crest SETSpITEITT Perret rests ‘ af bit is i ; ‘ ew! ' 1 a4 es i f m t 4 \ } - ‘ ae "eet ) 7 ~ Ny a* f / ur xe ‘ ¢ , . ‘ t ay ‘ Y i f c ' ‘ y , \ ry } a‘ ty Py . “1 ' é M . al U : i Te = $ 1 « ‘ ~ ‘ BA oe voy A \’ 1 es ' - i 4 ‘ e ri ( . TRANSACTIONS OF THE Be Opmee SS Oe 1 hy - OF EDINBURGH. VOL. XXIII. EDINBURGH: PUBLISHED BY ROBERT GRANT & SON, 82 PRINCES STREET, AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. . MDCCCLXIYV. PRINTED BY NEILL AND COMPANY, EDINBURGH. ROYAL SOCIETY OF EDINBURGH. THE KEITH, BRISBANE, AND NEILL PRIZES. The above Prizes will be awarded by the Council in the following manner :— I. KEITH PRIZE. The Kerry Prize, consisting of a Gold Medal and from £40 to £50 in Money, will be awarded in the Session 1869-70, for the “ best communication on a scientific subject, communicated, in the first instance, to the Royal Society dur- ing the Sessions 1867-68 and 1868-69.” Preference will be given to a paper containing a discovery. II. MAKDOUGALL BRISBANE PRIZE. This Prize is to be awarded biennially by the Council of the Royal Society of Edinburgh to such person, for such purposes, for such objects, and in such manner as shall appear to them the most conducive to the promotion of the interests of science; with the proviso that the Council shall not be compelled to award the Prize unless there shall be some individual engaged in scientific pursuit, or some paper written on a scientific subject, or some discovery in science made during the biennial period, of sufficient merit or importance in the opinion of the Council to be entitled to the Prize. 1. The Prize, consisting of a Gold Medal and a sum of Money, will be awarded at the commencement of the Session 1870-71, for an Essay or Paper having reference to any branch of scientific inquiry, whether Material or Mental. 2. Competing Essays to be addressed to the Secretary of the Society, and transmitted not later than Ist June 1870. 3. The competition is open to all men of science. 4, The Essays may be either anonymous or otherwise. In the former case, - they must be distinguished by mottoes, with corresponding sealed billets super- scribed with the same motto, and containing the name of the Author. 2 5. The Council impose no restriction as to the length of the Essays, which may be, at the discretion of the Council, read at the Ordinary Meetings of the Society. They wish also to leave the property and free disposal of the manuscripts to the Authors; a copy, however, being deposited in the Archives of the Society, unless the Paper shall be published in the Transactions. 6. In awarding the Prize, the Council will also take into consideration any scientific papers presented to the Society during the Sessions 1868-69 and 1869-70, whether they may have been given in with a view to the Prize or not. III. NEILL PRIZE. The Council of the Royal Society of Edinburgh having received the bequest of the late Dr Patrick Nr1Lu of the sum of £500, for the purpose of “ the interest thereof being applied in furnishing a Medal or other reward every second or third year to any distinguished Scottish Naturalist, according as such Medal or reward shall be voted by the Council of the said Society,” hereby intimate, 1. The Netty Prize, consisting of a Gold Medal and a sum of Money, will be awarded at the commencement of the Session 1871-72. 2. The Prize will be given for a Paper of distinguished merit, on a subject of Natural History, by a Scottish Naturalist, which shall have been presented to the Society during the three years preceding the Ist May 1871,—or failing presentation of a Paper sufficiently meritorious, it will be awarded for a work or publication by some distinguished Scottish Naturalist, on some branch of Natural History, bearing date within five years of the time of award. AWARDS OF THE KEITH, MAKDOUGALL BRISBANE, AND NEILL PRIZES, SINCE 1865, AWARD OF THE KEITH PRIZE. 20TH Brenniat Pertop, 1865-67, Professor C. Prazzt Smyrtu, for his paper on “ Recent Measures at the Great Pyramid,” published in the Transactions of the Society. -MAKDOUGALL BRISBANE PRIZE. 5TH Bienniat Periop, 1866-68. Dr Arex. Crum Brown and Dr Tuomas Ricuarp Fraser, for their conjoint paper on “The Connection between Chemical Constitution and Physiological Action,” published in the Transactions of the Society. AWARD OF THE NEILL PRIZE. 4tn Trisnniat Periop, 1865-68. Dr Wittram Carmicnart M‘Intoss, for his paper on “ The Structure of the British Nemerteans, and on some New British Annelids,” to be published in the Transactions. ENE iJ, ve itd ol, ite wor Avail acs 4 ine ¢ ‘ 4 7 a ‘i af : emesthilt ail rh hay ees E es baiting’? ai — re 7, . af : >, 9 i : i, $ te 5 _ aA att - a). : ss % ; ea ee eh “Sa a! “Ps Reh r] ' cee , ‘ z frst en ee a Silead ’ . Stn}, bnderlidiny if" aplie / Lacli real of e \ —— “ethane ‘ick 4 a > { . 4 ry c z a J a SO at i] - a « , . , pe eS aire : ; wil? * hy) a m1 MY i i 4 et at athe. coty Sdamesstint 7 a i a, “We bes pases A eget“ wal ty tS ata ih Dy snutronmiby tT oft sn Beelar li ail ali oy "abel lg So ae i DIRECTIONS TO THE BINDER FOR PLACING THE PLATES IN THIS VOLUME. Plate oT Meee Dr John Denis Macdonald’s peee on the Order and Classi- fication of Heteropoda, é . To face page 20 ay Illustrating Mr Wm. Turner’s Paper on ‘Ihe Sinictiare of the Chondracan- ia thus Lophi, with Observations on its Larval Form, . 76 Illustrating Mr Wm. Turner's Paper on the Structure of Lerneopoda Dal- manni, with Observations on its Larval Form, 88 Illustrating Mr Edward Sang’s Paper on the Deflection of the hess due to Solar and Lunar Attraction, : 94 VI Illustrating Sir David Brewster’s Paper on the Hivistonen of Acari ee the Lamine of Mica in Optical Contact, ; 96 VI. Illustrating Sir David Brewster’s Paper on Certain Vegetable and ane el Formations in Calareous Spar, : 98 VIL. Illustrating Professor William Thomson’s eee on the Seah: Cooling of the Harth, . : 170 ( Illustrating Dr John Denis Meedonaldis Ea eg on the Pnronontene Relationships of the Fixed and Free Tunicata, regarded as two Sub- IX Classes of equivalent value (figs. 1, 2); on the Zoological Character of the living Clio caudata, as compared with those of Clio borealis given in Systematic Works ‘(fig. Oe and Notes on the ease of the Genus Firola (fig. 4), . 192 X. ( Illustrating Sir David Brewster’s fears on the ‘Smee aca Optical xo Phenomena of Ancient Decomposed Glass, . 204 XI f Illustrating Sir David Brewster’s Observations on the Polar Aton of the { Atmosphere, made in St Andrews, . 240 Tlustrating Professor Allman’s Paper on a Pre. Trachial Stage in fhe xin} Development of Comatula, and its importance in relation to certain Aberrant Forms of Extinct Crinoids, . ‘ s 2 2. 202 XIV. ne an Illustrating Dr R. E. Scoresby-Jackson’s sane on the Influence of Weather XVIL upon Disease and Mortality, . 348 XVIII. XIX Illustrating Sir David Brewster's Description of the Lithoscope, an Instru- ; ment for Distinguishing Precious Stones and other Bodies, . . 424 XX. Illustrating Professor Kelland’s Paper on Superposition, . 474. XXI. f Illustrating the Rev. Robert Boog Watson’s Paper on the Great Drift XXII. Beds with Shells in the South of Arran, : 546 XO. enn Illustrating Professor Smith’s oe on some pout in the ee ey of XXVL the Great Pyramid, : 706 XXVII. XXVIII. § Illustrating Dr J. B. Pettigrew’s Paper on the Structure and Action of DOB: the Auriculo-Ventricular Valve, g 806 VOL. XXIII. PART III. C iy 2 iA rer ! it Gece Maly’ 2 > 7 i. aie : | Pe dtc) Vittnahahet ol¥s LAWS OF THE ROYAL SOCIETY OF EDINBURGH. AS REVISED 5ru JANUARY 1857. tng eye on (tH SP vu a if i" aif td taal itt abide , : ic re ete i il co a a ser — « Br, ¢ oP wath Py | a +44 ry y a oe " oF iy ? , oe acl ; ’ ' ry f , ig, ~ ef. ‘ ij va . f ie ait ws 4 ‘ J i ” i i oe | | a nip meres ie ; i pinagee e! 4 ge 1@ is a W2 pen oe ’ es i a Fr +iga by , yo Nal Meat Re” Me eaten * if 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.| I. THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Honorary Fellows. : Sie Every 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.* ILl. All Fellows who shall have paid Twenty-five years’ annual contribution shall be exempt 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 shall be 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 £38, 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. VOL. XXIII. PART III. d Title. The fees of Ordi- nary Fellows resid- ing in Scotland. Payment to cease after 25 years. Fees of Non-Resi- 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. XiV 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. ‘2 Members failing to pay their contribution for three successive years (due ap- plication 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. VI. The number of Ordinary Fellows shall be unlimited. Watt: 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. 1x, 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 of that 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. XV 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 circular for the meeting at which the Ballot is to take place. XItT. The election of Ordinary Fellows shall take place at the Ordinary Meetings of 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. ou, 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 the Royal Society of Edinburgh. Royal Personages. Recommendation of Honorary Fel- lows. Mode of Election. Election of Ordi- nary Fellows. Ordinary Meet- ings. The Transactions. How Published. The Council. Retiring Council- lors. Election of Office- Bearers. Special Meetings ; how called. Treasurer’s Duties. Auditors. XxVl deem it expedient to publish in the Transactions of the Society, and shall super- intend the printing of the same. XVI. The Transactions shall be published in Parts or Fasciculi at the close of each Session, and the expense shall be defrayed by the Society. 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, granting 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 last Ordinary Meeting in January 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. XXI. At the Extraordinary Meeting in November, a Committee of three Fellows shall be chosen to audit the Treasurer’s accounts, and give the necessary discharge of his intromissions. XV1l The report of the examination and discharge shall be laid before the Society at the last Ordinary Meeting in January, and inserted in the records. 0.458 The General Secretary shall keep Minutes of the Extraordinary Meetings of General Secretary's 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 See foe which a full account of the proceedings of these Meetings shall be entered; they 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 ee ae all the Books, Manuscripts, objects of Natural History, Scientific productions, and 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. OSS All articles of the above description shall be open to the inspection of the Use of Museum Fellows, at the Hall of the Society, at such times, and under such regulations, as ag the Council from time to time shall appoint. ; XXV. A Register shall be kept, in which the names of the Fellows shall be enrolled Register Book. at their admission, with the date. VOL XXIII. PART III. é Ril oe — Ch mi of riled “ta ‘oA tieds te OO asechcay pn Teh = Me ae is Rod tailia rays ieee oy s tea hie * ra ty as Fay At 1) Aaah ae eight? wu Nisei reaeeni_B wi! : perio + Bei % Rete r z ae 1" aA Hie ie ae Dil N | gilnw’ al shi L Inds 4 ilk Att patows BB! ; i. se. eth cs 5 ’ Bua? ty hey at Wy A op : A wer eee wh teh a Ree fi . . ‘ y es 3 : ; ‘ "Eh ee ca a ay —: 1 re 5 - “ “of el ; ¢ or CONTENTS. PART I. (1861-62.) PAGE . On the Anatomy and Classification of the Heteropoda. By JoHN Denis MAcponaLb, R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” (With two Plates, I., IT.), : : ; 1 — Il. Investigation of an Expression for the Mean Temperature of a Stra- tum of Soil, in Terms of the Time of Year. By Josery D. Everett, M.A., Professor of Mathematics, &c., in King’s Col- lege, Windsor, Nova Scotia, . ; 4 21 Ill. On a Difficulty in the Theory of Rain. By JAmEs DatmAnoy, Esq., . 29 IV. On the Pressure Cavities in Topaz, Beryl, and Diamond, and their bearing on Geological Theories. By Sir Davin Brewster, K.H., DCE RS., : ; ; : : 39 V. On the Theory of Numbers. By H. F. Tazot, Esq., 45 VI. On the Rain-Fall in the Lake District in 1861, with some Observa- tions on the Composition of Rain Water. By Joun Davy, M.D., F.R.SS. Lond. & Edin., é } : 53 VII. On the Structure of the Chondracanthus Lophii, with Observations on its Larval Form. By Wma. Turner, M.B. (Lond.), F.R.S.E., and H. 8. Wixson, M.D., Demonstrators of Anatomy in the University of Edinburgh. (With a Plate, III), : : 67 VIII. On the Structure of Lerneopoda Dalmanni, with Observations on its Larval Form. By Wm. Turner, M.B. (Lond.), F.R.S.E., and H. 8. Witson, M.D., Demonstrators of Anatomy. (With a Plate, IV.), f : : : : ‘ 2 77 IX. On the Deflection of the Plummet due to Solar and Lunar Attraction. By Epwarp Sane, Esq. (With a Plate, V.), : 89 xX b-GE XII. XIII. XIV. ay. VE XVII. CONTENTS. - On the Existence of Acari between the Lamine uf Mica in Optical Contact. By Sir Davip Brewster, K.H., D.C.L., F.R.S. (With a Plate, VI.), On Certain Vegetable and Mineral Formations in Calcareous Spar. By Sir Davip Brewster, K.H., D.C.L., F.R.S. (With a Plate, VIL.), , ‘ Memoir of the Life and Writings of Robert Whytt, M.D., Professor of Medicine in the University of Edinburgh from 1747 to 1766. By Wituiam Sevier, M.D., F.R.S.E., Fellow of the Royal College of Physicians of Edinburgh, Experimental Inquiry into the Laws of the Conduction of Heat in Bars, and into the Conducting Power of Wrought Iron. By James D. Fores, LL.D., D.C.L,, F.R.S., V.P.R.S. Ed., Corre- sponding Member of the Institute of France, Principal of the United College of St Salvator and St Leonard, St Andrews, . On the Density of Steam. By Professor W. J. Macquorn Ran- KINE, C.E., LL.D., F.R.SS. Lond. and Ed., &c., On the Secular Cooling of the Earth. By Professor Witt1am THom- son, LL.D., F.R.S., F.R.S.E. (With a Plate, VIII.) PART II. (1862-63.) On the Representative Relationships of the Fixed and Free Tunicata, regarded as two Sub-Classes of equivalent value; with some General Remarks on their Morphology. By Joun Denis Mac- DONALD, R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” Com- municated by Professor Mactacan. (With a Plate, IX.), On the Zoological Characters of the Living Clio caudata, as compared with those of Clio borealis given in Systematic Works. By JoHN Denis Macpona.D, R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” Communicated by Professor Macuacan. (With a Plate, IX. fig. 3), : PAGE 95 97 99 133 147 157 185 XVIII. XIX. XX. XXI. XXII. i, XXIV. XXV. XXVI. XXVII. XXVITT. CONTENTS. Notes on the Anatomy of the Genus Firola. By Joun DENIs MacponaLp, R.N., F.R.S., Surgeon of H.M.S. “Icarus.’’ Com- municated by Professor Mactacan. (With a Plate, IX. fig. 4), On the Structure and Optical Phenomena of Ancient Decomposed Glass. By Sir Davin Brewster, K.H., D.C.L., F.R.S., &. (With two Plates, X., XI.), : . : On the Polarisation of Light by Rough and White Surfaces. By Sir Davip Brewster, K.H., D.C.L., F.R.S., &., ‘ Observations on the Polarisation of the Atmosphere, made at St Andrews in 1841, 1842, 1843, 1844, and 1845. By Sir Davip Brewster, K.H., D.C.L., F.R.S., &. (With a Plate, XII.), On a Pre-Brachial Stage in the Development of Comatula, and tts umportance in relation to certain Aberrant Forms of Extinet Crinoids. By Professor ALLMan. (With a Plate, XIII.), Some Account of the Recent Progress of Sanskrit Studies. By J. Mir D:C.., bebe. : : ? 2 On Fagnani’s Theorem. By H. F. Tarot, Esq., On the Influence of Weather upon Disease and Mortality. By R. E. ScoresBy-Jackson, M.D., F.R.S.E., F.R.C.P., Lecturer on Ma- teria Medica and Therapeutics at Surgeons’ Hall, Hdin- burgh. (With Five Plates, XIV.—XVIII.), On the Anatomical Type of Structure of the Human Umbilical Cord and Placenta. By J. Y. Simpson, M.D., Professor of Medicine and, Midwifery in the University of Edinburgh, On Earth-Currents during Magnetic Calms, and their connection with Magnetic Changes. By Batrour Stewart, M.A., F.R.S., On the Great Refracting Telescope at Elchies, in Morayshire, and its Powers in Stdereal Observation. By Professor C. Piazzt SMYTH, VOL. XXIII. PART III. 4 of Xx1 PAGE 189 193 211 285 299 349 355 371 Xxil CONTENTS. PART TIT. (1863-64.) XXIX. Description of the Lithoscope, an Instrument for distinguishing Precious Stones and other bodies. By Sir Davip BREwsTER, K.H., F.R.S. (With a Plate, XIX.), XXX. On the Agrarian Laws of Lycurgus, and one of Mr Grote’s Canons of Historical Criticism. By Professor BLACKTE, XXXI. On the Limits of our Knowledge de the Theory of Parallels. By Professor KELLAND, XXXII. On the Temperature of Certain Hot-Springs in the Pyrenees. By R. E. Scorespy-Jackson, M.D., F.R.C.P.E., Lecturer on Ma- ° XXXII. On Superposition. By the Rev. Paiwip Keiuanp, M.A., F.R.S., Professor of Mathematics in the University of Edinburgh. Part II. (Continued from Vol. XXI. p. 273.) Ae a Plate, X-X.), XXXIV. On the Variations of the Fertility and Fecundity of Women accord- ing to Age. By J. Matraews Duncan, M.D., XXXV. On the most Volatile Constituents of American Petroleum. By EpmunpD Rona.ps, Ph.D., XXXVI. On Sun-Spots and their Connection with Planetary Bete By BatFrour Stewart, M.A., F.R.S., XXXVIT. On the freezing of the Egg of the Common Fowl. By Joun Davy, M.D., F.R.SS. Lond. and Ed., &. (Communicated by Pro- fessor MACLAGAN), XXXVILI. On the Morphological Relationships of the Molluscoida and Ceelen- terata, and of their leading Members, inter se. By JoHN DENIS MacponaLp, R.N., F.R.S., Surgeon of H.M.S. ‘ Icarus,” XXXIX. On the Great Drift Beds with Shells in the South of Arran. By the Rev. Ropert Boog Watson, B.A., F.R.S.E., Hon. Mem. Nat. Ver. Liineburg. (With two Plates, XXI., XXII), teria Medica and Therapeutics at Surgeons’ Hall, Edinburgh, PAGE 419 425 433, 471 475 491 499 515 523 CONTENTS. XL. On the Principal Deities of the Rigveda. By J. Murr, D.C.L., £D., : ; XLI. The Law of the Volumes of Aeriforms extended to Dense Bodies. By Rev. J. G. Macvicar, M.A., D.D., Moffat, . XLII. Biographical Sketch of Adam Ferguson, LL.D., F.RSE., Pro- fessor of Moral Philosophy in the University of Edinburgh. By JoHN SMALL, M.A., Librarian to the University, . XLII. On the Reputed Metrological System of the Great Pyramid. By Pro- fessor C. PrazziSmMytuH. (With five Plates, XXIII.—XXVIL.), XLIV. On the Theory of Isomertec Compounds. By Dr A. Crum Browy, XLV. On the Theory of Commensurables. By Epwarp Sana, Esq. XLVI. On the Structure and Action of the Auriculo-Ventricular Valves. By James B. Pettigrew, M.D. Communicated by W. TuRNER, M.B., Demonstrator of Anatomy in the University of Edin- ~ burgh, Proceedings of Statutory General Meetings, cc., List of Members Elected, : List of the present Ordinary Members, in the ay of their Election, List of Non-Resident and Foreign Members, elected under the Old Laws, » Honorary Fellows, ,, ellows Deceascd, Resigned, ihe Cahebiied: tom 1861 to 1864, Public Institutions, de., entitled to receive the Transactions and Proceedings of the Soctety, List of Donations continued from Vol. XXII, p- 750, Index, XXili PAGE 047 581 599 667 707 721 761 807 814 816 823 823 825 826 828 857 a A E e ' = ' ~ ne. 0 1 a: - —_ 4 O ; ne = 4 iy \ ie A ; ye ee he Nir ks \ ee y's cyt f — jo | : ALO Sere eT pate! 5 : kath > \ ‘ BAnGe af yh Woalt i rd i By ey mae ‘ ieee, wd RR Re > a: : we Ab, oh Aa Wee iy 4 b - : + ra Al é Ti dit Wierd aye i? “a rivry = fi ‘ “PETS, edb D mat + * ah Be 7 claPt he y tea ab B 7 t f : ; i i tab i x + , : " “ ’ , Pal » Te iad } : ; = ye a y ; . ‘ * = ¥ ’ ?7 . - an * me fa 5 at 4 dee, + una ATR wilh g ier edt p 4 BAS shine Aa yet 5 ag { 4 — Pd _-: 4 : R ‘ * . is ‘ , be 5 i A, , . : % 4 F \ y a ow | : ; a . » i . : 7 a - ‘3 oe 7 ¢ 2 x TRANSACTIONS. I1—On the Anatomy and Classification of the Heteropoda. By Joun DENIs Macponatp, R.N., F.R.S., Surgeon of H.M.S. ‘Icarus. (Plates I., IT.) (Read 30th January 1862.) Notwithstanding the rapid progress of zoology in other departments, the Heteropoda still remain imperfectly known, if one may form a judgment from the scantiness of definite information respecting them to be found in systematic works. Nearly all the available space is usually occupied with an exposition of the errors and doubts of the great men who gave us the first outlines of the order, while comparatively little is done to improve the subject, or make it intelligible to the student. Having had favourable opportunities of examining all the veritable genera of existing Heteropoda, I have attempted the arrangement of my notes in a con- nected form; and as they have been taken directly from nature, I am led to hope that some little may be thus added to what may be already known of the parti- cular species investigated.* It is usual to divide the Heteropoda into two families,—viz., Firolide and Atlantide ; but it appears to me that there is as little difference between Oxy- gyrus and Cardiapoda, as there is between the latter genus and Piroloides, while all three differ sufficiently «ter se to warrant their separation into three distinct families, in each of which two well-defined genera may be included; thus— 1. Firolide, Fir oloides (Lesueur), Firola (Perou and Les.) 2. Carinariide, Cardiapoda (D’Orb.), Carinaria (Lamarck), 3. Atlantide Ozygyrus (Benson), Ailanta (Lesueur). * Not having had the opportunity of consulting many of the original figures of the French naturalists, I have to acknowledge the great advantage I have derived from the study of Mrs Gray’s excellent etchings, in helping me to determine species, as also the descriptive letterpress of Dr Gray. Many of the anatomical particulars detailed by me had, of course, been previously observed by others; and though I have not clogged the paper with the separate announcements, dates, and authorities of every addition to our knowledge of Heteropoda,—which, indeed, would be no small task,—I can vouch for it, that all the facts embodied in the text have fallen under my own observation, and they may therefore be regarded either in one sense as original matter, or in another, as confirmation of what had been already made known. VOL. XXIII. PART I. A 2 MR MACDONALD ON THE ANATOMY The zoological characters of these three families and their genera are given in the following Table of Classification :— Heteropoda. I. Gymyosomara* (Firolide), Animal wholly naked or without a shell, 1. With slender tentacula, and destitute of true branchie, Visceral mass near the root of the filiform process of the metapodium,—Firoloides. 2. With rudimentary or notentacula, but furnished with true branchiz. Visceral mass con- siderably in advance of the base of the filiform process of the metapodium, —Firola. II. Tuecosomara worercurata (Carinariide). Animal in great part naked, but having the visceral mass protected by a shell. 1, Shell corneous, with an involute nucleus. Swimming-plate nearly opposite the visceral mass. Metapodium with filiform appendage,—Cardiapoda. 2. Shell calcareous, with spiral nucleus, Swimming-plate considerably in advance of the visceral mass, Metapodium laterally compressed, without filiform appendage,— Carimaria, III. Tuecosomata opercutata (Atlantide). 1. Shell corneous, with an involute nucleus. Operculum subtrigonal, with small lateral subapical nucleus,—Oxygyrus. 2. Shell calcareous, with a spiral nucleus. Operculum oval, with a large median sub- apical nucleus,—Atlanta, I have thus far anticipated myself in the construction of the preceding table, but as it affords a bird’s-eye view of the subject, it will be found convenient for reference as occasion may require. General Outline of the Order. The Heteropoda are pre-eminently distinguished by the laterally compressed and fin-like configuration of the body of the foot and propodium; the rudimen- tary state of the creeping disc (mesopodium), and the great length of the opercu- ligerous lobe (metapodium), or its homologue, often continued into a kind of caudal appendage. The remarkable transparency of the tissues of these animals reveals a great part of their internal structure to the anatomist without dissection, which is often a matter of great difficulty, arising from the same circumstance. They are all furnished with a cylindrical proboscis-like muzzle, and a well marked neck, large, mobile, and singularly beautiful eyes, lying in socket-like spaces, though invested with the common integument at the posterior part of the base of simple conical tentacula, except in the true /7role, in which the tentacula are absent, or at most very rudimentary. The auditory sacs in all contain single spherical otoliths, increasing by exo- genous layers, and revolving like planets on their axes, by the action of vibratile cilia lining the sacs. The large size of the lenses of the eyes, as compared with that of the otoliths, affords a character, which, although of a relative nature, is * T have made use of the convenient terms Gymnosomata and Thecosomata in a similar sense to that in which De Brainvitiz applied them to the Pteropoda. AND CLASSIFICATION OF THE HETEROPODA. 3 of much importance in distinguishing the Heteropoda. In Cardiapoda and Cari- naria, as well as in the naked genera, the acoustic sacs are, as it were, appended to the auditory nerves, which are of considerable length, and arise from the supra- oesophageal ganglia. In the latter particular the heteropods differ from most of the true gasteropods, in which the special centre of audition is incorporated with the subcesophageal ganglia. The oral aperture is circular, and at the extremity of a lengthy muzzle, within which the “‘ buccal,” or rather the lingual mass, appears to occupy but a small space. There are no labial or maxillary dental organs, but the lingual armature is highly characteristic of the order. In accordance with the laws of its develop- ment, the lingual ribbon gradually increases in breadth from before backwards. The rachis consists of a single series of plates, while there are three members in each pleura; and all the dental points are simple, sharp, and conical, either per- fectly straight and projecting backwards, or slightly curved and inclined more or less inwards. The segments of the rachis bear a variable number of simple teeth; but the internal pleural plates, whose attached surface occupies nearly, or quite the whole breadth of the pleurse, generally present one large dental process at the inner extremity, with a much smaller one somewhere near its base. The absence of this smaller tooth, or, when present, its internal or external position with respect to the larger one, may be taken into account in classification; but as the two outer members of the pleuree in all the Heteropoda are in the form of simple claw- shaped uncini, any specific characters afforded by them can only be of a relative nature, as to proportionate length, amount of curvature, thickness, &. On ex- hibiting my preparations and drawings to my respected friend, Mr W. S. Macteay, he saw very plainly that generic characters might be drawn from the rachis alone ; and it was with no small satisfaction that I enjoyed the concurrence of so great a man in my first attempt to effect a classification of the MHeteropoda, by their lingual dentition, which so often outlives the decay of the soft parts generally. The gills, or branchie, usually consist of a linear series of short claviform or tapering processes, with a loose cellular investment, presenting a longitudinal zigzag fold on the inner surface, giving rise to the plumose appearance sometimes so incorrectly represented in figures of these animals. In /rolotdes, however, I have never seen any vascular appendages of the nature of gills, and they are frequently absent, or inconspicuous even in Atlanta. In closing this general sketch, it only remains to be stated, that the sexes are distinct in Heteropoda, as was first suspected by M. LauriILLarp, who assisted the great Cuvier in his dissections. Mr Macteay further informed me that CuvieER, on the same account, was deterred from placing them amongst his Tecti- branchiata. Modern anatomists, however, have thought fit to contradict this opinion, though upon what grounds, except hearsay, it is difficult to determine. 4 MR MACDONALD ON THE ANATOMY I had originally intended to pass all the genera in review, dealing with the whole anatomy of each in the order observed in the foregoing table ; but this would extend the paper beyond reasonable limits, and perhaps prove monotonous to the reader, from the frequent repetitions of essentially the same anatomical particulars, however striking their modifications may be, in the different members of this natural order. I shall therefore first make selection of Firoloides and Atlanta for especial description, occupying, as I conceive them to do, the two extremes of the group; and those modifications to which I have alluded may be briefly noticed in a passing glance at the remaining genera, or at least the particular species which have casually fallen under my observation. Firoloides (Lesueur). While cruising in the South Seas, and subsequently in the neighbourhood of the West India Islands, I was fortunate enough to obtain numerous specimens of a solitary species of F%roloides, and which I find, if Iam not very much mistaken, has been several times named by different writers who may have met with it under such deceptive conditions as to mask its identity. Thus, the male and female of this species are represented in Plate XVI., Voy. la Bonite, figs. 8 and 1 respectively, though the former has been designated Firola de Keraudrem, as also Eydouxii, and the latter F. de Desmarest. I have traced it, moreover, under other names in certain less definite figures, illustrating the works of the French natur- alists, who appear to have had most to do with the Heteropoda from the very foundation of the order, though it is scarcely reconcilable with Lesueur’s figure of Firola Demerastiana (I, ¢, i, 39, t. 2, f, 1), which Dr Gray seems to regard as the type of the genus /7roloides. Now, though all this may be justly regarded as a stumbling-block to the student, he has still more to encounter in the literature of other genera. I shall therefore eschew the naming mania altogether, and simply attempt succintness of description, aided by fidelity in the figures, so as to render the species in question just as definite as if I were to add fresh synonyms to the existing confusion. It isa cheering reflection, however, to know that we have in the lingual dentition a guide that cannot be gainsayed, and whose ex- punging power may be safely applied to a host of mzs-applied cognomina with their bracketed italics. On entering Bass’ Strait in H.M.S. “Torch,” I obtained my first Firolordes, which was so perfectly transparent that, but for the brilliancy of its eyes, relieved by the dark pigment coat protecting the retinze, it would probably have passed unobserved. When immersed in sea-water, the eyes were seen rapidly swaying from side to side with the undulatory movement of the elongated and pliant body, no other parts being visible but the faintly rose-tinted visceral nucleus and the little buccal mass. AND CLASSIFICATION OF THE HETEROPODA. o The whole length of the animal did not exceed an inch and a quarter; and when placed under the microscope, the principal features of its anatomy were traceable through the integuments. (Plate L. figs. 1, 2, 3 and 4.) The head supported two delicate tentacule of moderate length and taper form, and a large and beautiful eye occupied a considerable dilatation at the back part of the base of each. The muzzle was rather slender, with a small truncated ex- tremity, within which was contained a minute buccal mass, lodging a short lingual sac. At the posterior part of this organ, the buccal artery terminated between two nodules of nervous matter (buccal ganglia) (Plate I. fig. 2, d), while a narrow oesophagus proceeded from its upper and fore parts. The principal viscera were clustered together at the hinder extremity of the body, which is abruptly truncated above, but produced inferiorly into a suddenly tapering tail (Plate I. fig. 4, g), terminating in a filamentous appendage (Plate I. fig. 1, n, fig. 4, h), marked at certain intervals by slightly dilated joints or rings, softly tinted with brownish pigment. This appendage is highly sensitive and mobile, trailing in an undulatory manner after the animal as it swims. I can safely say that it is neither a tapeworm nor an oviduct, though I am as yet unac- quainted with its use. The characteristic laterally compressed and fan-like foot (Plate I. fig. 1, g) of the Heteropod crested the ventral surface of the body at a little distance poste- rior to the centre, and near the fore part of the free margin of this organ a minute sucker-dise (Plate I. fig. 1, f) was distinctly visible. The body in this species is everywhere enveloped by a perfectly transparent homogeneous-looking integument, the inner surface of which is studded at irregular intervals with small clusters of cells, surrounding a larger vesicle (most probably cutaneous glands). Internal to this there is a stout muscular sheath (Plate I. fig. 2,0), which includes the buccal mass in front, and the visceral nucleus behind where it extends into the tail, the homologue of the operculigerous lobe of the foot in ordinary gasteropods. The preceding sketch will suffice to give a general idea of the animal ; but we shall now proceed to consider more in detail the anatomy of the organs of sense and the several organic systems, which will enable us to understand more thoroughly the modifications of this type occurring in the other genera. Organs of Sense and Nervous System.—tThe eyes of Firoloides (Plate I. fig. 1, b, fig. 2, 1), like those of other Heteropoda, are very large and beautiful, and situate at the posterior part of the base of the slender tentacula. They are invested by the common integument, and exhibit a very remarkable structure. A little bulb, some- what compressed from above downwards and constricted in front, forms the body of each. This is usually of a pale reddish-brown tint, and sparingly lined with darker pigment granules. A perfectly spherical lens of highly refracting material rests ina depression at its fore-part, and the lens itself is capped over by a strongly VOL. XXIII. PART I. B 6 MR MACDONALD ON THE ANATOMY curved meniscus, in which a cell-structure is often distinctly visible beneath the cutaneous covering. The acoustic capsules (Plate I. fig. 1, c, fig. 2, m) contain each a transparent glo- bular otolith, which is very much smaller than the lens of the eye. Several little prominences, on the inner surface of the capsules, represent those which poise off the crucial otolith of Sepia, from the wall of the vestibule in which it lies. The ear-sacs, moreover, appear to float freely within the muscular sheath, being connected with the cerebroid ganglia by long and delicate auditory nerves. The nervous system of this creature, from the peculiar mode of distribution of its ganglia and communicating or commissural cords, not a little resembles the homo-gangliate type. Two elliptical knots of nervous matter lying side byside, and blended together by theircontiguous borders, compose the cerebroid ganglia (Plate I. fig. 2,i) in which the combination of several smaller centres maybe distinctly traced in recent specimens. Two large nerve-trunks, derived from the cerebroid ganglia anteriorly, com- municate with the before-mentioned buccal ganglia, lying at the posterior extremity of the lingual cartilages, and give off nerves to the buccal mass and mouth. The optic nerves (Plate I. fig. 2, h) emerge from the posterior part of the outer border of the cerebroid ganglia, by a club-shaped base, and taper gracefully towards the eyes, at the back part of which they form a remarkably thick retinal expansion. The delicate auditory nerves arise immediately behind the optic, and thence passing outwards and backwards some little distance, reach the acoustic sacs (Plate I. fig. 1, c, fig. 2, m), upon the walls of which other more delicate filaments are also distributed. On examining the origin of the larger nerves, it would appear as though they communicated with each other in the median line by very faint strize traversing the substance of the cerebroid ganglia. From the posterior border of the latter bodies, two large nervous chords (Plate I. fig. 2, n) pass directly backwards, including between them the cesophagus (Plate [. fig. 1, e, fig. 2, @) and buccal artery (Plate I. fig. 2, e), and having reached the root of the swimming-fin, they join the fore part of the pedal ganglia (Plate IL. fig. 1, h, fig. 3, a)—two nearly circular but laterally compressed masses of nervous matter connected with one another by their contiguous surfaces. These ganglia give off numerous branches to the neighbouring parts, but from the inferior border of each a special nerve descends with the pedal artery, and is ultimately distributed to the swimming-plate, while two stout trunks, arising from the posterior part of the ganglia, blend together in a loose plexiform manner, and course backwards as asingle chord. This at first accompanies the oesophagus, to which it supplies several branches, next sends off a nerve of communication to the visceral ganglia, and, finally subdividing in the tail, is lost in the filamentous appendage. AND CLASSIFICATION OF THE HETEROPODA. 7 As far as I have yet discovered with any certainty, the visceral ganglia are two in number—viz., Ist, A minute nodule of neurine (Plate I. fig. 4, d), joined by the commissural nerve above mentioned, and situate at the angle between the origin of the visceral artery and the continuation of the maintrunk; and, 2dly, a much larger oblong subquadrilateral ganglion (Plate I. fig. 4, e), lying on the right wall of the intestine near its origin. From the superior angles of the latter body distinct branches take their rise; one in particular joining the former ganglion, while others are distributed to the heart and everted mantle with its sphincter-like opening. The digestive and internal generative organs are supplied with nerves from the inferior angles of the same nervous centre. Digestive System.—The proboscis of /trolotdes is susceptible of retraction and protrusion to a considerable extent, in which movements the fore-part of the common muscular sheath, and even the cesophagus itself, plays an important part (Plate I. fig. 2, g). The oral orifice (Plate I. fig.2, a) is terminal, rounded, and unfurnished with labial plates or mandibles of any kind. The buccal mass (Plate I. fig. 2, d) is small, and placed nearthe extremity of the muzzle, as above-mentioned. The lingual cartilages, in which the cell structure is beautifully marked, are oval in shape, wrapped to- gether by ligaments, and supplied with muscles to effect their varied movements. The tongue-sac is scarcely longer than the cartilages, terminating posteriorly in a rounded extremity, and the dental area exhibits a remarkable increase in its breadth from before backwards. The rachidian plates (Plate I. fig. 5, 0) being con- cave both in front and behind, are broadly (H) shaped, and bear a large central tooth, with a little comb of denticles on either side. The first or inner pleural plates (Plate I. fig. 5, 1) are destitute of a small inner tooth near the base of the large cusp, and the uncini very nearly equal the breadth of the pleurze, as given in Plate I. fig. 5. An elongated and somewhat flattened salivary gland (Plate I. fig. 2, c) lies along the lingual cartilage on either side, and communicates with the mouth by a very short duct. The cesophagus, proceeding from the upper and fore-part of the buccal mass, takes a course directly backwards, in close relationship with the buccal artery and nerves, and having reached the visceral nucleus, the canal exhibits a slight gastric enlargement, which receives the biliary ducts inferiorly from the supero- posterior wall of the stomach; a short intestine passes upwards and backwards between the heart and the abdominal viscera, and terminates in the anus (Plate I. fig. 4, 0) on a little prominence above the latter organs, and below and between two small anal lobes or leaflets (Plate I. fig. 4, p). The lining membrane of the stomach and intestine is richly ciliated, but the cilia increase both in size and activity as they approach the vent, around which they may be very distinctly observed. The apparently undulatory movement 8 MR MACDONALD ON THE ANATOMY produced by the consecutive action of the cilia within the canal, proceeds in a forward direction, though of course the current to which it gives rise takes an opposite course. As compared with the bulk of the animal, the liver (Plate I. fig. 4, f) is of small size; and its minute lobuli may be traced along the posterior wall of the short intestine and stomach, and for some little distance farther, in front of the internal organs of generation, which occupy the remainder of the visceral chamber. The Mantle, Respiratory and Circulatory Systems.—In Atlanta, Carinaria, and Cardiapoda the mantle permanently envelopes the viscera, and, keeping pace with the development of these organs, furnishes the materials of growth to the protect- ing shell. The course of the intestine, and the position of the heart and respi- ratory surface, all of which constantly preserve a definite relationship to each other, exhibit, with reference to the extremities of the body, the usual arrangement prevailing amongst the so-called praso-branchiate gasteropoda,—that is, the ali- mentary canal being bent upon itself, the rectum passes forwards, and the anus terminates it anteriorly; the branchiz also lie in advance of the heart, through which the circulation proceeds in a backward direction. In Firoloides, on the contrary, the mantle is everted and thrown backwards; and the parts above mentioned being more or less intimately connected with it, suffer a remarkable change of position, which will be better understood when we have considered the anatomy of the organs contained in the visceral nucleus. Thus, the free border of the mantle is, as it were, turned inside out, and so very much constricted as to circumscribe asmall oval opening (Plate I. fig. 4,n) on the right side of the visceral mass, and immediately in front of the rectum. This opening is surrounded by a. little sphincter muscle, which is intersected by numerous radiating fibres, so that ample provision is made for its contraction and dilatation, frequently observed with a degree of rhythmical precision in very recent specimens. I have never seen any branchial appendages, properly so called, in Firoloides, although one would imagine, had such been present, that they would be still more apparent in consequence of the eversion of the mantle. Apart from the idea that the general surface of the body may be more or less subservient to respiration, the position of the auricle of the heart points out the locality in which we might expect to find the organs especially adapted to this function. It must be observed, however, that immediately behind the heart, and above the anal lobes, arichly ciliated space or fossa (Plate I. fig. 4,q), with a prominent margin, is constantly present ; and Iam inclined to think that the little clusters of spherical cells, represented in Plate I. fig. 4, r, as occurring upon the pallial wall of the pericardium, may possibly be concerned in respiration, and in some way asso- ciated with the modification of the mantle above explained. The heart, consisting of a single auricle and ventricle, rests upon the mantle- chamber which lies between it andtherectum. The muscular fibres of the auricle AND CLASSIFICATION OF THE HETEROPODA. 9 (Plate I. fig. 4, s) divide and interlace with one another, leaving angular and irre- gular spaces between them. They are not so clearly to be traced in the ventricle (Plate I. fig. 4, t), the walls of which, nevertheless, seem to be somewhat thicker than those of the auricle. A circular constriction marks the union of the two chambers, and two valves guard the auriculo-ventricular opening. The base of the aorta is slightly dilated and highly contractile, being furnished with valves at its origin from the ventricle. It very soon gives rise to a large vessel which passes downwards and backwards to supply the viscera; but the great podo- cephalic division (Plate I. fig. 4, b) crosses over the alimentary tube from the left to the right side, and, having formed a few flexures, runs forwards alongside the cesophagus until it arrives a little in front of the pedal ganglia, where it curves downwards to give rise to the pedal artery (Plate I. fig. 3, c), which opens directly into the great ventral sinus at the root of the swimming-plate. From the origin of the latter vessel the main trunk courses forwards as the buccal artery, and, having reached the fundus of the tongue-sac, it is no further traceable. Generative System.—The external male organ lies on the right side of the body near its posterior extremity, and consists of two portions, one of which is of considerable length, terminating in a bulbous enlargement (Plate I. fig. 1, m), but the other is short, with the orifice or terminal part usually inverted. The follicles of the testicle converge to a duct, which exhibits a fusiform, though twisted dilatation (Plate I. fig. 1, 1) in its course, and which is, moreover, dis- tinguished by its coating of black pigment cells; but the duct does not appear to reach the external organ, or, if it does in this case, nothing of the kind is dis- coverable in the other genera of Heteropoda. The female orifice (Plate |. fig. 4, 1) is situated immediately above the root of the tail, and guarded on each side by a small laterally compressed leaf-like process, somewhat larger than the anal lobes previously noticed. The oviduct (Plate I. fig. 4, 1) is rather capacious, and once or twice doubled upon itself. The ovarian sacculi communicate with its inner extremity; and the impregnated ova, with which the duct is sometimes found distended, may be observed in all stages of yelk-cleavage, exhibiting further advancement as they approach the external opening, from which a delicate nidamental chord with ova, in single or two al- ternating series, may be frequently seen protruding (Plate I. fig. 6). Atlanta (Lesueur). As the remarks which I have to make on the anatomy of Atlanta have wide reference to all the species of the genus, I shall defer the perplexing question of specific determination to a future paper. General Sketch of the Genus (Plate II. Fig. 1). The shell of Atlanta is dextrally-spiral in the young state; but it subse- VOL. XXIII. PART I. C 10 MR MACDONALD ON THE ANATOMY quently becomes plan-orbicular, laterally compressed, and nearly symmetrical, bearing a dorsal keel of variable depth, literally nothing more than a thin fold of the shell itself, which thus presents a deep notch or slit at the corresponding part of the outer lip. The animal admits of complete retraction within its shell, and is furthermore protected by a delicate oval operculum, with a large sinistrally-spiral median, and subapical nucleus (Plate II. fig. 1’). The head of Aé/anta is supported by a kind of neck, with which the proboscis forms an angle more or less obtuse. The eyes are proportionately very large, and fronted by small conical tentacula; and all the parts of the foot are more compact than in Firoloides. Thus, the part corresponding with the tail in the latter genus is an obvious metapodium, bearing an operculum in the former. The swimming-plate is relatively stronger, and the sucker-disc better defined. The visceral mass also bears a larger proportion to the rest of the body. More Particular Description of the Foot and Retractor Muscle. The muscular fibres which fix Atlanta to the shell arise from a short oblique line commencing near the nucleus, and extending some little distance outwards and forwards on the upper or right wall of the tube. From this origin they pass round the columellar wall, gradually diverging from one another as they approach the mouth of the shell. Here they commence to blend with the proper muscular fibres of the foot, but more especially with those of the operculigerous lobe. This lobe forms the posterior part of the foot, from the inferior surface of the base of which the vertical fin bearing the sucker-disc springs. Thus the foot altogether may be said to consist of three distinct portions—viz., the swimming-fin (Plate II. fig. 1,j) in front, the operculigerous lobe (Plate II. fig. 1, 6) behind, and the sucker- disc (Plate IL. fig. 1, k), holding an intermediate position. These structures are mainly composed of a basis of muscular and areolar tissue, overlaid with common integument. The muscular fibres are disposed in ribbed bundles at the central parts requiring the greatest support, and cross one another diagonally over the general surface, so that mobility in every direction is amply provided for; but as all the parts of the foot lie in one vertical plane, corresponding with that of the shell, all the lateral movements of the animal are necessarily the more vigorous. The fin-shaped swimming-plate supports the mesopodium or sucker-dise on its posterior border near the base. The latter disc is divided by a longitudinal depression into two lateral lips or lobes, which meet together when the organ is contracted; but when it is fully expanded and brought into action, after the manner of its homologue, the creeping disc of the true gasteropod, it exhibits a more circular form, and as I have particularly observed in the case of Oxygyrus. glides over any resisting surface with imperceptible undulations. Into its central or concave part a muscular fasciculus, derived from the fibres of the great retrac- AND CLASSIFICATION OF THE HETEROPODA. 11 tor, is fixed, so as, probably, to assist in forming a vacuum when the animal is entirely supported by this small disc; and the epithelial cells on its outer surface are frequently tinted with a yellowish, red, or purple pigment. The metapodium bears the operculum (Plate II. fig. 1, A, and fig. 1’.) on its dorsal surface, and terminates in a point posteriorly. The inferior surface of this curiously constructed tail-piece presents a median vertical fold or reel, which gra- dually decreases in depth as it approaches the pointed extremity where it ends. On either side of this fold is a little fossa, deepening in front, and passing some little distance within the anterior margin. To this latter part is appended a small moveable and valve-like process (Plate II. fig. 1. «), whose use I have not yet dis- covered; but it is probable that it has some office in directing the path of the respiratory currents, when the animal is retracted into its shell; and this view is favoured by the fact that the floor of each fossa is richly ciliated, with the un- dulations proceeding from behind forwards. Organs of Sense and Nervous System.—The eyes (Plate II. fig. 1, e), as above- mentioned, are proportionately very large, and situated immediately above and in front of the cerebroid ganglia, capped over by a portion of common integument, which bulges out to enclose them. The outer and fore-part of this covering is beautifully rounded, smooth, and transparent, so as to form a kind of external cornea, lying directly over a brilliant spherical lens. Commencing at a zone cor- responding with the limits of the cornea, the cell-pavement of the integument, and the deeper muscular tissue, become more apparent; and in front of each cornea, towards its inner side, is a conical and contractile tentaculum (Plate II. fig. 1, c) of small size compared with that of the eye. The lens, which is com- pressible to a certain extent, and invested with a capsule of homogeneous mem- brane, lies in front of a cylindrical case, which is somewhat fuller at the inner and posterior part, where the optic nerve expands into the retina, and all stray luminous rays are absorbed by a dense coating of reddish-purple or black pigment cells extending forwards to the lens, upon which it encroaches in an annular form to about one-fourth of its diameter. At the inner side of the base of each eye there is a small projection upon which it rolls, obedient to the action of numerous small muscular bands that spring from the borders of a kind of socket, and are inserted into the organ at different points of its circumference. Thus the eyes enjoy a considerable range of motion, quite independent of the outer covering; and often, when the bright lens rolls within the margin of the pigmentary coating, the singular appearance of winking is produced. Both eyes generally move in concert, but each organ enjoys its own intrinsic movements irrespective of the other. The acoustic capsules (Plate II. fig. 1, g), consisting of homogeneous membrane with a ciliated lining, contain each a single vitreous-looking otolith, usually with a small cavity in its centre, around which the successive deposit of concentric layers 12 MR MACDONALD ON THE ANATOMY is distinctly apparent. In Firoloides, Firola, Cardiapoda, and Carinaria, the auditory nerves are of considerable length, so that the ear-sacs are, as it were, appended to them; but in Ad/anta, which embraces more of the characters of the true gasteropods, those sacs are closely applied to their proper ganglia. The gullet and anterior or buccal division of the aorta pass through a nervous collar consisting of four supra (Plate II. fig: 1. f), and two sub-cesophageal (Plate II. fig. 1, i) (pedal) ganglia, connected by two lateral commissural chords, each of which arises from the two superior ganglia of the corresponding side by distinct slips. The two anterior cerebroids supply the short but stout optic nerves to the eyes, while the acoustic sacs lie in the outer angle between these and the pos- terior ganglia, having no connection whatever with the sub-cesophageal or pedal nervous bodies. The two principal nerves supplied to the buccal mass and mouth arise from the anterior superior ganglia, pass forward on either side of the buccal artery, and at some little distance behind the lingual cartilages divide into a superior and inferior branch, and thus, communicating also with the buccal ganglia, are equally distributed to the muscular and other structures in this locality. The pedal ganglia give off branches to the several parts of the foot, and to the muscular sheath of the body, and two stout commissural nerve-trunks arise from their posterior border and join the visceral ganglia, which preside over the heart’s action and the functions of the neighbouring organs and parts. As there ismuch difficulty in tracing out the filaments derived from those ganglia in A ¢lanta, their homologues in /7roloides may be studied with advantage. Digestive System.—Although the cylindroid proboscis exhibits great pliancy in itself, the range of its movements is much augmented by the mobility of the neck. Destitute of labial teeth, the lining membrane of the mouth is prolonged into the fauces and cesophagus above and behind, being continuous with the lining of the tongue-sac inferiorly, blending with the borders of the dental ribbon, which doubles over the fore-part of the supporting cartilages (Plate IT. fig. 1, h), and thus projects into the oral cavity. The cartilages just noticed form the basis of the tongue, and consist of two principal pieces of an oblong figure, forming, by their union along the mesial line, a grooved pully-like surface, over which the lingual strap glides. In many gasteropods, a smaller piece of cartilage is articulated to the posterior extremity of each of the principal ones, so as to admit of greater mobility, and a certain amount of compression in the longitudinal direction; and I have reason to believe that corresponding pieces exist in the framework of the tongue of Atlanta. The cartilages are connected together and acted upon by trans- verse and oblique slips of muscular fibres, and small bundles pass from the inner surface of the tegumentary covering, to be inserted into them at different points. The lingual strap, commencing by a small point beneath the anterior extremity of the basal cartilages, at first passes a little forwards, then turns upwards and AND CLASSIFICATION OF THE HETEROPODA. 13 backwards, gradually increasing in breadth, and finally forms the floor of the tubular tongue-sac. The rachidian plates (Plate II. fig. 5, g, fig. 8,0) are quadrilateral, and thicker posteriorly than in front, so that the corresponding angles are much more clearly defined. Each plate bears a single sharp conical tooth, arising directly from the middle of the posterior border. The anterior and internal part of the first series of pleural plates (Plate II. fig. 8, 1.) abuts upon the members of the rachis, and there is never a small tooth on the inner side of the large terminal fang, though there is very generally a characteristic minute spine-like tooth (Plate II. fig. 8, 1”) a little to the outer side of its base. The two outer series of the pleurze (Plate II. fig. 8, 2, 3), as in all the other Heteropods, consist of simple tenaculiform hooks, varying in relative length, strength, and curvature, in the different species of the genus. The configuration of the teeth, and the mode of action of the whole dental apparatus, are adapted for seizing and transfixing living prey; indeed, all the Heteropods are eminently carnivorous, and commonly bolt their victims whole. I have taken a Firola, which I recognised by its dentition, from the stomach of Carinaria. 1 also found a whole Lurybia impacted in the gullet of another speci- men; and it is not an uncommon thing to meet with one of its own kind in the stomach of Atlanta, although it more usually preys upon the smaller Pieropods, Spiralis, or Creseis, for example. From the so-called buccal mass (Plate II. fig. 1, h) a lengthy cesophagus courses directly backwards, and having entered the base of the visceral chamber, it soon opens into the anterior and inferior wall ofa simple sub-globular stomach (Plate IT. fig. 1, y). This latter viscus lies a little below, and posterior to the heart (Plate II. fig. 1, y), and from its upper and fore part, a short intestine (Plate II. fig. 1, x) passes forwards above, and nearly parallel with, the cesophagus, and in close relation to the heart, to end in the vent (Plate II. fig. 1, s), deeply within the mantle cavity. The liver (Plate II. fig. 1, €)is a beautifully sacculated gland, of a pale-brown tint, often mottled with amber, black and red, commencing by a small pointed ex- tremity near the nucleus of the shell, and gradually increasing in bulk, until it reaches near the posterior wall of the stomach, into which a single short and stout biliary duct opens. I may notice here a conspicuous glandular body, which appears to me to be a renal organ (Plate II. fig. 1, u). This lies immediately above the rectum, and between the latter and the auricle of the heart, and is made up of densely clustered, minute, and rounded follicles, communicating freely with each other; but I can- not tell whether its very distinct oval outlet (u) opens into the heart, pericardium, or into the cavity of the mantle. Between the apparent position of this orifice and the arms there is a small prominence, bearing a well-defined pore (Plate II. fig. 1, t) that may communicate with it, or with an aquiferous system. VOL. XXIII. PART I. D 14 MR MACDONALD ON THE ANATOMY The Mantle, Respiratory, and Circulatory Systems.—The free border of the mantle (Plate II. fig. 1, n) is often beautifully fimbriated, and beset with cilia, both stationary and vibratile; and in the extended state, an angular fold of it (Plate II. fig. 1, 0) occupies the dorsal slit of the shell, and extends for some little depth between the laminze at the base of the keel. The branchiz consist of a variable number of clavate bodies (Plate II. fig. 1, p), in single longitudinal series floating from the dorsal wall or roof of the mantle; and to the left of these, but passing forwards more obliquely, there is a narrow, strongly ciliated band (Plate Il. fig. 1, q), in all probability in some way con- nected with respiration, when the animal is retracted into its shell. Large venous sinuses (Plate II. fig. 1, r), distinctly observable between the layers of the mantle, appear to convey the return blood from the gills to the auricle of the heart (Plate II. fig. 1, w). The extent of this chamber is very much less defined than that of the ventricle (Plate II. fig. 1, y), which communicates with it by a large opening, guarded by a couple of valves. The muscular bundles of the ventricular walls are also much stouter than those of the auricle, and form a close interlacement, in the interstices of which the lining and investing mem- branes seem to meet together. The great vessel arises posteriorly from the apex of the ventricle, and forms a short dilated axis (Plate II. fig. 1, a), from which two arterial trunks originate ; one of these (Plate II. fig. 1, @) passes backwards to supply the abdominal viscera, while the other (Plate II. fig. 1, z) runs forwards beside the cesophagus and the root of the swimming-plate, divides into the pedal and buccal arteries, in every respect conformable with those already described in Firoloides. Generative System.—It is very remarkable that there is, as nearly as possible, an equal distribution of males and females in the genus /7roloides, while the pro- portion of males to females in Atlanta is so very great, as to render it difficult to form a correct estimate. In my own experience, out of many hundreds of Atlante, I have only met with about twenty females. The follicles of the testicle (Plate I. fig. 1, Z) somewhat resemble those of the liver, but they are at once distinguished by their lighter colour and the nature of their contents, which usually present a finely granular basis, with fasciculated strize in the axis of every cavity and passage. The whole organ, though very similar in shape, is much smaller than the liver, between which and the inner wall of the shell-tube it lies. A stout cas deferens leads forwards from the base of the gland, and soon forms a fusiform enlargement (Plate II. fig. 1, 6) coated with black pigment; and from the small fore-part of which the duct still passes for- wards a little way, and then terminates in a leaf-like expansion (Plate II. fig. 1, v), having a fine cellular structure in the space between the adductor-muscle (Plate II. fig. 1, 7) and the rectum (Plate II. fig. 1, x). The external male organ is situated at the base of the neck, and may be AND CLASSIFICATION OF THE HETEROPODA. 15 represented as bifid, having an anterior part, conical and grooved, and a posterior apparently glandular and trumpet-like segment (Plate II. fig. 1, m). I have never been able to trace the vus deferens to this organ in any of the Heteropods ; and having found the mantle-cavity full of spermatozoa in Carinaria, I am dis- posed to think that the scheme must be similar to that which obtains amongst ordinary gasteropods, when the penis is imperforate. The ovary in the females is very similar to the testicle, both in shape and position, but the contained ova at once decide the difference, and the large thick- walled and convoluted oviduct, without the dark-coloured fusiform dilatation characteristic of the male sperm-duct, still further settles the question of sex. The aperture of the oviduct would appear to lie deep within the mantle. I could discover no opening in the position occupied by the penis in the male, though I have observed ova escape from beneath the margin of the mantle.* The characters of the operculum are also significant,—viz., as to its general form, the course of the lines of growth, the position, size, and appearance of the nucleus, the muscular impressions, and its smooth or dotted surface. Oxygyrus (Benson). The genus Caygyrus, established by Mr Benson, includes the Atlante of Rane, KERANDRIEN, and LAMANoN, characterised by having an involute instead of a spiral nucleus to the shell, greater fulness in the whorls, and a comparatively small amount of calcareous matter as a component, particularly near the mouth and in the keel (Plate II. fig. 3). The most striking difference that I have noticed between the soft anatomy of Atlanta and of Oxygyrus is that the testis is short and broad, lying at the base of the liver in the latter case; whereas it is much elongated in the former, extend- ing far inwards between the liver and the columnellar wall of the shell. The rachidian plates in all the Oxygyri, instead of a single dental process of Atlanta, bear three conical teeth on their posterior border; and these teeth are either all large and nearly equal in appearance (Plate II. fig. 5, e), or the middle tooth alone is well developed, while the lateral ones are rudimentary (Plate II. fig. 5, f). The pleure are essentially similar to those of Carinaria and Cardiapoda, pre- sently to be described, the most important character in all being the presence of a small conical, and often incurved tooth (Plate II. fig. 7, 1’), on a little shoulder * All the species of Atlanta present so close a general resemblance, that their nice discrimina- tion requires careful examination and comparison. The keel may be more or less, or not at all inter- posed between the peristome and the body whorl. It may be plain or wavy, though the shell never exhibits this latter character, as it does in Carinaria, The spire, as to its prominence, depression, evenness or obliquity, closeness or openness of its whorls, smoothness, dotted surface, or linear mark- ings, affords us characters which do not appear to have been hitherto sufficiently recognised. There is, moreover, in colour, which one would naturally regard as being of little importance, a scarcely ever failing peculiarity of species. 16 MR MACDONALD ON THE ANATOMY at the inner side of the principal fang of the first or internal pleural series (Plate II. fig. 7,1) ; whereas, if a smaller tooth is at all present in Atlanta, it is at a corresponding distance to the outer side of the larger one (Plate II. fig. 8, 1’). Firola (Lesueur). I have only met with one species of /iro/a (Plate I. fig. 7), which appears to be equally plentiful in the tropical parts of the two great oceans, Pacific and At- lantic. It is, I believe, #. Lesweurii, and about two inches long, or nearly the same size as Carinaria Gaudichaudi (Plate II. fig. 4). The body is elongated and cylindrical, with a full and rounded cephalic region, a muzzle reminding one of an elephant’s trunk, and a laterally compressed rudder-like tail. The filamentous appendage in my first specimens was either absent or accidentally broken off, and the latter accident happened to the head of several examples of this species taken in the West Indies. No tentacula, or even frontal processes, were at all visible; but the eyes were well developed, and appeared to make a nearer ap- proach to the eyes of Carinaria and Cardiapoda than do those of Firoloides. The acoustic capsules may be readily recognised by the brilliancy of the con- tained otoliths, alittle internal and posterior to the eyes; the auditory nerves being about equal to the optic in length, but very much more slender (Plate I. fig. 8, g). A fan-like foot (Plate I. fig. 7, g) springs from about the middle of the under surface of the body, the rudimentary mesopodium (Plate I. fig. 7, f) being situated on the free margin of the organ, somewhat nearer its anterior than its posterior extremity. The visceral nucleus (Plate I. fig. 7, k) occupies a deep notch on the dorsal surface of the body, near its hinder end, and is enveloped in a glistening fibrous coat, tinted with a madder-brown pigment. It is rather small, as compared with the size of the whole animal, but, being surmounted with distinct branchiz, one more indi- cation is afforded of the propriety of placing Firola between Firoloides and Car- diapoda ; and this conclusion is strengthened by the position occupied by the sucker-disc of the foot, and also by the characters of the generative organs, which indicate something intermediate between the two genera alluded to. The comparison of the lingual dentition of /7roloides, Firola, and Cardiapoda, will not only show how intimately they are related, but afford some assistance in determining their relative position with regard to the other Heleropoda. The rachidian plates of Fvrola (Plate I. fig. 9,0; Plate IL. figs. 5, 6) are quadri- lateral in figure, but about three times broader than they are long; the dental points, as in Frolotdes, form a broad comb, with astout central fang; but the teeth gradu- ally diminish in size towards the sides, and are so strongly marked, as compared with those of Firoloides, that it would be impossible to mistake the one for the other. The first series of pleural plates very rarely exhibit a slight rudiment of the small internal tooth so characteristic of Cardiapoda, Carinaria, and Oxygyrus, AND CLASSIFICATION OF THE HETEROPODA. 17 but the two lateral uncini present only the relative character of being compara- tively long and slender. Cardiapoda (D’Orb.) Looking upon Cardiapoda pedunculata, carinata, caudina, and placenta (figured respectively in D’Orb. Voy. Amer. Merid., t. 11, figs. 5,3,and 4; and Voy. la Bonite, t. 17, f. 11, 1-5), as probably the same species, I am at a loss to know what I should call my species, which is evidently the same thing. My first specimen, of which I immediately made a drawing (Plate I. fig. 10), was obtained in the 8.W. Pacific, and scarcely exceeded $ inch in length. The muzzle was much fuller and more cylindrical than that of Firoloides, and the buccal mass equalled about one-third of its extent. The eyes were remarkably broad, and closely resembled those of Carinaria and Oxygyrus. They were fronted by simple conical tentacula. The auditory sacs were visible through the stout integument at some little distance behind the eyes. The muscular sheath of the body exhibited a close and even tissue round the snout, head, and neck; but, on approaching the position of the foot, it formed itself into a number of longitudinal linear bundles, which passed, on the one hand, into the pedicle of the viscera, and, on the other, into the tail. The propodial foot (Plate I. fig. 10, ¢) crested the middle of the ventral sur- face, and on its posterior border it bore the mesopodial disc (Plate I. fig. 10, h), which was laterally bilobed, and more highly developed than it is either in Firo- - loides or Firola. The tail (metapodium) was rather remarkable in its appearance. Thus, being at first cylindrical, it soon exhibited a subterminal enlargement, from which again it suddenly tapered into a lengthy filiform appendage (Plate I. fig. 10, k). The enlargement just noticed was convex above, corresponding with the position of the operculum in Adlanta and Oxygyrus, while its inferior surface was expanded into a kind of disc, with a jagged, prominent ring-like border, densely coated with black pigment (Plate I. fig. 10, i). The use of this organ is yet unknown to me, but it appears to be homologous with the peculiar structure above de- scribed, as occurring on the under surface of the metapodium of Atlanta. The whole extent of the visceral nucleus, shell, keel, and all, scarcely equalled the expansion of the foot; and the internal organs in general were so invested with pigmentary matter that the heart (Plate I. fig. 10, m) was the only one distinctly apparent at a cursory glance. Numerous branches (Plate I. fig. 10, n), with a plain external surface and a zig-zag internal fold, protruded from beneath the dorsal lip of the shell, which was semicartilaginous, shallow, or scoop-shaped, with an involute nucleus, and a deep but very thin and delicate keel. The external male organ (Plate I. fig. 10, 0) resembled that of Carznaria, con- VOL. XXIII. PART I. | E 18 MR MACDONALD ON THE ANATOMY sisting of an interior grooved, and a posterior glandular portion,—the latter being homologous with the trailing bulb of Firoloides, and, I believe, also with the trumpet-like segment of Atlanta. The rachidian plates of Cardiapoda (Plate I. fig. 11, 0 ; Plate II. fig. 5, c), are broad and slightly concave in front, but rather more so behind, with the angles obtuse in front, and sharp and incurved posteriorly. The dental processes are only three in number,—the central one being large and broadly conical, and the lateral ones very small. The little tooth on the inner side of the principal fang of the first pleural series is distinctly developed, but the uncini do not appear to differ in any essen- tial particular from those of /irola. Carinaria Gaudichaudi (Plate II. Figure 4.) This species I found to have as wide a range as the Firola and Firoloides previously described. Its length varies from 1} to 2 inches, and altogether it looks like an Aélanta whose head and body had much outgrown the capacity of its shell. On comparing the shells of the two genera, they will be found to resemble one another in several particulars. Thus, they are both dextrally- spiral, with a distinct umbilicus in the axis of the spire, and a prominent keel on the dorsal border of the whorls; but both shell and keel in Carinaria are beautifully crimped transversely, and the last whorl increases very rapidly in keeping with the development of the animal, so that the mouth of the full grown shell is widely separated from its spiral nucleus. The body is pellucid and colourless, but slightly, or not at all, tuberculated. The inner surface of the integument, however, is studded at pretty equal dis- tances with little clusters of cells like those of Firoloides. M. Rang believed that a tuberculated epidermis was always present in Carinaria, forming a distin- guishing feature between it and /?rola, in which, according to him, the outer integument is always smooth (?) He makes allusion evidently to the little clusters of cells above noticed as the representatives in Firola of the tubercu- lations of Cariaria. The proboscis is abruptly truncated at its extremity, and very variable as to its length and fulness. The eyes are fronted by small tentacula, and the acoustic sacs, as in Cardiapoda, &c., are appended to long and delicate auditory nerves. The ciliated lining of the sacs in this species I have been enabled to observe more distinctly than in any of the other Heteropods described above. The abdominal fin is fan-shaped, with a thin transparent margin; and the sucker-dise is represented by a little cup-like dilamination of its posterior border. The tail, or metapodium, is laterally compressed, and tapers to a point, without supporting an obvious rudder-fin, like that commonly given in figures of Carin- aria mediterranea. AND CLASSIFICATION OF THE HETEROPODA. 