7Cut09 JYStL OY} JO spessoA *pojou JON “pe}0U ON | Aq poposaad ‘yywoq | a3 Z.0 0g "SoA LOU *pornyesty 10M Iojoutr pouostod oy4 Ayrare1}x9 rot1eysod ‘sojnuiut =| yostsAyvavd oye7du00 }J9[ OY} FO STOssoaA “od ‘sfep §yoqy | g ueyy sso'yT fq pepesdad ‘qyveq “13 CL-0 ‘od *SOAIOU LOJOUL FO ‘yjeap ox10joq AIT t}O Ur “son Uru sisAqerved 0390] utoo peureser jo [wasoquy | ‘sfepg ynoqy | g ury} ssory | fq popooord ‘yyroq | +18 1-0 ‘0d i “£19A.0001 *pernyesty ora “FG ULY4 Ssoy Aq prmorjoy ‘soazou Ayrutea}xe ro119}s0d pue sinoy ‘SoynULuL 10jOUL pouostod jo FYSIE OY} JO spossoA | GL UBy}osoyY | G uLyY sory | sisfpeaed ej}oTdur0—9 ‘I9 T.0 | ‘<[snosueynoqus ; *sumojdurkg jo ssmojdmsg | auomeouauumo0 E BONE jo pur won poy “aso TOT IGT x wOryeInNG, -SIULUIpe TaaM4y JO POUT, -0q [VAIO UT ar “eid "20 $6 "Sq € “OM | -onyezjooyeyding | TTT Axx ‘20 GT ‘sql § “od ‘0d ‘TIAXX “uni doaye 'SqI F ‘qqry | -[4qyour Jo oprpoy "TAO ‘sad G1g “OC oq "AXX "sd QGP ‘901.7 ‘og "KISS "20 G "SQ & “4IqQe yy ‘0g ‘TIIXX “eid *ZO 9 “Sq[ 8 ‘Sod, -O1}e jo ayeyding EPOX ‘818 QZ “Od ‘od 1x "sad 96g “od ‘0g "xox, "sid 096 “oq ‘oq "XIX ‘s19 0OE “Od ‘oq TIIAX ‘sad QOS “og ‘0g *“IIAX ‘S19 F0GZ “od ‘0g TAX wntdorye "819 GGF “Sor | -[Aqjout Jo oprpoy “AX “HISTO AA *pofojduigy TEE S}I pue [VU eouvysqng equin “ponuyvoo—-SENAWIGHd Xd FO AUVNWAS UVINIVIE 731 CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. “Aroaooer £q ‘ES PoeMOT[OF ‘SoATOU 104 Ueyy ssoy -oul oy} Fo stskjeaed pue sanoy ‘soqnu ejotduroo ‘stskjeared € uey} oop | -Iut g ynoqy | Tesouss ojofduroouy | “aS GO.O ‘od ‘sI8 OJZ “od 0g XIXXX *AIOA -oo0r Aq paMmoy[or 02 ‘soAIOU 10JOUL pouos *poinyesty O10M uey} ssoy -tod ay} Fo stsdyeaed Fj Aqrmea}xe o1zeysod pur simoy eyotdutoo ‘stsAyeavd }ysIt Oy} JO sessed | g URYY oA0TT ‘QINUIME [ | Tetoues oyordmoouy | “1d 9.0 0g ‘sa8 61¢ “OG ‘od TIAXXX “Areaoo0r £q paeMoTpoF ‘soaTou 104 -our oq} Jo sisAjered ‘sojnu ejoTdutoo puv ‘stsAT ‘skep F | -1m } ynoqy | -eavd yeaoues pejarg | “19 G0.0 0g ‘sid JOP “Od ‘od | ‘ITAXXX *£IOA ‘somntu =| -ovat Aq paMorpoy ‘sunoygynoqy | -tut g ynoqy | ‘stsf{eaed ojotdmoouy | “1s [0.0 ‘0d ‘SIS OGG ‘Sor,7 ‘0d TAXXX : ‘stsAyoaed *SoqNUTUL pue suouter} 4y4s17s ‘soynuyurg | ¢ ueyz ssorT | Aq popeserd ‘yyvoq | “si g ‘od "20 g “Sq] 6 “Od ‘od "AXXX ‘sisA[vared ' pue sxowes 4 {oT]s _ ‘SoINULU F ‘saynurm Z | fq popeoead ‘yyveq | ‘s19 ¢.Z 0d ‘20 © 'sqy ¢ “od 0d *\TXXX "4ST oy} 2oqye Ajoqerp -omllmr =§=paurojzad stM juotTIedxe pZ ‘stsATered ey, ‘TIT jueutsod *sojnu pue szouler 4ySr71s XH Ul se 4Iqqer cures | TUL Oy ody ‘pejou JON | fq poposerd ‘yyvoq "SI G Auar "20 } Sql G “0d OG TITXXX *£19A0001 *soqNUTUL ‘sojnu Aq poMoypoF ‘sxouLer} ! eg UeyyoLoyy | “1M YZ ynoqY | jycrjs pue sisdjereg ‘S13 Z ‘og ‘zo £) ‘sq, g “og ‘og TIXXX *£raaooo1 Lq *So]NUTUL *soy0u pemorpoy ‘suxoydurds GI ueyy ssory | TU OF Imogy | o14d4,eaed yysis Aro A ShoKGap “AJsnoaueynoqng ‘S| F 0d ‘od XXX “soyNUTUL “snoomue}ueys ‘HIOA [LIOR] @ G wey} ssoryT | -Ur 4soully ‘yyrog | “19¢.9 | oyur uorjoofur Ag 20 § 'SQT € “Od Wal “XXX - ‘Kroaovor fq *soqNUTUL pomoryoy ‘‘o7p ‘soarout ‘mntdorye-[éq4 ‘pojou yony | 2 wey} ssory | 13va oy} Jo sisdyvavg | “18 ¢.0 ‘A[snoourjnoqng | “zo g ‘sq, g “IIqqey | -eut Jo oyeydtng ‘XIXX ‘surojduifg jo ‘sumoyd EvcchaccFoecchevgue ors) ; ye : “quoulrtedx wegen * Ss |4 ane mona OHH ‘asoqd UOTIQIY XG, qSTO AA pefoduagy a a woryeng -S(UJUIpt W20A\4 JO potyoyyt S}L pus [CUIny eouRysqug Toqunyy -0q [BAIOJUT ‘panuyvoo—STNAWTUAd Xe HO ATVWNINOS AVTINGVE DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN 732 *SO]NUTUL QT *SoNUIUL TZ ‘payou JON ‘skep g ynoqy *pornjesi] o10M Ayrureryxe or1eysod qYSr oy} JO spasse\ | ‘skep g ynoqy ‘poinyesiy oom. QPSNU sNTUIe90.1} -809 }Y.SILOY} JO STassa \ ‘pojou JON *pornyesiy oom Aytaeayx9 LIor1eysod qystt oy} Jo stesse, | sep ¢ynoqy ‘sXup 9 jnoqy ‘sumojd mg jo woryeIng “8040 NT *soJNUIU g ‘soqnu “Ta g jnoqy *SoJNUIUI g uryy ssary ‘oynu “Tar T ynoqy *soynUrM G uvyy ssory -pajou yo’ *so}NUTUL @ uey} ssory “soyNUlUr G ueyy sso'T ‘staojdug jo jUSMEOMETIULOD pue woryer4 -SIULUIPY M0AAy -Oq, [BAIOJUT -stsfyeaed pue siouler} 4017s 4q papasaad ‘yyroq ‘sts{Tered pue sxower} 4 SIs Aq popasard §‘yyvoq *£10A 0001 Aq pomorpoy ‘soarou I5BA OY} JO soyouRAq OVIpPIVa Ax0jIq1Y -ur oy} jo siskjereg “(spd -nd uo ydooxo) oucy ‘SOA OU I0jOu ay} Fo stsdéT -ered ayetduioo Aq pomoroy ‘stsATered [esoues ojo;dutoour 4q pepeoaad ‘qyvoq "SOAIOU 1OJOUL peuostod 013 Jo stsAT -ered ojotduos fq pomoypoy ‘stsk,ered [e1oues ojo,duroour 4q popesard ‘yyvoq *SOAIOU 10}OUL poetostod 043 Jo stséT -eird oyotduroo Aq pomorpoy ‘stsATeared [e19ues oyo[dutoout Aq popaserd ‘“qyraqq ‘SoA TOU Iojour pauostod ayy jo sisAyered oye, -m109 pue stsfjeared [e1oues ojotduroour Aq poepasard ‘qyeoq ‘SOAIOU 10}OUL oY} jo stskjvred oyord -u109 pue stsdyeared [etoues oyopduroour fq popessid + ‘yyroq ‘I8 LO ‘S18 0% 18 L.0 13 L.0 "IS T-0 “13 T.0 “OOF “es0q ‘od Of ‘A[snooueynoqng *youutoys Ag od od ‘og og -A[snooueynoqns “WOM TG TUX, JO POTN “20 JL, “sqy § “0G ‘od “TITATX “zo €Q ‘sq, ¢ “od ‘od “TIA'TX ‘wuntdo.rye ‘20 F sq, GO. «| -[Ay}a Jo oprpoy TATX 20 & “Sql § “SAQ@ YT Wut “ATX ‘sI8 [9p “OM ‘0g “ATIX ‘sid cEg “Od ‘od LU “sas Z1e “od ‘0d TITX "SIS OGE “OC. ‘od ‘TTX ‘mnidozye-[hq4 ‘s18 OOP ‘Sor, | -out zo oyeydjng wbx “A310 -pokopdugy ee ae S}I pus [eUITYy eouvisqny Ioq un jy ‘Penuyjvoo—SUINAWIGAIXH FO AUVWWOAS UVTINAVL 733 CHEMICAL CONSTITUTION AND PHYSIOLOGICAL ACTION. *pomnyesiy o10M Ayrures}xe rotzeysod qysta 04} JO spessaA, *pornyesty or0M aPSNUE sNIUIe00I} -888 JOT OY} JO Spassa A. "$00 NT *sptoves ‘SoNUIU F | OG Wey} ssory *SO|NUIUL G *ONULUL T ‘soqnUTUL ‘soyNUIM GT | 9 Wey} ssory ‘spuooes OE | ‘spuooosge pue sojnurugg | puesoynurug *SOINUIU QZ | ‘soyNULUL QT od ‘skep ¢ ynoqy *SOJNUIUL Z ‘TW avy} ssey pure sinoy *soqnULuL 0G Ueyy oL0T, | Z ULqy ssory pojou 40 NI ‘suseds pure stsjer -ed £q popoooad ‘yyveaq ‘stsATeared pue ‘suseds ‘tory -ouny Xoefor oy} Jo agoreressexe ‘sq uty INOF OY} UI ssouyys kq pepesoad ‘qyveq ‘sts AT -ered pue ‘stuseds ‘morjouny xopor ay} JO WoleIescexo fq popessad ‘qyvoq ‘stsATeaed pue ‘suseds ‘uory -oun} xefor JO wor} -elosovxe ‘ssouyiijs fq popoosord ‘qyvoq “kieaover Lq po -MOT[OF “S}UOWOAOUL S[vUILUe OY} UI ssou -HMs Jo sorLcop jure, *soArOu Iojour 943 Jo stsAT -ered oyopduroo Aq pomorpoy ‘stsATeaed [eroues ojetdutoout kq papeovord ‘qyx0q "SOATOU 10JOUL pouostod 043 Fo stsAT -ered ojordutoo Aq pomorfoy ‘stsAyvaed [eqoues oje[d uroout hq popeooerd ‘yyvoq ‘SOATOU 10} -out peuostod oy} jo stskjered ojotdutoo fq pepesord ‘yyeoq *£I0A -o00r Aq pomMoTpoy ‘SoAIOU 10}OUL ot} jo stsdjered oyopduog *poejom JON “sano, 0% Uey} sso'T *poyou JONT ‘sumojdurfg jo ‘smojdusg | yuameoueutut09 jo pue worjery TWOryeing -SIUIUIPe WAdM4 -9q [BAIOJUT “13 T ‘Id 6.0 ‘Id GZ-0 ‘13 Z.0 13 T.0 "19 GLO ‘IS GT.0 "18 G0 "18 40.0 od od od “og od og ‘A[snooueynoqng "20 $6 ‘sqI ¢ “od *Z0 § “Sq ¢ “od 'Z0 $9 ‘sql g “og ‘20 $9 ‘sq ¢ “oq. 20 TFL ‘SQLS “taqeyy ‘sId 062 “Od ‘S13 10 “og ‘sid OCP “od ‘SIS [ZG ‘S017 “poe “eso “TONTQIY XH JO POmdPeTL “FUS1O Syl pur [eWIUy ‘od TIAT ‘od TAT ‘od “AT ‘og “ATT “e109 S,NOSILSIUHD Iq Jo oyero[yoorpé Fy ‘IIIT ‘od dada ‘od TT ‘od a ‘mnrdorye -{fyj0 Jo eprpoy TIX -pokoydung, “queued xny souRysqnug Pa neh XN “penuy7u0g—STNAWIYAd Xd FO ALTVIAINONS UV INAVL QE VOL. XXY. PART II. DRS CRUM BROWN AND FRASER ON THE CONNECTION BETWEEN 734 ‘pomnyesiy o10M Aytuter}x9 xor1e}sod qystx 0} JO spossoA *poInyesty O10M Aywiea}x9 ro149}sod ‘6L uvy} ssey pue sinoy % uvy} e107 ‘06 Uey} ssoy pue sinoy Urq} O10, *sfep JYstx oy} JO spossoA | E uRYy ssory *SoJON ‘sfep @ wey} ssory ‘skep ‘skup [eI0A0g ‘skep [et9a0g ‘smmojdurkg jo wOTyeING, ‘soy nUrUL y— uegy ssory “SOPNULUT G ‘soJNUIUL G *soJNUIUL G ‘SoJNUIU G ‘soqnu Tm J jnoqy “pojoul JON ‘sumojd ug jo hicejvatsyayeceyaraaecoly) pure aoryer4 -SIUIMIpe 1998 A\4 -0q [BAIo}UT ‘SOAIOU 10JOUL polos -1od oy} Jo stskteaed ajotdui09 pur ‘sory -1UId1}X9 aot1e}sod ey} jo sjuoureAour orpouseds ‘stsAyeaed [e1oues oyopduroour ‘SOI}IUIO1] Xo LOTIO} We oy} jo wseds ormoy &q popooord § ‘qywoq ‘stsX[vard puv SOT}IUIEI}xXO IOLIE}Ue ey} Jo wseds oru0y fq pepoosaad ‘yyrog ‘SOAIOU 10}OUL pouostod ayy zo stsfT -eivd oyatduios Aq pomoroy ‘sts \Secretaries to the Ordinary Meetings. Professor Tarr, Davin Smitu, Esq., Treasurer. Dr Macracan, Curator of Library and Museum. COUNCILLORS. Dr A. Crum Brown. James Sanverson, Esq. . Dr Burt. Hon. Lord Neaves. Dr Matruews Duncan. R. W. Tomson, C.E. Wiiiam Turner, M.B. Gerorce Rosertson, C.E. Dr Joun Muir. Professor Prazzt SMYTH. Rev. THomas Brown. Patrick Dupceon, Esq. of Cargen. The following List of Honorary Fellows was submitted before being printed in the billet of the first ordinary meeting :— I. FOREIGN. Professor Bensamin Prince, Director of the United States Survey. M. Cousin pe Remusat, Paris. Frreprich Wouter, Gottingen. II. BRITISH. James Prescott Jove, LL.D., Manchester. Cuartes Wueatstone, D.C.L., London. PROCEEDINGS OF STATUTORY GENERAL MEETINGS. 743 Professor PLayrarr conveyed to the Society thanks from M. Curvreovt for his election as an Honorary Fellow. The Treasurer gave in his annual printed Report, certified by the Auditor. On the motion of Dr Burt, Gzorce AvuLpso Jaminson, Esq., was.elected Auditor for the year 1867-68. It was announced from the chair that the Council had awarded the Keith Prize for the biennial period ending April 1867 to Professor C. Prazzt Smyvu, for his paper on “ Recent Measurements made at the Great Pyramid,” published in the Transactions. On the recommendation of the Council, it was agreed that a ballot should take place at next meeting for Dr Rosrerr Daun, who had resigned his seat in 1845, and who now desired to be re-elected. ; The Meeting then adjourned. (Signed) D. Mitye Home, V.-P. Monday, 23d November 1868. At a Statutory General Meeting, Davin Minne Home, Hsq., Vice-President, in the Chair, the Minutes of the Statutory Meeting of 25th November 1867 were read and con- firmed. ‘ The following Office-Bearers were elected for 1868-69 :— Professor Curistison, M.D., President. His Grace the Duke of ARGYLL, | Honorary ice Premionts JAMES Davip Forzss, LL.D., _ Professor C. Ixnzs, Professor Lyon Piayrair, C.B. D, Mitne Home, Esq., Professor KELLAND, The Hon. Lord Nzaves, Professor Sir Witt1am THoMSoN, Dr Joun Hurron Baxrour, General Secretary. Dr Grorce James ALLMAN, Professor Tarr, Davin Smitu, Esq., Treasurer. Dr Mactaean, Curator of Library and Museum. Vice-Presidents. | Secretaries to Ordinary Meetings. 744 PROCEEDINGS OF STATUTORY GENERAL MEETINGS. COUNCILLORS. Dr Joun Muir. Patrick Dupcxon, Esq. of Cargen. Rev. THomas Brown. Dr Hucu Ciecuorn. JamzEs Sanverson, Esq. W. Ditrmar, Esq. R. W. THomson, C.E. Dr James M‘Barn, Surgeon, R.N. Grorcs Rozertson, C.E. Dr Wititam Rosertson. Professor Prazzi SMYTH. Tuomas STEVENSON, C.E. The following List of Honorary Fellows was submitted before being printed in the billet of the first ordinary meeting :— Gustav Rosert Kircuuorr, Professor of Physics in the University of Heidelberg. Rupotpy Vircuow, Professor of Pathological Anatomy in the University of Berlin. The Szcrerary announced that the Council had awarded the Makdougall Brisbane Prize for the biennial period 1866-68 to Dr Atrxanprr Crum Brown and Dr THomas Ricard Fraser for their conjunct paper on the Connection between Chemical Constitution and Physiological Action, which had been printed in the Transactions. The Secretary announced that the Council had awarded the Neill Prize for the triennial period 1865-68 to Dr Witi1Am CarmicuarEt M‘Inrosu for his paper on the British Nemerteans and on some New British Annelids, which was submitted to the Society last session, and is to be printed in the Transactions. The Meeting then adjourned. (Signed) Pum Keanp, V-P. LIST OF MEMBERS ELECTED. 745 LIST OF MEMBERS ELECTED. December 2, 1867. Joun F. M‘Lewnan, Esq., Advocate. Dr Rosert Daun (Re-admitted). January 6, 1868. Rey. Dr Davip AITKEN. Dr Rosert M. Fereuson, February 3, 1868. J. W. Larpray, Esq. of Seacliff. W. Wituiams, Esq. March 2, 1868. J. Samson GamaGee, Esq. Rey. D. T. K. Drummonp. Rev. JosepH TayLor Goopsir. Major J. H. M. Saaw Srewart, R.E, Madras. March 16, 1868. Joun J. Stevenson, Esq. Rev. James F, Montcomery. April 6, 1868. Joun Dick Peppiz, Esq., Architect. Col. Szaton GuTHRIE. SamvueE. Ratzicu, Hsq. Dr Tuomas SmitH Maccatt. April 20, 1868. Rev. Dr Tuomas GuTarie. Tuomas Key, Esq. Avam Gituigs Suita, Esq., C.A. Joan Macmitian, Esq., M.A. December 21, 1868. Ouiver G. Mituzr, Esq. Wiuiam Dickson, Esq. ALEXANDER Bucuan, Esq. Professor H. C, Fizemine JEnKin. Joun Leveson Doveras Stewart, Esq. Joun Penper, Esq. of Nateby Hall. January 4, 1869. Isaac Anperson-Hewry, Esq. of Woodend. Georce Exper, Esq. Sir Cuartes A. Harttey, C.H. Davin MacGizsoy, Esq., Architect. Rey. THomas Metvitte Raven, M.A. ALEXANDER Howe, Esq., W.S. Viscount WALDEN. Professor ALEXANDER Dickson. January 18, 1869. Dr W. C. M‘Intosu. Dr Henry MarsuHatt. Dr WitiiaAmM RUTHERFORD. February 1, 1869. Dr R, Craic Mactacan. VON SOXGV. PART cle 9H 746 LIST OF MEMBERS ELECTED. February 15, 1869. James Dewar, Esq. March 1, 1869. Rev. H. CaLpERwoop, LL.D. March 15, 1869. Principal Sir ALEXANDER Grant, Bart, LL.D. Captain T. P. Wuire, Royal Engineers. April 5, 1869. Dr Joun Witson JouNsTon. May 17, 1869. Rosert Henry Bow, Esq., C.E. May 31, 1869. Maurice Lorutan, Esq. of St Catherine’s. Joun M‘Laren, Esq., Advocate. 