19 The visceral mass under protection of the shell is elevated, as it were, upon a short pedicle springing from the dorsal region, at a point considerably posterior to the swimming-fin. A row of reddish-tinted branchiz protrude beyond the mantle margin, and, as in Cardiapoda, the heart and intestine are distinctly visible through the shell (Plate II. fig. 4’, b, d). The rachidian plates of Carinaria (Plate II. fig. 5, d, and fig. 6, 0) are not unlike those of Cardiapoda, but the dental processes in each are perfectly char- acteristic. flanked on each side by a rudimentary tubercle. The small internal tooth of the first pleural series is more highly developed in Carinaria than in Oxygyrus ; and all the members of the pleuree (Plate IT. fig. 6, 1, 2, 3.), are much stouter in the former than in the latter genus, though they are somewhat exceeded in this respect by those of Cardiapoda (Plate I. fig. 11, Thus, Carimaria is distinguished by three large subequal teeth, 1,25.8;) REFERENCES TO THE FIGURES. PLATE I. Fig. 1. Firoloides. Fig. 4. Visceral Mass, &c., of Firoloides (female). : a. Great nerve supplying on the sides of the 9 a. Tentacula, h Pedal ganglia. branches to the tail, opening, b, Eyes. i. Heart. and connecting the| J. Oviduct. e, Auditory sac. k. Rectum. pedal with the vis-|m. Flexure of J. ‘ oe an rae l. aaa eth ceral ganglia. n. Oval opening of the fee fot Ne eee Oe eee |. bacAmtetior), divsiow. of mouth. ‘ : ee hs ‘ Gaal spuielidaee the aorta. o. Anal aperture in front Fig. 2. Head and Muzzle of Firoloides. a, Mouth. a, Cerebroid ganglia, b. Lingual sac. k. Tentacles. ce. Salivary glands. | 1. Eyes. d. Buccal ganglia. m. Auditory sacs. e. Buccal artery. n. Nerve trunks connect- jf. Buccal nerves, ing 2 with the pedal g. CAsophagus. ganglia. h. Optic nerves. o. Muscular sheath. Fig. 3. Pedal Ganglia and Great Vessels of Firoloides, . Pedal ganglia blended together by their con- tiguous surfaces, and giving off nerves to the foot and neigh- bouring parts. a 6. Anterior division of aorta. ce. Pedal artery. d. Buccal artery. c. Esophagus. d, Cardiac ganglion 2 e, Principal visceral gan- glion, sending a con- spicuous nerve to the mouth and its sphincter muscle. f. Liver. g. Metapodium, h. Caudal appendage. 2. Vagina, k, Small leaflets or lobes of a ciliated papilla. p. And between, two little leaflets like k. q. Ciliated elevation, with depressed centre, pro- bably a respiratory organ. r. Little clusters of cells, noticed at p. 8. s. Auricle of the heart, t. Ventricle. u. Muscular sheath. Fig. 5. Lingual Dentition of Firoloides. o. Rachis. | 1-3. Pleure. Fig. 6. Nidamental Chord of Firoloides, Fig. 7. Firola (considerably enlarged), a. Buccal mass. g. Swimming-fin b. Gsophagus, h. Penis. ce, Hye. 2. Branchie, d. Auditory sac. k. Visceral mass. e. Pedal ganglia. 1. Metapodium. J. Mesopodium. 20 MR MACDONALD ON THE ANATOMY OF THE HETEROPODA. Fig. 8. Brain and Organs of Sense of Firola. | Fig. 10. Cardiapoda in motion. a. Upper cerebroids, send-| ¢. Optic nerves. a. Buccal mass, 7. Curious structure no- ing off anterior and| f. Trunks communicat-| 6. sophagus. ticed at p. 17. posterior branches. ing with the pedal| c. Tentacula. k. Caudal process. b. Lower cerebroids, giv- ganglia, d. Eyes. l. Visceral mass. ing off motor nerves} g. Auditory nerve. e. Ear-sacs. m. Heart. to the eyes. h. Acoustic sacs. f. Pedal ganglia, n. Branchie. c. Buccal nerves. 7. Lens, g. Swimming-plate. o. Penis. d. Motor nerve of the| k. Body of the eye, h. Sucker-disce. | eye. l. Retina, Fig. 11. Lingual Dentition of Cardiapoda. Fig. 9. Lingual Dentition of Firola Lesueuri. o. Rachis. 1’ Small inner tooth of o. Rachis. | 1-3. Pleure. 1-8, Pleure. first pleural series. PLATE II. Fig. 1. Atlanta. Fig. 3. Oxygyrus, n. s. a, Mouth. U. Glandular organ, pro- References as in Fig. 9. b. Buccal mass. bably renal. c. Tentacula, v, Expanded orifice of Fig. 4. Carinaria, d, Tentacular (2) tuber- the sperm-duct. eee, : cle at the inner and! w. Auricle of the heart. me oe reg g.P ropodium. fore part of the! 2. Intestine. a iets = h. Moan 7e, . Ventricle. . . a. 1luin. e nee A Herne: division of | “ = eae food in th = f. Cerebroid ganglia. aorta, 5 pa ae > Sage. = g. Ear-sac. a. Aortic axis, Ae ak siehisel ; ’ h, Salivary glands. 8. Visceral artery. f. Pedal ganglia. ?. Pedal ganglia. y. Stomach. oa ie 5 , j. Propodium, 6. Dilatation of sperm- Fig. #. Shell and Viscera magnified. k. Mesopodium. duct. | a. Gullet. c. Branchie. i. @sophagus. e. Liver, b. Rectum. d. Heart. m., Penis. Z. Testicle. n. Mouth margin. n. Origin of retractor} Fig. 5. The Rachidian Plates characteristic of the o. Carinal fold of n. muscle, genera of Heteropoda. fe eels Heo Soe a. Firoloides. e and f. Two divisions of q- Ciliated line. . Tongue-like process. i, Waele Oxygyrus, probably : : : a Met: warn? ie = eae c, Cardiapoda. distinct genera. hile dage bat! tare ets d, Carinaria. g. Atlanta. t. Aquiferous pore ? w. Vertical fold. Fig. 1’. Operculum of 1, magnified. Fig. 6. Lingual Dentition of Carinaria. Fig. 2. Oxygyrus. Fig. 7. Do. do. Cardiapoda. a, Buccal mass _ and, d. Propodium. : ares e. Mesopodium. Fig. 8. Do. do. Atlanta. b. Tentacula. J. Metapodium. o. Rachis diapoda, Carinaria, c. Eyes. g- Operculum. 1-3. Pleure. and Oxygyrus. 1’. Tooth common to Car-|1”. Tooth characteristic of Fig. 2’. Operculum of 2, magnified. Atlanta. | TRANSACTIONS OF THE ROYAL SOCIETY, EDINBURGH. VOL. XXIII. PLATE 1 Ee = — —— J. DENIS M'‘DONALD,R.N., DELT. ¥.Schenck 12 R! Exchange Edin? TRANSACTIONS OF THE ROYAL SOCIETY, EDINBURGH. VOL, XXIII. PLATE II. J. DENIS M'DONALD, R.N., DELT. F { -Schenck 12,h! Exchange Edin? ( 21 ) Il.—Investigation of an Expression for the Mean Temperature of a Stratum of Soil, in Terms of the Time of Year. By Josepn D. Everett, M.A., Professor of Mathematics, &c., in King’s College, Windsor, Nova Scotia.* (Read 3d February 1862). 1. It is a well-known property of simple harmonic functions, that the sum of any two or more of them having the same period, is itself a simple harmonic function having the same period as its components. The same thing must be true of their mean, since this is equal to the sum divided by a constant; and it will still be true when the number of components is indefinitely great, and the mean becomes an integral. 2. Let v denote a variation of temperature which is a simple harmonic func- tion of the time #, so that v= A sin (nt+ E), where ¢ is expressed in arc at the rate of an entire circumference to the year. The mean value of v for any assumed interval of time will be fva fu taken between limits corresponding to the beginning and end of the interval. Performing the operations indicated, it will be found that the expression for the mean temperature of an interval equal to the - th part of a year, ¢ being the time for the centre of the interval, is 3. If in last section represent a variation of temperature at depth 2, below the surface of the ground, then, by the theory of underground conduction, A and E are functions of x Hence the mean value v at time ¢ for a stratum of soil will be f° dx be taken between limits, corresponding to the top and bottom of the stratum. The * See article by the Author, in the Edinburgh New Phil. Journal, vol. xvi., 1861. VOL. XXIII. PART I. ay 22 PROFESSOR J. D. EVERETT’S INVESTIGATION OF AN EXPRESSION soil is here supposed to be uniform as regards its thermal qualities; and its sur- face, as also the bounding planes of the stratum, horizontal. 4. We propose to effect the integration above indicated, and deduce convenient formule for the coefficients in the expression, for the mean temperature of a stratum in terms of the time. The data to be supplied by observation are the temperatures at all times of the year, at two arbitrarily assumed depths. The observed temperatures must be reduced to harmonic expressions (one for each depth), and from these it is easy to deduce the harmonic expression for the temperature at any third depth. We may therefore assume that the harmonic expression for the temperature at the centre of the stratum is known; and we shall find it convenient to compare the amplitudes and epochs in this expression with those in the expression for the mean temperature of the stratum. Let the former expression be v=A,+A, sin(t+E,)+A, sin (2¢+E,) + &e. and the latter V=A,+m, A, sin (¢+E,+a,) +m, A, sin (2¢+ E,+a,) +&e. We have to find the values of the constants m, m,, &c., which express the ratios of the amplitudes in the two series, and of a, a,, &c., which expresses the differ- ences of epoch. 5. By the theory of underground conduction, the temperature at depth x below the centre of the stratum will be rc —a2/ — e TC Gok Se OF at (1+5,- rz) Sd 9 ie on k | gin (21+ 8,-2.7) + &e. the general term being io wees oe ° NEC +A, e - Sin ({ nt+E,—2, /—— e denoting the base of Napierian logarithms, 7 the ratio of circumference to diameter, / the conductivity of the soil referred to unit volume, and ¢ the capacity for heat similarly referred. 6. We will first suppose that the expression for the temperature at the centre of the stratum is simply c v=sin t. Then we shall have — a/ = é (+ mC v=e . Sin mK 7 and if £ be the thickness of the stratum, the mean temperature at time ¢ will be - v dx g 23 FOR THE MEAN TEMPERATURE OF A STRATUM OF SOIL taken between ane and +; é Now J va =f" sin ( t—x %, ) de “ Vee cos (-«/£) — sin (1-2 =) 7 % ik TC 2/F and using z to denote 4 ae a we shall obtain as the value of 4 vdz between g the given limits, the expression =; (ete, | sin z (sin ¢+ cos ¢) Vee —z (=e ) eos z (cos ¢+ sin 7) (e+e ‘) Sin Z Cos (:-3) ae soul » Dex/2 + : (¢ e*) cos # sin ( /— 22/2 pry 7): Putting (c+ ‘) sinzg=P. (¢e ) cos z=Q, ae wi T Q : 7 Mo /D .COS (:-3) + Mf * sin (*-7) a simple harmonic function of ¢, which can be reduced to the form V=m . sin (+a) we have by making Pp at Ne I tan ({+«) =@ and her OEE: : JP? +? = a: Q see (7+ +a). a 7. The values of m and a can be found by the formule of last section ; but more convenient formule when z is small are obtained by developing in ascending powers of z. For the value of im we hav 2 —2 P+ @) = 35 (¢ iow —2 cos 22) <1, (ae +S +60.) 23 ee &c. ) (22)" , 2a’ | Ge) (s+ : * [10 +&e,) ~ 22 D aS +i* aber 24 PROFESSOR J. D. EVERETT’S INVESTIGATION OF AN EXPRESSION a series which converges with extraordinary rapidity, and may be used even for large values of z. Extracting the square root, we have ee m=1+ 75 Z — 5670 * + &e. 8. For the value of the acceleration 4 we have (1 ae ta pte) (1-45+ zee) Now, the first factor of the numerator is obviously greater than the first factor of the denominator, and it may be shown’ that the second factor of the numerator exceeds the second factor of the denominator by the quantity,— 2? 24 28 28 13” 65" 67 [rot which is positive for all values of z not greater than unity. Hence, for all such values of z, tan (F + a) is greater than unity, and therefore a is positive; that is to say, the phases of temperature are earlier for the mean than for the centre of the stratum. es — tan 2, the first factor is always finite and posi- €—e tive for finite and positive values of z. Hence, when tan z is zero or infinity, 9. In the expression tan ( Z + «) is also zero or infinity. And we know from general considerations that when z=0,a=0. Hence it may be shown, that when z is of the form > where dis any integer (not including zero), A +a=% OF a=z -}. For all other values of z, é = 4 + ¢ — is never equal to unity. @eé—€ 10. We have hitherto been supposing the expression for the temperature at the centre to be,— +a will be unequal to z, since the factor v=sin t. To render our results applicable to the general term A sin (n¢+ 5), in the expression for the temperature at the centre (§ 3), and the corresponding term m A sin (nt + E+) FOR THE MEAN TEMPERATURE OF A STRATUM OF SOIL. 25 in the expression for the mean temperature, we have merely to substitute z/n for z, as will readily appear upon trial. Making this substitution, we have VA — 2 i vn — 2/1 IPs (c "Ge : .) sin 2/2, Q= ( —e Hf COs 2V/n, P tan (F+ «) = ay m= - Q sec G+ +a) : (1.) = 2 ey eee c marl (14 Ft! +4975" + &e. ) (2.) — 1 2,4 1 4,8 = 1+ pana — rary? a OlCry. he vue ! (3.) NAD —2/n us e +e tan (f+) ee tan 2/7 2) — 2zn/n 1 1 — 2Qe/n eos .; +e = tale tan Wn=——_5,, . tan wn, ; (4.) e —1 l-—e 3 Assume on ee a then tan (+ «) = tan a a) .tanzv/n, . : : (5.) —2z/n Or assume tan 9=e then tan (G+ a) = sec 29 . tanzVn, . (6.) Also, from (§ 8.) es t v vd 3 30 an (j+«) = i rae 1 nz? — —n?zt — &e. Nv: 1 g2 — syn! + &e. 2 2 =1+ gu + gu + &e. : : (7.) whence 29,2 24 sne +—n2* + &e. 9 tan @== yy aoa ao 2+ aMa + gna + &e. = set + &. : : : sit) (8.) the next term being set. * 105 A good approximation to the value of m will generally be obtained by assuming tan w=n2" s and putting M=SEC. w. 11. From equations (8) and (8), we learn, that when nz? is small, the in- VOL. XXIII. PART I. G 26 PROFESSOR J. D. EVERETT’S INVESTIGATION OF AN EXPRESSION crease of amplitude is nearly proportional to the fourth power, and the accelera- tion to the square of z; and z is by hypothesis proportional to the thickness of the stratum being equal to half the thickness multiplied by J . It is important to observe, that the values of m and a are entirely independent of the depth of the stratum below the surface of the ground. The approximate values of m and tan a are— 1 n?z*, tan «=—N2"; pee 3 45 whence also, approximately,* 1 1 log, m = — N24 a=5nz. 45 3 These two last expressions are useful in estimating the corrections due to length of bulb, in the reduction of observations made with underground thermometers. Both the corrections are to be applied subtractively, the former to Napierian logarithm of amplitude, and the latter to epoch in circular measure. 12. At Calton Hill, Edinburgh, where underground temperatures have been observed, the value of wh r is 1156, the unit of measure employed being the French foot ; hence for a stratum 2 French feet thick z=-1156, and for a stratum 1 French foot thick z=:0578. The corresponding values of log, m and a for the annual and half-yearly terms are given below :— Log. m a in Circular Measure. Annual term, 2 feet stratum, : : . ‘00000397 -00445 oe Be Z aoa : : . °00000025 ‘00111 Half-yearly term, 2 #8 ; : . *0000159 “00891 ee el | ‘0000010 *00223 13. For strata 24 and 12 French feet thick, the values of m and a are as under :-— Values of m. Values of a. Annual Term. Half-yearly Term. Annual Term. Half-yearly Term. 24 feet Stratum,” . . 108005 1:2999 35 42 $3 23 12 feet Stratum, . . 1:0051 1:0204 9 10 18 14 * More nearly, es. PPh ae log, Mee gaan a ve oes FOR THE MEAN TEMPERATURE OF A STRATUM OF SOIL. 27 The annual term in the expression for the temperature at the depth of 12 feet in the same locality, as derived from direct observation, is— 2°31 sin (t+ 179° 15’) Hence the annual term in the expression for the mean temperature of the first 24 feet will be— 2-31 x 1-08 sin (+179° 15’ + 35° 42’) = 2°50 sin (¢+ 214° 57’). 14. To correct for difference between temperature of bulb and that of stem, the following method may be adopted :— Let the observed temperatures be represented by the expression V=A,+P, cos ¢+Q, sin ¢+ P, cos 2¢+Q, sin 2é, and the mean temperature of the stem by the expression v=aA,+p, cos ¢+q, sin ¢+p, cos 2t+q, sin 2¢. Then if 7 denote the ratio of the capacity of the stem to that of the bulb, and U the corrected value of V, we have U+rv=(14+7) V; or U=V +7 (V—v). Hence the correction for A,is . . - + r(Aj—a) PAS! Gene e ne bap, Qis. 2. TQi—mH) and so on for the other terms. A different mode of correction is described in Principal ForBEs’s paper, “ Ac- count of some Experiments on the Temperature of the Earth,” &c., Trans. ‘Roy. Soc. Edin., Vol. XVI. Part IT. 15. For the theory of underground conduction, and the use of harmonic functions in connection therewith, reference may be made to two papers on «Underground Temperature,” by Professor W. THomson and the Author, Trans. Roy. Soc. Edin. ,Vol. XXII. Part II. (April 1860). - a a oh Fig ae ae ee er ‘ > tie y gh 4 aursnionantl as a in ~ le bun Dodge re edie 4 sale Iie be a ", | Ci dee Clty at iti cast es ; my Thuis waka hele 2 aneenem i a 5 eb aay: Teh eve (eS ae A Ay ¢ ee | q 7 } wm at rae i . . - 7 : ~~ a -? 4 ; “i +n s wy ‘A . ; ‘J : ie ie : ° i “ i> feplt Veter > hein ae ‘a iV . AR FT Th * As ae "> i es eto ; ‘ : duties! “a i x <» i div) Suis: ceili . ree ‘ . peas « uenett av ee th AN eta +e" , f g ¥r af. : a ke it = a oe ( 29 ) Ill.— On a Difficulty in the Theory of Rain. By James Datmanoy, Esq. (Read 7th April 1862.) Nearly a hundred years ago,* Dr Heserpen of London made the following experiment :—Having prepared three exactly similar rain-gauges, he placed one of them on the roof of Westminster Abbey, another on the roof of a neighbouring house, but at a much lower level, and the third in the garden of the same house. At the end of twelve months he found that the gauge on the roof of the Abbey had received 12099 inches of rain, the gauge on the neighbouring house-top 18:139 inches, and the gauge on the ground 22°608 inches. This paradoxical result required, of course, to be confirmed by other observers, and in other localities; and the similar results obtained by Dopson, Dauton, Howarb, and especially by Araco at the Paris Observatory, and by Puituips at York, have amply supplied all that was wanting in this respect. It may be noted in passing, as a curious fact, that in Dr James Hurron’s “ Theory of Rain” there is no allusion to Dr HEBERDEN’s observations, though these were published in the ‘‘ Philosophical Transactions” + fourteen years before Dr Hurron’s Theory was read to the Royal Society of Edinburgh. t Of the attempts which have been made to reconcile Dr HEBERDEN’s observa- tions with facts and principles already established, that of Dr Franxuin is the most plausible, and it has been very generally accepted as the true explanation. At first sight, indeed, it seems capable of explaining every difficulty; and it is only when more carefully examined, and especially when tested quantitatively by actual results, that its inadequacy becomes apparent. As, however, many may be disposed to question this conclusion, I am glad to be able to rest the proof of it on the following quotation from Sir Joan HERscHEL’s treatise on Meteorology.§ Having alluded to the fact that, during the year 1833-34, the quantity of rain received on the top of York Minster, at the height of 213 feet, bore to that received on the neighbouring ground the ratio of 1: 1:706, the learned author proceeds as follows :—“ The usual account given of this phenomenon (KorEmrTz) is, that rain falling from a high level, and therefore colder than air at the surface of the ground, arriving in an atmosphere nearly or quite saturated with moisture, condenses on itself, or causes the condensation, in the chilled air, of an additional * 1766-67. Teli ie, t 1784. § Encyclopedia Britannica, 8th edition, article Meteorology, par. 109. VOL. XXIII. PART 1. H 30 MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. quantity of vapour. But it is evident that this cause, though not uninfiuential, is totally inadequate to account for so great a difference. Admitting a given weight of rain to arrive at 213 feet from the ground, with the temperature of the region at which it was formed unaltered, and supposing it to acquire, in the remaining 213 feet, the full temperature of the air (both of them extreme and even extravagant suppositions), admitting, too (though hardly less extravagant), the mean height of the formation of rain to be 12,000 feet, it would bring down with it a cold of 40° Fahr., which would condense (whether on the drops or in satu- rated air, if diffused through it) only GAS = 0:42 of its weight, = one-seven- teenth of the quantity to be accounted for.” Although this demonstration does not really admit of being strengthened, yet, as showing how a similar conclusion was reached in a different manner, I beg to refer to a short paper in the 20th volume of the “ Transactions of the Royal Society of Edinburgh,” entitled, “On the Weight of Aqueous Vapour which is Condensed on a Cold Surface under given conditions,” in which I have endea- voured to prove experimentally that, taking the observations at York during the three winter months of the years 1832-33, 1833-34, 1834-35, the increment which the rain received in falling between the level of the top of the Museum and the ground, a height of 44 feet, was above 600 times greater than it would have been if the condensation of aqueous vapour by cold had been the only cause in operation. For these reasons, therefore, it seems necessary to reject this explanation, though one of such likelihood as to have suggested itself, independently, to Dr FRANKLIN, M. Borsciraup, and Professor PuILLirs. The eminent meteorologist Luke Howarp proposed* an explanation which, however, seems to differ from the one just considered chiefly in that it supposes the cold, on which the condensation of vapour depends, to originate, in some unex- plained way, in the atmosphere itself, instead of being brought down by the rain from the upper regions, There is another mode of accounting for the difficulty under consideration, which has been advocated by Mr Jevons} and other writers.{ According to this theory, the deficiency of rain in the upper gauge is produced by wind—the gauge itself, or the building on which it stands, giving rise to eddies which partially obstruct the entrance of the rain into the mouth of the gauge. That wind may affect the indications of a rain-gauge, has been proved by the interesting experiments of Professor A. D. Bacue of Philadelphia.§ Having placed gauges at the four angles of a high square tower, at a height of ten inches * Report of British Association for 1834, p. 563. + Philosophical Magazine for December 1861, p. 421. + Dr Srarx in Transactions of the Royal Scottish Society of Arts, vol. v. p. 66. § Report of British Association for 1838, Transactions of the Sections, p. 25. MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. 31 above the parapet, he found that the gauges at the lee side of the tower received more rain than those at the windward side; but that, the same arrangement con- tinuing, when gauges were also placed on poles at the height of six feet above the parapet, there was observed scarcely any difference between their indications. The bearing which these results have on the present question will afterwards be noticed; but neither these, nor any similar facts which writers have adduced, seem to meet the special difficulty to be explained—namely, that of three gauges, at three different levels, and each variously placed as respects surrounding objects, the lowest gauge always receives more rain than the middle one, and the middle gauge more than the upper one. But that which seems an unanswerable objection to this mode of explanation, is the fact that, when the upper and lower gauges have been inspected after a perfect calm, and when the rain fell perpendicularly, the upper gauge was still found to contain less rain than the lower one. This fact is recorded very ex- pressly by Araco,* and also by PHILLIPs.t+ While, therefore, it is denied, for the reasons now adduced, that the difficulty under discussion can be accounted for by the effect of wind, it is not disputed that, under certain circumstances, wind does modify the indications of a rain-gauge. Sir Joun HerscuHeEt concludes his notice of the attempts which have been made to account for the phenomenon, in these words :;—“‘ The real cause is yet to seek, and there is no more interesting problem which can fix the attention of the meteor- ologist. Visible cloud rests on the soil at low altitudes above the sea-level but rarely, and from such cloud only would it seem possible that so large an accession of rain should arise.” I was first led to think of this puzzling question a good many years ago, and the result of my repeated attempts to find a solution of it is contained in the following hypothesis, which, in spite of its many defects, I venture humbly to submit to the consideration of those who take an interest in meteorology. The hypothesis begins by taking for granted the truth of Dr Hurron’s “Theory of Rain.”§ It assumes that the spherules of water composing the clouds from which rain proceeds are, at their first formation, so small, that the terminal velocity of their descent is almost insensible. It further assumes that these minute globules coalesce, at innumerable points, into drops of sensible magnitude, and fall in the shape of rain; while portions of the cloud, which do not thus coalesce, are floated downward in a current of air, and fill the whole space between the clouds and the earth with minute particles of water. This medium, consisting of cloud carded out, as it were, by the downward * (Euvres, tome xii. pp. 409, 416. { Report of British Association for 1833. See Transactions of Sections, pp. 403, 404. Report for 1884, p. 561. t Article Meteorology, par. 109. § Transactions of Royal Society of Edinburgh, vol. i. p. 41. a2 MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. current of air, and dispersed through a very large space, is assumed to be so rare as not to affect the transparency of the atmosphere; and it is the constant float- ing down of this medium in a current of air which, according to the hypothesis, is the principal and almost sole cause of the phenomenon to be accounted for. But it will be necessary, at this point, to answer a question which may naturally be anticipated,—namely, whether there be any proof, from theory or observation, that rain is actually accompanied by a downward current of air and floating moisture. Theoretically, two causes may be assigned for such a current. The first is the continual displacement of the air by the downward motion of the drops of rain; for, the effect of bodies in rapid motion to draw after them any light matter in their neighbourhood, such as air or smoke, is familiar to every- body; and that the drops of rain should have this effect will not seem impro- bable, when it is remembered that the largest of them may attain a velocity of nearly 400 inches per second. The second cause of the downward current of air which theory suggests, is the cold which rain brings with it from the upper regions. This must render the air inside the limits within which the rain is falling heavier than the air outside those limits, and thus co-operate, in an obvious way, with the former cause. But in order to prove that theory is in this case borne out by observation, I adduce the two following quotations from writers of unquestionable authority. Professor Puriuips, in his first Report* on the observations at York, makes the following remark :—‘ I have noticed in several instances the fact, that the wind which accompanies the fall of rain takes the line of the rain-drops them- selves; and on the Minster, in particular, this was very strikingly illustrated when, with my friends Mr JonarHan Gray and Mr WILLIAM Gray, junior, I watched the progress of a storm for thirty miles down the vale of York. The wind was insensible, except during the fall of rain, and then it came downward with the drops.” This testimony establishes the fact, that rain is sometimes observed to be accompanied by a downward current of air so strong as to be described as a “wind.” It also records two other facts, which have a bearing on the hypothesis ; the first of these is, that on the occasion on which the downward wind particu- larly attracted notice, the observers were not standing on the ground, but on the top of the Minster, at the height of 213 feet ; and the second fact is, that the rain and downward wind began and ceased simultaneously, which affords a strong presumption in favour of their being connected as cause and effect. The other quotation which I have to adduce is from Emerson TENNENT’s “ Ceylon,”} and is as follows :—*“ The first fall of rain was preceded by a down- * Report of British Association for 1833, p. 404. +, Vol. i... p69. MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. 39 ward blast of cold air, accompanied by hailstones, which outstript the rain in its descent.” In this case the coldness of the hailstones and the velocity of their fall pro- duced so rapid a current as to be described as a ‘“‘ downward blast ;” and it is probably only when the hail or rain falls with unusual violence, as in this case, that the vertical direction of the wind is perceptible to an observer at the level of the ground. But if, for the reasons which have been adduced, it be granted that rain is always accompanied by a downward current of air, of greater or less velocity, it seems necessarily to follow that this current, originating, as it must do, in the very region of cloud, will descend charged with minute particles of water. Having thus proved, as I hope, both by theory and observation, that rain is accompanied by a downward current of air, mingled with minute globules of water, I shall now endeavour to explain the twofold agency of such a current, in causing the indications of equal rain-gauges to vary with their height above ground. The first and most obvious way in which the downward current produces this effect, is by filling the entire space through which the rain falls with a constantly renewed supply of very minute globules of water. The rain-drops must, of course, absorb as much of this watery medium as they come in contact with, each drop growing in size during the whole time of its descent; and the necessary result must be, that if two equal gauges receive each an equal number of rain-drops, the gauge nearest the ground will indicate the most rain. But, with reference to the process thus described, it will naturally be asked, what becomes of the multitude of minute globules of water which are not absorbed by the rain-drops? The answer to this will, it is hoped, be found in the follow- ing explanation of the second and less obvious way in which the downward cur- rent affects the indications of rain-gauges placed at unequal heights above the ground. Taking for granted, then, that during rain a slow current of air carrying minute globules of water is continually descending from the region of cloud, I now assume that these minute globules of water, in the course of their descent, often come into contact with one another, and coalesce into drops of sensible magnitude; and this again leads to the inference that globules which, at a higher level, descended chiefly by participating in the motion of the downward current of air, acquire, after their coalescence, a velocity and momentum which enable them not only to outstrip the current, but also to resist being carried out of their downward direction by any lateral motion which may happen to be impressed upon the current. This process of coalescence, it is conceived, becomes more and more rapid as the resistance of the ground begins to tell on the velocity and downward direc- VOL. XXIII. PART I. I 34 MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. tion of the current; and, judging from facts of observation, it seems to be at some point less than 40 feet from the ground that a great and sudden coalescence of the small globules of water takes place,—the effect, probably, of the current being first retarded and then forced into a lateral direction, and of the irregular mingling together of the particles of water to which this gives rise. The hypothesis next assumes as true the following important proposition,— namely, that while a rain-gauge, placed at some height above the ground, receives all drops having a sensible magnitude, it receives none of those globules which are so minute that the velocity of their descent, though partly the effect of gravity, is chiefly due to the motion of the downward current of air on which they float. These very minute globules, it assumes, are borne by the current past the mouth of the gauge, and continue to descend until, by the coalescence of a great number of them, a drop is formed large enough to fall into a lower gauge if placed in its path. This essential point of the hypothesis may be illustrated by what is observed when wind blows through a room having two windows opposite to each other. In such a case the leeward window is no sooner closed, than the breeze, if gentle, is scarcely felt within the room, though the other window remain open; and the obvious reason is, that the air inside the room, being now supported at all points, resists the entrance of any more air by the open window. In a similar manner, it is conceived, the slow downward current of air and floating mois- ture fails, as the hypothesis assumes, to find entrance into the mouth of a rain-gauge, and is forced to turn aside and to continue its descent towards the ground. But here the question may occur, what will be the result if this downward current be combined with a current of wind at right angles to it? One effect doubtless will be, to accelerate that process of coalescence which, it has been assumed, takes place among the minute globules of water in the downward current. And this more rapid coalescence would evidently tend to increase the indication of the upper rain-gauge, and thereby to equalise it with that of the lower gauge, were it not that this tendency is more than counterbalanced by the wind uniting with the downward current of air, to turn aside from the mouth of the gauge, not only the very smallest of the globules of water, as during a calm, but also the smaller of those globules which, under ordinary circumstances, would have fallen into the gauge. It appears therefore that, as respects its ultimate effect, the wind increases the difference between the indications of the upper and lower rain-gauges, and this is in accordance with observation. But besides the wind, which, it has been shown, increases the ordinary effect of the downward current, there are a few causes which seem to lessen or mask its influence. Thus, it is well known that, on some rare occasions, the quantity of rain in the upper gauge equals, and even exceeds, the quantity in the MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. 35 lower gauge; and one or two circumstances which might tend to produce such an equality may be mentioned. If, for example, the upper gauge were placed rather close to the top surface of a tower or building, and nearer to one side of it than to the other, then, in accordance with Professor Bacue’s experiments, when the wind blew from the direction of the more distant side, the indication of the gauge might be expected to be greater than if the wind blew from the near side ; and thus it would not be surprising if, in certain directions of the wind, the indi- cation of the upper gauge became nearly or quite equal to that of the lower one. Again, there are two other causes, opposite to each other in character, which, it might be expected, would tend to equalise the indications of the upper and lower gauges. The first of these is when the rain falls, more or less plentifully, but in extremely small drops; and the second is when the rain falls in large drops and very copiously. In the former case, the very small terminal velocity of the drops would give rise to a downward current of air so slow as scarcely at all to hinder the entrance of the minute globules of water into the upper gauge, or accelerate their coalescence into drops as they approached the ground; and the ultimate effect would be, a tendency to equalise the indications of the two gauges, by allowing more than the usual quantity of water to enter the wpyper gauge. In the latter case, again, the downward current of air might be so strong as to reach the level of the ground, and this also would tend to equalise the indications of the two gauges; but, on this occasion, it would do so by allowing J/ess than the usual quantity of water to enter the lower gauge. Having explained what I conceive to be the twofold agency of the downward current in producing the paradoxical results under consideration; and having also noticed some of the causes which may serve occasionally to modify these results; it would now have been desirable to test the hypothesis quantitatively ; but unfortunately the want of data renders it impossible to do so in a satisfac- tory manner. There is, however, one point on which a numerical estimate, even if it were only a probable one, is essential. I mean respecting the quantity of water, in theshape of minute globules, which a given volume of the atmosphere must be assumed to contain, in order to account for some of the more remarkable results recorded at York or elsewhere. I shall, therefore, now endeavour to make a rough approximation to this quantity, the chief object in view being to deter- mine whether the quantity of moisture would be so great as to render necessary the supposition of visible cloud throughout the space where rain is falling. In selecting a case for such a purpose, recourse cannot be had to those rare in- stances in which 380 inches or more of rain fell in the course of twenty-four hours; for in none of these does it appear that the observations were made at more than one level. Perhaps the winter observations at York will furnish as severe a test of the hypothesis as can be found, at least as regards the ratios of the quantities of rain 36 MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. received at different levels. It is true that the maximum quantity of rain which fell continuously in a given time, cannot be determined by means of this series of observations, for the intervals between the consecutive observations were too long to admit of this; but still it is possible to assume a value which may be sup- posed, on good grounds, rather to exceed than fall short of the actual maximum rate. The following table* contains an abstract of the winter observations at York to which allusion has just been made. It exhibits the depth of rain which fell into gauges, at three different levels, during a period of 270 days, comprising the months of December, January, and February, of the years 1832-33, 1833-34, 1834-35 :— | | | Height of the Gauge above Saga | the ground, rion | in feet. ; Ground. gang e....)'s ey Bee 0 17°32 Museum gauge, . ... . 44 Zt] Minster gauge (sateen. 213 8°65 The remarkable fact to be learnt from this table is, that the Ground gauge received 30 per cent. more rain than the Museum gauge, the difference of level being only 44 feet; and 50 per cent. more than the Minster gauge, the difference of level being 213 feet. As respects the rate at which the rain fell, the table shows that the Ground gauge received 17:32 inches in the course of 270 days,—that is, on an average, 0:064 inches in twenty-four hours. This, of course, is the mean rate for the whole period, including fair and rainy weather; but what is wanted is the largest quantity which fell continuously in a giventime. Sir Joun HErscuex states,} that ‘‘ it is considered, in the greater part of England, a heavy rain if an inch fall in the course of twenty-four hours.’ Therefore, guided by this, it is proposed to assume, that on one of the 270 days included in the York observations it rained continuously for twenty-four hours; and that, during this period, the Ground gauge received one inch of rain, the Museum gauge 0°7 of an inch, and the Minster gauge 0°5 of an inch,—these quantities bearing to each other the same ratios which, as the fourth column of the above table shows, the whole quantities bear to each other. Adopting, then, these data, the hypothesis assumes that, on the occasion in * Report of Brit. Assoc. for 1835, p.173. N.B.—The error in the Minster column is corrected. t Art. Meteorology, par. 115. MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. 37 question, and within the period of twenty-four hours, a current of very minute globules of water—equivalent, in all, to a depth of half an inch of rain—was floated downward past the level of the Minster gauge, without giving any indication of its passage; and that of this half inch, a portion, equivalent to 0:2 of an inch, changed its form while descending between the levels of the Minster and Museum gauges,—the larger part of this quantity combining to form drops of a size sufficient to admit of their falling into the lower of these two gauges, and the remainder coalescing with drops of rain already formed, and thereby rendering each drop larger than when it passed the level of the Minster gauge. The effect of this coa- lescence of the minute globules of water with each other, and with the larger rain- drops was, according to the hypothesis, to raise the indication of the Museum gauge to 0°7 of an inch,—that is, 0°2 of an inch above the indication of the Minster gauge. Again, it is assumed that the current, now containing a quantity of water equivalent only to a depth of 0°3 of an inch, was carried past the level of the Museum gauge without leaving any trace of its passage, and was by a similar process of coalescence, but much more rapid than what took place at the higher level, converted into drops which, owing to the cessation of the downward current as it approached the ground, were now no longer, even the smallest of them, carried past the mouth of the gauge placed there, but entering it, raised its indica- tion to one inch,—that is, 0°3 of an inch above the indication of the Museum gauge. Having traced the agency of the downward current thus far, the next step ought to be to ascertain the velocity of the current. But it is difficult to find any data for making such an estimate; for though it may be inferred, that the velocity of the downward current of air which accompanies rain will have some direct relation to the quantity of rain which falls in a given time, and to the degree of cold which it brings down with it, yet, unfortunately, from not knowing what that relation is in some actual instances, no use can be made of the general principle. Since, however, it is necessary to arrive at some estimate on this point, there are one or two considerations, connected with the hypothesis itself, which seem to suggest a lower limit, at least, to the velocity of the downward current. In explanation of this, let it be assumed that (it being during winter) 3000 feet was the height of the clouds from which the one inch of rain fell in twenty- four hours. Also let it be assumed that the diameter of the drops of rain was uniformly one-tenth of an inch, which, as respects bulk, is greatly nearer the lower than the higher of the two limits to their size which Professor Lest has assigned. Then, one inch of rain being supposed to fall in twenty-four hours, it follows that the number of drops which would fall on any particular spot in the same time would be fifteen,* and the interval of time between the consecutive drops would be ninety-six minutes. In order, therefore, to keep the space between the clouds and the earth replenished with the minute globules of water, the * Playfair’s Geometry, Supp., B. III. Prop. xxi. VOL. XXIII. PART I. K 38 MR DALMAHOY ON A DIFFICULTY IN THE THEORY OF RAIN. downward current ought to have a velocity of at least 3000 feet in 96 minutes,— that is, about 7 inches per second, or gths of a mile per hour. In a table given by Dr Tuomas Youne,* it is stated that a wind blowing at the rate of two miles an hour is just perceptible; and as the downward wind recorded by Professor PHiLuips was distinctly felt, it may be concluded that its velocity exceeded two miles an hour. Therefore, in adopting 7 inches per second, or 2ths of a mile per hour, as the estimated velocity of the downward current in the present case, there is, at least, the certainty that it is considerably less than a velocity which observation has proved to be possible. And now, let it be imagined that a hollow prism reaches vertically from the level of the Minster gauge to the ground, and that the area of its base is equal to one square inch; also let attention be directed only to that portion of the current which may be supposed to descend through the prism ;—it is evident that in the course of twenty-four hours, or 86,400 seconds, its volume will amount to 7 x 86,400=604,800 cubic inches. This volume consists of air and minute glo- bules of water, the latter being, by supposition, equal in weight to half a cubic inch of water = 126°23 grains. Hence, according to this estimate, each cubic inch of the atmosphere between the levels of the Minster and Ground gauges, and within the limits of the raining space, would contain, besides the aqueous vapour due to its temperature, only ae = (00021 gr. of condensed vapour,—z.e¢., less than half the quantity which would be requisite to saturate it, if dry, at zero of Fahr. If, therefore, this estimate be at aJl near the truth, it seems to follow that even such remarkable results as those of the winter observations at York may be accounted for by the presence in the atmosphere of a quantity of condensed vapour too small to give rise to the appearance of visible cloud. Before bringing the paper to a close, there remains to be noticed what, at first sight, might seem to be a new source of difficulty, namely, the fact that when the elevation on which a rain-gauge is placed, instead of standing detached like a house, or tower of a cathedral, forms part of a mountainous country, the ordinary effect of elevation, in appearing to diminish the quantity of rain, is no longer observed. Such aresult, however, presents no real difficulty; for when the current of air carrying minute globules of water which accompanies rain descends on an elevated, but, atthe same time, extended and uneven surface, the resistance offered to its downward progress ought, according to the hypothesis, to produce nearly the same effects as at the level of the ground. In concluding this attempt to explain a long standing difficulty in the theory of rain, I do so with an + nfeigned sense of the very imperfect manner in which it has been executed, but, at the same time, with a good hope that it will be found to be based on a true principle. * Lectures, vol. i. p. 457. ( 39 ) IV.—On the Pressure Cavities in Topaz, Beryl, and Diamond, and their bearing on Geological Theories. By Sir Davip Brewster, K.H., F.R.S. (Read 3d March 1862.) In the years 1823 and 1826 I communicated to this Society two papers “On the Existence of Two New Fluids in the Cavities of Precious Stones and other Minerals.” These two fluids were generally found together in the same cavity, though sometimes the cavities were occupied only by one of them. They were perfectly transparent and immiscible. The denser of the two occupied the angles of the cavities, or the necks, or narrow passages, or canals which united two or more larger cavities; while the rarer fluid floated, as it were, on the other in deep cavities, or filled the body of shallower ones, with the exception of a circular vacuity, which diminished and disappeared with the slightest increase of temperature, or enlarged itself and disappeared in consequence of the fluid being converted into vapour. The denser of these fiuids does not appear to expand more than oil or water by the application of heat ; but the other is ¢#venty-one times more expansible than water. It evaporates at temperatures from 74° to 84°. The vacuity in it disap- pears by the heat of the mouth or of the hand, and it returns to its former state by a violent effervescence, producing a number of minute vacuities, which finally unite inone. The refractive power of the expansible fluid varies from 1:1311 to 12106, while that of the denser fluid is 1-2946, which is greatly less than that of water. From the few experiments which I was able to make on these fluids when taken out of the cavities, it has been inferred that they are hydro-carbons. The distribution of these cavities, in the specimens which contain them, is a subject of peculiar interest. They are often found singly, and of different sizes, at different depths in the mineral; but they most frequently occur in strata, and of such different magnitudes, that the two fluids are distinctly seen in the largest, while the rest gradually diminish till they disappear in black points, which the microscope can hardly descry. Three or four strata nearly parallel to one an- other, and with cavities of different sizes, rarely occur. In general the strata lie in planes, frequently intersecting one another, and having no connection with the primitive or secondary planes of the crystal. In some specimens the planes of the strata are curved, and in rare cases the sections of these planes are curves of contrary flexure. In 1844 I was led to re-examine several hundred specimens of topaz with a more perfect microscope and a fine polarising apparatus, with the view of ascer- * The American and French mineralogists have given the name of Brewstolinc to the volatile, and Cryptoline to the dense fluid. VOL. XXIII. PART I. L 40 SIR DAVID BREWSTER ON THE taining the nature and properties of certain crystalline deposits which I had noticed, and to which I had referred in my earliest observations.* In these new researches, the results of which were published in two papers in the Transactions of this Society for 1845, I discovered two new classes of phenomena which had escaped the notice of preceding observers, and which threw much light on the formation of the minerals in which they were exhibited. In many specimens of topaz from Brazil and New Holland, I discovered numer- ous cavities, filled with crystals of various primitive forms, and with different physical properties. These crystals are either fixed or moveable. Some of the fixed crystals are beautifully crystallised, and have their axes of double refrac- tion coincident with those of the specimen which contains them. In some cavi- ties there is only one crystal, in many two, three, and four, and in a great number the crystals actually fill the cavities to such a degree, that the circular vacuity in the fluid cannot take its natural shape, and can often be scarcely recognised among the jostling crystals. Upon the application of heat to these crystals, some of them gradually lost their angles, and melted slowly, till not a trace of them was visible. Others melted with greater difficulty, and some resisted the most powerful heat I could apply. The crystals which melted easily were quickly reproduced,—sometimes reappearing in a more perfect form, but frequently running into amorphous shapes or granular crystallisations. While some of the crystals were resuming a tabular form, their tints, under the polarising microscope, gradually rose in the scale of colours as their thickness increased; and when there happened to be numerous crystals in the specimen, the whole field of the microscope was filled with brilliant portions of light which they polarised. While making these observations, crystals of a different kind presented them- selves tome when the specimens which contained them were exposed to polarised light. These crystals were embedded in the topaz; and as their axes of double refraction were not coincident with those of the mineral, they were seen in the obscure field of the microscope, brilliant with all the colours of polarised light. They often polarise five or six orders of colours, and in general they have beauti- ful crystalline forms, which are visible in the microscope even in common light. In some specimens of Brazil topaz, the embedded crystals occur in groups of sin- gular beauty, consisting of prisms and hexagonal plates, connected apparently by filaments of opaque matter. In all these specimens the crystals had a distinct outline, whether they were examined in common or in polarised light; but I have met with topazes in which the embedded crystals had no visible outline in common light, and which never could have been detected but by the polarising microscope. In one of these, an amorphous crystal, nearly spherical, lay In a * See Edinburgh Transactions, vol. x. p. 21, note, and plate i. fig. 10, plate ii, figs. 20, 21; p. 419, note, and plate xix. fig. 4. PRESSURE CAVITIES IN TOPAZ, BERYL, AND DIAMOND. 41 crowded group of small fluid cavities, none of which had entered it,—a proof that the cavities had been formed in the topaz when soft, and when it imprisoned the previously indurated crystal. The other class of phenomena to which I have referred is of a still more remarkable nature, and has a more direct bearing on geological theories. About thirty years ago I communicated to the Geological Society the singular fact that I had found in a diamond a small cavity, round which four luminous sectors were seen in polarised light,—a phenomenon which clearly proved that the diamond, when in a soft state, had been compressed by an elastic force proceeding from the cavity. This inference countenances the opinion that the diamond was of vegetable origin; and as this gem was a sort of outlaw in the mineral world, the idea that it had once been in a plastic state, like amber and other gums, and sus- ceptible of compression, did not startle the mineralogists who believed in the ordinary doctrine of crystallisation. The insulated fact, therefore, and the pro- bable inference from it, excited no notice; and it was not till the same pheno- menon had been observed more frequently in the diamond, and in other mine- rals supposed to be of aqueous formation, that its geological importance was likely to be acknowledged. In the Koh-i-noor diamond, which the Princr-Consort kindly permitted me to examine in 1852, I found three black specks, scarcely visible to the eye, but which the microscope showed to be irregular cavities, surrounded with sectors of polarised light. In the two smaller diamonds which accompanied the Koh-i- noor, there were also several cavities surrounded with luminous sectors, and the same polarising structure which indicated the operation of compressing and dilating forces.* In order to obtain more information on this subject, I examined nearly fifty diamonds lent me by Messrs Hunt and Rosxit1, and in almost all of them I found numbers of cavities, of the most singular forms, round which the substance of the stone had been compressed and altered in a remarkable manner. The shapes of the cavities sometimes resembled those of insects and lobsters, and the streaks and patches of colour in polarised light were of the most variegated kind. In examining a large number of diamonds, which adorn some of the oriental objects in the East India Company’s Museum, I found that all these stones contained large cavities, and were coarse or flawed diamonds, which could not be cut into brilliants, or used in rings or other ornaments. It seems, in- deed, to be a general truth, that there are comparatively few diamonds without cavities and flaws, and that this mineral is a fouler stone than any other used in jewellery. Some diamonds, indeed, derive their black colour entirely from the number of cavities which they contain, and which will not permit any light to pass between them. * In 1820 I discovered similar cavities in amber, &c. See Edin. Phil. Journal, vol. ti. p. 334. } See Edin, Trans, 1815, vol. viii. p. 157; or Journal de Physique, 1816, vol. Ixxxii, p. 367. 42 SIR DAVID BREWSTER ON THE Having found in diamond so many Pressure Cavities, as we may call them, round which the substance of the stone is compressed, I had some expectation of finding them in other minerals; and upon re-examining the numerous plates of topaz in my possession. I succeeded in discovering several under such remark- able circumstances, that I submitted a description and drawings of them to this Society in 1845. In searching for this phenomenon with the polarising micro- scope, we first observe four sectors of depolarised light; and if the magnifying power is sufficient, we shall find, in the centre of the black cross that separates the sectors, a small opaque speck, which is the cavity or seat of the compressing force. This cavity is frequently of a rhomboidal form, and often only the 3000th or 4000th of an inch in diameter. It is always opaque, as if the elastic substance which it contained had collapsed into a black powder; and I have met with only one cavity in which there was a speck of light in its centre. The polarised tint in the luminous sectors varies from the faintest blue to the white of the first order. In most cases the elastic force has spent itself in the compression of the topaz,— the cavity remaining entire, and without any apparent fissure by which a gas or a fluid could escape. I have discovered, however, other cavities, and these gene- rally of a larger size, in which the sides have been rent by the elastic force, and fissures, from one to six in number, propagated to a small distance around them. These fissures have modified the doubly refracting structure produced by com- pression, but the gas or fluid which has escaped has left no solid matter on the faces of fracture. Soon after the publication of these results, I discovered still more remarkable cavities in a specimen of beryl brought from India by the Marchioness of TwEED- DALE, who was so kind as to present it to me. In cutting the crystal, Mr SanpEr- son found that one end of it was foul, and produced a luminous ring round a candle. This ring, similar to the rings seen in certain specimens of Iceland spar, was produced by long and irregularly tubular cavities, parallel to the sides of the hexagonal prism. As the tubes had been cut across by the lapidary, their con- tents had escaped; but whatever the contents were, whether fluid or gaseous, they had compressed the beryl, and produced the four luminous sectors around each cavity. This aggregation of luminous sectors produced a mass of depolarised light, which completely effaced the black cross of the uniaxal system of rings exhibited by the mineral. Different degrees of compression were produced by cavities of different sizes; but the resulting tint was generally a white of the first order, rising in some cases to a yellow of the same order. Such is a brief notice of the fluid and pressure cavities which exist in mine- rals, and which have a very obvious bearing on geological theories. Some of these facts have been upwards of forty years before the public,* and along with * Edinburgh Philosophical Journal, vol. ii, p. 334, 1820. PRESSURE CAVITIES IN TOPAZ, BEKYL, AND DIAMOND. 43 others, more recently discovered, have been widely circulated in British and foreion journals; and yet none of our geologists have made the slightest refer- ence to them, either as difficulties to be explained, or arguments to be advanced in support of their own views. In 1822 Sir H. Davy, when he was acquainted only with the existence in minerals of water, petroleum, and gas, did not hesitate to regard such facts as ‘seeming to afford a decisive argument in favour of the igneous theory of crys- talline rocks ;”* and in my paper of 1826, I was driven to the conclusion, “ that the cavities containing the two new fluids were formed by highly elastic sub- stances, when the mineral itself has been either in a state of fusion, or renderéd soft by heat.” At this time I was acquainted only with the two new fluids, and some of their chemical and physical properties; but when I had studied their arrangement in strata, this opinion acquired additional weight. Had these cavi- ties been arranged in planes parallel to the primitive or secondary faces of the crystal, some argument might be urged in favour of their aqueous formation ; but when it was found that the strata of cavities traversed the crystal in all possible directions, that they were bent also into curves of contrary flexure, and that even individual cavities had a curvilinear shape, it was impossible to resist the conclusion that the cavities were formed, and thus capriciously distributed, when the substance of the crystal was in a soft or plastic state. This conclusion derives additional strength from the fact that the water cavities in crystals depo- sited from an aqueous solution are never thus arranged. The discovery of pressure cavities in topaz and diamond may be considered as completing the evidence for the igneous origin of these minerals, and of the rocks which contain them. We know that gas, in a state of compression, exists in minerals. In the pressure cavities we have not only the seat of an elastic force, but its direct action upon the substance of the crystal. Though of equal density throughout, as is proved by the equality of its polarised tints, the crystal has its density increased round the pressure cavity,—the density being a maximum close to the cavity. Such a structure is impossible in crystals formed by aqueous deposition, and hence there is not a single example of a pressure cavity in any of them. They exist, however, in amber and in glass—substances that have once been in a plastic state; and I have produced them artificially by compressing a solution of gum arabic between two plates of glass, so as to include some bubbles of air. The air in these cavities, being exposed to changes of temperature, com- presses the circumjacent gum, and gives it that variation of density which pro- duces four luminous sectors in polarised light, exactly of the same character as those which are found in topaz and diamond. The existence of crystals of different physical properties in the cavities of minerals, and of embedded crystals either shooting through their mass, or occur- * Philosophical Transactions, 1822, p. 367. VOL. XXIII. PART I. M 44 ON THE PRESSURE CAVITIES IN TOPAZ, BERYL, AND DIAMOND. ring in groups, or lying singly with their optical axes in every direction, admit of no other explanation than that which is afforded by supposing the surrounding mineral to have been in a state of fusion, and to have either contained the elements of the embedded crystals, or to have surrounded them when previously formed. Although, as I have already stated, no British geologist has seen the import- ance of the preceding facts, and their direct bearing on geological theories, yet they have been recently referred to,* and their value fully appreciated, by French geologists. In a discussion with M. Evie pe Beaumont on the formation of mineral veins, M. Fournet,} the distinguished Professor of Geology at Lyons, has given a full and interesting account of this class of phenomena, and has adduced them to prove that mineral veins are formed by the injection of mineral matters in the state of fusion. In opposition to this argument, M. Etiz pp Beaumont makes the following observations :—‘ It is difficult,” says he, “‘to admit that crystals of quartz containing two oily fluids, one of which is volatile at the temperature of 81° Fahr., have crystallised in a bath of quartz in fusion. But quartz forms part of the gangues of the greater number of veins, and quartz with fluid cavities is far from being a rarity.” t M. Fourner§ has, we think, removed this difficulty ; but without entering into the question as one of geology, we may safely assert that difficulties attaching to any theory are not arguments against it, especially if there are only two theories, and if equal difficulties attach to them both. We are so utterly unacquainted with the conditions under which the primitive rocks were formed, with the temperatures which prevailed at their formation, and with the pressures to which they must have been subject, that we are not entitled to charge any theory with difficulties which have their origin in our own ignorance, or in the very nature of the subject. We may never understand how the cavities in topaz have such singular and complex forms as those which I have described and delineated,—how these cavities should contain in one specimen two im- miscible fluids, the one dense and the other volatile, and in another specimen various crystals, of different primitive forms and physical properties. We may never understand how a series of these cavities could have arranged themselves in lines now straight and parallel, now curved and concentric, and now radiating from a centre; or how strata of these cavities could traverse the topaz in all directions with surfaces of single or double curvature. We may not be able to explain the special difficulty started by M. Exir pr Beaumont, and yet it is abso- jutely certain that an elastic force, emanating from a pressure cavity, could not have compressed the topaz which surrounded it, unless the mineral had been in a soft and plastic state, or in the state of fusion. * Dausree, “ Etudes sur le Metamorphisme,” 1860, p. 36. t+ Comptes Rendus, &c,, tom. li, p. 42, tom. liii, pp. 88, 610; and Fourner, “ Geologie Lyonnaise,” Lyons, 1861, pp. 588, 715. t{ Comptes Rendus, &e., 15th July 1861, tom hii. p. 83, note. § Geologie Lyonnaise, p. 536. ( 45°) V.—On the Theory of Numbers. By H. F. Tazort, Esq. (Read 21st April 1862.) The object of this paper will be, to give a connected view of some theorems of importance, which are often found in books rather obscurely demonstrated, and in some cases are inaccurately given, or are liable to exceptions which are not mentioned. § 1. On Fermat's Theorem, and Wilson’s Theorem. The most convenient starting-point for this investigation seems to be the well-known theorem, ‘‘If p is a prime number, and (#@+1)” is expanded by the binomial theorem, all the coefficients, except the first and last, are divisible by p. For it is obvious, in the first place, that all the coefficients are integers. If we multiply #+1 into itself, any number of successive times, the coefficients arise from the multiplication and addition of integers, and are therefore themselves integers. Next, the binomial theorem gives the coefficients in the form —1) p(p—1) (p-2 p Pe: ) P@ ae ) ke. Let us consider any one of these, for instance the last; then, since a) is an integer, the numbers 2 and 3, found in the denominator must divide some of the factors in the numerator. But they cannot divide p, it being a prime by hypothesis; consequently, they divide (p—1) (p—2), therefore — is an integer. But this integer is the quotient of the coefficient divided by ». Therefore, p divides this coefficient, and so for all the others. This is the place to introduce a convenient notation, invented, I believe, by Gauss. If a and 6 are two numbers which, when divided by the number x, leave the same remainder, Gauss says that they are congruous to each other, according to the modulus n; which he expresses thus, a = 6 (mod. mn). The sign = is imitated from = the sign of equality, and implies, not that the numbers are really equal, but that they are equivalent (under certain circumstances only). For, if a= 6 (mod. 2) this would not, in general be the case with a different modulus. I propose in the present paper sometimes to use the word equivalent instead of congruous. VOL. XXIII. PART I. N 46 MR H. F. TALBOT ON THE THEORY OF NUMBERS. If any number a is divisible by n, it is equivalent to zero, with modulus x, which is written @ = 0 (mod. 7). To return to the last theorem. If p is a prime, | Aes” (e+ 1) =(a? +1) + (v Nahi, Pee ay * + &e.) Therefore we have the congruence or equivalence, (¢+1)’= za? +1 (mod. p). For all the other terms vanish, their coefficients being all divisible by », whence, p= 0 (mod. p) = ==) A ae a) = 0: and so on. Take this equivalence (a+1P = a2?+1 and suppose # —1 2 leat Next suppose 7 == 2 8? == 2?+1 But we found 2’ = 2 , 8? = 8 Next suppose z —3 “. 4° = 3? +1 But we found 3” = 8 oS 4 And so on till we reach a? =a. a being any number. Transposing, we have a’—a = 0 (mod. p). In other words, the prime number p divides a’—a, or a (a’~'—1). It therefore divides one of the two factors a, or @—'—1, whence we obtain Fermat’s celebrated theorem,—“ If p is a prime number, which does not divide a, it necessarily divides a?—'—1.” Next let us consider a beautiful theorem first given by Lacrance. If pis any prime number, and an equation be formed of p—1 dimensions, whose roots are the series of natural numbers, 1, 2,3, . . . . (p—1), all the coefficients of this equation (except the first and last) are divisible by p. Example.—Let the roots be 1, 2, 3, 4, 5, 6, the equation will be a —21 &° +175 a —735 2° +1624 2? —1764 24+ 720=0 and each coefficient except the first and last is divisible by 7. Assuming LAGRANGE’s theorem as proved, we can deduce a remarkable consequence from it. Let Z be the last coefficient, it is the product of all the roots, or Z=1, 2,3, .... (p—1). Z is always positive, because the equation has an ever number of dimensions. Therefore the equation may be written thus :— (w,~*+Z) + Aa’? + Ba’? + &e.=0; But by LAGRANGE’s theorem, A= 0 (mod. p), B=0, &e. MR H. F. TALBOT ON THE THEORY OF NUMBERS. AZ And therefore all the terms of the congruence may be omitted except the two first. . g?—*4+Z= 0, whence—x?— = Z. In other words, if Z is divided by p, it leaves the same remainder as x#’—* does, when divided by p, but with a contrary sign; x being any one of the p—1 numbers, which are less than p. The simplest case is when v=1. In this case the theorem gives— —1=Z or Z+1=0 (mod. p); which result, expressed in other words, is:—“ If p be any prime number, the product of all the numbers less than p, or 1, 2, 3, ... . (py—1), augmented by unity is divisible by p.” This is the celebrated theorem, known as “ Witson’s Theorem,” of which neither its inventor nor WARING, who first published it, could find any demon- stration. It was first demonstrated by Lacrance (Berlin Memoirs, 1771). We have not employed Frrmat’s theorem in demonstrating it, therefore it is well to show that the latter can be deduced from it. Thus, we have found a? —*== — Z (mod. p). But we have found Z=-— 1. And therefore 2’—* = 1 (w being any number less than ~), which is Fermat’s theorem. § 2. On Associate Numbers. By Witson’s theorem, the product of all the numbers 1, 2, 3, . . . . (p—1), is congruent to —1 (mod. p). Another demonstration of this is given in Gauss’s *« Arithmetical Researches” (French translation, p. 57). It is there said that Ever discovered that this product, omitting the first and last numbers 1 and p-1, could be divided into pairs of associate numbers, the product of each of which is = 1 (mod. p), while the product of the remaining two numbers, 1 and p—1is obviously = — 1 (mod. p). So that the product of the whole series 1, 2, 3, .... p—1, is=W— 1 (mod. p), as we found before. In the passage quoted, the following example is given:—The numbers less than 13 can be multiplied in pairs, thus :—3 x 9=27=1 (if we omit the multiples of 13), which we write 3 x 9==1 (mod. 13). Also, 2x7 = 1, 4x10 =1,5x8=1, and 6x11=1. But, on the other hand, 1x12 ==— 1. Therefore the whole product 1, 2,3,....12=—41. In this theorem of Euer’s, the product of each pair = 1, with the excep- tion of one pair, which is = —1. I have found that there exists another and very different system of associate numbers, in which the product of each pair is== —1; and therefore, the product of the whole is = — 1 whenever the number of pairs is odd; but if it is even, in that case the product of one pair always deviates from the rule governing the rest, and is = +1. So that in all cases the product of the whole is = — 1. 48 MR H. F. TALBOT ON THE THEORY OF NUMBERS. We will take the same example as before, the number 13. The associate numbers are l,12...2,6...3,4.-.. 7,11 and 9, 10, the product of each pair being = — 1 (mod. 13). Thus, for example, 7x11=77. Rejecting 78, a multiple of 13, there remains —1. But the remaining pair of numbers, 5 and 8, produce the product 40, which, rejecting 39, a multiple of 13, is equiva- lent tol. Therefore 5x8 = 1 (mod. 13). It will be observed that the num- bers have different associates in EuLER’s system and in this system, 2 being associated with 6, and not with 7, &c.; except that 1 is still associated with 12, and 5 with 8. I will add some other examples of this new system of associate numbers. If the prime number be 5, the associates are 1, 4, whose product = — 1, and 2, 3 whose product = +1. This prime is of the form 42+1, therefore the num- bers less than it form 2 pairs, an even number; therefore the product of one pair deviates from the rest, as was observed before. Other examples of this, in primes of the form 4n+1, are, »=13. This case has been given before. The associates are written one over the other in the following table, and the deviating pair stands by itself :— a 2 3 - 9 | 5 12 6 4 i LU 8 In the case of p=17 we find,— 7 Cee ee Tea 4 6. 38 10 penne: ithe oF The sum of the deviant pair is always equal to the prime number. Thus, 4418=17. It is worth remark, that the same holds in Euuer’s system, where the deviant pair are always 1 and p—1, whose sum =p. It will make the nature of these associate numbers plainer, if we subtract p from each of those which exceed ie The remainders will be negative num- bers, less than? + . Thus, if y=17, writing the associates one above the other, and their product in the lowest line, 1 2 9 3 6 5 7 4 eer _8 Raye 0 ee eS uy a. 16 =18)6 21g ..1aieih-555 a3 or sea uc a a OB ye eS en ST “< Rule to find the pair of numbers which deviate from the rest. Find the number a less than oe such that 1+.’ is divisible by p, which can always easily be done, and has only one solution. Then # and —z are the pair required. MR H. F. TALBOT ON THE THEORY OF NUMBERS. 49 If now we turn to primes of the form 47+3, the numbers less than p form 2n+1 pairs, an odd number, .’. the product of each pair = — 1, and there are no deviations. For example, if p=7, the associates are 1 2 4 6 3 5 If p=11, they are 1 2 3 4 6 LORaeo a 8 9 We will now pass to the consideration of another system of associate numbers, which I do not find mentioned in the books. Theorem.—lIf p is a prime number of the form 47+ 1, and the series of natural numbers 1, 2, 3, &c., be taken as far as P ioe. (which will be of the form 2n, and therefore an even number), then the squares of these se numbers can be divided into associate pairs, in such a way that the sum of each pair shall be divisible by p. Example.—Let p=17, .. Bo =8. The 8 squares may be divided into pairs, so that each pair is divisible by 17, as follows :— 12442, 224.8%, 3245%, 62472. It is plain that each number can have only one associate. For let a have the as- sociate b ... a? +4 = 0 (mod. p). If ¢ were another associate, we should have a? +c? = 0 (mod. p), and .-. 6?—c? = 0 (mod. p); that is, » must divide one of the factors of 0?—c?. But these areb+candb-—c. And b+¢ is less than p, because 6 and ¢ are each less than, or equal to, Much more is —c less than p. But p cannot divide numbers less than itself, therefore a has only the associate b. It remains, however, to show, that each number has an associate. This follows from the well-known theorem,—“ That every prime of the form 4n+1 is the sum of 2 squares, in one way only.” Sometimes one of the squares is unity. For example, the prime 17 is the sum of 1+i6=1°+4’. When this happens, the other associates are easily de- duced. Thus, multiplying the equation 1? + 4?=17=p by 2’, we have 2° +8’ =2? . p, which being divisible by p, is = 0 (mod. p) .. 27+ 8? = 0, and 2 has the associate 8. Similarly, 37+ 12? = 0, but 12 exceeding = or 8, we substitute for it p—12, or 5, .. 324+5? = 0, and 3 has the associate 5; and so on. But when the prime p is the sum of 2 squares, neither of which is 1, we proceed a little differently. Thus, let p=29, which =4+25—2?+5’. Multiply the least of these numbers, a, by the number which will give a product nearest to the prime 29, and the difference will of course be less than a. ‘Thus, if we VOL. XXIII. PART I. ) 50 MR H. F. TALBOT ON THE THEORY OF NUMBERS. multiply the congruence 2? + 5? = 0 by 15’, we get 307+ 75? = 0, and rejecting the multiples of 29, we get 1+(—12)? =0, or 1+127 = 0 (because 75= 3 x 29 — 12). And upon trial it will be found that 1+12’, or 145, is divisible by 29. Having thus found a pair of squares, such as 1 +a? = 0, we find all the others from it by simple multiplication, and rejecting the multiples of 29. If we had not found this pair 1+q’ at first, we should at any rate have approximated to it. Another mode is the following :—Since 2?+5°=29=p and 5 is not divisible by 2, add 29 to it .-.27+34 = p =0 (mod. p), and dividing by 2°, 12+177=0 v 14+(-12f =0, .. 1412? =0, as before. p being a prime of the form 4n+1, we have in all cases p=m?+n’, and having ascertained the values of m, n, we can derive from them other numbers a, 8, ¢, d, such that a? +0? = 0, +d =0, &ec.; from which a curious theorem arises,— If the prime number p divides both a*+0’, and c?+d’, it also divides both ac+6d and bc—ad. Exumple.—29 divides 2?+5°? and 3°+7°. Therefore, it divides 5°'7—2:3 and 2°7 +5'3. Demonstration.—Because a?+6?=0 and c4+d?=0, -. @2 +e’? =0 and ac +a*d? = 0, .. by subtraction 0’c?— a’d? = 0, the factors of which being bc + ad and bc—ad, p must divide one of them. [M.] Permute the letters a, 0, in this result, since it is immaterial which is which; therefore p divides one of the two factors, wc+6d, or ac—bd. [N.] Comparing the results M and N, we see that if p divides ac+bd in the second of them, it divides dc—ad in the first. It appears from what precedes, that a prime p of the form 4n+1 always divides some number of the form 1+a’, where a is less than ae . Annexed is a table of the values of @ for the first prime numbers of that form, from 5 to 109. 5 divides 1+ 2? 61 divides 1+ 11? ee AR am I 13.) 0c Ea 1 areal So... | eae DO ssc OF La Thao Sith a LS eG 100s: ok., wo? Ae ete HictenOe 109», er 1a 334 DS, sas. be leat The law which governs these results is not manifest, therefore, although the prime p always divides a number of the form 1+.” ( x less than P=) , yet x must be found by tentative methods. We will here add a few more examples of a theorem previously mentioned :— The prime 13=2?+3? and divides 1+5? .. 3-5—1:2=13, and 2:-5+1:3=13. The prime 41=4°+ 5° and divides 149? ... 4:9+1-5=41, and 5-9—1:4=41. The prime 61=5?+ 6 and divides 1411? .. 5:11+1-6=61, and 6-11—1:5=61. MR H. F. TALBOT ON THE THEORY OF NUMBERS. ol Although a prime of the form 47+ 1, is always the sum of 2 squares, yet a rule is wanting to determine these squares. The following answers for one case :— Let p be the prime. Try if 2p—1, isa square, and if so, call it 9’. ele Gea 2 gil\, Then p={ 7) + (45) Example.—Let p=1861 .-. 2p —1=8721=61?=g? ... p=30? + 31?. § 3. Remarks on Barlow’s Theory of Numbers. Peter Bartow, of the Royal Military Academy, a mathematician of eminence. and author of a volume of tables most useful to all persons engaged in numerical computations, and believed to be exceedingly accurate, published in 1811 a work entitled “ An Elementary Investigation of the Theory of Numbers.” This book, which gives much useful information on a subject at that time little known to the English reader, contains a few errors which ought to be pointed out, lest they should acquire credit, by having appeared in a work of authority. I. It is well known that mathematicians have never been able to find the demonstration of FERMAt’s theorem, which asserts that a” + b"=c’", is an impossible equation, if m is an integer number greater than 2. Nevertheless, Bartow, at p. 169 of his work, professes to give a demonstration of this theorem. Subsequent. mathematicians, however, have tacitly ignored BarLow’s demonstration, and the question has continued to be proposed from time to time by the French Institute and other learned societies, without receiving any solution. It is worth while, therefore, to inquire for what reason BarLow’s demonstration has been put aside. Before treating of the general problem, to satisfy the equation a” + b"=c’", he treats of the particular case a’ +6’=c’, and as he treats this exactly in the same way pp. 132-140, one explanation will suffice for all. It appears to me that the error of the demonstration lies in p. 189, where he obtains an equation =s 2 — = 6, and says, jirst, that because 7, s, 7, are prime to each other, each of the above fractions is in its simplest form; and, secondly, that they each contain a factor in their denominator, that is not common with the other denominators ; and there- fore, these fractions cannot, anyhow combined, be equal to an integer, by Corol- lary 2 of Art. 13. But this theorem is not true. Take for example the equation 8 : : Ae o.=8. According to the theorem, S cannot be an integer, because the fractions are in their lowest terms, and each denominator contains a factor, that as not common to the other denominators. But on trial, we find that S=2, an integer. Turning, therefore, to the Corol- lary mentioned, which is found at p. 20, we see that it rests upon a theorem in p. 19, viz.:—‘* The sum of two fractions in their lowest terms, of which the denominator of the one contains a factor not common with the other, cannot be an integer.”” This may be admitted; but Cor. 2, which follows, appears to be a2 MR H. F. TALBOT ON THE THEORY OF NUMBERS. erroneous, viz.:—“ Cor.2. Jn the same manner it may be shown, if there be several fractions, and one of them be in its lowest terms, and contain a factor in its denominator, that is not common to all the other denominators, the sum of these fractions cannot be an integer.”” As BARLow’s demonstration of Fermat’s theorem reposes on this Corollary, that demonstration falls to the ground, and a true demonstration of the theorem still remains to be sought for. II. There is a well known and very remarkable theorem, that ‘‘ Every prime number of the form 47 +1 is the sum of two squares, and in one way only.” The most simple proof of this appears to consist in the following series of propositions :— (1.) The product of the sum of two squares bya similar quantity is likewise the sum of two squares, and in two ways,— Because (a? + b?) (c? +d?) =(ac + bd)? + (ad—be)? ; and also, =(ac— bd)? + (ad + be)? (2.) The sum of two squares can only be divided by a quantity of like form. (3.) By Wixson’s theorem, a prime p always divides 1, 2, 3, . . . . (p—1)+#]1, and this product may be written L (p12) AR 2) © SOBA See) See. or, (p—1) (2p—2?) (8p—3?) .. . &e. or omitting the multiples of p, and observing that the number of factors is even, if p is of the form 47+1, the product may be written x2 eS ete | L 2s ae yee Therefore p divides Q’+1 the sum of two squares. Therefore p is itself the sum of two squares. BaRwow, at p. 205 of his work, gives the converse of this theorem, and says, that a number of the form 42+ 1 is necessarily a prime number, if it is the sum of two squares, in one way only. Suppose, however, that we take for example the number 45. This is the sum of two squares 36+9, and in one way only. Nevertheless, the number 45 is not a prime, as it ought to be by this rule. This shows how much caution is necessary in writing on this branch of mathematics. The fact is, the theorem only holds good in case the two squares are prime to each other. Now, 36 and 9 are not so; and, consequently, the conclusion that their sum is a prime number is erroneous. With this limitation, however, I believe the theorem is correct. There is one apparent exception, however, which should be pointed out. The square of a prime number of the form 42+1 is of the same form, and is the sum of two squares in one way only. ‘Thus, 5?, or 25=16+9 and 13’, or 169=144+425. The test, therefore, appears to fail in these instances. But in fact it holds good; for 25 is not only the sum of the squares 16+9, but also of 25+0, and this consideration applies to all similar cases. ( 53 ) VI.— On the Rain-Fall in the Lake-District in 1861, with some Observations on the Composition of Rain-Water. By Joun Davy, M.D., F.R.S., Lond. and Edin. (Read 7th March 1862.) Before entering on the main subject of this paper, the composition of rain- water, I shall give a brief account of the rain that has fallen in the Lake- District during the year just past; and this I shall do chiefly by means of tables. The quantity of rain registered has been so greatly in excess of any former year, that of itself it is deserving of record, and the more so, comparing the weather which has prevailed here with the weather in the south, for the most part, happily for the harvest, as remarkable for an opposite state, an excess of dryness. The first table I shall give will convey a general idea of the meteorological phenomena during the period, as it includes in its several columns almost all the conditions appreciable, which have an influence on climate. [am indebted for it to a very accurate and zealous observer, Mr Samuen Marsuauu of Kendal. The plus and minus marks in it refer to averages: in the instance of the rain-gauge derived from an experience extending over forty years; in the instance of the thermometer and barometer over a period only one year less, and during the whole time using the same instruments. The second table relates solely to the rain-fall: it contains the recorded results of the amount monthly at the several places named. For the means of forming it, [ am indebted to the resident gentlemen or their agents, by whom the record has been kept. The area comprised—extending in one direction from Kendal to Keswick and its neighbourhood, and in the other direction from Coniston to Patterdale—pretty well represents the Lake-District at large. * The third table shows the number of rainy days at the several places, that is, the days in which any rain had fallen during the twenty-four hours. The fourth table is designed to show the quantity—that an unexampled one— which fell in the month of November. As in the third table, the record of the rainfall is more limited as to localities than that of the second table, owing to the circumstance, that only some of the registrars recorded regularly their obser- vations daily. ; VOL. XXIII. PART I. Pp DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. 54 jo uvoyy “MS| €. te) BLT MSF = | 61 "“MS| 2 + | 86 PANS!) 9) "1 51 "Me | 6. te | AT ‘MS! G + | 1G ‘MS| £ + | ‘TN 9 = |:8 aN Ge | © NG | Be S| 6B "MS| FL+ | 86 ‘MS| G + | OT eA NSH tS) Sari GL ae f[oeae 96F-8 + | L69-09 G.9F| -6F 920-8 |¢-F8 | L-¢e 968-1 1/6-98 | 1-88 8G-€ |L-08 | 1-3¢ 8F8-¢ |9-8¢|0-9¢ 2128 |€:2¢ | 0-09 988-9 |6-L¢ | 6-19 600-8 |¢-6¢ | 1-69 OIL-0 |F-0¢ | 1-9¢ L¥G-0 |8-G# | 8-0 L¥6-L |G-OF | 6-3 GFL-G |L-LE | 3-68 CFLS SEE L-¥8 souomr | ao | nd, dard) eewos ‘TO8T NI IVANGY NI ACVW SNOILVAUISAO 6-F§ €-GL L3G LIP L-GG &-0¢ 0-98 9-€L 0:66 1-98 L.9F €-18 0-SF 6-66 €:P 9-01 6-Ge POLI 1-18 G-G6 0-FE 8-L9 6-16 6-9¢ 8:83 6-88 peraneonaoy, | aBog ‘sSBI) UO Ja}OMOWIOY YT, F101 + 81F-1— Lob-0— 696-4 + 116-0 + gee-1 + 016-0 — G48.3 + 100-0 + ger-1 + 010-3 + 6CL-z + £$9-0— ‘mRO IY — a0 + 0Z8-LF/E-8% 106-48] 1 00L-88| $81 F3G-1G] BE GL19-49| 98g 868-69) SF G81-89| FF 806-6¢| for 893-19] o3 IFE-9F 6 C8T-ZF! FLz $88-68 61 8GL-F8) 11 “uUBoW | “OTT ‘punory oy} logy qooj ¢ ‘opvyg Ul JojyoWOMEYY, ‘om ‘suvoll 3-29 | 9F0-0— | 90L-63 6II-63 061-08 { jenucy €¢| 896-0 + | 18-62] 196-83 968-08) * ‘toquiesaq 3S | O9T-O— | €0F-63 LF6-83| ILT-08) * ‘toquioaony $9| 961-0 + | P8L-6z| 1L0-63 F9T-08) © 2090990 0L| FOL-0 — | 189-63 $96-83 666-64} * ‘toquioydag 91} £00-0— | G0L-62 908-66| 860-08 * + 4snény 91| L83-0— | 6-63 600-62/ 886-62, ° ° ‘Aine 46L| L10-0 + | 6FL-62| L88-63| 700-08, °° ‘oune 9L| 906-0 + | Z06-63| FSF-62| 613-08) - ‘ACTA 3L| 686-0 + | 86-66] GLF-63 10F-08) °° ‘Tady GG| 806-0— | 94-63] 939-8Z/ SCT-08 °° “yorey 1G | 680:0— | 169-62) €96-82| G¢F-08| * ‘Axenaqo,y go) LZ8-0+ | 156-62 068-63| 642-08, ° ‘Arenuee xo] EGE | uso | cu | xe *‘SHINOJ -sajatuoreg ATA VL TVOINOTOUOALYTY JO AMVNWAS—'T DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. 55 TABLE II. Lesketh i High _ | Seath ._ |Patter- nowons, [onda | Hom [Eameigg) Weey | hee, [Bie How | Cot | ate, raewin| it at side. dale January, 3°745 | 6°69 6:094| 6:084| 3°68 9:080] 13:5) 9-88} 4:208| 2-29| 3-50 February, | 5°743| 12:08 | 13-390| 8-114} 9-02 | 13:614|] 9-2 18-27 | 9:295| 7-06 |14-70 March, 7:947|11-67 | 15-299} 9-959| 12:03 | 15-603] 11°5| 26:08) 6-681| 7-51 |12-20 April, 547 “99 1:185| -640; 1:05 1:247 3 82; ‘907; -96) -60 May, FLO) 1-10 1:643 |) 1:290; 1:30 792) 2°7| 4°61) +550) 1-41) -12 June, 3°009| 4:62 3°651| 3°678| 3°94 2:°559| 4:0| 7-70] 3:154]| 2-08] 1:12 July, 6°886| 9:56 8:470| 8-756; 9°60 8641 | 11:5; 14:59 | 8-284} 4:91] 8-18 August, . | 8°312|10°96 | 17:508| 9°527| 11°61 | 15-913] 12:0} 25:20] 7-580) 7-02 /18-25 September,| 5°848) 9°52 | 16-277 | 7:°884| 11°75 | 12-460] 10:0 17-42} 9:114] 7:40 17-21 October, . | 3°528) 5°76 9:049 | 4°373] 8-20 5°170| 5:0} 9:07) 3:580| 3-24|°7°70 November, |11:396 | 18-88 | 20:168 /14:437| 17:07 | 21-408) 17-0| 35-41 |13-838 |11-49 | 7-15 December, | 3°026| 7-20 | 10°490| 5°166) 4:50 9:-771| 65| 13°62| 7-270} 4:98| 9-10 60-697 | 99:03 |123:219 | 80-708) 93-75 |116-258 |102°2 |182°67 |74-417 |60-35 |94-83 TABLE III. Lesketh Mons. | Kendal.| aniyiz. | Grasmere, | Troutbeck. [Borrowdale |S"! house | Castle side. January, 11 14 5 Ash 7 17 6 15 February, .& | 16 16 10 15 17 17 1) 16 March, 28 28 13 7 25 25 24. 29 April, 8 7 PO 7 i, 7 6 9 May, 3 8 8 6 6 6 6 10 June, 8 11 14 8 15 15 10 10 July, a2) 26 24 21 23 23 22 28 August, 21 24 26 21 23 23 27 24 September, 17 19 21 7, 19 19 24 23 October, 12 14 ee 11 ite ili 11 17 November, 23 22 25 23 24 24 24 |; 20 December, 13 16 15 14 iy iy) 16 14 179 205 141 181 204 204 188 215 * “ Not taken daily.” t+ Mirehouse is four miles NNW. from Keswick. 56 DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. TABLE IV. November Fisskeut Seathwaite, A The How, ra 1861. ae ai SOE Borrowdale. Keawick. Troutbeck. Gatti 1 0:47 0°673 = 0°362 0:654 0:°367 2 17 035 ‘600 471 3 iat 270 4 10 ‘409 Sete 184 407 aig 5 36 *202 2°43 384 817 631 6 98 “405 1-22 102 742 101 7 10 057 -092 123 161 8 ia °157 cee *210 236 9 i 66 e | 10 07 088 on *246 1:000 | 11 85 680 2°21 ‘696 1:355 1:822 12 2°73 1:588 4:24 2°150 2°305 349 13 17 228 *85 006 360 14 012 voy 200 173 097 / 15 37 220 140 ea 16 “be A3e, 118 | 17 06 113 fe 1) eee "170 be rate ee 633 | 20 “79 “204 4:02 *336 *840 1°335 | OMI 1:67 ‘904 4:88 ‘966 2°505 “895 22 1:55 ‘900 ‘45 1:012 1:510 267 23 ‘ol 430 as 082 178 Sax 25 1:05 393 2°38 “660 1660 3°612 26 4°83 2-240 7°52 3°730 3160 "062 27 09 -065 1:00 254 -042 ‘473 28 37 440 es 036 492 ‘903 29 1:30 689 oe *300 1:945 470 30 “75 497 301 ‘740 1:180 "428 be oe eee eee Eee 18:88 | 11°396 | 35°31 | 13-838 | 21-408 | 14-441 The general results, as shown in these tables, may be pointed out as briefly the following :— 1. A prevalency of south-west winds. 2. The annual temperature very slightly in excess of the mean. 3. The atmospheric pressure very slightly below the mean. 4, The number of rainy days slightly in excess, and varying at the different stations, and in no regular ratio with the quantity of rain. * The gauge at Seathwaite, I have been informed, was not examined daily, only on the days specified in the table. As observations were made on the 25th, 26th, and 27th, there can be no doubt respecting the correctness of the amount, 7°52 inches, during the twenty-four hours. In the preceding table, the number of rainy days at Seathwaite is given as the same as at Keswick, where a strict account was kept. It is believed by those acquainted with the two localities, nine miles only apart, that when there is rain at Keswick there is a certainty of rain at Seathwaite. DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. 57 5. The total amount of rain greatly in excess; the excess, with few excep- tions, increasing towards the higher mountains of the district, and especially at Seathwaite in Borrowdale, a spot nearly central amongst them. This excess of rain at all the stations, I may remark, has not only been con- siderable, but even unprecedented. Mr John Dixon, the observer at Seathwaite, states, that there the quantity registered has “‘ exceeded any former year, for the last fifteen years, by 22 inches,”—this period comprising, I believe, the whole time that a record of the rain fallen has been kept there: and from Mr W. Rumney, in the employ of James Garth Marshall, Esq., I learn that the rain-fall this year at Coniston is as much as 23 inches in excess of the average of the last twenty- five years. I need hardly remark that such an excess of rain, especially the fall in November, was productive of floods. ‘These, though they occasioned some damage, have been less destructive than might have been expected, probably owing to the peculiar features of the country, the many receptacles for water, such as the lakes afford, and the ready discharge of water, where there are no lakes, through well worn and deep water-courses: moreover, the agricul- tural character of the district—so much of it pastoral, so little of it broken up by the plough—may have been another safeguard. A rainy, cool season, is commonly a healthy one. This year has not, I believe, been an exception. The health of the inhabitants generally, from all I can learn, has been equal to, if not above the average. I have not heard of any unusual sickness during the months of most rain, except at Keswick and at Bowness, at each of which I am informed typhus or typhoid fever has prevailed, and has been in several instances fatal. The occurrence of the disease in both has been attri- buted, and probably justly, to neglected drainage, and to the neglect of other sanitary measures, in Keswick especially, in the lower part of the town, which is subject to being flooded. I shall now proceed to my main subject. The observations which I have made on the composition of rain-water were begun in August 1860, and, with occasional interruptions when from home, have been continued up to the present time—and this daily, whenever there has been any rain. Two methods have been employed in conducting them, one microscopical, the other chemical. First, Of the Microscopical —These observations have been made either on single drops of rain, or on two or three collected on a glass-slide, and evaporated to dryness at a low temperature, and, as soon as dry, subjected to the micro- scope, using an object-glass either of one-eighth, or of a quarter of an inch focal distance. Oftener, however, a larger quantity of rain-water has been employed, taken from the rain-gauge, viz., one or two measures, the measure holding - twenty-five grains of water, which has been evaporated in a watch-glass, and VOL. XXIII. PART I. Q 58 DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. when reduced to a drop or two, has been poured on a glass-slide, and reduced to dryness in the same manner as the first mentioned. Secondly, Of the Chemical—tThe rain used in these trials has always been collected in the rain-gauge. The ordinary test employed has been a solution of nitrate of silver, the extreme delicacy of which is so well known. And, besides its great delicacy, it has the advantage of taking effect immediately. It has com- monly been used without any concentration of the rain-water by evaporation. Occasionally the whole, or the greater portion of the rain collected in the gauge during the twenty-four hours, has been reduced by evaporation to a small volume, and in this state has been made the subject of experiment. The rain-gauge, it may be mentioned, is of copper, both the funnel and the vessel the recipient. It stands about 25 feet from the ground on a grass-plat in the garden adjoining my house, which is about a quarter of a mile in a northerly direction from the village of Ambleside, and is about 140 feet above the sea-level, and about 30 feet above Windermere. Having premised thus much, I shall now give some of the results, and in the order just sketched out. lst, Of the Rain-drops.—I shall describe from my notes, taken at the instant the observations were made, a certain number of these results, specifying the kind of weather which prevailed at the time. They are at least recommended by their simplicity, and from being free as much as possible from any source of error. I shall begin with one which was obtained before I entered regularly on the inquiry. 1. June 2, 1858.—The sky, at 1 p.m., after a fine early morning, became unusually overcast with dark clouds, producing an obscurity exceeding that occasioned by the then last eclipse, that of July 1851. Some rain fell in large scattered drops. A few were collected on a glass-slide. They left, when evapo- rated, a circular stain, distinguishable by its greyish hue, most strongly marked in its marginal outline. Under the microscope it was seen to consist of dark particles chiefly ; they were of irregular forms, like soot particles, and intermixed with them there were some minute crystalline groups. 2. On the 30th August 1860, after a fall of -90 inch of rain during the preced- ing twenty-four hours, the wind westerly and strong, there were occasional showers in large drops. A few of these drops, evaporated on a slide, exhibited under the microscope a delicate crystallization. Drops from another shower during the day showed the like crystallization, with which was one crystal, a cube, like that of common salt, and about ;3;th of an inch in diameter. 3. September the 1st.—Showery; the wind from the same quarter; the rain- drops smaller than those of yesterday. Some of them leave no stain on glass; some only a just perceptible stain. 4. September the 6th.—During the night a slight shower (‘01 inch). Rain- DR DAVY ON THE RAIN-FALL IN THE LAKE-DISTRICT. 59 drops collected in the usual manner, left a circular marginal stain, conspicuous to the unaided eye. Under the microscope it was seen to be formed of minute crystals, of numerous granules, and of many spheroidal particles like pollen. 5. September the 8th.—Slight rain in the afternoon, the morning overcast; ‘06 inch of rain only during the preceding twenty-four hours. th of an inch. Dorsal surface some- what convex. A pair of dark-coloured spots is seen at the anterior end. At the posterior a couple of fine hairs projects backwards. An aggregated mass of refracting globules, probably the remains of the yelk, lies in the centre of the body in what may be supposed to be the intestine. A series of appendages projects beyond the sides of the larva. The anterior pair, evidently antennze, are three-jointed, the terminal segment possessing two hairs projecting from its free end. Behind the antenne, and distinctly arising from the ventral aspect, are two pairs of swimming limbs. Each limb consists of a basal and two terminal segments, one in front of the other. Each terminal segment is furnished with hairs; the anterior possesses two at its outer end, the posterior has only one at its outer extremity, but in addition is furnished with three along its anterior margin, each arising from a papilla-like projection. Distinct muscular fibres, transversely striped, were seen in the body of the larva, evidently connected to the basal segment of the limbs. Of mouth and anus we saw no indications. The further development of the larva we had no opportunity _ of tracing. PLATE III.—Ezplanation of Figures. Fig. 1. Lateral view of Chondracanthus Lophii. The constriction t, separating the cephalic u, and thoracic parts, the pair of antenne, a, at the anterior part of the head, and the number and direction of the dorsal and lateral processes, are represented. The two spirally twisted strings of ova project from the posterior part of the animal. The thoracic feet are indicated at dd. Fig. 2. Ventral aspect—a, antenna; 6, hook; c, foot-jaws ; dd, thoracic feet; ee, ventral mesial processes ; /, posterior end of alimentary canal; g, abdomen; h, cement organ. Fig. 38. Highly magnified view of the distal segment of one of the antenne, The continuity of the parenchymatous substance of the hairs with that in the interior of the antenna itself is re- presented. Fig. 4. Left hook organ—i, terminal hook; &, basal portion; /, frame. In A, the ventral aspect, in B, the outer aspect is represented. Fig. 5. Ventral aspect of cephalic portion. The relations of the antenne a, hooks 6, mouth s, foot-jaws c, and the origin of the first pair of thoracic feet d, are exhibited. Various muscular bands for the foot-jaws, and portions of the longitudinal muscles are seen. Fig. 6. Enlarged view of foot-jaws of left side. C 1st, D 2d, EH 3d foot-jaw. Fig. 7. Alimentary canal, with its lateral cceca and small terminal cul-de-sac. The muscular fibres in its wall are represented. Fig. 8. Abdominal portion—m, proximal segment, with its somewhat bivalve-like shape; n, distal segment, bearing hair-like papilla; 0, ova-strings; 7, villus-like projection for attachment of male, VOL. XXIII. PART f. x 76 MESSRS TURNER AND WILSON ON THE CHONDRACANTHUS LOPHII. Fig. 9. Dissection of abdomen showing the connection of the cement organ h, with the investing material of the ova-strings, 0. The portion of the proximal segment marked m in this and Fig. 8, being turned on one side; p, longitudinal muscular bands. Fig. 10. Ramifying ovary, with contained ova, in one of the lateral lappets of the thorax. Fig. 11. F, Villus-like projection to which the male is attached. G, Enlarged view of two of the epithelium-like structures. At 7, Fig. 8, the projection is shown in situ. Fig. 12. Side view of male, to the hook organs of which a portion of the villus-like projection is still connected. Fig. 13. Ventral aspect of male. Fig. 14. Natural length of male and female without the ova-strings. Fig. 15. Successive stages in the development of the ova. Fig. 16. Anterior foot of left side of larva. The division into two terminal segments is seen, with the mode of connection of the hairs to them. TRANSACTIONS OF THE ROYAL SOCIETY, EDINBURGH. VOL. XXIII. PLATE III XS SANA F. Schenck, 12 Rt Exchange, Edin H. S. Winson, M.D., Delt. ONES) VIII.—On the Structure of Lerneopoda Dalmanni, with Observations on its Larval Form. By Witutam Turner, M.B. (Lond.) F.R.S.E., and H. 8. Winson, M.D., Demonstrators of Anatomy. (Plate IV.) (Read 7th April 1862.) The first example of this, apparently little known, species of Parasitic Crusta- cean appears to have been noted by Professor Orro.* The celebrated Swedish naturalist Retzius was, however, the first to give, in 1829, an anatomical descrip- tion of it.} He named it Lernwa Dalmanni. His description was accompanied by several figures, which, though in many respects imperfect, enable one to recognise the chief external characters of the animal. He found three specimens at Christian Sound, in the nasal cavity of Raia Batis. Von NorpMannt obtained from Rupourut the specimen discovered by Orro, but it was so injured, that he adopted, in his account of the anatomy of the animal, the description of Rerzius. Some years afterwards, in 1836, Kroyer|| added it to the Danish fauna. He © states that he obtained two specimens from the nasal chamber of a skate brought to him by a fisherman from Aal-back, and that specimens from Iceland had been for several years in the possession of the Natural History Society. As naturalists had now begun to subdivide the old Linnean genus Lernza into various genera, Kroyer added this animal to the genus Lerneopoda of Dr BLAINVILLE, and, con- tinuing its specific name, termed it Lerneopoda Dalinanni. Since the time of Kroyer but little attention appears to have been bestowed on this parasite by systematic writers. Mitne Epwarps§ mentions it only briefly, and is inclined, from the elongated and cylindrical form of the cephalic part, and from the development of two processes from the ventral aspect of the posterior end of the body, to place it in the genus Brachiella. It does not appear to have been, as yet, recognised as a British species, for no mention of it is made in the systematic works of Barrp and Gossz. The for- tunate detection by one of us (Dr Witson) of several specimens, early in the pre- sent year, in the nasal cavities of more than one skate, caught by the Newhaven fishermen, has enabled us to add it to the British fauna, and to investigate its anatomy. * Mikrographische Beitrage Von A. v. Nordmann. Berlin, 1832. t+ Kongl. Vetenskaps Acad., Handlingar, Stockholm, 1829. P. 109. Frorieps Notizen, vol, xxix. N7617, p. 6. + Op. Cit. p. 139. || Naturhistorik Tidskrift, vol. i. p. 264. Okens Isis, 1840, p. 746. § Hist. Nat. des Crustacées, vol. iii. p. 516. VOL. XXIII. PART I. xe 78 MR W. TURNER AND DR H. S. WILSON ON THE Female (figs. 1, 2).—This is evidently one of the largest of the Lerneade. It presents decided indications of being divided into two great segments,—an ante- rior, or cephalo-thoracic, and a posterior or abdominal. The division is indicated by a well-marked constriction or neck. Immediately in front of this neck a pair of long arms arise from the sides of the cephalo-thorax. The cephalo-thorax in a fully grown specimen is ,4,ths of an inch in length. It projects almost at a right angle from the anterior extremity of the abdomen. It is elongated, and somewhat compressed laterally. On its dorsal surface, about the junction of the anterior and middle thirds, a pair of antennz is situated (figs. 3, b). Their bases are partially concealed, and connected together by a crescentic fold of the chitinic integument of the animal, the convexity of which fold is directed backwards. Each antenna is 3-jointed: the basal segment short and broad; the second much longer; the terminal smaller, and possessing a pair of hooks at its free end (fig. 5). In front of the antennz, and therefore close to the anterior extremity of the head, a complicated buccal apparatus is met with (fig. 3, ¢, fig. 6). Situated in the middle line is a short conical snout, at the free extremity of which a rounded oral aperture exists. The animal appears to possess the power of retract- ing and projecting this snout at pleasure. On each side of the snout is a short stump-like process, slightly bifid at its extremity. For the due examination of the structures about the mouth, the higher powers of the microscope are necessary. The buccal apparatus consists of an oral aperture, of two lip-like structures, and of a pair of jaws. The lower lip is strengthened by a peculiar arrangement of chitinic bands, which have been represented in fig. 9. Projecting not only from the margin, but also partially from the inner surface of this lip, are a number of fusiform bristle-like papille. On the inner surface of the central part of this lip several very delicate, faintly transversely-barred lines pass downwards and backwards as far as a chitinic bar, which stretches across the lip from margin to margin. The upper lip (fig. 8) consists of two chitinic concavo-convex plates, which fit into each other, their concave aspects being directed to the buccal cavity. The inner plate is shorter than the outer, and bears a row of long slightly undulating, transversely striped, rod-like structures, fringed at their free ends. The outer plate is covered at the margin, and for some distance on its dorsal aspect, by sharply pointed, conical, bristle-like papille. The lips are supported at their bases on a chitinic plate, more immediately continuous with the plates of the lower lip, and to which the upper lip is apparently connected by a moveable joint. This plate is so arranged as to be folded upon itself in such a manner as to enclose tubular spaces (fig. 6, b), in which some of the muscles of the buccal apparatus are included. When the lips are drawn asunder, so as to expose the buccal chamber, a pair of elongated scythe-like jaws (mandibles) is seen (fig. 9). These are attached STRUCTURE OF LERNEOPODA DALMANNI. 79 laterally close to the angles of junction of the lips. They lie obliquely across the cavity, and therefore cross each other. In some of the specimens the free ends of these mandibles projected externally through the oral aperture (fig. 7). Deeply serrated strong teeth, about six in number, with intermediate smaller teeth between the three terminal ones, are placed along the concave posterior margin of the unattached extremity of each jaw. Each mandible is articulated externally to the chitinic plate which supports the lips. The muscles which move the jaws do not present any distinct transverse striation. They are marked by delicate longitudinal strize, which resemble nuclei in their appearance. Connected laterally to the outer aspect of the upper lip is a very small pro- jecting structure, which Kroyer has described as a touch organ, and which may evidently be considered to be a labial palp (fig. 8, a). It consists of two segments, from the terminal one of which three papilla-like hairs project. The basal segment has, along its line of articulation with the terminal, a short hook- supporting tubercle, and from its outer surface, about half way towards the base, there is an elevation fringed with very short bristles. The stump-like processes, between which the snout, bearing the mouth, lies, have been termed by Kroyer the second pair of antenne (fig. 6, d, fig. 10). They correspond very nearly, both in structure and relation to the mouth, to the © appendages which V. NorpMANN has described and figured in Achtheres percarum as the upper jaws, or metamorphosed first pair of feet. Each of these structures is segmented and laterally compressed, and arises by an elongated base, which is not merely on the same line with the base of the snout, but extends forwards beyond it for a short distance towards the anterior extremity of the cephalo-thorax. Each possesses a bifid free extremity, the posterior division of which, smaller than the anterior, is armed with a well-marked terminal hook. Along its posterior margin are two elevations, studded with short, blunt, cylindrical bristles (fig. 10, a). Immediately above the lower of these elevations is a smaller space covered with conical hairs. The anterior division, very much larger than the posterior, is thickly studded, especially on its outer surface, with a corresponding bristle- like arrangement (fig. 10, b). Springing from the anterior and inner part of each of these modified feet is a segmented palp-like structure, set with three or four conical papillze at its free extremity (fig. 10, c). At the inferior margin of the anterior extremity of the cephalo-thorax is a somewhat pendulous nipple-like structure, which has been named by RErztus the chin (figs. 4, b). It consists simply of a projection of the integument, which can be retracted or protruded at pleasure. A pair of elongated cylindrical arms arises from the sides of the cephalo-thorax immediately in front of the constricted neck (fig. 1, ©). When fully extended, each arm measures an inch, but it can be contracted by the animal at least one-half. The arms pass almost vertically upwards in the direction of the long axis of the 80 MR W. TURNER AND DR dH. S. WILSON ON THE abdomen. They lie side by side, and almost parallel to each other. Each arm ends superiorly in an expanded structure, concave on its upper aspect, which performs the office of a clasper. The adjacent surfaces of the two claspers are flat, and, when the arms are in their normal position, these surfaces are accu- rately adapted to, but not continuous with each other, so that they can be drawn asunder without any difficulty. The arms, therefore, cannot be regarded as blended together at their extremities. Lying in the concave upper surfaces of the apposed claspers is a curved cartilaginous-like bar (fig. 2, a), the convex outer surface of which is closely embraced by them. The bar has in its interior a dis- tinct cavity. Projecting from the surface of the bar which is in apposition with the claspers, is a small papilla, along the axis of which the central cavity of the bar extends. Between the superior margins of the flattened apposed surfaces of the claspers a slight depression exists, into which the papilla of the bar fits. Two small oval openings exist at the bottom of this depression, one belonging to each clasper. Each communicates with a long and slender tube, which passes through the substance of the clasper to be continuous with the central canal of the cylin- drical part of the arm. The substance of the bar, when examined microsco- pically, without the addition of any reagent, appears to be structureless. After digesting thin slices in ether, and subsequently boiling them for some time in acetic acid, a very beautiful cellular structure is perceived. These cells are about the size of primordial cartilage cells. In them the nucleus is elongated, and be- tween it and the cell-wall a delicate concentric arrangement is seen. There is evidently a difference between the chemical composition of the bar and the chitinic integument of the animal, for on steeping a specimen for some hours in a chromic acid solution, whilst the colour of the latter was very slightly affected, that of the bar was changed to a dark brown, almost black. Both the claspers and the cylindrical portions of the arms contain powerful muscles, by the contraction of which the arms can be very much shortened, at which times they have a very crenulated appearance. These muscles are trans- versely striped, and are arranged both in longitudinal and circular bundles. A canal extends along the centre of each arm, which communicates at its root with the general cavity of the body. This canal is irregularly subdivided by connective tissue bands passing across it. It is by means of the arms that this crustacean attaches itself to the skate on which it is parasitic. When examined 7m sztu, the arms could be traced passing along the space which separates two of the nasal laminee from each other. They then enter a canal of calibre sufficient merely to contain them. This canal dilates at its end into a comparatively large space, lined by a distinct smooth vascular membrane. In this cavity the claspers, with the bar which they embrace, are situated. The bar lies transversely, its long axis corresponding to that of the space in which it is situated; and as the canal, in which the cylindri- STRUCTURE OF LERNEOPODA DALMANNI. 81 cal portions of the arms lie, is at right angles to the long axis of this space, it is impossible to draw the bar and claspers out without dissecting away the wall of the cavity. We have already mentioned, that M. Epwarps has seen reason to think, that owing to the elongated cephalo-thorax, and the existence of posterior abdominal appendages, this parasite possesses characters which hardly permit it to be classed along with the other known Lerneopoda. To these we may add the very im- portant one, that the arms are not united at the tip. For although they are in close apposition by the fiat surfaces of. their clasper-like terminations, yet the parasite, when removed from the fish to which it is attached, can spontaneously withdraw one or other arm, or both, from the transverse cartilaginous-like bar, so as to separate the claspers completely from each other. After withdrawing the claspers from the bar, the animal does not appear to possess any power of re-attaching them to it. This character of ready separation of the ends of the arms from each other would also prevent us from placing the animal, as has been suggested by M. Epwarps, in the genus Brachiella. Projecting from each side of the cephalo-thorax, immediately in front of the root of each arm, is a well-marked bulb-like protuberance, noticed both by Rerzius and Kroyer, and termed by them the eye-like spots, although, from their colour and structure, they do not consider them to be eyes (fig. 3, a). Each has the ap- pearance of a segment of a sphere. Through the semi-transparent integument of the most prominent part, a quantity of reddish-brown granules, aggregated in elon- gated masses, may be seen. Low magnifying powers also enabled us to detect a very peculiar rod-like structure, connected apparently to the deep surface of the eye- like spot. It commences in a slightly dilated bulb-like part, which passes back- wards and outwards, around the base of the arm on its own side, and terminates in a dilatation similar to that by which it commences. The exact structures to which it is connected at its two ends we cannot say with certainty; but it is probable, from its position, that it may act as a sling for the support of the base of the arms. The rod has a diameter of 3+zth of an inch, the bulb of 74sth. Its structure is characteristic, so that it can at once be distinguished from the sur- rounding parts. It possesses an axial portion, which is about one-third the dia- meter of the entire rod. Under high magnifying powers this presents a corrugated aspect, which reminded us of the well-known appearance of the coagulated medul- lary sheath of a nerve fibre. Surrounding this axial structure is a very trans- parent substance, which has many of the microscopic characters of chitine. The abdomen is y>ths of an inch long, “ths broad. It ends posteriorly in a rounded elevation on each side, between which is a depression, so that it possesses an inverted heart-shaped form (fig. 1, c; fig. 2, b). It is slightly convex on the dorsal, almost fiat on the ventral aspect. It has an imperfectly defined segmented appearance, owing to the existence of three circular depressions in the chitinic in- VOL. XXIII. PART I. : Z 82 MR W. TURNER AND DR H. S. WILSON Ol] THE tegument, by which it is divided into four segments. These external depressions correspond to folds which project into the visceral cavity, and to which powerful muscles are connected. When these muscles are contracting, the segmentation is more manifest. The first segment lies immediately behind the roots of the long arms, and possesses on each side a bulging, corresponding in appearance, but smaller, to the eye-like spot on the cephalo-thorax, already described. The third segment has a similar pair of protuberances, placed, however, more on the ventral surface. The fourth segment is as large, or even larger than the conjoined first three seg- ments. In the median line of its ventral surface, close to the posterior margin, is the longitudinal slit-like anal aperture. This opening is bounded on each side by a well-marked fold of integument (fig. 12, a). Attached to the outer aspect of each fold is an elongated cylindrical process, which projects downwards, and is slightly curved. It is a little broader at the free than the attached end. Each of these posterior abdominal appendages is x ths of an inch long. Two elongated ova strings project also from the ventral surface. They spring from it posterior and external to the anus. The intestinal canal lies in the axis of the cavity of the abdomen. I¢ is retained in its position by numerous delicate bands, which pass from it to various parts of the inner surface of the wall of the cavity. It is of almost uniform calibre throughout, and presents a crenulated appearance. Distinct muscular fibres, arranged longitudinally and circularly, enter into the formation of its wall. It terminates posteriorly in the slit-like anal aperture. At the anterior end of the abdomen the canal bends, so as to pass into the cephalo-thorax, along the axis of which it extends. It makes a slight bend towards the dorsal aspect of the anterior extremity of the cephalo-thorax, so as to open at the oral aperture. The canal is more dilated in the cephalo-thorax than in the abdomen. It com- municates with the buccal chamber, not by a broad expanded opening, but through a chink-like fissure, between two plates of chitine. Lying in the visceral chamber external to the alimentary canal, is a quantity of what appears to the naked eye to be merely brown granular material. From its position, colour, and general appearance, it probably represents the liver in this creature. When highly magnified, it looked like gland tissue, for it con- sisted of vesicular dilatations, or saccules, apparently containing cells and granules. Special collections of a similar gland-like substance are to be seen at the roots of the arms, and extending for some distance along their central canals, in the eye- like spots, the lateral dilatations of the abdomen, and the posterior abdominal appendages. The ovaries, two in number, are situated in the abdominal cavity, and are con- fined to the fourth segment. They lie on each side of the intestine. Each consists of a ramified system of tubes, which communicate with a duct. This duct runs almost parallel to the intestine. It opens on the ventral aspect of the fourth seg- STRUCTURE OF LERNEOPODA DALMANNI, 83 ment, close to the posterior margin. The orifice is supported by chitinic bands. The cement organ consists of a simple delicate tube. It commences in the anterior part of the abdomen, and passes backwards close to the lateral wall. Its posi- tion may be frequently recognised through the integument without dissection, especially in the living animal. It joins the ovarian duct close to the genital orifice. In all the animals we examined the ovaries were distended with ova. They formed opaque, white masses, readily seen through the semi-transparent integument of the abdomen. The ova-strings are xsths of an inch long, cylindrical in form, of greater circum- ference at their attached than free ends. They are slightly curved, the con- cavities being directed inwards. The ova lie in longitudinal rows, with a spiral tendency. When a transverse section is made through an ova-string, the ova at the periphery are seen to be very elongated, whilst those in the centre are nearly circular. When the ova-strings rupture, in order that the ova may be discharged, they burst along the inner concave aspect. The margins along the line of rupture become everted, and thus the exposure of the ova in the interior of the string is facilitated. The animal possesses a very powerful muscular system. The largest bands are situated on either side of the dorsal and ventral mesial lines, being attached to folds of the chitinic integument. The buccal apparatus, antennz, and arms, have special muscular arrangements. In many,of our dissections the complex structure of striped muscular fibre was very beautifully illustrated. Resolution of the fibre in some cases into fibrillze, in other into discs, not unfrequently taking place. - We have looked carefully for a nervous system, and think that we have seen appearances indicative of its existence. We slit open the animal along the dorsal mesial line, and carefully removed the ovaries and intestinal canal. On examin- ing the internal surface of the abdominal wall with a magnifying power of 200 diameters, collections of cells could be seen in many places. These were especially manifest in the space between the roots of the two arms. These cells had many of the characters of nerve-cells, such as delicate outlines, granular contents, aud connecting processes. The processes from many cells were evidently two in num- ber, though, from the close manner in which the cells were crowded together, it was not possible to distinguish in some more than one process, and in others again none could be observed. The investigation of the arrangement of the nervous system in these creatures is evidently attended with considerable difficulties, partly owing to the delicacy of the structures, and partly on account of the strong ventral muscular bands and the gland-tissue surrounding the intestinal canal, the presence of which interferes greatly with its due examination. If the female be carefully separated from the skate, and placed in clean sea- water, we have found it possible, by occasionally changing the water, to keep the 84 MR W. TURNER AND DR H. S. WILSON ON THE animal alive for three weeks. If, in the act of separation, the bar be removed from the claspers, death takes place at an earlier period. Male.—We have not succeeded in finding the male of this species. Following the rule pursued by these parasites, we had expected to have seen it attached to the body of the female, but we have carefully searched the different specimens we have obtained without meeting with it. Rerzius makes no mention of the male. Kroyer thinks that he found on one of his specimens a male attached at the anus. He describes a creature “‘ about one-third of a line long, with somewhat of a crustacean form, with two 2-jointed antenne, a 3-jointed thoracic portion, a curved tail, and two strong hooked feet. The head appeared to present the trace of an eye. He can say nothing further about it.” Larva.—Neither Retzivus nor Kroyer have given any description of the larva. In two of our specimens the ova were in such a stage of development that we were enabled to examine the form of the larva. In some of these ova the larva could be studied at the stage immediately preceding the rupture of the ovum; in other cases the free larvee were obtained. Length of larva, 77th of an inch; breadth, scth. When viewed from dorsal aspect, its shape appears ovoid (fig. 13). When a profile view is made the ventral surface appears nearly flat, the dorsal very convex (fig. 14). A pair of antennee project from the ventral surface close to the anterior margin. They possess indications of being three segmented, the terminal one having at its free end a pair of long hairs. The limbs consist of two pairs; the anterior pair arises from the ventral surface, close to the antennze. Each limb is bifid (fig. 15, A). The upper branch bears four or five very long hairs at its extremity ; the lower, in addition to two long hairs at its free end, has a spinous hook projecting from it. The posterior pair arises from the ventral aspect, nearer the posterior than the anterior end of the larva. Each limb is shorter and thicker than the anterior, and in none of the specimens examined could we see, on a dorsal view, their extremities projecting beyond the lateral margin of the larva. Each divides into two branches, one somewhat larger than the other (fig. 15, B). A strong spinous hook, which appears to be capable of retraction within a sheath, arms the branches of each limb. In addition to these appendages the larva possesses a somewhat complicated arrangement, springing from the ventral aspect, close to the posterior margin. It consists of a triangular prolon- gation, folded over the posterior part of the convex dorsal aspect, so that the apex only can be seen when the dorsal surface is looked down upon. It gives off laterally three pairs of processes, each of which has connected to it two lappets, bearing long pinnate hairs (fig. 16). It terminates by a lappet- like process, which bears short, stiff hairs. The antennee, limbs, and tail-like appendages, have transversely striped muscular fibres connected to them. The STRUCTURE OF LERNEOPODA DALMANNI. 85 intestinal canal commences behind the antennae, by a trumpet-shaped mouth. It passes backwards and upwards towards the convex dorsal aspect, then curves downwards and forwards towards the ventral aspect, and ends abruptly close to the oral opening. In the cavity of the body there are numerous collections of oil drops, especially towards the posterior end of the larva. The eye-spots are situated on the dorsal aspect, not far from the anterior margin. Two large branched masses of dark-red granules may be seen, one close to the eye-spots.- the other farther backwards; and in the free larva these masses are connected by long streaks of reddish pigment. The further development of the larva we have had no opportunity of ob- serving. AppENnDuM, June 24th.—When we read our paper before the Royal Society. none of the more typical and best-known species belonging to the genus Lerneo- poda had come under our notice. Since that time, through the liberality of Mr Rosert Brown, we have had the opportunity of examining three specimens of the L. elongata, which were obtained by him attached to the eye of a Greenland shark (Scymnus borealis) caught in Ponds Bay, Davis’ Strait, in the summer of last year. We have especially directed our attention to the distal extremities of the arms, with the view of making a comparison between the mode of attachment of this species to the cornea of the shark, and that of LZ. Dalmanni to the skate. The arms of Z. elongata taper abruptly at their distal ends, and are connected to a small, rounded, horny, or chitinic disk. This attachment is evidently of a very close and intimate description, for in attempting to separate them from it, the substance of the arms gave way, rather than permit the connection between them and the disk to be severed. We could not say with absolute certainty whether the structures composing the arms were anatomically continuous with that of the disk, but there were appearances which led us to suppose that the chitinic in- vesiment of the arms was continuous with that of the disk. The arms them- selves are evidently not united at their tips, except through the medium of the common plate to which they are both connected. In our specimens we saw no- thing to lead us to suppose that the arms were inserted into the substance of the cornea, as is stated by Barrp* to have been the case in the specimen he examined, for the disk was undoubtedly attached to the surface of the cornea. Of the two eyes of the shark obtained by Mr Brown, one had two parasites connected to, it, the other only a single one. But each cornea had, in addition, a number of circular * British Entomostraca, p. 334. VOL. XXIII. PART I. 2A 86 MR W. TURNER AND DR H. S. WILSON ON THE markings on its outer surface, evidently the scars which indicated the former at- tachment either of the same, or other parasites. A similar appearance was described and figured by Grant in his specimen.* It will thus be seen that there are con- siderable differences in the mode of attachment of the L. elongata and Dalmanni. These differences are doubtless due to the varying nature of the localities in which they are met with. The L. elongata, being adherent to a flat surface, has connected to the ends of its arms a sucker-like disc; whilst the Dalmanni, being to some extent buried in the substance of the skate, has the clasper-like termina- tions of its arms attached to a transverse bar, which is lodged in a special cavity. The comparison which we have been enabled to make between the L. elongata and Dalmanni has convinced us that the differences existing between them are so great, that the latter animal ought no longer to be included in the genus in which it is at present placed. The mode of termination of the arms at their dis- tal ends presents such striking peculiarities, that, conjoined with the elongated head, the flattened, inversely heart-shaped abdomen, and the existence of poste- rior abdominal appendages, we consider it ought to constitute a new genus. * Brewster’s Edin. Journal of Science, 1827, p. 150. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. STRUCTURE OF LERNEOPODA DALMANNI. 87 PLATE IV.—Exzplanation of Figures. . Profile view of Female, a little below natural size; a, cephalo-thorax ; 6, ‘‘ eye-like spot ;” c, prehensile arms terminated by apposed claspers (bar not indicated); d, abdomen; e, abdominal appendages ; f, ova-strings. . Ventral aspect of female; cephalo-thorax seen raised above its normal position ; arms dis- tinct up to the apposed claspers, which embrace the transverse bar, a; 6, abdomen, the four segments faintly indicated. At its posterior extremity may be seen the integumen- tary folds bounding the anal fissure, and having connected to them the abdominal appen- dages. Close to these are the ova-strings. 3. Dorsal aspect of cephalo-thorax, enlarged; a, bulb-like protuberance (‘‘ eye-spot’’) b, antennz (their connected bases are indicated); c, buccal apparatus, consisting of a central conical mass bearing the mouth, by the sides of which are the two lateral, short, stump-like processes (modified feet) ; d, integumentary fold for protecting the oral appa- ratus. . Profile of cephalo-thorax, enlarged ; a, dorsal aspect, with antenne, base of modified feet and protective fold indicated ; 6, projectile process (“ chin”). —_ bo aN So Antenne ; dorsal aspect magnified, Buccal apparatus; ventral aspect magnified; a, dorsal and ventral lips, containing be- tween them the oral slit; 6b, chitinic arrangement supporting the lips, and affording protection to their muscles; c, labial palp; d, stump-like process (modified foot), to which a palp-like structure is connected. 7. Oral aperture, enlarged ; a, dorsal (upper) lip, presenting an inner plate bearing numerous rods, and an outer, fringed with papille; 6, ventral (lower) lip, also bearing papille. Close to the latter, and projecting for a short distance through the buccal orifice, are seen the jaws. 8. Portion of upper lip, greatly magnified ; a, labial palp. 9. Lower-lip, greatly magnified, and having connected to its base a pair of jaws; aa, chitinic masses for supporting the upper lip. 10. Stump-like process or modified foot, magnified ; a, posterior hook-bearing terminal divi- sion; 6, anterior portion studded with short bristles; c, its palp. = 11. Portion of upper lip magnified, to which is connected a chitinic arrangement, presenting a chink (‘ pharyngeal fissure”) ; a, commencement of the esophagus. 12. Posterior extremity of the abdomen, enlarged; a, anal folds, to which the abdominal ap- pendages are attached, and between which the slit-like anal aperture lies; 6, ova-strings passing from the genital orifices. 13. Dorsal aspect of the larva; a, antenna; 6, first pair of limbs. 14, Profile of the larva; the intestinal canal, bent upon itself, is indicated. 15. A, anterior limb of the larva. B, posterior limb of the larva. 16. Caudal appendage of the larva. One of the lappet-bearing masses has been raised, so as to show the opposite aspect, : aay Se fail pin = 4 ‘ hg wih An i n tp “ y é i oe iy ’ ie sly’ ot A ey : as A : ited or ay a] v ane sts T ci >| : “ ij ctrl ere ou ot “idan rai - Ms , 5 A arta et | : hie dhs ; Ai i , nf ads ' z } ie fran} Pt - shed v. ae RANSACTIONS OF THE ROYAL SOCIETY, EDINBURGH. VOL. XXIII. PLATE 1V x NSN G 4, : F.Schenck, 12 Ri Pxchange, Edin? . S. Witson, M.D., Delt. IX.—On the Deflection of the Plummet due to Solar and Lunar Attraction. By Epwarp Sane, Esq. (Plate V.) (Read 21st April 1862.) As the means for making observations on the heavenly bodies become more and more exact, astronomers are compelled to introduce new refinements into their calculations; new inequalities are discovered, and the computation of those whose sources are already known has to be carried to a greater number of approxi- mative steps. Discussions on the amount of solar parallax, of aberration and of nutation, are now carried on to the third and fourth decimal fraction of a second; with such a refinement of computation, it seems almost impossible to proceed too far in the refinement of theoretical deductions, and on that account, it may not be inopportune to discuss the influence which the sun’s and moon’s attraction exert — upon the direction of the plumb-line. The strict and symbolical investigation of this subject presents no difficulty, and offers no point of any interest to the analyst; it will therefore be sufficient to exhibit the matter in what may be called a popular light; the more so, that the reasoning will thereby lose none of its strictness. The direct attraction of the sun upon a body on the surface of the earth amounts to about the 1600th part of gravitation, and a pressure equal to it, applied horizontally, would deflect the plummet by an angle of 128 seconds. The statement, that a body weighing one pound, that is, a body attracted to the centre of the earth by 7000 grains, is also attracted to the sun by 44 grains, is rather startling. We might expect that direct evidence of so strong an attrac- tion should have been afforded by mechanical phenomena. The earth’s attraction is at once manifested to us by the pressure which every substance exerts upon that below it, or by the rapidity with which it descends, when left free to move. But there is no solid matter intervening between us and the sun, to resist gravitation towards it, and we are unable to perceive the motion sun-wards, because all surrounding bodies partake of the same motion. In one second of time the earth is deflected from its rectilineal course by about one-eighth part of an inch; now, in that time, its linear motion is about 17 miles; and we may obtain some remote idea of the curvature of the earth’s orbit, by imagining a circle which deviates from its tangent by one-eighth part of an inch at the distance of 17 miles from the point of contact. The centre of the earth is carried round the sun in an orbit due to the attrac- VOL. XXIII. PART I, 2B 90 MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. tion upon a material point situate at that centre, and all bodies on the earth par- take of that motion; but the sun’s attraction varies inversely as the square of the distance, and is greater for a body on the near side, less for one on the farther side of the earth. Hence a body on the near side would tend to describe an orbit more curved, one on the farther side an orbit less curved, than the earth’s actual orbit; and in either case, there is a tendency to augment the distance between the body and the earth’s centre. Thus, as is well known to every one who has studied the theory of the tides, the sun’s attraction tends to raise the ocean on the farther as well as on the near side of the earth. The perceivable part of the sun’s attraction is therefore the difference between the attraction on a body placed at the earth’s centre and that on a like body placed at the surface ; or, more strictly, is the resultant of the sun’s actual attrac- tion, and of a repulsion equal in intensity, and parallel in direction to the attrac- tion which the sun exerts upon a like body placed at the earth’s centre. If we put D for the distance of the sun, R for the radius of the earth, and a for the sun’s zenith distance, the intensity of the attraction is almost proportional to (D—R cos «)—?=D—?+2D—*R cos a+ 3D—*R? cos a? + &e. Now, the first term of this series represents the attraction at the earth’s centre, wherefore the remaining terms tt ea {25 cosa+3 yy, cos a” + &e. \ represent the disturbing influence. The value of the fraction - is about —a and even the first term of the series amounts to a very small quantity ; wherefore, neglecting the succeeding terms, we may hold that, for all practical purposes, the formula D-?x = COS a, represents the amount of the disturbing influence exerted in the direction of the attracting body. This influence is zero when the sun is on the horizon, and is greatest when the sun is in the zenith or nadir. But when the sun is in the zenith or nadir, the disturbing influence is exerted directly upwards, and cannot tend to deflect the plummet; in fact, the deflecting tendency is proportional to the sine of the zenith distance as well as to the above quantity, so that the tendency to deflect the plummet is finally represented by DS Foc2 = cosa. sina =D~?x sin 2a, Hence, the plummet is most drawn aside when the attracting body is 45° above or below the horizon. For the earth’s mean distance D~? may be taken to represent 128’; and, MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. 91 therefore the deflection of the plummet due to the sun’s attraction may be stated as — . cos 2a(O). The moon, though much nearer to us than the sun, is yet so small in com- parison, that the effect of a pressure equal to her attraction would only derange the plummet through one second. In this case, however, the ratio of D to R is only as 60: 1, and therefore the deflection due to the moon’s influence is V 60 or three times that due to the sun. These expressions represent almost exactly the deflections corresponding to the mean distances of the two luminaries; they would, if we were to seek for extreme precision, need to be varied in proportion to the third power of the hori- zontal parallax. The deflection of the plummet takes place in the vertical plane passing through the attracting body; and the actual position of the apparent nadir point may be obtained by referring it to co-ordinate axes drawn, the one from north to south, . the other from east to west through the true nadir. Putting « for the ordinate measured southwards, y for that measured west- wards, A for the north latitude, 6 for the north declination, and h for the hour angle, we easily obtain _ sin 2a ()) e=—sin 2a.sin 6?—cos 2A.sin 26. cos h + sin 2A. cos 6%. cos h? y= +sin A .sin 26.sin h + cos A. cos & . sin 2h, the values being in terms of the maximum deflection assumed as unit. These form the equation of an elliptic epicycloid produced by carrying the centre of one ellipse round the circumference of another, the periodic times being 24" and 12° respectively, and the motions being such as to generate areas uni- formly round the centres. Like all epicycloids, these curves change their appear- ance with every change in the constants; they have distinct phases, according as the observatory is within the arctic circle, above latitude 45°, on the parallel of 45°, below latitude 45°, intertropical, or on the equator. These phases are figured in the accompanying drawings, in which the hour angles are marked from the meridian ; and which explain, better than any words can, the remarkable changes which the motions of the nadir point undergo as the attracting body changes its declination. The line AB represents ¢5 -for the lunar deflection, and = for the solar. It may be well to advert to some of the leading features. When the observatory is within the arctic circle, and when the attracting 92 MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. body does not set, the apparent nadir describes a circuit round the true. As the declination decreases, the orbit shows a tendency to form a cusp towards the true nadir, and when the moon or sun comes just to graze the horizon the cusp is formed. When the declination becomes so low that the moon sets, the orbit has a convolution inwards; and as the declination approaches to zero, the two sweeps of the orbit coalesce into an ellipse whose circumference is gone over twice daily. So soon as the moon passes to the south of the equator, what may be called the day part of the orbit takes the place of the night part for the corre- sponding north declination; so that the same diagrams answer, merely changing the hour marks by 12 hours. For all places above 45° of north latitude the day is larger than the night part of the curve when the moon is north of the equator. For places on the parallel of 45° the two branches of the curve touch each other on the meridian, whatever be the declination, and for places below 45°, the intersection with the meridian are, as it were, interchanged. For places on the equator, the orbits are always varieties of the hour-glass curve, merging into a simple line when the declination is zero. There are two ways in which we may attempt to exhibit these phenomena. One is to prepare a spherical level ground to such a large radius of curvature as that the second may be divided into several hundred parts. The motions of the air-bubble will be opposite to those of the nadir point. The other is to direct an extremely powerful telescope to look directly downwards into a basin of mercury, and thereby to examine the motion of the image of the cross wires. But in neither of these ways shall we be able to trace motions exactly like those in the drawings, because actually the disturbances caused by the sun and moon are commingled, while the declinations are continually changing. The complexity of the resulting motions may be exemplified by reducing any one of the drawings to one-third part of the scale, so that it may represent the solar deflection, and by carrying its centre round any of the lunar curves for the same latitude, observing at the same time the distinction between the lunar and the solar day. These speculations are interesting, not merely from the singular and unex- pected beauty of the results, but also from their bearings on the higher branches of practical astronomy. They show us that the cross-level of a transit instru- ment is subject to a semi-daily oscillation, amounting at new and full moon to two forty-fifth parts of a second; and that the surface of the mercury in the collimation trough imitates, as far as it is able, the tidal motions of the sea. Let us suppose that, by help of instruments capable of that degree of preci- sion, we are endeavouring to determine the obliquity of the ecliptic true to the fourth decimal part of a second—we place our instruments in the observatory of St Petersburg, in Lat. 59° 56’ 30’, to observe the sun’s meridian altitude at the MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. 93 summer and the winter solstice. On account of the deflection, our summer observations give *’0050 too little, and our winter ones -’0012 also too little, thus giving the obliquity ‘0019 too small. Simultaneous observations are carried on at Madras, in Lat. 13° 04/10’ north. At the summer solstice the sun is north of the zenith, and its altitude, counting from the south point of the horizon, is 0019 too much, while the altitude at the winter solstice is too little by 0047, thus giving the obliquity too great by “0033. Hence observations made at St Peters- burg and at Madras must differ from each other to the extent of “0052, in deter- mining this primary astronomical quantity. Or if in the year 1857, we had sought to determine the greatest inclination of the moon’s orbit, the greatest meridian altitude must have been :0145, and the least -0009, each too little, as seen from St Petersburg, giving the obliquity 0068 too small; while, as seen from Madras, the upper passage would have appeared -0082 too far north, and the lower -0164 too far south, making an error in excess of :0124, and thus the discrepancy of the two determinations would have amounted to -’0192, or about the fiftieth part of a second. From these examples it appears, that we cannot carry our astronomical re- searches safely to the hundredth parts of seconds, without having taken into account the displacement of the nadir point. It is vain to seek to eliminate this source of error by the multiplicity of observations, because the influence varies periodically with the hour of the day, the moon’s age, the position of the node, and even that of the apogee. VOL. XXIII. PART I. 2.¢ Oo ts S = 4, th<@ Aa a 7 war oY . ar) ane ¢ e) % ; i ba i é. x! oe seal wi aS he deg - a ‘< rn ; bul an) bites roneery an ‘dante aa Fail? Real tps fail ae “i yaVafore: | nite Moti bam, 4 Sf Lie table be formed, or a curve constructed. ae re 6. “II. Let now the bar experiment [for conduction] be made in the usual way, only with greater precautions than perhaps have hitherto been taken (in- quiring into the effect of the number and size of a the holes, and correcting the thermometers for the unimmersed parts of the scale). Register the final temperatures at different distances from the source of heat, the bar being very long. The curve ab, we know, is nearly a logarithmic. Project it graphi- cally, and by drawing tangents, ascertain the rate Fig. 2. of decrement of temperature for a small increment of length, or = for any v number of points of the bar,—or else, calculate this, taking thermometric indications by threes [twos], and assuming a modulus for each point. Hence we aliep icaee| ee da| dt form a second table, of x, v corresponding, —™, and av from Table I., or from a graphical curve of the MN ieleg | | ts observations on which it was founded, we add the : Rolle somnti column of the momentary loss of heat due to all Regia a du P external causes, or ae corresponding to v observed. 7. “TI. We may now construct with abscissze x, and ordinates . the experi- mental curve aG, whose area will express the total escape of heat from the bar, or from any part of it. Thus the area xa! £& will represent the escaped heat from the portion of the bar wa’. I should have no doubt of being able to approximate to this area, with fully the accuracy which the inevitable errors of apparatus and observa- 136 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY tions admit of in other respects; and I am particularly anxious to throw aside every pretence of over-refinement. Now, this area is proportional to the difference of the flow of heat across the section of the bar at z and that ata’. We have, there- fore, by taking any number of areas, the differences of such fluxes, or by approximating to the whole areas ¢x@ (which, I think, might quite well be done), we have numbers proportional to the fluxes themselves at 7, 2’, a, &c. If these numbers are j h proportional to a in Table II., the Newtonian law is a * igor a correct; if otherwise, the deviation will appear, and also the law, or at least num- bers giving an empirical law. As I fancy this method to be new and important, pray preserve this letter, and let me know at the same time whether you see any flaw in the argument. You will probably not like the mechanical quadra- tures; but what else are our experiments but mechanical quadratures in many cases? And this is an experiment on paper capable, I apprehend, of being better measured than an experiment to measure heat with a thermometer. 8. “IV. It would be a most interesting verification to repeat the whole, with the same bar having a new surface given to it, which would radiate twelve or fifteen times faster, which I believe might be done.” 9. My correspondent having expressed some doubt as to the accuracy with which the quadratures could be performed, I thus wrote from Phoesdo, on the 11th October 1850: “ The mechanical integration I spoke of could be got rid of thus :—Treating a small part of the curve ab (in my former letter) as a logarithmic, calculate from it for each point ; these numbers should be pro- portional to the corresponding ordinates of the curve a8. Nevertheless, I suspect that in practice the method formerly proposed would be more exact.” It will be seen presently, that the quadrature of the areas proved to be practicable and accurate, and that it was the method adopted. 10. In a letter, a few weeks later, the conclusions are carried further. “ To Professor Kelland. “ Edinburgh, 11th November 1850. “In my letter of the 26th September, I explained a form of experiment, by which I proposed to test the fundamental assumption of the Mathematical Theory of Heat. I shall now show that the same experiment performed on bars of different metals, will give at once and directly, the constant of conducting power for each metal, which, so far as I know, has never been done by experiments on bars only, such experiments having given hitherto merely relative results. FourRIER INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 137 has shown (p. 406) [ of the Théorie de la Chaleur | that when the thickness of bars is small, though the temperature of equilibrium varies from the axis to the surface, the temperature at any point is very approximately in a constant ratio to the temperature of the central point of the section to which it belongs; so that the bar may be regarded as a bundle of parallel rods, in each of which the temperature varies with the length according to the same law. Now, the experimental curve a@ of my last letter represents the momentary loss of heat at every point of the axis of the bar in thermometric degrees ; the area of the curved space x a unit of transverse section near the axis, represents the number of cubical units of volume of the material, raised 1° by the heat flowing through [across] unit of section, near the axis of the bar at the point 2. The specific heat of the metal being known, we can convert this amount of heat or flux across # into absolute measure ; for the Flux is = — ee and s is known by Table I. of my former letter. Thus every experiment becomes an independent means of find- ing K, and that without reference to the state of the surface, which has always been a difficulty in comparing different metals with unlike radiating surfaces.” 