1846 1868 1866 1867 1848 1856 1849 1845 1823 1867 1862 1849 1820 1843 1835 1867 1862 1830 1858 1843 1861 1866 1850 1863 1857 1862 1854 1869 1864 1859 1861 1835 1861 1867 1856 1833 1869 1857 1847 1869 1865 - 1866 1840 1860 1823 1863 1856 1844 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY. Corrected up to 1st November 1869. N.B.— Those marked * are Annual Contributors. *Alex. J. Adie, Esq., Rockville, Linlithgow *Rey. Dr David Aitken, 4 Charlotte Square *Col. Sir James H. Alexander of Westerton *Rev. Dr W. Lindsay Alexander, Pinkie Burn, Mussel- burgh Dr James Allan, Inspector of Hospitals, Portsmouth *Dr G. J. Allman, Professor of Natural History, 21 Manor Place *David Anderson, Esq., Moredun, Hdinburgh Dr Thomas Anderson, Prof. Chemistry, Univ., Glasgow Warren Hastings Anderson, Hsq., Isle of Wight *Thomas Annandale, Esq., 34 Charlotte Square 10 *T, C. Archer, Esq., Director of the Museum of Science and Art, 9 Argyle Square *His Grace the Duke of Argyll, K.T., (Hon. VicE- PRESIDENT), Inverary Castle Charles Babbage, K.H., London David Balfour, Esq., Trenaby Dr J. H. Balfour (GENERAL SECRETARY), Professor of Medicine and Botany, 27 Inverleith Row *George I. Barbour, Hsq., 11 George Square *Hon. Lord Barcaple, 3 Ainslie Place Dr Thomas Barnes, Carlisle Edmund Chisholm Batten, M.A., Lincoln’s Inn, London Dr Bennett, Professor of Institutes of Medicine, 1 Glen- finlas Street 20 *George Berry, Esq., 2 Windsor V'errace, Portobello *Adam Black, Esq., 38 Drummond Place *Hugh Blackburn, Esq., Prof. Mathematics, University, Glasgow *Professor Blackie, 24-Hill Street *John Blackwood, Esq., 3 Randolph Crescent *Rev. Dr W. G. Blaikie, 9 Palmerston Road Ernest Bonar, Esq. *Robert Henry Bow, Esq., C.E., 7 South Gray Street *Dr Alex. Crum Brown, Prof. of Chemistry, 4 Rillbank Terrace *Dr John Brown, 23 Rutland Street 30 *Rev. Thomas Brown, 16 Carlton Street William Brown, Esq., 25 Dublin Street *W. A. F. Browne, Bsq., Post-Office Buildings *A.H. Bryce, D.C.L., LL.D., 42 Moray Place *David Bryce, Esq., Architect, 131 George Street His Grace the Duke of Buccleuch, K.G., Dalkeith Palace *Alexander Buchan, Hsq., 18 Fettes Row f *Dr W. M. Buchanan, 3 Carlton Terrace *J. H. Burton, LL.D., Advocate, Craig House *Rey, Henry Calderwood, LL.D. Professor of Moral Philosophy, Craigrowan, Merchiston 40 *Alfred R. Catton, B.A. *David Chalmers, Esq., Kate’s Mill, Slateford Robert Chambers, LL.D., St Andrews *William Chambers, Esq. of Glenormiston, 13 Chester Street Dr Christison, D.C.L., Professor of Materia Medica (PRESIDENT), 40 Moray Place Dr H. ¥. C, Cleghorn, Stravithy, St Andrews *Thomas Cleghorn, Esq., Advocate, 26 Queen Street Dr Thomas R. Colledge, Lauriston House, Cheltenham 1829 1829 1850 1866 1843 1843 1863 1854 1830 1829 1853 1852 1823 1851 1841 1862 1868 1867 1848 1867 1869 1869 1869 1867 1863 1867 1866 1839 1868 1867 1860 1863 1851 1859 1866 1869 1856 1855 1866 1863 1866 1859 1868 1858 1852 1859 1828 1864 1858 1867 1867 1867 1867 1868 The Right Honourable Lord Colonsay, London A. Colyar, Esq. *50 *Dr James Scarth Combe, 36 York Place *Thomas Constable, Esq., 11 Thistle Street Dr John Rose Cormack, 7 Rue d’Aguesseau, Paris Andrew Coventry, Hsq., Advocate, 29 Moray Place *Charles Cowan, Hsq., Mount Grange *Sir James Coxe, M.J)., Kinellan J, T. Gibson-Craig, Esq., W.S., 24 York Place Sir William Gibson-Craig, Bart., Riccarton Rev. John Cumming, D.D., London *James Cunningham, Esq., W.S., 50 Queen Street 60 Liscombe J. Curtis, Esq., Ingsdown House, Devonshire *H. W. Dallas, Esq., 125 Princes Street James Dalmahoy, Esq., 9 Forres Street *Nicholas Alexander Dalzell, Esq., Conservator of Forests, Bombay *Dr Robert Daun, 6 Picardy Place *David Davidson, Esq., Bank of Scotland *Henry Davidson, Esq., Muirhouse *Wrancis Deas, Esq., LL.B., Advocate, 32 Heriot Row *James Dewar, Esq., 15 Dublin Street * Alexander Dickson, Professor of Botany, University of Glasgow 70 *William Dickson, Esq., 38 York Place Henry Dircks, Hsq., C.E., London *W. Dittmar, Esq., Bonn *James Donaldson, Esq., LL.D., 20 Great King Street *David Douglas, Hsq., 41 Castle Street Francis Brown Douglas, Esq., Advocate, 21 Moray Pl. *Rey. D. T. K. Drummond, B.A., 6 Montpelier *G. Stirling Home Drummond, Esq., Blair-Drummond *Patrick Dudgeon, Esq. of Cargen *Dr J. Matthews Duncan, 30 Charlotte Square 80 *Sir David Dundas, Bart. of Dunira *Rev. Dr John Duns, 4 Mansion-House Road, Grange *Dr James Dunsmure, 53 Queen Street *George Elder, Esq., Knock Castle, Wemyss Bay *W. Mitchell Ellis, Hsq., Wellington Lodge, Portobello Robert Etheridge, Hsq., Clifton, Bristol *William Euing, Esq., Glasgow *J. D. Everett, LL.D., Prof. Nat. Phil., Queen’s College, Belfast *James Falshaw, Esq., C.E., 26 Castle Street *Dr Fayrer, Professor of Surgery, Calcutta 90 *Robert M. Ferguson, Ph.D., 12 Moray Place Frederick Field, Esq., Chili Dr Andrew Fleming, H.M.I.S., Bengal Major James George Forlong, Bombay John Forster, Esq., Liverpool *Dr John Foulerton, Manila *Professor Fraser, M.A., 20 Chester Street *Dr Thomas R. Fraser, College *Frederick Fuller, Esq., Professor of Mathematics, Uni- versity, Aberdeen Dr Charles Gayner, Oxford 100 *Dr Arthur Gamgee, 27 Alva Street J. Samson Gamgee, Esq., Birmingham 1861 1868 1845 1850 1867 1869 1851 1824 1860 1868 1868 1867 1867 1867 1833 1837 1864 1854 1869 1867 1859 1855 1862 1869 1859 1828 1869 1839 1864 1855 1858 1840 1863 1860 1825 1869 1865 1863 1850 1869 1867 1867 1866 1839 1868 1868 1863 1865 1856 ( *Archibald Geikie, Esq., Geological Survey Office, India Buildings, George IV. Bridge *Rey. Joseph Taylor Goodsir, 11 Danube Street *L. D. B. Gordon, Esq., C.E., London *Lieut.-Col. W. D. Gosset, R.E., Portsmouth *Dr Andrew Graham, R.N. *Principal Sir Alexander Grant, Bart., 21 Lansdowne Crescent *Rev. Dr James Grant, D.C.., 18 Great King Street Dr Robert EH. Grant, Prof. Comp. Anat., Univ. Coll., London 110 *Dr Frederick Guthrie, M.A., Prof. of Physics, School of Mines, London *Col. Seton Guthrie, Thurso *Reyv. Dr Thomas Guthrie, 1 Salisbury Road *Dr D. R. Haldane, 22 Charlotte Square *Prederick Hallard, Esq., Advocate, 7 Whitehouse Ter- race *James H. B. Hallen, Esq., Canada Alexander Hamilton, LL.B., W.S., The Elms, Whitehouse Loan Dr P. D. Handyside, 11 Hope Street *Rev. Dr Hannah, Glenalmond Professor Robert Harkness, Queen’s College, Cork 120 Sir Charles A. Hartley, C.E., Sulina, Mouth of the Danube *Sir George Harvey, 21 Regent Terrace *G. W. Hay, Esq. of Whiterigg *James Hay, Hsq., 3 Links Place, Leith *Dr James Hector, New Zealand *Isaac Anderson-Henry, Esq. of Woodend, Hay Lodge, Prinity Lieut. John Hills, Bombay Engineers David Milne Home, Esq. of Wedderburn (VicE-PReEsI- DENT), 10 York Place * Alexander Howe, Esq., W.S., 17 Moray Place Dr Adam Hunter, 18 Abercromby Place *Robert Hutchison, Esq., Carlowrie Castle *The Right Hon. John Inglis, D.C.L., LL.D., Lord Justice- General, 30 Abercromby Place *Professor Innes, M.A., Inverleith House Edward J. Jackson, Fisq., 6 Coates Crescent William Jameson, Esq., Surgeon-Major, Saharunpore *George A. Jamieson, Esq., 58 Melville Street Sir William Jardine, Bart., LL.D., of Applegarth, Jardine Hall, Lockerby *Professor H. C. Fleeming Jenkin, 5 Fettes Row *Charles Jenner, Esq., Haster Duddingston Lodge *Hon. Charles Baillie, LL.D., Lord Jerviswoode, 10 Strathearn Road 140 * Alex. K. Johnston, LU.D., March-Hall Park, Prestonfield Dr John Wilson Johnston, India *T. B. Johnston, Esq., 9 Claremont Crescent *William Keddie, Esq., 5 India Street, Glasgow *Dr Alexander Keiller, 21 Queen Street Rey. Prof. Kelland, M.A. (VICE-PRESIDENT), 20 Claren- don Crescent *Thomas Key, Esq., 42 George Square *J. W. Laidlay, Esq., Seacliff *Charles Lawson, Hsq., 35 George Square *Charles Lawson, jun., Esq., 34 George Square 150 *Dr Laycock, Professor of the Practice of Medicine, 13 Walker Street 130 748 *Hon. G. Waldegrave Leslie, 4 Heriot Row *James Leslie, Esq., C.E., 2 Charlotte Square *Dr W. Lauder Lindsay, Gilgal, Perth * William Lindsay, Esq., Hermitage-Hill House, Leith Thomas Login, Esq., C.E. *Professor Lorimer, Advocate, 21 Hill Street *Maurice Lothian, Esq. of St Catherine’s *Dr W. H. Lowe, Balgreen, Slateford *Dr Stevenson Macadam, 25 Brighton Place, Portobello 160 *Dr James M‘Bain, R.N., Logie Villa, York Road, Trinity *Dr Thomas Smith Maccall, Polmont *John M. M‘Candlish, Esq., 4 Doune Terrace *John M‘Culloch, Esq., Banker, 11 Duke Street Dr Wm. Macdonald, Prof. Civ. and Nat. Hist., St Andrews : *W. Macdonald Macdonald, Esq., St Martins *David MacGibbon, Esq., Architect, 89 George Street John Mackenzie, Esq., 11 Abercromby Place Dr Maclagan (CuRaTOR), Prof. of Medical Juris- prudence, 28 Heriot Row A Lieut.-Col. R. Maclagan, Royal Engineers, Bengal *Dr R. Craig Maclagan, 5 Coates Crescent *Dr William C, M‘Intosh, Murthly *Peter M‘Lagan, Esq. of Pumpherston, M.P. *Join M‘Laren, Esq., Advocate, 5 Rutland Square *Jobn F. M‘lennan, Esq., Advocate, 81 Princes Street *Jokn Macmillan, Esq., M.A., 16 Buccleuch Place *John Macnair, Esq., 33 Moray Place Sir John M‘Neill, G.C.B., Granton House *Dr R. B. Malcolm, 126 George Street Dr Henry Marshall, Clifton, Bristol *J. D. Marwick, Esq., 10 Bellevue Crescent *Professor David Masson, M.A., 3 Rosebery Crescent *James Clerk Maxwell, Esq., late Prof. Nat. Phil., King’s College, London, Glenlair, Kirkpatrick-Durham *Sir William Stirling-Maxwell, Bart., Keir *Edward Meldrum, Esq., Bathgate *Graeme Reid Mercer, Esq., Ceylon Civil Service John Miller, Esq., C.E., M.P., 2 Melville Crescent *Oliver G. Miller, Esq., Panmure House, Forfarshire Dr Patrick Miller, The Grove, Mount Radford, Exeter *Thomas Miller, Esq., A.M., LL.D., Rector, Perth Academy 190 Rear-Admiral Sir Alexander Milne, R.N., Inveresk *Dr Arthur Mitchell, 6 Laverock Bank Villas Joseph Mitchell, Esq., C.E., Viewhill, Inverness *Dr John Moir, 52 Castle Street *Rev. James F. Montgomery, 7 Walker Street *Dr Charles Morehead, 6 Chester Street *John Muir, D.C.L., LL.D., 6 Greenhill Park Dr John Ivor Murray, Colonial Surgeon, Hong Kong Dr Sheridan Muspratt, Liverpool Robert Nasmyth, Esq., 5 Charlotte Square 200 *Hon. Lord Neaves, LL.D. (VicE-PRESIDENT), 7 Char- lotte Square *Thomas Nelson, Esq., Abden House, Prestonfield *James Nicol, Esq., Prof. Nat. Hist., Aberdeen *Hon. Lord Ormidale, 14 Moray Place *David Page, LL.D., 44 Gilmore Place Dr Richard Parnell, Melrose *Dr Alexander Peddie, 15 Rutland Street 170 180 1868 1869 1849 1859 1834 1852 1865 1849 1863 1827 1850 1869 1865 1836 1818 1840 1859 1832 1860 1862 1852 1837 1859 1869 1863 1864 1849 1846 1853 1840 1864 1834 1844 1829 1859 1868 1837 1839 1863 1866 1855 1846 1866 1850 1843 1847 1844 1868 ( 749 *John Dick Peddie, Esq., Architect, 33 Buckingham Terrace John Pender, Esq., Manchester ‘ *W. Pirrie, Esq., Professor of Surgery, Marischal College, ' Aberdeen. 210 *Lyon Playfair, C.B., LL.D., M.P. (VICE-PRESIDENT), 4 Queensberry Place, South Kensington, London Mungo Ponton, Hsq., W.S., Clifton, Bristol Hyre B. Powell, Esq., Director of Public Instruction, Madras *James Powrie, Esq., Reswallie, Forfar *Hon. B. F, Primrose, 22 Moray Place *Samuel Raleigh, Esq., 30 George Square Very Rev. I. B. Ramsay, Lh.D., 23 Ainslie Place *W.J. M. Rankine, Esq., C.H., Prof. Civil Engineering, University, Glasgow Rev. Thos. Melville Raven, M.A., Crakehall, Bedale *Rev. Francis Redford, M.A., Silloth 220 David Rhind, Esq., Architect, 54 Great King Street William Richardson, Esq., Cheltenham Martyn J. Roberts, Hsq., Crickhowell, South Wales *George Robertson, Esq., C.H., 47 Albany Street Dr Montgomery Robertson, Mortlake, Surrey *Dr William Robertson, 28 Albany Street *Dr E. Ronalds, Bonningtor Road *Alex. James Russell, Esq., C.S., 9 Shandwick Place J. Scott Russell, Esq., 5 Westminster Chambers, Lon- don *Robert Russell, Esq., Pilmuir, Leven, Fife 230 *Dr William Rutherford, Professor of Physiology, King’s College, London *James Sanderson, Esq., Surgeon-Major, 17 Claremont Crescent *Rey. D. F. Sandford, 19 Rutland Street *Edward Sang, Esq., 2 George Street *Dr Schmitz, International Institution, London *Hugh Scott, Esq. of Gala, Galashiels Sir William Scott, Bart., Ancrum *Professor Sellar, LL.D., 15 Buckingham Terrace Dr Sharpey, Prof. Anatomy, Univ. Coll., London Sir James Y. Simpson, Bart., M.D., Prof. of Midwifery, 52 Queen Street 240 Ven. Archdeacon Sinclair, Kensington *William F. Skene, LL.D., W.S. (VicE-PRESIDENT), 20 Inverleith Row *Adam Gillies Smith, Esq., C.A., 5 Lennox Street Arch. Smith, Esq., Lincoln’s Inn, London David Smith, Esq., W.S. (TREASURER), 10 Eton Terrace *Dr John Alexander Smith, 7 West Maitland Street *Dr John Smith, 20 Charlotte Square *R. M. Smith, Esq., 4 Bellevue Crescent *Professor Piazzi Smyth, 1 Hillside Crescent *Professor Spence, 21 Ainslie Place 250 *Dr James Stark, 21 Rutland Street Henry Stephens, Esq., Red Braes Cottage, Bonnington *Moses Steven, Esq. of Bellahouston, 12 Manor Place David Stevenson, Esq., C.E., 25 Royal Terrace *John J. Stevenson, Esq., Glasgow ) 1848 1858 1868 1869 1866 1848 1823 1848 1844 1830 1854 1861 1846 1840 1843 1866 1842 1863 1864 1847 1849 1855 1822 1867 1861 1849 1867 1869 1864 1829 1864 . 1853 1866 1866 1862 1840 1869 1868 1858 1834 1847 1863 1864 1864 1855 1864 1861 1863 *Thomas Stevenson, Hsq., C.E., 17 Heriot Row *Rey. Dr Stevenson, Prof. Eccl. Hist., 37 Royal Terrace Major J. H. M. Shaw Stewart, Royal Engineers, Madras *John L. Douglas Stewart, Esq. of Nateby Hall, 13 Coates Crescent *Dr T. Grainger Stewart, 32 Queen Street 260 *Patrick James Stirling, Esq., LL.D., Kippendavie House Captain T. D. Stuart, H.M.I.S. *William Swan, Esq., Professor of Natural Philosophy, St Andrews Archibald Campbell Swinton, Esq., Kimmerghame James Syme, D.C.L., Millbank House, Canaan Dr John Addington Symonds, Clifton, Bristol : *Professor P. Guthrie Tait, M.A. (SECRETARY), 17 Drum- mond Place Dr Taylor, Pau, France Right Rev. Bishop Terrot, 9 Carlton Street Dr Allen Thomson, Prof. Anatomy, Univ., Glasgow 270 *Dr Fraser Thomson, Perth James Thomson, Esq., C.E., Norfolk Square, Hyde Park London *Dr Murray Thomson, Roorkee, Kast Indies *R. W. Thomson, Esq., C.E., 3 Moray Place *Sir William Thomson, Prof. Nat. Phil. (VicE-PRE- SIDENT), Glasgow *William Thomas Thomson, Esq., Bonaly *Dr Wyville Thomson, Prof. Nat. Hist. and Geology Belfast Sir W. C. Trevelyan, Bart., Wallington, Morpeth *William Turnbull, Hsq., 14 Lansdowne Crescent *Professor Turner, M.B. (SECRETARY), 6 Kton Terrace 280 *Most Noble the Marquis of Tweeddale, K.T., Yester House, Haddington *Peter Waddell, Hsq., Claremont Park, Leith *Viscount Walden, Yester House, Haddington *Arthur Abney Walker, Esq., 32 Melville Street James Walker, Esq., W.S., Tunbridge Wells *William Wallace, Ph. D., Glasgow Dr James Watson, Bath *John K. Watson, Hsq., 14 Blackford Road *Dr Patrick Heron Watson, 16 Charlotte Square *Rev. Robt. Boog Watson, Madeira, 4 Bruntsfield Place Edinburgh 290 Allan A. Maconochie Welwood, Esq. of Meadowbank and Pitliver *Captain T. P. White, Royal Engineers, 1 Drummond Place *W. Williams, Esq., Veterinary College, Clyde Street *Dr Thomas Williamson, 28 Charlotte Street, Leith Dr Isaac Wilson Professor John Wilson, College *Dr J. G. Wilson, 9 Woodside Crescent, Glasgow *Dr Alexander Wood, 10 St Colme Street *Dr Andrew Wood, 9 Darnaway Street Dr Wright, Cheltenham 300 *Robert S. Wyld, Esq., W.S., 19 Inverleith Row *James Young, Esq., Limefield, Mid-Calder *Dr John Young, Professor of Natural History, Glas- gow 303 Fellows elected between the commencement of the Session and the 1st January of the following year are entered under the latter date, by which their Subscriptions are regulated :—Thus, Fellows elected in December 1867 have the date of 1868 prejixed to their names. VOL. XXV. PART II. 91 ( 0} LIST OF THE PRESENT ORDINARY MEMBERS, Corrected up to November 1, 1869. IN THE ORDER OF THEIR ELECTION. PRESIDENT. Dr CHRISTISON. HONORARY VICE-PRESIDENT, HAVING FILLED THE OFFICE OF PRESIDENT His Grace tHE DUKE OF ARGYLL, K.T. Date of Election. 1818 Patrick Miller, M.D., The Grove, Mount Radford, Exeter. 1820 Charles Babbage, Esq., F.R.S., Lond. Sir John F. W. Herschel, Bart., F.R.S., Lond. William Macdonald, M.D., F.R.C.P.E., Professor of Natural History, St Andrews. 1822 Sir W. C. Trevelyan, Bart., Wallington, Northumberland. 1823 Captain Thomas David Stuart, of the Hon. East India Company's Service. Warren Hastings Anderson, Esq. Liscombe John Curtis, Esq., Ingsdon-House, Devonshire. Robert Christison, M.D., Professor of Materia Medica. 1824 Robert E. Grant, M.D., Professor of Comparative Anatomy, University College, London. 1827 Very Rev. Edward Bannerman Ramsay, M.A. Camb., LL.D. 1828 John Forster, Esq., Architect, Liverpool. David Milne Home, Esq., Advocate, of Milne-Graden and Wedderburn. 1829 A. Colyar, Esq. Right Hon. Sir William Gibson-Craig, Bart. ef Riccarton, Right Hon. Lord Colonsay. Venerable Archdeacon Sinclair, Kensington. James Walker, Esq., W.S. 1830 J. T. Gibson-Craig, Esq., W.S. James Syme, D.C.L. Oxon., M.D. Dub., M.D. Bonn. Thomas Barnes, M.D., Cavlisle. 1832 Montgomery Robertson, M.D. 1833 Rear-Admiral Sir Alexander Milne, R.N. His Grace the Duke of Buccleuch, K.G., Dalkeith Palace. Alexander Hamilton, LL.B., WS. Date of Election. 1834 1835 1836 1837 1839 1840 1841 1842 1843 1844 1845 1846 LIST OF ORDINARY MEMBERS. 751 Mungo Ponton, Esq., W.S., Clifton, Bristol. Isaac Wilson, M.D., F.R.S., Lond. William Sharpey, M.D., LL.D., F.R.S., Professor of Anatomy, University College, London. John Hutton Balfour, A.M., M.D., F.R.S., Professor of Medicine and Botany. William Brown, Esq., F.R.C.S.E. David Rhind, Esq., Architect. John Scott Russell, A.M., London. Archibald Smith, M.A., Camb., F.R.S., Lincoln’s Inn, London. Richard Parnell, M.D. Peter D. Handyside, M.D., F.R.C.S.E. David Smith, Esq., W.S. Adam Hunter, M.D., F.R.C.S.E. Rev. Philip Kelland, A.M., F.B.S., Professor of Mathematics. Francis Brown Douglas, Esq., Advocate. Alan A. Maconochie Welwood, Esq., of Meadowbank and Pitliver. Martyn J. Roberts, Esq., Crickhowell, South Wales. Robert Chambers, LL.D. Sir John M‘Neill, G.C.B., LL.D. Sir William Scott, Bart., of Ancrum. Right Rev. Bishop Terrot. Edward J. Jackson, Esq. James Mackenzie, Esq. John Miller, Esq., of Leithen. James Dalmahoy, Esq. James Thomson, Esq., Civil Engineer, London. Robert Nasmyth, Esq., F.R.C.S.E. A. D. Maclagan, M.D., Professor of Medical J: urisprudence. John Rose Cormack, M.D., F.R.C.P.E., 7 Rue d’ Aguesseau, Paris. Allen Thomson, M.D., F.R.S., Professor of Anatomy, Glasgow. Joseph Mitchell, Esq., Civil Engineer, Viewhill, Inverness. Andrew Coventry, Esq., Advocate. John Hughes Bennett, M.D., Professor of Physiology. D. Balfour, Esq., of Trenaby. Henry Stephens, Esq. Archibald Campbell Swinton, Esq., of Kimmerghame. Sir James Y. Simpson, Bart., M.D., Professor of Midwifery. David Stevenson, Esq., Civil Engineer. Thomas R. Colledge, M.D., F.R.C.P.E. Thomas Anderson, M.D., Professor of Chemistry, Glasgow. A. Taylor, M.D., Pau. Alexander J, Adie, Esq., Civil Engineer. L. D. B. Gordon, Esq., C.E., London. L. Schmitz, LL.D., Ph.D., International Institution, London. Charles Piazzi Smyth, Esq., F.R.S., Professor of Practical Astronomy. (oe LIST OF ORDINARY MEMBERS. Date of Election. 1847 Sir William Thomson, M.A. Camb., LL.D., F.R.S., Professor of Natural Philosophy, Glasgow. John Hill Burton, LL.D., Advocate. James Nicol, Esq., Professor of Natural History, Aberdeen. William Macdonald Macdonald, Esq., of St Martins. John Wilson, Esq., Professor of Agriculture. Moses Stephen, Esq., of Bellahouston. 1848 Thomas Stevenson, Esq., C.E. James Allan, M.D., Inspector of Hospitals, Portsmouth. Henry Davidson, Esq. William Swan, Esq., Professor of Natural Philosophy, St Andrews. Patrick James Stirling, Esq. 1849 Sir William Stirling-Maxwell, Bart., of Keir and Pollok. William Thomas Thomson, Esq. W. H. Lowe, M.D., F.R.C.P.E., Balgreen. Honourable Bouverie F. Primrose. David Anderson, Esq., of Moredun. W. BR. Pirrie, M.D., Professor of Surgery, Aberdeen. His Grace the Duke of Argyll, K.T., Inverary Castle. The Most Noble the Marquis of Tweeddale, K.T., Yester House. Edward Sang, Esq. 1850 William John Macquorn Rankine, LL.D., F.R.S., Professor of Civil Engineering, University, Glasgow. Alexander Keith Johnston, LL.D. Sheridan Muspratt, M.D., Liverpool. James Stark, M D., F.R.C.P.E. (Re-admitted.) Lieutenant-Colonel W. Driscoll Gossett, R.E. Hugh Blackburn, Esq., Professor of Mathematics, Glasgow. James Scarth Combe, M.D., F.R.C.S.E. 1851 Sir David Dundas, Bart., of Dunira. E. W. Dallas, Esq. Rev. James Grant, D.D., D.C.L., one of the Ministers of Edinburgh. 1852 Eyre B, Powell, Esq., Madras. : Thomas Miller, A.M., LL.D., Rector, Perth Academy. James Cunningham, Esq., W.S. Alexander James Russell, Esq., C.S. Andrew Fleming, M.D., Bengal. 1853 James Watson, M.D., Bath. Lieutenant-Colonel Robert Maclagan, Bengal Enginecrs. Rev. John Cumming, D.D., London. Hugh Scott, Esq., of Gala. Greme Reid Mercer, Esq. 1854 John Addington Symonds, M.D., Clifton, Bristol. Robert Harkness, Esq., Professor of Mineralogy and Geology, Queen’s College, Cork. Sir James Coxe, M.D., F.R.C.P.E. LIST OF ORDINARY MEMBERS. 753 Date of Election. 1854 Ernest Bonar, Esq. 1855 Stevenson Macadain, Ph.D. Robert Etheridge, Esq., Clifton, Bristol. Right Honourable John Inglis, D.C.L., LL.D., Lord Justice-General. Wyville T. C. Thomson, LL.D., Professor of Geology, Belfast. Thomas Wright, M.D., Cheltenham. James Hay, Esq. R. M. Smith, Esq. 1856 David Bryce, Esq. William Mitchell Ellis, Esq. George J. Allman, M.D., F.R.S., Professor of Natural History. Honourable Lord Neaves, LL D. Thomas Laycock, M.D., Professor of the Practice of Medicine. Thomas Cleghorn, Esq., Advocate, Sheriff of Argyleshire. James Clerk Maxwell, Esq., F.R.S., Jate Professor of Natural Philosophy, King’s College, London. 1857 John Ivor Murray, M D., F.R.C.S.E., Colonial Surgeon, Hong Kong. John Blackwood, Esq. W. M. Buchanan, M.D. Thomas Login, Esq., C.E. : Edmund C, Batten, M.A., Lincoln’s Inn, London. 1858 Thomas Williamson, M.D., F.R.C.S.E., Leith. Robert B. Malcolm, M.D., F.R.C.P.%. Frederick Field, Esq., Chili. James Leslie, Esq., C.E. Cosmo Innes, Esq., Professor of History. Alexander Campbell Fraser, M.A., Professor of Logic. Rey. William Stevenson, D.D., Professor of Ecclesiastical History. 1859 William F. Skene, LL.D. G. W. Hay, Esq., of Whiterigg. Robert Russell, Esq. Joseph Fayrer, M.D., F.R.C.S.E., Professor of Surgery, Calcutta. George Robertson, Esq., C.E. Lyon Playfair, C.B., Ph.D., F.R.S., M.P., 4 Queensberry Place, South Kensington, London, W. John Brown, M.D., F.R.C.P.E. Rev. John Duns, D.D. Lieut. John Hills, Bombay Engineers. Major James George Forlong. 1860 William Robertson, M.D., F.R.C.P.E. Frederick Guthrie, M.D., Professor of Physics, School of Mines, London. George A. Jamieson, Esq. Patrick Dudgeon, Esq., of Cargen. William Chambers, Esq., of Glenormiston. 1861 W. A. F. Browne, Esq., F.R.C.S.E., one of H.M. Commissioners in Lunacy for Scotland. Rev. Thomas Brown, VOL. XXV. PART II. 9K 754 LIST OF ORDINARY MEMBERS. Date of Election. 1861 James M‘Bain, M.D., R.N. Peter Guthrie Tait, A.M., Professor of Natural Philosophy. John Muir, D.C.L., LL.D. William Turner, M.B., Professor of Anatomy. William Lauder Lindsay, M.D. James Lorimer, A.M., Professor of Public Law. Archibald Geikie, Esq., F.R 8., Director of the Geological Survey, Scotland. George Berry, Esq. James Young, Esq. 1862 Rey. William G. Blaikie, D.D. Edmund Ronalds, Ph.D. Thomas C. Archer, Esq , Director of Museum of Science and Art. James Hector, M.D. Nicholas Alexander Dalzell, A.M. Hon. Lord Barcaple, LL.D. Rev. Robert Boog Watson, Madeira. 1863 H. F. C. Cleghorn, M.D., Stravithy, St Andrews. John Stuart Blackie, Esq., Professor of Greek. Edward Meldrum, Esq. Charles Lawson, Esq., of Borthwick Hall. Alexander Peddie, M.D., F.R.C.P.E. William Jameson, Esq., Surgeon-Major, Saharunpore. Murray Thomson, M.D., Roorkee, India. John Young, M.D., Professor of Natural History, University of Glasgow. David Page, LL D. J. G. Wilson, M.D., F.R.C.S.E. J. Matthews Duncan, M.D., F.R.C.P.E. W. Dittmar, Esq. Honourable Lord Ormidale. Joseph D. Everett, D.C L., Professor of Natural Philosophy, Queen’s College, Belfast. — Honourable G. Waldegrave Leslie. Honourable Charles Baillie, Lord Jerviswoode. James Sanderson, Esq., Surgeon-Major. Charles Cowan, Esq. John Alexander Smith, M.D., F.R.C.P.E. 1864 Alex. Crum Brown, M.D., D.Se., Professor of Chemistry. Alex. Wood, M.D., F.R.C.P.E. Andrew Wood, M.D., F.R.C.S.E. . Robert William Thomson, Esq., C.E. James David Marwick, Esq. ; Rev.. Daniel F. Sandford. Robert 8. Wyld, Esq., W.S. Peter M‘Lagan, Esq , of Pumpherston, M.P. William Lindsay, Esq. Date of Election. 1864 1865 1866 1867 LIST OF ORDINARY MEMBERS. W. Y. Sellar, M.A., Professor of Humanity. Robert Hutchison, Esq., Carlowrie Castle. Rev. John Hannah, D.D., Glenalmond. William Wallace, Ph.D. Arthur Abney Walker, Esq. John Foulerton, M.D., F.R.C.S.E., Manila. Alfred R. Catton, M.A., Camb. Rey. Francis Redford, M.A., Rector of Silloth. John Moir, M.D., F.R.C.P.E. James Powrie, Esq., of Reswallie, Forfar. Charles Jenner, Esq. ; Charles Lawson, jun., Esq. Alexander Keiller, M.D., F.R.C.P.E. William Euing, Esq. Fraser Thomson, M.D., Perth. John M‘Culloch, Esq. T. Grainger Stewart, M.D., F.R.C.P.E. Colonel Sir James E. Alexander, of Westerton. Charles Morehead, M.D. David Masson, M.A., Professor of Rhetoric and English Literature. David Douglas, Esq. John Macnair, Esq. James Spence, Esq., F.R.C.S.E., Professor of Surgery. Thomas Nelson, Esq. Adam Black, Esq. Thomas Constable, Esq. James Dunsmure, M.D., F.R.C.S.E. Arthur Mitchell, M.D. Patrick Heron Watson, M.D., F.R.C.S.E. John Smith, M.D., F.R.C.P.E. James Falshaw, Esq., C.E. John K. Watson, Esq. David Chalmers, Esq. T. B. Johnston, Esq. George F. Barbour, Esq., of Bonskeid. David Davidson, Esq. Peter Waddell, Esq. Sir George Harvey. George Stirling Home Drummond, Esq., of Blair-Drummond. Frederick Fuller, Professor of Mathematics, Aberdeen. Andrew Graham, M.D., B.N. William Turnbull, Esq. Archibald Hamilton Bryce, D.C.L., LL.D. Francis Deas, LL.B., Advocate. 