11. The preceding extracts sufficiently set forth the principles on which the experiments were conducted, and I have preferred using the exact words in which I first sketched them, because it serves to fix the date, and also because they were in every point carried out in practice. 12. The experiments referred to in the present paper were all made between the 6th November 1850 and the 17th April 1851. They refer to the conductivity of Wrought-Iron alone. I do not here intend to describe the experiments in detail, nor to enter into the particulars of the reductions (which would require the engraving of some elaborate curves) ; nor do I offer the final results as thoroughly satisfactory to myself, though I hope, at a future time, to be able to lay before the Society these details, and to carry out the reductions in a way which will leave little to desire in the way of numerical precision. 13. The causes of the delay in publishing the results were these :—The thermometers, on whose exactness and comparability (especially at high tempera- tures), the accuracy of the experiments materially depended,were furnished to me by a Paris maker, who, at that time, enjoyed the highest reputation for trust- worthiness and precision. I soon found, however, that some of the instruments were unfit for my purpose, that one or two were disgracefully bad, and that others were not entirely reliable at all points of their scales. The worst thermometers were rejected, and the remainder were used with every possible precaution, and were farther checked by other instruments in my possession. A severe illness in November 1851, before I had resumed my experiments for the winter, brought the series to an abrupt conclusion. Fortunately the data for wrought-iron were VOU SAM, PART T. 2P 138 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY quite complete. The effects of my illness continuing, I contented myself during the succeeding summer (1852) with deducing the best results I then could from the data which I had obtained, trusting to make a more thorough examination of them when the Errors of the Thermometers should be accurately known. The various curves of temperature, velocity of cooling, &c., were most carefully pro- jected on a large scale, and the different stages of reduction carried out precisely as I had projected in my first letter, printed above. The smoothness and regu- larity of the primary curves (statical and dynamical), of Arts. 5 and 6, left little to desire. The values of the subtangents and various derivative quantities were equalized by the aid of graphical interpolation in the manner so ably used and recommended by Sir Joun Herscusz x, in several of his researches. As every step of the reductions was subjected to the test of graphical representation, it is not likely that any material error occurred in the calculation. 14. In October or November 1852 (at Clifton, where I then resided), I brought these provisional calculations to a close, with the results which I shall presently state. I did not abandon the idea of a more rigorous reduction of the observa- tions, and I was fortunate enough to induce the late Mr WE.suH, of the Kew Ob- servatory, to undertake the examination of the scales of the principal thermometers used, and especially of that one employed for the highest temperatures, in which a portion of the column being detached, for the purpose of extending the range, the verification was a matter of some delicacy. Mr Wexsu’s tables of corrections are now in my hands. The application of them will involve some labour, and perhaps the entire reconstruction of the interpolating curves, and a repetition of the calculations depending on them. I confess myself to blame in allowing so many years to elapse without bringing these computations to a satisfactory con- clusion, as well as for not extending the observations to other substances, as originally proposed. The state of my health has not been favourable for such tasks, which are necessarily of an irksome and tedious kind. I hope still to execute, at least the desirable revision of the temperatures and reductions. But upon looking again (after some years’ interval) at the previous calculations and their results, I feel warranted in publishing both the methods and the conclusions, as worthy of considerable confidence, and as still I believe new. Indeed, I incline to think that I have been perhaps too fastidious in withholding the results ob- tained, until they should have received the utmost precision which I can give them. 15. As I entertain the idea of publishing a supplement to this paper, with cor- rected details, I shall not now dwell upon the intermediate steps of the inves- | tigation. I shall, however, insert (chiefly from my full journal-notes of 1851) such a description of the apparatus and modes of observation, as may, I hope, materially assist any one in pursuing the experiments for other metals from the point where my labours unfortunately terminated; as it is not very probable that, under present circumstances, they will be resumed by me. INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 139 General Account of the Experiments. The Statical Experiment, on the Permanent Temperatures of a long Bar. 16. It has already been stated that these experiments were made in the winter and spring of 1850-51. The material was wrought iron. 17. Some experiments were made on an iron bar one inch square and seven feet long, marked B. But those of which the results will be here given (and which I considered as more trustworthy), were made with a beautiful bar, 14 inch square and fully eight feet long, manufactured on purpose for me, and without charge, through the kindness of Mr Roserr Napter of Glasgow. This bar was marked D. 18. It was used in two conditions as to surface,—Ist, With a bright semi- polished surface, such as that of well-kept steam-engine rods or pistons - 2d, After being covered with thin white paper, applied with the least possible quantity of paste. The paper used was what is known in the stationery trade as “tea-paper,” and was found to answer the purpose perfectly well. It was employed with the view of testing the conduction of one and the same sub- stance when the radiation of the surface varied in a great proportion (as 1: 8, according to Leste), and also in order to render the surfaces of different bars alike, for which paper is no doubt better fitted than the black varnishes which have been sometimes used for this purpose.* 19. The bar D was heated at one end by means of a cast-iron cup or crucible, finely adjusted to it by filing, and containing melted lead or solder. This was kept in a fluid state, and at as uniform a temperature as possible, by means of a powerful gas furnace. The whole was placed ona table, in a spacious apartment, without a fire, chiefly lighted from the north, and of which the temperature was nearly constant. The bar, with its attached crucible, was supported, at a height of 15 inches above the table, by means of three seasoned mahogany props thinned to an edge above, so as to make the contact with the metal as small as possible. The heated end was maintained at about the temperature of melting lead: by raising the gas flame on the one hand, or by immersing a piece of solid lead in the fluid on the other, the temperature could be regulated with wonderful exact- ness by my able assistant, Mr James Linpsay, who acquired great dexterity in the management of the heat, a tedious process, as the experiments lasted six, eight, and even ten hours.t The bar was sufficiently long to prevent the farther end from being sensibly raised in temperature. * This precaution was a source of considerable trouble to Mr Duspretz, See Ann, de Chimie, tom, xix. + The first thermometer of the series along the bar has to be incessantly watched for this pur- pose, or, better still, a thermometer with the bulb dipped into the lead in the crucible, kept as near the melting point as possible. So dextrous did my assistant at last become, that for hours this last thermometer was prevented from wavering, even at that high temperature, above a very few degrees of Fahrenheit. 140 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY 20. Thermometers were inserted in cylindrical holes, drilled in the upper side of the bar. The holes were 0°28 inch diameter. Contact with the thermometer was secured by mercury poured into the colder holes, and an amalgam or fusible metal in a semifluid condition in the hotter ones.** There were usually about ten thermometers inserted in the bar, at distances varying from three inches to eight feet from the zero point at the crucible. Those nearest to the source of heat were defended from its action by two or three interposed polished metal plates, which were found to act efficiently. 21. When after several hours of exposure to steady heat, the bar attained a normal temperature at its various points, the instant was to be seized, when the casual fluctuations became inappreciable, not only on the thermometers nearest to the source, but also in those at a distance. For though the source of heat may, for a time, appear quite steady, the wave of temperature arising from - some antecedent irregularity may still be travelling along some remoter portion of the bar. Experience, and the patient entry of a number of successive observa- tions of all the thermometers, can alone secure the desired precision. These experiments must never be made in a hurry. . 22. A modification of this mode of observing which occurred to me in the course of these experiments, possesses important advantages, and may be used as acheck. I call it the method by stepping. One and the same thermometer was transferred to the successive holes in the bar, beginning with the hottest and going on to the coldest, and the temperatures were read in each case. In this mode of operating, each hole was in the first instance provided with its mercury or amalgam, and with its proper thermometer as before ; and the thermometer was only withdrawn, and the stepping thermometer introduced, when the temperature indicated by the latter (after being held in the hand to cool) reached as nearly as possible the degree known to belong to the hole in which it was to be immersed. It of course took the exact temperature almost instantly, without either heating or cooling the mercury in the hole; and so on to the end. It is an important recommendation of this method, that a single reliable thermometer may be made to perform the whole work, the others being merely used as rough indicators. Nor is there any danger of error arising from slight changes in the temperature of the Source of heat subsequent to the commencement of the readings; for expe- rience shows, that the wave of disturbance of temperature advances much slower along the bar than the stepping process can be perfectly well gone through. On the whole, this is an immense facility for the extension of such experiments; as * It was found that when mercury was used for these last, the surface became hotter by con- vection than the central part of the hole, contrary to the law of the distribution of heat in a solid bar, and consequently an undue (though perhaps hardly sensible) amount of heat was thereby dissi- pated. I may add, that I ascertained by actual experiment, that the boring of several additional holes between the extreme holes of a bar did not sensibly disturb the conduction of heat when the intermediate holes had thermometers surrounded by mercury inserted in them. INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 141 the possession of ten or more reliable thermometers is of itself a condition of suc- cess difficultly attainable. 23. In all cases the free temperature, or that to be deducted from the readings of the thermometers, in order to get the true excess of statical temperature along the bar, was obtained by inserting a well-compared thermometer into a hole con- taining mercury drilled in a similar but short bar of iron, supported in the free air of the room in the neighbourhood of the long bar and similarly exposed, but without artificial heat. Dynamical or Cooling Eaperimenis. 24. These experiments (see Art. 5) are requisite to determine the rate of | the superficial dissipation of heat at any point of a bar of given material and section, by the joint influence of radiation and convection. The object is to obtain the “Velocity of Cooling” in terms of the Temperature shown by a thermometer sunk in the bar. For this purpose a short bar of iron marked C was prepared, 14 inch square and in other respects similar to the bar D used for the Statical process, except that it was only 20 inches in length. A hole was bored in the centre of one side, into which a thermometer might be introduced with amalgam round it, as in the previous experiments. First of all, a high uniform temperature was communicated to this short bar, in the following way: A cylindrical iron vessel containing fusible metal (four parts of lead, three of tin, and three of bismuth were commonly used) was suspended vertically over a powerful gas-burner, the heat being confined so as to act on the cylinder, by means of an exterior cylindrical chimney, also of iron. The diameter and length of the cylindrical vessel was such as to admit easily the entire bar C, which had a ring at each end, so as to allow it to be more easily introduced and withdrawn by means of a hook. The metal-bath being duly heated and prepared, the experimental bar was first wrapped in several folds of paper, so as to prevent the sudden chill of the fluid metal on its immer- sion. The bar was then introduced and withdrawn a few times, each end being alternately lowest, so as to equalise the temperature of the bar as much as possible. When hot enough (which is ascertained by a thermometer in the metal bath), it was withdrawn, shaken, and the paper envelope rapidly cut off. The naked bar was then wiped and laid horizontally on two blunt-edged props, so as to stand (as in the case of the other bar) 15 inches above the table. Mercury pre- viously warmed was introduced into the hole or holes (I had usually two or three near the centre of the bar), and thermometers inserted. The temperatures were read off from minute to minute (the time being given by an assistant), and the rate of cooling thus determined. The readings, both in these and all the other experiments, were made by myself, with exceptions too trifling to require notice, and the rate of cooling was deduced graphically or by calculation. VOL. XXIII. PART I. 2 142 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY 25. The Statical and Dynamical forms of experiment on the relations of a given bar to heat (oth of which are required for the solution of our problem), each present their peculiar difficulties. But there is one difficulty in connection with the latter, which I think it right to mention, because I did not succeed in wholly removing it when temperatures approaching 200° Cent. (392° Fahr.) are to be employed. The object of the Dynamical experiment (as already explained), is to find the rate at which any point of the bar in the Statical experiment is, in point of fact, parting with its heat by the surface, ascertained in terms of the temperature shown by the thermometer sunk into it at that point. But when a bar has been wniformly heated in all its parts by immersion in the metal- bath, the distribution of heat over any transverse section is not at first the same as when the bar in the statical experiment has attained a permanent temperature ; nor the same as when the bar under experiment has cooled to a certain extent. In fact, FourrEr’s analysis shows, that in the early stages of cooling of a body at first heated uniformly, the temperature includes in its expression certain circular functions, which, by and by (and in good conductors very rapidly), become in- sensible. Such oscillations affecting the rate of cooling (or = a) are perceptible in the experiments which I have made, and influence the determination of this important quantity in the highest part of the scale. The general tendency of the effect is manifestly to make the rate of cooling of the thermometer, sunk to the axis of the bar, at first too small. For the bar being uniformly heated from centre to surface when it is withdrawn from the metal-bath, it is only as the superficial parts cool that the central parts begin to lose heat, which they supply to the surface. Next, the rate of superficial cooling will be relatively somewhat accelerated, and a fresh demand upon the interior will occur. These gushes of heat will gradually disappear, and, as I have said, are in good conductors only at first perceptible.* 26. The initial irregularities at temperatures approaching 200° Cent. are the greatest difficulties which met me in this inquiry, and I fear that they have been but partially overcome. We are precluded from obviating them by the natural expedient of heating the bar initially to a much higher temperature, and allow- ing it to cool spontaneously down to that at which the observations commence. For even polished iron changes the condition of its radiating surface at tempera- tures which considerably exceed 200° Cent., so that this plan is inadmissible. In fact, the heat was pushed in these experiments quite to the limit.+ I have fully stated this difficulty, in order that future experimenters may be prepared to con- tend with it. Electroplating might possibly succeed, though I fear not. * This interpretation of the physical origin of the periodic functions in the cooling of bodies was given in the Encyclopedia Britannica, Sixth Dissertation, Art. (674). When the circular functions have exhausted themselves, the exponential portion of the expression for the temperature alone remains. See Fourier, Théorie Analytique de la Chaleur. + When coated with paper, the paper begins to singe at a temperature slightly above that of melting tin, or 442° Fahr, INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 143 The Reductions. 27. The fundamental observations are those on the permanent temperatures of a long iron bar heated at one end, and measured by thermometers placed at fixed intervals along the bar (Art. 16, &c.). These were projected in a curve (which approximates to, and has usually been treated as a logarithmic curve), of which the length of the bar is the axis, and the temperatures (or rather excesses of tem- perature above the surrounding space) the ordinates. This curve of statical tem- perature was verified in all its parts as follows :—The first projection was made from one of the completest and most satisfactory of the sets of observations, in- cluding the temperature of ten or eleven points along the bar. Other sets of observations were recorded, in which the fundamental temperatures differed more or less from these, the source of heat being either more or less intense. But each group of observations, while it may be treated separately, may also be regarded as belonging to distinct parts of one common curve (so long as the bar and its surface are unchanged). We are thus enabled to interpolate temperatures not corresponding to observed points in the primary experimental curve, and to verify them indefinitely. This process of interpolating independent groups of observa- tions is peculiarly suited to the graphical method of reduction, and has been pursued with entire success. 28. Tangents were drawn and subtangents measured, and also calculated from ordinates, for different points of the statical curve. The table of (where v is the excess of temperature of any point of the bar at a distance 2 from the origin at the heated end) is thus formed (see Art. 6). The values being again projected in terms of v, are graphically equalised. 29. Next, the dynamical experiment of the cooling of the short bar (Art. 24) is treated by projection; the temperatures being laid out in a curve in terms of the time (@¢.) From the tangents to this curve the rate of cooling (3) , in terms of v, is calculated, and also projected and equalised. 30. These last numbers are erected as ordinates upon the original line repre- senting the axis of the long bar in the statical experiment, asin fig. 3, Art. 7. The dv dt’ each point along the bar. The area of this last curve between the ordinate cor- responding to # and infinity, represents the total loss of heat from the surface of the bar on the cooler side of x, and consequently the whole flux of heat across the section at x, since that flux is the quantity of heat necessary to compensate the whole loss of heat from the surface of the bar beyond x, the bar being, by hypothesis, in a permanent condition. The determination of this area by the quadrature of the successive parts is not difficult, as this curve also approximates to a logarithmic, whence the area between successive ordinates, and also that adjoining the asymptote, can be calculated with sufficient exactness. perpendiculars are the values of —, in terms of the ascertained measure of v at 144 PRINCIPAL J. D. FORBES ON AN EXPERIMENTAL INQUIRY 31. By comparing the fiux of heat thus found, across any section of the bar, with the value of pa for that section, we can test the accuracy of the law of conduc- tion as usually assumed. We can also ascertain, with reference to the units of measure employed, the exact conductivity of the bar, whether constant or varying with temperature. 32. The processes above mentioned having been gone through with great care, partly in 1851, but principally in the summer of 1852, I arrived at the following conclusions, which I transcribe Jiterally from my note-book of the last named year. It is to be observed, that two entirely independent series of observations are here compared—those made with the naked iron bar marked D, or that which had its surface moderately polished (Art. 18), and those with the same bar when covered with “ tea paper,” in which case the forms of the curves are altogether altered, owing to the increased radiation of the surface. Memorandum of 1852.* “ Results of preceding investigations. 33. “ A. For naked 14 inch iron bar. 5 Total Flux (F) of Heat, r Actual Temperature. Excess above a corresponding to bee ( i) » proportional Centigrade. Air. pe ihine. XIUL } dx oa to K.f § by Diag. XVII. 25 12 15 0136 50 37 52 ‘0130 75 62 93 “0131 100 87 1:31 ‘0126 125 112 aley gis 0122 | 150 137 2°08 -0112 175 162 2°43 -0100 | 200 187 2°72 ‘00875 | 34. “ B. For covered 14 inch iron bar. dv F Temperature. Excess. as Flux. Diag. XVIII. (@) Diag. XIV ae 25 12 15 29 0147 50 37 52 qn 0138 75 62 92 1:18 -01238 100 87 138 1:56 0118 125 112 187 2-00 -0107 150 137 235 2°45 -0107 175 162 295 3°00 “0102 * The diagrams referred to in this memorandum are all drawn out, but are not engraved pend- ing the revision of the scales of the thermometers. + K expresses the absolute conducting power in terms of the thermal capacity of water. INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 145 35. “ Finat Resutt.—tThe projections of both the observed series of numbers ‘representing the conductivity in terms of the temperature projected in Diagram F XIX., give a value of @v pretty regularly decreasing from -0150 at 0° C. to ‘0092 daz at 200°.” 36. In order to reduce the unit in the last column of these tables to the absolute unit K, which expresses the amount of heat necessary to raise one cubic foot of water by 1° Cent., we must multiply the numbers in the final columns by the specific heat of iron, and also by its specific gravity. These numbers are respec- tively 0°114 (ReGNAvLT) and 7:79. Their product is 0888. Assuming the uni- form decrease of the conductivities with increasing temperature, and making use of both the series,—as indicated at the close of the preceding paragraph,—and adapting them to the water unit, we obtain the following approwimate numbers. The numbers in the second column refer to the following units—the English foot, the minute, and the centigrade degree.* The third column has the centi- metre substituted for the foot.+ Conducting Power of Wrought Iron. Temperature, Centigrade. Units: the Foot, Minute, and Units: the Centimetre, Centigrade Degree. Minute, and Cent. Degree.* 0° 0133 12°36 25° 0127 11°80 50° 0120 11°15 75° 0114 10°59 100° 0107 9°94 125° 0101 9°38 150° 0094 8°73 ES" “0088 8:18 200° "0082 7:62 37. It will be recollected that these numbers are offered as approximate only. * Or (more fully) it expresses in centigrade degrees the temperature communicated to a cubic foot of water in one minute, across a plate of iron one foot thick, whose surfaces are maintained at a constant difference of temperature of one degree centigrade. } This is perhaps the most convenient unit of conductivity for general use. The original ther- mal unit of Fourier (who first gave a correct definition of this quantity) was referred to the minute and the metre as the units of time and length, to the interval from the freezing to the boiling point of water as the unit of temperature and the unit of heat was the quantity required to melt one kilo- gramme of ice (Théorie, Arts. 68, 69). It is plain from Art. 59, and others of the same work, that Fourier had no idea that the conductivity varied with the actual temperature—an admission which must be held to leave the Newtonian law true in form only, since the flux is proportional in any one substance not to = only, but is also a direct function of v. VOL. XXIII. PART I. 7, 5} 146 PRINCIPAL FORBES ON THE CONDUCTION OF HEAT IN BARS, ETC. When the revision of the scales of the thermometers has been applied to the results (which will necessitate the re-construction of the diagrams), I intend to publish the final results for iron in a sequel to this paper. 38. The following consideration, however, as it encouraged me to go through the labour of the provisional calculation, makes me believe that the results will not be materially altered. Indeed, it is one of the advantages of the method here employed, to render us in some degree independent of the precision of the ther- mometers. Since the same thermometers were carefully used in both the stati- cal and dynamical experiments, the outstanding errors of temperature, as read off, will affect both results, if not exactly to the same amount, at all events in the same direction. The final columns of the tables of page 144, containing the conducting powers, depend on the ratio of two quantities—the flux of heat (F) at any point, depending partly on the dynamical, partly on the statical experi- ment, and the differential co-efficient at depending wholly on the statical ex- periment. The thermometric error will make both these quantities too great, or else both too small, and the ratio will be but slightly affected. Sr Anprews, 21st April 1862. Postscript. The diminishing conducting power of iron with increased temperature har- monises with similar facts in electricity, thus adding a fresh analogy to those adverted, to in Art. 2 of the preceding paper. According to the recent experi- ments of ArRNDTSEN (Poggendorf’s Annalen, May 1858), the resistance to the transmission of electricity through iron is increased nearly one-half by a rise of temperature of 100° Cent. 28th April 1862. Green) XIV.—On the Density of Steam. By W. J. Macquorn Rankine, C.E., LL.D., F.R.SS. Lond. and Edin., &c. (Read 28th April 1862.) 1. The object of the present paper is to draw a comparison between the results of the mechanical theory of heat, and those of the recent experiments of Messrs FarrBairn and Tate on the density of steam, published in the “ Philoso- phical Transactions” for 1860. General Equation of Thermodynamics. 2. The equation which expresses the general law of the relations between heat and mechanical energy in elastic substances was arrived at independently and contemporaneously by Professor CLausius and myself, having been published by him in Poacenvorrr’s ‘‘ Annalen” for February 1850, and communicated by me to the Royal Society of Edinburgh, in a paper which was received in Decem- ber 1849, and read on the 4th of February 1850. The processes followed in the two investigations were very different in detail, though identical in principle and - in results; Professor Ciausius having deduced the law in question from the equivalence of heat and mechanical energy as proved experimentally by Mayvrer and JouLE, combined with a principle which had been previously applied to the theory of substantial caloric by Sapy Carnot, while by me the same law was deduced from the “hypothesis of molecular vortices,”’ otherwise called the ‘ cen- _ trifugal theory of elasticity.” 3. Although, since the appearance of the paper to which I have referred, the notation of the general equation of thermodynamics has been improved and simplified in my own researches, as well as in those of others, I shall here pre- sent it, in the first place, precisely in the form in which I first communicated it to this Society, in order to show the connection between that equation in its original form, and the law of the density of steam, which has since been verified by the experiments of Messrs Farrparrn and Tate. The equation, then, as it originally appeared in the twentieth volume of the “ Transactions of the Royal Society of Edinburgh,” p. 161, is as follows :— a Ua tw dU). = — oH [av v- av) ~ 5, fs eritn Geni > in which the symbols have the following meanings :— 7, the absolute temperature of an elastic substance as measured from the zero of gaseous tension, a point which was then estimated to be at VOL. XXIII. PART I. 2s 148 MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 274°°6 Cent. below that of melting ice, but which is now considered to be more nearly at 274° Cent., or 493°:2 Fahr. below that temperature. k, A constant, expressing the height on the thermometric scale of the tem- perature of total privation of heat above the zero of gaseous tension. This constant was then only known to be very small; according to later experiments, it is either null or insensible. nM, The ideal or theoretical weight, in the perfectly gaseous state, of an unit of volume of the substance, under unity of pressure, at the temperature of melting ice. C, The absolute temperature of melting ice, measured from zero of gaseous tension (that is to say, according to the best existing data, C= 274° Cent., or 493°:2 Fahr.) V, The actual volume of unity of weight of the substance. OV, An indefinitely small increment of that volume. ov, An indefinitely small increment of temperature. U, A certain function of the molecular forces acting in the substance. + 6Q/, The quantity of heat which appears, or — dQ’, the quantity of heat which disappears during the changes denoted by OV and 67, through the actions of molecular forces, independently of heat employed in producing changes of temperature ; such quantity of heat being expressed in equiva- lent units of mechanical energy. The equation having been given in the above form, it is next shown (in the same volume, p. 163), that the differential co-efficients of the function U have the following values :— dU _1 dP qv =¥ — CaM—; : ; : f ; d . (2) dU x @P Grane OM faV- Oe 4. The physical law of which the general equation just cited is the symbolical expression, may be thus stated in words:—The mutual transformation of heat and mechanical energy during any indefinitely small change in the density and tem- perature of an elastic substance, is equal to the temperature, reckoned from the zero of absolute cold, multiplied by the complete differential of a certain function of the pressure, density, and temperature ; which function is either nearly or exactly equal to the rate of variation with temperature of the work performed by indefinite expan- ston at a constant temperature. 5. It may be remarked, that the quantity,— il dP g=k byp. log. "+o (hyp. log. V—U) = & hyp. log. r + ae av. . (4) («% being the real specific heat of the substance in units of mechanical 4 energy), is what, in later investigations, I have called the “ thermody- MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 149 namic function ;” and that by its use, and by making «=0, equation 1 is reduced to the simplified form, — 60 = rip — k or; : : : : ». (5;) but the following notation is more convenient: Let o% denote the whole heat absorbed by the substance, not in units of mechanical energy, but in ordinary thermal units, and J the value of an ordinary thermal unit in units of mechanical energy, commonly called “ JouLE’s Equivalent,” so that Jdh=hor— dQ ; then the general equation of thermodynamics takes the form Joh=r09. ‘ i ; : 2 > 6.) 6. For the purposes of the present paper, the most convenient form of the thermodynamic function is that given in the second line of Equation 4; but it may nevertheless be stated, that in a paper read to this Society in 1855, and which now lies unpublished in their archives, it was shown that another form of that function, viz. P, V aV o= (4+ C *) hyp. log r—[ivar, : : : =. «Gh-) was useful in solving certain questions ; Py Vo denoting the same thine with = : 7 Sate S Swit! OnM in Equation 1. Application of the General Equation of Thermodynamics to the Latent Heat and Density of Steam. 7. At the time when the general equation (1.) was first published, sufficient experimental data did not exist to warrant its application to the computation of the density of a vapour from its latent heat. But very soon afterwards, various points, which had previously been doubtful, were settled by the experiments of Mr Jouts and Professor Witu1aM THomson; and in particular Mr Jouts, by his experiments published in the “ Philosophical Transactions” for 1850, finally de- termined the exact value of the mechanical equivalent of a British unit of Heat. to which he had been gradually approximating since 1843—viz., J=772 foot-pounds ; and Messrs JouLE and Tuomson in 1851, 1852, and 1853, made experiments on the free expansion of gases, especially dry air, and carbonic acid, which established the very near, if not exact, coincidence of the true scale of absolute temperature with that of the perfect gas-thermometer ; that is to say, those experiments proved that « in the equation (1.) is sensibly =0. When, with a knowledge of these facts, equation (1.) is applied to the phenomenon of the evaporation of a liquid 150 MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. under a constant pressure, and at a constant temperature, it takes the following form :— egy where J denotes JouLE’s equivalent, or 772 foot-pounds per British unit of heat (a degree of Fahrenheit in a pound of liquid water); h, The heat which disappears during the evaporation of 1 lb. of the liquid ; that is, its datent heat of evaporation in British units :— T, The absolute temperature (=temperature on Fahrenheit’s scale +461°2 Fahr.). P, The pressure under which the evaporation takes place. V, The volume of 1 lb. of the vapour. v, The volume of 1 1b. of the liquid. As the latent heat of evaporation of various fluids is much more accurately known by direct experiment than the volume or density of their vapours, the most useful form in which the equation (8.) can be put, is that of a formula for computing the volume of a vapour from its latent heat, viz. :— Jh V=v+ dP’ ° > ° ; e (9.) oe dr 8. Results of this formula were calculated by Messrs JouLE and THomson, and by Professor Cuausius for steam, and showed, as had been expected, a greater density and less volume than the law of the perfectly gaseous condition would give. Some results of the same kind, and leading to the same conclusion, were also computed by me and published in the ‘ Philosophical Transactions” for 1853-54 But for some years no attempt was made by any one to make a table for practical use of the volumes of steam from equation (9.); because the scientific world were in daily expectation of the publication of direct experi- mental researches on that subject by M. Reanavur. 9. At length, in the spring of 1855, having occasion to deliver, to the class of my predecessor, Professor GorpoN, a course of lectures on the mechanical action of heat, and finding it necessary to provide the students with a practical table of densities of steam founded on a more trustworthy basis than the assumption of the laws of the perfectly gaseous condition, I ventured upon the step of pre- paring a table of the densities of steam for every eighteenth degree of Fahren- heit’s scale, from 86° to 410° inclusive, with the logarithms of those densities and their differences, arranged so as to enable the densities for intermediate temper- atures to be calculated by interpolation. Those tables were published in a litho- graphed abstractof the course of lectures before mentioned, which is now out of print. The same tables, however, have since been revised, and extended to every MR Ww. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 151 ninth degree of Fahrenheit, from 32° to 428°, and have been printed at the end of a work, “ On Prime Movers.” An account of the original tables was read to the British Association in 1855.* 10. In the unpublished paper before mentioned, as having been read to this Society in 1854, the densities of the vapours of ether and bisulphuret of carbon, nnder the pressure of one atmosphere, as computed by equation (9.), are shown to agree exactly with those calculated from the chemical composition of those vapours. 11. The method of using equation (9.), to calculate the volume of one pound of steam, is as follows :— I. Calculate the total heat of evaporation of steam from 32°, at a given tem- perature T° on Fahrenheit’s scale, by Reanavtt’s well-known formula 1091-7 +0°305 (T°—32°). . ; , A -- “(10 Il. From that total heat subtract the heat required to raise one lb. of water from 32° to T° Fahr, viz., ¢ being the specific heat of water ; the remainder will be the latent heat of evapo- ration of one Ib. of steam at T°; that is to say, ‘ii h = 1091-7 + 0°305 Msp aJ DET SLE maT BE) 32° In computing the value of the integral in this formula, use has been made of an empirical formula founded on M. RegNavut’s experiments on the specific heat of water, as to which, see the “‘ Transactions” of this Society for 1851, viz. :— on * edT=T—T’ +0-000000103{(T—39°1)?—(T’-39°1)3}. =. =. (1L-A,) an III. The absolute temperature is given by the formula, pea Baar ee IV. The value of 7 = is deduced from the following formula, first published in the ‘‘ Edinburgh Philosophical Journal” for July 1849 :— 1 8, com. logy P=A-—=- 4; - rie ea Nas PA.) from which it follows that dP B 2C 7 = 2-3026 P ( ie =i) ane Tama oor. Gay * The reason for using 9° Fahr, as the interval of temperature is, that it is equal to 5° Centigrade and to 4° Reaumur; so that the tables can be applied with ease to any one of those three scales. VOL. XXIII. PART I. 2T 152 MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. the values of the constants for steam being,— A, for pounds of pressure on the square foot, . ‘ 8:2591; log. B for Fahrenheit’s scale : : 2 . =3'43642; log. C - 5) : : i . =65'598"3. V. The volume of a cubic foot of liquid water at the temperature T may be computed with sufficient accuracy for the present purpose by the following formula :— r ) v nearly = 0°00801 (sg7 ae (15.) VI. These preliminary calculations having been made, the formula 9 can now be applied to the calculation of the volume of one pound of steam (making J=772); and by this process the tables already mentioned were computed. Comparison of the Results of Theory, with those of Messrs FarrBairn and TaTE’s Experiments. 12. The experiments of Messrs Farrsairn and Tate on the density of steam are described in a paper which was read to the Royal Society of London, as the Bakerian lecture, on the 10th of May 1860, and published in the “ Philosophical Tranactions” for that year. The results of those experiments give what is called the “ relative volume” of steam: that is, the ratio which its volume bears to that of an equal weight of water at the temperature of greatest density, 39°1 Fahr. ; but in the following table of comparison, each of those relative volumes is divided by 62:425, the weight of a cubic foot of water at 39°-1 in lbs., so as to give the volume of one lb. of steam in cubic feet. The numbers of the experiments are the same as in the original paper; those made at temperatures below 212° being numbered from 1 to 9, and those made at temperatures above 212° from 1’ to 14’. MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 153 Comparison of the Theory, with the Experiments of Messrs FAtrBAIRN and Tats. Weeiben Volume of one 1b. of Steam Pureeonce of Experi- Bos STS a hae sn bs Difference. > ment. "| By Theory. By Exper. Exper. Vol. i 136-77 132-20 132-60 —0:40 ct 2. 155°33 85:10 85-44 —0'34 ze 1s 3. 159°36 77°64 78:86 = 1,99 eB 4. 170-92 60°16 59-62 40-54 tl ie 5. | 171-48 59-43 59°51 | —0-08 us ES 6. 17492 55:18 6507 | +011 taht 7. | 182-30 47-28 48-87 | —1:59 eh 8. 188°30 41°81 42°03 — 0:22 —7ly 9. 198°78 33°94 34:43 —0:49 — 7 le 242°90 15°61 15:11 + 0:50 + 35 2. 244:82 14:77 14°55 + 0:22 + ss 3’, 245:22 14:67 14:30 + 0°37 + a5 4’, 255°50 12°39 L207 + 0:22 oe BY. 263-14 10-96 10-40 +0:56 5k neh 6. 267-21 10:29 10-18 | 40-11 ected ". 269°20 9:977 9-703 +0:274 +35 8’. 274:°76 9-158 9°361 —0'2038 — yz 97 273°30 9:367 8-702 +0°665 temina 10’. 279°42 8°539 8249 + 0°290 + ay | Aye 282°58 8:145 7964 +0°181 + 74 LO 287°25 7603 7:340 + 0:263 + ss to’. 292°53 7:041 6:938 +0°103 + ds 14’, 288°'25 7494 7:201 + 0°293 + Remarks on the Differences between the Theoretical and Experimental Results. 13. The differences between the theory and the experiments as to the volumes of steam at temperatures below 212°, are, with few exceptions, of very small relative amount; and they are at the same time so irregular, as to show that they must have mainly arisen from causes foreign to the data used in the theo- retical computations. 14. Above 212° also, the differences show irregularity, especially in the case of experiments 8’ and 9’, where a fall of temperature is accompanied by a diminu- tion instead of an increase in the volume of one pound of saturated steam, as determined by experiment. ut still those differences, presenting as they do, in every case but one, an excess of the theoretical above the experimental volume, show that some permanent cause of discrepancy must have been at work ; although they may not be regular enough to determine its nature and amount, nor large enough to constitute errors of importance in practical calculations relating to steam-engines. 154 MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 15. So far as it is possible to represent those differences by anything like a formula, they agree in a rough way with a constant excess of about 0:27 of a cubic foot in the theoretical volume of one pound of steam above the experimental volume; and this also represents in a rough way the difference between the curves, whose ordinates express respectively the results of the theoretical formula and those of an empirical formula deduced from the experiments, so far as those curves, as shown in a plate annexed to the paper referred to, extend through the limits of actual experiment on steam, above 212°. 16. As the principles of the mechanical theory of heat may now be considered to be established beyond question, it is only in the data of the formula that we can look for causes of error in the theoretical calculation. I shall now consider those data, with reference to the probability of their containing numerical errors. I. Total Heat of Evaporation—lIt is very improbable that this quantity, as computed by M. Reanauur’s formula, involves any material error. Il. Sensible Heat of the Liquid Water.—The empirical formula from which this quantity is computed was determined from experiments by M. ReGnav.t, which agree extremely well amongst themselves. (For the investigation of the formula, see “ Trans. Royal Soc. Edin.,” vol. xx. p. 441). The subtraction of the sensible heat from the total heat leaves the latent heat, upon which the increase of volume depends; hence, to account for an error in excess of the formula for the volume by means of an error in the computation of the sensible heat, it must be supposed that the specific heat of liquid water above 212° increases much more rapidly than M. Reanavtt’s experiments show, so as to produce a correspond- ingly more rapid diminution in the latent heat of evaporation. It is easily com- puted, for example, that to account for an error in excess of 0°27 of a cubic foot in the volume of one pound of steam at 266°, by an error in defect in the sensible heat, we must suppose that error to amount to about 24 British thermal units per pound of water ; but such an error is altogether improbable. Ill. Absolute Temperature.—tThe position of the absolute zero may be con- sidered as established with a degree of accuracy which leaves no room for any error sufficient to account for the differences now in question. IV. Function The same may unquestionably be said of this function; which represents the mechanical equivalent of the latent heat of evaporation of so much water as fills one cubic foot. more in the vaporous than in the liquid state. MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 155 V. The Volume of one Pound of the Liquid Water is itself too small to affect the question. VI. The received value of the Mechanical Equivalent of a unit of Heat cannot err by so much as stoth part of its amount. Conclusions. 17. It appears, then, that none of the data from which the theoretical calcu- lations are made are liable to errors of a magnitude sufficient to account for the differences between the results of those calculations and the results of Messrs FAIRBAIRN and TaTe’s experiments, small as those differences are in a practical point of view. Neither does there appear to have been any cause of error in the mode of making the experiments. There remains only to account for those differences, the supposition that there was some small difference of molecular condition in the steam whose density was measured in the experiments of Messrs FarrBairn and — TaTE, above 212°, and the steam whose total heat of evaporation, as measured by M. Reenavtt, is the most important of the data of the theoretical formula,—a difference of such a nature as to make a given weight of steam in Messrs Fatr- BAIRN and TATE’s experiments occupy somewhat less space, and therefore require somewhat less heat for its production, than the same weight of steam in M. Rzc- NAULT’S experiments at the same temperature. That difference in molecular condition, of what nature soever it may have been, was in all probability con- nected with the fact, that in the experiments of Messrs FarrBairn and TATE, the steam was at rest, whereas in those of M. RecnavuLt it was in rapid motion from the boiler towards the condenser. It is obvious, however, that in order to arrive at a definite conclusion on this subject, further experimental researches are required. VOL. XXIII. PART I. 2 XV.—On the Secular Cooling of the Earth. By Professor Witt1am Tuomson, LL.D., F.R.S., F.R.S.E. (Plate VIIL) (Read 28th April 1862.) 1. For eighteen years it has pressed on my mind, that essential principles of Thermo-dynamics haye been overlooked by those geologists who uncompromisingly oppose all paroxysmal hypotheses, and maintain not only that we have examples now before us, on the earth, of all the different actions by which its crust has been modified in geological history, but that these actions have never, or have not on the whole, been more violent in past time than they are at present. 2. It is quite certain the solar system cannot have gone on, even as at present, for a few hundred thousand or a few million years, without the irrevocable loss (by dissipation, not by annihilation) of a very considerable proportion of the entire energy initially in store for sun heat, and for Plutonic action. It is quite certain that the whole store of energy in the solar system has been greater in all past time than at present; but it is conceivable that the rate at which it has been drawn upon and dissipated, whether by solar radiation, or by volcanic action in the earth or other dark bodies of the system, may have been nearly equable, or may even have been less rapid, in certain periods of the past. But it is far more probable that the secular rate of dissipation has been in some direct proportion to the total amount of energy in store, at any time after the commence- ment of the present order of things, and has been therefore very slowly diminish- ing from age to age. 3. I have endeavoured to prove this for the sun’s heat, in an article recently published in ‘“ Macmillan’s Magazine,” * where I have shown that most pro- bably the sun was sensibly hotter a million years ago than he is now. Hence, geological speculations assuming somewhat greater extremes of heat, more violent storms and floods, more luxuriant vegetation, and hardier and coarser grained plants and animals, in remote antiquity, are more probable than those of the extreme quietist, or “ uniformitarian” school. A “ middle path,” not generally safest in scientific speculation, seems to be so in this case. It is probable that hypotheses of grand catastrophes destroying all life from the earth, and ruining its whole surface at once, are greatly in error ; it is impossible that hypotheses assuming an equability of sun and storms for 1,000,000 years, can be wholly true. ® March 1862. VOL. XXIII. PART I. 158 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 4. Fourier’s mathematical theory of the conduction of heat is a beautiful working out of a particular case belonging to the general doctrine of the ‘“ Dissi- pation of Energy.”* A characteristic of the practical solutions it presents is, that in each case a distribution of temperature, becoming gradually equalised through an unlimited future, is expressed as a function of the time, which is in- finitely divergent for all times longer past than a definite determinable epoch. The distribution of heat at such an epoch is essentially ¢nzt7al—that is to say, it cannot result from any previous condition of matter by natural processes. It is, then, well called an “ arbitrary initial distribution of heat,” in Fourter’s great mathematical poem, because it could only be realised by action of a power able to modify the laws of dead matter. In an article published about nine- teen years ago in the “ Cambridge Mathematical Journal,”+ I gave the mathe- matical criterion for an essentially initial distribution; and in an inaugural essay, “ De Motu Caloris per Terre Corpus,” read before the Faculty of the University of Glasgow in 1846, I suggested, as an application of these principles, that a perfectly complete geothermic survey would give us data for determin- ing an initial epoch in the problem of terrestrial conduction. At the meeting of the British Association in Glasgow in 1855, I urged that special geothermic surveys should be made for the purpose of estimating absolute dates in geology, and I pointed out some cases, especially that of the salt-spring borings at Creuz- nach, in Rhenish Prussia, in which eruptions of basaltic rock seem to leave traces of their igneous origin in residual heat.} I hope this suggestion may yet be taken up, and may prove to some extent useful; but the disturbing influences affecting underground temperature, as Professor PHILLIPs has well shown in a recent inaugural address to the Geological Society, are too great to allow us to expect any very precise or satisfactory results. 5. The chief object of the present communication is to estimate from the known general increase of temperature in the earth downwards, the date of the first establishment of that ‘‘ consistentior status,” which, according to LEIBNITz’s theory, is the initial date of all geological history. 6. In all parts of the world in which the earth’s crust has been examined, at sufficiently great depths to escape large influence of the irregular and of the annual variations of the superficial temperature, a gradually increasing tempera- ture has been found in going deeper. The rate of augmentation (estimated at only zisth of a degree, Fahr., in some localities, and as much as th ofa degree in others, per foot of descent) has not been observed in a sufficient number * Proceedings Royal Soc. Edin., Feb. 1852. ‘ On a Universal Tendency in Nature to the Dissipation of Mechanical Energy.” Also, ‘‘ On the Restoration of Energy in an Unequally Heated Space,” Phil. Mag., 1853, first half year. t Feb. 1844.—‘‘ Note on Certain Points in the Theory of Heat.” { See British Association Report of 1855 (Glasgow) Meeting. PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 159 of places to establish any fair average estimate for the upper crust of the whole earth. But 2th is commonly accepted as a rough mean ; or, in other words, it is assumed as a result of observation, that there is, on the whole, about 1° Fahr. of elevation of temperature per 50 British feet of descent. 7. The fact that the temperature increases with the depth implies a continual lossof heat from the interior, by conduction outwards through or into theuppercrust. Hence, since the upper crust does not become hotter from year to year, there must be a secular loss of heat from the whole earth. It is possible that no cooling may result from this loss of heat, but only an exhaustion of potential energy, which in this case could scarcely be other than chemical affinity between substances forming part of the earth’s mass. But it is certain that either the earth is becoming on the whole cooler from age to age, or the heat conducted out is generated in the interior by temporary dynamical (that is, in this case, chemi- cal) action. To suppose, as LYELL, adopting the chemical hypothesis, has done,* that the substances, combining together, may be again separated electrolytically by thermo-electric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfil the expectations of its ingenious inventor by going for ever. 8. It must indeed be admitted that many geological writers of the “ Uniformi- tarian” school, who in other respects have taken a profoundly philosophical view of their subject, have argued in a most fallacious manner against hypotheses of violent action in past ages. If they had contented themselves with showing that many existing appearances, although suggestive of extreme violence and sudden change, may have been brought about by long-continued action, or by paroxysms not more intense than some of which we have experience within the periods of human history, their position might have been unassailable ; and certainly could not have been assailed except by a detailed discussion of their facts. It would be a very wonderful, but not an absolutely incredible result, that volcanic action has never been more violent on the whole than during the last two or three cen- turies; but it is as certain that there is now less volcanic energy in the whole earth than there was a thousand years ago, as it is that there is less gunpowder in a “ Monitor” after she has been seen to discharge shot and shell, whether at a nearly equable rate or not, for five hours without receiving fresh supplies, than there was at the beginning of the action. Yet this truth has been ignored or denied by many of the leading geologists of the present day, because they believe that the facts within their province do not demonstrate greater violence in ancient changes of the earth’s surface, or do demonstrate a nearly equable action in all periods. * Principles of Geology. 160 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 9. The chemical hypothesis to account for underground heat might be re- garded as not improbable, if it was only in isolated localities that the tempera- ture was found to increase with the depth; and, indeed, it can scarcely be doubted that chemical action exercises an appreciable influence (possibly negative, how- ever) on the action of volcanoes; but that there is slow uniform “ combus- tion,” “eremacausis,” or chemical combination of any kind going on, at some great unknown depth under the surface everywhere, and creeping inwards gradually as the chemical affinities in layer after layer are successively saturated, seems extremely improbable, although it cannot be pronounced to be absolutely impossible, or contrary to all analogies in nature. The less hypothetical view, © however, that the earth is merely a warm chemically inert body cooling, is clearly to be preferred in the present state of science. 10. Potsson’s celebrated hypothesis, that the present underground heat is due to a passage, at some former period, of the solar system through hotter stellar regions, cannot provide the circumstances required for a paleeontology continuous through that epoch of external heat. For from a mean of values of the conduc- tivity, in terms of the thermal capacity of unit volume, of the earth’s crust, in three different localities near Edinburgh, which I have deduced from the observations on underground temperature instituted by Principal Forses there, I find that if the supposed transit through a hotter region of space took place between 1250 and 5000 years ago, the temperature of that supposed region must have been from 25° to 50° Fahr. above the present mean temperature of the earth’s surface, to account for the present general rate of under-ground increase of temperature, taken as 1° Fahr. in 50 feet downwards. Human history negatives this supposition. Again, geo- logists and astronomers will, I presume, admit that the earth cannot, 20,000 years ago, have been in aregion of space 100° Fahr. warmer than its present surface. But if the transition from a hot region toa cool region supposed by Potsson took place more than 20,000 years ago, the excess of temperature must have been more than 100° Fahr., and must therefore have destroyed animal and vegetable life. Hence, the farther back and the hotter we can suppose Poisson’s hot region, the better for the geologists who require the longest periods; but the best for their view is LerpnitTz’s theory, which simply supposes the earth to have been at one time an incandescent liquid, without explaining how it got into that state. If we suppose the temperature of melting rock to be about 10,000° Fahr. (an extremely high estimate), the consolidation may have taken place 200,000,000 years ago. Or, if we suppose the temperature of melting rock to be 7000° Fahr. (which is more nearly what it is generally assumed to be), we may suppose the consolidation to have taken place 98,000,000 years ago. 11. These estimates are founded on the Fourier solution demonstrated below. The greatest variation we have to make on them, to take into account the differ- ences in the ratios of conductivities to specific heats of the three Edinburgh rocks, PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. [61 is to reduce them to nearly half, or to increase them by rather more than half. A reduction of the Greenwich underground observations recently communicated to me by Professor Everert of Windsor, Nova Scotia, gives for the Greenwich rocks a quality intermediate between those of the Edinburgh rocks. But we are very ignorant as to the effects of high temperatures in altering the conductivities and specific heats of rocks, and as to their latent heat of fusion. We must, there- fore, allow very wide limits in such an estimate as I have attempted to make; but I think we may with much probability say that the consolidation cannot have taken place less than 20,000,000 years ago, or we should have more underground heat than we actually have, nor more than 400,000,000 years ago, or we should not have so much as the least observed underground incre- ment of temperature. That is to say, I conclude that Lernirz’s epoch of “ emer- gence” of the “ consistentior status” was probably between those dates, 12. The mathematical theory on which these estimates are founded is very simple, being in fact merely an application of one of FouriEr’s elementary solu- tions to the problem of finding at any time the rate of variation of temperature from point to point, and the actual temperature at any point, in a solid ex- tending to infinity in all directions, on the supposition that at an initial epoch the temperature has had two different constant values on the two sides of a certain infinite plane. The solution for the two required elements is as follows :— do V = da Jkt. a 2V psa bah D= y+ 7 f Wet dze & 0 where x denotes the conductivity of the solid, measured in terms of the thermal capacity of the unit of bulk ; V, half the difference of the two initial temperatures ; v,, their arithmetical mean ; f, the time; a, the distance of any point from the middle plane ; v, the temperature of the point at time ¢; and, consequently (according to the notation of the differential calculus), e the rate of variation of the temperature per unit of length perpendicular to the iso- thermal planes. 13. To demonstrate this solution, it is sufficient to verify—(1), That the expression for v fulfils the partial differential equation, dv_ ,,@°0, dita as FouriEr’s equation for the “ linear conduction of heat;” (2) That when ¢ = 0, VOL. XXXIII. PART I. 7p 162 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. the expression for + becomes v,+ V for all positive, and v,—V for all negative = is the differential co-efficient with reference to x, of the expression for v. The propositions (1) and (3) are proved directly by differentiation. To prove (2), we have, when ¢ = 0, and 2 positive, values of #; and (3), That the expression for 2 ig C= U,+ Jad , dze~* or according to the known value, 34/7, of the definite integral we wae, 0=0, 4 Vi . and for all values of ¢, the second term has equal positive and negative values for equal positive and negative values of z, so that when ¢ = 0 and @ negative, v=v,— V. The admirable analysis by which Fourier arrived at solutions including this, forms a most interesting and important mathematical study. It is to be found in his “ Théorie Analytique de la Chaleur.” Paris, 1822. 14. The accompanying diagram represents, by two curves, the preceding expressions for aia and v respectively. 15. The solution thus expressed and illustrated applies, for a certain time, without sensible error, to the case of a solid sphere, primitively heated to a uni- form temperature, and suddenly exposed to any superficial action, which for ever after keeps the surface at some other constant temperature. If, for instance, the case considered is that of a globe 8000 miles diameter of solid rock, the solution will apply with scarcely sensible error for more than 1000 millions of years. For, if the rock be of a certain average quality as to conductivity and specific heat, the value of x, as | have shown in a previous communication to the Royal So- ciety,* will be 400, to unit of length a British foot and unit of time a year; and the equation expressing the solution becomes alt. Vine Mik <7 16008, dx 35:4 # ‘ and if we give ¢ the value 1,000,000,000, or anything less, the exponential factor becomes less than €~°° (which being equal to about es may be regarded as in- sensible), when w exceeds 3,000,000 feet, or 568 miles. That is to say, during the first 1000 million years the variation of temperature does not become sen- sible at depths exceeding 568 miles, and is therefore confined to so thin a crust, that the influence of curvature may be neglected. * On the Periodical Variations of Underground Temperature. Trans, Roy. Soc. Edin. March 1860. PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 1638 16. If, now, we suppose the time to be 100 million years from the commence- ment of the variation, the equation becomes do__V__,~:e0vo0000005 dx 354000 The diagram, therefore, shows the variation of temperature which would now exist in the earth, if, its whole mass being first solid and at one temperature 100 million years ago, the temperature of its surface had been everywhere suddenly lowered by V degrees, and kept permanently at this lower temperature: the scales used being as follows :— (1) For depth below the surface,—scale along OX, 10 quarter inches, or a, represents 400,000 feet. (2) For rate of increase of temperature per foot of depth,—scale of ordinates parallel to OY, 10 half inches, or 6, represents ; an of V per foot. If, for example, V= 7000’, this scale will be such that 10 half inches, or 0, represents =~. of a degree per foot. (3) For excess of temperature,—scale of ordinates parallel to OY, 10 half inches, or 6, represents 1 - or 7900°, if V=7000°. Thus the rate of increase of temperature from the surface downwards would be sensibly a of a degree per foot for the first 100,000 feet or so. Below that depth the rate of increase per foot would begin to diminish sensibly. At 400,000 feet it would have diminished to about = of a degree per foot. At 800,000 feet it would have diminished to less than = of its initial value,—that is to say, to 1 ° ° Cae ° ° less than ,-., of a degree per foot; and so on, rapidly diminishing, as shown in the curve. Such is, on the whole, the most probable representation of the earth’s present temperature, at depths of from 100 feet, where the annual variations cease to be sensible, to 100 miles ; below which the whole mass, or all except a nucleus cool from the beginning, is (whether liquid or solid) probably at, or very nearly at, the proper melting temperature for the pressure at each depth. 17. The theory indicated above throws light on the question so often discussed—Can terrestrial heat have influenced climate through long geological periods? and allows us to answer it very decidedly in the negative. There would be an increment of temperature at the rate of 2° Fahr. per foot downwards near the surface, 10,000 years after the beginning of the cooling, in the case we have supposed. The radiation from earth and atmosphere into space (of which we have yet no satisfactory absolute measurement) would almost certainly be so rapid in the earth’s actual circumstances, as not to allow a rate of increase of 2° Fahr. per foot underground to augment sensibly the temperature of the sur- 164 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. face; and hence I infer that the general climate cannot be sensibly affected by conducted heat at any time more than 10,000 years after the commencement of superficial solidification. No doubt, however, in particular places there might be an elevation of temperature by thermal springs, or by eruptions of melted lava, and everywhere vegetation would, for the first 3,000,000 or 4,000,000 years, if it existed so soon after the epoch of consolidation, be influenced by the sensibly higher temperature met with by roots extending a foot or more below the surface. 18. Whatever the amount of such effects is at any one time, it would go on diminishing according to the inverse proportion of the square roots of the times from the initial epoch. Thus, if at 10,000 years we have 2° per foot of increment below ground, At 40,000 years we should have 1° per foot. 1° ” 160,000 5) 2” 2 oP) - 4,000,000 ES ” ts» » 100,000,000 ~ oa as It is therefore probable that for the last 96,000,000 years the rate of increase of temperature under ground has gradually diminished from about 3th to about 2th of a degree Fahrenheit per foot, and that the thickness of the crust through which any stated degree of cooling has been experienced has gradually increased in that period from +th of what it is now to what it is. Is not this, on the whole, in harmony with geological evidence, rightly interpreted ? Do not the vast masses of basalt, the general appearances of mountain-ranges, the violent distortions and fractures of strata, the great prevalence of metamorphic action (which must have taken place at depths of not many miles, if so much), all agree in demonstrating that the rate of increase of temperature downwards must have been much more rapid, and in rendering it probable that volcanic energy, earthquake shocks, and every kind of so-called plutonic action, have been, on the whole, more abundantly and violently operative in geological antiquity than in the present age ? 19. But it may be objected to this application of mathematical theory—(1), That the earth was once all melted, or at least melted all round its surface, and cannot possibly, or rather cannot with any probability, be supposed to have been ever a uniformly heated solid, 7000° warmer than our present surface temperature, as assumed in the mathematical problem ; and (2), No natural action could possibly produce at one instant, and maintain for ever after, a seven thousand degrees’ lowering of the surface temperature. Taking the second objection first, I answer it by saying, what I think cannot be denied, that a large mass of melted rock, exposed freely to our air and sky, will, after it once becomes crusted over, present in a few hours, or a few days, or at the most a few weeks, a surface so cool that it can be walked over with impunity. Hence, after 10,000 years, or, indeed, I may say after a single year, its condition will be sensibly the same as if the actual — lowering of temperature experienced by the surface had been produced in an PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 165 instant and maintained constant ever after. I answer the first objection by say- ing, that if experimenters will find the latent heat of fusion, and the variations of conductivity and specific heat of the earth’s crust up to its melting point, it will be easy to modify the solution given above, so as to make it applicable to the case of a liquid globe gradually solidifying from without inwards, in consequence of heat conducted through the solid crust to a cold external medium. In the meantime, we can see that this modification will not make any considerable change in the resulting temperature of any point in the crust, unless the latent heat parted with on solidification proves, contrary to what we may expect from analogy, to be considerable in comparison with the heat that an equal mass of the solid yields in cooling from the temperature of solidification to the super- ficial temperature. But, what is more to the purpose, it is to be remarked that the objection, plausible as it appears, is altogether fallacious, and that the problem solved above corresponds much more closely, in all probability, with the actual history of the earth, than does the modified problem suggested by the objection. The earth, although once all melted, or melted all round its surface, did, in all probability, really become a solid at its melting temperature all through, or all through the outer layer, which had been melted; and not until the solidification was thus complete, or nearly so, did the surface begin to cool. That this is the true view can scarcely be doubted, when the following arguments are considered. 20. In the first place, we shall assume that at one time the earth consisted of a solid nucleus, covered all round with a very deep ocean of melted rocks, and left to cool by radiation into space. This is the condition that would supervene, on a cold body much smaller than the present earth meeting a great number of cool bodies still smaller than itself, and is therefore in accordance with what we may regard as a probable hypothesis regarding the earth’s antecedents. It in- cludes, as a particular case, the commoner supposition, that the earth was once melted throughout, a condition which might result from the collision of two nearly equal masses. But the evidence which has convinced most geologists that the earth had a fiery beginning, goes but a very small depth below the sur- face, and affords us absolutely no means of distinguishing between the actual phenomena, and those which would have resulted from either an entire globe of liquid rock, or a cool solid nucleus covered with liquid to any depth exceeding -50 or 100 miles. Hence, irrespectively of any hypothesis as to antecedents from which the earth’s initial fiery condition may have followed by natural causes, and simply assuming, as rendered probable by geological evidence, that there was at one time melted rock all over the surface, we need not assume the depth of this lava ocean to have been more than 50 or 100 miles; although we need not exclude the supposition of any greater depth, or of an entire globe of liquid. PART I. VOL. XXIII. 22 166 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 21. In the process of refrigeration, the fluid must (as I have remarked regard- ing the sun, in a recent article in “ Macmillan’s Magazine,”* and regarding the earth’s atmosphere, in a communication to the Literary and Philosophical Society of Manchester+) be brought by convection, to fulfil a definite law of distribution of temperature which I have called “ convective equilibrium of temperature.” That is to say, the temperatures at different parts in the interior must differ according to the different pressures by the difference of temperatures which any one portion of the liquid would present, if given at the temperature and pressure of any part, and then subjected to variation of pressure, but prevented from losing or gaining heat. The reason for this is the extreme slowness of true thermal conduction; and the consequently preponderating influence of great currents throughout a continuous fluid mass, in determining the distribution of temperature through the whole. 22. The thermo-dynamic law connecting temperature and pressure ina fluid mass, not allowed to lose or gain heat, investigated theoretically, and experimen- tally verified in the cases of air and water, by Dr Joute and myself,t shows, therefore, that the temperature in the liquid will increase from the surface down- wards, if, as is most probably the case, the liquid contracts in cooling. On the other hand, if the liquid, like water near its freezing-point, expanded in cooling, the temperature, according to the convective and thermo-dynamic laws just stated (S§ 21, 22), would actually be lower at great depths than near the sur- face, even although the liquid is cooling from the surface; but there would be a very thin superficial layer of lighter and cooler liquid, losing heat by true conduc- tion, until solidification at the surface would commence. 23. Again, according to the thermo-dynamic law of freezing, investigated by my brother,§ Professor James THomson, and verified by myself experimentally for water, || the temperature of solidification will, at great depths, because of the great pressure, be higher there than at the surface if the fluid contracts, or lower than at the surface if it expands, in becoming solid. | 24. How the temperature of solidification, for any pressure, may be related to the corresponding temperature of fluid convective equilibrium, it is impossible to say, without knowledge, which we do not yet possess, regarding the expansion * March 1862. + ‘* Proceedings,” Jan. 1862. ‘On the Convective Equilibrium of Temperature in the Atmosphere.” t Jour, “ On the Changes of Temperature produced by the Rarefaction and Condensation of Air,” Phil. Mag. about 1844, Tomson, ‘‘ On a Method for Determining Experimentally the Heat evolved by the Compression of Air; Dynamical Theory of Heat, Part IV.,” Trans. R, 8. E., Session 1850-51; and reprinted, Phil. Mag. Jovure and Tuomson, “On the Thermal Effects of Fluids in Motion,” Trans. R. 8. Lond., June 1853 and June 1854. Jourz and THomson, “ On the Alterations of Temperature accompanying Changes of Pressure in Fluids,” Proceedings R. 8. Lond., June 1887. § “ Theoretical Considerations Regarding the Effect of Pressure in lowering the Freezing-Point of Water,” Trans, R.8. E., Jan. 1849. || Proceedings R, 8S. E., Session 1849-50, PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH, 167 with heat, and the specific heat of the fluid, and the change of volume, and the latent heat developed in the transition from fiuid to solid. 25. For instance, supposing, as is most probably true, both that the liquid contracts in cooling towards its freezing-point, and that it contracts in freez- ing, we cannot tell, without definite numerical data regarding those elements, whether the elevation of the temperature of solidification, or of the actual tem- perature of a portion of the fluid given just above its freezing-point, produced by a given application of pressure, is the greater. If the former is greater than the latter, solidification would commence at the bottom, or at the centre, if there is no solid nucleus to begin with, and would proceed outwards; and there could be no complete permanent incrustation all round the surface till the whole globe is solid, with, possibly, the exception of irregular, comparatively small spaces of liquid. | 26. If, on the contrary, the elevation of temperature, produced by an appli- cation of pressure to a given portion of the fluid, is greater than the elevation of the freezing temperature produced by the same amount of pressure, the _ superficial layer of the fluid would be the first to reach its freezing-point, and the first actually to freeze. 27. But if, according to the second supposition of § 22, the liquid expanded in cooling near its freezing-point, the solid would probably likewise be of less specific gravity than the liquid at its freezing-point. Hence the surface would / crust over permanently with a crust of solid, constantly increasing inwards by | the freezing of the interior fluid in consequence of heat conducted out through the crust. The condition most commonly assumed by geologists would thus be produced. | 28. But BiscHor’s experiments, upon the validity of which, so far as I am | aware, no doubt has ever been thrown, show that melted granite, slate, and | trachyte, all contract by something about 20 per cent. in freezing. We ought, | indeed, to have more experiments on this most important point, both to verify | Biscuor’s results on rocks, and to learn how the case is with iron and other unoxydised metals. In the meantime we must consider it as probable that the | melted substance of the earth did really contract by a very considerable | amount in becoming solid. 29. Hence, if according to any relations whatever among the complicated | physical circumstances concerned, freezing did really commence at the surface, | either all round or in any part, before the whole globe had become solid, the | solidified superficial layer must have broken up and sunk to the bottom, or to | the centre, before it could have attained a sufficient thickness to rest stably on | the lighter liquid below. It is quite clear, indeed, that if at any time the earth | were in the condition of a thin solid shell of, let us suppose 50 feet or 100 feet | thick of granite, enclosing a continuous melted mass of 20 per cent. less specific 168 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. gravity in its upper parts, where the pressure is small, this condition cannot have lasted many minutes. The rigidity of a solid shell of superficial extent so vast in comparison with its thickness, must be as nothing, and the slightest dis- turbance would cause some part to bend down, crack, and allow the liquid to run out over the whole solid. The crust itself would in consequence become shattered into fragments, which must all sink to the bottom, or to meet in the centre and form a nucleus there if there is none to begin with. 30. It is, however, scarcely possible, that any such continuous crust can ever have formed all over the melted surface at one time, and afterwards have fallen in. The mode of solidification conjectured in § 25, seems on the whole the most consistent with what we know of the physical properties of the matter con- cerned. So far as regards the result, it agrees, I believe, with the view adopted as the most probable by Mr Hopxins.* But whether from the condition being rather that described in § 26, which seems also possible, for the whole or for some parts of the heterogeneous substance of the earth, or from the viscidity as of mortar, which necessarily supervenes in a melted fluid, composed of ingredients becoming, as the whole cools, separated by crystallising at different temper- atures before the solidification is perfect, and which we actually see in lava from modern volcanoes; it is probable that when the whole globe, or some very thick superficial layer of it, still liquid or viscid, has cooled down to near its temperature of perfect solidification, incrustation at the surface must com- mence. 31. It is probable that crust may thus form over wide extents of surface, and may be temporarily buoyed up by the vesicular character it may have retained from the ebullition of the liquid in some places, or, at all events, it may be held up by the viscidity of the liquid; until it has acquired some considerable thickness sufficient to allow gravity to manifest its claim, and sink the heavier solid below the lighter liquid. This process must go on until the sunk portions of crust build up from the bottom a sufficiently close ribbed solid skeleton or frame, to allow fresh incrustations to remain bridging across the now small areas of lava pools or lakes. 32. In the honey-combed solid and liquid mass thus formed, there must be a continual tendency for the liquid, in consequence of its less specific gravity, to work its way up; whether by masses of solid falling from the roofs of vesicles or tunnels, and causing earthquake shocks, or by the roof breaking quite through when very thin, so as to cause two such hollows to unite, or the liquid of any of them to flow out freely over the outer surface of the earth; or by gradual subsidence of the solid, owing to the thermo-dynamic melting, which portions of it, under intense stress, must experience, according to views recently published by my brother, Pro- * See his Report on ‘“ Earthquakes and Volcanic Action.” British Association Report for 1847. _ PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 169 fessor JAMES THomson.* The results which must follow from this tendency seem sufficiently great and various to account for all that we see at present, and all that we learn from geological investigation, of earthquakes, of upheavals and subsidences of solid, and of eruptions of melted rock. 33. These conclusions, drawn solely from a consideration of the necessary order of cooling and consolidation, according to BiscHor’s result as to the relative specific gravities of solid and of melted rock, are in perfect accordance with what I have recently demonstrated + regarding the present condition of the earth’s interior,—that it is not, as commonly supposed, all liquid within a thin solid crust of from 30 to 100 miles thick, but that it ison the whole more rigid certainly than a continuous solid globe of glass of the same diameter, and probably than _ one of steel. * Proceedings of the Royal Society of London 1861, “On Crystallization and Liquefaction as influenced by Stresses tending to Change of Form in Crystals.” ¢ Ina paper “ On the Rigidity of the Earth,” communicated to the Royal Society a few days ago. April 1862. Co e VOL. XXIil. PART I. | 7 pales igi wud | te jhe iA Ney da or nye: lun eis %e9 on 1G Ath . ’ uf 7 wn ae SE ue yf Meroe ni dou. lo he ‘narewascesdipann en - & cna MA: oc inna Vidalia 6h ties ourmia sorters eelialllinb Hoty, hase ve Jo can *peithexhesii riers bey hy o thang Sid Vo Mritidnicon, Rangmey ted ee " Lfor aid) nt sittin hiepil, Dur ey negen-eienie i Neh site. hig Mm our olen: ald: ty 22 Ig émils. dsodky: Wash oy ie Spa! ng bheas Sotunpih on poise neal bir ileal Paap . set - é be ‘ . “as oy) che eter Opal fede y Dat ik awd A | Li Revd ye Sees i i Ei: n'y) wes ree ‘ my aot +1 ca —* i ‘ j rt % va ay ie Kartcne 1 . andl ‘i a ai ram _ "9! ‘ Ws3 l i - ‘ 7 . a = ' by “2 a, . _ PG =f — he ia Oe f ¥ 9 ‘ ; ’ ‘ ize A ! i ; : Arhiu Wy PLATE VII Royal Soc. Trans. Edi VouxXXTTL INCREASE OF TEMPERATURE DOWNWARDS IN THE EARTH ; @=2VKt oes dv _V_NP' NP = bE a=y' WP = area ONPA+a=2,f/"y' dx v—v=V- 0 Stab 22x oi a ee 222 __ axb __6xb eed *8xb -9xb b MS 790"Fabr 2 en om oe 8 ton “ UO 2 ee 1) A axl5 ax 2-0 W.& AK. Johnston Fdinkirgh \ ave TLt Cir 3 XVIL—On the Representative Relationships of the Fixed and Free Tunicata, re- garded as two Subclasses of equivalent value; with some General Remarks on their Morphology. By Joun Denis Macponatp, R.N., F.R.S, Surgeon of H.M.S. « Tcarus.” Communicated by Professor Mactacan. (Plate IX.) (Read 15th December 1862.) My first precise views of the structure of the Tunicata were formed by the perusal of Mr Huxey’s masterly papers dealing with the anatomy of Salpa, Py- rosoma, Doliolum, and Appendicularia, in the Phil. Trans. for 1851, Part II.; and I have since had abundant opportunity of verifying all the important facts, made known by that original observer, in the papers to which I have alluded. Having thus acknowledged my guide in this field of research, I can scarcely claim much originality as relates to pure anatomy; but I hope that the method here adopted, in opening up this interesting subject, will be found in keeping with ‘nature, as it is the result of much study and practical investigation. I must first beg the question, and next endeavour to support it, that the class Tunicata may be conveniently divided into two subclasses—viz., the fixed. or stationary, and the free or locomotive. The latter, from their habit of life, are also commonly denominated Pelagic; while the former, by general consent, chiefly following the suggestions of M. Mitnse-Epwarps, have been divided into the Simple, the Social, and the Compound, as given in the following table :— Tunicata. I. Fixed or stationary. 1. Solitary, or simply segregate. a, Sessile (recumbent or erect), or pedunculate, : : ! 3 Simple. 2. Organically blended in communities. a. Sessile or pedunculated on a common axis, ; ; : t Social. b. Immersed in a common test substance, ; j ; . : Compound. II. Free or locomotive, Pelagic, Of the fixed Tunicata, it would appear that Pelonaia and Chelyosoma* pre- sent characters which at once distinguish them from all the other members of the subclass. Thus, in the genera named, the branchial membrane seems to be closely adherent to the subjacent textures, without forming a distinct sac, * We are much in want of more accurate information respecting these genera) Mr Huxtey remarks, loc. cit. 588, “ In Pelonaia, the hypopharyngeal band has disappeared. It is a Salpa in which the oral and cloacal orifices have approximated, while the ‘ gill’ has become obliterated ;” and in a note at the bottom of the page he says, “ Chelyosoma would appear to resemble Pelonaia in the absence of any distinct branchial sac; but Escuricut’s figures are not very clear.” VOL. XXII. PART II. 3B 172 MR J. D. MACDONALD ON THE REPRESENTATIVE RELATIONSHIPS though finely areolated and thrown into parallel folds; whereas, in all the re- maining fixed Tunicata, a branchial sac may be demonstrated, the respiratory slits or meshes being in general longitudinal, and disposed in many transverse series. On the other hand, the respiratory system in the free or Pelagic section presents no less than four distinct types, as occurring respectively in the genera Pyrosoma, Doliolum, Salpa, and Appendicularia. These may be defined as follows :— Branchial membrane sac-like, with transverse slits in single longitudinal series, strengthened by longitudinal non-ciliated bars. Apertures terminal or subter- minal—P YROSOMA. Respiring by an upper and a lower “ gill-band,” connected with each other later- ally, and with the walls of the atrium ; having branchial slits, but no supporting longitudinal bars. Apertures terminal—Do.ioLum. Respiring by a central inferior gill-band, with free borders and transverse ciliated stripes, but without slits or bars. Apertures terminal or subterminal— SALPA, ce. Pharynex ciliated below without a distinct “ gill-band ;” branchial slits reduced to two ciliated openings on the sides of the rectum. Apertures approximated hemally —APPENDICULARIA. As far as the respiratory system is concerned, therefore, the fixed Tunicata exhibit at least two well-marked types, and the Pelagic group four, which are equally distinct, and, as I conceive, of equal importance, demanding fair consider- ation in systematic arrangement. Moreover, I am quite satisfied that there are very striking representative relationships existing between the fixed and free Tuni- cata; and in order to exhibit these the more clearly, I have drawn up the annexed circular scheme or table, in which it will be seen that each subclass has its simple, social, and compound groups, and their mutual representatives may be at once recognised. Thus, Appendicularia represents the equally curious genus Pelonaia, Doliolum the remaining simple Tunicata, Sa/pa the social, and Pyrosoma, the com- pound group, but, in particular, the Botryllians. Any one accustomed to draw comparisons and analogies will readily perceive that there is something more than simple coincidence in all this, particularly as the characters employed are so comprehensive, bearing successively on habit of life, habit of body, social habit, mode of gemmation, and respiration. It would be quite as easy to draw up two circles as one, or the characters might be thrown into rays instead of circles, but the result in all cases would be virtually the same. I always pay respect to the maxim, that “ characters can only be taken as natural when they have been proved to be so;” and I know also that groups must be found, before trustworthy characters can be chosen to effect a classifica- tion. When we find Nerites breathing air, and feeding on the green leaves of the TIONS OF THE ROYAL SOCIETY, EDINBURGH. VOL. XXIII. 70 face page 772. apie OF THEAFFINITIES g, ConCodeategy an ChOMICS Ree 7 Jig Lootds <, QO Paton, % SQ Ree & ul > SS ike : Ey eS = ’ a oe a % on = ge gs 2 i hers & Me sc Ca ea % m Regd See : io Se Car. eat Sa Si Sema \ Peso S/ VE, BiLsi 2 Pomme ee Se Ley ol atte 7s I TUNICATA | taeat aie oa oe ee : o-8 3 2 \ 3 wy Wi S : & ‘ ! x= : a = d = & 2 ! } i h, ¥ 0 & § = as Nica! No, a3 \ t x. i % SX, uus vo ie = x oA 3 z av AP, oo ie won Se = Nea ae ee ee OF THE FIXED AND FREE TUNICATA. 173 forest, Nerites breathing in the mountain streams, Nerztes in brackish waters, Nerites on the beach in fellowship with Zittorina, and in the sea itself, one would say that habit of life would afford anything but a natural character. Nor indeed would it in the case given, and in many others that might be adduced; but it certainly affords us the simplest and most natural primary division of Z’unicata, _and the other characters adopted in the table appear to answer their purpose equally well. | The idea has been too commonly entertained, that the Pelagic Tunicata, so called, compose a group only commensurate with the compound, the social, or the simple, taken separately, but I trust that a candid analysis of the preceding table . will serve to free the judgment from an accustomed bias in this particular, and show that the fixed and the free Tunicata form two subclasses of at least nearly equal value in a zoological point of view; and I almost imagine, though myself affected by the prejudice to which I have alluded, that the balance is rather in favour of the Pelagians. Though we may readily, as by a kind of empiricism, recognise a difference between the stmple, social, and compound Tunicata, it is by no means easy to give _ them an intelligible definition. Indeed, I can safely say, as a student of the Tuni- _eata, that I have long known more of the existence of a difference than of its pre- cise nature, and this can scarcely be arrived at by the study of books alone. In- | deed, the whole subject is even now shadowy and ill defined, notwithstanding the ereat light that has been shed upon it by the labours of Saviany, MactEay, | Fremine, Minne-Epwarps, and, in particular, Professor Hux Ley. The term Compound is just as applicable to a tree of Perophora, as it is to one of Sertularia ; but that term is restricted to another group, including forms that differ remarkably inter se, such as Botryllus and Sigillina, for example, their | great characteristic being, as far as I can see, more or less complete immersion of | the zooids in acommon test, with or without vascular intercommunication. This | immersion of the zooids is an important feature, as no common cloacal system }can otherwise exist ; but, inasmuch as it may occur without the formation of | cloacze, it links the soczal group with such compound Tunicaries as possess a com- /mon cloacal system. Furthermore, the branched and undermining form of this system, in several genera, indicates the passage to the Botryllian punctate, linear, or reticulate type, in connection with which latter, as a genetic character, several | zooids are developed from a single ovum, as in Pyrosoma. The process of gemmation, on the other hand, is much more Senn in the social than in either the simple or compound Ascidians. Thus, we scarcely ever “find incipient buds springing from, or beyond others little farther advanced in the two latter, while such is the rule in the former group. | That the increase of the connecting substance, or “ascidiarium” of Hux.ey, proceeds part passu with the gemme, and is, in fact, in advance of them in the 174 MR J.D. MACDONALD ON THE REPRESENTATIVE RELATIONSHIPS social Ascidians, as in the Polyzoa, can scarcely be denied; and upon it is im- pressed a limited law of growth or extension which is subservient to the forces determining the development of the zooids. Thus, while both progress in harmony, there are obvious indications of the co-existence of independent powers. The primary fixed point, or, as it were, the potential germ of the ascidiarium, taken in the abstract, will be found to be very differently related to the zooids in the compound as compared with the social Ascidians. Thus, the point of attachment of a Perophora or Chondrostachys, for example, may be looked upon as homologous with the cloacal side of the apex, so called, in Pyrosoma, Plate IX. fig. 1 a, or to the corresponding part in Botryllus, Plate IX. fig. 2 a’, the attached surface of the latter genus, Plate IX. fig. 2 a, being equivalent to the exterior side of the apex in the free Pyrosoma, and to the summit of the axis, produced in Chondrostachys, Plate IX. fig. 1 a, and depressed in Diazona, which latter genus appears to me to be more conformable with the social than with the compound group. The hzmal surface of the zooids, we therefore find, is turned in opposite directions in Chondrostachys and Botryllus,—viz., in the former case, towards the summit of the growing axis, and, in the latter, towards the margin of the encrusting common test, or, in other words, the zooids face outwards in one instance and inwards in the other. Though all the gemme augmenting the community are dorsal in both examples given, yet, in Botryllus, and especially in Pyrosoma, they are being continually thrown forward, so as ultimately to be in advance of the parent zooids, whereas in the social group, the anterior aspect of the primary zooid being turned towards the surface, upon which the rudimentary ascidiarium is fixed, the new gemme arise within extensions of the connecting substance in a truly retrograde direction,—.e., centripetally, or towards the summit of the central axis thus formed. In the beautiful species of Botrylloides, of which there are many in the — Australian seas, I have frequently observed a rear-rank of gemme advancing to usurp the place of their parents, which had for some time previously played their part at the fore; and indeed it is only in this way that the linear and reticulate cloacze (along the sides of which two rows of zooids are at most to be found), can be produced. The bell-shaped antroversion of the “ascidiarium’” in Pyrosoma appears to be necessitated by the position of the ‘“cyathozooid,” so accurately described by Professor Huxtey, and of the cloacal apertures of the four “ascidiozooids” sur- rounding it, as also by the peculiar mode of advance of the gemmz, and the forward extension of these palliovascular stolons, which are in all Tunicata inti- mately connected with the growth and nutrition of the test. The proximal surface of Botryllus, being fixed, presents so great antroversion of the mass as happens in Pyrosoma, which, in consequence of being quite free, RELATIONSHIPS OF THE FIXED AND FREE TUNICATA. 175 admits of the full play of this tendency, aided by a more rapid development of the zooids. Moreover, it would appear, that the margin of the external opening of the common cloaca is permanent, progressively advancing with the newly formed zooids, thrusting themselves forwards between it and the parents from which they sprung. Whereas, in Botryllus or Botrylloides, where there is but one effective row of zooids bordering the cloacze at any particular time, the margins of the openings must be continually undergoing repair and decay. On comparing an expansion of Botryllus with one of Flustra, or any other polyzoon, it is curious to observe that the zooids lie virtually face downwards in the latter, and face upwards in the former; and this is certainly one amongst many points of difference existing between the Polyzoa and the Compound Tunicata, while it favours the view that the Polyzoa hold the same relationship to the Brachiopoda* that the compound hold tothe simple Z'wnicata, or, to ex- tend the question, that a Gorgonia bears to an Actinia. A test which is common to a number of individuals, 7.¢, an Ascidiarium, affords the first bond of union or community occurring in Junicata. The next is obviously the establishment of a common cloacal system; and, lastly, as it would appear, the most important condition, truly suggesting the designation compound, is the intercommunication of the Pallio-vascular systems of the zooids, either as connected with the process of gemmation alone, or with the nutrition of the common test. Systems of intercommunicating stolons, having no connection whatever with gemmation, frequently present themselves in the compound genera; thus, in Leptoclinum and others, they are simple, or simply branched without reticulation ; while, in Botryllus, they are compound, reticulate, and open a com- munication between the zooids. The cloacal, like the branchial aperture, may open upon the external surface of the common test, or it may open into a definite common cloacal system either directly or by a tributary canal. The character and arrangement of the common cloacze are of great importance in classification, and it is much to be regretted that so little definite information respecting them is to be found in systematic works. Whenever the opportunity presented itself, I have always endeavoured to unravel their curious schemes of arrangement, and often found it a matter of great difficulty; but so far as I have been able to generalize them, they are given in the following classification, which will be also found to afford a simple exposi- tion of the leading features of the Tunicata as a whole. As a matter of course, many characters in the minor distinctions here em- ployed must, and have been, previously adopted by others. Thus, Mr W. S. M‘Leay and Dr FLEmine have passed in review nearly all the available characters in the Simple Tunicata, and M. Mitnz-Epwarps has done the same with the * The ventral valve being the valve of attachment in the Brachiopoda as in the Polyzoa. VOL. XXIII. PART II. 3 C 176 MR J. D. MACDONALD ON THE REPRESENTATIVE social and compound groups. I hope, therefore, that this will be sufficient apology, without complicating the table by continual reference to authority. CLASS TUNICATA. Marine molluscoid animals, fixed or free, invested by an outer coat or tunic of variable consistency, and communicating with the exterior by an inhalent and an exhalent orifice for respiratory currents, conveying also the materials used as food; having a ciliated and variously modified pharynx adapted for respiration, and an atrial chamber for the discharge of the respired water and excretions, a reversible circulation, sexes combined, and the power also of developing by gemmation, which property pre-eminently distinguishes them from the mollusca proper. SUB-CLASS I. ANIMALS FIXED OR STATIONARY. I. Branchial membrane closely adherent, or more or less perfectly sac-like, simply areolated, or distinctly retiform ; the meshes disposed in many transverse series without non-ciliated sup- porting bars. 1, Gemme springing directly from the parent with a temporary bond SIMPLE } TUNICATA. of union, . > : A. Branchial membrane adherent, not forming a distinct sac. Ten- Genera. tacula, o. Branchial folds transverse, } Pelonaia. B. Branchial membrane more or less perfectly sac-like. 1. Tentacula o, . : , ; : - : ; . (2) Chelyosoma. 2. Tentacula simple, liver rudimentary, animal sessile (erect or re- cumbent), a. Branchial folds, o, 3 : Ascidium. b. Branchial folds longitudinal. 1. Branchial aperture higher than the cloacal, . Cynthia. 2. Apertures on the same plane. a. Protected by a D-shaped apercular fold of the test common to both, . : . : Peroides. b. Simple or naked. 1. Ovary and testis on right side, . ; Pandocia, 2. Ovary and testis on the left side, .. Dendrodoa. 3. Tentacula compound. Branchial folds numerous, longitudinal ; liver well developed. a. Sessile (erect), apertures on the same plane, . : Cesira and Molgula ? b. Pedunculated (pendulous) cloacal opening, the higher or subterminal, . : . : : : : Boltonia and Cystingea. RELATIONSHIPS OF THE FIXED AND FREE TUNICATA. 177 TABLE OF CLASsIFICATION—continued, 2. Gemmez springing separately from a definite “ascidiarium (Huz.), and communicating indirectly through a central common vascular system, . Socrat Tunicata. A. Zooids branchial (Huw.), pedunculated, springing from a scandent or Gener repent corneous axis, with a central permanent vascular system common to the offsets, d : : : : ‘ Perophora. B. Zooids intestinal (Huz.) 1. Pedunculated. a, Standing upon a repent ramose cartilaginous case, with a central canal (usually not permanent), communicating with the offsets, . ; ‘ : ; : 3 ‘ Clavellina, b. Developed centripetally on an erect, simple, cylindrical stem, permeated by numerous longitudinal canals communicating with the offsets, though rarely with each other, , Chondrostachys. 2. Sessile, clustered in irregular circles on a simple depressed axis, Syntethys. And, probably, . , : 4 : : i . (2) Diazona. 3. Gemme arising separately from the parent, with or without vascular inter- communication, but always immersed in a common test or “ascidi- arium,” . : : : s ; : : : ‘ Compounp TunicaTa. A. Pallio-vascular system simple, i.¢., not intercommunicating. Gena 1. Excretory aperture opening directly upon the surface. Cloace o. a, Biabdominal (Polyclinian). Zooids in irregular circles, one above another, . : : : : ; : Sigillina. b. Abdominal (Didemnian). 1. Zooids in one or two rows at unequal distances from centres, . : : : i : : Distomus. 2. Zooids without distinct circumscription. a. Abdominal viscera beside the thorax, s Eucelium. b. Abdomen pedunculate, . : : Didemnium. 2. Excretory aperture opening into a common cloacal system. a. Cloaca superficial reticulate, with tributary canals diverging from the zooids in the intervening spaces. a. Thorax double, . , : F , : Diplosoma. b. Thorax simple, ; ; : Leptoclinum. b. Cloace deeply excavated, dendritic, formed by the con- fluence of converging canals. 1. Biabdominal (Polyclinian), a, Systems diffuse. a. Branchial aperture 6-rayed, : : Amarecium. §. Branchial aperture 8-rayed, ; Parascidium. b. Systems circumscribed. - Without central cavities, . I ; Aplydium. . With central cavities, ‘ Y ; Polyclinum. 178 MR J. D. MACDONALD ON THE REPRESENTATIVE TABLE OF CLASSIFICATION—continued, : ‘ : : ; : CompounpD TUNICATA. B. Palliovascular system intercommunicating. Genera. 1. Excretory apertures opening directly into punctate, linear, or reticulate cloacz. a. Biadominal (Polyclinian). 1. Systems single, isolated, or gregarious in whole relief, pendunculated (?), : : : ‘ : Syneecium. 2. Systems numerous, masses crusting. a. In half relief projecting above the surface, (?) Sidnyum. b. Not projecting above the surface, 2 ? Polychnoides. b. Thoracic (Botryllian). , a, Cloace punctate, . : : : é : Botryllus. b. Cloace linear or reticulate, - : : ‘ Botrylloides. SUB-CLASS II. ANIMALS FREE LOCOMOTIVE. PELacic TUNICATA. Genera. Il. Branchial membrane, sac-like, with transverse slits in single longitudinal series, strengthened by longitudinal non-ciliated rods, apertures terminal or sub- terminal, : : : : ; : ; . Pyrosoma, III. Respiring by an upper and a lower gill-band, connected with each other laterally and with the walls of the atrium ; having branchial slits, but no supporting longitudinal rods. Apertures terminal, . : : : - . . Doliolum. IV. Respiring by a central and inferior gill-band with free borders, and transverse ciliated stripes, but without slits or rods. Apertures terminal or sub-terminal. 1. Intestine short, and simply folded upon itself. A. Sexual zooids concatenated in chains, 1. Ciliated stripes with pouch-like recesses at their outer ends, . Pegea. 2. Ciliated stripes of gill-band, simple, ; : : : . Salpa. B. Several zoids permanently united in circles, as in Pyrosoma, : . Pyrosomopsis. — 2. Intestine extended directly forwards from a cecum-like proventriculus. The anus, and with it the ejaculatory duct, opening near the branchial orifice, Orthoceta. (Salpa pinnata.) V. Pharynz ciliated below, without a distinct gill-band. Branchial slits reduced to two ciliated openings on the sides of the rectum. Apertures approximated heemally, ; ; : : : é : 4 : : : Appendicularia. The lobing, and other particulars connected with the apertures, afford simple and easily recognisable characters, which are often distinctive of genera; but, as the Table might be rendered too complex by their introduction, I have omitted them. They may, however, be readily supplied by the student for his own con- — venience. I have drawn up the preceding scheme of classification chiefly with the view of illustrating the principles set forth in the first part of the paper. My own doubts I have expressed with a query (?), and even independent of these RELATIONSHIPS OF THE FIXED AND FREE TUNICATA. 179 many errors may be patent to zoologists, better conversant with the Tunicata than myself. Such, indeed, can only be expected to occur in thus dealing with so comprehensive a subject. I believe, nevertheless, that our acquisitions, as well as those things which are yet desiderata in the interesting study before us, are made much plainer in an attempt of this kind, however imperfect, than perhaps in any other way. The following genera may require brief comment in reference to their zoological characters, and the position assigned to them in the Table :— Chelyosoma. The absence of branchial tentacula in this genus, and what has been already said of it, p. 171, suggests a position for it near Pelonaia. Peroides (mihi). Peroides isan Australian genus discovered by me on the Bellona reefs, lat. 21. 51. S., long. 159. 28. E., but as [have given an account of it, with figures, to the Lin- nean Society, I need only allude to its leading features, which are these,—animal recumbent on the left side; apertures simple on the same plane, and protected by a D-shaped operculum, composed of an indurated fold of the test common to both. Cynthia, Cesira and Molgula. The term genus was received by the earlier zoologists in a much wider sense than that to which we now confine it; and, as might be expected, this has since given rise to much confusion, requiring considerable research to clear up satis- factorily. Thus, under the head of Cynthia, several distinct genera were included by Savieny, and we consequently find that the restricted genus, as understood by Professor Fores, is represented as having a “ circle of tentacular filaments,” i.é., simple tentacula; whereas Dr FLEm1neG gives Cynthia the character of “ Ten- tacula compound,” which could only be applied to a very different genus. It is also remarkable that without any reference to Professor Forses’s genus Molgula, in a paper read before the Linnean Society and published in the Transactions, I described two Australian Ascidians accurately conformable to SavieNny’s genus Cesira, and which, singularly enough, very closely represent the two British species of Molgula described by Professor ForBes ; and my impression has ever since been, that Cwsira and Molgula are synonyms of one and the same genus. Knowing, however, the great and respected authority which this view calls into question, I cannot be positive on the subject, but merely direct attention to it in the hope of setting it right. Chondrostachys (mihi). This name I have given to a very beautiful social Ascidian, which I first VOL. XXIII PART II. 3D 180 MR J. D. MACDONALD ON THE REPRESENTATIVE dredged up in deep water in Bass Strait. The particulars of its anatomy, with several figures, were published in the Ann. and Mag. Nat. Hist. at the time; and it has since been obtained by Mr F. N. Rayner, R.N., late surgeon of H.M.S, “« Herald,” in the neighbourhood of Torres Strait. It may be remarked, that the whole mass is quite colourless and pellucid, but in other respects it is sufficiently described in the table. Diazona. It has often appeared to me that Diazona was more closely related to the Social than to the Compound Tunicata, from the similarity of its structure to that of Syntethys. The position assigned to it in the table is quite in accordance with the definitions there given. Diplosoma (mihi). This genus I have found both in the S.W. Pacific and in the West Indies. The mass is gelatinous and filmy, and the thorax in the zooids is double—a con- dition that may be traced even long before the young escapes from the ovum. It was described and figured in the Transactions of the Linnean Society as the first step towards the still more paradoxical development of the ovum in Bo- tryllus and Pyrosoma. Synecium and Sidnyum. Though certain general considerations have induced me to place these genera near the true Botryllians, | cannot yet say whether they have an inter-communi- cating palliovascular system or not; and asit would be equally wrong, should such be the case, to place them anywhere else, they may remain where they are until the question is settled, and the (?) is removed. Polyclinoides (mihi). I have applied this term to an Australian genus of compound Ascidians, dis- tinguished from BGotryllus by having a distinct abdomen, and the generative organs pedunculated, forming a post abdomen,—and from Polyclinum, by possessing a compound palliovascular system, and fewer zooids surrounding the cloace ; besides which the mass is thin and encrusting, as in Botryllus. The branchial aperture is considerably elevated, and six-lobed. The superior margin of the cloacal opening is much produced, and three-lobed at the extremity, which is simple in Botryllus. Pyrosomopsis (mihi). A name which I have applied provisionally to a curious genus of Salpians, in RELATIONSHIPS OF THE FIXED AND FREE TUNICATA. 181 which the gemmee are permanently united in circles, and thus described in my notes :—“‘ This form presents seven perfect Salpians disposed in a circle, radiating, with their posterior extremities approximated near the centre, and enveloped ina common membrane, like a medusiform disc. ** Respiratory openings occupying one surface of the disc, the anterior or orifice of ingress being marginal, and the posterior central. The testis and a diverticulum of the alimentary canal forming two elongated papilliform processes, projecting from the posterior extremity of each animal (but within the common envelope), and convening towards the centre of the disc. Intestine forming an open arch, with its convexity directed backwards, across which the long and nar- row duct of the testis passes to open into the respiratory chamber. Each zooid bearing a solitary embryo communicating with the sinus system, and enclosed in a spherical capsule. “ Otolithic sac rather prominent, and projecting from the under surface of the ganglion. “* Hypopharyngeal band,’ or gill and muscular system in every respect as in ordinary Salpe. . “ The arrangement of the zooids in this case very much resembles that in Py- rosoma, more especially the primary circle of the latter; but the whole economy in other respects is Salpian. Taken in the towing-net, lat. 32. 53.S., long. 15600 E., and subsequently in other localities.” Orthocela (Salpa pinnata of Authors). It would be quite as philosophical to include the whole of the cheilostomatous Polyzoa under one generic term, as to group all the strikingly diversified animals of the Salpian type as mere species of the genus Sa/pa. Under a similar impres- sion, SAVIGNY set about the establishment of seven new genera ; but their claims as such do not seem to be generally admitted by zoologists. With regard to the genus here under consideration, I find the following obser- vations amongst my notes :— “While cruising in the S.W. Pacific, we frequently met with a Salpian answering perfectly to the description of Salpa pinnata, though this is rather in- definitely given by M. Dz BuarnvitxE; and in our late voyage to the West Indies in H.M.S. ‘Icarus,’ apparently the same species frequently made its appearance in the towing-net, together with Salpa zonaria, and numerous other species. It appears to me that the said S. pinnata, if I have correctly identified it, deserves to be removed from the genus Salpa, and placed by itself, until other species are | added to it with the same generic characters. The propriety of this step, how- | ever, may be better seen when the principal features of the anatomy of the animal have been passed in review. ‘In some instances specimens attain a length of about two inches, with a 1382 MR J. D. MACDONALD ON THE REPRESENTATIVE proportionate bulk, but in general they are much smaller ; and from the delicacy of the test, the body very readily collapses, offering a serious obstruction to the study of their internal anatomy. “« The test may be described as semi-gelatinous, smooth, and, with the excep- tion of a long cylindrical process, springing from the dorsal region anteriorly, it is everywhere free from angles and projections. The body is full, and rounded in the middle, from whence it rather suddenly tapers towards the anterior and posterior openings, which are simple and very small, closed by numerous narrow and encircling muscular bands. “ The muscular system is very complex, consisting of circular, diverging, and inter-communicating bands ; four, in particular, ascend at nearly equal intervals upon the dorsal process. The anterior pair, however, soon unite, and form a single slip, which is connected with the others by transverse fibres. “ As well as I could make out, the lining membrane of the respiratory chamber passes across the base of the dorsal process without entering it. “ The gill-band is simple and lengthy, communicating at the oral end with a rudimentary epipharyngeal extension of the same structure. The ciliated stripes are very narrow, and do not increase much in width outwardly. The curved ciliated sac at the anterior end of the gill, and the fine ciliated line connecting this on either side with the anterior extremity of the endostyle, were very dis- tinctly visible in the specimens examined. “The nervous ganglion occupies a position corresponding with the anterior fixed end of the gill, but on the inferior aspect of the body. The auditory sac, otolithes, and pigment, present nothing unusual. ‘“ The endostyle is long and narrow, extending from a point above and to the right of the heart to near the branchial opening. The mouth is situate at the posterior extremity of the gill-band, and leads into a distinct oesophagus, which in its turn opens into an elongated stomach, with a large cecal pouch, directed upwards and backwards, intervening. The stomach takes a straight course directly forwards, and gradually passes into the intestine, which is slightly curved downwards anteriorly, where it ends in the vent, immediately below the base of the dorsal process. A small transparent and’ highly refracting duct, arising by several radicles in the vicinity of the rectum, courses backwards on the right side of the alimentary canal, and having arched to the left over the caecum or proventriculus, it opens into the commencement of the stomach. The office of this system, first made known by Professor HuxLEy, is not even yet well understood, though I have myself traced it through all the divisions of Tunicata, even in the microscopic compound forms. ‘The heart, compared with the size of the animal, is small, and situate near the posterior extremity of the ‘ endostyle,’ on the right side of the stomach. “On either side of the ventral surface of the body there is a narrow cylin- RELATIONSHIPS OF THE FIXED AND FREE TUNICATA. 183 -drical organ—the ‘ violet-line’ of M. De Biartnvitte—about half the length of the -endostyle. These may possibly be renal, but I am not aware that any definite office has been assigned to them, though corresponding structures certainly occur in numerous other cases also. They consist of a membraneous envelope, contain- ing an abundance of large cellular bodies, with transparent spherical granules of uniform size, both within and amongst the cells. “ The testis consists of a number of long tubular czeca, forming an elongated whitish mass, lying immediately beneath the brownish-yellow stomach and in- testine, and terminating anteriorly in a fine ejaculatory duct, which opens into the branchial chamber a little behind the vent. The gemmiparous zooids are de- veloped singly.” Haplanation of Plate IX. figs. 1, 2. | Fig. 1. Vertical section of a single system of Botryllus, to show its relationship to Pyrosoma. a’. Floor of the cloacal chamber. a. Surface of attachment. b’, Lateral extension of the ascidiarium. b. Border of the cloacal opening, in the formation of which the zooids themselves take part. Fig. 2. Theoretical diagram, illustrating the morphological difference between Chondrostachys A, as a social, and Pyrosoma B, a compound Pelagic Tunicary. a. Summit of the axis of Chondrostachys, corresponding with the apex of the free Pyrosoma. a’, Cloacal side of the apex of Pyrosoma, equivalent to the point of fixity of Chondrostachys. b, Growing circumference, or border of the cloacal opening of Pyrosoma, considered as an antro- version of the axis or ascidiarium. The arrows indicating the orifices of ingress and egress show that there is no necessary in- version or alteration of the relations of the zooids, either as to each other or to the ascidiarium, in the theory of antroversion, as applied to Pyrosoma, or of retroversion as regards Chondrostachys. VOL. XXIII. PART II. - 3) fr * if x riven | Suey 5 19) 8 ? ron] F lI ( 7185.4) XVII.—On the Zoological Characters of the Living Clio caudata, as compared mith those of Clio borealis given in Systematic Works. By Joun Denis MacpoNALD, R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” Communicated by Professor MactaGan. (Plate IX. fig. 3.) (Read 5th January 1863.) Great credit is due to those observers who have been enabled to give to science both clear and comprehensive views of the anatomy of creatures which have only been presented to them in a spirit-preserved, opaque, brittle, and con- tracted state; for it is certain that their penetration in this respect could not be successfully brought into exercise without the aid of much knowledge, both bibliographical and practical. Yet there are many whole animals, and, in par- ticular, parts of animals, which must be seen in the living state, to be at all comprehended by even the most brilliant mind; and this fact has induced me to make drawings and notes of many interesting matters connected with the pelagic mollusca, when the living animals fell casually under my own observa- tion. In the present communication, however, I shall confine myself to the genus Clio. Good figures are in general more valuable than even lengthy descriptions ; for though it would not be very easy to make a good figure from an imperfect * description, a very excellent description may be formed from an indifferent figure. On consulting all the figures of Clio available to me, I found most of them far short of nature, and all quite incapable of affording a just conception of the living and fully expanded animal; nor, indeed, can I say that any descriptions, of the members of the genus extant answer much more than the purpose of mere recognition, in a popular sense. In the widest sense of the word, the physiognomy of Clo caudata, in the expanded state, is as remarkable as that of any animal in creation. The head, or that enlargement in front which is separated from the body by a slight cervical constriction, is fronted on either side by two small tentacula, one of which has been supposed to be an eye pedicle, though there is no proof that Clio enjoys one whit more visual faculty than any other Pteropod. Cuvier remarks, that “some have asserted the existence of eyes;” and subsequent writers say , that those in Cio, though minute, have a very complete organization. For my own part, however, I cannot say that I have ever been able to detect them, though J should be sorry, on this ground alone, to affirm that they are not pre- sent. But the little tentacula just noticed are quite insignificant, in comparison VOL. XXIII. PART II. 3 F ‘ 186 MR J. D. MACDONALD ON THE ZOOLOGICAL CHARACTERS with the jour long, conical, and perfectly retractile arms, which spring imme- diately in front of them. These arms are dotted over with minute rudimentary suckers, arranged quincuncially, and from between them arises a curious shovel- shaped and retractile proboscis. This latter organ is broad and depressed, termi- nating in a point anteriorly, and having, on the upper surface, a large oral opening with a thin circular lip. The dental armature of this proboscis is, with the excep- tion of that of Pnewmodermon, the most formidable amongst mollusca. In the middle of the floor of the mouth, and quite exposed from above, is a globular tongue, mainly composed of two broadly oval cartilages, overlaid with a lingual pavement of teeth, leading into a short saccule posteriorly. The median series of plates are crescentic, with the concavity directed backwards, and armed with a principal conical fang in the middle, and a rudimentary one on either side. The lateral plates are numerous, and bear a simple conical tooth on the inner side, with a small shoulder externally. In front of the tongue, the anterior or inferior lip is furnished with a transverse row of minute hooks, one in the centre, and an outlying one on either side, being larger than the rest. Behind the position of the tongue, and on each side of the oral cavity, is a shallow evertile pouch, lined with large gently curved conical teeth, which appear to enjoy a twisting or cork-screw action while they are being everted, so as to pierce and secure living prey when both cheek-pouches are brought forcibly in apposition. The upper or posterior lip is wholly unarmed, so as to admit of its expansion in receiving prey thus seized, probably torn up and forced backwards into the gullet by this most efficient and wonderful armature. Speaking of the lateral oval plates of Plewrobranchea, StEBoLD observes,—* To _ the same category belong the spines which Escuricut found upon the pharynx of a Clio, and described as jaws placed laterally, as in the Articulata, and fur- nished with long sharp comb-like projections or teeth,” giving a very false idea of the organs just noticed in Clio caudata, if they are indeed the same or similar in the northern Clio. The description of the head, tentacula, arms, proboscis, and dentition of Clio caudata just given, for the simple reason that it has been taken from life under favourable circumstances, will be found to agree but little even with the recog- nised characters of the genus, at least as they occur in systematic works. I have observed, moreover, that without any other apparent distinguishing feature some of the southern Clos had simple tapering tails (Clio a longue queue of the French), while others have three prominent ridges (the dorsal one frilled) meeting in a point posteriorly, so as to give a depressed trigonal section. On comparing a Clio with a thecasomatous pteropod, Hyalewa for example, the mouth and dental system in the former case will be seen to occupy the most advanced position, while in the latter they have receded so far within the limits of the foot as to give the animal an acephalous. appearance, and this view OF THE LIVING CLIO CAUDATA. 187 alone warrants the whole of the Pteropoda to be included under the term Cepha- lophora. The ease with which naturalists interchange names without any conciliatory explanation, is certainly a great stumbling-block to the beginner. Thus, if he were to fall in with Clio caudaia, as | have done, and immediately consult all the authorities within his reach, in some modern work he may find a figure of the creature he is in quest of, though denominated Clio australis, but on still further inquiry as to the authorship of that figure, he discovers that it is a lineal de- scendant of a figure of Clio a longue queue, given in the “ Voyage de la Bonite.” _Now, on comparing this with De BLaINnvILLe’s figure of Clio australis, he may probably perceive even generic differences between them; but, continuing his | search, he looks over one or two other modern books, and one can scarcely say whether his mind is settled, or his confusion is made still greater, to encounter stereotype repetitions of the figure of the said Clio australis of DE BLAINVILLE | boldly named Clio borealis. If there is indeed such an animal as Clio australis, and M. DE BLAINvVILLE’s figure is a correct representation of it, it is obvious enough that the species borealis and australis are members of the same genus; but as both differ so re- | markably from the so-called C. caudata, and the broad trigonal-tailed species, of | which I have given a short notice and figure, it strikes me that there are ample | grounds for the establishment of a new genus, to receive, at least, the two last- | mentioned species, while at the same time it will become apparent how little the nature of the respiratory system can be depended upon for generic characters, though it may be of great specific value. Not desiring to add unnecessary names to a list already large, | merely sub- } mit the views above expressed to the consideration of zoologists, who may form | their own judgment on the matter. The more important characters are simply | as follows :— Tentacula, two, minute, on either side of the head anteriorly; Cephalic arms, | four, perfectly retractile, long, and conical, with sucker points still more rudi- | mentary than those in Clio; Proboscis exsertile, broad, depressed, and pointed | in front; Oral aperture, superior, oval, with minute lower lip uncini; Cheek | pouches shallow, but evertile, and furnished with curved conical teeth ; Lingual pavement broad, with a median series. Setting the above characters aside, however, the original object of the paper | has been to show the great importance of the study of all soft, collapsible, and | contractile animals in the living and expanded state; for I am much of opinion. ' that the Northern Clio, examined in this way, will be found to present very similar | characters, or such as could not be arrived at by the most patient dissection of | spirit-preserved specimens. MR J. D. MACDONALD ON THE LIVING CLIO CAUDATA. Explanation of Plate IX. fig. 3. 1. Cho caudata, &c. 2. The second species alluded to in the text. Both are about the natural size; and the appearance presented by a trans- verse section, near the caudal ex- tremity, is given immediately below each figure, 3. Enlarged figure of the head, proboscis, and cephalic arms of Clio caudata in the expanded state. a. Proboscis, &c. b. Its pointed extremity. ec. Oral cavity. d. Anterior or lower lip, armed with teeth. d’. Do., magnified. 7d . Tongue with lingual pavement. . Portion of the lingual dentition magnified, . Lateral or cheek pouches, with their . Do., magnified. . The four cephalic arms, with their minute . One of the suckers magnified: 1. lateral . The four minute tentacula, of which the i. Head. . Swimming fins, . Auditory sac, with otoconia. curved conical teeth. suckers. view ; 2. in face. posterior pair is regarded as eye pe- dicles, . ¢ 189") XVIII.— Notes on the Anatomy of the Genus Firola. By Joun Drenis Macponatp, R.N., F.R.S., Surgeon of H.M.S. “Icarus.” Communicated by Professor Macniacan. (Plate IX. fig. 4.) (Read 5th January 1863.) In a successful haul of the towing net, off the Island of Sardinia, | obtained a very beautiful “rola, which gave me a good opportunity of testing the truth of my former conclusions with regard to the economy of the Heteropoda in general, and of Firola in particular; and I have great pleasure in submitting the facts arrived at, with the accompanying enlarged figure of the visceral nucleus and the neighbouring parts, to the Royal Society of Edinburgh, as an appendix to my paper “On the Anatomy and Classification of the Heteropoda,” already brought under its consideration.* I find that the relationship between /irola and Firoloides is even closer than I had originally imagined, and with the exception of the presence of gills in the former genus, nearly every anatomical point occurring in one may be distinctly traced out in the other, only differing in relative characters. To avoid unnecessary repetition, I shall simply explain the accompanying figure, and enlarge in passing upon any matters of importance that may suggest themselves. Explanation of Plate IX. jig. 4, a. Integument. 6. Muscular sheath. ec. Visceral nucleus, including the stomach, intestines, liver, testis, &c. d, Vesicula seminalis. All these organs are invested by an oval capsule, with its long diameter directed obliquely downwards and forwards, having the stomach at the lower end, and the trumpet-like vent above, and in front, lying in relation to the Sinus-system, the heart, great vessel, and cesophagus. e. Seminal opening. f. Intestine. g. Anal orifice, plicated internally, and richly ciliated. h. Gills, with their zig-zag folds, giving the organs a pinnate appearance, which is often in- correctly given in figures of the Heteropoda. ?, Ciliated fossa fronting the gills, the cilia disposed in a circular band, and undulating in the direction of the arrows, k. Sinus-system, communicating directly with the auricle of the heart (m), and everywhere intersected with muscular bundles and fibres. 1. Circular opening, leading into what I have been induced to regard as an inverted mantle- cavity, whose walls are much lobulated and highly contractile, so that the sea-water is ejected through the opening which is guarded by a sphincter. A vis e fronte effect * Trans, Roy. Soc. Hd., vol. xxiii. p. 1. VOL. XXIII. PART II. 3G 190 MRJ. D. MACDONALD ON THE ANATOMY OF THE GENUS FIROLA. would appear to be exerted on the blood entering the sinus-system ; for during the contrac- tion of the muscular fibres of the latter, and the systole of the auricle, diastole of the mantle-chamber is taking place. A great deal has been said about vital expansion in human physiology, but the instance just given is one in which the expansion of one chamber is facilitated by the contraction of another, having no internal communication with it; and this I believe to be the office of the remarkable organ in question, as an appendix to the auricle, which communicates so freely with the sinus-system. m. Auricle of the heart, or rather its proper position ; for its limits do not appear to be accu- rately defined. . Ventricle, with its closely interlaced muscular substance. . Principal vessel. . Gsophagus. . Stomach. . Long nerve-trunk, extending from the pedal ganglion to No. 2. . A small nodule of neurine, which, as I imagine, is chiefly respiratory, though it also sends filaments to the great vessel and esophagus. NS eo "Sse of 8 3. A stout commissural-nerve, connecting No. 2 with 4, The cardiac and visceral ganglion. 5. A conspicuous nerve, supplying the sphincter and radiating muscular fibres of the mantle opening, arising, as in Firoloides, from the ganglion No. 4. 6. A large commissural-nerve, passing from No, 2 to 7. A large saucer-shaped ganglion, lying immediately below the ciliated fossa (7). I can now safely say, that a body corresponding to this, though much smaller in Firoloides, is truly nervous ; but I cannot hazard any theory as to its office, though it is obviously in some way connected with that of the ciliated fossa,—probably with respiration. In my former paper, I stated my reasons for believing that the sexes are separate in the Heteropoda, and I am sure that this point will require no further proof, though, as far as the sanction of authority is concerned, the more general conviction even now is, that the sexes are combined. The uncertainty existing on the subject amongst zoologists, cannot be better represented than by the follow- ing quotation, verbatim, of Note 9, p. 264, Dr Burnert’s translation of SIEBOLD’s “ Anatomy of the Invertebrata” :— “* The penis is double, and at the right side of the base of the visceral sac, with Carinaria and Pterotrachea (MILNE-Epwarps, Ann. d. Se. Nat., xiii. 1840. p. 195; xviii. p. 328, Pl. x., fig. 3). Quoy and Garmarp (Voy. de l’Astrolabe, Mollusq., Pl. xxviii. fig. 10; or Isis, 1834, Taf. iii. fig. 10), have figured a long bifid penis, with Phyllirrhoé amboinensis ; and so, if with the other Hetero- poda, the penis is not retractile, as appears to be the case with Carinaria, accord- ing to MitnE-Epwarps this species would be a male; while Phyllirrhoé bucephalus, figured by Peron (Ann. du Museum, xv., fig. 1; or Kossz, De Pteropodum ordine, Diss. fig. 1), apparently without a penis, would bea female, although D’Or- BieNY (Voy. dans Amer. Mér.; or Isis, 1839, p. 519), regards this genus as hermaphrodite. With Aé/anta, there is a simple, pointed penis on the right side —_—e) MR J. D. MACDONALD ON THE ANATOMY OF THE GENUS FIROLA. 191 of the neck, directly near the arms; but as Rane (Mém., loc. cit., p. 378, Pl. ix. : or Isis, 1832, Taf. vii.) has found this penis with all the individuals he has examined, it may be questioned if the sexes are really separate with this Heteropod. « The internal genital organs of Atlanta and Phyllirrhoe, should be thoroughly studied for the elucidation of this point.” There are a good many references made in this note, but no satisfactory infor- mation is derived from any of them. The paucity of female Atlante, as indicated by M. Rane having only encountered the males, is perhaps the most interesting point. This was for a long time my own experience also, but on several occasions I have been fortunate enough to obtain indisputable females. | Though the position of Phyllirrhoé amongst the Nudibranchs and not with the | Heteropods, has been long recognised by zoologists, I may make the following remarks in passing, to clear up a desideratum in the note. First of all, the bifid penis of this mollusc is perfectly retractile, and its testicular follicles are included within the saccule of the ovaria, so as to form perfect hermaphrodite glands. The primary vas deferens and oviduct are blended together; and subsequently to the formation of stout fusiform spermatheca, the common tube divides into outer ovi- duct and outer vas deferens, the one passing into a wide glandular uterus, and the | other into one of the limbs of the intromittent organ. The bisexual nature of the | animal was known to Cuvier, though he could not have given this interpretation of it. Having examined some hundreds of recent Heteropoda, particularly the species of Atlanta, it struck me as being very odd, that I had never in a single instance succeeded in tracing a vas deferens onwards to the external male organ. This finally | led me to believe that the penis was imperforate, and as in Onchidium, Aplysia, Melo, and numerous other Gasteropoda, far in advance of the spermatic opening, both being held in communication by a ciliated groove, more or less capable of being converted into a canal. Of the truth of this doctrine, |] am now fully con- vinced, for the outlet of the spermatic duct, as given in the figure, and which is even quite prominent in /7roloides, is so palpable as to admit of no question; and on closely examining the duplex penis, I find by the simple test of focussing, that the so-called perforation and internal canal are nothing more than an external, deeply-grooved, and ciliated tract, the office of which is obvious enough. i. : 4 ; hae si colacal . yr ahi Serotec kn mi Rae ut, ». dais eenbegs ol yi ay fine \ rte easel med su a al las: Bipspsn sa) ay oN inf ar . PE White Sie 1 yoeur pone y be ,: Pr eee te Shiteyuit Tents te cw bis "ae i? keel 4 P goles Aiea ebyas Gaon bal 4, Bit st at ir. J be a n latar rime ra treayorts Mga +e Sadie clan ane ters | Lito oniet MF Saher. ve eect ite nf ies - is bt etn 4 cabec vet Sai ; sig beat ye hae oh orth euahees a Res ‘és tf. soi heed 4 “ rir%e ied 4. Pe y Aykis} ¥ a ry “Utey ae eee et, ¥ yy prs . ‘ 7 i a # mia 7 Pw nag ‘os ey wae y bane Perna 4 pat wi » “ J ota & Pe j ' a 7 } x A 7 y y + hd pele. ME elise) Rye CR aie aa « de ‘ ee ye : “+, n J | Nay at Re Ob Se iy | ts ’ ( 4 s pbit ‘ . ion me Beha icsgeits | ioe le mn | 4 Z af a pet DD , i 4 ~ wy ) \ =. ‘op, a.) > “he £4 free u Te Bio $; : ie] O29 = igtan P i \ 4 \ ye pay és nN { x ec oily a . } aeerarY pe if, ita Shae? OT beer wih hs ie x 7 7 Phas 5 * 3 ga: * mt - ei ae ,% . é - Ti x} +f As on 1 : es ne is =e : eo ~ ‘ " ACTIONS OF THE ROYAL SOCIETY, EDINBURGH. PLATE IX VOL. XXIII. | Fig. 3. . 5 = MDONALD R.W. DELT. F Schenck 12.R! Exchange Edin? 1 * Cr see XIX.—On the Structure and Optical Phenomena of Ancient Decomposed Glass. By Sir Davip Brewster, K.H., D.C.L., F.R.S., &e. (Plates X., XT.) (Read 5th January 1863.) The disintegration of solid bodies by means of active or feeble solvents, or by those invisible processes which go on during long periods of time, has, so far as I know, been studied neither by the chemist nor the natural philosopher. In 1837 Isubmitted to this Society a paper “On the Optical Figures produced by the Disintegrated Surfaces of Crystals,’* containing experiments which I believe have not been repeated, and results which no person has attempted to explain.} Since that paper was published, my attention was called to the structure and properties of decomposed glass, in consequence of having had occasion to study the action of its coloured films, in absorbing definite parts of the spectrum. The specimens, however, which I received for this purpose from the late Marquis of NortHampron, Mrs Buckuanp, and Mr Cuinpren, and referred to in my “ Experiments on the Connection between the Phenomena of the Absorption of Light and the Colours of Thin Plates,” { did not enable me to investigate the con- dition of the elementary films, and the process by which the various states of the glass were produced ; but having received, while in Rome in 1857, very fine speci- mens from the museum of the Marquis of Campana, and more recently other speci- mens from Nineveh, from Mr Layarp, I have been able to obtain the results con- tained in the following paper, and represented in the drawings which accompany it. The decomposition of glass in its early stages is finely seen in the brilliant colours which cover its surface. These colours are those of thin plates, and tints of the third and fourth orders in NEwtTon’s scale are produced in the course of thirty or forty years on the inner surfaces of panes of glass in stable windows. The elementary films which display these colours are not in optical contact with the glass beneath them, though they adhere to it very firmly. They may be removed by the point of a knife ; and in this state the powder is white by reflected light, and semitransparent when surrounded with water. * Edin. Trans., vol. xiv. p. 164. + Since this paper was written, I have received from Professor Von Kosett, of the University | of Munich, a very interesting paper, entitled ** Ueber Asterismus und die Brewsterschen Licht- | figuren,” in which he gives an account of my experiments, and adds many new and important ones of his own, illustrated with three plates. It is published in the Sitzungsberichte der Koniglichen Baierischen Akademie der Wissenschaften: Sitzung der Math.-Phys. classe, 8 Feb, 1862. A very full and excellent abstraet of this Paper appeared in the Parthenon of 6th Sept. 1862. { Phil. Trans,, 1837, p. 245. VOL. XXIII. PART II. 3H 194 SIR DAVID BREWSTER ON THE STRUCTURE AND Even when the glass has been exposed only to the air of the atmosphere, these coloured films are produced sometimes in twenty or thirty years on the surface of glass, whether formed by fusion or by artificial grinding and polishing. But as other surfaces of glass, similarly exposed, and of a much greater age, show no marks of decomposition, it seems evident that the rate of decomposition must depend upon the composition of the glass, and probably on the temperature at which its elements have been combined. A very remarkable case of rapid decomposition presented itself to me in a fine plate-glass prism, made for Mr Tausot by FRAUNHOFER at Munich, and presented to me by that distinguished philosopher. On the 23d March 1833 I made accurate drawings of its three faces, on each of which there was a circular spot, in which the decomposition showed itself in three rings or orders of the colours of thin plates. In one of these spots, half of which is cut off by the edge of the prism, the colours in 1833 were three orders, the innermost being a — yellowish-green of the third order. This spot is about a quarter of an inch in diameter. Another spot about the same size is perfectly circular, the outermost ring being the white of the jist order, rising in the centre to purplish-blue of the second order. The third spot, about the 16th of an inch in diameter, is perfectly circular, the innermost tint being a ed of the second order. These colours, which are very difficult to be seen, are those observed at the polarising angle of the - glass, when the reflected light is nearly extinguished by an analysing prism. Upon examining these decompositions after an interval of thirty years, I can- not observe any change in the rings and colours. They seem to be fainter than before, and, what is very remarkable, two long irregular streaks of decomposition, — one an inch long, and the other nearly two inches, have entirely disappeared. In the shortest of these lines of decomposition, the tints of some parts rose from blue to yellow in the longest, and in a very small circular spot the tint was only blue. The pause in the process of decomposition in the three circular spots, and the disappearance of the long streaks, is very remarkable,—and the more so, as they must all have been formed during a period certainly not greater, but probably very much less, than twenty years. Is it not possible that the particles which have separated from the glass by the action of the decomposing cause, and — ceased to be in optical contact with it, may have returned into optical contact when the decomposing cause no longer existed, as might have been the case with the prism if kept, as it has been, in dry air since 1833? That this is not an unreasonable supposition, may be inferred from an experiment published in 1816, in which one of the surfaces of a fissure made artificially in a thick plate of glass was so much separated from optical contact with the other surface, as” to reflect totally light incident upon it at a certain angle. “ After standing an hour the fissure began to disappear, and in the course of a day it was as OPTICAL PHENOMENA OF ANCIENT DECOMPOSED GLASS. 195 _ completely closed as if it had never been made,”* the surfaces having returned into optical contact. When we examine the surface of decomposed glass, either before or after the removal of the film, we find it composed of an infinite number of cavities, in the middle of each of which the decomposition has begun. At this point a particle of glass, of a certain size, has detached itself, and a film is formed by the ageregation of other particles of the same size. This decomposition extends itself in all directions, but more quickly downwards beneath the first particle that was detached. The consequence of this is the formation of a cavity or cup, which would | be part of a hollow sphere if the centres of decomposition were at great distances and few in number. In general, however, these centres are innumerable, cover- | ing the whole surface of the glass. From this cause, the decomposition round | any one centre meets the decomposition round other centres, and the form of the cavity is an irregular polygon, the shape of which depends upon the distances of the centres of decomposition. The lines in which the decompositions meet one another resemble the meshes of a net, or the lines which separate the small films or partitions that confine between them small quantities of gas, forming the froth of champagne, beer, and other liquids. | When the cavities of decomposition are very numerous and equally diffused, | they are often so minute as to be invisible, and their existence is shown by | different degrees of roughness, as if the surfaces of the film had been ground, and | sometimes by producing halos or rings round the flame of a candle. | In several specimens the surfaces of the films are perfectly specular, showing | that particles of the same size have been uniformly detached from the original | surface, and that the decomposition has not taken place around and beneath dif- | ferent centres. | When we consider the different states of fusion and cooling to which glass is exposed, whether it is formed by flashing, or blowing, or moulding, it is evident | that the processes of decomposition must take place in spots or in lines where the | elements of the glass have been less perfectly combined, or where the cohesive } forces are more feeble. In many films, where the decomposition has been pretty uniform, there are | often numerous centres distant from each other, where very deep cavities have | been formed. These cavities are perfectly circular, as in Plate X. fig. 1, and | Plate XI. figs. 6, 7, 8, &., and have different diameters and different degrees | of depth. In other films these circular cavities are crowded together so closely as | to occupy the whole of its surface, as in Plate XI. figs. ll and 13. . In many specimens the centres of decomposition lie in straight lines, and | Near each other, as shown in Plate X. fig. 5. One cavity thus encroaches upon * Phil. Trans., 1816, p. 73. 196 SIR DAVID BREWSTER ON THE STRUCTURE AND another, and a long groove is excavated, the bottom of which is formed of spherical cavities of different depths and breadths, depending on the distances of the centres of decomposition, and the rapidity with which the decompositions have taken place. The form of the grooves is thus very irregular, being wide at one place and narrow at another, and occasionally not rectilineal. When the centres of decomposition are very near each other and equidistant, the grooves are very narrow and shallow, and form straight lines of uniform breadth. These grooves or lines of cavities lie in different directions, frequently crossing one another at various angles. In some specimens they are perfectly parallel, and are often not more than the 500th or 1000th of an inch in breadth, having the appearance of lines of uniform thickness. When the cavities are of considerable size, and nearly or perfectly spherical, they sometimes present remarkable phenomena. Round one or more points of the spherical films or cavities, a fresh decomposition has taken place, and-formed smaller spherical cavities, sometimes almost touching one another, as in Plate X. fig. 4, and Plate XI. fig. 6; and occasionally so numerous, that I have found from fifteen to twenty formed upon the same cavity. In some cases the decomposition has produced shallow cavities, which, from interfering with one another, have become polygonal. In some specimens this secondary decomposition has taken place at such a great number of points, that the infinitely small cavities which it has formed appear like specks of black powder, making the cavity more or less — opaque, according to the distance of the specks, or the number of films of which the cavity is composed. When the cavities do not interfere with one another, they are occasionally — ellipsoidal, and egg-shaped, though formed from one centre of decomposition. Specimens of these structures are given in Plate X. fig. 3, and Plate XI. figs. 7 and 12, seen by ordinary transmitted light. In Plate X. fig. 5, are shown circular cavities, and cavities in lines of uniform and variable breadth. The com- pound film consists of many elementary films, but only three or four are shown — in the figures, as they alone are visible in the specimen. If we remove with a lancet those films in succession, we shall find that each film contains all the cavities existing in the compound one,—the spherical or polygonal cavity, whether deep or shallow, being joined to, or forming part of the film. When examined on one side all the cavities are convex, as shown in Plate XI. fig. 11; and when examined on the other they are concave, as shown in Plate XI. fig. 13. In comparing this structure of the films with the process of decomposition shown in Plate X. fig. 1, it is not easy to understand how the concave or convex parts of the film are united to and form part of the general film. The process of decomposition having begun at one point, where the cohesion of the particles is the feeblest, it advances, forming round that point a number of spherical films, before the decomposition has commenced on the surrounding glass. When the surface OPTICAL PHENOMENA OF ANCIENT DECOMPOSED GLASS. 