756 LIST OF ORDINARY MEMBERS. Date of Election. 1867 Arthur Gamgee, M.D. Sheriff Hallard. Thomas R. Fraser, M.D. Thomas Annandale, Esq., F.R.C.S.E. D. R. Haldane, M.D., F.R.C.P.E. John M. M‘Candlish, Esq. James Donaldson, LL.D., Rector of the High School James Richardson, Hsq. James H. B. Hallen, Esq., India. Henry Dircks, Esq., C.E., London. Charles Gayner, M.D., Oxford. William Keddie, Esq., Glasgow. P Rev. W. Lindsay Alexander, D.D. 1868 John F. M‘Lennan, Esq., Advocate. ‘Robert Daun, M.D. (Re-admitted.) Rev. David Aitken, D.D. ; Robert M. Ferguson, Ph.D. = J. W. Laidlay, Esq., of Seacliff. ; W. Williams, Esq., Veterinary College. J. Samson Gamgee, Esq., Birmingham. Rev. D. T. K. Drummond, B.A. Oxon. Rev. Joseph Taylor Goodsir, Major J. H. M. Shaw Stewart, Royal Engineers, Madras. John J. Stevenson, Esq. Rey. James F. Montgomery. John Dick Peddie, Esq., Architect. Colonel Seaton Guthrie. Samuel Raleigh, Esq. Thomas Smith Maccall, M.D., Polmont. Rev. Thomas Guthrie, D.D. Thomas Key, Esq. Adam Gillies Smith, Esq., C.A. John Macmillan, M.A. 1869 Oliver G. Miller, Esq. John Leveson Douglas Stewart, Esq., of Nateby Hall. Alexander Buchan, Esq. H. C. Fleeming Jenkin, Esq., Professor of Engineering. William Dickson, Esq. ; John Pender, Esq., Manchester. Isaac Anderson-Henry, Esq., of Woodend. George Elder, Esq., Knock Castle, Wemyss Bay. Sir Charles A. Hartley, C.E., Sulina, Mouth of the Danube. David MacGibbon, Esq., Architect. Rev. Thomas Melville Raven, M.A., Crakehall, Bedale. “I LIST OF ORDINARY MEMBERS. Date of Election. 1869 Alexander Howe, Esq., W.S. Viscount Walden, Yester House. Alexander Dickson, M.D., Professor of Botany, University of Glasgow. William C. M‘Intosh, M.D., Murthly. Henry Marshall, M.D., Clifton, Bristol. William Rutherford, M.D., Professor of Physiology, King’s College, London, R. Craig Maclagan, M.D. James Dewar, Esq. Rev. Henry Calderwood, LL.D., Professor of Moral Philosophy. Sir Alexander Grant, Bart., LL.D., Principal of the University of Edinburgh. Captain T. P. White, Royal Engineers. John Wilson Johnston, M.D., India. Robert Henry Bow, Esq., C.H. Maurice Lothian, Esq., of St Catherine’s. John M‘Laren, Esq., Advocate. VOL. XXY. PART II. Oats 10 15 20 ) NON-RESIDENT MEMBER, ELECTED UNDER THE OLD LAWS. Sir Richard Griffiths, Bart., Dublin. LIST OF HONORARY FELLOWS. His Royal Highness the Prince of Wales. FOREIGNERS (LIMITED TO THIRTY-SIX.) Louis Agassiz, J.B. A. L. Léonce Elie de Beaumont, Robert Wilhelm Bunsen, Michel Eugene Chevreul, James D. Dana, LL.D., Jean Baptiste Dumas, Charles Dupin, Christian Gottfried Ehrenberg, Elias Fries, Frangois Pierre Guillaume Guizot, Wilhelm Karl Haidinger, Christopher Hansteen, Hermann Helmholtz, Gustav Robert Kirchhoff, Albert Kolliker, Johann von Lamont, Richard Lepsius, Rudolph Leuckart, Urbain Jean Joseph Leverrier, Baron Justus von Liebig, Henry Milne-Edwards, Theodore Mommsen, Prof, Benjamin Peirce, Cambridge, Massachusetts. Paris. Heidelberg. Paris. Newhaven, Connecticut. Paris. Do. Berlin. Upsala. Paris. Vienna. Christiania. Heidelberg. Do. Wurzburg. Munich. Berlin. Leipzig. Paris. Munich. Paris. Berlin. United States Survey. 25 30 34 10 15 19 LIST OF HONORARY Adolphe Pictet, Lambert Adolphe Jacques Quetelet, M. Le Comte De Remusat, Henri Victor Regnault, Auguste De la Rive, Gustav Rose, Angelo Secchi, Karl Theodor von Siebold, Bernard Studer, Rudolph Virchow, Friedrich Wohler, FELLOWS. 759 Geneva. Brussels. Paris. Do. Geneva. Berlin. Rome. Munich. Berne. Berlin. Gottingen. BRITISH SUBJECTS (LIMITED TO TWENTY BY LAW X.) John Couch Adams, Esq., George Biddell Airy, Esq., Thomas Carlyle, Esq., Arthur Cayley, Esq., Charles Darwin, Esq., Cambridge. Greenwich. London. Cambridge. Down, Bromley, Kent. Sir John Frederick William Herschel, Bart., Collingwood. James Prescott Joule, LL D., William Lassell, Esq., Rev. Dr Humphrey Lloyd, Sir William E. Logan, Sir Charles Lyell, Bart., John Stuart Mill, Esq., Sir Roderick Impey Murchison, Richard Owen, Esq., Lieut.-General Edward Sabine, R.A., George Gabriel Stokes, Esq., William Henry Fox Talbot, Esq., Alfred Tennyson, Esq., Sir Charles Wheatstone, D.C.L., Clifpoint, Higher Broughton, Manchester. Liverpool. Dublin. London. Do. Cambridge. Lacock Abbey, Wiltshire, Freshwater, Isle of Wight. London. ( 760 ) LIST OF FELLOWS DECEASED AND RESIGNED, FROM NOVEMBER 1867 TO NOVEMBER 1869. HONORARY FELLOWS DECEASED (FOREIGN). Marie Jean Pierre Flourens, Paris. Jean Bernard Leon Foucault, Paris. Carl Friedrich Philip von Martius, Munich. Christian Friedrich Schénbein, Basle. HONORARY FELLOWS DECEASED (BRITISH). Thomas Graham, Esq. Earl of Rosse. ORDINARY FELLOWS DECEASED. James Anstruther, Esq., W.S. Professor G. A. Walker-Arnott. James Begbie, M.D. . William Brand, Esq., W.S. = Sir David Brewster. John Burt, M.D. Henry Cheyne, Esq., W.S. Right Honourable Sir George Clerk, Bart. Allan Dalzell, M.D. John Davy, M.D. Right Honourable Lord Dunfermline. Robert Dyce, M.D., Professor of Midwifery, Aberdeen. Principal James David Forbes, St Andrews. Robert Hamilton, M.D. William Bird Herapath, M.D. ‘Rev. Professor Robert Lee, D.D. Professor Patrick C. Macdougall. Patrick B. Mure Maeredie, Esq., Advocate. Thomas Mansfield, Esq., Accountant. Dr Manson, Nottingham. Robert Mayne, Esq., Indian Civil Service. Rev. William Muir, D.D. LIST OF FELLOWS DECEASED AND RESIGNED. VOL. XXV. PART II. Dr Frederick Penny. James Richardson, Esq. William Seller, M.D. Sir James South. Alexander Thomson, Esq. of Banchory. James Wardrop, Esq. ORDINARY FELLOWS RESIGNED. Robert Campbell, Esq., Advocate. Alexander A. Eugene Mackay, M.D. Right Rev. Bishop Morrell. Rev. Leonard Shafto Orde. 761 ( 762 ) The following Public Institutions and Individuals are entitled to receive Copies of the Transactions and Proceedings of the Royal Society of Edinburgh :— . ENGLAND. The British Museum. The Bodleian Library, Oxford. The University Library, Cambridge. The Royal Society. The Linnean Society. The Society for the Encouragement of Arts. The Geological Society. The Royal Astronomical Society. The Royal Asiatic Society. The Zoological Society. The Royal Society of Literature. The Royal Horticultural Society. The Royal Institution. The Royal Geographical Society. The Statistical Society. The Institution of Civil Engineers. The Institute of British Architects. The Hydrographical Office, Admiralty. The Medico-Chirurgical Society. The Atheneum Club. The Cambridge Philosophical Society. The Manchester Literary and Philosophical Society. The Yorkshire Philosophical Society. The Chemical Society of London. ‘The Museum of Economic Geology. The United Service Institution. The Royal Observatory, Greenwich. The Leeds Philosophical and Literary Society. The Historic Society of Lancashire and Cheshire. The Royal College of Surgeons of England. SCOTLAND. Edinburgh, University Library. Advocates’ Library. College of Physicians. Edinburgh, Highland and Agricultural Society. Royal Medical Society. Royal Physical Society. Royal Scottish Society of Arts. Glasgow, University Library. St Andrews, University Library. Aberdeen, University Library. IRELAND. The Library of Trinity College, Dublin. The Royal Irish Academy. = ; COLONIES, &e, The Asiatic Society of Calcutta. Library of Geological Survey, Calcutta. The Literary and Historical Society of Toronto. University of Sydney. CONTINENT OF EUROPE. Amsterdam, Royal Institute of Holland. Berlin, Royal Academy of Sciences. Physical Society, Berne, Society of Swiss Naturalists. Bologna, Academy of Sciences. Bonn, Cesarean Academy of Naturalists. Bourdeaux, Society of Physical and Natural Sciences. Brussels, Royal Academy of Sciences. Buda, Literary Society of Hungary. Copenhagen, Royal Academy of Sciences. Frankfort, the Senkenbergian Museum. Geneva, Natural History Society. Giessen, University Library. Gottingen, University Library. Haarlem, Natural History Society. Jena, D. Gegerbaum, Editor of Zeitschrift Medi- cinisch-Physikalisch Gesellschaft. Leipzig, Royal Saxon Academy. Lille, Royal Society of Sciences. Lisbon, Royal Academy of Sciences. Lyons, Agricultural Society. Milan, Royal Institute. Moscow, Imperial Academy of Naturalists. Munich, Royal Academy of Sciences of Bavaria (2 copies). Neufchatel, Museum of Natural History. Paris, Royal Academy of Sciences. Geographical Society. Royal Society of Agriculture. Society for Encouragement of Industry. Geological Society of France. Ecole des Mines. Marine Depot. ... Museum of Jardin des Plantes. Rotterdam, Batavian Society of Experimental Philosophy. St Petersburg, Imperial Academy of Sciences. Archeological Society. Pulkowa Observatory. Stockholm, Royal Academy of Sciences. Turin, Royal Academy of Sciences. 763+) Turin, M.-Michelotti. Upsala, Society of Sciences. Venice, Royal Institute. Vienna, Imperial Academy of Sciences. Geological Society. Geologico-Botanical Society. UNITED STATES OF AMERICA. Boston, the Bowditch Library. Academy of Arts and Sciences. Society of Natural History. New York, State Library. Philadelphia, American Philosophical Society. Academy of Natural Sciences. Washington, the Smithsonian Institution. Observatory. Yale College, United States. (All the Honorary and Ordinary Fellows of the Society are entitled to the Transactions and Proceedings.) The following Institutions and Individuals receive the Proceedings only :— ENGLAND. The Scarborough Philosophical Society. The Whitby Philosophical Society. The Newcastle Philosophical Society. The Geological Society of Cornwall. The Ashmolean Society of Oxford. The Literary and Philosophical Society of Liver- pool. Meteorological Office, 116 Victoria Street, London, SCOTLAND. The Philosophical Society of Glasgow. The Botanical Society of Edinburgh. The Geological Society of Edinburgh. The Meteorological Society of Edinburgh. IRELAND, The Natural History Society of Dublin. COLONIES, * The Literary and Philosophical Society of Quebec. The Library of the Geological Survey, Canada. The Literary Society of Madras. China Branch of Asiatic Society, Hongkong, North China Branch of the Royal Asiatic Society, Shanghae. The Royal Society of Victoria. CONTINENT OF EUROPE. Utrecht, the Literary and Philosophical Society. Paris, Editor of L’Institut. Cherbourg, Society of Natural Sciences. Sicily, Catania, Academia Govenia de Scienze Naturali. UNITED STATES. H. T. Parker, Esq., Harvard College, Cambridge. Peabody Academy of Science, Salem, Massachu- setts, LIST OF DONATIONS. (Continued from Vol. XXTY. p. 830.) DONATIONS. DONORS. TRANSACTIONS AND PROCEEDINGS OF SociETIES, ACADEMIES, UNIVERSITIES, &c.— Amsterdam.—Catalogus van de Boekerij der Koninklijke Akademie van The Academy. Wettenschappen gevestigd. Deel ii. Stuk 2. 8vo. Jaarboek van der Koninklijke Akademie van Wettenschappen gevestigd. Ditto. 1866, 1867. 8vo, Processen-verbaal van de gewone vergaderingen der Koninklijke Ditto. Akademie van Wettenschappen, van Mei 1867 tot en met April 1868. 8vo. Verhandelingen der Koninklijke Akademie van Wettenschappen. Ditto. Deel xi. 4to. Verslagen en Mededeelingen der Koninklijke Akademie van Wetten- Ditto. schappen. Natuurkunde, Deel i1.; Letterkunde, Deel x. xi. 8vo. Rapport fait 4 l’Académie Royale des Sciences des Pays-Bas, Section Ditto. Physique. 8vo. Baltimore.— Peabody Institute of the city of Baltimore. History of The Institute. Baltimore. 1868. 8vo. Basle.—Festschrift herausgegeben von der Naturforschenden Gesellschaft The Society. in Basel zur der fiinfzigjahrigen Bestchens, 1867. 8vo. Verhandlungen der Naturforschenden Gesellschaft in Basel. Theil Ditto. iniy., v. Heft 1. 8vo. ; Berlin,—Abhandlungen der Kéniglichen Akademie der Wissenschaften. ‘The Academy. 1866, 1867. 4to. Monatsbericht der K6nigliche Preussischen Akademie der Wissen- Ditto. schaften. March—December, 1868; January, February, 1869. 8vo. Die Fortschritte der Physik in Jahre 1865, dargestellt von der The Society. Physikalischen Gesellschaft zu Berlin. Jahrgang xxi. Abth. 1, 2. 8vo. Berne.—Beitraege zur Geologischen Karte der Schweiz herausgegeben von The Natural His- der Geologischen Commission der Schweizerischen Naturforschen- tory Society of den-Gesellschaft auf rosten der Hidgenossenschaft. Lieferung, Berne. 3-5. 4to, Mittheilungen der Naturforschenden Gesellschaft in Bern, No. Ditto. 603-653. 8vo. Matériaux pour la Carte Géologique de la Suisse. Liv. 6e. 4to. Ditto. Bombay.—Journal of the Bombay Branch of the Royal Asiatic Society. The Society. No, 24. 8vo. Meteorological and Magnetical Observations made at the Government The Observatory. Observatory, Bombay, in the year 1864. 4to. Boston.—Bulletin of the Public Library. Nos, 8 and 9. 8vo. The Library. Sixteenth Annual Report of the Trustees of the Public Library, Ditto. 1868. 8vo. Annual of the Boston Society of Natural History, 1868-69. 8vo. The Society. VOL. XXV, PART II. IN 766 LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND PRocEEDINGS OF SocIETIEs, &c.—continued. Conditions and Doings of the Boston Society of Natural History for 1866-67, 1867-68. 8vo. Memoirs read before the Boston Society of Natural History, Vol. i, Parts 1-3, 4to. Proceedings of the Boston Society of Natural History. Vols. x., xi. 8vo. Bourdeaux.—Mémoires de la Société des Sciences Physiques et Naturelles de Bourdeaux. Tomes iv., v., vi. 1,2. 8vo. Bremen.—Abhandlungen herausgegeben von Naturwissenschaftlichen Vereine zu Bremen, Bandi. Heft 1-3. 8vo. Brussels—Mémoires couronnés et autres Mémoires. 8vo. Mémoires couronnés et Mémoires des Savants étrangers publiées par lAcadémie Royale Belgique. Tome xxxilil. 4to, Mémoires de l’Académie Royale des Sciences, des Lettres, et des . Beaux-Arts de Belgique. Tomes xxxvi.,xxxvil. 4to. Bulletin de Académie Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique. Tomes xxiii, xxiv., Xxv., Xxvi., XXVii. Nos. 1, 2, 3,4. Svo. Biographie Nationale publiée par l’Académie Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique. Tome i. Partie 2; Tome ii, Parties 1, 2. 8vo. Tables Générales et Analytiques du receuil des Bulletins de l’Académie Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique. Tomes i.—xx. 8vo. Annuaire de Académie Royale des Scierces, des Lettres, et des Beaux-Arts de Belgique. 1867, 1868-69. 12mo. Annales de l’Observatoire Royale de Bruxelles publiées aux frais de lV Etat, par le directeur A. Quetelet. Tomes xvii, xviii. 4to. Annuaire de lObservatoire Royale de Bruxelles, par A. Quetelet. 1869. 12mo. Cadiz.—Almanaque Nautico para 1869, 1870, calculado de orden de S. M. en el Observatorio de Marina de la Ciudad de San Fer- Tomes xix., xx. nando. 8vo. Caleutta.—Proceedings of the Asiatic Socicty of Bengal. 1867, 1868, No. 1, 1869. 8vo. Journal of the Asiatic Society of Bengal. Part i., Part ii., 1867-69. Extra No. 8vo. Do. Index. Vols. xxxv., xxxvi. 8vo. Memoirs of the Geological Survey of India. Paleontologia, v. Pts. 1-4, 4to. Memoirs of the Geological Survey of India. Vol. vi. Pts. 1 and 2. 8vo. Annual Report of the Geological Survey of India, and of the Museum of Geology, for 1866-67. 8vo. Catalogue of the Meteorites in the Museum of the Geological Survey of India. 8vo. Cambridge.—Transactions of the Philosophical Society. Vol. x. Part 1; Vol. x. Part 2, 4to. Cambridge (U.S.)—Memoirs of the American Academy of Arts and Sciences, Vol. ix. Part 1. 4to., Proceedings of the American Academy of Arts and Sciences. vil. 8vo, Proceedings of the American Association for the Advancement of Science. 15th Meeting. 8vo. Catania,—Atti dell’ Accademia Gioenia di Scienze Naturali. 1867. 4to. Vol. Tomo 1. DONORS. The Society. Ditto. Ditto. The Society. The Society. Royal Academy. Ditto. Ditto. Ditto. Ditto. Ditto, Ditto. The Observatory. Ditto. The Observatory. The Society. Ditto. Ditto. The Survey. Ditto. Ditto. Ditto. The Society. The Academy. Ditto. The Association. The Academy. LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND PROCEEDINGS OF SocIETIES, &c,—continued. Christiania —Meteorologiske Iagttagelser paa fem Telegrafstationer ved Norges Kyst. 1866. 4to. Meteorologiske Iagttagelser paa Christiania Observatorium, 1865-66. 4to. Meteorologiske Iagttagelser det Sydlige Norge. 1863-66. 4to. Meteorologische Beobachtungen an der Kéniglichen Universitits- Sternwarte zu Christiania. 1837-63, 4to. Norske Universitets-og Skole-Annaler udgivne af Universitetes Seeretair. Jan., Aug., Oct. 1866; March 1867; Feb., March 1868. 8vo. Det Kongelige Norste Frederiks Universitets Aarsberetning, for 1864-67. 8vo. Nyt Magazin fur Naturvidenskaberne. Bind xiv. Hefte 2-4; Bind xv. Heft 1, 2,3. 8vo. Forhandlinger i Videnskabs-Selskabet 1 Christiania, Aaret 1864, 1865, 1866, 1867. 8vo. Forslag til en Forandret Ordning af det Hoiere Skolevxsen. Deel 1., il., Wi. 8vo. Columbus (U.S.)—Twenty-first Annual Report of the Ohio State Board of Agriculture. 8vo, Connecticut—Transactions of the Connecticut Academy of Arts and Sciences. Vol. i. Parti. 8vo. Copenhagen.—Det Kongelige danske Videnskabernes Selskabs Skrifter femte rekke. Naturvidenskabeilg og Mathematiske Afdeling. Bind vii, 4to. Oversigt over det Kongelige danske Videnskabernes Selskabs, for- handlinger og dets Medlemmers Arbeider. Aaret 1865-67. 8vo. Cornwall—Journal of the Royal Institution of Cornwall, with the 49th Annual Report. No.7. 8vo. Dresden.—Novorum Actorum Academie Cesaree Leopoldino-Caroline Germanice Nature Curiosorum. Tomes xxxii., xxxiv. 4to. Dublin—Journal of the Royal Geological Society of Ireland. Vol. i. Part 3. 8vo. Journal of the Royal Dublin Society. Nos. 36, 87. 8vo. Edinburgh.—Transactions of the Botanical Society, Edinburgh. 8vo Transactions of the Highland and Agricultural Society of Scotland. Vol ii. Parts 1, 2 (Fourth Series). 8vo. Proceedings of the Royal Physical Society for Sessions 1862-63, 1863-64, 1864-65, 1865-66. 8vo, Transactions of the Royal Scottish Society of Arts. 4,5. 8vo. Transactions of the Edinburgh Geological Society. Vol.i. Parts 1, 2. 8vo. Journal of the Scottish Meteorological Society. New Series. 15-20. 8vo. Conference on Technical Education, held at Edinburgh, 20th March 1868. 8vo. Forty-first Annual Report of the Royal Scottish Academy. 1868. 8vo. Florence.—Memorie della Societa Italiana delle Scienze fondata da Anton- mario Lorgna. Tomei. Parte 1. 4to. Frankfort. —Abhandlungen herausgegeben von der Senckenbergischen Naturforschenden Gesellschaft. Band vi. Heft 3,4. 8vo. Tageblatt der 41 Versammlung Deutscher Naturforscher und Aerzte. 1867. 4to. Volk ix: Vol. vii. Parts 3, Nos. 767 DONORS. The Royal Obser. of Christiania. Ditto. The University of Christiania. Ditto. Ditto. Ditto. The R. Univ. of Norway. The Society. The Royal Com- mission. The Board. ‘The Academy. The Royal Aca- demy of Sciences. The Society. The Institution. The Academy. The Society. Ditto. The Society. The Society. The Society. The Society. The Society. The Society. The Conference, The Academy. The Society, The Society. Ditto, 768 LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND PROCEEDINGS OF SOCIETIES, &c.—continued. Geneva.—Mémoires de la Société de Physique et d’Histoire Naturelle de Genéve. Tome xix. Parties 1,2. 4to. Glasgow.—Proceedings of the Philosophical Society. Vol. iii. Nos. 5 and 6; Vols. iv., v., and Vol. vi., Nos. 1-4. 8vo. Transactions of the Geological Society. Vol. ii. Part 3; Vol. iii Part i. 8vo. Report of the Professor of Astronomy in the University for 1868. 8vo, Gottingen —Abhandlungen der Kéniglichen Gesellschaft der Wissenschaften. Band xiii. 4to. Nachrichten von der K. Gesellschaft der Wissenschaften und der Georg-August Universitat aus.dem Jahre 1867, 1868. 12mo. Grcenwich.—Astronomical and Magnetical and Meteorological Observa- tions made at the Royal Observatory in the year 1865. London, 1867. 4to. Haarlem.—Archives Néerlandaises des Sciences Exactes, et Naturelles, publiées par la Société Hollandaise des Sciences’ Haarlem. Tome i. Liv. 5; Tome ii. Liv. 1,2. 8vo, Naturkundige Verhandelingen van de Hollandsche Maatschappij der Wettenschappen te Haarlem. Deel xxiv., xxv. 4to. Archives du Musee Teyler. Voli. Fase. 3,4. 8vo. Halifax, Nova Scotia.—Proceedings and Transactions of the Nova Scotian Institute of Natural Science. Vol ii, Part 1. 8vo. Harvard University.—Catalogue of the Officers and Students of Harvard University, for 1866-67. 8vo. Catalogus Universitatis Harvardiane, 1866. 8vo. Reports of the President and Treasurer of Harvard College, 1865-66. Cambridge, Mass., 1866. 8vo. Report of the Trustees of the Museum of Comparative Zoology at Harvard College in Cambridge, Mass., for 1866. 8vo. ‘iel.— Schriften der Universitat. Band xiii., xiv. 4to, Kénigsberg.—Astronomische Beobachtungen auf der Kéniglichen Universi- tits-Sternwart zu Konigsberg. 1865. Fol. Schriften der K6niglichen Physicalish-Oekonomischen Gesellschaft zu Konigsberg. 1865, Abth. 1, 2; 1866, Abth. 1,2. 4to. La Haye—Archives Néerlandaises des Sciences Exactes et Naturelles. Tome ii., Liv. 3-5; Tome iii., Liv. 1, 2. 8vo. Lausanne.—Bulletin de la Société Vaudoise des Sciences Naturelles. ix., Nos. 55-57. 8vo. Leeds.— Annual Report of the Philosophical and Literary Society. 1866-67, 1867-68. 8vo. Report of the Proceedings of the Geological and Polytechnic Society of the West Riding of Yorkshire for 1867, 1868. 8vo. Leipzig.—Abhandlungen der Philologisch-historischen Classe der Konig]. Sachsischen Gesellschaft der Wissenschaften. Band v. No. 3. 8vo. Berichte tiber die Verhandlungen der Kéniglich Sichsischen Gescll- schaft der Wissenschaften, Math. Phys. Classe. Nos. 1, 2, 4, 5. Phil. Hist. Classe. 1866, No. 4; 1867, Nos. 1, 2. 8vo, Tafeln der Egeria mit Zugrundelegung der in den Abhandlungen der Konigl. Sachs. Gesellschaft der Wissenschaften in Leipzig ver- ffentlichten Stérungen dieses Planeten berechnet und mit einlei- tenden Aufsatzen versehen von P. A. Hansen. 8vo. Von der Methode der Kleinsten Quadrate im Allgemeinen und in ihrer Anwendung auf die Geodasie, von P. A. Hansen. 8vo. Publications of the Astronomical Society. Nos, 1 to 8. 4to. Vol. DONORS. The Society. The Society. The Society. The Author. The Society. The University. The Observatory. The Society. Ditto. The Museum. The Society. The University. Ditto. The College. Ditto. The University. The University. The Society. The Society. The Society. The Society. The Society. The Society. Ditto. The Royal Saxon Academy. Ditto. The Society. Leyden.—Annalen der Sternwarte in Leiden. London.—Proceedings of the Society of Antiquaries. LIST OF DONATIONS. DONATIONS, TRANSACTIONS AND PROCEEDINGS OF SOCIETIES—continued. Vierteljahrsschrift der Astronomischen Gesellschaft. iii.; iv. Heft 1. 8vo. Preisschriften gekrént und herausgegeben von der Fiirstlich Jablo- nowskischen Gesellschaft zu Leipzig. 8vo. Tertullian’s Verhaltniss zu Minucius Felix nebst einem Anhang iiber Commodian’s Carmen Apologeticum, von Adolf Ebert. 8vo. Uber Aarstellungen des Handwerks und Handelsverkehrs auf antiken Wandgeniilden, von Otto Jahn. 8vo. Jahrgang i.,, ii., Erster Band. 4to. Liverpool.—Proceedings of the Literary and Philosophical Society of Liver- pool. Nos. 20,21. 8vo. Transactions of the Historic Society of Lancashire and Cheshire. Vol. vi. 8vo. Vol. ii. Nos. 3-7; Vol. iv. Nos. 1,2. 8vo. Transactions of the Society of Antiquaries. Vol. xli, Parts 1, 2. 4to, Journal of the Society of Arts for 1867-68, 1868-69. 8vo. Memoirs of the Astronomical Society. Vols. xxxv., xxxvi. Monthly Notices of the Royal Astronomical Society for 1867-68 and 1868-69. 8vo. Journal of the Chemical Society (New Series) for 1867-69. Catalogue of the Library of the Chemical Society. 8vo. Transactions of the Clinical Society. Vol. i. 8vo. Annual Report of the Geologists’ Association, with List of Members for 1867-68. 8vo. Quarterly Journal of the Geological Society. ment. 8vo. Quarterly Journal of the Geological Society. Vols, xxiii.—xxv. List of the Geological Society of London, November 1867. 8vo. Journal of the Royal Asiatic Society of. Great Britain and Ireland. Vol. iii. Parts 1,2. 8vo. Journal of the Royal Geographical Society, Vols. xxxvi., xxxvii. 8vo, Proceedings of the Royal Geographical Society. Vols. xi—xiii. Report of the Committee of the Harveian Medical Society, for the Prevention of Venereal Diseases. London, 1867. 8vo. Journal of the Royal Horticultural Society. Vol. ii. Parts 5, 6. 8vo. Proceedings of the Royal Horticultural Society. Vol. i. Nos, 8-11, 8vo. Proceedings of the Royal Institution of Great Britain. 1-4. 8vo. Transactions of the Royal Society of London. elvii. Parts 1-2; Vol. clviii. Parts 1,2. to. ato Proceedings of the Royal Society of London. Vol. xv. No. 93; Vol. 8vo. Nos. 92-94. Supple- Vol. v. Parts Vol. clvi. Part 2; xvi. Nos. 94-101; Vol. xvii., Nos. 106-111. 8vo. List of the Royal Society of London. Nov. 1866 and 1868. 4to. Royal Society Catalogue of Scientific Papers. Vols. i., ii. 4to. Transactions of the Royal Society of Literature. Vol. ix. Parts 1, 2. 8vo. Proceedings of the Royal Medical and Chirurgical Society of London. Vol v. No. 8; vi. Nos. 1-3. 8vo. Transactions of the Royal Medical and Chirurgical Society. Vol. 50. 8vo. VOL. XXV. PART II. 769 DONORS, The Society. The Royal Saxon Academy. Ditto. Ditto. The Observatory of Leyden. The Society. The Society. The Society. Ditto. The Society. The Society. Ditto, The Society. Ditto, The Society. The Association. The Society. Ditto. Ditto, The Society. The Society. Ditto. The Society. The Society. Ditto, The Institution. The Society. Ditto. Ditto. Ditto. The Society. The Society. Ditto. 90 LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND PROCEEDINGS OF SOCIETIES—continued. Journal of the Statistical Society. Vol. xxx. Parts 2-4; Vol. xxxi. Parts 1-4; Vol. xxxii. Part 1. 8vo. Journal of the Linnean Society. (Botany) Vol. x. Nos. 41-49; Vol. xi. (Zoology) Vol. x Nos. 38-45. 