197 of the glass begins, or is ready to decompose, the spherical film then forming will - extend itself over the glass, and form part of the general film. If the decompo- sition has begun at different times round different centres, and proceeded with different velocities, the spherical film in every cavity, whether deep or shallow, will extend itself over the general surface. If this is a correct account of the pro- cess, then we ought to find in every cavity a central portion having no connection with the general film, because formed previous to the decomposition of the general surface. When we remove the outer crust from the decomposed glass, we find this to be the case. The central portions are removed with the outer crust; and in some cases I have found the cavities filled with that portion, in consequence of no decomposition having taken place on the general surface. It is difficult to comprehend the nature of the molecular forces under which _ these singular decompositions assume peculiar forms. There is no difficulty in | understanding how, in a homogeneous surface of glass, decomposition round a centre should excavate a perfectly spherical cavity, and how its ultimate form should be changed into that of irregular polygons, by the interference of decom- | positions advancing from surrounding centres; but it is a singular circumstance _ that the glass should be in any one place in such a state of molecular incohesion, | that the decomposition should follow a law which produces a perfectly ellipsoidal | cavity. Nor does it seem less remarkable that after a cavity, either spherical or _ ellipsoidal, or irregularly polygonal, has been formed, spherical cavities should be | formed on different parts of the films which compose them. The preceding observations have been made on films of glass from Nineveh | and Rome, after the opaque or outer films had been removed. Each film, there- | fore, has on one side all its cavities concave, and on the other side all of them ' convex, like a bundle of watch-glasses. Each film consists of many films, which | can be separated by the thin blade of a knife or lancet, adjacent films differing from one another only in their thickness and colour. The films, though adhering | with some force, are not in optical contact, as they freely admit water, and other | fluids between them, and display the fringes of thin plates produced by the dif- | ferent thicknesses of the interposed films of air. The mode in which the decomposition proceeds round different centres is shown in Plate X. fig. 1, taken from a specimen of glass from Nineveh. The | same structure is less perfectly seen in fig. 2, taken from glass found also at | Nineveh. When the glass has lain on damp earth, the decomposition has taken place very irregularly round separate centres. It consists of two thick crusts of opaque _ vitreous matter, enclosing a plate more or less thick of pure glass, with deep ex- | cavated cavities on both of its surfaces. A specimen of this kind breaks by the | pressure of the finger like the slice of an apple. In a finely-shaped glass bottle | found near Cheltenham, and presented to me by Mr Sypney Doset1, a thick grey | crust of iridescent films, of uniform thickness, covers the whole of its surface, and VOL. XXIII. PART II. 31 198 SIR DAVID BREWSTER ON THE STRUCTURE AND gives it the appearance of granite. The iridescence of the films is, however, dis- tinctly seen; and when the crust is removed the transparent green glass appears, with its excavated surface. The decomposition of glass goes on rapidly in water. In a wine bottle brought up from the wreck of the “ Royal George,” very considerable films were formed on its surface. Bottles of the form called “ magnums,” which were found in the Cherwell, near Oxford, by Mr R. THomas, were encrusted with films of consider- able thickness. From one of these Mr Tuomas detached a circularly-shaped film about half-an-inch in diameter, which had a spiral crack proceeding from its centre, and having eight or nine circumvolutions. This film, which was one of unusual thickness, was a single one, as is shown by its producing none of the colours of thin plates at any inclination, and by its action on common and polar- ised light. Though perfectly transparent, its surface is not specular, but mottled with the colours of striated surfaces, the points of decomposition by which they were produced being visible by high magnifying powers. From the facts I have mentioned, it is evident that the decomposition of glass is accelerated when it is exposed to the action of acids and alkalies in damp localities, and particularly to the ammonia so abundant in stables. M. Brame, of Paris, having seen a notice of the decomposed glass from Nineveh, which I had read at the British Association some years before, was led to submit thick plates of glass to the action of powerful solvents. Ina short time circles were produced analogous to those which I had observed in the Nineveh specimens. * 20) Ls 218 SIR DAVID BREWSTER 1842, April 13.—Barom.3012. Fine day. R=Maximum Polarisation. Height of Neutral Point above Apparent Time. In Zenith. In Horizon. the Antisolar Point, 5h 48m py, see ari Le] 2 6.20) my 29 294 17. 55 6 64 292 « 19 40 7a0U., i 19 465 19665, 30} 19: £04 754 , . 22 10 At 7" 32™ the maximum polarisation was 323, the greatest ever observed. (See p. 250.) 1842, April 20.—Barom. 30:02. Apparent Time. Wind west; very fine day. Height of Neutral Point above the Antisolar Point. 22° 50 19 21 20 55 20 10 24 8 5h 50™ p.m. 6.29" « 6189 -Ly,, Fh 15 ar oo ee 1842, April 26.—Barom. 30-00. night. Apparent Time. Not a cloud in the sky from morning till Height of Neutral Point above the Antisolar Point. 5h 21m pw 13°. -437 GiuhGe., 13 | uae Gad ai. 19 28 Rn Bites 20 10 i a 19 15 1842, April 29. Apparent Time. Height of Neutral Point above the Antisolar Point, 5 54m pu, 18° aa vi, 18 35 onde Kis 22 25 1842, May 15.—A haze. sem te. Height of Neutral Point above R=Maximum Polarisation. In Zenith. In Horizon. the Antisolar Point. 65 29™ p.m. aRs}y 15° PR Say 646°". 2 § oR 28 12 ts OG 203 a 24 6 826, 232 ie 19 59 1842, November 14.—Barom. 29:6. Fine frosty and clear morning. R=Maximum Polarisation. In Zenith. In Horizon. opi 193° Apparent Time. 8h 56™ aM. Giles 9 16 9 31 9 43 Ode) i Height of Neutral Point above the Antisolar Point. 19° 50’ 16 40 15 22 16 0 14 30 13 45 ON THE POLARISATION OF THE ATMOSPHERE. 219 1842, November 20.—Barom. 29°74. Cold and clear. Reeen Bina R=Maximum Polarisation. Height of Neutral Point above . In Zenith, In Horizon. the Antisolar Point. 10h 8™ a.m. 214° =a 1g7" 'b foes”. at Me, : 17 30 ye ae * a 16 25 foe39\! ws be 45 15 io 65, 15 5 11 0. ,, Neutral point lingering in the horizon. 1842, November 21.—Barom. 29°77 ; therm. 31°. Frosty morning. Apparent Time R=Maximum Polarisation. Height of N eutral Point above : In Zenith, In Horizon. the Antisolar Point. gh 1™ am. sie nae 2172 LO/ Ba lag s ,, 263° | 193° 20 25 a aes tare 15 46 12 22 pm. Neutral point below land horizon; bands scarcely visible in horizon. 12 43 ,, Neutral point in horizon. BuO, 55 16 30 The decrease in these numbers as the sun’s altitude increased is very interest- ing. The light of the sky was increasing till noon, whereas, when the numbers increase, the light of the sky diminishes. The observations on the 14th, 20th, and 21st Nov. were the only morning ones I made. 1842, December 28.—Barom. 29°56. Sky very fine at 11" 38". Apparent Time R=Maximum Polarisation. Height of Neutral Point above : In Zenith. In Horizon. the Antisolar Point. 11» 38" p.m. 29° eee 17° 20 11 58 ,, 27 183 V7) 1 Me 0) vie ree ae 18 25 HIZB G5 ase he oe 6 eat... 143 ot 22 15 See in p. 237 the state of Baniner’s neutral point at this date, when a halo of 45° encircled the sun. 1843, February 2.—Barom. 29:05. Snow storm with wind. Aareameny ine R=Maximum Polarisation. Height of Neutral Point above ge cs In Zenith, In Horizon, the Antisolar Point. 9» 55™ a.m. 243° 173° Polarisation of the sun’s light by the snow hardly perceptible, whether we look towards or from the sun. ee 2. 5 p.m. Neutral point in sea horizon. ae SOP iy eb! Die: ames 263 193 14 35 1843, February 14.—Barom. 29:45. Bitter cold day ; frost in the morning. : R=Maximum Polarisation. Height of Neutral Point above Apparent Rime, In Zenith. In Horizon. the Antisolar Point. 28 48™ a.m. Neutral point below horizon. ... 1 se vera 8 Neut. pt. oar Pt. logy 232 1 45 {in horizon i" VOln SX. PART II. 3P 220 SIR DAVID BREWSTER 1843, March 25.—Barom. 29:97. A ‘Ti R=Maximum Polarisation. Height of Neutral Point above Ppere re eee In Zenith. In Horizon. the Antisolar Point. 4> 35™ am, 25° Neutral point in horizon, 10) ‘var Selo we, as ane LT» 30 baddee\, 28 aa 18 3k Grioa., 294 ae 17 736 1843, June 21.—Barom. 29°75. Fine day; wind west. s tT R=Maximum Polarisation. Height of Neutral Point above PP BNE Ans In Zenith. In Horizon, the Antisolar Point. by > N. pt.in é h 1 ° bg 7 19m aw, O74 203 | ae ee \ 9° 40} SA ee ae =e 16> at gis0'%,, 29 a 19 22 Or 164s.. 30 * 18 29 1844, February 3.—Barom. 29:90. Snow covering the ground. ik t Ti R=Maximum Polarisation, Height of Neutral Point above ee ala In Zenith. In Horizon. the Antisolar Point. 45 7m am, 26° 23° 18° 20’ 1844, February 21.—Barom. 29:28. Snow partially covering the ground. Apparent Time R=Maximum Polarisation. Height in Neutral Point above F In Zenith, In Horizon. the Antisolar Point. 35 30™ a.m. + bl ate 13° 9B 4™40'> §, 284 ahs 12 35 4 LON pay 283 a 17 34 4°40° * nd +: 19 24 1844, June 10.—Barom. 29°70. Apparent Time. R=Maximum Polarisation. Height of Neutral Point above In Zenith. In Horizon. the Antisolar Point. 75 36™ a.m. iets sit 2159 SA a) 4400 4, ae = 21° 20 Biddots 243 224 21 35 Bih2 a Q74 234 21 50 1844, June 13.—Barom. 29°4. Windy; wind south-west. m tT R=Maximum Polarisation. Height of Neutral Point above Dae. In Zenith. In Horizon. the Antisolar Point. 72 Om a.m. Neutral point in horizon, 2) Ti Ae Wet Ooh 243 203 1394 "2 In the following observations, the altitude of the sun was not estimated. The numbers in the fourth column are the altitudes of the neutral point above the horizon. 1845, April 15. Atsterend Tine R=Maximum Polarisation. Height of Neutral Point above mt ; In Zenith. In Horizon. the Horizon. 5) 48™ a.m, 263° 223° a. zoe Gy ALB. ks 274 244 18 50 ON THE POLARISATION OF THE ATMOSPHERE. 221 In the normal state of the atmosphere, as represented in the Map, Plate XII., namely, when the sun is in the horizon, ArAGo’s neutral point is about r 18}° above the horizon, or above the antisolar point; but when the sun is 11° or 12° above the horizon, and the antisolar point as much below it, the neutral point is in the horizon, and consequently only 11° or 12° above the antisolar point.* As the sun descends to the horizon, and the antisolar point rises, the distance of the neutral point from the latter gradually increases; and when the sun reaches the horizon, the neutral point is 184° above it, and therefore 183° distant from the antisolar point. After the sun has set, the distance of the neutral point from the antisolar point increases; that is, it rises faster than the sun descends, and its maximum distance, when the twilight is very faint, is about 25°. When the sun is advancing to the meridian, and the light of the sky is in- creasing, the distance of the neutral point from the antisolar point diminishes, as shown in the morning observations on the 14th, 20th, and 21st November 1842. On a Secondary Neutral Point accompanying Araco’s Neutral Point. When the sea horizon was terminated by a dark purple belt about 13° above it, I observed that the vertical bands of the polariscope became brighter over that belt. The same phenomenon was seen, but less distinctly, over the land horizon. It was difficult to measure the amount of this new polarising influence, but it was obvious that we should observe it separately when the neutral point came above the belt. In this case, it would eclipse, as it were, the neutral point, which would recover itself when it emerged from the belt. It was obvious also, that when the negative or oppositely polarised bands came over the belt, the new polarising influence would extinguish them where they had the same polarising force, and form a secondary neutral point, the primary one being then out of the belt. On the 8th of June 1841, at 5’ 50" p.m, when the polarised bands were strongest, both on the land and sea horizon, I watched the rise of the neutral point, which, as I had foreseen, did not appear first im the horizon, but about 13° above it, the compensation taking place where the vertical or positive polarisa- tion was weaker than in the horizon. We had now the singular phenomenon of a neutral point with positive polarisation on each side of it. When this phenome- non was more fully developed under a favourable state of the horizon, the positive * In abnormal circumstances, sometimes only 7°, 8°, 9°, or 10°, as in 1842, February 15 and 16, 222 SIR DAVID BREWSTER polarisation was overcome by the advancing negative polarisation. The negative polarisation was then immediately below the ascending neutral point; but at a certain distance (a few degrees below the neu- tral point), the negative polarisation was com- pensated by the excess of positive polarisation close to the horizon, and the beautiful pheno- menon was seen of two neutral points, a primary and a secondary, separated by bands of negative — polarisation, as shown in the annexed figure. 1841, June 10, 6" 40°.—The neutral point a little above the horizon, with vertical or + polarisation on both sides of it. The new verti- cal polarisation had more than compensated the horizontal, or negative polarisation, and left a balance of positive polarisation, which soon dis- appeared when the rising horizontal polarisation overpowered it. 1842, Feb. 22.—Both on this day and on the 13th, the neutral point was above the horizon, though not visible, being eclipsed or masked by the cause which produces the secondary neutral point. Over a space of 34° above the sea, the positive bands almost wholly disappear before the negative bands are perceptible, and the neutral point is 5° high when the secondary neutral point is distinct in the sea horizon. Although I have observed the secondary neutral point more than twenty-two times, it has generally appeared under slightly different forms, varying with the intensity of the new polarising cause which produces it, and with the point of the horizon where the neutral point rises. It is unnecessary to describe these different forms,—I shall mention only an observation made on the 21st April 1849, under very favourable circumstances. At 6° 22™, when the primary neutral point was about 15° high, the secondary neutral point was 2° 50’ high, the negative bands covering a space of 8° or 9° between” them, the positive bands being above the sea-line. A fog prevailed to some extent, and above the sea-line there was the dark purplish belt previously men- tioned, over which the positive bands were stronger than on the part of the sky above it. Fig. 3. Observations on Basinet’s' Neutral Point. In the year 1840, when M. Baztnet had occasion to visit the sea coast, he proposed to observe if the neutral point of Arago varied in its height as the sun rose or set, and to observe it also when the sun was beneath the horizon; but he was allured from these observations by a circumstance which he had never even suspected, namely, the existence of a second neutral point above the setting sun, ON THE POLARISATION OF THE ATMOSPHERE. 223 and nearly as high in the atmosphere as the neutral point of Araco. “I after- -wards,”* he says, “ determined, a great number of times, the position of this new neutral point which appeared in the west, even when the sun was just on the horizon before setting, and in the east when he had risen only a few degrees. A very imperfect estimate made me sometimes believe, that this new neutral point was a little less high than that of AraGo.” The following observations on this neutral point were made generally on the same day, and even in the same hour, as those on ARAGo’s neutral point, and | therefore under the same atmospherical influences. 1841, May 12.—Wind west in the evening. mean iane: Height of Neutral Point above the Antisolar Point. 8" 10™ p.m. 16° 4’ 1841, May 16.—Barom. 29:24. Windy. MeaasTiine, Height of Neutral Point above the Antisolar Point. 7) O™ p.m. 83° 1841, June 10.—Barom. 29:27. Very fine sky. hen ae Height of Neutral Point above the Antisolar Point. 10210™ 4m. Sun’s altitude about 50°, 2° or 3° Te (eee Sve ells 735 |, ey 7 52 |, i4**: 5 g he: 16 37 8 21 .,, . Sunsets. 15 DoT STOLE ty ila 15 8 52 ,, 16 | 95 ON 8 os & 16, 42 9 15°, 16° 90 1841, September 6.—Barom. 29°55. Mean Time Height of Neutral Point above the Antisolar Point, 6h 30m 16° 15’ 6 45 14 45 6 58 12 55 Cite 8 13 8 1841, September 12.—Barom. 29°75. Sky clear. Mekn Tine. Height of Neutral Point above the Antisolar Point, 6h 54™ 18° 53’ een) 18 20 1841, September 29.—Barom. 28:73. After rain sky clear. Height of Neutral Point above Mean Time. the Antisolar Point. | 5h 46m 12° 53’ | 5 BT 14 55 6 7 16 15 * Comptes Rendus, &c., 1840, tom. xi. p. 619. VOL. XXIII. PART II. 3 Q 224 SIR DAVID BREWSTER 1841, October 23.—Rainy day; cleared up at 3° p.m. F R= Maximum Polarisation. Height of Neutral Point above Mean Time. In Zenith. In Horizon. the Antisolar Point. 4h 21m 2M ue 17° 33 27 274° 254° 15 35 30 ne igre 14 30 39 oat 15, ee 45 26 251 14 22 53 ase 15 63 1841, November 2. Te Height of Neutral Point above the Antisolar Point. 4h 50m 14° 51’ 1841, November 4.—Barom. 30:2. Foggy day; sky tolerably free from clouds. Height of Neutral Point above Mean ene: the Antisolar Point. 35 13m 14° 4’ Ase 19 0 4 14 17 48 1841, November 25.—Barom. 29°63. Splendid day. R= Maxi Polarisation. Height of Neutral Point ab specitines, 6 gt ee, | 10" 31™ p.m, aie he 3°, 20 Eg aie a7h° 253° 6 24 ee ae : as 12 5 BOA 283 264 ts 27 3 10 oe 16 35 ”? 1842, January 29.—Barom. 29:93. Fine day; clear sky; snow covers the ground partially. re t Ti R=Maximum Polarisation. Height of Neutral Point above Puen apc In Zenith. In Horizon. the Antisolar Point. gh 39m 27° 212° 16° 35) 3 63 nos bo 17 38 A sae iB ite ode 17), ot 1842, February 15.—Rain in morning, then a fine day. * t Ti R=Maximum Polarisation. Height of Neutral Point above 1 oe ge aa a In Zenith. In Horizon. the Antisolar Point. 4h 95m a aon 21° -5o8 4 44 Hee Bo 20 24 4 55 215 223°in S.E. Hor. 20 30 At this hour clouds rose in the S., N., and N.E. horizon; a. dark band of distan : haze 6° or 8° high rose above the sea horizon. 1842, February 21.—Fine day ; wind west. Height of Neutral Point above Apparent Time. the Antisolar Point. 4h 35m 18°" 7" 5 8 18) 32 1842, March 2.—A wet day; the place of the sun was seen only as a whit spot. The polarisation everywhere feeble. . a4 ON THE POLARISATION OF THE ATMOSPHERE. 225 2h 20™.—The neutral point was 75° above the horizon, or about 54° above the sun. The polarisation was negative from the neutral point to the horizon beneath the sun, and positive to the horizon opposite to the sun. 1842, March 16.—Barom. 29:96. The sun occasionally shining through a thickish haze in a China-ink sky without any blue; the wind in the south-west, and slight. 10+ 45™.—Sun’s altitude about 303°; the polarisation below the sun was negative down to the horizon ; the neutral point was 30° above the sun, or more than 60° high! 1842, April 5.—Barom. 30:07. Splendid sky. Apparent Time. R=Maximum Polarisation. Height of Neutral Point above In Zenith. In Horizon. the Antisolar Point. 65 23m 30° 263° NOR a luge 6 58 es sists 18 46 ed 303 i 15 45 The polarisation was unusually great, equivalent to a rotation of the plane of polarisation of about 29°; it became stronger as it grew darker. N.B.—This day and April 8th were the only days on which I was able to observe the three neutral points, and determine their place. (See pp. 217 and 229.) 1842, April 8. Apparent Time R=Maximum Polarisation. Height of Neutral Point above In Zenith. In Horizon. the Antisolar Point. 6h Om 241° 183° 17° 6" 6 25 id be 18 20 6 45 27k ee 19 11 tas 998° 2 “ 21 5 v*. 20 bad Pe 19 31 1842, April 13.—Barom. 30°12. Fine day. Bese rent ge NG arama 1 elght ot Metis shots 5h 51m ae ae 18° 50' G23 29° 223° 133, (0) 6 58 294 on 18 40 7 ee ae 17 35 7 21 303 ea zr ar At 7" 32™, the maximum polarisation or rotation was 324°, the greatest ever observed. (See p. 235.) 1842, May 15.—A haze. é R=Maximum Polarisation. Height of Neutral Point above Apparent Time, In Zenith. In Horizon. the Antisolar Point. 6h 34m 15° 15° 18° 10 6 48 ile ae 19 55 7 28 203 a 17 44 8 29 23h jah ise a 226 SIR DAVID BREWSTER 1842, November 14.—Barom 29:6. Fine frosty and clear morning. ‘ R=Maximum Polarisation. Height of Neutral Point above Apparent Time. In Zenith. In Horizon. the Antisolar Point. 8h 58™ aw, 252° 193° a” 7 1842, November 21.—Barom. 29°77. Frosty morning. Thermometer 31°. Height of Neutral Point above the Antisolar Point. gh 4™ 4M. 18 36 Apparent Time. 1842, December 28.—Barom. 29°56. Appsrent Tina, , Riana Telia isin of ae 115 40™ am. 29° EN. T3044" Ce eee 27 183° 13 3g af Torii we i 25 25! 23 PM ee cal 27 30! g tay Bt- 143 s 27 48! These remarkable results were doubtless owing to the causes which produced the following phenomenon :—At 1" 4", when the neutral point started away from the sun, a white halo of 45° appeared round the sun, and continued till 2" 31". It was slightly brown on its inner rim. At 1 23™ the altitude of the halo was 32° 10’, and the sun’s altitude 8° 30’, so that the radius of its outer rim was 23° 40’. When the vertical bands of the polariscope passed over the apex of the halo, their intensity was increased, and when they passed over the halo in a direction parallel to its horizontal diameter their intensity was diminished. As the crystals of ice, by which the halo was produced, are doubly refracting, one of the pencils must have been weaker than the other, an effect which would be produced if the surfaces of the crystals were not perfectly smooth. * The polarisation of the sky was greatly reduced by the crystals of ice floating in the air, which produced the halo. 1843, March 25.—Barom. 29:97. i t Time R= Maximum Polarisation, Height of Neutral Point above ppareny ne In Zenith. In Horizon. the Antisolar Point. 5b 46m 28° Bae iste Dip 6 it 291 at 17: Al 1843, April 17.—Barom. 29°84. Fine day; wind east. Height of Neutral Point above Apparent Time. the Antisolar Point. 62 33m 17° 32 | 18 4 7 33 18 44 1843, April 29.—Barom. 29°63. Wind east. The heat of the rising sun very great, and the vapour rising copiously from the ground. Everything more than * See Phil. Trans., 1819, p. 146. ON THE POLARISATION OF THE ATMOSPHERE. 227 a quarter of a mile distant invisible. The sun shone occasionally, showing his _ pale white disc. Apparent Time. 10" 20" a.m. The bands were negative from the zenith through the sun to the horizon, and positive to the opposite horizon. The maximum polarisation was 90° from the sun, but was so weak that it was compensated by the refraction of a plate of ground glass, at an angle of incidence of about 30°, the negative bands being then scarcely visible. 9» 55m, The vapour still rising copiously, and the place of the sun not visible. The bands were hardly visible, the polarisation, when a maximum, being compensated by the refraction of a plate of glass, at an angle of 5°. 1843, May 3.—Barom. 29°65. Easterly haur. Apparent Time. 44 25™, Mist flying before the sun, and the neutral point oscillating from near the sun to the zenith as the mist thickens. 1843, June 21.—Barom. 29°75. Fine day ; wind west. é R=Maximum Polarisation. Height of Neutral Point above Apparent Time. In Zenith. In Horizon. the Antisolar Point. 75 46m 2. so0 15° 55’ 8 33 29° ae ie On 9 14 30 ane 16 28 1844, Feb. 3.—Snow covering the ground. Apparent Time. R=Maximum Polarisation. Height of Neutral Point above In Zenith. In Horizon. the Antisolar Point. 4h ]]m 26° 23° 17° 55’ 1844, April 15. Height of Neutral Point above Apparent Time. the Antisolar Point. 5h 54™ 2086) 6 50 18 10 1844, June 10.—Barom. 29°70. Apparent Time. R=Maximum Polarisation. Height of Neutral Point above In Zenith. In Horizon. the Antisolar Point. gh 20m 243 18° 14’ In anormal state of the sky, when the sun is rising or setting in a fine day without clouds, the neutral point of BaBrnet is situated about 18° 30’ above the | sun. Owing to the great quantity of light in the neighbourhood of the sun, this | neutral point is not so easily seen as that of Araco, and escaped the scrutiny of that distinguished observer. In high latitudes it is above the horizon the greater | part of the year, and, being above the sun, it is of course always visible in a clear | sky, when he is above the horizon. When the sun is in the zenith, this neutral point coincides with the sun’s centre, its distance from the sun gradually increasing | till it becomes 18° 30’ at sunrise or sunset, when the sun’s altitude is nothing. \ Like that of Araco, the neutral point of Basrnet must be accompanied, in / certain states of the horizontal sky, with a secondary neutral point, but I have never had an opportunity of observing it. VOL. XXIII. PART II. 3R 228 SIR DAVID BREWSTER Observations on the Neutral Point below the Sun. This neutral point, which I discovered in 1842, is much more difficult to be seen than that of BasineT. In November, December, and January, it cannot be seen in our latitude, unless when, early in November and late in January, a high degree of polarisation in the sky brings it above the horizon at noon. The following interesting remarks of M. Basrinert on his successful attempt to confirm the existence of this neutral point, explain in the clearest manner the causes of the difficulties which were experienced, and which every future observer will experience in observing this remarkable spot, with its surrounding polarisa- tions :— “On the 23d July,” says M. Banrnet, “ after having observed from half-hour to half-hour the polarisation of the sky below the sun, the regularity of this polarisation appeared to change after 4"; and from 43" to 54" I observed in placing the bands horizontally— “ 1st, A space without polarisation below the sun. *«« 2d, Below this space a second space, when the bands were certainly seen ; and, “« 3d, Lower still a neutral space, where no bands were seen ; and, ‘4th, In approaching to the horizon, a fourth space, where the bands were very visible. The phenomenon is therefore no longer doubtful ; but the immense brightness of the sun in a clear day, the intense illumination of the atmosphere in the region immediately below him, and the reflexion from the strongly illumi- nated earth, all concurred in rendering this observation difficult to make, and very painful to the eyes, even if we take the precaution of shielding the head and the Taek from the direct rays of the sun, and the reflexion from the earth. M. Brewster was doubtless guided in his research by theoretical views, otherwise it appears to me very improbable that, by merely observing the atmospherical polarisation, he could have made the remarkable discovery of this neutral point, so difficult to see, and which, after him, I have several times tried in vain to rediscover. . . . . . The small quantity of polarised light which is observed between the neutral point of BrewsrEr and the Sun, seems to me to reach the limit which it is possible to observe, and perhaps to exceed the limit which it is possible to measure.” * , 1841, Nov. 17.—Barom. 29°43. Apparent Time. 12" 0", The polarisation between the sun and the horizon decidedly negative, but no _ neutral point there. | * Comptes Rendus, &c., 1846, tom. xxiii. p, 234. ON THE POLARISATION OF THE ATMOSPHERE. 229 1842, Feb. 16.—Barom. 30:16. Apparent Time. 125 0m, §Sun’s altitude about 21°13’; a China-ink muddy sky, There is clearly a neutral space below the sun, and a little above the horizon. The bands on the sun and below him are negative; but as the negative polarisation becomes very weak, it must pass into a neutral point. 1842, Feb. 18.—Cold, wind west, and rather stormy. Apparent Time. 12 0™, The neutral point below the sun was distinctly seen, the polarised bands being negative over and below the sun, and below the neutral point positive down to the horizon. The sun’s altitude was about 22°, and the distance of the neutral point from the sun about 15°. 1842, Feb. 21.—Barom. 20:44. Fine dry day; wind west. Apparent Time. Distance of Neutral Point from Sun. 12 39m, Neutral point 64° above the horizon, 195 0) The positive polarisation between the neutral point and the horizon was compensated by the refraction of one plate of glass, at 20° of incidence. The neutral line was convex towards the sun in the west horizon. 1842, March 10.—Sky clear in zenith ; wind west. Apparent Time. 11° 15™. The neutral point distinctly seen below the sun. 1842, April 3.—Barom. 29°8. Fine clear sky; cold; hail in the afternoon. Apparent Time. 11° 45™. Neutral point below the sun very distinctly seen, the sun’s altitude being about 394°, and the height of the neutral pomt 263°. The distance of the neutral point from the sun was 13°. The bands over the sun down to the neutral point were negative, and those below it down to the horizon positive, 1842, April 5.—Barom. 30°07. Splendid sky. Apparent Time. Distance of Neutral Point from Sun. 128 27™, Neutral point seen distinctly below the sun. L227 15° 25’ 12 538 14 40 12 56 15 45 4 18 15 35 4’ 33 15 22 N.B.—AII the three neutral points were observed, and their places ascertained this day, and also on April 8. (See pages 217 and 225.) 1842, April 6—Barom. 30:05. Considerable haze. Apparent Time. Distance of Neutral Point from Sun. 8> 51™, Neutral point distinctly seen below the sun. Lion Tear nos 1842, April 8. Apparent Time. 2h 7m, The neutral point below the sun beautifully seen. Estimated distance from the sun, 160: 230 SIR DAVID BREWSTER 1842, April 15 and 17. Apparent Time, 35 0m, Neutral point below the sun distinctly seen. 3 30 1842, April 20.—Barom. 30°02. Very fine day; wind west. Apparent Time. Distance of Neutral Point from Sun. 12» 10m 11° .20' 12 37 10 40 2021 12> 0 3 45 12 35 The maximum polarisation was very great. 1842, April 25.—Thin hazy clouds before the sun. Apparent Time. 12 11™, Sun’s alt. 454°, Alt. neutral point below sun 34°. Distance below sun 113°. 1842, April 26.—Barom. 30:08. Not a cloud in the sky from morning till night. Apparent Time. Distance of Neutral Point from Sun. 115 jm 12? 05h 11 46 12 30 3 30 14 35 3 35 15 6 4 10 17 45 1842, April 27.—Barom. 30:04. Singularly fine sky. Apparent Time. Distance of Neutral Point from Sun. 1 ob 45m 12° 5 12 12 A fog from the sea has just come on, and has driven the neutral point beneath the horizon, the bands being negative all the way to the horizon. — 1 20 The fog has diminished, The neutral point is now seen near the horizon, playing up and down from 4° to 6° above the horizon, as the fog becomes denser or rarer ! 1842, April 28.—Barom. 30. Fine sky; wind east. Apparent Time. Distance of Neutral Point from Sun. 11h 24m 10° 55’ 1842, April 29. Apparent Time. Distance of Neutral Point from Sun. 115 4m 117 20" 1842, May 3.—China-ink sky ; wind east. Apparent Time. Distance of Neutral Point from Sun. 115 29m 10° 15’ be 9 25 1842, May 16.—Barom. 30°3. Thick haze; sun faintly seen. Apparent Time. ; 8" 49™ am, Neutral point below the horizon. The sun now quite hid, and no bands seen below him. A great glare of light, anda sort of guaqua- versus polarisation. N.B.—When the neutral point is out of the plane passing through the sun, the zenith, and the observer, it arises in certain cases from there being a greater haze on one side of the plane than on the other. \ ON THE POLARISATION OF THE ATMOSPHERE. 231 1842, May 17.—Barom. 30°22. Haze all the day. Apparent Time. 11" 0™. The neutral point beneath the horizon. 12 30 Several neutral points, three at least below the sun, as the haze flies past in diferent thicknesses. 1842, Aug. 17.—Barom. 28°8. Fine day ; sky clear at 2°. Apparent Time. 2h 9m. Neutral point seen both below and above the sun, 1842, Aug. 28.—A diffused haze came over a bright blue sky. Apparent Time. 34 49m, The neutral point below the sun was almost in the horizon, and Basinet’s neutral point near the zenith. 5 30 Sun invisible; mist thick ; and the polarisation everywhere positive, and very feeble. 1843, Feb. 13.—Barom. 29-7. Fine sky. Apparent Time. Distance of Neutral Point from Sun. 1h 10m 15° 0’ 1843, Feb. 16.—Barom. 29°15. Fine sky. Apparent Time. Distance of Neutral Point from Sun. 12F 57™ I’ .25! 1843, April 30.—Barom. 30:07. Notacloud. Neutral points distinctly seen, | both above and below the sun. Apparent Time. 4h 15m, Neutral point under the sun still above the horizon. 1843, June 15.—Barom. 30°03. Splendid day; wind east. Apparent Time. Distance of Neutral Point from Sun. 122 Jgm 8° 10’ Ean sO 9 49 1844, May 3.—Barom. 30°15. Apparent Time. ; 11" 3m, The neutral point below the sun distinctly seen. In order to see it well, I look at it perpendicularly through a plate of glass. The bands on each side of it are increased in intensity, the bands above being reversed. When the sky is clear the neutral point under the sun approaches to the sun as his altitude increases, and coincides with the sun’s centre when he is in the zenith. As the neutral points of ARAGo and BaBinet may be seen before the sun has risen, and after he has set, they are comparatively distinct and limited in their area; but as the neutral point below the sun never can be seen unless when the suo is shining, it has a less defined boundary and a wider area, owing to the tlood of light in which it is generally enveloped. Hence arises the great difficulty of seeing it, and of detecting the form of the lines of equal polarisation which surround it. For the same reason, we can hardly expect to see the secondary neutral point, which must accompany it, when it rises or sets on a sea horizon in a condition to produce that phenomena. VOL. XXIII. PART II. 38 232 SIR DAVID BREWSTER On the Place of Maximum Polarisation, and its Intensity. Next in importance to the determination of the place and movements of the three neutral points is the determination of the place and intensity of the maxi- mum polarisation of the atmosphere. In order to obtain these elements, a polarimeter, or instrument for measuring degrees of polarisation, is required. M. Araco constructed a very ingenious polarimeter, and I have described two forms of a polarimeter in the ‘‘ Transactions of the Royal Irish Academy for 1841;”* but these instruments are too complex to be used from hour to hour during transient conditions of the atmosphere, when observations must be made with great facility and quickness. I was therefore obliged to use the following instruments. 1. Into one end of a tube 5 or 6 inches long and 1} of an inch wide I inserted a band polariscope, and in the axis of the tube I placed in a trough several (six to twelve) well annealed thin glass plates with their surfaces inclined to the axis of the tube at such an angle as to equal or compensate the average maximum polarisation to be measured. This compensation was effected more simply by adding or removing one or more plates when those in the trough had been pre- viously placed at a fixed angle to the axis of the tube. It is obvious that, by giving the pile of plates a motion in one plane so as to vary the angle of refraction of the incident light, we should have an instrument for measuring all degrees of polarisation. I preferred, however, to use a polarimeter, all the parts of which were absolutely fixed. In looking through this instrument we have a circular field SA, and when we direct it to the region of maximum polarisation, with the polarised bands parallel to SA, S being towards the sun, we shall see an interruption in the bands somewhere between S and A. If this interruption, or point of com- pensation, is at the point 2 in SA, I call Se the measure of the maximum degree of polarisation at the time of observation. After some practice, I had no difficulty in estimating by the eye when the neutral line was at 1 or 14, or 2 or 24, without placing marks at 1, 2, 3, &c., on a plate of glass at the end of the tube. Having found that So Si Se, &¢., corresponded with degrees of polarisation, measured by the rotation of the plane of polarisation, I thus had a measure of the maximum polarisation of the atmosphere at the time of observation.+ When it was necessary to measure very small degrees of polarisation, I pre- ferred using a polarimeter with a single plate, to one with a pile of plates Fig. 4. * Vol. xix. part ii. + See Phil. Trans. 1830, pp. 69, 183, 145, 287, and Trans. Irish Acad., vol. xix. part ii. ON THE POLARISATION OF THE ATMOSPHERE. 233 receiving the light at very small angles of incidence. This instrument, shown in _ the annexed figure, consists of two tubes of the same length, one of which, EFHG, Fig. 5. moves within the other ABDC. One plate of glass, EL, longer than AB, moves round a joint at E the end of the tube EFHG, resting upon C the end of the tube ABDC, so that when this tube EFGH is pushed in, the plate EL forms a greater angle with the axis of the tube, and when it is pulled out a smaller angle. Now, if AB=EF, BF will be = AE, the tangent of the angle ACE, AC being radius, or of the angle of incidence of rays that fall upon EL parallel to the axis of the tube. The degrees of rotation, R, therefore, of the planes of polarisation produced by the refraction of the plate EL at different inclinations to the axis of the tube may be calculated from the formula— R= 9 — 45°, and Cot. 9 = cos”. (i— 7’); 2 being the angle of incidence, and 7 the angle of refraction. The values of R, the measures of the degrees of polarisation, being laid down on the tube EF, we have a polarimeter which gives us direct measures of the polarisation of atmo- spherical, or any other kind of polarisation, when it does not exceed the maximum polarisation produced by the refraction of one plate. In this instrument the zero of the scale is at F, and B is the index. In place of one plate, EL, we may use two, three, or more plates, and thus obtain a measure of all degrees of polarisation. If is the number of plates, the value of R will be as follows :— R=9—495°, Cot. 9 = cos" (1—7’). In the instrument which I constructed the radius AC was 1°13 inch, or — inch, and the scale on FB was laid down from the following table, the index of refrac- tion of the plate EL being 1°51. Angles of Incidence 2. Angles of Refraction ¢’. Rotation R, Length of Tangent. One Ont 0? 0’ 30.0 19 20 1 0°655 inches. 40 34 25 31 2 0:968 47 46 29 22 3 1:244 63.517 32 4 4 15156 57 39 84 -1 3) 1°784 61 25 308 6 2074 234 SIR DAVID BREWSTER Angles of Incidence 7. Angles of Refraction 7’. Rotation R. Length of Tangent. 64° 40’ 36° 46’ 7 2°386 inches. 67 29 37.048 8 2-726 70 0 38 29 9 3104 (2 39) 7 10 3°544 . By setting off the tangent 0-655 inch from the zero at F, we obtain the place of 1° of rotation, and so on with the rest. The polariscope P is then placed at the end FH of the tube. Having observed the maximum polarisation of the atmosphere by the polari- meter, and its place, we take its altitude A, and by means of the sun’s altitude A’, observed or computed, we obtain the distance D of the place of maximum polari- sation from the sun :— D=180°—A +A’. The following are all the values of D which I obtained. I have added the values of R or the degrees of polarisation in the zenith and in the horizon, when they happen to have been measured :— Observations in 1841. Apparent Time, Values of D. | doopeeitiage gooey April 28. 3h Om 88° 16’ BOA BG 79 15 + ae May 17. 1 20 99 183° 153° June 6. 4 45 +90 163 294 POG ag 30 +90 254 242 un 16r ‘10-99 92 35 a re al pce 4 Wn. GQ 88 26 30 15’ 29 Sept. 15. 10 18 88 4 27 0 262 Oct. 26. 4 30 93 28} 274 Dec. 17. 9 Tam. Appt. +90 27 244 . te... o Of o> time, 4.00 28 27 Observations in 1842. Apparent Time. Values of D. scrars ae ett Jan. 7. ._ 99 0" am. 120° Haze 244° April 5 6 58 +90 303° 264 i DOL 249 84 25 17 re) 2 25 86 95 19 ” ” 3 39 88-207 Le » 8 4 32 90 27 iz are are ie AO) 90 23 9 ” 12 0 90 93 or) 2 1 10 90 ; 95 » 26. 10 53 am 90 29 gee ay 8 SSG 88 29 ” ” 3 42 88 99 » 2cul0 Al An 87 29 » 248 11 34 am, 87 29 ry) 28 1 50 ” 88 99 29 1 384° 55 875 29 ON THE POLARISATION OF THE ATMOSPHERE. 235 Omitting the three extreme values of D,—viz., 79° 15’, 99°, and 120°,— the mean of all the other values is 89°; but, considering that five of the values of D are _ marked as more than 90°, we may conclude that 90° is, in the normal state of the atmosphere, the distance from the sun of the place of maximum polarisation, and 45° the corresponding angle of incidence. This determination of the place and angle of maximum polarisation affords a highly probable explanation of the azure colour of the sky. Sir Isaac NEwton considers this colour asa “ Siue of the first order, though very faint and little, . for all vapours, when they begin to condense and coalesce into small parcels, become first of that bigness whereby such an azure must be reflected.”* Professor CLAustus considers the vapours to be vesicles or bladders, and ascribes the blue colour of the first order to reflection from the thin pellicle of water. In reference to these opinions the following facts are important :— 1. The azure colour of the sky, though resembling the b/ue of the first order, when the sky is viewed from the earth’s surface, becomes, as observed by Mr GuaisHeEr in his balloon ascents, an “ exceedingly deep Prussian blue” as we ascend to the height of five or six miles, which is a blue of the second or third order. | 2. The maximum polarising angle of the atmosphere being 45°, is that of air, and not that of water, which is 53°. 3. At the greatest height to which Mr Guatsuer ascended, namely, at the height of five, six, and seven miles, where the blue is the brightest, “ the air is almost deprived of moisture.” Hence it follows that the “exceedingly deep Prussian blue” cannot be pro- duced by vesicles of water, but must be caused by reflection from the molecules of air, whose polarising angle is 45°. The faint blue which the sky exhibits at the earth’s surface, is therefore not the blue of the first order, and is merely the blue of the second or third order rendered paler by the light reflected from the aqueous vapour in the lower regions of the atmosphere. Immediately after the values of D, I have placed the values of R, or the degree of maximum polarisation, in order to show the relation between these two quantities; but as the values of D were taken only when it was convenient, the numbers R do not show the maximum intensity of the polarisation of the ‘atmosphere. I have therefore selected the following from several hundreds of observations recorded in my journal. Mean Time. Rotation in __ Rotation in Zenith. Horizon, 1841, April 13, 78 32m 322° Ans 9° ” 16. 7 37 32 99° ” » ie he NO 303 281 * Newton’s Optics. 3d Edit. Book ii. part 8. Prop. vil. p. 232. See also Prop. v. p. 228, from which it would appear that by “ small parcels” Newton meant solid globules of water. VOL. XXIII. PART II. 37 236 SIR DAVID BREWSTER Mean Time. Reger. sae a 1842, May 14. 7> 35m 303° 29° 1842, Sept. 29. 4 37 303 Very frequently the value of R, was 29 The following observations show the changes which take place in the maxi- mum polarisation in a few hours :— Mean Rotation Rotation Apparent Rotation Rotation Time. in Zenith. in Horizon. Time. in Zenith. in Horizon. 1841, May 12. 45 12™ 303° 25° 1842, Dec. 24.12 38 264 ee att) 27 241 eet Dy ae: 28 aa ale ties! aatil 303 28h ie ies aie 27 val erlios it. 688 304 29 i set) ico) 2a 29 ea PP ee 282 28} er. a ae: 27k Apparent Time. “ a On Oe 293 1842,April16. 6 0 23 Much less| 1... °V) a7. al 48 263 es easel eonatnn ier ts 24 213 A fi ic a YY 233 16} ane OF Ur ates 274 203 UP ln Wea ap 24 we para OEY Be 294 243 1 tear 88 O71 atanihs Ans wader 32 291 = rth. Gees UB 29 de ty 4 Ad 271 ie nda 2a 288 29 Aiea a ART bi 7 282 Mf TOMAS SHAT SES Sieg 27h 18} Soho sus 5) ED POR 28 S Lib eis Go Hees 27 183 > ” ” it 1 294 eee Pr) : 2 eo 163 ! Hazy ” 7 24 30 1843, Feb. 16. 3 28 293 244 » Sept. 13. 5 58 293 ginny pier inley 8 294 264 ” ” ” d 31 29 ” »” 9 5 + 30 a ae ge 293 The great rotation, amounting to 32}° on the 13th April 1842 at 7» 32™, the greatest ever observed, was occasioned by an unusually favourable state of the sky. (See pp. 230 and 235.) I consider 30° as the maximum rotation in a normal state of the sky. Having, in a normal state of the atmosphere, fixed the locality of the three neutral points, and determined the place and degree of maximum polarisation, we have the means of ascertaining approximately the form of the lines of equal polarisation, and of constructing a map of them when the sun is in the horizon. In a paper published in Johnston’s Physical Atlas, | have shown how this may be done, and have given two projections of these lines—one on a plane passing through the zenith of the observer, and perpendicular to the line joining the observer and the sun, and the other on the plane of the horizon. These two projections on.a reduced scale, and without any of the numbers upon the larger ones, are given in Plate XII. and in the Physical Atlas. It will be seen from these projections that the lines of equal polarisation approximate to lemniscates like the isochromatic lines in biaxal crystals. On the Polarisation of Clouds and Exhalations. The polarisation of clouds and other vapours presents some interesting phe nomena, and should be studied in climates more genial than ours. ON THE POLARISATION OF THE ATMOSPHERE. 237 On the 29th June 1850, at about 8° 30™ p.m., several reddish-white clouds appeared in the south-west sky at different heights, and in the zone of maximum polarisation. They were illuminated by the setting sun, and the sky around, and of course behind them, was of a deep blue. Upon looking at one of these clouds through Nicol’s prism, I found that its reddish-white light was polarised in a plane at right angles to that in which the light of the sky was polarised. When the sky was dark by the disappearance of the blue polarised light in one position of the prism, the cloud was bright; but when the sky was brightest in a rectangular position of the prism, the cloud was of a dark blue colour. July 15, 1850, 9" 12” p.m.—All the clouds to the east of the plane passing through the sun and moon, between the south-west and south, are black seen against the sky; but when we view them with a Nicol’s prism, so as to extinguish as much as possible the polarised light of the sky, the clouds are white seen against the dark sky. When the Nicol’s prism is turned round 90°, they again become black. ' | July 1, 1850, 8" 30" p.m.—A fine rainbow, with the secondary and super- numerary bows, appeared in the south-east. When the bands of the polariscope crossed either of the two bows at right angles, the bands at the intersection were very brilliant. When the rainbows were invisible from the great faintness of their light, they became visible, that is, the invisible portion became visible, when crossed with the bands of the polariscope. This effect did not seem to be pro- duced when the bands crossed the supernumerary bows. When the sun shines upon a light transparent vapour interposed between the observer and terrestrial objects, these objects are indistinctly seen through the light reflected by the vapour. As this light is partially polarised, it may be } extinguished by a Nicol’s prism, or a pile of thin plates of glass, or by reflection } at the polarising angle from a glass plate. The terrestrial objects are then seen } with great distinctness. This mode of obtaining improved vision of objects } imperfectly visible, or of seeing objects not otherwise visible, may occasionally } be of great use at sea. On the Theory of Atmospherical Polarisation. When the atmosphere is illuminated by the sun, his rays fall upon the aerial particles which compose it at all angles of incidence. In the immediate vicinity of the sun, where the angle of incidence is 180°, there is no polarisation. The polarisation increases with the angle of incidence, and becomes a maximum, ‘as we have seen, at about 90° from the sun. It now diminishes with the angle of incidence, and becomes nothing at 180°, the point opposite to the sun. At all these points the polarisation is said to be vertical, being in the vertical plane passing through the sun and the observer. 238 SIR DAVID BREWSTER In addition to the vertical polarisation produced by the direct illumination of the aerial particles, there must be an opposite polarisation by which the neutral points are produced. M. Araco, M. Basrnet, and, we believe, every other writer on the subject, have sought for this counter-polarisation “in the secondary illumination which the same aerial particles receive from the reflexion of the rest of the atmosphere, which sends to them light polarised horizontally,’’* or oppositely to the light polarised vertically. That is, all the phenomena of atmospherical polarisation are produced by the opposite action of two lights polarised by reflexion, the one vertical, arising from the direct illumination of the aerial particles, and the other horizontal, produced by a secondary illumina- tion of the same particles by the rest of the atmosphere. This theory of atmospherical polarisation, omitting all consideration of the light polarised by refraction, never appeared to me satisfactory. There is no evidence whatever that such a secondary reflexion exists, even in a perfectly cloudless sky, and still less evidence that, if it did exist, it would be capable of neutralising the light polarised by reflexion at considerable distances from the antisolar point. It must be very feeble when the neutral point is about to dis- appear at the close of twilight; and as the polarisation by direct reflexion must be visible when the secondary reflection ceases to be visible, this cessation ought to be marked by a return of the neutral point to the antisolar point, the place which it would occupy were there no secondary reflexion. Were the neutral points produced by a secondary reflexion, their distances from the antisolar point and from the sun ought to be affected when the sky is more or less covered with clouds; but though I have observed the neutral point of AraGo in a clear part of the sky, I never observed that its distance from the antisolar point was changed when the rest of the atmosphere was obscured by clouds. : On these grounds I was led to the opinion that the neutral points must be produced by the opposite action of two polarised lights which had nearly the same relative intensity, and this opinion was strengthened by observations which I had made on the polarisation of light by refraction and transmission through piles of glass plates. In these experiments, published in the “ Philosophical Transactions” for 1814, I observed phenomena analogous to neutral points, that is, the co-existence in the transmitted light of rays polarised by reflexion, and rays polarised by refraction, but I did not observe the effect where the intensities of these rays were such as to neutralise each other. . Guided by these views, I never doubted that the three neutral points in the atmosphere, and the partial polarisation of the light which it reflects, are produced by the opposite action of lights polarised by reflexion and refraction ; and con- * BazineT, Comptes Rendus, &c. 1846. Tom. xxiii. p. 233. ON THE POLARISATION OF THE ATMOSPHERE. 239 sidering the congeries of separate molecules which constitutes the atmosphere as arough or dispersing surface, I made a series of experiments on such surfaces as were likely to act upon light in the same manner as the aerial molecules. In these experiments, which have been already communicated to the Society,* I found that such surfaces not only polarised partially the incident light, but pro- duced neutral points, like those of the atmosphere, by the opposite action of the rays which they polarised by reflexion and refraction. * See page 205. VOL. XXIII. PART II. 3U ish * Trans. Royal Society Vol. XXHTZLATE XIL (rahe) XXII.—On a Pre-Brachial Stage in the Development of Comatula, and its im- portance in relation to certain Aberrant Forms of Extinet Crinoids. By Professor ALtMAN. (Plate XIII.) (Read 16th February 1863.) While engaged last autumn in examining with a hand-lens the contents of a phial into which I had transferred some of the refuse of the dredging-boats employed in the oyster fishery on the coast of South Devon, my attention was attracted by a minute organism which adhered to a fragment of one of the larger Sertularidans. Under this low power it resembled somewhat a Campanularia, with the polype expanded; but, on being removed with a portion of the substance to which it was attached, and placed in a glass trough under the compound microscope, I found that it had closed up, and now resembled in form a cup surmounted by a pyramidal lid, and supported on the summit of a long jointed stem (Plate XIII., fig. 3). After it had remained for some time in this condition, I observed the pyramidal lid begin to. ‘open. by the separation of its sides, and numerous long flexile appendages to'issue from the cup (figs. 1 and 2). I saw that I had now before me a remarkable crinoidal type, likely to be of much significance in its bearing on the general morphology of the order, and more especially interesting, as affording a key to the nature of certain extinct genera of Crinoids. It is the object of this communication to give some account of the points, which a very careful examination has enabled me to make out in the only specimen which I was fortunate enough to obtain. For convenience of description, the little Crinoid may be divided into the body and the stem. The body consists of a calyx or cup-like portion, covered by a pyramidal roof. The calyx is composed chiefly of five large plates, very distinct, and united to one another by simple suture. Between the lower edge of these plates and the summit of the stem is a narrow zone, in which no distinct indica- tions of a composition out of separate plates can be detected. Between the upper angles of every two contiguous large plates there may, with some care, be made out a minute intercalated plate; there would thus be five of these little intercalated plates, which, though by no means so evident as the five large plates which alternate with them, are sufficiently so to leave no doubt of their presence. The entire length of the body and stem is about y,th of an inch, and that of the body alone about 2,th of an inch. The pyramidal roof which closes the cup in the contracted state of the ‘animal is composed of five large triangular plates, each supported by its base upon the upper edge of one of the large plates of the calyx, and with the small intercalated plates encroaching upon its basal angles. When the animal is VOL. XXIII. PART II. 3X 242 PROFESSOR ALLMAN ON A PRE-BRACHIAL STAGE retracted, the triangular plates become approximated to one another at their edges, and then each will form the side of a pentangular pyramid. The height of this pyramid is about equal to the depth of the cup, so that the entire body has then somewhat the appearance of two nearly equal pyramids placed base to base ; but when the animal is about to expand, the sides of the roof separate from one another, and opening outwards like the segments of a calyx in an expanding flower-bud, allow the fiexile appendages already mentioned to come into view; and these, gradually elongating themselves, finally fall down gracefully over the edge of the calyx (fig. 1). Both the calyx and roof are solidified by the deposit in them of mineral matter. The deposition, however, takes place in such a way as to leave a mul- titude of minute spaces free from it, so that the whole presents a kind of reticu- lated structure, which, while it is a characteristic echinodermal feature, adds much to the elegance of the little Crinoid. The membranous basis in which the earthy matter is deposited extends a little beyond the margin of the valve-like plates of the roof, and by transmitted light may be seen forming also a narrow transparent contour round the entire body. Long flexile appendages, or cirri, have already been mentioned as rising out of the calyx. These, in the expanded state of the animal, are thrown out between the edges of the five diverging plates of the roof, and thence hanging down all round over the calyx, afford an additional element in the beauty of our little Crinoid. I have counted fourteen of these cirri, but they may be more numerous, for it is very difficult to determine their exact number. They appear to be cylin- drical, with a canal occupying their axis; and as far as they can be traced back- wards, they are seen to be furnished with two opposite rows of rigid sete or fine blunt spines (fig. 4). Between every two opposite setze a transverse line may be seen stretching across the cirrus, and indicating its division into tranverse seg- ments. Of the base of the cirri I can say nothing. I have never succeeded in getting a view sufficiently deep into the space included within the five roof- plates, to allow of my tracing those appendages to their origin. Besides the long extensile cirri now described, there is also an inner circle of short, apparently non-extensile, appendages. It was only occasionally that YT succeeded in getting a glimpse of these; they appear to constitute a circle of slightly curved rods or narrow plates, probably five in number, which arch over the centre, and are provided along their length with two opposite rows of little tooth-like spines; they seem to be articulated to the upper or ventral side of the calyx by their base, and may be seen in a constant motion, which consists in a sudden inclination upon their base towards the centre, followed immediately — by a resumption of their more erect attitude. Our little Echinoderm is very irritable, and on the slightest annoyance the cirri are suddenly withdrawn, and the valve-like plates of the pyramidal roof IN THE DEVELOPMENT OF COMATULA. 243 instantly closed down over them. In this retracted state it may remain fora long time, wearying the patience of the observer, who may have to wait for hours together before he can again obtain a satisfactory display of its structure. The interior of the calyx is occupied by a reddish-brown visceral mass, obscurely visible through the walls; but I have not succeeded in obtaining a glimpse of the mouth, nor have I been able to discover the anal aperture. The stem consists of a column, composed of a pile of segments solidified, like the walls of the body, by the deposit in them of earthy matter, and presenting also the same peculiar reticulate structure. Three or four of the upper segments are somewhat globular or bi-conical, giving a moniliform appearance to this part of the stem, while lower down the segments become cylindrical. Those situated near the middle of the stem have a prominent ridge running round their centre; while in those nearer the root the ridge disappears, and a simple line takes its place. Indications of a differentiated axis are visible through the whole length of the stem. The stem admits of slight flexure from side to side, and during life the animal may be every now and then seen swaying through a smallare. The whole of the stem is enveloped in a transparent membrane, which is particularly distinct on the upper part, and is a simple continuation of that which has been already mentioned as investing the body. The multiplication of the segments in the stem seems to take place by the divi- sion of the pre-existing ones, and this division seems indicated by the transverse ridges which, in several of the segments, may be seen running round the centre. In attempting to determine the exact affinities of the remarkable little organism now described, an important question presents itself at the outset: Are we to regard it as a mature form, or only as a transitional state in the development of some other? Everything tends towards the adoption of the latter view, and I think there can be no doubt that the little Echinoderm now described is one of the early stages in the development of a Comatula. That it had been seen by J. VY. THompson seems evident, from his celebrated memoir on “ Pentacrinus Europzeus,”* where some of the figures which accompany that memoir appear to be made from an organism identical with that here described, though the want of completeness in the description, and of sufficient detail in the figures, have left this part of the history of Comatula in a very imperfect state. Again we find what we must regard as the same organism, figured by Dusar- pin. This naturalist figures in plate i. fig. 18 of his Histoire Naturelle des Zoo- phytes Echinodermes, a minute animal, which he observed at Toulon in 1835, and which he considers as the young Comatula at the commencement of its stationary existence. Ihave no doubt that the distinguished French naturalist had before * Joun V. Tuompson, ‘‘ Memoir on the Pentacrinus europeus.” Cork, 1827. 244 PROFESSOR ALLMAN ON A PRE-BRACHIAL STAGE him, when he made his drawing, the little animal which forms the subject of the present paper, or at all events, the same phase of a nearly allied species; but his figure, while it gives a better idea of the form of the roof than THomson’s, throws no light on the composition of the calyx, and is in other respects so deficient in detail as to render it of little use in working out the relations and significance of the little Crinoid. v Taking for granted, then, that the subject of the present paper is a pre-brachial stage in the development of Comatula, it will hold an intermediate position be- tween the free larvee described by Buscu,* and the fixed Pentacrinus stage described by J. V. THompson.+ A comparison of our larva with the adult Comatula is full of interest. In order, however, that this comparison may be made with advantage, it will be necessary, in the first place, to endeavour to assign their true value to the several plates which enter into the composition of the body-walls of the larva. Now, the narrow zone which intervenes between the five large hexagonal plates and the summit of the stem, corresponds undoubtedly to the centro- dorsal piece which, in the adult Comatula carries a set of articulated appendages. Whether this piece is to be regarded as the homologue of the true basilar zone in the typical Crinoidea, or rather as a modified superior joint of the stem, is a point not immediately obvious. I entirely agree, however, with JoHANNES M@LLER, in viewing the centro-dorsal piece in Comatula as a metamorphosed stem joint; for not only do we fail to detect in this portion of the calyx a composition out of distinct plates, but, what is of more importance, it is from this very piece that the articulated appendages are developed,—these being, as shown by the analogy of Pentucrinus, properly appendages of the stem. If this be the true interpretation of the part in question, then the five large plates, which are superimposed upon it in our larva, and which here constitute almost the whole of the calyx, will correspond to the true basalia, which imme- diately surmount the stem in such forms as Platycrinus, and the great majority of the Crinoidea, while the five small plates intercalated between their upper angles will represent radialia; for it is manifest, as shown by the larval Comatula in a more advanced stage—for a preparation of which I am indebted to the kindness of Dr CARPENTER—that it is in the position of these little plates that the proper arms will subsequently arise. * Buscu, “ Beobachtungeniiber Anat. und Entwickel. einiger Wirbelosen Seethiere.” Berlin, 1851. + Tuompson, loc. cit. Since reading the present paper, I met with an abstract of a paper on the “Embryogeny of Comatula rosacea,” by Professor Wyvittt Tomson, in the “ Proceedings of the Royal Society of London” for Feb, 5, 1863. In this paper Professor Tomson gives us the results of aseries of valuable observations in which he has traced the development of the larva beyond the stage — at which it was left by Buscu, and has further elucidated its earliest stages. He has not, however, earried it up to the point which it is the object of the present paper to describe; while the very careful and complete researches of Carpenter, referred to below, would seem to start from a point a little in advance of that here described. IN THE DEVELOPMENT OF COMATULA. 245 I believe this to be the correct view of the parts in question; but if we should _ prefer to regard the single centro-dorsal piece as representing a zone of coalesced basalia, then we must view the five large plates as parabasalia ; for that they are not radialia is manifest from the undoubted relations of the five small interca- lated plates, which must still be considered as radialia, whatever interpretation we give to the centro-dorsal piece. The signification of the five large triangular roof-plates still remains to be determined. Now, I have no hesitation in re- Fig. 1. garding these as inter-radialia greatly developed, and, in consequence of the slight development > of the radialia, brought into contact with the upper edges of the basalia, to which they are a “a united, not by immoveable suture, but by a G moveable articulation. In accordance then with ing op Se these views, the analysis of the body of Coma- < ula in the pre-brachial stage, which constitutes A the subject of the present paper, will stand as in the annexed woodcut, fig. 1.* ; 5 iter There is scarcely any more striking feature Pen bie Pre prashioy Con deate in our young Comatula, than the long tentacula- C. Centro-dorsal Piece. 4 ‘ fetus : é 1. Basalia, . 5 like appendages or cirri which, in the expanded 2. Radialia, ps state of the animal, are protruded between the 8. Inter-radialia,. . 5 Arms, ‘ 0 edges of the five roof-plates. A few of those ap- pendages, in an imperfectly extended state, are shown in Dusarpin’s and Tuomp- SONn’s figures above referred to. Though I have never succeeded in getting a view of their bases, I would regard them as ambulacral feet greatly developed, and otherwise peculiarly modified. Their general resemblance in structure to the ‘‘ tentacula,” which lie in the ambulacral grooves upon the arms, pinnule, and disc of the more advanced Comatula, is quite in accordance with this view. It is more difficult to give a satisfactory account of the long inflexible toothed plates, which, in our larva, lie between the tentacula and the centre; and I con- fess myself unable to decide as to their real nature, for their structure seems inconsistent with the idea of their being an internal series of m odifiedcirri. We are now prepared to institute a comparison between our pre-brachial _Comatula and the adult animal. This comparison will show a composition alto- gether different in the two cases. In the adult Comatula, the only distinct pieces * Dr Carpenter informs me that he has detected in an early stage of the larval Comatula, an unsymmetrical “anal” plate, which he regards as one of a first series of inter-radials (the rest of this series being usually abortive), and which is afterwards lifted by the development of the anal funnel into a much higher position. I have sought in vain for this plate in my specimen, and am of opinion that in the stage to which this specimen belongs, the plate does not exist. It is quite possible, however, that though it has here escaped detection, it may yet be found in specimens better suited for observation. VOL. XXIII. PART II. oa 246 PROFESSOR ALLMAN ON A PRE-BRACHIAL STAGE which we find in the calyx are a large centro-dorsal portion, carrying the articu- lated dorsal appendages, and the five radii, each composed of three radialia, the first of which is directly attached to the centro-dorsal piece, while the third carries two largely developed pinnulose arms. There is no trace of basalia, and no trace of © the five triangular roof-plates of the larva. It will be thus seen, that instead of the five minute plates representing the radii in the larva, we have here the radii, consisting each of three well-developed radialia, and constituting the principal — portion of the calyx, while the arms totally absent in the larva, are in the adult so developed as greatly to exceed in magnitude the whole of the remaining portion of the animal. The composition of the calyx in our pre-brachial Comatula has a special in- terest, when we view it not only in relation to that of the adult, but to that of the typical forms of extinct Crinoidea. Its large and very distinct basalia show, that in this early stage it is not alone in the presence of a stem that Comatula approaches the typical Crinotdea, but that its calyx also, so different in the adult from the calyx of the typical forms, is here constructed upon essentially the same plan as that which we meet with in such genera as Platycrinus, which we may regard as presenting the type composition of this part.* As no trace of distinct basalia can be found in the adult Comatula, these elements must have either coalesced with some of the others in the progress of development, or, what is more probable, have been obliterated by the encroachment of the radii and centro- dorsal piece.t In the fossil genus Solanocrinus, and in the living genus Comaster, founded by Acassiz for the Comatula multiradiata of Goupruss, though afterwards sup- pressed by JoHANNES MULLER, as founded on characters which he had not been able to confirm in any living species, we have a Comaiula in which five small basalia alternate with the radii, but are not large enough to form a continuous zone, separating the radialia from the centro-dorsal piece. Solanocrinus would thus represent a stage in the development of Comatula before the basalia had become entirely obliterated, and therefore intermediate between the subject of the present paper and the adult. : A series of highly valuable, but as yet unpublished observations, have been made by Dr CarPEenTER, on the development of Comatula, in which he has traced the progress of the animal from a very early period after the first appearance of the arms to its final detachment from the stem. - In the earliest of these stages, Dr CaRPENTER has found the five roof-plates still present, and he informs me that * It should be borne in mind, that while the basal zone of Platycrinus appears to depart from the type, by having only three distinct basalia, these pieces easily admit of a further analysis into the typical number five. . From a letter which I have received from Dr Carpenter since the above paragraph was — printed, I find that he has instituted a nearly similar comparison between the calyx of the young Comatula and that of the adult typical crinoid., IN THE DEVELOPMENT OF COMATULA. 247 he has seen them in the progress of development finally disappear by absorption. _ Dr Carpenter’s observations, which set out from a stage a little in advance of that of our larva, will doubtless throw much light on the steps which inter- vene between the stage here described and the fully-developed Comatula; they are illustrated by a beautiful series of drawings and preparations, and it is greatly to be desired that their author may not delay long in giving them to the public. One of the most interesting features in our little Jarva, is the light which it seems capable of throwing upon the nature of certain extinct forms. The description by GueTTaRD,* in the middle of the last century, of a living speci- men of Pentacrinus caput meduse, and the discovery by THompson,} towards the beginning of the second quarter of the present century, that the Comatula, in their young state, are stalked Crinoids like Pentacrinus, must be regarded as the two grand steps in our knowledge of the morphology of the Crinoidea by which we have been enabled to establish the relations which exist between the extinct stalked forms and the dwellers in our present seas. It is however the normal types of the fossil Crinoids that our knowledge of the living forms has hitherto chiefly tended to elucidate; and there are still numerous aberrant types, such as Haplocrinus, Coccocrinus, Stephanocrinus, &c., whose affinities can scarcely yet be regarded as in all respects satisfactorily deter- “mined. I believe that the little animal which forms the subject of the present paper will help us towards a clearer conception of the relations of some of these, and enable us to assign their true significance to certain points in their struc- ture which have presented difficulties in the way of a satisfactory morphological analysis. The Devonian genus Haplocrinus will here at once suggest itself—so remark- able by its tall pyramidal roof and rudimentary arms. In this genus, the summit segment of the stem undergoes no metamorphosis, and the centro-dorsal piece of Comatula is accordingly wanting, while the stem is immediately surmounted by the basilar zone, consisting of five basalia. To this succeed the five radii, rendered irregular by two of these radii consisting each of a single radiale, while the three others are each composed of two radialia. Lastly, alternating with the radii, are the five sloping sides of the pyramidal roof, and these I think must be recognised as the exact equivalent of the five valve-like plates of the pre-brachial Comatula, and therefore znter-radialia, here separated from the basalia by the greater deve- lopment of the radialia ; for not only their position, but the discovery by JOHANNES MULLER of rudimental arms in this genus, is inconsistent with Romrr’s view, that : the roof-plates are the arms of Haplocrinus in a condition similar to that of the * Mém., de l’Acad. Roy. des Sciences, 1755. + Memoir on the Pentacrinus ewropeus, Cork, 1827; and afterwards in the “ Edinburgh New Philosophical Journal,” 1836. 248 PROFESSOR ALLMAN ON A PRE-BRACHIAL STAGE arms in Cupressocrinus. The following diagram, fig. 2, exhibiting an analysis of Haplocrinus, will render the relations here insisted on more apparent. Fig. 2. Again, in the singular Devonian crinoid Coccocrinus, J. MULLER, we have the roof in the [N form of a depressed pyramid, composed chiefly of five large pointed pieces, whose apices meet Ry, wa in the centre, and which are also plainly inter- CONG ibe radialia and homologous with the sides of the be drawn at the extremities of the major Fig. 5. and minor axes, meeting in T, and let a hyperbola, having same centre and focus, be so drawn as to pass through T, and — cut the ellipse in K. Then the elliptic quadrant PQ is so divided in K, that — PK—KQ=PT-TQ=a-4, or the dif- ference of the semiaxes of the ellipse, © ~ which is Facnant’s theorem (Saumon, p. 298). Now, let the point T advance con- Fig. 6. tinually along the hyperbola, and the intercepted arc will of course always be divided at the same point K. Ulti- Fig. 7. mately, the point T may be supposed to attain the asymptote at an infinite r distance. The two tangents TP, TQ, are then parallel to the asymptote. Their — MR TALBOT ON FAGNANI’S THEOREM. 289 difference is equal to the difference of their extremities which touch the ellipse, and are cut off by any line at right angles tothem. Call this difference D. The intercepted arc is then a semi-ellipse, because, when tangents are parallel, the line joining the points of contact passes through the centre. Now we have PK—-QK=PT—QT=D, and BK—AK=a—6; therefore, by sub- traction, PB-QA=D-—(a—6). But the are PB=QZ, .. QZ—QA=D-—(a—-0). But ZA is a quadrant of the ellipse, therefore this quadrant is so divided in the point Q, that the difference of QZ and QA is a known straight line=D-—(a—0). Now, it is by no means obvious, whether or not we have thus obtained a division of the elliptic quadrant different from the one we first obtained. This point can only be settled by a rigorous demonstration ; the result of which gives this curious theorem D=2 (a—b). From which we see that QZ—QA=a—b=BK —KA, so that the elliptic quadrants BA and ZA are divided at corresponding points K and Q, and the are AK=AQ. And since the tangent at Q or QT is parallel to the asymptote, it follows, by parity of reasoning, that the tangent at K is parallel to the other asymptote. Moreover, if we draw MCN through the centre, at right angles to PT and QT, it is plain that D=PM+QN, or since these lines are equal, 2(a—6)=D=2QN ... QN=a-—6, hence the point of division Q is such, that the perpendicular let fall from the centre on the tangent at Q, cuts off from it a portion QN=a—b. It remains, therefore, to demonstrate @ priori the theorem we have just indi- cated, viz., that QN=a—b, whence the other properties mentioned will follow. We shall, at the same time, obtain the demonstration of many other theorems. Let CA, CB, be the semi-axes of an ellipse, denoted by a,b. Complete the rectangle BCAD. Let A, B, be the semi-axes of a hyperbola, having same } centre and focus, and so drawn as to pass through the point D, whose co- ordinates are a,b. Then, according to Satmon (Conic Sections, p. 298), the | co-ordinates of the point P, which is the ; BIE? E- * 5 3 3 intersection of the two curves, are, «?= —% pe a We shall reverse this order of reasoning, and suppose a hyperbola drawn with | centre C, axis in the line CA, and passing through the points D and P, and then ‘show that such a hyperbola has the same focus with the ellipse. In the first _ |place, then, the point whose co-ordinates are x#?= > y= se lies in the ellipse, VOL. XXIII. PART II. 4% 290 MR TALBOT ON FAGNANI’S THEOREM. 2 for those co-ordinates verify the equation to the ellipse s +=1. The substitu- b tion gives es & a+b eb. =1, which is identically true. ie at+b Secondly. By hypothesis, the equation of the hyperbola 43 ‘or yi is satisfied B? by the values z=a, y=b, which gives (1) a sg , and also by the other values jee a? y= b* a+b’ atb ; . : a® Be” which gives (2) Git Pua e 1. Subtracting (2) from (1) Bea Aer dy ==) (a+b) A? (a+b) B? z : = which gives the remarkable result A’: B?:: @: 0, showing that the elliptic semi-axes are in the duplicate ratio of the hyperbolic ones. Hence if A?=ka, B?=kb (& being an indeterminate.) To determine its value, we resume the equation (1), ma = 1 : : a Tih? which gives Ta kb ~ 1» Whence k=a =D: Therefore the squares of the semi-axes of the hyperbola, are A’=a (a—b), =b (a—b). From whence, by addition, A? + B?=a@?—D’. It remains now to verify the confocality of the two curves. If Cis their com- — mon centre, and F the focus of the ellipse, we have CF’=a’—0’, by the property of the ellipse, and if F’ is the focus of the hyperbola, we have CF?=A? + B? by the property of the hyperbola. .-. if F and F’ are the same point CF? =CF? or a?—b?=A? + B?. But we have shown that this equation exists, and therefore the curves are confocal. Thus we have proved that the squares of the Ly re co-ordinates of the point P, where the confocal ellipse and hyperbola intersect, are,— 3 3 z =aiP WF at a® +b at+b Let CQ be the conjugate to CP. -. (2) CP? + CQ?=a7+-6" by a propels of the Therefore (1) CP?=2?+7’?= =a?—ab+b? — beau ERNE alps. Subtracting (1) from (2), we find CQ?=ab. a Let CN be perpendicular on the tangent PN, then by another property of the MR TALBOT ON FAGNANI’S THEOREM. 291 ellipse, CN . CQ=ab; whence CN’ . CQ?=a2b". Divide this equation by CQ?=ab -- CN?=abd, and... CN=CQ. But now, since CP’=a’+?—ab, and CN?=ab, there- Seo PN?=CP?—CN?=a?+0?~2ab, ... PN=a—6, which is the theorem we under- took to demonstrate.* It is curious that CQ when prolonged, becomes the asymptote of the hyper- bola. Perhaps we have already offered sufficient proof of this, but the reader may not object to see it proved in another manner. dy a b? 2 2 The equation to the ellipse taal CIOS ta ea But the value 3 of | — at Facnanr’s point is ;, a Therefore == ee 2 But by the property of Ne hy- ots if C be the centre and CA, CB (or A, B), the semi-axes, the asymptote CD will be found by completing the rectangle ACBD, and joining CD. . the asymptote makes, with the axis CA an B angle, whose tangent =Or=e and the other asymptote makes an equal angle below the axis, Fig. 10. ; B d. whose tangent is therefore —-{7. But we found as = therefore, the tangent to the ellipse at the point P, or (#, y) is parallel to the second asymptote. Con- sequently, the conjugate semi-diameter CQ, is a portion of that asymptote. Since the two curves are confocal, they ought to intersect at right angles. Let us verify this. We have seen that the equation to the ee gives 2 fas A Bat Fagnani’s point. But the equation to the hyperbola = = ues 1 gives a SB* oA Bt A at the same point SY ae BoB BoB But these two results, = in the ellipse, and = in the hyperbola (neglecting the signs) are reciprocals. Therefore at the point of intersection the two curves make angles with the axis, whose tangents are reciprocals, and therefore they intersect at right angles. Hence this curious theorem “ At the point of intersection P, the normal to the hyperbola is parallel to one of its asymptotes.”’ * These properties, viz., that CN=CQ=/ab, and that PN=a—b are proved by Briyxxey in quite a different manner (Trans. of the Royal Irish Academy, vol. ix. p. 146, &c.). He likewise proves, that if CQ produced cuts in O, the circle described on the axis major as diameter, a perpen- dicular let fall from O on the axis, cuts the ellipse in Fagnanv’s point. But I have shown that CQ produced is the asymptote of the hyperbola, .-. an ordinate to the ellipse at Fagnani’s point, passes through the intersection of the asymptote and circle. In other words, the common chord of the ellipse and hyperbola, being produced, becomes the common chord of the circle and the two asymptotes. 292 MR TALBOT ON FAGNANI’S THEOREM. For that normal is tangent to the ellipse, and the asymptote coincides with the conjugate diameter. Now, let us draw three vectors to the hyperbola, from the centre, making the angles 0, 0’, 6”, respectively with the axis. The first to be drawn to a point infinitely distant (and, therefore, it will be the asymptote), the second to the point D, and the third to the point P (see fig. 8). Then, if we call tan 6=¢, we have the following curious property,— tan ¢=2? tan #’=é B Aa” Gee i : . For tan =F) and tan é a and tan ¢ = at the point where the curves inter- sect} iand 2 = Jaa Since @ is less than 45°, and .-. tan 6 less than 1, the angles 0, 6’, 0”, become suc- cessively smaller. Another remarkable property is the following (see fig. 9):—At the point P, where the curves intersect, and where the elliptic quadrant is algebraically divided according to Facnant’s theorem, the line PN intercepted by the perpen- dicular CN on the tangent, is a maximum. For if we examine in any ellipse what must be the position of the point P, in order that PN may be a maximum, we shall find it to be characterized by those values which we have already shown to belong to P in Facnani’s theorem. This may be shown as follows :— In any ellipse, let C be the centre, CP, CQ, conjugate diameters, PN a tangent, and CN or p the perpendicular to it. ab a b? We have ars i sea 27,2 But OP? =a? +0" CY =a? +0? Se. ; Subtract CN? =p? 242 ane eee ‘ ‘ : : abe Let this be a maximum. Therefore since a?+0° is constant, ei p’, moust be a «iis . n : ae minimum, or putting a’/?=n, and p?=a, then 77% is a minimum. Differentiating this, we find t=/n; or p’=ab. From this value we find CQ?=ab, and .. CQ=p, and PN?=a?+l?—ab—ab; .. PN=a—b. And as these were the values which we found before for the same lines, it is evident that P is the same point which we were considering before. Therefore, at the point P, which may be called Facnanrs point, the line PN is a maximum. MR TALBOT ON FAGNANI’S THEOREM. 293 Additional Remarks. I will here add two or three other theorems, which have suggested themselves in the course of this inquiry. If BCA is an ellipse, and P is Facnanr’s point, and the tangent OPT is drawn terminated by the axes produced, then OP=CA, and PT=CB. Demonstration —Let CA=a, CB=b, CN=a, 2 2 PN=y. The equation is“, +=1. At Faewanr’s point we have, 3 3 Cy ae ay ce ab and y at+b 3 3 4 4 Therefore a+b= & =e Hence a(a + 6) =— and b(a+ d= Whence by addition (a+)? Be + ae ae ce Now we have by a general property of the ellipse cT=£ and oo=", whence or=% + which we have just proved to be equal to (a+). Therefore we have the curious result, OT=a@+ 0. Now, OR OP 2 Cis MP a or, ao OP a a & — a? 0 9 e Lea: a Therefore OP=(a+ b) 2 And since at FaGNant’s point ee it follows that OP=a. And similarly it is shown that PT=0. From whence the following curious theorem follows,—It is well known that if OCT is a right angle, and OT is a line of given length, which moves so as to keep its extremities constantly in the lines CO, CT, then any point P of the line OT will generate an ellipse. But there is only one position of the line OT in which it touches the ellipse. Theorem.—If the generating line OT touches the ellipse, the point of contact P is FAGNANI’s point. Hence, if we let fall the perpendicular CX upon OT, then OX=PT=semi-axis minor. For OP=a, and we have seen in the course of this investigation, that PX=a—b «. OX=OP—PX=b. The following corollary is also worth remarking. OP~—are BP=PT—arc PA. VOL. XXIII. PART II. 4. 294 MR TALBOT ON FAGNANI’S THEOREM. And also the following:—Of all the lines, which touch the ellipse, and are terminated by the axes produced, the shortest is OT, which touches at FaGnant’s point. The simplest proof of this, is by the doctrine of infinitesimals. Let the line of constant length OT (which we called above the generating line) assume another position O’T’, it will now be a secant to the ellipse, and P will occupy another point in the curve. But if the position O’T’ be taken infinitely near to OT, and P’ to P, then O’T’ must be considered as still being a tangent; and thus we see that the tangent at P’, limited by the axes produced, has the same length which it had before [the part OP having gained an infinitesimal quantity 6, and the part PT having lost exactly the same], which is the character of aminimum. There- fore, OT is the minimum tangent, terminated by the axes produced. It is curious, that while OT=a+6 is the Minimum of its kind, PX=a—6 is the Maximum of its kind, as we proved in another part of this Memoir. This result may also be obtained by the differential calculus, as thus :-— CA” af 0 Laon w B CBB? t OC=om ay orp -%. & : Tig. 12. . ae wet y And when OT is a minimum, a*dax b*dy a =-_— y . ere : h es th fng 727 = — YY ; But by differentiating the equation to the curve, “;+77=1, we tind 7; = —"F” which is always true. . 6 bé 2 Dividing the first of these equations by the second, we get == x whence 7 = C 3 2 . . . . _ which is the property which characterises Facnanr’s point. I will terminate this paper, by giving some remarkable properties of confocal ellipses and hyperbolas. . Lemma.—Let XY be the directrix of an ellipse, and P any point, we have by a a property of the ellipse t HPs sb xen 5) 1 e being the excenitricity, _HP é 7 eo MR TALBOT ON FAGNANI’S THEOREM. 295 Therefore, calling CN, 2, we have, when the point is at the extremity of the minor axis, Ae Be BO 2: HB ; CN+ PX i 18 OG 3 2 = é Therefore a=ex+HP and HP=a-—ex. This equation to the ellipse may often be useful. Theorem A.—If an ellipse and hyper- bola are confocal, the line from the focus Fig. 13. to the point of intersection equals the distance between the Vertices. Let S, H, be the foci, P the point of intersection, a, b, the semi-axes of the ellipse; A, B, ee those of the hyperbola, and V its Vertex, SP+HP=2CA, and SP—HP=20V 2HP=2(CA—CV)=2VA HP=VA=a-A. Fig. 14, _ The distance CH, between the centre and focus is usually expressed by ae, or ¢ times the semi-axis major. But since in theorems concerning two or more con- focal conics, CH is the only invariable line, it is convenient to denote it by unity. We will therefore in the sequel suppose CH, or a=1; and, therefore ex. It must be borne in mind that the condition of confocality gives the following rela- tion between the axes,— a? —b?=1= A? + B?. Theorem B.—The same suppositions being made as in the last theorem, the co-ordinates of the point of intersection have the values f= Ady ye Bb. And CP the central distance of the point of intersection, is equal to VB, which also has the value,— V A? +a?—1. For we proved in the last theorem that HP=a—A, but by the Lemma ( putting e==) a HP=a—= x _ Therefore, a= A, or w=Aa. It remains to find the value of y. 296 MR TALBOT ON FAGNANI’S THEOREM. Take the equation to the ellipse = eke ca and substitute for 2 its value Aq, oy re ees Fae a =1—A?=B?, ». y=Bb. And a similar result is obtained from the equation to the hyperbola, viz.— a? y? A? BF For this gives, by putting for z its value Aa, 2 a=, - : Ya 2_1=)? “2. = DD. The remainder of the theorem is thus demonstrated,— Since v= Aa, and y=Bb, CP? =a? + y?= A?a? + Bb? = A?a? + (1— A?) (a?—-1)=A’ +a?—1=A?+0? —VB?; and therefore CP= VB. From hence we derive the following remarkable property of confocal conics :— If two ellipses and two hyperbolas have all of them the same foci, and inter- sect in four points, 4, /, m, n, forming a curvilinear quadrilateral, the straight lines /m, kn, which form the k diagonals of this quadrilateral, are equal to each other. we Demonstration —Let the semi-axes of the ellipse 3 and hyperbola nearest the centre be called a, b, and A, B; C Hi and let those of the ellipse and hyperbola farthest from — Fig. 15. the centre be called a’, 0’ and A’, B’. Let the co-ordinates of the point J! be # andy. FHOSEHOE PU, 2 220K 2 Hy those.ot. © zm: ¥, THOSCOL 1 ccoarenn Uae Then the square of the diagonal §= 4m=(x,—«)*+(y,—y)? And of the diagonal kn = (@,— @)? + Y3—Yo)™ What we have to prove, therefore, is that these two expressions are equal. Now, since the point 7 belongs to the ellipse whose semi-axes are a, b, and also to the hyperbola whose semi-axes are A, B, we have «e-Aa y =Bb. And for similar reasons, = aD Ad nD t =A’ ay,=Bb Therefore, xa,=Aax A’a’ And t,%,=Aa’ x Ma; And therefore, v,=2,7;, each side being the product of the four semi-axes a major. MR TALBOT ON FAGNANI’S THEOREM. 297 In a similar way it is shown that vy, = 773, each side being the product of the four semi-axes minor. Now, we wish to prove the equality of the expressions (2, —#)’ + (y,—y)? and («3-2») + (Ys— Yo)”, Subtract from them respectively the quantities —2 (vx, +yy,) and —2 (x,%,+Y3Y>) which we have just proved to be equal. The remainders will be ater +y ty’. And Genelia Ui- AE hee And now it is required to prove that these two remainders are equal. But we have proved in theorem B, that x? +y?=A?+a?—1; and by similar reasoning, v7 +y7=A? +071. ‘ Therefore (a’+7°)+(a’+y,)=—2+the sum of the squares of the 4 semi-axes major. And by similar reasoning, (#,’ +22") + (w;'+y;°) is equal to the same quantity. Therefore the two remainders are equal; and therefore the theorem is demon- strated. From this theorem several others may be deduced, by giving extreme values to the four curves. In the first place, if the two ellipses are drawn infinitely near to each other, and likewise the two hyperbolas infinitely near to each other, then, because con- focal conics always intersect at right angles, the small quadrilateral formed by the four intersections will be a rectangle, and of course its diagonals will be equal. Next suppose that the axis minor of the first ellipse is infinitely diminished, ‘the quadrant of the curve will be reduced to the straight line CH, extending from the centre to the focus. At the same time let the semi-axis major of the first hyperbola be infinitely diminished, and the vertex of it will then coincide with the centre, and the curve itself will become a straight line in the direction of the axis minor produced to infinity. The four curves will thus be reduced to one ellipse and one hyperbola, and two rectangular straight lines. The quadrilateral figure then becomes BCVP (see figure 14), and our theorem asserts that in that case CP = BV, the truth of which was independently proved in theorem B. Now, let the other hyperbola also have its axis minor infinitely diminished, its ’ vertex will then coincide with the focus, and the curve will be reduced to the straight line HA produced to infinity. The line CP then becomes CA, and BV VOL. XXIII. PART II. 4M 298 MR TALBOT ON FAGNANI’S THEOREM. becomes BH (see fig. 14). Our theorem asserts, that in this case CA=BH, the truth of which is otherwise manifest. Again, let CA, CB, and CX, CY, be the semi-axes of the two confocal ellipses, but let the confocal hyper- boles be reduced as before to the straight lines CBY (produced to infinity), and AX (produced to infinity), the intersections of the first hyperbola with the ellipses C AX will be B and Y, those of the second A and X. The Fig. 16. diagonals will become the lines BX and AY; and our theorem asserts that in this case BX =AY, which may be proved independently as follows :— Let the semi-axes of the smaller ellipse be a, 6, and of the larger one a, £. Since they are confocal, a? —b? = a?—g?, and therefore a+h =a? +b. But a? +B? = AY?, and a? +b? =BX?, Therefore AY=BX. This theorem may be thus enunciated :— “ Tf the alternate vertices of two confocal ellipses : are joined, the lines joining them are equal.” The co-ordinates of (x, y) the point of intersection of a confocal ellipse and hyperbola, may also, if preferred, be readily deduced from first principles, as follows :— 2 2 Given the confocal ellipse and hyperbola whose equations are twa and a Nate the co-ordinates at the point of intersection ? vy =1, with the condition that a?—b? = A? + B’=1 to find the values of w and y : 5 ; B? ; The equations give respectively y?=0? ee w and y?=75-2°—B’. Equating > (Bear + A? ? ( A*a? B’, and a?—1 for b?, we find that B?+b?=a?— A, which is also equal to Bq? + 52A?, and therefore may be omitted on both sides of the equation, which reduces itself — these values of y’, we find B?+8?=« ) . Now, substituting 1—A? for 2 Op he a whence 2= Aa. Additional Note—In the second page of this Memoir it is said, that the total deviation tends to increase without limit. To this it may be objected, that the successive deviations may possibly form a diminishing series, having a finite sum. 7 But it can be easily shown that two successive deviations, when they are small, are (very nearly) equal to each other. Moreover, after diminishing to a certain extent, the deviations increase again, having one maximum and one minimum value in the course of one entire revolution round the circle. MAP OF - to Illustrate op SCORESBY -JACKSON'S PAPER 6 5 4 3 Pe = 7] Wa TF SHETLAND > ISLANDS SCOTLAND Foula’ | ] | | | ON MEDICAL METEOROLOGY, | | | Stations of the Meteorological Society @ Eight Large Towns underlined Red 2 PN. Ronaldsha Seale of English Miles eeekeetO)nn 20; 53040 | | | } | Ga IsLANDS ae | | | | Butt of Lewis |eek PENTLAND DFIRTH a 2 ro Zz Mois. | (G ampbel WIL, House FIRTH OFS G7 poe of @ lagtire Girvan Lanark /g Se "Dingle Aya aaa 2. 4) @Manl pi Su ‘ H \ {i | 4 Banff *.--- _ Newb slig0 @ \) is e hl UAE: we as ee qh ae lat v va innards He ) SMonenaven @Fette cain | tthe Ht Jerwick Valls Zz 5 \s W&A K Joimston Eduuburgh 2 A “a 7 A i é i ] eg vom t Bt mn Rn 5 F ' 7" a 7 ’ a = Se th ATEN I i ee - he Temperature (Fahrenhett/ J857 to 1862, Absolute Highest Mean of Day @@&% Mean Tenperaue Mear of Night Absolute LOWES mmm Mean Daily Range a! whe Oe — Se Se ara 7 | i Bea ME? 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SS = a = SSS —— === SS PJ “See it ; r S7 S < \" Y a EEE = WN Y ai == OK risa LN lta Gy “iy y enn, S LOK LY a OS em Ubi a= UY yf" ZZ os Ss ees << GALLE ALI, G44; —— Ey Yj LY —— LZ / A A ee a —— J a. == =. ee a i Loe ii y ‘ , Wi I) \ < {= \ ¥ Ws oS SS SS [} 5 ey ‘ <> s 4 We : Yj yj SS “ < . 0 of < Ly 1 \ \ \ . — ae = MORTALITY PER 9 asi SS oresby Jackson, MD.F.R.S.B. cted by R.E.Sc onsiru cases of the Tiubercalar Class ra Deaths trom all Specitied Causeswm Deaths trom Lymotic Distascsmm= Deaths trom Dis Deaths from all Canrses the Respiratory Orgarise™ At all Ages. p Deaths trom Diseases of Trans. Roy. Soc. Edi, Vol XXMLPLXVA an Mist e annt and Diarrhoea mms at all Ages. Deaths from te VOUS OE SCOTLALTN A Ce Deaths trom Bronchitis MORTALITY PER 00,0 i 5; i = ann y El) L. | S 2S f 4 i PPA)! ) | HLL, y Mi Ht) A MTT Wy, Phihisis Pulmonalisemmemm and Preumoniovme:m at all Ages. S \ \ \ . : a | \ \ \\ \ 7, : \ \\ \ \ \ c \\ = i mt \ ' " \ My WA { Mit WIT] WATE Hy Hii) Ht \ lt | Il NID y / tay ELT ES Ce } / Trans. Ray. Soc. Edin. Vol XVIM.PLXVIL € ————$_ Edinburgh 4 7 & — : 5-20 yeaT Sem § L0-COVCAT Swmmmm 60-&c. yearss Deaths trom all Causes a diferent Ages: 0-8 years Tr ay m oa y. y a eS Poe, d a7 - Z ee r «7 -_ a * Fo -a J ad a * » B 0 a he . ”) ‘ ¥ ~ ‘ . . ERRATU M. I regret that, owing to the circumstances under which the last of the Meteorological data were obtained, an error has crept into one of the tables, and from the table, some- what into the text also, The Meteorological data for the quarter ending December 1862 were obtained from the Observatory, on slips of paper, from time to time, as they were reduced, I was obliged in this way to anticipate their publication, as the time for reading my paper was fixed for the 2d of February. Unfortunately, in constructing Table B, the slip of paper with the figures representing the number of rainy days, the rainfall in inches, and the direction and force of the winds for November 1862, was employed in the October column, the figures which ought to have been there finding their way into the November column. This error in Table B still exists. The errors in the smaller tables of the text, arising from this transposition, are not of serious import ; and indeed, if they had not occurred, the inferences drawn from the tables would generally have been only more apparent. The errors do not exist in Tables A and C, nor in the Diagrams ; and in order to correct the errors of the smaller tables, it is only necessary to test the accuracy of the figures, by reference to one of the latter tables, in the few instances in which the rainfall and winds of October and November 1862 are quoted as illustrations. ( 299 ) XXV.—On the Influence of Weather upon Disease and Mortality. By R. E. Scorespy-Jackson, M.D., F.R.S.E., F.R.C.P., Lecturer on Materia Medica and _ Therapeutics at Surgeons’ Hall, Edinburgh. (Plates XIV.—XVIIL.) (Read 2d February 1863.) The subject to which I have to invite the attention of the Society this evening is one of no modern origin, the name of Hippocrates, amongst others of the fathers of medicine, being commonly associated with it. There is, indeed, perhaps no branch of medical inquiry whose history dips more deeply into the obscure pages of antiquity. The influence of weather upon disease and mortality has been acknowledged as a potent external force in every age, from that eminently speculative and credulous period when physicians professed to receive their diagnostic as well as their therapeutic inspirations from the stars, down to our own day. And yet there is perhaps no question in the whole cycle of medical sciences which has made slower progress than the one we have now to consider. People believe that the weather affects them. They speak of its influence, some- times commendingly, more frequently with censure, on the most trivial occasions ; but beyond a few commonplace ideas, the result of careless observation, or perhaps acquired only traditionally, they seldom seek a closer acquaintance with the subject. Our language teems with medico-meteorological apophthegms, but they are notoriously vague. The words which are most commonly employed to signify the state of the weather at any given time, possess a value relative only to the sensations of the individual uttering them. ‘The general and convertible terms—bitter, raw, cold, severe, bleak, inclement, or fine and bracing, convey no definite idea of the condition of the weather; nay, it is quite possible that we may hear these several expressions used by different persons with reference to the weather of one and the same place and point of time. In order, then, to render medico-meteorological researches more trustworthy, we must be careful to employ, in the expression of facts, such symbols only as have a corresponding value in every nation. As a matter of purely medical inquiry, the influence of weather is also too fre- quently neglected. So true is this, that when we examine the literature—at least the modern literature—of the subject, we find it to be most meagre, and very few are the statistics which we meet with to guide us in a further research. When I say, that in a medical point of view the influence of weather has been disregarded, I speak relatively to the amount of labour bestowed upon other branches of medical science; and I do not for a moment ignore the valuable con- tributions to this department which have been made from time to time by phy- Sicians of distinction. In France, Belgium, Germany, Italy, and America, as well VOL. XXIII. PART Il. 4N 300 DR R. E. SCORESBY-JACKSON as in the United Kingdom, there have been many physicians during the present century, who by their labours have enriched this peculiar branch of medicine ; and if I do not frequently quote their writings, it is neither from a want of respect to them individually, nor from a desire to underrate what they have accomplished, but simply because my time is very limited ; and, further, because [ think it will tend far more to the progress of the inquiry to pursue my own researches independently of any other investigations. It is well known that the influence of external causes upon the constitutions of living creatures differs materially with locality. These causes are not only numerous of themselves, but they are moreover capable of producing an infinite variety of results, according to their several combinations. ‘Their effects are as distinct in different countries, as are the features of men of different nations. Therefore, conclusions derived from investigations pursued here can have no dependence upon the knowledge acquired by physicians in other countries; nor can any discrepancy which may be observed between the results of such several investigations serve to impugn the accuracy of individual deductions. Jt is quite possible that the results evoked by CaspPER in Berlin, QuETELET in Brussels, Boupin in Paris, Emerson in Philadelphia, and Guy in London, as well as those by the Registrars- General of the United Kingdom, may differ widely in many essential points, and yet the inferences of each observer be correct in themselves. The same may be said of the researches of Sir JAMES CLARK, CLESs, EpMonps, Emerson, Forssac, Francis, Fucus, HAvitANnD, HALLER, HirscH, KerrH JonNston, LOMBARD, MADLER, Marc p’Espine, Martin, Meyer, Mitne-Epwarps, MuUnry, Ransomes, RIcDEN, ScHUBLER, TRIPE, VILLERME, and of many other careful observers. My object is to examine the relations which exist between the weather and the health of a community as closely as I may find it practicable to do so; and in pursuing this inquiry, my desire is to divest myself of all foregone theory, and to make the facts which I have collated speak for themselves. We have the strongest indication of the utility of such investigations in the fact, that, whether we do or do not possess a knowledge of the etiological and therapeutic influence of meteorological phenomena, we invariably act as if we were most intimate with the subject. Delicate persons crave for, and physicians often recommend, change of climate, which in many instances is a term convertible with change of weather, though it often means nothing more than change of scenery and of mental or physical occupation. If it be a good thing for a sick man to change his residence, it must be a proper thing for him to know what it is that he is avoiding, and what it is that he is to acquire in exchange for it in another place This must remain an exceedingly difficult question to solve, until we have statistics from every health resort, showing the correlations of weather and disease in each. Weare not to assume that because certain conditions of weather, as indicated by meteorological instruments, in this country are opposed to recovery from certain ON THE INFLUENCE OF WEATHER UPON MORTALITY. 301 diseases, that, therefore, patients so suffering are not to be sent into any country where meteorological instruments afford exactly or even nearly parallel readings. In other words, in estimating the value of a foreign climate, or the different climates of our own country, we are not to depend so much upon a comparison of the meteorological data of the several places as upon the relations subsisting between the meteorological data and the prevalent diseases and death-rate of one and the same locality. Each spot of ground aspiring to the reputation of a health resort must first have this problem solved for it, and then we may with greater safety institute a general comparison. All that we can do in our present investigation is to find out, if it be contained in our data, what is good and what is objection- able in the climate of certain localities in Scotland, as evidenced by the general death-rate, and by the mortality from several causes. This will not in any way affect the character of the climates of Torquay, Bournemouth, Algiers, or Rome, except in so far as there may have been a line of investigation pursued in any of these places parallel with that now under consideration, so that a com- parison may be instituted between the two; for, to argue, that because a given condition of temperature, atmospheric pressure, and humidity in Scotland is accompanied by a certain ratio of mortality, therefore, meteorological data being equal, the same death-rate will be observable in Torquay or Madeira, would be most fallacious: all other things being equal, the death-rate would also coincide ; but it requires much more than mere meteorological analogy to establish such a parallelism. But the present inquiry may serve another, and perhaps still more important, purpose. By far the greater number of cases requiring medical treatment do not involve the consideration of change of residence; nevertheless, I venture to assert that in all of them the weather plays an important part; and it cannot be otherwise than right for the physician to know whether he has, in the atmosphere around his patient, a foe or an ally in the treatment of his malady. In medical prognosis, a knowledge of the influence of weather is of essential Service; and as an agent operating upon the therapeutic action of drugs, weather forms a most important study. I do not pretend that this is by any Means an exhaustive inquiry; nor have I strained my facts to meet any so-called natural laws. On the contrary, the facts speak for themselves, some- times making positive, sometimes negative assertions, and often enough hovering between the two, leaving us as much in doubt as before, but with a stimulus to deeper research into the influence of those numerous external agencies which are under the immediate control of the Great First Cause of all. An inquiry into the causal relations subsisting between weather and disease is beset with a multitude of difficulties. In the first place, we ought not to attri- bute to the weather any effect upon the mortality of a given population, until we have abstracted all other causes which might have operated in a similar manner, 302 DR R. E. SCORESBY-JACKSON and to which such effect might altogether or in part be due: a task which is not very readily accomplished. Again, we cannot, if we would attain a rigid accu- racy, attribute fluctuations in the death-rate to vicissitudes of weather, until we obtain a uniform climate over the entire area of observation, and this we shall never acquire. It may perhaps be objected to the results of my investigations, that it is not fair to apply the average of the climate of all Scotland to the death- rate of the eight larger towns; that the towns have a climate distinct from that of the rural and insular districts, and that each town has one of its own. That is quite true; but it is an objection which may with equal propriety be urged against the application of the climate of any large town to the mortality of its several parishes, the particular climate of each of which may, and often does, differ from that of its neighbour. But I prefer to consider the town districts alone, because it is in them that we meet with the mass of disease and the multiplied mortality ; and as to the applicability of the general climate to a local — death-rate, we may regard it in this way, that the climate of the townsisa climate within a climate, and that, whatever difference there may be between the containing and the contained, any modification of the larger must in a corre- sponding manner affect, if not in degree, at least in kind, the smaller. Another objection might suggest itself in the returns of the cause of death made to the Registrar-General. It may be said that many of these returns are, at least, inexact; as, for example, when it is stated that death was caused by dropsy, the accumulation of fluid being merely a symptom of the real dis- order: or, where the certificate tells only half the truth, as when a person who is dying of one disease is accidentally cut off by an intercurrent attack of another kind which would not have proved fatal but for the moribund condition of the patient at the time when it took possession of him; in such a case one class 0 disease is robbed of a victim which another gains by an adventitious circum- stance. These and many other objections might be raised against investigations into the influence of the weather if we would be satisfied with nothing short of logical exactness ; but we may undoubtedly arrive at an approximate knowledge of its effects if we are careful to avoid error in the main features of the inquiry. The influence of external causes upon the constitutions of living creatures varies with locality, the variety depending upon the character of the causes, whether individually or combined. In a general way, these causes may be classed into two leading groups, as in the following order :— A. Untversat Causes, arrecting Nations, as,— 1. Position of a Country relative to—The Equator—water in motion (e.g., the sea with its currents ; rivers, springs, extensive lakes)—stagnant waters (e.g., canals, shallow lakes, marshes)—mountains, forests, arid plains, fields of ice. 2. Aspect of a Country,—General elevation and configuration, geological structure, physical and chemical properties of its soil, state of cultivation. 3. Atmospheric Phenomena.—Temperature, barometric pressure, direction and force of winds, humidity, insolation. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 303 B. Locat Causes, arrectine Districts anp InpivipvALs, as,— 1, Meteorological Phenomena—Abnormal heat or cold, abnormal drought or humidity, abnormal fluctuations of the barometer (i.e. of atmospheric pressure), pernicious winds, ozone, electricity, diurnal phenomena, seasonal changes. 2. Habitation—Situation (town or country, on the coast or inland), elevation, construc- tion, drainage, ventilation, heating, lighting, overcrowding. 3. Dietetics—Price of food, quality of “food, quality and quantity si potable water, and of water for all domestic purposes. 4, Personal—Dress, occupation, habits and pursuits. Although it may not be advisable to consider these several modifying causes in detail, nevertheless it is necessary that a passing glance should be accorded to them, in so far as they relate to this country. Scotland, in its mainland, extends between 54° 38’, and 58° 40’ 30” of north latitude, and 1° 46’, and 6° 8’ 30” of west longitude. Including the circumjacent islands its limits are wider. ‘The length of the mainland between its extreme points is 276 miles. Its breadth varies so greatly that no general idea can be given of it in one sum; it ranges from about 30 to 175 miles. In its general outline and configuration, Scotland is very remarkable. On glancing at a map of the country, the attention is at once arrested by the peculiar indentations of the coast line. In several situations the land is almost bisected by the prolon- gation of the sea into its interior, forming what are called Firths and Lochs, which serve to increase very considerably the shore of the country. The coast line, followed in all its sinuosities, occupies probably more than 3000 miles; but taking only the larger inlets of the sea into consideration, the circumference is probably about 2500 miles, which gives one mile of seaboard to every eleven square miles of surface ; the estimated area of Scotland, inclusive of the Islands, being 31,324 square miles, or 20,047,360 acres. The ratio of seaboard to area over the whole of Europe is about one to twenty-five; Greece and Denmark being the only countries which approach Scotland in respect of proportional extent of coast. The islands of Scotland constitute about one-ninth of the entire area. It is obvious from these facts, that the sea, as an external cause operating upon the constitutions of the inhabitants, must be in the highest degree potent. And it is fortunate for Scotland that the influence of the sea is benign—unlike its action on the ice-bound shores of Labrador. It owes its mitigating influence, so far as Scotland is concerned, to the prevalence of westerly winds across its waters, tempered by the Gulf-stream ; whereas, on the opposite shores of the Atlantic, the cold counter (Arctic and Hudson Bay) currents have a directly opposite tendency. Besides the firths and marine lochs adverted to, Scotland possesses also many inland lakes, which, although not of magnitude comparable with those of the . New World, tend materially to increase the aqueous element of its physical geography. The larger river-basins add also to the bulk of water in and around the country; in short, there is perhaps no point in Scotland more than a few miles VOL. XXIII. PART II. 40 304 DR R. E. SCORESBY-J ACKSON from a large body of water, and probably none more than forty miles distant from the sea. The same may be said with respect to the proximity of mountains; for there is scarcely any point commanding an extensive general view, from which a range of mountains may not be seen. There are five principal mountain chains, all of which assume a direction from N.E. toS.W. Besides these there are many detached groups, all of which exert a peculiar influence upon the climate. Forests do not form a special characteristic of Scotland, nor is there any barren plain within or near the country to modify the condition of the atmosphere in its passage across the land. But the ice-fields of arctic regions, lying not very far northward of Scotland, do probably exert a modifying power. The geology of Scotland is one of the most striking features of the country; and that the structure of the land, together with the physical and chemical char- acteristics of the soil upon its surface, exercises a powerful influence upon the dis- tribution of disease, I do not for a moment doubt ; so much, indeed, am I impressed with the belief of this, that I have been for some time collecting materials, witha — view of showing, more distinctly than has hitherto been done, the relations which these circumstances bear to each other. The following table will serve to indicate the condition of the inhabitants of Scotland, during the several years under investigation, with respect to other external causes which might possibly divide with the weather the responsibility of determining the death-rate from all causes, or from any particular disease. TABLE sHowinc THE AMOUNT AND Deraits oF THE Poor-LAw EXPENDITURE IN EACH OF TE Years FRoM 1852 To 1861 INCLUSIVE; ALSO THE STATE OF THE Fi1Ars-PRICES OF THE COUNTS EDINBURGH FOR THE Crops FROM 1855 To 1861 INCLUSIVE :— General Sanitary Measures, 393 532) 6,259) 6,355) 1,677: 1,122 1861. | Aven Year. 1852. | 1853. | 1854. | 1855. | 1856. | 1857. | 1858. | 1859. | 1860. Poor-Law. £ £ £ Ag 38 35 aS £ £ £ Relief of Poor on the Roll, | 401,954| 411,135) 428,708) 461,243) 486,689, 492,118) 496,297 512,751) 518,546] 531,233 474, Relief of Casual Poor, . 25,986| 24,114} 24,386) 27,356 22,188) 20,869] 27,915] 25,752) 22,218) 24,118 24,4 Medical Relief, . . . 21,436) 21,737) 27,874| 27,166) 24,008’ 24,205] 24,948) 25,691] 26,738 Management, . . . . 51,644) 52,352| 56,068) 58,767} 61,462, 63,142) 66,307| 67,166] 67,048 Law Expenses, .. . 13,266) 13,036; 9,780) 10,290) 8474 7,637) 7,165} 9,753) 8,750 Poor-House Buildings, . 21,186) 21,644) 25,850) 20,605) 24,847, 27,277| 18,066) 16,250 19,973 Total Expenditure, . | 535,865) 544,550) 578,925) 611,782 629,345 636,370) 640,698] 657,363 Franrs-Prices. Sx Ue iis: fet tsy hp. Se psss VDE SAD BIAS’ MDetlesaiaDe Wiheatyradlistsas 4) 7 ae a wise 70 9|40 0/38 4/40 1) 44 8 wan: 2d, ARE has an deh 68 0] 35 0} 385 6! 387 0| 42 O Barleyarmrlstsmrem wee oe cae ie 40 6| 36. 4| 27 3/31 74 37 6 Sy {0 eh eh i Sate to ate SOmOn 320 O25. “On 29 SOn oor G 4 SO. ae “a AGE 36 0/28 0} 22 6 | 27 0} 32 6 Oats, 1st, . 29°76) 23 0) 22 6) 23. 01/25 10 i 2d... 27 6 |-20. 0 | 20 6) 21. 0 | 22 6 Pease and Beans, 45 0| 37 6| 37 3) 3910) 43 8 Oatmeal, 21 3/19 2)16 53/16 83) 18 9 ON THE INFLUENCE OF WEATHER UPON MORTALITY. 305 There remains, then, only one more subject for preliminary consideration, and that is, the sources of the different data employed in the following pages. The meteorological data are taken from the collected returns from the stations of the Meteorological Society of Scotland, as reduced by the Astronomer-royal. The stations of the Society have a mean latitude of 50° 30’ N.; a mean longitude of 3° 4 W.; and a mean elevation of 222 feet nearly. It will be observed that the meteorological data are deficient in two points, namely, concerning electricity and ozone. Unfortunately, I have no means of applying these subtile agencies to the mortality of the years under examination ; with respect to electricity, indeed, I have no information whatever ; and concerning ozone, I have nothing trust-worthy. It is true that the Meteorological Society’s reports contain the results of observations made with the usual test-papers in different parts of the country; but I submit, with all deference, that until the chemistry of ozone is more fully understood, its physiological action cannot be accurately defined. So long as it is left to each ob- server to determine the amount of ozone present at his station by the varying depth of colour on a slip of paper, our knowledge of the true quantity present must depend upon very slender evidence, and consequently be of very questionable accuracy. It is quite possible that six different observers might, with exactly the same indi- cation on the test-paper, refer the amount of ozone present to as many different shades on the reference paper. Whether the paper itself affords a true indication of the presence of ozone, and to what extent, in the atmosphere, is a disputable matter. At all events, under existing circumstances, I should hesitate in com- paring the ozone returns with the death-rate. With respect to the humidity or dryness of the atmosphere, I have employed only three columns, showing, respectively, the number of rainy days, the amount of rain in inches, and the degree of saturation, as deduced by Mr GuaisHeEr: full satu- ration=100. Ihave therefore omitted the readings of the dry and wet bulb thermo- meters, the temperature of the dew-point, and the elastic force of vapour. I have also omitted from the tables, although plotted in the diagrams, the absolute highest and absolute lowest temperatures at any of the stations; these are exceptional records, and can have no general application to the subject of the present inquiry. The mortality tables are constructed from the returns made by the Registrar- | General. The period over which my investigations extend is six years, namely, from 1857 to 1862 inclusive. This, I conceive, is quite long enough to indicate the relationship existing between the weather and mortality in non-epidemic years. I would, however, have made the period seven years, by including 1856, but I found | that the meteorological data for that year were not trust-worthy ; a circumstance arising from the newness of the Society, the inexperience of the observers at many | of the stations, and a want of proper correction for the errors of the instruments then employed. The absolute facts concerning the meteorology and mortality of the seventy- 306 DR R. E. SCORESBY-JACKSON two months are derived as already described ; but for the arrangement and calcu- lations in the several tables, and for the inferences therefrom, mentioned in the text, [am alone responsible. The inquiry is led into the influence of weather upon mortality from all causes, from all specified causes, from zymotic diseases, from typhus, from scarlatina, from diarrhoea, from tubercular diseases, from phthisis pulmonalis, from diseases of the respiratory organs, from bronchitis, and from pneumonia, at all ages; and from all causes at four different periods of life—namely, under five years of age, between five and twenty, between twenty and sixty, and from sixty upwards. In order to simplify the comparison of the meteorological with the mortality tables, and to render the fluctuations of the death-rate more distinct, I have reduced the number of deaths in every case to the ratio per 100,000, living in the eight larger towns at the time when the deaths were recorded, taking the esti- mated population for each of the six years as the standard of reference. Whether I have obtained a strictly correct estimate of the population of the eight towns or not, I cannot positively say; that given in the reports of the Registrar-General required considerable correction after the taking of the census in 1861. In con- sequence of this alteration, I had to recalculate my tables. In their present form the tables are calculated upon the following basis :— ; Vous Population of the Deaths from all Causes in : Right Large Towns. the Hight Large Towns. Tao, ghey . «« uOswge 93,361 Aaa SS eee aero 23,420 1659, . : . 4... S6siiel 22,345 1860, .) .° 2-2 “s 3B7 E86 26,028 ieee EUs >!) eeeta 23,130 1862, . 9. 2 2). 893/850 24 965 Average, 868,796 Total, 143,249 In the mortality tables, each of the months of thirty-one days is reduced to — the value of thirty days, and the death-rate of February of each year is raised to the same value, so as to have uniformity over the whole seventy-two months. The red dots upon the map indicate the situations of the meteorological stations ; the red lines, the positions of the eight large towns, namely, Glasgow, Edinburgh, Aberdeen, Dundee, Perth, Greenock, Paisley, and Leith. The diagrams which I have constructed to illustrate the paper, are, I venture to believe, not without considerable value. They present to the eye at one glance, the whole scheme of the investigation, and will probably leave a more vivid impression upon the minds of those who care to examine them than would result from an unaided examination of the tables, or a perusal of the text. | Of the three larger tables, the first (A) is arranged to represent a gradually descending ratio of mortality, the several months of the six years being placed im ~ the order of the death-rate,—that in which the greatest number of deaths occurred — + " ON THE INFLUENCE OF WEATHER UPON MORTALITY. 307 being at the top, that in which the lowest mortality took place being at the foot of the table. Opposite the mortality column are placed the several meteorological readings and deductions of the corresponding months. The columns are then divided into four distinct sections, each comprising eighteen months, .the means of which are offered for comparison with each other, and with the means of the seventy-two months which are given alone in every third column. To have carried this table out to the extent of showing, in a similar manner, the order of the death-rate from the several classes of disease and individual diseases, as in the other tables, would have demanded more space than could reasonably be accorded. The materials for such extension, however, are given, and the arrange- ment might easily be made. The second table (B) is constructed to represent the meteorology, and the death- rate from all and several causes at all ages, and from all causes at several ages, in the consecutive order of the months in each year: the means and totals of each year are given in separate columns, and the last column shows the means of the six years. The third table (C) is arranged for the purpose of comparing the meteor- ology and mortality of the several corresponding months of the different years, the mean of each of the 420 shorter columns being calculated in order to show more distinctly the character of the various deviations. I may also mention that each table was calculated independently of the others; on this account the general averages occasionally differ to a very trifling extent. I.—TuHE INFLUENCE OF WEATHER UPON MORTALITY FROM ALL CAUSES. In the following details, I shall endeavour to show, as succinctly as possible, the influence of weather upon mortality from all and several causes; but I can- not pretend to exhaust the information which the tables and diagrams contain. I shall content myself with pointing out the prominent features of the inquiry ; the facts from which they are drawn being placed without reserve before the Society, the inferences which I deduce from them are open to criticism, and nothing can fulfil my own desires more fully than an exposure of error, whether of fact (7.¢., of calculation) or of reasoning. Season.—tThe influence of season upon mortality is not very distinctly under- stood, especially with reference to certain individual causes of death, opinions differing widely as to the months which determine the maximum and minimum of mortality from such particular causes. Here I would draw attention to the difference between mortality and disease; we shall fall into error if we suppose | that the season of highest mortality is always the season of greatest sickness. It not unfrequently happens that certain seasons which are characterised by a maximum of sickness are at the same time distinguished for their low rate of VOL. XXIII. PART II. 4P 308 DR R. E. SCORESBY-J ACKSON mortality ; and contrariwise, seasons which may be somewhat remarkable for the general health of the public, may, by their influence upon one or two classes present a high death-rate. It isa very difficult matter to obtain accurate statistics of the prevalence of disease over a large community. After collecting a mass of statistics of disease from several dispensaries and hospitals, with a view of com- — paring the rate of morlility with the rate of mortality as given in this paper, I was obliged, after much labour, to abandon the morbility statistics, as next to worthless. Therefore this paper points to disease only through mortality. If we turn to Table A, and regard the position of the months in the several sections, we shall find that while certain of the months are widely distributed through the column, others are arranged more compactly; but in no instance are the six corresponding months of the different years encompassed by one section of : the column. If we apply to the several sections (from above downwards) respec- — tively, the names maximum, major, minor, and minimum of mortality, and — arrange under each title the number of corresponding months found in the section, — we shall at once see how many of the years approached to uniformity of mortality, — and how many were exceptional. mooaet : : ry peat Mortality. Moret Mortality. Aontaltey January, « . ss 1 1 Pebraary. es 4 2s 3 a March, eefge ke ea AL 1 1 April, 2 2 2 ate May, 3 2 1 June, a 4 2 July, 1 2 3 August, iin Bae Oe 1 ate 5 meprember,. Osh vfs 33 1a 1 5 October] atuh/cml doen site ee 4 2 November,, . s, 5 ) L 5 wish December, 5. vA 1 i : Total, 18 18 18 18 This table shows us the distribution of the months, but not their order as — determined by an average of the six years; for this we must look to Table C, and taking from it the means of the several columns, showing the mortality from all it follows :— Month. Death-rate. Month. Death-rate, ‘January, . ; . 265°3 May, Maximum, i February, . : . 2657-4 Minor, ~ June March, : : . 249°8 l July, “December, . ; . 247-9 October, Major, . jae «Bale 3 . 242-8 | Minimum, | August, November, . : » 2004 September, Mean 225°7 ON THE INFLUENCE OF WEATHER UPON MORTALITY. 309 If we revert to the previous table, we find that January, March, and December. have a like distribution over the maximum, major, and minor sections, the deter- mining years being in the maximum, and an exceptional year in each of the two following sections, and we might have expected that these months would all have preceded February, which only contributes three years to the maximum section; but in the latter table we find February in its true place, taking prece- dence of March and December. This arises from the exceptional years of the latter months having a much lower rate of mortality than any of the Februaries. Before proceeding to examine the meteorological data in detail, we have here an opportunity of testing the influence of weather in a general way. If the weather had anything to do with the placing of the exceptional years, we shall expect to find that in the months of January, March, and December, those years which contribute to the major and minor sections will be more temperate than those whose months enter into the maximum section. In the case of November, severity of weather ought to characterise the exceptional year, and there ought, moreover, to be some marked peculiarity in the meteorology of the exceptional August. It will be unnecessary to test the other months at this stage. We begin with January, and instead of quoting figures, let us take the general remarks contained in the meteorological reports as our guide. The four Januaries of the maximum section are those of 1861, 1862, 1860, and 1857, in the descend- ing order of their mortality; the exceptional January in the major section is that of 1859; that in the minor section, the January of 1858. The relations which the months of the different years bear to each other, will be still better under- stood in this form :— Y Maximum. Major. Minor. ee Mortality Mortality Mortality 1861, bei ae 3046L 1862, : ; 5 296°6 | fecomh > fii 16 e808 | Fe ie tl thng ens ok BRD ms PBB ors, 250, eae Ae 243°4° ee | Reco el lo vile » # 214-0 January 1861.—{I quote from the Meteorological Reports) “ From these returns we gather that the month of January was still, like so many of the preceding ones, below the average in temperature, though in a less degree; the barometrical pressure was unusually high; but otherwise there are no remarkable differences in the other meteorological elements.” Dr Srark says of the same month,—‘‘ The intensely cold weather which set in about Christmas, and, after a, partial intermission, recurred during the earlier part of January, exhibited the usual effect of low temperature in this country, in largely increasing the number of deaths.” January 1862.—Meteorological Report: “From these returns we gather that 310 DR R. E. SCORESBY-JACKSON in January 1862 the most remarkable features were the great depth of rain, the large number of rainy days, the large amount of cloud, and the small amount of sunshine,—each of these quantities being more extreme than ever before regis- tered in a January month. The mean temperature was also high, though not to so great a degree.” Registrar-General: “January was a comparatively mild month for the season, with a mean temperature rather above the average, an unusual amount of mild south-westerly breezes, a consequently greater fall of rain, and a greater degree of humidity of the atmosphere than is usual during that month. This mild weather was, however, often interrupted by the wind suddenly veering to the north and east, and blowing with a keenness all the more severely felt, and the more detrimental to the health of the people from the previous mildness.”’ January 1860.—Meteorological Report: ‘ For the month of January we thus find that the mean temperature, though 1°°5 higher than that of the preceding months, is yet 1°°7 less than the average of former Januaries, constituting there- fore a particularly severe month, as additionally manifested by the black-bulb temperature by day being 6°-2 less than the average, and by night 3°°3 less,—the hours of sunshine being less, and the amount of cloud rather greater. The mean humidity has also been greater, as well as the amount of rain, with an unusual preponderance of north-east wind.” Registrar-General: “ The past quarter, com- ing as it did after the wintry weather which prevailed during November and December, was one of the most severe which has been experienced in this country for at least thirty-four Januaries, if not for a much longer period.” Such are the reports of the weather of those months whose death-rate is above the average of the six Januaries; from this point the weather ought to improve. January 1857.—Meteorological Report: “January. The weather wasasnearly as possible an average in point of severity.” Registrar-General: ‘“‘ During January the weather was generally open, though the month began and ended with a snow- storm.” This month, although below the average mortality of the six Januaries, still contributes to the maximum section. January 1859.—Registrar-General: “The weather during the quarter was mild for the season, but stormy and rainy to an extent scarcely remembered to have been equalled within the recollection of the oldest inhabitants. The winds, which, during almost all the quarter, were from the west and south-west, were unusually high, and brought much rain with them.” The Meteorological Report is too extensive for quotation; in substance it is the same as the remarks of the Registrar-General. It should be mentioned, however, that whilst there was a remarkable increase of rain in the western counties, there was at the same time a remarkable deficit in the eastern counties. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 311 January 1858—Meteorological Report: As showing the general mildness of the month, it may be mentioned that at Sandwick, wall-flower, stock, carnation, and borage were in flower, so as to yield a bouquet on the Ist of January, while the hepaticas were in flower on the 4th. At Aberdeen, the hazel and snowdrop were in flower on the 25th; and at Banchory House the Rhododendron ponticum was in flower on the 29th. The thrush was often heard singing during the month at Scourie, and the lark at Aberdeen.” Registrar-General: ‘“‘ The weather dur- ing the first two months of the quarter was unusually mild and open; and though the mean temperature was gradually falling during January and February, it was not till the lst of March that winter, with its frosts and snow, fairly set in over the country.” Thus far, then, whatever we may meet with in detail, we must be impressed with the fact that the general term of a “‘ mild” or “ open” January corresponds with a low rate of mortality, a ‘“‘severe” January with a high rate of mortality. We next proceed to consider the months of March, and, in order to avoid long quotations, if we find that the exceptional months were “ mild,” we may assume that the four months of the maximum section were more or less “ severe.” Y Maximum Major Minor Pay: Mortality. Mortality. Mortality. 1860, . . . 283-2 ie et ) P2568... .. . .257°8 1862, .°. -, 2567 1857, . . . 250-0 a een CE My i130 232°0 oe 1861, - 220:2 March 1859.—Registrar-General: “This month has therefore been charac- terised, even more intensely than the last, by an unusual amount of west wind, a low barometer, and, on the western coast, abundant rain and equable tempera- ture. On the eastern coast, the rains have been scanty, but the temperature high.” March 1861.—Registrar-General: “The months of February and March however, have both been above the average temperature; and as this increase of temperature has been attended with a greater fall of rain and a greater amount of humidity than usual, while there has been a diminution in the proportion of cold arid east winds, and a preponderance of high winds from the west and south-west, there has been a free circulation of air, and no such stagnation of the atmosphere as would allow the excessive moisture to become hurtful.to the living inhabitants. Hence the mortality of February and March has been below the average of former years; and if the weather continues favourable, as it appears : to be giving every indication of doing, the present year may prove, like the census year 1851, a year of low mortality, and of prosperity and heavy crops to the farmer.” Here “mildness” characterises also the months of lower mortality. VOL. XXIII. PART II. 4Q 312 DR R. E. SCORESBY-JACKSON We may test the months of December in a similar manner by ascertaining the character of the exceptional years. Wear Maximum Major Minor ' Mortality. Mortality. Mortality. 1859, . . . 263-4 1862, . . . 259-0 LSS Lu aaST 7 1858, . . . 250°0 fi ‘eee le HOGA eet ee Pe 241-4 he Gey: eT) Ae Be af 915-7 December 1861.—Registrar-General: “From the returns it appears that the month of December, in the important feature of mean temperature, has been nearly normal, and thereby between three and four degrees warmer than the two last. Decembers.”’ December 1857.—Registrar-General: ‘“‘ During the quarter the weather was unusually mild,—so much so, indeed, that even sprigs of hawthorn in full blow, and several spring flowers, were gathered at Christmas; and in the north, a second and abundant crop of cranberries was gathered the second week of December.” The months of November present only one exceptional year, and that alone contributes to the maximum section; it will be sufficient to ascertain whether it is remarkable for its “‘ severity.” Y Maximum Major cari Mortality. Mortality. 1858, . . . 2661 a feng Sul 236-0 1BGReats) uly < hace 234-7 | “2 TGS $.. siarh. hae 231°3 Mom 220 USCC. i. wea 58k 230-0 Tee CS ee: 2245 November 1858.—Registrar-General: ‘During November, again, the mean temperature of the month was 2°.2 below the average, and severe, stormy weather, accompanied by keen frost and falls of snow, prevailed during the third week of the month.” We have, however, an anomaly in November 1861, in which, with the lowest death-rate of all the Novembers, we find the following description of the weather: —‘ Hence it appears that the month of November has been cold, wet, and windy, to an unprecedented degree. The barometer was lower, and more uniformly low than in any month of the last six years. The mean temperature was lower than in any November through the same time.” It will be noticed, however, that there is not a great difference in the death-rate between the several years entering into the major section. And, lastly, concerning the months of August. One of these months only presents an exceptional death-rate; it is that of the year 1857. The months of September present also an exceptional month, likewise that of . xj ON THE INFLUENCE OF WEATHER UPON MORTALITY. 313 1857, but not to so great an extent as is witnessed in the case of the aberrant August; and forasmuch as the cause in both instances is obviously identical, it will be sufficient to explain it in reference to August only. ae Major Minor Minimum ae Mortality. Mortality. Mortality. Roa =. . 22a sce mapceur let Nye 2y 7" 199-5 meas desc: ras) oil’ os 192-4 : oo Me 178-7 cae oe LEIS (all alee aha a at 1731 sO Qumb ss i fabs nae 168:4 August 1857.—Registrar-General : ‘“‘The mean temperature in August realised the very unusual height of 60°, and as July also, and the beginning of September, had mean temperatures higher than usual, bowel complaints (diarrhoea, dysen- tery, and cholera) became so prevalent and fatal, that instead of only 56 dying from these complaints in every hundred thousand persons, as in 1856, no fewer than 112 deaths occurred in a like population in 1857.” We proceed now to consider the influence of the several meteorological phenomena upon the mortality from all causes more in detail, and first we have to consider The Influence of Temperature upon Deaths from all Causes. Turning to Table A, we find that although the column of mean temperature does not increase in value so evenly as the column of mortality diminishes in value from above downwards, nevertheless over the whole of the two columns there is a distinctly inverse relationship; and if we compare the means of the four sections previously described, we find that the relationship existing between temperature and deaths from all causes is as follows :— Mean of Mortality. Pagers Maxmmum Section, .. ... «= \« 269°49 38°3 Miror-Sechlomy ray oe ete ee 233:°25 43:1 Miimor SeChlOn pres) aah as) ete. 214:26 49-5 Minimum Section, . . ... . 185:85 54:3 Mean of the 72 Months, 225°71 46:3 To ascertain the difference of influence between a high and low mean tempera- ture, I have constituted, out of the six, three factitious years; for the one, taking all the lowest temperatures of the six corresponding months ; for another, the highest temperatures; and for the third, the mean of the six corresponding months. The death-rate of the three may be compared month by month. [Obviously, one dis- advantage of such an arrangement is, that by associating the sequent months of different years we at once dissolve the continuity of effect which the weather exer- cises over mortality. It is important, in estimating the value of weather as an etio- 314 DR R. E. SCORESBY-JACKSON logical agent at any given time, that at least the character of the weather imme- diately preceding the period under examination should be ascertained, the influence of sustained heat or cold, for example, as will be shown hereafter, being remark- able. Nevertheless, when the period of comparison extends over an entire month, I think we may safely believe that the fluctuations in the death-rate—in so far as they are dependent upon weather at all—are dependent upon the weather of the particular month in which the deaths are recorded. This is not uniformly so Suppose, for example, that the fourth week of January were intensely cold, and the subsequent month of February comparatively mild, it is quite possible that a large number of deaths, caused by the cold of January, might fall to be registered in February; so that if either of the months were examined separately, an erro- neous impression concerning the influence of temperature would result. If the periods of observation had been daily or weekly, I would on no account have separated them, because necessarily the ratio of deaths of one day, or even of one week, must often be, to a certain extent, modified by the weather of the previous days or week; but, I repeat, where each subject of comparison extends over a whole month, errors from such a cause as I have now explained must be very trifling. It is, however, to obviate such errors that I have constructed Table B, in which both the meteorological and necrological data are arranged appositely in the order of the sequence of the months of the several years. This explanation is also offered to objections which may be raised against the order of the months in Table A.] I need not mention the years from which the several months are taken ; that will be seen on reference to the larger table :— - January. | February. March. April. May. June. Months of Lowest Mean Temperature, 35:5 280-8 34:0/330°6 3782567 41°: 3022-71491 225-4159°410150)_ é , Highest, . 39:6 243'4 40° 246:9 43:0.232-0.45-4.223°3 519 193-558-9219-3| Mean of the Six Years, . . . |37'4265°338-2/257:439°8 ec Phan 208-6) — ae a | July. ° | ° ° ° ° Months of Lowest Mean Temperature, 53:8 19235441 92-4/50°2/182°5 44-91205+3 37:1 » Highest, bs 59-0 181-3 60-0 224-1 56-1/210°8/ 49-6 208-043-7 Mean of the Six Years, . . . (|06°8 i a ea eile aT 21909 alee | August. | September. | October. | November. | December. | 234-7 5102634 931°3/44-9915-7| so-5237 aaa If this table speak truly, it leads to the conclusion, that for every diminution — of mean temperature below 50° there is a corresponding increase of mortality; but that from mean temperatures above 50° a diminution is favourable to vitality, at least if the temperature have been for any length of time above 50°. In | other words, mean temperature and mortality from all causes have an inverse relationship below 50°, a direct relationship above 50°. But it must be borne in rn ON THE INFLUENCE OF WEATHER UPON MORTALITY. 315 mind that the change is gradual: thus, in May, with a temperature of 51°-9 there is a mortality of 193-5, which is still below 225:4, the mortality corresponding with a mean temperature of only 49°-1. But if this be a rule, then the months of April and July are exceptional, the April with a lower mean temperature hav- ing also a slightly higher death-rate, the anomaly perhaps depending upon other meteorological elements. The April with the higher mean temperature and the lower death-rate had a mean barometric reading of 29°751, and a rain-fall of 3°20 inches; the other April had a mean barometric reading of 30°177, and a rain- fall of only 1:04 inches,—the one a low atmospheric pressure with a surplus humidity, the other a high rate of atmospheric pressure with a deficit of moisture. If I had selected the April of 1860, whose mean temperature is only 0:2° above the one in the table, namely 41°5°, the rule would have been sustained, the death-rate for that month being 290:2. The July with the lower temperature and lower death- rate had a mean barometric reading below the average of the six years with a rain-fall above it; the July with the higher mean temperature and death-rate had a barometric reading above the average of the six years with a rain-fall below the average. The July of 1857, with a mean temperature only one degree below that in the table, had a death-rate of 210°5. Monthly Range of Temperature.—The relation of monthly range of tempera- ture to the death-rate from all causes is also shown in Table A, the means of the four sections being as follows :— Section. Mortality. ree ee Maximum, Si Otieuk tpl eudrn 269.49 36°4 MANION, F Celot tsi | Get aGe Lay Leas 37:2 Biinor pele? Meet rset Gh hee 24D 39°6 Mime elisa eli, pas 185985 33°9 If we adopt the same plan as with the mean temperature, constituting out of the Six two excessive years, and comparing them with the mean, we have the follow- ing results : January. | February. March. April. May. June. | Months of greatest Monthly Range, |50°1|253-2/56-0\250-156-0|257-8/61-0/227°1|54°7|210-4|66-5/213:3 | Months of least, é » _ |21-7296-6|29-0246-927-0/283-2/32-2|290-2|31-2/228-4)97-3/215-0 | Means of the Six Years, . . . |84-1/265-3/38-3/257-437-3/249-8/41-9|242-8/41-6/219-5/39-5|208-6 July. August. | September.| October. | November. | December. | Months of greatest Monthly Range, |46°5|210-5|53-0|224-1/55-0)194-6/47-0/208-0 50°0.231-3140°8.257-7 | Months of least, _,, , _ {26-2|192-3/25-11173-1/27-7|165-0|29-6)21 0-4|26-5/230-0|22-7/259-0) | Means of the Six Years, . . . |34-6/204-5/35-7/189-4/37-8|187-7|36-2\198-2/33-9|237-1'32-1/247-9 | VOL. XXII. PART U. 4k 316 The two last tables, I think, point to this, that for three quarters of the year the relationship of monthly range of temperature and the death-rate from all causes is inverse—the greater the range the lower the mortality ; but that during the months of July, August, and September, the relationship is direct—the greater DR R. E. SCORESBY-J ACKSON the range the greater the mortality. Mean Daily Range of Temperature.—The relationship as shown in Table A. is as follows :— Section. Maximum, Major, Minor, Minimum, . Means, The result of constructing two excessive years out of the six is as follows :— Months of greatest Mean Daily Range, Months of least as Means of the Six Years, 9-6 [243-4/10-8/250°1 Mortality. 269:°49 233°25 214:26 185°85 225°71 January. | February. March. 11°9|257-8 9+3/256°7 10°7/249-8 7:1 |296°6) 8-6/251°3 8-4 [265°3)10°0/257°4 Mean of the. Daily Ranges. 9°8 11:6 13-0 13°8 12:0 June. April. May. 15°3227-1/19°71193-5117:21218-3)_ 12:0 243°6)14-1 228°4/12-6/215°0) 13°9/242°8 ee 14-9208: | Months of greatest Mean Daily Range, Months of least Ay Be Means of the Six Years, July. August. | September. 13°1/192°3)11- -01178:111-0/165-0 14: ie 7p3e O|16: 01199° 514:6194:6 14: lob 5|13- he ‘4/13°3)187°7 12°7/204-4/11°0284-7| 9:5/241- / October. | November. Decembaiil 10-9210-4| 8-1|230-0) 8-1/257-7| 11-8)198-2} 9-9237-1) 8-6247-9) These tables indicate a similar relationship between mortality from all causes — and the mean daily range of temperature as was noticed with respect to the monthly range of temperature, namely for three quarters of the years an inverse relationship, the greater the daily range the less the death-rate, but during the months of July, August, and September, a direct relationship, the greater the daily range of temperature the greater the mortality. It will be noticed in the latter table that March and November do not quite conform. The Combined Influence of Temperature and Humidity. It is difficult to obtain data for this inquiry, there being few months which, with equal mean temperatures, show at the same time a marked contrast in their hygrometric condition. I have, however, endeavoured in the following table to show the relative effect upon the death-rate of a dry and humid cold :— | ‘ ON THE INFLUENCE OF WEATHER UPON MORTALITY. 317 MEAN OF THE SIX YEARS. Dry Cob. Hum Corp. Months. Temp. | fai | dity. | tality. | Temp. | fails | ity. | tality. | femp.| dale | duty. | tality Joma, «| ars ea) o8 | anoal| 353/32] 6 |Stta| | ta | [as Fo, - | asa] a0] or | aoral fet] 3] 3 | eal is | Sea |S [les March. . . . | 998) 905] 86 | 2498/( 5551 T95 | &5 | 2578| 392 | 204| 88 |2500 Bale c cosas] = | ena| 3] 228) ee | eooel | sae | fae? Means, . . | 397 | 295 | 86 | 2538| 30-7| 201 | 852| 9534| 307 | 303 | se1|o473_ In this table there is a tendency to support the general belief that a diy cold is more fatal than a humid cold; the four Januaries, it will be seen, oppose the idea of such a law, the greater death-rate being with the two humid months; two of the Aprils also conflict with the generally accepted law, the humid month, even with arather higher mean temperature, having the greater mortality. In the months of March, and again in one of the comparisons of the months of April, it will be noticed, that whilst the order of the months is correct as to the amount of moisture indicated by the rain-fall in inches, nevertheless, if the humidity as deduced by Mr Glaisher’s tables had been strictly taken as the test, the order ought to have been reversed. But it often happens that, as in the instances above referred to, whilst the amount of rain which may have fallen during a month may be higher than the mean of the six corresponding months, nevertheless, the amount of moisture in the atmosphere, as exhibited by a re- ference to Mr Glaisher’s tables, may be below the average humidity of the six corresponding months. It behoves us, then, to compare both of these indices to the amount of moisture in the atmosphere with the temperatures below the means of the six corresponding months separately, and this is done in the follow- ing tables :— Months in which both the Mean Temperature and the Months in which the Mean Temperature is below, but Rainfall are below the Mean of the Six cor- the Rainfall above the Mean of the Six responding Months. corresponding Months. Mortality. Mortality. Pemmary ty TOo7. (Yi. . (i. 3253+2 January) 1860). o.)\). uo i. 2806 a USGL La ee. heb 8041 Pebruary 860; 4 2/5) «0 ee0'6 Hebruary 1858, — 0 . . . 2a(°7 March, sy VGG25 00. abe) 00's meren. V8o7, ee. 250-0 April SST, ee er SSG os UGSSs aR Lich SU ME26 T'S April 1LSB9). eRe isp oy B22 ap MSG Os ee us) bys, Oo Aée S08 tee April LEGOsnsage ’ -niaden aZoO2 Mean, . . 