8vo. Transactions of the Linnean Society. Vols. xxv., xxvi. Part 2. 4to. Proceedings of the Linnean Society. Session 1868-69. 8vo. List of the Linnean Society. 1867 and 1868. 8vo, General Index to the first 25 vols. of the Transactions of the Linnean Society. 1867. 4to. Proceedings of the Mathematical Society. Nos. 12-15. 8vo. Report of the Meteorological Committee of the Royal Society for 1857. 8vo. Meteorology. Report on an Inquiry into the Connexion between Strong Winds and Barometrical Differences, London, 1868. 8vo. Proceedings of the Meteorological Society. iv. Nos, 34-41. 8vo. Transactions of the Pathological Society. Vol. xix. Calendar of the University of London for 1868. 8vo. Transactions of the Zoological Society of London. Vol. vi. Parts 1-7. Ato. Proceedings of the Zoological Society of London for 1866, 1867. ~ 8vo. Jund.—ULunds Universitets Ars-Skrift-Mathematik och Naturvetenskap, 1866-67; Philosophi Sprakvetenskap och Historia, 1866, 1867 ; Theologi, 1866; Medicinska vetenskaper, 1866. Lund. 4to. Lyons.—Mémoires de |’Académie Impériale des Sciences, Belles-Lettres, et Arts de Lyons. > Classe des Lettres. Tomes xii., xiii, Classe des Sciences. Tomes xiv., xv., xvi. 8vo. Annales de la Société d’Agriculture, d’Histoire Naturelle, et des Arts utiles de Lyon, Tomes ix.,x. 8vo. Madrid.—Libros del Saber de Astronomia del Rey D. Alfonzo X. de Cas- tilla, copilados, anotados y comentados por Don Manuel Rico y Vol. iii. Nos. 31, 382; 8vo. Sinobas. Tom.v. Pt.1. Fol. Massachusetts——Proceedings of the Essex Institute at Salem. Vols. iv., v., Nos. 1 and 2. 8vo. Melbourne.—Transactions and Proceedings of the Royal Society of Vic- toria. Vols, vili., ix., Part. 1. 8vo. Statistics of the Colony of Victoria for the year 1867. Part 3 (Inter- change); Part 4 (Law, Crime, &c.) Fol. Milan.—Memorie del Reale Istituto Lombardo di Scienze e Lettere—Classe di Lettere, e Scienze Morali e Poktiche. Vol. ii. Fasc. 8-10; Vol. iii. Fase. 1-10; Vol. x. Fase. 5, 6. Classe di Scienze Mate- matiche e Naturali. Vol. ii. Fase. 9, 10; Vol. ii. Fasc. 1-9; Vol. x. Fase. 8-5. 4to. Rendiconti Reale Istituto Lombardo—Classe di Lettere e Scienze Morali e Politiche. Vol. iii. Fase. 1-10. Classe di Scienze Matematiche e Naturali, Vol, iv, Fasc. 1-10, 1866, 1867. Svo. Rendiconti Reale Istituto Lombardo de Scienze e Lettere, Vol. i. Fase. 1-20; Vol. 11. Fase. 1-10, 1868-69. 8vo. Solenni Adunanze del R. Istituto Lombardo de Scienze e Lettere. Vol. i. Fase. 4. 8vo. Annuario del Reale Istituto Lombardo di Scienze e Lettere. 1864. 12mo. ; Serie ii. DONORS The Society. The Society. Ditto. Ditto. Ditto. Ditto. The Society. The Society. The Committee of the Meteorolo- gical Society. The Society. The Society. The University. The Society. Ditto. The University. - The Academy. The Society. The Academy of Sciences, Madrii. The Institute. The Society. The Australian Government. The Institute. Ditto. Ditto. Ditto. Ditto. LIST OF DONATIONS. ar DONATIONS. DONORS. TRANSACTIONS AND PROCEEDINGS OF SocIETIES—continued, Montpellier —Mémoires Académie des Sciences et Lettres de Montpellier. The Academy. Section des Sciences, Tomes i.—v., Tome vi., Fase. 1; de la Section de Médecine, Tomes iii., iv., Fasc. 1,2; de la Section des Lettres, Tomes ii., iv., Fasc. 1. 4to. Moscow.—Bulletin de la Société Impériale des Naturalistes. Nos. 3,4, The Society. 1866; Nos. 1, 2, 1867; Nos. 1, 2, 1868. 8vo. Munich.—Sitzungsberichte de Kénigl. Bayer. Akademie der Wissenschaften The Academy. zu Miinchen. Band i. Heft 1-4; Band ii. Heft 1-4. 1868. 8vo. Abhandlungen der Koniglich Bayerischen Akademie der Wissen- Ditto. schaften. Band xi. Abth. 2. Historischen Classe. Band ix. : Abth. 3.; Band x. Abth. 3. Mathematisch-Physikalischen Classe. Band x. Abth. 1. 4to. Munchen Gehalten in der Offentlichen der K. Akademie der Wissen- Ditto. schaften am 28 Marz 1868, von August Vogel. 8vo. Almanach der Koniglich bayerischen Akademie der Wissenschaften Ditto. for 1867. 12mo. Resultate der Miinchener Meteorologischen Beobachtungen, 1857— The Royal 1866. 8vo. Observatory. Beobachtungen des Meteorologischen Observatoriums auf dem Hohen- Ditto. peissenberg von 1851-1864. 8vo. Annalen der Koniglichen Sternwarte. Band xv., xvi. 8vo. Ditto. Naples.—Atti della Reale Accademia delle Scienze e Belle-Lettere di The Academy. Napoli della Fondazione sino all’anno 1787. 4to. Atti dell’Accademia delle Scienze Fisiche e Matematiche. Vol. ii. Ditto. 4to. Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche. Ditto. Anno iii. Fase. 7-12; Anno iv, Fasc. 1-12; Anno v. Fase. 1-12; Anno vi. Fase. 1-5, 4to. Rendiconto delle Tornate e dei Savori Geller adeanid di Scienze Morali Ditto. e Politiche. Jan., Aug., Dec. 1868. 8vo. Neuchatel.—Actes de la Société Hélvétique des Sciences Naturelles. The Society. Comte-Rendu, 1866. 8vo. Bulletin de la Société des Sciences Naturelles de Neuchatel. Tome Ditto. vil., T. vili. No. 1. 8vo. New York.—Report (Annual) of the Regents of the University of the The University. State of New York, on the Condition of the State Cabinet of Natural History. 1863-64—-65-66. 8vo. Report (Annual) of the Trustees of the New York State Library for The Trustees. 1863-64-65—-66-67. © 8vo. Ohio.—Report (Twentieth Annual) of the Ohio State Board of Agriculture The Board. for 1865. Columbus, 1866. 8vo. Oxford —Astronomical and Meteorological Observations made at the Rad- The Observatory. cliffe Observatory, Oxford, in the years 1864-66, Vols. xxiv., XY, KEVIN BVO! Palermo.—Giornale di Scienze Naturali ed Economiche publicato per cura The Institute. del Consiglio di perfezionamento annesso al R. Instituto Tecnico di Palermo. Vol. ii. Fasc. 2, 3,4; Vol. iv. Fase. 1, 2, 3. 4to. Paris,—Annales des Mines. Tomes x., xi., xii., xiii, xiv., xv., Liv. 1. 8vo. The Ecole de . Mines. Annales Hydrographiques. No. 4, 1867; Nos. 1-3, 1868. 8vo. The Dépét de la Marine. Publications of the Dépét de la Marine, with Charts, Nos. 408, 422, Ditto. 428, 433, 485, 437, 436, 439, 440, 442, 443, 444, 447. 8vo. Bulletin de la Société de Géographie. Nov. Dec. 1867, Jan. Sept. The Society. 1868. 8vo. hie LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND ProceEDINGs oF SocieTIEsS—continued. Comptes-Rendus Hebdomadaires des Séances de l’Académie des Sciences. 1867-68, 1868-69. 4to. Mémoires de |’ Académie des Sciences de I’ Institut Impérial de France. Tome xxxvii. Premiére Partie. 4to. Nouvelles Archives du Muséum d'Histoire Naturelle. 1-4; Tome ii. Fase. 1-4; Tomes iii., iv. 4to. Philadelphia.—Journal of the Academy of Natural Sciences of Phila- delphia. New Series. Vol. vi. Parts 1,2. 4to. Proceedings of the Academy of Natural Sciences of Philadelphia. Vol. 1. 1841-43 ; Vol. iii. 1846-47; Vol. iv. 1848-49 ; Vol. vii 1854-55 ; 1862, Nos. 1-6; 1866, Nos. 1-5. 8vo. Proceedings of the American Philosophical Society. Vol. x. Nos. 76-80. 8vo. Rotterdam.—Nieueve Verhandelingen van het Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. Deel i. Stuk 1-3. 4to. Salem (U.S.)—Proceedings of the Essex Institute. Vol. v., Nos. 5,6. 8vo. Shanghai.—Journal of the North China Branch of the Royal Asiatic Society. No, 4. 8vo. St Petersburg.—Annales de ]’Observatoire Physique Central de Russie, 1863, (with Supplement), 1864, St Petersburg, 1865-66. 4to. Bulletin de l’Académie Impériale des Sciences de St Petersbourg. Tome x. Nos. 1-4; Tome xi. Nos. 1-4; Tome xii. Nos. 1-8; Tome xiii. Nos, 1-3. 4to, Compte-Rendu Annuel adressé 4 8. Exc. M. de Reutern, par le Direc- Tome i. Fase. teur de l’Observatoire Physique Central A. T. Kupffer, 1864. St Petersburg, 1865. 4to. Compte-Rendu de la Commission Impériale Archéologique pour l’Années 1865 et 1866, 4to (atlas fol.) Mémoires de |’ Académie des Sciences de St Petersbourg. Vii® série. Tome x. Nos. 3-16; Tome xi. Nos. 1-18; xii., Nos. 1-3. 4to. Switzerland.—Verhandlungen der Schweizerischen Naturforschen Gesell- schaft in Rheinfelden. Am. 9, 10, 11 Sept. 1867. 8vo. Toronto.—Canadian Journal of Industry, Science, and Art. New Series. - Nos. 63-67. 8vo. The Canadian Journal of Science, Literature, and History. Vol. xii. No. 2. 8vo. Truro.—Journal of the Royal Institution of Cornwall, with the 49th Annual Report. No. vii. 8vo. Turin.— Atti della Reale Accademia delle Scienze. Vol. ii. Disp. 1-3; Vol. iii. Disp. 1-8. 8vo. Memoire della Reale Accademia delle Scienze. Serie seconda. XXlll., xxiv. 4to. Bollettino Meteorologico dell’Osservatorio Astronomico dell’Uni- versita 1867, 1868. 4to. Upsala——Nova Acta Regie Societatis Scientiarum Upsaliensis. Fase. 2. 4to. Utrecht.—Aanteekeningen van het verhandelde in de Sectie-Vergade- ringen van het Provinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen ter gelegenheid van de Algemeene Vergadering, 1866, 1867. 8vo. Meteorologische Waarnemingen in Aederland en Zijne Bezittingen en Afwijkingen van Temperatuur en Barometerstand of vele Plaatsen in Europa utigegeven door het Koninklijk Nederlandsch Meteoro- logisch Instituut, 1864. Utrecht, 1865. 4to. Nederlandsch Meteorologisch Jaarboek, 1864, 1865, 1866, 1867. Utrecht, 1866. 4to. Vol. i. Disp. 3-7 ; Tomo Vol. vi. DONORS. The Academy. Ditto. - Natural History Museum, Paris. The Academy. Ditto. The Society. The Society. The Institute. The Society. The Russian Go- vernment, The Academy. The Russian Go- vernment. The Commission. The Academy. The Society. The Canadian In-. stitute. Ditto. From the Institu- tion. The Academy. Ditto. The University. The Society. The Society. The Institute. The Meteorologi- cal Institute of Utrecht. Washington.—Astronomy. LIST OF DONATIONS. DONATIONS, TRANSACTIONS AND PROCEEDINGS OF SoclETIES—continined. Verslag van het Verhandelde in Algemeene Vergadering van het Pro- vinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen gehonden den 16 October 1866, 1867. 8vo. Naturkundige Verhandelingen uitgegeven door het Provinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen, Deel i. Stuk 1. 4to. Venice—Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. Tomo xii. Dispensa 4-9, 8vo. Victoria.—Statistical Register of Victoria, with Astronomical Calendar for 1855. 8vo. Statistical Summary of the Progress of the Colony of Victoria to the Year 1865. Melbourne, 1865. 8vo. Statistics of the Colony for 1867. Parts 1-8. Melbourne. Fol. Statistical Fables of the Colony of Victoria. Fol. Melbourne, 1865. Statistical Notes on the Progress of Victoria in relation to Agricul- ture and Live Stock, from 1835 to 1867. Melbourne. 4to. Vienna.—Jahrbuch der Kaiserlich-K6niglichen Geologischen Reichsanstalt. Band xvii, No. 4; Band xviii. Nos. 1-4. 8vo, Verhandlungen der Kaiserlich-Koniglichen Geologischen Reichsan- stalt. 1867, Nos. 10-18; 1868, Nos. 1-18. Jahrbiicher der Kaiserlich-Koéniglichen Central-Anstalt fiir Meteoro- logie und Erdmagnetismus, von Carl Jelinek und Carl Fritsch. Band i, 1864. 4to. Verhandlungen der Kaiserlich-Kéniglichen Zoologisch-Botanischen Gesellschaft in Wien. Band xvii. 8vo. Die Fossilen Mollusken des Tertiar-beckens von Wien, von Dr Moritz Hornes, 4to. Denkschriften der Kaiserlichen Akademie der Wissenschaften. Phil. Hist. Classe. Band xviiimMath-Nat. Classe, Band xxvi , xxvill.— Philosophisch. Hist. Classe, Band xv, 4to. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften. Math.-Nat. Classe (Mineralogie, Botanik). Band liv.—lvi. Heft 1-3.—Math.-Nat, Classe. B. lv., Ivi, Heft 1-3.—Phil.-Hist. Classe. B. liii., Heft 1-3; B. lvi., lvii., Heft 1-3; lviii., Heft 1-3. 8vo. Almanach der Kaiserlichen Akademie der Wissenschaften. 1868. 8vo. 1867, Astronomical and Meteorological Observations made at the United States Naval Observatory, during 1851-52 and 1865. 4to. Washington, 1867. Discussion of Meteorological Phenomena observed at the U.S. Naval Observatory, from June 1842 to January 1867. 4to. Report of the Board of Regents of the Smithsonian Institution for 1865 and 1866. 8vo,_ .- é; Smithsonian Contributions to Knowledge. Vol. xv. 4to. Miscellaneous Collections of the Smithsonian Institution. Vols. vi., vii. 8vo, Memoirs of the National Academy of Sciences, Vol. i. 4to. Annual Reports of the Commissioner of Patents for 1865 and 1866, 8vo. Twenty-Second Annual Report of the Board of Trustees of the Public Schools of the City of Washington. 1867. 8vo. Monthly Reports of the Department of Agriculture for 1866-67. 8vo. Report of the Secretary of War, with accompanying paper. ington, 1866. 8vo. Wash- VOLE. xOSV, PART il: 773 DONORS. The Society. Ditto. The Institute. The Registrar- General. Ditto. Ditto. Ditto. Ditto. The Society. Ditto, The Society. The Society, The Geol. Society of Vienna. The Academy. Ditto. Ditto. The United States Government. The Observatory. The Smithsonian Institution. Ditto. Ditto. The Academy. The United States Patent Office. The Trustees. The Commis- sioner. The American Go- vernment, 9P 774 LIST OF DONATIONS. DONATIONS. TRANSACTIONS AND PROCEEDINGS OF SOCIETIES— continued. Report on Epidemic Cholera, Washington, 1867. 4to. Whitby.—F orty-Fifth and Forty-Sixth Report of the Literary and Philo- sophical Society. 8vo. Zurich_—Neue Denkschriften der Allgemeinen Schweizerischen Gesell- schaft fiir die gesammten Naturwissenschaften, [Nouveaux Mé- moires de la Société Helvétique des Sciences Naturelles.] Band xxli,, mit xx Tafeln, 4to. Abbe (Cleveland), Dorpat and Poulkova. Washington, 1867. 8vo, Arneth (Joseph). Die Antiken Cameen des K. K. Miinz und Antiken Cabinettes in Wien. Fol. —— Die Antiken Gold und Silber Monumente des K. K. Miinz und Antiken Cabinettes in Wien. Fol. -—— Die Cinque Cento Cameen und Arbeiten des Benvenuto Cellini und seiner Zeitgenossen im K. K, Miinz und Antiken Cabinettes in Wien. Fol. Baars (Herman). Berelning om den Internationale Fiskerindstilling i Boulogne- sur-Mer, 1866. 12mo. Les Péches de la Norwége. Boulogne-sur-Mer, 1866. 8vo. Balfour (John Hutton). Obituary Notice of Professor John Goodsir. Edin- burgh, 1867. 8vo. Begbie (James), M.D. On the Causes of Death in the Scottish Widows’ Fund Life Assurance Society, from 1st January 1860 to 3lst December 1866. Edinburgh, 1868. 8vo. Bert (Dr Paul). Note sur un cas de Greffe Animale. 8vo. Recherches Expérimentales pour servir a |’Histoire de la Vitalité propre des Tissus Animaux. Paris, 1866. 4to. —— Recherches sur les Mouvements de la Sensitive (Mimosa pudica, L.). Paris, 1867. 8vo. -—— Notes d’Anatomie et de Physiologie Comparées. Paris, 1867. 8vo. —— Sur un Monstre double Autositaire de la Famille des Monosomiens. Paris, 1863. 8vo. Bigsby (John J.), M.D., F.G.S. Flora and Fauna of the Silurian Period, with Addenda. London, 1868. 4to. Boeck (Thorvald), Oversight over Literattur, Love, Forordninger Rescripter M.M. Vedrorende de Norske Fiskeriar. Christiania, 1866. 8vo. Boué (Ami). Recueil d’Itinéraires dans la Turquie d’Europe. Tomes i., ii. Vienna, 1854. 8vo. Broch (Dr O. J.). Traité Elémentaire des Fouchons Elliptiques. Fase. 1, i1., Christiania, 1866-1867. 8vo. Brown (Robert). Das Innere der Vancouver-Inseln. 4to. Being a German translation of his paper. Brunn (Dr H.). Ueber die sogenannte Leukothea in der Glyptothek St Majestat Konig Ludwigs I. Munich, 1867. 4to. Brusina (Spiridione). Contribuzione pella Fauna dei Molluschi Dalmati. Vienna, 1866. 8vo. Burckhardt (Dr Fritz). Ueber die Physikalischen Arbeiten der Societas Physica Helvetica, 1751-1787. Basel, 1867. 8vo. Caruana (A. A.). Enumeratio Ordinata Molluscorum Gaulo-Melitensium (of the late Mr Giuseppe Mamo). Malta, 1867. 8vo. Caspari (Dr C. P.). Ungedruckte unbeachtete und wenig beachtete Quellen zur Geschichte des Taufsymbols und der Glaubensregel. Christiania, 1866. 8vo. DONORS. The War Office, US. The Society. The Society. The Author. Ditto, Ditto. Ditto. Ditto. Ditto, Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. LIST OF DONATIONS. DONATIONS, Castello de Paiva (Barone de). Monographia Molluscorum Terrestrium, Fluvialium, Lacustrium, Insularium Maderensium. Olisipone, 1867. 4to. Catalogue of the New York State Library for 1865. Law Library. First Sup- plement. 8vo. of the Printed Books and Manuscripts in the Library of the New College, Edinburgh. 1868. 4to. —— Index to the Catalogue of Books in the Bates Hall of the Public Library of the City of Boston, First Supplement. Boston, 1866. 8vo. —-— of the Surgical Section of the United States Army Medical Museum, Washington, 1866. 4to. —— of the Printed Books in the Library of the Faculty of Advocates, Part iii. Edinburgh, 1867. 4to. ——— of Contributions transmitted from British Guiana to the Paris Universal Exhibition. London, 1867, 8vo. Catlow (Joseph Peel), M.R.C.S. Principles of Aisthetic Medicine. London, 1867. 8vo. Chevreul (M. E.). De la Baguette Divinitoire du pendule dit Explorateur et des Tables Tournantes au point de vue de |’Histoire, de la Critique et de la Méthode Expérimentale. Paris, 1854. 8vo. Notes Historiques sur la nature immédiate de Amer de Welter et de VYAmer au Minimum. Paris, 1864. 4to. —~— Considérations sur |’Histoire de la Partie de la Médecine qui concerne la Prescription des Remédes. Paris, 1865, 4to. ——— Rapport sur ses cours du Muséum en Général. Paris, 1866. 8vo, —— Histoire des Connaissances Chimiques. Paris, 1866. 8vo. Des Arts qui parlent aux Yeux. Paris, 1867. 4to. Examen Critique au point de vue de |’Histoire de la Chemie d’un écrit Alchimique intitulé Artefué Clavis Majoris Sapientiz. Paris, 1867. 4to. Childs (Geo. W.). Account of the Proceedings connected with the Opening of ' the Public Ledger Building, Philadelphia. * 1868. 8vo. Cohen (Henri). Description des Médailles Grecques, Romaines, &c. Paris, 1869. 8vo. Coleman (Rev. Lyman), D.D, The Great Crevasse of the Jordan and of the Red Sea. 8vo. Cooke (Rev. T. F.), M.A. Authorship of the Practical Electric Telegraph of Great Britain, London, 1868. 8vo. Crisp (Edwards), M.D. On some Points connected with the Anatomy of the Hippopotamus. 8vo. Cunningham (Alexander W.). Notes on the History, Methods, and Technolo- gical Importance of Descriptive Geometry. Edinburgh, 1868. 8vo, Danube,—Mémoire sur les Travaux d’Amelioration exécutés aux Embouchures du Danube, par la Commission Européene (4to), accompagné d’un Atlas de 40 Planches. 1867. Fol. Day (St John Vincent), C.E. Malleable Iron Manufacture and the Richardson Process. Glasgow, 1868. 8vo. Present State of some Branches of Iron Metallurgy. Glasgow, 1868. 8vo, Delesse (M.), et Lapparent (M. de). Revue de Géologie pour les Années 1864 et 1865. Paris, 1866. 8vo. Diemer (Joseph). Genesis und Exodus nach der Milstater Handschrift, Band i, ii. Vienna, 1862. 8vo. Dircks (Henry), C.E., F.C.S. Inventors and Inventions. London, 1867. 8vo. The Polytechnic College. A proposed Institution for aiding depressed Talent to complete Works in progress connected with Science, Litera- ture, or Arts, London, 1867. 8vo. DONORS. The Author. The Trustees, The College. The Library. The American Government, The Faculty. The Committee of Correspondence of British Guiana. The Author. Ditto. Ditto. Ditto. Ditto. Ditto, Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. The Commission. The Author. Ditto. The Authors. The Author. Ditto. Ditto. 776 LIST OF DONATIONS. DONATIONS, Dorna (Alessandro, Prof.), Catalogo delle Leoneidi o Stelle Meteoriche del periodo di Novembre Osservate nel 1867 al regio Osservatorio di Torino. _ 4to. Drifts (Auriferous), in Australasia, by ‘“ Research.” Melbourne, 1868. 8vo. Ekker (A. H. A.), Exeunte Octobri. 1868. 8vo. Erdmann (A.). Sveriges Geologiska Undersékning pa offentlig bekostnad Utford under ledning af A, Erdmann. Nos, 26-30, with Charts. 8vo. Exposé des Formations Quaternaires de la Suede. Texte 8vo; Atlas 4to. Carmen, ad filiolum. Amsterdam, Stockholm, 1868. Fayrer (Joseph), M.D. Address delivered at the Annual Meeting of the Asiatic Society of Bengal. Calcutta, 1868. 8vo. Flora Batava, afbeelding en beschrigving van Nederlandsche Gewassen door Wiglen Jan Kops, vervolgd door Jhr. F. A. Hartsen, afgebeeld onder opzigt van J. C. Sepp en Zoon. Nos. 200-207, Amsterdam. 4to. Fouqué (M. F.). Premier Rapport sur une Mission Scientifique 4 l’Ile de San- torin. Paris, 1867. 8vo. —— Rapport sur les Phénoménes Chimiques de l’Eruption de ]’Etna en 1865. 4to, ——— Rapport sur les Tremblements de Terre de Cephalonie et de Mételin en 1867. Paris. 8vo. Gamgee (Arthur), and Wanklyn (J. Alfred), On the Action of Permanganate of Potash on Urea, Ammonia, and Acetamide, in strongly Alkaline Solu- tions, 8vo. Geikie (Archibald), F.R.S. Memoir of the late James David Forbes, D.C.L., LL.D., F.R.S. Edinburgh, 1869. 8vo. - —— Address to the Geological Section of the British Association, 1867. 8vo. Gianelli (Giuseppe Luigi). Ato, Gunther (Gustav Julius). Armour Plating, with a Description of a new system of Iron or Steel Armour. London, 1868. 8vo. Guthrie (Frederick), Ph.D. Elements of Heat and of Non-Metallic Chemistry. La Vaccinazione e le sue Leggi in Italia. 1864. London, 1868, 8vo. Hammer Purgstall. Geschichte Wassaf’s. Bandi, Wien, 1856. 4to. Handyside (Dr). Observations on Arrested Twin-Development. 8vo. Hertzberg (N.), Indberetning om nogle Lererseminarier 1 premmede Lande fra en Reise 1866 og 1867. Christiania, 1868. 8vo. Hinrichs (Gustave). Atomechanik oder die Chemie eine Mechanik der Pana- tome. lowa-City, Etats Unis, 1867. 4to. Hirsch (A.), et Plantamour (H.). Nivellement de précision de la Suisse, exécuté par la Commission Géodésique Fédérale sous la direction des auteurs. Liv.i. Genéve, 1868. to. Holmboe (C. A.). Ezechiels Syner og Chaldeernes Astrolab. Christiania, 1866. 4to. James (Col. Sir Henry). Determination of the Positions of Feaghmain and Haverfordwest Longitude Stations on the Great European Arc of Parallel. London, 1867. 4to, Jenkin (Fleeming), On the Education of Civil and Mechanical Engineers. Edinburgh, 1868. 8vo. DONORS. The Author, Ditto. Ditto. The Editor. The Author. Ditto. The King of Holland. The Author. Ditto. Ditto. The Authors. The Author. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. The Authors. The Author. The Secretary of State for War. The Author. LIST OF DONATIONS. DONATIONS. Journal (American) of Science and Arts, conducted by Benjamin Silliman. Nos. 129-140. New Haven. 8vo. Karajan (Th. G. von). Das Verbriiderungs buch des Stiftes S. Peter zu Salz- burg aus dem achten bis dreizehnten Jahrhundert mit Erlanterungen. Wien, 1852. Fol. Kronecker (L.). Uber Systeme von Functionen mehrer Variabeln. Berlin, 1869. 8vo. Lawson’s Pinetum Britannicum. Parts xxix._xxxii. Imp. fol. Lea (Isaac), LL.D. Check List of the Shells of North America (Unionide), 8vo. ——— Tables of the Rectification of Mr T. A. Conrad’s “Synopsis of the Family of Naides of North America.” Philadelphia, 1866. —— Observations on the Genius Unio, together with descriptions of new species in the family Unionide, and descriptions of new species of the Melanide, Limneide, Paludinz, and Helicide, with 24 Plates. Vol. xi. 4to. Lesley (J. P.). Notes on a Map intended to illustrate five types of Earth-sur- face in the United States, between Cincinnati and the Atlantic Seaboard. Philadelphia, 1866. 4to, Leuckart (Rudolf). Die Menschlichen Parasiten und die von ihnen herriih- renden Krankheiten. Ein Hand und Lehrbuch fiir Naturforscher und Aerzte. Leipzig, 1868. 8vo. Maclaren (Charles). Select Writings, Hdited by Robert Cox, FS.A., and James Nicol, F.R.S.E. Vols. i. and i. 8vo. Maestri (Pierre). Rapport soumis a la Junte Organisatrice sur le programme de la VI™ Session du Congrés International de Statistique. Florence, 1867. 8vo. Mailly (Ed.). L’Espagne Scientifique. Brussels, 1868. 12mo, Manuscripts. Facsimiles of National Manuscripts of Scotland, selected under the direction of the Right Hon. Sir William Gibson-Craig, Bart., Lord Clerk-Register of Scotland, and Photo-zincographed, by command of Her Majesty Queen Victoria, by Colonel Sir Henry James, R.E., Director of the Ordnance Survey. Parti. 1867. Folio. Facsimiles of National Manuscripts of England, selected under the direc- tion of Colonel Sir Henry James. Parts iii., iv. Fol. Martius (Dr Carl Friedrich Phil. von). Beitrage zur Ethnographie und Sprachenkunde Amerika’s zumal Brasiliens. 2 vols. Leipzig, 1867. 8vo. Meiller (Andreas von). Regesten zur Geschichte der Markgrafen und Her- zoge Osterrichs aus dem Hause Babenberg. Wien, 1850, 4to. Miklosich (F.). Monumenta Lingue Paleoslovenice e Codice Suprasliensi. Vindobone, 1851. 8vo. Mitra (M. L.)}. The Ultimate Structure of Voluntary Muscular Tissue, and the Mode of Termination of Motor Nerves. Edinburgh, 1867. 8vo, Modderman (W.). De Wettelijke Bewijsleer in Strafzaken Utrecht, 1867. 8vo. Molison (A. R.). Against the Theory of the Retarding Influence of Tidal Action on the Axial Motion of the Earth, and showing the true Source of Tidal Energy. 8vo. Mueller (Ferdinandus), Ph.D., M.D. Fragmenta Phytographie Australiz, Vols. iii. and v. Melbourne, 1862-66. 8vo. Murchison (Sir Roderick Impey), Bart., K.C.B. Siluria; a History of the Oldest Rocks in the British Isles and other countries. Fourth Edition. London, 1867. 8vo. Neilreich (Dr August). Nachtrage zur Flora von Neider-Oesterreich. 1866. 8vo, VW OS SOO. ART TE. Wien, OtT DONORS. The Editor. The Author. Ditto. Charles Lawson, Esq. The Author. Ditto. Ditto. Dr J. Young. The Author. Mrs Maclaren. - The Author. Ditto. The Secretary of State for War. Ditto. The Author. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. 9Q 178 LIST OF DONATIONS. DONATIONS. Neilreich (Dr August). Diagnosen der in Ungarn und Slavonien bisher beo- bachteten Gefasspflanzen welche in Koch’s Synopsis nicht enthalten sind. Wien, 1867. 8vo., Nomenclature of Diseases, drawn up by a Joint-Committee appointed by the Royal College of Physicians of London. London, 1869. 8vo. Oettingen (Dr Arthur von). Meteorologische Beobachtungen angestellt in Dorpat un Jahre 1867. Dorpat, 1868. 8vo. Paine (Martyn), A.M., M.D. The Institutes of Medicine, 8th edition. New York, 1867. 8vo. Peters (Dr). Report on the Longitude of Elmira. Albany, 1864. 8vo. Report on the Longitude and Latitude of Ogdensburgh. Albany,1865. 8vo. Pictet (M. Adolphe). Sur une Nouvelle Déesse Gauloise de ]a Guerre. Paris, 1868. 8vo. Plantamour (E.). Des Anomalies de la Température Observées a Genéve pen- dant les quarante Années 1826-65, 4to. —— Résumé Météorologique de l’Année 1866 et 1867, pour Genéve et le Grand Saint-Bernard. 8vo. Pollender (Dr A.). Ueber das Entstehen und die Bildung der kreisrunden Oeff- nungen in der ausseren Haut des Blutenstaubes, Bonn, 1867. 4to. —— Neue Untersuchungen iiber das Entstehen, die Entwickelung, den Bau, und das chemische Verhalten des Blutenstaubes, Bonn, 1868. 4to. —~— Wem gehiihrt die Prioritaét in der Anatomie der Pflanzen dem Grew oder dem Malpighi. Bonn, 1868. 4to. Priestley (William O.), M.D. Lectures on the Development of the Gravid Uterus. London, 1860. 8vo. ~~ Quatrefages (M. de). Observations relatives 4 un ouvrage de M. Claparéde, intitulé Les Annélides Chétopodes du Golfe de Naples, et Réponse 4 ses Critiques. Paris. 4to. Quetelet (Ad.). Observations des Phénoménes Périodiques pendant les Années 1865 et 1866. Brussels. 4to. —— Physique Sociale, ou Essai sur le développement des Facultés de ’Homme. Brussels. 8vo. -—— Mémoire sur ]a Température de l’Air 4 Bruxelles. 1867. 4to. —— Des Lois Mathématiques concernant les Etoiles Filantes, 8vo. Sur les Phénoménes Périodiques en Général. 8vo. Communications extracted from the Annales de l’Observatoire Royale de Bruxelles. 8vo. Rankine (W. J. Macquorn), Mechanics (applied), Edinburgh, 1857. 4to. Rein (Dr J. J.). Der Gegenwirtige Stand des Seidenbaues. Frankfort-on- Maine, 1868. 8vo. REPORTS :— Report of the Superintendent of the Coast Survey, showing the Progress of the Survey during years 1863-64 and 1865. 4to. Report on Epidemic Cholera and Yellow Fever in the United States Army during 1867. 4to. Tenth, Eleventh, and Twelfth detailed Annual Reports of the Registrar- General of Births, Deaths, and Marriages in Scotland. Edinburgh, 1867-1869. 8vo. Thirteenth Annual Report of the Registrar-General on the Births, Deaths, and Marriages registered in Scotland during the year 1867. 8vo. Quarterly and Monthly Returns of the Births, Deaths, and Marriages registered in the Divisions, Counties, and Districts of Scotland for 1867-68, 1868-69. 8vo. DONORS The Author. The College. The Author. Ditto. Ditto, Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto, Ditto. Ditto. Ditto. The United States Government. The War Office, Washington. The Registrar- General. Ditto. Ditto. LIST OF DONATIONS. DONATIONS. Reports—continued. Report of the Commissioner of American Patents for 1863 and 1864. Washington. 8vo. On the Amputations at the Hip-Joint in Military Surgery. Washing- ton, 1867. 4to. Robertson (George), F.R.S.E. Recent Marine, Hydraulic, and Sanitary En- gineering in Scotland. Edinburgh, 1867. 8vo. . Tide Signals as well as Storm Signals. Edinburgh, 1868. 8vo. Rive (Professeur A. de la). Notice sur Michael Farady sa vie et Travaux. Genéve, 1867. 8vo. Rutherford (William), M.D. Electronus: A Physiological Demonstration given in the Physiological Laboratory of the University of Edinburgh, 8vo. Rizzoli (Francesco). Nuovo processo operatorio per la cura di una vasta aper- tura Uretro-Cisto-Vaginale. Bologna, 1867. 8vo. -—— Masseterotomia intrabuccale per la cura di una Anchilosi del Mascellare inferiore Memoria. Bologna, 1869. 4to. Ryan (Matthew). The Celebrated Theory of Parallels. Second Edition, with Supplement Appendix. Washington, 1866. 8vo. Sars (Michael). Mémoires pour servir 4 la Connaissance des Crinoides Vivants. Christiania, 1867. 4to. Schumann (J.). Die Diatomeen der Hohen Tatra, Wien, 1867. 8vo. Schmidl (Dr Adolf). Die Grotten und Hohlen von Adelsberg, Lueg, Planina und Laas. Wien, 1854. Fol. Plates. — Die Grotten und Héhlen von Adelsberg, Lueg, Planina und Laas, Wien, 1854. 8vo. Seguin (M.). Réflexions sur l’Hypothése de Laplace relative a ]’Origine et a la Formation du Systéme Planétaire. Paris, 1867. 4to. Settimanni (Capt. Cesar). D’une Nouvelle Methode pour déterminer la Parallaxe du Soleil. Florence, 1869. 8vo. Sexe (S. A.) Merker Efter en tistid i Omegnen af Hardangerfjorden. Chris- tiania, 1866. 4to. Smart (Andrew), M.D., F.R.C.P.E. Reports to the Lord Provost and Magis- trates of the City of Edinburgh, on the Pathological Appearances, Symptoms, Treatment, and Means of Preventing Cattle Plague. Edin- burgh, 1866. 4to. Smyth (Prof, C. Piazzi), F.R.SS.L. and E., F.R.A.S. On Intensified Gravity in Centrifugal Governors of Driving Clocks and Steam-Engines, 12mo. —— Life and Work at the Great Pyramid. Vols. 1-3. Edinburgh, 1867. 8vo. On the Antiquity of Intellectual Man, Edinburgh, 1868. 8vo. Sproat (Gilbert Malcolm). Scenes and Studies of Savage Life. London, 1868, 8vo. Stevenson (Thomas), C.E. On ascertaining the Intensity of Storms by the Calculation of Barometric Gradients. 8vo. Storer (David H.), M.D. History of the Fishes of Massachusetts. Cambridge, 1867. 4to. Struve (Otto). Jahresbericht am 24 Mai 1867-68, dem Comité der Nicolai- Hauptsternwarte. St Petersburg. 8vo. Tabule Auxiliares ad Transitus per Planum primum verticale reducendos inservientes. St Petersburg. 1868. 8vo. Sundt (Gilert), Om Szdeligheds-Tilftanden 1 Worge 3 die, Beretning. Chris- tiania, 1866. 8vo. —— Om Husflideni Norge. Christiania, 1867. 8vo. Teale (James). A Dynamical Theory of the Universe. Manchester, 1868, 8vo. 179 DONORS, The Commis- sioner, The American Government. The Author. Ditto. Ditto. v Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. 780 LIST OF DONATIONS. DONATIONS. Tebbutt (John, jun.). Meteorological Observations made at the Private Observatory of John Tebbutt, jun. Sydney, 1868. 8vo. Thomson (J. T.), F.R.G.S. Sequel to some Glimpses into Life in the Far East. London, 1865. 8vo. Thomson (Murray), M.D. Report on Meteorological Observations in the N.-W. Provinces of India. Roorkee, 1868. Fol. Thomson (William Thomas), Address delivered to the Students of the Edin- burgh School of Design. Edinburgh, 1869. 8vo. Tillman (S. D.), A.M. A new Chemical Nomenclature. Albany, 1866. 8vo. Tschudi (J. J. von). Die Kechua-Sprache. Abtheilung i, ii., iii. Vienna, 18538. 8vo. Uger (C. R.) Morkinskinna, Pergamentsbog fra forste Halvdel af det Trettende Aarhundrede. Christiania, 1867. 8vo. Vogel (August). Denkrede auf Heinrich August von Vogel. Munich, 1868. Voit (Carl). Ueber die Theorien der Ernahrung der thierischen Organismen, Munich, 1868. 4to. Waage (P.) et C.M. Guldburg. Etudes sur les Affinités Chimiques, Christiania, 1867. 4to. Watson (J. Forbes), A.M., M.D. Index to the Native and Scientific Names of Indian Plants and Products. London, 1868. 4to. Wetherill (Charles M.). Experiments on Itacolumite. 8vo. Woodward (Henry). Man and the Mammoth. London, 1869. 8vo. Will (H.). Jahresbericht iiber die Fortschritte der Chemie, etc., Register zu den Berichten fiir 1857 bis 1866. 8vo. Jahresbericht iiber die Fortschritte der Chemie, ete., fiir 1866, Heft 1-8; fiir 1867, Heft 1. Giessen. 8vo, Winnertz (Joh,), Beitrag zu einer Monographie der Sciarinen, Wien, 1867. 8vo. Ximenez (EI.R.P.F.F.). Las Historias del Origen de los Indios de esta Pro- vincia de Guatemala. Vienna, 1857. 8vo. DONORS. The Author, Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. The Authors, The Author. Ditto, Ditto. The Editor. Ditto. The Author, Ditto. ( 781 ) INDEX TO VOL. XXV. Anperson (Professor Tuomas). On the Products of Destructive Distillation of Animal Substances. Part V., 205. Animal Substances, Products of the Destructive Distillation of. By Professor AnpERson, 205. Annelids, New British. By W. Carmicuaret M‘Intosu, M.D., 305. Archimedes’ Burning Mirrors. By Joun Scott, 123. Atropia, its Action on Cold-Blooded Animals. By Dr Tuomas R. Fraser, 449. Atropia and Conia, Physiological Action of the Ammonium Bases derived from. By Dr A. Crum Brown and Dr Tuomas R. Fraser, 693. B Bebeeru or Greenheart Tree, Alkaloids in the Wood of. By Professor Mactacan and Dr Arruur GamMGEE, 567. Boulder-Clay of Europe. By Davip Mitne Hos, 655. Brewster (Sir Davip). On the Motion, Equilibrium, and Forms of Liquid Films (Plates L., LCL ed Ub Brown bos A. Crum), and Fraser (Dr T. R.). On the Connection between Chemical Constitu- tion and Physiological Action. Part I. On the Physiological Action of the Salts of the Ammonium Bases derived from Strychnia, Brucia, Thebaia, Codeia, Morphia, and Nicotia, 151. On the Connection between Chemical Constitution and Physiological Action. Part II, On the Physiological Action of the Ammonium Bases derived from Atropia and Conia, 693. Bucuan (ALexaNpER). ‘The Mean Pressure of the Atmosphere and the Prevailing Winds over the Globe for the Months and for the Year. Part II. (Plates XXV.—XXVII.), 575. Burning Mirrors of Archimedes. By Joun Scort, 128. C Caytey (Professor). On Polyzomal Curves, otherwise the Curves of ,/ 0+ eh V + &e.—0, jg Chemical Constitution and Physiological Action. By Dr A. Crum Brown and Dr Tuomas R. Fraser, 151, 693. D Davy (Joun). On the Temperature of the Common Fowl (Gallus domesticus), 119. Destructive Distillation of Animal Substances, Products of the. By Professor AnpERson, 205. VOL. XXV. PART II. IR 782 INDEX. Dicxson (Professor ALEXANDER). On the Development of the Flower of Pinguicula vulgaris, L. : with Remarks on the Embryos of P. vulgaris, P. grandiflora, P. lusitanica, P. caudata, and Utricularia minor (Plates XXVITI.-XXX.), 639. E Embryos of Pinguiculas and Utricularia minor, By Professor Dickson, 639. . F Fraser (Dr Tuomas R.). On the Connection between Chemical Constitution and Physiological Action. (See Dr A. Crum Brown), 161. — An Investigation into some préviously undescribed Tetanic Symptoms produced by Atropia in Cold-Blooded Animals, with a Comparison of the Action of Atropia on Cold-Blooded Animals and on Mammals, 449. — and Prof. A. Crum Brown. On the Connection between Chemical Constitution and Physiological Action. Part IT., 693. G Gallus domesticus (Common Fowl), Temperature of. By the late Dr Joun Davy, 119. GamcEE (Dr ArtHur), and Professor Maccacan. On the Alkaloids contained in the Wood of the Bebeeru, or Greenheart Tree, 567. H Hegel and the Metaphysics of the Fluxional Calculus. By W. Ropertson Smitu, M.A., 491. J Jenkin (Professor Freemine). On the Practical Application of Reciprocal Figures to the Calculation of Strains on Framework (Plates XVII.—XXILI.), 441. L Lichenicolous Micro-Fungi. By Dr W. Lauper Linnsay, 513. Linpsay (Dr W. Lauper). Observations on New Lichenicolous Micro-Fungi (Plates XXIII, © XXIV.), 513. Liquid Films, Motion, Equilibrium, and Forms of. By the late Sir Davip Brewster, 111. M M‘Inrosu (Dr W. Carmicnar.). On the Structure of the British Nemerteans, and some New British Annelids (Plates I1V.—XVI.), 305. Mactacan (Dr T. J.). Observations on the Temperature of Newly-Born Children, 435, MacraGan (Professor), and Dr Arrnur Gamcer. On the Alkaloids contained in the Wood of the Bebeeru, or Greenheart Tree (Nectandra Rodiewi, Schomb.), 567. Mean Pressure of the Atmosphere for the Months and for the Year. By ALEXANDER Bucnan, 575. Mite Home (Davin). On the Boulder-Clay of Europe (Plate XXXI.), 655. Molecular Vortices, Thermal Energy of. By Professor W. J. Macquorn Rankine, 557. N Nectandra Rodiwi, Alkaloids in the Wood of. By Professor Maczacan and Dr Artuur GAMGEE, 567. Nemerteans, British, their Structure. By Dr W, Carmicuact M‘Intosn, 305. ay (o.8) [S) INDEX. - Physiological Action and Chemical Constitution. By Dr A. Crum Brown and Dr Tuomas R. Fraser, 151, 693. Pinguicula vulgaris, Development of the Flower of. By Professor Dickson, 639. Polyzomal Curves. By Professor Caytezy, 1. Prevailing Winds over the Globe. By ALEXANDER Bucuan, 5795. R Rankine (Professor W. J. Macauorn). On the Thermal Energy of Molecular Vortices, 557. Reciprocal Figures, their Practical Application to the Calculation of Strains on Framework. By Professor FLEEMING JENKIN, 441. Rotation of a Rigid Body about a Fixed Point. By Professor Tarr, 261. S Scorr (Jonny). On the Burning Mirrors of Archimedes, with some Propositions relating to the Concentration of Light Produced by Reflectors of Different Forms (Plate III.), 123. Smity (W. Ropertson). Hegel and the Metaphysics of the Fluxional Calculus, 491. Strains on Framework. By Professor Fienmine JENKIN, 441. T Tarr (Professor). On the Rotation of a Rigid Body about a Fixed Point, 261. Temperature of the Common Fowl (Gallus domesticus). By the late Dr Joun Davy, 119. Temperature of Newly-Born Children. By Dr T. J. Mactacan, 435. - Tetanie Symptoms produced by Atropia. By Dr Tuomas R. Fraszr, 449. Thermal Energy of Molecular Vortices. By Professor W. J. Macavorn Rankine, 557. Tuomson (Sir Witi1am). On Vortex Motion (Plate III.*), 217. Vv Vortex Motion. By Professor Sir Wrttiam THomsoy, 217 END OF VOLUME TWENTY-FIFTH. PRINTED BY NEILL AND COMPANY, EDINBURGH. SS estatatatabaasutsassssssnigssarsisgsssaeeestseieeet ieee ees pipsisiesssssensesss: sphgissii iti, SSEEET SH Seerenree eres testa rialisfesustss 3 + eet pstisstiginiestseasissyssotesrasapeesseceeeseseast bgatensetoasstiesiuistegeretscstecss Tae titted pireatess ret pi sinise 1g resesasiets HEHEHE