268-0 Mean, . . 266-9 318 DR R. E. SCORESBY-JACKSON Months in which both the Mean Temperature and Months in which the Mean Temperature is below Humidity are below the Mean of the Six but the Humidity above the Mean of the corresponding Months. ' Six corresponding Months. Mortality. Mortality. January; 1857R 2 ae aoe January 1860;°°.-."). 2) BROS Hebrudty LS56, 63) e.My OS 2ST é 186h! co oe OE as 1000," at. OBO OO Mareh . -1862,° °°." |. (oS) Marchy }LSba ss eT O April T1857, - me ee April 159,055 55/92) GBIF in 1860; .. 0 Sea Mean, . . 260:4 Mean, ..- 75! Here, then, we have conflicting results. Following the rain-fall as our guide to the hygrometric condition of the atmosphere, we conclude that a dry atmo- sphere promotes mortality; if we refer the humidity present in the atmosphere to the standard calculated by Mr Glaisher, we are forced to an opposite opinion. Let these results be estimated only at their true value; the data are too few to render them of very great importance, but they may serve for comparison with other investigations. It must be remembered, however, that it is the temperature that binds me down to so few data. I shall have occasion hereafter to inquire into the value of the relative quantity of moisture in the atmosphere separately. Before passing from the consideration of the influence of temperature upon mortality from all causes, there is one other important feature which ought to be mentioned,—namely, the aggravating influence of continued cold. The growing mortality consequent upon a continued low temperature is seen in the following table, where it is contrasted with the means of the mean temperature and mortality of the six corresponding months :— November. December. January. February. March. 39°1 34°°1 35°°5 34°-0 38°-4 Mean Temp, 230°°0 257°7 280°8 330°6 283°:2 Mortality. Average of the Six corresponding f 237%1 247°9 265°3 257°4 249°8 Mortality. * Months, . RIM 39°5 38°°8 37°°4 38°°2 39°°8 Mean Temp. Year 1860, In like manner the evil effects of a continued high temperature may be seen in the following table, in which the mean temperature and mortality of the warmer — months of 1857 are contrasted with those of the averages of the six corresponding ~ months of the years 1857-62 inclusive :— June. July. August. September. October. 57°4 58°:0 60°-0 5671 49°-6 Mean Temp. 213°:3 210°5 224°-1 210°'8 208°-0 Mortality. Average of the Six corresponding ( 208°6 204°5 189%4 187°7 1982 Mortality, Months, . =) 5 POR 55°-9 56°8 57°'3 52°°5 47°-2 Mean Temp. ~ Year 1857, The Influence of Vicissitudes of Atmospheric Pressure. When we notice that the average monthly range of the barometer for the six } years under examination is not more than 1-262 inches, it behoves us toremember how much is implied in the oscillation of the barometer even to the extent only — ON THE INFLUENCE OF WEATHER UPON MORTALITY. 319 of a single line. It indicates either a vast increase or diminution of pressure upon every point of surface of the body,—a pressure which normally is equal to that of fifteen pounds of dead weight to the square inch, and yet, a pressure so wonderfully adapted to our necessities that we are unconscious of its presence. So that, although in dealing with this part of the inquiry we are confined, with very few exceptions, to movements within the thirtieth inch of the barometric scale, we are not to suppose that such limited movements are of trifling, but that they are of all-important value. Mean Height of Barometer reduced to Sea-level and 32° F. A comparison of the means of the four sections in Table C, between the mean height of the barometer and the mortality from all causes, leaves us in uncer- tainty as to the relations which these circumstances bear to each other. It is indicated in the following table :— Section. Mortality from all Causes. Mean Height of Barometer. Maximum-Section, /-.-. .°. 269°49 29°800 MtOMSechOne. else ye 233°25 29:868 Minor Section,» . aw 5. 214-26 29-862 Minimum Séction; ©... 185:85 29°842 Weare ek) a are ras PPT 29-848 The mean height of the barometer for the whole of each of the six years, as com- pared with the mortality for the corresponding periods, is shown as follows :— Year. US A eg) Mean Height of Barometer. EGO er ks! ce phshhpy hs 244°2 29°785 Den M cS ENEP tginsy avira 229°2 29-812 5? Sl a a rere 227°5 29°893 MS DGMME Ts Su cad we te) 225°5 29:°916 : EKO). SPN ns Meee rey 214-9 29-838 CES 0 a ee 212°7 29:817 -Means, ;. 2). }-! 225°7. 29°843-° ~ In both of these tables the lowest reading of the barometer comemnonae with the highest death-rate. In both, the two lowest readings of the barometer cor- respond respectively with the highest and lowest death rates, with a minute fractional difference in. the latter table, the second lowest reading being that of the mean of 1862. _ In the latter table the highest barometric reading corresponds with the mean of the mortality; in the former, the highest barometric reading Stands opposite a much higher death-rate. The only point of resemblance between the two being that first mentioned, indicating a maximum of deaths with a mini- mum of atmospheric pressure. But we must not remain satisfied with the value of this indication alone. VOL. XXII. PART II. 4s 320 DR R. E. SCORESBY-JACKSON In the next table we have three factitious years constituted,—the first, by those of the several corresponding months which possess the highest barometric read- ings; the second, by those which exhibit the lowest barometric readings; and the | third, by the means of the six corresponding months :— Months: Highest Lowest Mean Mortality Mortality Mean Barometer. | Barometer. | Barometer. |with Highest.| with Lowest.| Mortality. January, . . « + 380-065 29:529 29:°818 214-0 280°8 265°3 Rebriarys.°t. wea 3 30°052 29°681 29-869 251°3 228°1 257°4 ESC) ee nk a 29:°852 29507 29°701 257°8 220°2 249°8 Rs C1 caw Da oe 39°177 29-751 29-916 223-5 222-7 242°8 i A 30:070 29:310 29°923 225°4 228°4 219°5 SUMO hy Pench ately 30°032 29-674 29-892 219°3 219-1 208°6 Sule) eee 30:050 29-735 29°851 181°3 192°3 204°5 Ameust, J; ei at 30°014 29°575 | 29°840 224-1 1924 189-4 September, SRA Ast 29:979 29-722 | 29°845 195-9 Vital 187-7 October; 29-936 29-620 29-784 | 173-1 204-4 198-2 Novemberoe "7: 30-115 29°855 29-881 | 2313 236-0 2371 December, 261.) a); 30:020 29°651 | 29°806 | 241-4 263°4 247-9 Means, °°" . Gaia 30°030 29°676 | 29°843 | 219-9 | 222:1 | 225:7 In this table there is evidently a good deal of conflict ; but upon the whole year it corroborates the indications of the preceding tables, inasmuch as the aver- age mortality with a low barometer is higher than that with a high barometer. But it is curious to observe that the average barometric reading of the whole term of seventy-two months corresponds with a higher necrological reading than either the absolute highest or the absolute lowest readings of the barometer, as is more distinctly seen thus :— Mean of the Absolute Highest Barometric Readings, 30:030 Mortality, 219-9 Lowest 29°676 pS 2220 Mean of the whole Term of 72 Months, ee bageeiaa 29-843 225-7 be} This, then, would indicate that high and low barometric readings are both more conducive to vitality than a medium reading; and, moreover, it serves to deepen the impression that a low barometer is more fatal than a high reading ; because, although 29°843 is the exact mean of the whole term of seventy-two months, — nevertheless it approximates nearer to the mean of one peices lowest than to — the mean of the absolute highest, for 30-030 + 29°676 = "853. 4 In order to ascertain whether any month or season ane give a stronger indi- cation of the influence of atmospheric pressure upon the death-rate than is shown by the mere absolute highest and lowest barometric readings, and also whether — the corresponding months into separate groups as would in any way contrast, touching the circumstance of atmospheric pressure :— ON THE INFLUENCE OF WEATHER UPON MORTALITY. 321 Barometer above Barometer below Year. eee Mortality. Year. ee Mortality. Months. Months. 1858 30:065 214-0 1857 29-698 253-2 1859 29°864 243-4 1860 29-529 280°8 January,. . . 1861 30:038 3804°1 1862 29-686 296:6 Average mortality, 253°8 276-9 | 1858 29-998 237-7 1857 29-840 250-1 1860 29°932 3306 1859 29-709 246°9 February, . . 1862 30°052 251°3 1861 29-681 228°1 Average mortality, 273-2 2407 | 1857 | 29-804 2500 | 1860 | 29-639 283-2 | | 1858 29°852 257°8 1861 29°507 220-2 March, . . . ( 1859| 29-707 232-0 1862 | 29-698 256-7 | Average mortality, 246°6 253°3 1858 | 29-942 227-1 1857 29°767 243:6 | 1860 29:978 290:2 1859 29°751 229-7 April, 1861 380:177 223°5 1862 29°881 2500 | Average mortality, 246'9 238°8 1857 29:959 219°3 1858 29°823 210°4 1859 30:046 193°5 1860 29°831 240:0 eager a) Oe) Sy L861 30:070 225°4 1862 29°810 228°4 a ee | | Average mortality, 212:7 2263 | 1357} 30-020 213-3 sé) | 29-674 219-1 | 1858 30:082 219°3 1862 29°733 2150 | 7a 1859 29:934 188-6 | mee heh) TEL 29-961 196-4 Average mortality, 2044 217-0 1858 29:°887 224-0 1857 29°8382 210°5 1859 30:050 181°3 1861 29-619 204°4 ivy: |) . b - 1860 29:988 214°8 1862 29°735 192°3 Average mortality, 206'7 2024 (1857, 30-014 224-1 1860 | 29-575 192-4 1858 29-943 199°5 1861 29-774 ork | Be | 1859 | 29-850 178-7 = we ae 7” 11862). 29-885 168-4 Ay oe ett \ Average mortality, 192°7 18207" | 1857 | 29-882 2103 | 1859 | 29-722 177-7 | 1858 29-898 194:6 1861 29'723 165:0 | 2 1860 29-868 182°5 bat Nee es | P ous MASE 29-979 195-9 Al mi Lore 13H Average mortality,| 195:9 IVA tools 322 DR R. E. SCORESBY-JACKSON Barometer above Barometer below Year. een ine Mortality. Year. pean Mortality. Months. Months. 1857 29-803 208°0 1859 29-667 188-0 1858 29-892 205°3 1860 29-784 210°4 October, . : 1861 29:936 173°1 1862 29-620. - 204-4 | Average mortality, 195°5 200°9 1857 30°115 231:3 1859 29°855 236-0 | 1858 29°956 2661 1861 29°544 224:5 N 7 1860 29-919 230°0 fon sie ae ee Pe oO Meee. OS Bay 234-7 Average mortality, 240°5 230°2 1857 29:989 215°7 1858 29°703 250°0 s 1861 30:020 241°4 1859 29°651 263°4 ' Weaohes ae ben ae 1860 29°709 257-7 iikey con oe i, bi 1862 29-767 | 259-0 Average mortality, 228°5 257 5 Therefore, of the averages of the twelve months, six give a higher death-rate with a barometric reading above the average of the several years for those months, and on the other hand, six present a higher death-rate with the barometer below the average. It is more distinctly seen thus :— Bena Soe othe a Months which give a High Death-rate with Months which give a High Death-rate with a High Barometer. a Low Barometer. d Hebruary, % o's 2) beast = (oto January, .( SOOl . 7 eee Arora sf Stal eglsty he nsAp anak ets ubbeeo Marehy>.. ... 4004 7. a) ae Sy 44) clon ee teal Pe ae DO, May; . s/s « b ».< 3 ees ANISE Se cache (aM ainde. diyet (Ozer, Vane mF oi. oA ge September, i fey 2) 1 wan oe SOS October, ge November, )irarna yo tree yet ao December, . 92’: \.) OSS Mean of Mortality, 225'99 Mean of Mortality, 238-65 Here again, then, it is plain that the accumulated mortality of those months in which there is a high death-rate with a low state of the barometer, is greater than the accumulated mortality of those months in which the death-rate and barometric reading are both above the average. It is noticeable that the average death-rate of those months in which there is a direct relationship between the barometer and the mortality, corresponds exactly with the mean death-rate of the whole term of six years, whilst the average death-rate of the months in which the relationship between the barometric reading and the mortality is inverse, is much higher. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 323 Now, if I take the mean of the averages of all the months with a barometric reading above the mean of the six corresponding months, and the mean of the averages of all the months with a barometric reading below the mean of the six corresponding months, the result is the same, though not, of course, so distinctly shown :— Jan. Feb. | March. | April. May. June. | Means. Average mortality of the months with a mean height of barometer above the mean of the six corresponding months, Average mortality o} of the months eal 253°8| 273:2| 246°6| 246:9]) 212°7| 204:4 a mean height of barometer below the mean of the six Se date months, 276°9 | 241°7| 253°3| 238°8| 226:3) 217-0 July. | August.| Sept. Oct. Noy. Dec. oy piality. of tho. months with) mortality of the months with a mean height of barometer above the mean of the six corresponding months, ‘ Average mortality of the months with a mean height of barometer below the mean of the six Saunton o months, 206-7 | 192-7 | 195:9) 195°5| 240°5| 228-5) 224:8 202°4| 182-7| 171:3) 200:9| 230-2) 257-5 | 225-0 Again: the mean height of the barometer for the whole period of six years is 29°843. Now, if I take this reading as a standard of reference, I find that of the seventy-two months thirty-eight afford a higher, and thirty-four a lower mean reading, and the result, in regard to the ratio of mortality from all causes, is the Same as was observable when I employed the means of the corresponding months as standards of reference; namely, that the mortality is greatest with a low read- ing of the barometer: or more clearly thus :— Average mortality of thirty-four months, in which the mean height of the barometer for each month was below 29-843, , : : ‘ ; ‘ : : ; 228:14 Average mortality of thirty-eight months, in which the mean ere of the barometer for each month was above 29°843, . " ‘ : , ; ; 223-52 Excess of mortality with a low barometer, 4:62 Again: if I arrange the months in seasons, representing winter by the months December, January, and February, and the other seasons accordingly, I find that of the eighteen winter months, the mean height of the barometer in ten was below, and in eight above 29°848: of the eighteen spring months the mean height of the barometer in ten was below, and in eight above 29°843: of the eighteen VOL. XXIII. PART Il. AT 324 DR R. E. SCORESBY-J ACKSON summer months, the mean height of the barometer in seven was below, and in eleven above 29'843; and of the eighteen autumn months, the mean height of the barometer in seven was below, and in eleven above 29°843. The average mortality of these several groups of months is seen thus :— WINTER. Average mortality of ten winter months, each with a mean height of barometer below 29-843, 258°6 ss 55 eight 55 xi above ... 254:8 Excess of mortality with low barometer, 3°8 SPRING. ten spring months, each with a mean height of barometer below 29-843, 238-7 — eight a 4 above ... 235°8 Excess of mortality with low barometer, 2°9 SUMMER. ey seven summer months, each with a mean height of bar. below 29°843, 200°97 *: eleven _ above ... 200-76. arom Excess of mortality with low b eter, 0-21 AUTUMN. 3 ne eleven autumn months, each with a mean height of bar. above 29-848, 214-5 seven = a5 below... 197-0 Excess of mortality with high barometer, 17-6 think that, although it is not a law without exceptions, there is an indication of a law, if the data be sufficient to determine it, of an increased mortality with a low barometer. But I must speak guardedly on this point, because the result of the inquiry differs from those obtained by many acute investigators; and I think it right to mention particularly that it is opposed to the opinion of talented investigators who have made similar observations in Berlin, Dresden, and Paris. And I may mention, moreover, that the results which are shown with referen to the influence of drought and humidity upon the death-rate from all causes ar j also opposed to those obtained by some of the same observers. At the close of the paper I shall present the principal data in a different form, in order to test still more rigidly the accuracy of these inductions. 7 ON THE INFLUENCE OF WEATHER UPON MORTALITY. © 325 The Range of the Barometer.—Intimately associated with the previous inquiry concerning the influence of the monthly mean height of the barometer upon the mortality, is that of the influence of the monthly range of the barometer. Re- ferring to Table C, we find the following relations exhibited between the two in the several sections :— Section. Mortality. Monthly Range of Barometer. Maximum Section, 2. 6. . »269°49 1-564 REnomeeeion,, 2%. sii 28a Oh 1:363 MinormSeehOtle.. jee) sit, 6: 221426 1:163 Minimumesechione 2. so. 2,4 . Lad 0-961 Means, ‘ 225:71 QD, The following table is composed of three factitious years, constituted severally of months in which the monthly range of the barometer was greater than in any of the corresponding months, of months in which the range was less than in any other of the corresponding months, and of the mean monthly range of the six corresponding months of the different years. Mean Greatest Least Mean Mortality Mortality | Mortality of Months. Barometric | Barometric | Barometric | with High with Low | the Six cor- Range. Range. Range. Range. Range. responding Months. wanwany, » « . 1-855 1:026 1:486 243°4 304-1 265'3 Hepruary, . . ©. 2-079 1:289 1:540 330°6 250-1 257-4 NEN a 27021 1:270 1-593 250°0 232°0 249°8 ji 1:860 0°734 1-277 290-2 223°5 242°8 Vy 1339 0°498 0:956 210°4 193°5 219°5 OMIM Pi fn se 1-102 0652 0:877 219-1 188°6 208°6 Ue 1:0838 0-745 0:865 181:3 214°8 204°5 Peuoust, .. |. 1:167 0661 0:'942 178°7 2241 189-4 September,. . . TPL 72 0993 1:082 165:0 195:°9 187-7 October, .°. . 1°872 1:201 1:417 204:4 17371 196-2 November, .. 2129 1:295 1:695 236-0 224-5 237-1 December,. . . 1:8538 1:204 1:429 263°4 259:0 247°9 Means, .-| = . 1:627 0:964 1:263 231:04 223:60 225°68 Both of these tables direct us to the conclusion that the mortality from all causes bears a direct relation to the range of the barometer: the greater the range | of the barometer the greater the death-rate, and vice versa. And this is another | item in favour of the supposition that the mortality from all causes is greater with a low than with a high barometer, because the greatest range of the baro- meter is exhibited when the mean reading of the instrument is low. In the ‘latter table four months oppose what has now been stated respecting the in- fluence of the barometric range; they are January, July, August, and September; VOL. XXIII. PART II. 6 326 DR R. E. SCORESBY-J ACKSON and this they do whether the results of the highest and lowest ranges only be compared, or a comparison of all the six corresponding months in each case be instituted. The Influence of Drought and Humidity. We have already seen that, with reference to mean temperature, the relative amount of humidity in the atmosphere is important. We are now briefly to exa- mine into the influence which the various hygrometric conditions of the atmo- sphere exert upon mortality from all causes independent of other meteorological elements. It should always be remembered, however, that the amount of mois- ture necessary to the saturation of a given quantity of air varies with tempera- ture,—the warmer the atmosphere the greater the quantity of moisture requisite to saturate it, and vice versa. We may test the influence of the relative amount of moisture upon mortality from three points: jirst, with reference to the number of rainy days; second, with reference to the quantity of the rainfall in inches ; and, third, with respect to the relative saturation of the atmosphere with mois- ture, as ascertained by means of Mr Glaisher’s hygrometric Tables. Number of Rainy Days.—A rainy day, it may be premised, does not neces- sarily mean one on which rain continued to fall throughout, nor even during many hours; a shower of rain is sufficient to constitute a rainy day. Nor has the term any reference to the amount of rain deposited in a given time; very little or very much rain may fall on a rainy day. Hence, we often find, that with ten rainy days in one month, there is a greater rainfall than in fifteen rainy days of another month. In the several sections of Table C, the relative number of rainy days to the mortality from all causes is as follows :— wr peewee = le ead : . . P 7 7 ‘ fl : 4 Section. Mortality. Number of Rainy Days. Maximum Section, |. . eet e . 2269-49 15-1 Mayor Section, pif. . G24. 6 -. 31288725 13:7 Minor Section... 4b... ce eaeiee 2. ees 15:4 Minimum Section.) . .. 0) ) 2 yeeSa- 15:3 Mieaniss9-7 (oar en eon 14:9 A Table consisting of three factitious years, constituted of months with the greatest number of, and months with the fewest rainy days, together with the means of all the corresponding months, shows the following result. Where two months are alike in the number of rainy days, the one in which most or least rain fell is taken :— ON THE INFLUENCE OF WEATHER UPON MORTALITY. 327 January. | February. March. April. May. June. Months with Most Rainy Days,. . |21 |296°6/17 |246-9/22 |220-2/16 |243-6/16 |228-4/20 B 5:0 Months with Fewest Rainy Days, . {14 |214:0; 6 |237-7/11 (232-0) 9 /223-5/13 /219-3/11 /188°6 Meansof the Six Corresponding Months, |16-6/265-3/12°1/257-4)16-1/249-8)12-2/242-8/13-0 fe a July. August. |September.] October. | November. | December. Months with Most Rainy Days, . . {22 Months with Fewest Rainy Days, . {11 Means of the Six Corresponding Months, |16°5 5 - 192°3/22 |173°1/19 |165-0\22 210-4 19 |224-5)21 |259:0 214°810 /224°1/13 |195°910 |204:4)10 |266-1/13 |241-4 204-5)16-0/189-4:15'3 187-7 16°7)198-2 15°2/237:1/16°2/247°9 | | ‘In this Table the general indication is, that the mortality is greatest in those months which have the greatest number of rainy days. There are certain ex- ceptions. March is the first month in which the general order is reversed, and ‘in which, therefore, there is the highest mortality with the fewest rainy days. But if, instead of comparing only the months of the absolute highest and abso- Inte lowest number of rainy days, we compare the four months which are below the mean of the six with the two that are above the mean, we find that the general rule holds good,—those months with the highest number of rainy days giving the average mortality 251-7, whilst those months with the fewest rainy days give an average mortality of only 249:1. The same may be said of July, where the average mortality of the three months with the greater number of rainy days is 206-9, whilst the average death-rate of the months with the fewest rainy days is only 2022. The months of August, September, and November, | which, in the above Table, oppose the general indication, continue so to do even | when all the months are compared. ‘Thus, the average mortality of the Augusts with most rainy days is only 177-9, whilst the average of those with the fewest rainy days is 200°7. Of September, in the same order, the proportion is 171°3 (most) to 195:9 (fewest). Of November, 229-7 (most) to 244°4 (fewest). Quantity of Rain im Inches. Table C. shows the following results :-— Section. Mortality. Rain in Inches. Maximum Section, Pee Mee 2949 3°18 Mayor Section. . 4 5. oe §62380:25 3°06 Minor Scctionwes i 2 3 (:’ Leys 214726 3°27 MinimumySectionyes. 4 0 fe foes -185'85. 3°18 Means) us. 220871 3°17 With the factitious years constituted as in the previous case, we have the following results :— 328 DR R. E. SCORESBY-J ACKSON Mean Rainfall ; : ; : Mica Mors Monts. Most Rain. Least Rain. 0 Seer e Mewaliy vale ee ee mgs of the WNoscihi ix Months. | January, . . 5-32 277 3-82 296-6 | 253-2 | 265°3 February, . . 3°38 Ls 2:32 246-9 Zone 257-4 | March,. . . o'10 1:95 3°55 220-2 257°8 249°8 by ADEM sss 3°20 1:04 211 PPAF) 223°5 242°8 Vailas. oe Sst 2 3°89 0:29 2:07 228-4 193°5 2195 SUNG ME eee oe 4:34 2°04 2°98 219:1 188°6 208°6 SUEY, ot 4°31 1:82 3:14 224-0 2148 204°5 August, eae 6:44 DOT 3°39 173-1 LTSy 189°4 September,. . 5:27 1-92 3°24 165:0 182:5 1877 | October, .. . 5:14 2-36 4°41 2104 208:0 198-2 November, ‘ 6:63 2°38 3°37 224°5 266-1 237°1 December,. . 5°20 2°98 3°85 259:°0 241-4 247°9 a a | ee Means, . 5°82 1:91 318 | 224-16 220°49 225-7 In the latter Table we see the same indication of a tendency to increase of mor- tality with increase of rainfall, the exceptional months being, as in the case of the number of rainy days, March, July, August, September, and November, but in this_ case April also slightly opposes the general indication. It is observable that, in both instances, whether with an excess or deficit of the rainfall, the mortality is below that of the average of the six corresponding months taken over the whole year. Now, if instead of being content with the indications as given by a com- parison of the month of absolute highest with the month of absolute lowest rain- fall, we compare all the months which have a rainfall above the average rainfall of each group of corresponding months, with all the months which have a rain fall below the mean of the six corresponding months, we obtain the following result :— Average Mortality of those Average Mortality of those Months which have a Rainfall} Months which haye a Rainfall greater than the Mean of the less than the Mean of the Six corresponding Months. Six corresponding Months. January. a. ee 273°60 257°10 Pebruary, . « 4 268°53 24636 | CeCe. Sen Veta 236°30 263°66 + April, ap haw eye 238:°76 246°93 + May, eee i ewes 226°26 212°73 June, Ce faa s 217:05 204'40 daly. as bole 206:90 202-20 ATpUStso, © «fe Meme 184°75 19860 + September; 3/45 pase. 184:50 191:00 + Oktoper,]: |. 201°23 195-16 November. 47 ove. 7. 231-72 242:46 + December, . . . . 255°56 240°16 Means, . 227:°09 225-06 | : ON THE INFLUENCE OF WEATHER UPON MORTALITY. 329 This Table still leads us to the same opinion,—namely, that the relationship existing between the amount of rainfall and the mortality from all causes is direct over the whole year, although it may be inverse as regards those months which in the latter Table are distinguished by the sign +. Humidity.—It remains to be seen what may be the character of the relation- ship between the death-rate from all causes and the amount of moisture in the atmosphere, as indicated by the hwmidity column. The sections of Table C give us, with respect to humidity, the following results :— Sections. Mortality. Humidity (Sat. — 100). Maximum Section, 269°49 87 Major Section, 233-25 86 Minor Section, 214-26 84 Minimum Section, 185°85 84 Means, 225-71 85 In the foregoing Table we have an indication of a direct relationship between its two elements,—the greater the humidity the greater the mortality, although in the minor and minimum sections the figures representing the average amount of moisture are identical. In the following Table I have taken the average mor- tality of those of the six corresponding months whose humidity is above the mean of the six, and the average mortality of those months whose humidity is below the mean of the six. The results are seen thus :— Average Mortality of those Months which have Average Mortality of those Months which have a Humidity above the Means of the Six corresponding a Humidity below the Means of the Six corresponding Months. Months. January, (Aver. Mean Temp.36°°73) 236-86 | January, (Aver. MeanTemp. 38°20) 293°86 + February, ( S A 39°85) 244°10 | February,(_,, A 34°-90) 284:15 + March, : + 253°36 | March, i 246°60 April, +251°82 | April, 224:90 May, +224°70 | May, 193-50 June, +210°16 | June, 207:06 July, + 208:87 | July, 195-90 August, . + 189:50 | August, : ; 189-10 September, . : ; : + 188°55 | September, ; : , 186-15 October, (Aver. Mean Temp, 48°30) 189-70 | October, (Aver. Mean Temp. 46°°C0) 206-70 + November, oe 5s 39°97) 232-00 | November,(_,, 5 39°-10) 242°20 + December, : + 249-70 | December, 246-03 Mean, 223°28 Mean, 226'346 Here, for the first time, we meet with an indication of a dry air, irrespective of temperature, being more fatal than a humid atmosphere. Nevertheless, eight _ of the months tend to a conclusion in conformity with that which the former ' Tables have suggested, four of the months only conducing to an opposite opinion. If we seek an explanation in the mean temperature of the several months which determine the result of the latter table, we find that, with the exception of VOL. XXIII.:PART II. ] 4x 390 DR R. E. SCORESBY-JACKSON January, the average mean temperature of those months which show an increased mortality with deficient moisture is below the average mean temperature of the corresponding months whose humidity was greater. If this be worth anything, it tends to corroborate a previous suggestion that diy cold is more fatal than humid cold. , On the Influence of certain Winds. We have no winds in this country which bear comparison, in point of inten- sity, with such as are the bane of other lands. Of Siroccos, Harmattans, Simooms, Samiels, Khamsins, or Solanos, we have none. But we have an east wind; and although it is by no means the prevalent wind of the country, nevertheless, from its harshness, and from its evil influence upon certain classes of disease, it has acquired a just notoriety. Table C. furnishes us with the following comparisons. The figures represent the average number of days on which the different winds blew. N.W. or Mortality. Section. N. N.E. KE. Variable. ' Maximum,.| 2°91 | 2°22 | 3°00 | 3°36} 3:09 | 5°67 | 5:13 | 3:22 1:90 269°49 Major, ...| 215 | 2:00 | 317) 3:14} 280 | 5-97 | 5-44 | 2°86 2:58 233°25 Minor, ...| 1:90 | 2°02 | 3:03] 2°62 |. 2:86 | 6:72 | 6°22) 3-08 2°12 214-26 Minimum,.| 1:58 | 1:72 | 3:00] 2:88 | 3°28 | 6:57 | 6:33 | 2°64 2°58 185°85 Means, ..| 2°13 | 1:99 | 3°06 | 3°00 | 3°01 | 6:23 | 5°78 | 2°95 2-29 225-71 In the foregoing Table we have a general indication of a direct relationship between mortality from all causes and winds from a point between N. and E., and of an inverse relationship between mortality from all causes and winds from a point between 8. and W. ‘The due E. wind shows little or no predominance in any one section more than another. The S.E. wind shows a tendency to blow directly as the mortality, but not uniformly through all the four sections. The due S. wind, with the exception of the first section, blows inversely as the mor- tality. The N.W. wind affords no determinate relationship. With respect to the number of calm days, or days on which the wind was so light and changeable as to afford no fixed direction, all that can be said is, that there are fewest of such days in the maximum section. As it would require too much space to compare the relative frequency of the different winds with the death-rate month by month, it must suffice to do so year by year. This is done in the following Table, in which the average mor- tality of the years with the greatest number of days of each wind is compared ~ with the average mortality of the years with the fewest days of each wind:— ON THE INFLUENCE OF WEATHER UPON MORTALITY. 39] Average Mortality of the Bee es chich the num-| N NE eee nse oS We. pei ING, 30. vor V- ber ofdaysofeach Wind> 2295 2353 2358 2383:0 2220 2201 2189 227-4 221:9 was above the Mean of the Six, . bees Average Mortality of the Years in which the num- berofdaysofeach Wind) 223°7 2206 2206 2183 2274 2867 2324 2233 2994 was below the Mean of the Six, . Bae If this be a true guide to the relationship existing between the prevalence of certain winds and mortality from all causes, then it is manifest that all winds between N.W. and 8.E. (north about) are directly related to the death-rate, whilst those winds blowing from points between S.E. and W. (south about) have an in- verse relationship. It would seem, moreover, that calms, or light shifting winds, are less frequent when the mortality is high than when it is low. Force of Winds.—There is nothing in Table A. to lead us to a decision as to the influence of the relative force of wind upon mortality from all causes. The force is there given in lbs., and, according to the several sections, stands related to the death-rate in the following manner :— Section. Mortality. Force of Wind in lbs. AIRC mE ys Aer | oye Stet ES EG Oea 1:654 Major, ae o loh wen iy eeu hy Boro 1:630 Minoan wea mem Cte i oe 2 yy om G Wee z iim, eee ewe, re OP te SB a: 8o 1:346 icc Gey, WL ah lie hee lwye APO oe 6.4! Ug 1592 Two factitious years, constituted of the months which show the greatest wind force of the six, and those which show the least, respectively, afford the follow- ing comparison :— Mortality of each Month Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec. of the Greatest Wind $ 243°4 330°6 232:0 222°7 219°3 215°0 192°3 173-1 177-7 210°4 224°5 215°7 Force, Do. do. Least do. 253°2 251-3 256-7 293:5 193°5 196-4 214°8 168-4 195-9 204-4 230°0 241°4 From this table it is evident, that our data do not furnish us with determinate information regarding the influence of the pressure of the wind upon mortality. There can be no doubt, however, and perhaps, if the data prove anything at all, they prove this, that whatever be the exact pressure of the wind, it acts in a two- fold manner upon the death-rate, each separate influence compensating the other. If we have high winds, and stormy weather on that account, the death-rate will | be increased not only by the fatal exhaustion caused to debilitated persons, but also by the casualties which invariably occur both afloat and on shore during ‘gales of wind. On the other hand, when the pressure of wind is low, the atmo- sphere is stagnant, becomes loaded in many localities with pestilent effluvia, and sickness, usually of the zymotic class, prevails. A breeze of wind on land sweeps 302 DR R. E. SCORESBY-JACKSON out the hotbeds of disease, clearing them of the products of animal and vegetable putrefaction, and rendering them wholesome habitations for the human family ; just as in another sphere of usefulness it turns up the surface of the wide ocean, preserving its waters from corruption, and imparting the very essence of life to its creatures. RECAPITULATION. Such is a brief sketch of the first part of the subject which at the outset I pro- posed to lay before the Society. I have before said, that this is by no means in- tended to be an exhaustive treatise, and I repeat that I have not even exhausted all the information which the tables and diagrams are capable of affording. In both there is still abundance of materials for further research, even concerning the influence of weather upon mortality from all causes of which alone I am now speak- ing, which may be thrown into a variety of shapes for the purpose of elucidating peculiar theories. I have done nothing more than examine the leading character- istics of the subject; and that without endeavouring either to propound or substan- tiate any theory whatever. I am neither disappointed that my results do not always coincide with those obtained by other investigators of cognate subjects, nor am I gratified with the idea of raising opposite views. In some points, the results of my inquiries harmonise with those of several observers in other countries, while in some they are diametrically opposed; but this does not at all imply a want of accuracy, either on their part or mine; it is quite competent for the results to differ, and yet each be right regarding the particular locality to which he refers. I have endeavoured to treat the investigation in the simplest manner, by merely putting questions to the collected facts, and leaving them to supply the answers ; and in the present recapitulation I would have it distinctly understood, that I do not assert that these statements inviolably express the influence of weather upon — mortality in the towns of Scotland; but I think it very probable that they do so generally. It will be a matter of no small interest to learn from the circumstances of the next six years whether the present suggestions are tenable or not. There does not appear to me to have been during the six years from which the facts are gathered any fluctuation of other external agencies worthy of particular atten- tion. Sanitary improvements are occurring from time to time, and when they are such as to affect a large community, a diminution in the death-rate should, — to a certain extent, be ascribed to them; the other matters of importance, as the price of food and the like, have already been given in a tabular form. It is pro- bable, then, that in Scotland the death-rate from all causes is influenced by A. Temperature. 1. Below 50° Fahr., the relationship existing between mean temperature and the death-rate from all causes is inverse—the lower the temperature the higher -— ON THE INFLUENCE OF WEATHER UPON MORTALITY. 393 the mortality; but above 50° the relationship becomes direct, the death-rate in- creasing with the temperature. The months during which the latter condition is observable, are probably July and August; but in Scotland the mean temperature does not often rise so high as to render it a cause of alarm. 2. Over the whole year the relationship between the monthly range of tem- perature and the death-rate is inverse; but during the months of July, August, and September, it is direct. A similar relationship exists between the mean daily range of temperature and the death-rate. 3. It is probable that dry cold is more fatal than humid cold. 4. Extremes of temperature are always fatal, but eminently so when long sustained. B. Atmospheric Pressure. 1. The results afforded by comparison of the relative height of the barometer with the death-rate from all causes are conflicting, but there is probably a pre- ponderance in favour of the supposition that the relationship WPA eEE the two is inverse in the colder, and direct in the warmer months. 2. The relationship between the monthly range of the barometer and the death-rate is direct. C. Drought and Humidity. The relationship existing between humidity (irrespective of temperature) and mortality appears to be direct in the colder, and inverse in the warmer months. D. Winds. Winds blowing from a point between N.W. and 8.E. (north about) attend a high death-rate. Winds blowing from a point between S.E. and W. (south about) occur more frequently during months in which the mortality from all causes is low. If in the foregoing tables the difference between the mortality with this and with that kind of weather be often apparently trifling, it must be remembered that one or two deaths, more or less, per 100;000 living, is a matter for serious consideration. _ It must be remembered also, that in the mortality from all causes, there are many compensating influences at work which tend to reduce and soften what would otherwise appear as remarkably prominent features in the inquiry. As a single , example of this, it is plain that if deaths from diarrhoea were excluded, the death- rate from all causes would be relatively higher in cold weather than it now appears to be, for deaths from diarrhoea being low in cold and high in warm weather, tend to equalise the surface over the whole rate of mortality. VOL. XXII. PART II. 4AY 304 DR R. E. SCORESBY-JACKSON IL—Tue INFLUENCE OF WEATHER UPON MORTALITY FROM SPECIAL CAUSES. It must be quite obvious that to have repeated the foregoing inquiries with each | class of disease, or still more so with each individual disease, would have carried me far beyond the limits of a single paper. The tables and diagrams together. however, are sufficient to enable any one desirous of information concerning the influence of weather upon mortality from any of the diseases there given, to comprehend readily enough the relationship which the several meteorological data bear to the death-rates. All that I can venture to do with the remainder of the collected facts will be to trace out the more apparent bonds of union between the . weather and the several diseases; and I may mention, in passing, that the reason why I have added to the titles and diagrams a representation of the deaths from all specified causes, is simply to afford an opportunity of determining the propor- tion which the death-rate from any individual disease bears to the entire mor- tality ; this could not have been ascertained by a reference to the death-rate from all causes, since that comprises many deaths from causes which are not stated, and which might therefore be attributable to any of the diseases in the Registrar- General’s Schedule. Following the order in which the diseases are arranged in the tables, I shall confine my remarks either to the class of diseases or to one of the representative diseases, as seems to promise most interest. A. The Influence of Weather upon Mortality from Zymotic Diseases. This class of diseases may be dismissed with very few remarks; not because the inquiry is either uninteresting or unimportant, but because it is very complex, and would require more time than can at present be afforded to treat it as it deserves. I shall speak of zymotic diseases only as a class. The influence of season in determining the death-rate from these disorders may be inferred from the following order of months, the ratio of deaths being that afforded by the averages of the six corresponding months as in Table C. Month. Mortality. Month. Mortality. JGMUary,) cathe aye aera September, ) ) 6 60.0 04.) (OST November,;: .y0 w/o) x 5) eer 6:6 UNE yrs ont ay neers ee December, “2 (ope we weed April.) 4. po Os -» aR February, 2 2 0' Weiew oer eOCre August, + *.9'2) (80>) OO iia October, 4108. TR Caleta. 79970 Mays go; saqgire:) tol. ieee March: ‘spc ieee OOS June, = ee '4 : 07 Misaiir cakes Sie es on ye re OO uaes Perhaps the questions of greatest interest with respect to zymotic diseases are those which refer to the mean temperature, mean height of the barometer, di tion and force of wind, and the rainfall. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 399 The relationship existing between the mean temperature of the month and its death-rate from zymotic diseases is seen in the following table, in which, out of the seventy-two months, those with the highest and those with the lowest death- rate from such causes are selected :— Jan. Feb. | March. | April. May. | June. jAverage. | Mean temperature of the months in which __ the highest death-rate occurred, | Mean temperature of the months in which ) the lowest death-rate occurred, . . 39°6 | 39°3 | 39:2 | 42-7 | 49°8 | 58-9 39'3 | 35°38 | 39:5 | 454 | 49°5 | 57-2 July. | August.| Sept. Oct. Nov. Dee. Mean temperature of the months in habeas * \ the highest death-rate occurred, COD): RE Mec ene | eoeren | tea Mean temperature of the months in ine the lowest death-rate occurred, 59:0 | 560 | 53°7 | 495 | 88:5 | 44:9 | 47°36 Hence it appears that the influence of temperature upon the death-rate caused by zymotic diseases as a class is variable, and that the above data afford no indication of any general law. The following table is constructed upon the same principle as the former, and refers to the mean height of the barometer :— Jan. Feb._ | March. | April. May. June, /Average. Mean height of the barometer for the months in which the highest death- -| 29:864| 29-840) 29-804) 29-767| 29-959) 30-032 rate occurred, . . Mean height of the Parone: for mt months in which the lowest death- 30:065| 29:998 29-852) 30-177] 29-823) 29-961 rate occurred, | July. | August.| Sept. Oct. Nov. Dec. Mean height of the barometer for the months in which the highest death- + 29-887) 30-014) 29:882) 29-784) 29-956) 29-703) 29-874 rate occurred, . Mean height Me thie baroitetae (or mh months in which the lowest death rate occurred, | 30-050) 29-885) 29-723) 29-936) 29-544) 29-989] 29-917; f The preceding table scarcely points to any general law, unless it be this, that during the colder months of the year the relationship existing between the height of the barometer and the death-rate from zymotic diseases is inverse, whilst during the warmer months it is direct. The months July and November do not conform ‘to such a law; it may be remarked, however, that the July with the high death- rate was much cooler than the other, whilst the November with the high death- rate was rather warmer than its associate. 336 DR R. E. SCORESBY-JACKSON The following table is arranged in the manner of the two previous tables, and refers to the amount of the rainfall in inches :— Jan. Feb. March. | April. | May. | June. Average.| Rainfall of the months in which the )| ,. : : 16 : highest death-rate occurred,. . s fe a eae eats oo eee Rainfall of the months in which the i] lowest death-rate occurred, s Rainfall of the months in which the ) 431 | 1:87 | 3-82 | 5:14 | 2:38 | 4.00 | 3:05 highest death-rate occurred,. . Rainfall of the months in which ite lowest death-rate occurred, P 2°76 | 3:35 | 5:27 | 3:34 | 663 | 3:37 3:08 Eight of the months show a higher death-rate with a greater rain-fall, whilst the remaining four present a higher death-rate with a smaller rain-fall; never- theless the average quantity of rain of both the years so constituted is almost identical. As it would be tedious to reproduce in the text the relative prevalence of all the winds given in the tables, it may suffice to select one of them, and to infer from the fluctuations in that the relative frequency of others. The wind which — blows on the greatest number of days in the year is that from the south-west ; it will therefore be the one most suitable to our present purpose. Jan. | Feb. | March. | April. | May. | June. |Average. Days of south-westerly wind in i: 11-0 | 10°5 months with the highest death-rate, Days of south-westerly wind in the months with the lowest death-rate, \ 50 3'5 4°5 70 | | | tees a8 | 65 | 30 | 65 | 68 July. | August.| Sept. Oct. Noy. Dec. Days of south-westerly wind in the ) ‘ . f r ; ; months with the highest death-rate, { on oF ee of an eS ot Days of south-westerly wind in the ¥ : . : - : ; months with the lowest death-rate, \ | oe Oe 60 Bo ce | a er In this table there appears no indication of a law of the wind affecting the death-rate; the averages of both the factitious years are somewhat above the — average frequency of south-westerly winds over the six years. I find, on arranging the due east winds in the same manner, that the average of the twelve months — with the highest death-rate is 3°46, whilst the average of the months with the lowest death-rate is 2:88 ; and that both of these averages are somewhat below the average frequency of due east winds over the six years, which is 3°5. | It will be interesting, in the last place, to ascertain whether the relative force ON THE INFLUENCE OF WEATHER UPON MORTALITY. 337 of the winds exerts any influence upon the death-rate from zymotic diseases. The following table is constructed like the former, the figures representing the force of the winds in pounds weight :— Jan. Feb. | March. | April. | May. June. |Average Pressure of the winds during the months ! ; , s : ‘ with the greatest death-rate, 295 | Uae | 188) P18 | 1°79 | 1:36 Pressure of the winds during the months \ 2-36 with the least death-rate, ne ate ber July. | August. Sept. Oct. Noy. Dec. Pressure of the winds during the months with the greatest death-rate, ; Pressure of the winds during the months 1-11 | 1°04 1:38 | 2°34 | 1°09 | 1:80 | 1-64 with the least death-rate, Lett | O68 25) 188.) 128 72:86). 2082.) 68 The average force of the winds over the six years is 1:59, and therefore in both of the extreme years of the above table the averages are rather high. It might have been supposed, that when the death-rate from zymotic diseases was higher, the relative pressure of the wind would have been low, indicating ca/m rather than breezy weather ; but if the above table proves anything, it is the very oppo- site of that. That the weather has to do with fluctuations in the death-rate from zymotic diseases no one will doubt, but the manner of its operation it is difficult to explain. In countries where marshes form an ample source of some of these diseases, the effects of temperature and humidity are obvious enough; but in this country, in which the germs of such diseases spring from unrecognised sources, the influence of the weather in bringing them hither, developing, and propagating them, is not so plain. [ make no comments upon the foregoing facts; it was not to be expected that any very striking results would be deducible from a mere compari- son of the meteorological data with the death-rate from a class of diseases com- prehending so great a variety. In the tables I have given the death-rates from three diseases of the zymotic class—viz., Typhus, Scarlatina, and Diarrhoea— and it would have been interesting to have shown the effects of meteorological phenomena upon each of these, but that must be left to another opportunity. B. The Influence of Weather upon Mortality from Phthisis Pulmonalis. Instead of examining the influence of weather upon the tubercular class of diseases as a whole, it will perhaps be more profitable to confine my remarks to one, and that the most fatal, of such diseases. The order of the months according to the death-rate from phthisis, from the highest to the lowest, following the means of the six corresponding months as in Table C, is as follows :— VOL. XXII. PART II. 47 338 April, March, May, June, February, . January, The average ana ee ratio of deaths from phthisis -niltnorent™ per 100,000 living at all ages, in the eight larger towns of Scotland, during the six years 1857-62 inclusive, is exhibited in the following table, together with some of the meteoro- DR R. E. SCORESBY-J ACKSON 35°9 351 33°6 33°95 32°3 30°6 July, December, November, August, September, October, logical characteristics of the corresponding periods :— Mor- Year. tality 1860 32°4 1862 30:1 1858 29°5 1857 29°4 | eh SGt 29-1 1859 28-7 Average, | 29:7 The following table is constructed upon the plan of those previously given with other subjects of investigation ; the months are not those of the same years, but — those of any year in which the highest or lowest death-rate from phthisis occurred. Mean temperature with highest mortality, Mean temperature ‘with lowest mortality, ; Monthly range of temperature with highest mortality, . Monthly range of temperature with lowest mortality, . Daily range of temperature with highest mortality, Daily range of temperature with lowest mortality, Mean height of barometer with highest mortality, . Mean height of barometer with lowest mortality, Range of barometer highest mortality, . Range of barometer with lowest mortality, A Rain in inches with highest mortality, Rain in inches with lowest mortality, . Days of N., N.E., and E. winds with highest mortality, Days of N., N.E., and E. winds with lowest mortality, iit ; 4 : : : ; ; : : 7 ‘ ; : 27-1 8:2 9-6 30°088 29-864 1-026 1-855 3°09 4:21 6:0 10 Mean of the Monthly Ranges of Temperature. 31:3 30:0 Feb. Mar. 34:0 | 38-4 89°3 | 43-0 85:0 | 27-0 56:0 | 33-2 LO || DS 108 | 10-9 29-932) 29°639 29°840| 29-707 2079} 1-981 1-289) 1-270) 2°69 | 3:52 1:54 | 4:18 8-0 6:0 15 4:0 Mean of the Daily Ranges of Temperature. 11:8 15 Mean of the Total of Mean Total Height of ee Rainfall in | Po¥ of N., Barometer. Barometer. Inches. E. Winds. 29-785 1°444 37°88 105-0 29°812 1:218 45:29 74:0 29-916 1:294 33°91 74:0 29-893 1:236 30°56 98°8 29°838 1-099 45:07 83:0 29°817 1:289 37°17 76:0 29°843 1:263 38°31 85:1 April. 41-5 41:3 82:2 39°0 14:9 13°5 29°978 29-751 1-860 1:289 1:18 May. 50°2 49°5 35°5 54:7 15-0 14:8 29°831 29°828 1-228 1-339 2:18 2°81 8-0 8:5 June. 53:0 57-2 27:5 82°3 13°38 13°6 29-674 29-961 1-102 0-694, 4°34 2°35 11-0 14-0 July. Aug. 58:0 | 54-4 53°8 | 56-0 465 |271 26:2 | 26-4 141 |12:8 13-1 |12°6 29°832| 29:575 29-785} 29-885 0-850) 1-080 0-790} 0-944 27 | 3819 3°87 3°0 3°88 6:0 4:0 70 | ff Sept. | Oct. | Nov. | Dee. 53-4 |46:0 |39°4 | 34-0 537 |45°8 |37-1 | 418 82°9 |29'6 |33°3 | 35°5 277 «+|43°8 |33:3 | 22:7 14:1 |109 Ser | 8:7 11:0 |12:0 |11:0 8-7 29-979] 29-784 29-956] 29-651 29-723] 29-667] 29:897| 29-767| 29°80 0-993] 1-261] 1-872} 1-853 1-172} 1-236] 1-513| 1-204) 1 2:44 | 5-14] 2:38] 3-66] 5:27 | 460 | 6:32 | 520 6:0 40 {10:0 | 80 30 | 10:0 2:0 2:0- ON THE INFLUENCE OF WEATHER UPON MORTALITY. 339 From the foregoing tables it would seem :— 1. That a low mean temperature of the winter months gives rise to an increase in the death-rate from phthisis, and that this relationship is the more clearly observable if the low temperature be sustained for some time without intermission, as in the case of the months from November 1859 to February 1860 inclusive. A high summer temperature does not seem to increase the fatality of phthsis. It is only when the temperature of winter is remarkably low that the increased death-rate from phthisis is distinctly traceable to that cause. 2. That the relationship between the monthly range of temperature and the death-rate from phthisis is uncertain, and that the latter is not under the control of the former. 3. That the daily range of temperature exerts no constant influence upon the death-rate from phthisis. 4. That there is no constant relationship observable between the mean monthly height of the barometer and the death-rate from phthisis. 5. That if there be any indication of a constant relationship between the monthly range of the barometer and the death-rate from phthisis, it is that the death-rate increases with the range. 6. That the rainfall bears no constant relationship to the death-rate from phthisis. It is possible, however, that it may be inverse in the colder and direct in the warmer months. 7. That possibly an increase in the number of days during which north, north- east, and east winds prevail, may give rise to an increase in the death-rate from phthisis. C: The Influence of Weather upon Mortality from Bronchitis. The influence of the weather upon diseases of the respiratory organs differs greatly from its influence upon phthisis pulmonalis. In the former, the atmo- sphere comes immediately into contact with the seat of the malady; in the latter, it merely touches a local manifestation of the disease. It is the oversight of this difference that leads to so much disappointment in the employment of change of climate as a remedial agent. In selecting a locality for the residence of a patient afflicted with a disease of the respiratory system,—as bronchitis, asthma, or the laryngeal affections,—too much care cannot be observed in matters meteoro- logical; but, in choosing a winter resort for a phthisical patient, there are many circumstances of more weighty importance than the weather, to the consideration ‘of which meteorology ought to be subordinated. Change of climate as a remedial agent in the treatment of consumption is exceedingly valuable when properly employed, but equally mischievous when used without a due regard to all the 340 DR R. E. SCORESBY-JACKSON circumstances of the case. To treat consumption by change of climate on meteor- ological grounds alone, is simply to endeavour to combat a symptom without reference to the pathology of the disease, and it would be quite as reasonable to expect a cure from the mere use of a poultice or a cough mixture. To dispatch a consumptive patient to a foreign country only for meteorological reasons, if he be unable to enjoy the change, in spite of the anxiety, fatigue, and discom- forts which must attend the sacrifice of his ordinary pursuits, the separation from his friends and a sojourn amongst strangers, is not useless only, but cruel. But this is a digression from which, perhaps, it would be better that I should refrain. The order of the months according to the death-rate from bronchitis, from the highest to the lowest, following the means of the six corresponding months as in Table C, is as follows :— JAMA s yo) 2am August, . . 89-1 | August, . . 19°7 | September, . 48:6 | September, . 267 Means, . 1045 22-7 61:3 369 | q It is noticeable, that the order of the months, according to the death-rate in infancy and old age, is very nearly the same as that according to the death-rate from bronchitis; whilst the order of the months, according to the death-rate be- ON THE INFLUENCE OF WEATHER UPON MORTALITY. 343 tween five and twenty years, is more like that observed with phthisis, the order of the months, according to the death-rate between twenty and sixty years, appearing to hover between the two. The range of the death-rate between the month with the highest and the month with the lowest mortality varies with the period of life. As already adverted to, it is 33°6 in infancy, 19-2 in old age, and only 5-4 in youth. In adult life, over a period of forty years, the range is 24:2. I shall not extend my paper by pursuing the same investigations with this as with the previous subjects of inquiry. There is only one more question I will ask of the facts now before me. It is this,—What is the effect of protracted cold in winter, and of sustained heat in summer, upon the death-rates at different periods of life? The question is answered in the following table. The periods selected for the inquiry are from November 1859 to April 1860, and from May to October 1857 :— | Noy. Dec Jan. Feb. | March. | April. Mean Temperature in 1859-60 : ‘ , 39°4 | 34:0} 35:5 | 34:0] 388-4 | 41:5 Average of the Six corresponding Months . ; 39°56 | 383 | 87:4 | 382 | 39:8 | 43-2 Death-rate 0-5 ya 1859-60 . ; . | 107-8 | 114-4 |131°2 | 155-2 | 131-2 | 130-4 Average, &c. : : : 4 a ee ar So oe 2 oso \LOT-3 | Death-rate 5—20 years 1859-60 . ; : 23:6 | 2382 | 274!) 28:3] 26:9 | 26:8 Average, &c. : ; ; Dea 22-7 239i) 24-1 94-3) | Qo7 Death-rate 20-60 years, 1859-60 : : GaAs) 77-3.) 791 | 861 | 762") 77-5 Average, &c. : ‘ ; Cleo O7-on ly 2'ao) OO! 702, | 67-9 Death-rate 60 &. years, 1859- 60 . ; : 41:5 | 49-0 | 42:8 | 60°7 | 48-4 | 55-2 Average, &c. : : 5 ; : ‘ 41:3 | 43:5 | 45:9 | 44:0 | 41:5 | 42:71 May. June. July. Aug. Sept. Oct. Mean Temperature in 1857 , : : 49°8 | 57-4 | 58:0 | 60:0 | 56-1] 49°6 Average, &c. ; ; F : 50°3 | 55:9 | 56°8 | 57-2 | 52:5 | 47-2 Death-rate 0-5 years, 1857. : / |100:2 | 90:7 | 100°3 | 1145 | 111-0 | 936 Average, &c. : ; 2 : ; 97:2 | 91:3 |. 96:1 | 89:1 | 92-2 | 96:2 Death-rate 5-20 ee 1857. : ; : 22°69 Zoe 2O9el> LO-4 Perot? 29'9 Average, &c. 3 : : 2 PaO Daron lilo, lol 9: 7 ule 2 OS seo 5 Death-rate 20-60 years 1857 ; : : f 61:0 | 63:4 | 56:6 | 59°3 | 51:3 | 57:4 Average, &c. : : : : 63:2 | 59:2 | 547] 51:7 | 48:6] 51-0 eath-rate 60 &e. EPS, 1851 : . i 5 35°3 | 34:1 | 32°38 | 31:0] 30:0 | 34:0 Average, &c. p ‘ : ; F 30°2 | 34:9 | 31:2 | 28:7 | 26:7 | 28:8 From the foregoing table it would seem :— 1. That a protracted low temperature in winter largely increases the death- rate amongst children under five years of age; and that the death-rate rises almost immediately upon the fall of the thermometer, and falls again so soon as the temperature begins to rise. . ’ 344 DR R. E. SCORESBY-JACKSON 2. That a continued low temperature perceptibly increases the death-rate amongst those between five and twenty years of age, though to a much less extent than in infancy; and the mortality curve does not rise so suddenly upon the fall in the curve of temperature. 3. That continued cold also raises the death-rate amongst adults, more per- ceptibly than in youth, but less than in infancy. 4. That in old age continued cold is prejudicial, but the death-rate does not rise so suddenly as either in infancy or in adult life. 5. It would appear from the foregoing remarks, that severe winter weather induces acute inflammatory diseases in infancy and adult life, rapidly cutting off its victims; that it increases the death-rate of the aged by aggravating chronic diseases; and that it probably cuts off only those in youth who are previously debilitated by some exhausting disease, as phthisis. 6. That a high temperature in summer, especially if long sustained, increases infantile mortality. 7. That such high summer temperature scarcely affects the death-rate in youth. 8. That it slightly increases the mortality in adult life. 9. And that it also slightly increases the death-rate of the aged. 10. That care ought to be taken to avoid exposure to the direct influence of the weather when the mean temperature sinks below 39° in winter, or rises above 57° in summer. III.—GENERAL RESUME. In the foregoing investigations. I have employed as the standards of reference either the means of the six corresponding months, or the means afforded by the six years. In many instances I have drawn my conclusions from the com- parison of two extreme years, factitiously constructed out of the whole term of seventy-two months. I have been urged to such modes of investigation for the sake of conciseness, having had to treat of a comprehensive subject within too narrow limits. In conclusion let me place the data before the Society in one other form, which will serve both as a check upon the previous inductions, and also as a reswmé of the entire subject. I shall employ as the standards of reference, in this instance, the means of the six corresponding seasons, and compare with them the major and minor readings, respectively, of the eighteen months comprised in the several periods from which the means are derived. It is unnecessary, or, at least, would occupy too much space, to repeat the minor meteorological details; I shall therefore restrict the present inquiry to the influence of mean temperature, the mean height of the barometer, and the humidity as represented by the rainfall in inches. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 345 Resumé: On the Influence of Mean Temperature. Average monthly mean temperature of the six winters (Dec., Jan. Feb.), . 38°1 Py i springs (March, April, May), 44°-4 e “ ‘ summers (June, July, Aug.), 56°°6 5 3 s autumns (Sept., Oct., Nov.), 46°4 In the following table the upper lines represent the average mortality of the months whose mean thermometric readings are severally above the standard of reference, whilst the lower lines represent the average mortality of the months with thermometric readings below the standard :— AT ALL AGES FROM FROM ALL CAUSES AT All Zymotic oe ore 0-5 5-20 20-60 | 60, &e. Causes. |Diseases, EASES | G8 Years. | Years. | Years. Years. Average mortality of ten winter months, with a mean temperature above 38°1, . Average mortality of eight winter months, With a mean temperature below 38°11, . Average mortality of eight spring ’ months, ‘with a mean temperature above 44°°4, . 245°51) 63:90 | 29°25] 25°49 |116°60) 23:23) 64°71) 41:10 27111) 64:12) 31°74) 3369 | 123:17) 24:04| 74:64] 48-76 223°81| 45°41} 34:17] 19-09 99°48) 24:25| 63°41] 36°72 Average mortality of ten ae months, with a mean temperature below 44°°4 \ 248'35| 54:44) 35°46] 23°74 | 111°58| 2453] 70:02) 42°01 Average mortality of eleven summer EtG with a mean temperature above 56° 201'40} 49:09} 29°43) 9°70 94:73) 20:96 | 54°57) 31:13 Average mortality of seven summer months, with a mean temperature below 56°°6, Average mortality of nine autumn months, with a mean temperature above 46°°4 Average mortality of nine autumn a ‘with a mean temperature below 46°°4 199'97| 45:°29| 30°77| 13:19 88°36) 23°19 | 56:20 | 32°37 190°22) 54:56) 23:10} 11°32 92°28) 20°06] 49°60} 28:12) 225:14) 65:11 | 25:-47| 18°47 | 107-61) 22°77) 58-11] 36°40 The foregoing table— 1. Corroborates the suggestion previously made, that the relationship between mortality from all causes and mean temperature is ¢zverse when the mean tem- perature is below 50°, and direct when the temperature is higher. Probably the bad effects of a high mean temperature are not perceptible until it has been maintained for some time at or above 56°°6. In general terms, the relationship between mean temperature and mortality from all causes is inverse in winter, spring, and autumn, but direct in summer. 2. Seems to indicate a relationship between mean temperature and mortality from zymotic diseases similar to that between mean temperature and death from all causes; namely, znverse in winter, spring, and autumn, but dzect in summer. The previous suggestion was, that the relationship was variable and uncertain. _ 3. Corroborates the suggestions previously made concerning the influence of mean temperature upon the death-rate from Phthisis Pulmonalis; namely, that a low winter temperature increases the mortality from phthisis, but only to a remarkable extent when the mean temperature is very low, and continuously so ; and that a high summer temperature does not increase the fatality of phthisis. VOL. XXIM. PART IL. 5B 346 DR R. E. SCORESBY-JACKSON It may be stated, generally, that the relationship between mean temperature and the death-rate from phthisis is slightly inverse all the year round. 4. Substantiates the previous statement that the relationship between mean temperature and the death-rate from bronchitis is znverse all the year round, and that such relationship is most distinct in winter. 5. Supports the previous statement, that the relationship between mean temperature and mortality from all causes is inverse at all ages in winter, spring, and autumn; and that such relationship is most distinct in infancy, and least so in youth. Italso corroborates the statement that a high mean summer tempera- ture increases infantile mortality; but it is opposed to the suggestion that a high mean summer temperature also increases the death-rate from all causes at other periods of life. Resumé: On the Influence of the Mean Barometric Pressure. Average monthly mean height of barometer of the six winters, . . . . 29°829 * s : springs, ©. |. «> .eaaey ~ - * summers, . .. . “. 296 s Pa 7 autumn, . 6) 5 > oR In the following table, the upper lines represent the average mortality of the months whose mean barometric readings are severally above the standards of re- ference, whilst the lower lines represent the average mortality of the months with barometric readings below the standard :— | AT ALL AGES FROM From Att CAUSES AT All| Zymotic ee oo SP LOS 5-20 | 20-60 | 60, &c. Causes. |Diseases. SEE eae See Years, | Years. | Years. | Years. Average mortality of nine winter months, with mean height of barometer above 29° 829, Average mortality of nine winter months, with mean height of barometer below 29: 829, Average mortality of eight spring months, with mean height of barometer above 29 847, Average mortality of ten spring months, with mean height of barometer below 29° 847, \ 254°26) 58:00} 31°69} 29°51 |116°91) 22°68) 68°92) 45°67 Average mortality of ten summer months, with \ 259°52| 70:00} 29°02} 28°76 |122°15) 2450} 69°55) 43°35 235°85| 47°12] 34°68] 22°24 | 10430) 24°64) 67:06) 39°89 238°72) 53:00 | 35°06] 21:22 | 107°72| 24-22) 67°10] 39°46 mean height of barometer above 29° 861, 202°97| 49°44 | 29°30} 10°30 | 95°50) 21°30} 54°76 31°39 | Average mortality of eaght summer months, with mean height of barometer below 29: 861, Average mortality of eleven autumn months, with mean height of barometer above 29°837, Average mortality of seven autumn months, with mean height of barometer below 29°837, 19819) 45°41) 32°01) 11°99 | 88°06) 22°50} 55-76 31:90 214°57| 61°64) 24:97] 15°93 | 105°06) 21°65} 55:08} 32°70 196°86] 57°00| 23:20) 13:27 | 91:90) 21:04) 51°91} 31°57 The foregoing table— 1. Corroborates the previous suggestions, that over the whole year the rela- tionship between the mean height of the barometer and the death-rate from all — causes is inverse ; that the relationship is cnverse in winter and spring, and that it is direct in autumn; but it opposes the suggestion of an inverse relationship in summer. ON THE INFLUENCE OF WEATHER UPON MORTALITY. 347 2. Substantiates the suggestion, that the relationship between the mean height of the barometer and the death-rate from zymotic diseases is inverse in the colder, but dzrect in the warmer seasons. 3. Confirms the statement, that there is no constant relationship observable between the mean monthly height of the barometer and the death-rate from phthisis, the results both of the two colder and of the two warmer seasons being opposed to one another. 4. Suggests a direct relationship between the mean height of the barometer and the death-rate from bronchitis in winter, spring, and autumn; but an inverse relationship in summer,—a suggestion which, although not without conflict, is supported by the results previously obtained. 5. Shows that the influence of barometric pressure upon the death-rate from all causes varies with age. In infancy the relationship between the mean height of the barometer and the death-rate from all causes is probably inverse in winter and spring, but direct in summer and autumn: in youth the relationship is in- constant; in adult life it is also uncertain; in old age it is possibly nearly the opposite of that which obtains in infancy. Resumé: On the Influence of Drought and Humidity. . Average monthly rainfall of the six winters, . . . . . . . 98°83 inches, i 3 - SLINGS). 7. cet ae RE De a i if Suunners. 1) 2) Meme eee teal Osl fen prs - A GEMS | ie oo eta Oe k, In the following table the upper lines represent the average mortality of the months whose mean rainfall is severally above the standard of reference, whilst | the lower lines represent the average mortality of the months with a rainfall be- low the standard :— AT ALL AGES FROM FROM ALL CAUSES AT All Zymotic Aa ve 0-5 5-20 20-60 | 60, &e. Causes, |Diseases, Ebohisis.| Bzonchitts, Years. | Years, | Years- | Years. 257'06| 69°44 | 29:20) 27:48 |120°37) 24:12] 69°21) 43°66 Average mortality of nine winter months, with a rainfall above 3°33 inches,. . Average mortality of nine winter months, with 5° rainfall below 3°33 inches, verage mortality of nine spring months, “with : 5p oe : ; é : ; intall above 2:58 inches, 239:29| 52°80} 34:33] 22°24 |108'97| 24:49] 66:18] 39-42 || Average mortality of nine spring months, with \ 103-43 | ) | 256°72) 58°55 | 31:52] 30°80 |118°68) 23:06] 69°26] 45°36 a rainfall below 2°58 inches, 235'60, 48:00] 35°44) 21°10 24°40 | 67:99 | 39°88 _ | Average mortality of eight ‘summer months, with a rainfall above 3°17 inches, . | Average mortality of ten summer months, with a rainfall below 3° 17 inches, Average mortality of seven autumn months, with a rainfall above 3°67 inches, Average mortality of eleven autumn months, with a rainfall below 3°67 inches, 198°60) 45°12] 30°24} 13°42 | 88°55} 29°84) 55°61} 31°51) 202'65| 49°60 | 29°72) 9:15 95°11} 21:02) 54:88] 31°69 | 205'53) 60°30) 23°36) 15°27 |100°13] 20°77 | 52°90) 31-47 | 209:05| 59°55 | 24°88} 14°66 | 99°83] 21°82] 54-45] 32°76! | 348 DR R. E. SCORESBY-JACKSON ON THE INFLUENCE OF WEATHER, ETC. The foregoing table— 1. Suggests a direct relationship between the rainfall and the death-rate from all causes in winter and spring; but an inverse relationship in summer and autumn,—a suggestion which the previous results tend to support. 2. Suggests a direct relationship between the rainfall and thedeath-rate from zymotic diseases in winter, spring, and autumn; but an inverse relationship in summer. This suggestion also is nearly supported by the previous results. : 3. Shows that there is a slight indication of an inverse relationship between — the rainfall and mortality from phthisis in winter, spring, and autumn ; but of a direct relationship in summer. These indications, however, are not very distinct, and are not well substantiated by the previous results. 4. Indicates a direct relationship between the death-rate from bronchitis and the rainfall in spring, summer, and autumn; but an inverse relationship in winter. This is not distinctly observable in the previous results; and probably — the note appended to the fifth suggestion, under bronchitis, is the true explanation — of the inconstancy of the relationship. 5. Shows that the influence of the rainfall upon the death-rate from all causes — varies with the periods of life. In infancy the relationship appears to be direct — in winter and spring, doubtful in autumn, and inverse in summer. At other periods of life the relationship is scarcely perceptible. ] i 2 | > 7 a hd Here I must close my paper. I offer it as a slight contribution to medical climatology, and I trust there will be found in it something worthy of the con- sideration of those who take an interest in that still very obscure science. The interpretations that I have given of the facts at my disposal are such as I think they will bear without straining; but I place both facts and comments before the Society, so that any one who is interested in the matter may judge for himself. a a f BLE A IN WHICH THE ONTHS, WITH THE 2 T I T TI AT T 7 ~ M IR METE 0! INGS AND DEpwcTION: > HE TOP AND THE LOWEST A ABLE (0) W: S, ARE ARRANGED IN THE HE RATIO OF MORTALITY FROM ALL CaUsEs, THE R BL A M OROLOGICAI EAD) HIGHES' ATIO BEING EACH COLUMN R ‘HE ORDER OF 1 TIO ST AT THE FOOT OF THE T. > , § DIVIDED IN To FouR Srorions or Hig: , CORRESPONDI AXIMUM I ; MAJOR, Minor, AND 2 , EANS a IN vEN ID HE SECOND, AND THE ME. 4 ANS OF THE O00 Mean of | Af yean | 2" | sfean if rahe Mean) sen pean [sean Mean Mean u “rent MERE ee eae of ame | 60%, | of Hera re |p A r Mean | Monthly | 2") sfean| ofthe |*fean ey i | de |e Sita fe Se el a: | see ea ly [a it] ad | sean acne nce |” | ee | Np || Mae 9562 |stezn| snr flon, |WHole} pera- whole. Sec- nBe of) the ot each tl of of of if Hamt ronal on. & | ton, era | foo |whole|peruture. wlioie| Terspe, | Se lwtite | sea aver, | SEC he: of | otn| of | of | stn] of OF fot | Mean TIN tures. fires: tlon. Tempe: | SE lynte| Sea iva, | Seton] whole ) Bar cca] te, | Rainy] See" | the | Rain | Soe" the alty. | eaen| of Mean|ifean|))|fean| ifean z WINDS. | a ks and 32%. 0) ays. A | Sec- Ss merit Sul han ‘ c Top. | 3306 340 39:2 286 FO ee [Per*) tion. PPO sactes| Hon. [Me — 270) See: Iytite| N- | eaen| the | S| eaen | une | = Ea besa bass sal cece Pl Isc cca Lnssl cc Jon. | 804-1 86°38 404 9) 2 107 29932 = — | | | Sect. twhole! Sect. {whole each | the | SE | each | the | © | eae of | gy. | of | of | yy | of | of | yy. ean! Moan) Calm) Mean} Afean| Foree | 3 82/9 87-4 0 2-079 13 pees Sect. |whole See y each | the each | tho | Y* | nw. | of | of | or | of fean Jan. | 2966 884 42:0 848 82 30:033 9 2:69) = 85 = j | =f BEG Sect. |whole. Sect. pehole YANG cach | tho | vartefeaen | the |avica | ooh ‘April | 2902 41-5 43:9 Pie Be 71 29686 re 14 3-09) 90 Bi 20 bay, mal olnol SSG SSS EIGEN Ea het} ines | Sect March] 283:2 384 14-0 305 oe 149 29:978 : eal 552] 90 aa 10 | 30 30| | a0 +0 60 =i aa] lnes IS : Tan, | 280: 365 306 314 Ano 115 29639 aueet By 82 Zo. 10 20 50 a0 80 50 a a 239 é 89" Aq % aon 81 5 i 9 fs : 40 ‘ 50 0 \ 3:0) a Die M0 363 Ton Ba 97 29.956 Beto 18 Bs 50 20) in au 20 30 a $0 20 es Dec. 418 46:2 37-4 Pip 87 29651 ah 10 89 A 30} 30 +0 310 | 60 8.0 50 20! 1:05 Mar 2073|20p-40] [805/988] | 40/401] | 36 | a8 560 [364 | 119 | 98] | 29098 rea 21 a io] | | 30 20 ee cm | 31 aA 30 24 78 Bd 37! 30-0 40:8 : i 52 | 29-800 1-587 | 1-564 oe | 89 10 | int oy 30 30 Sey 4.0 26 3. ‘i ane 42:5 332 34°8 a 29°709 1-426 ee 3:18} | 85 | 87 Saeel! _|os 10 30 : | 60 4.0 . 1-09 i F : B B E 9:5| 9.94 a J 30 Qu +0 30 857 398 31:6 501 98 29'698 1-322 Wy 90 £0 Boy 2'5) 2:22 15) 3:00 0:5 }3°36 5 90 9.0 £ 167 é 3 2 5 | : ; 5 0:5 | 8:08 | 567 ei 0 ‘ oe Bob, | 218 404 re 358 ate ee 20698 1-534 ae 88 3-0 | eo £0 70 ae 3:09) G5 567 ia 613 T5\ 929) A aa fe rer layne , cet 343 56:0 ; bed 1-402 87 35 5 5 £0 20 3 a 8:0 3K aul ii f 5 b 108 ‘ abt 5 3 : 0 ‘ F 3:0 ‘ Heth 200 502 515 37'8 397 137 aaa 1.289 i 89 20 20 ay 15 20 30 70 10 10 136 Deo | 250:0 nat ae B45 49:5 O8 29881 1-204 14 89 50 00 rau 6:0 30 an 7.0 40 +0 6 eo, | 25 399 44:0 357 25:2 ae 29708 2021 16 BS 30 20 2 a 50 105 Be 20 20 180 2 2:0 2 34 i "0 ‘ : 36 Tob, | 2469 405 454 a 1297 U7 its 10 3:0 70 30 £0 7:0 Ko 10 20 L77 April | 2436 42°7 48°7 pede 29:0 98 99709 ely) 08 Ot 12 a 8:0 50 50 3:0 10 57 May | 2100 i a 993 306 Be 29-864 1855 vy 238 8 20 a at 29 30 wel | lies ee a 180 Tob, | 287: 5 F any 355 15: ae 1459 1 ie 10 0: % ‘| 30 3: s rl 20 ’ A | pa Bau oe 30°5 49:0 ie 29/831 1928 18 2-98 90 3:0 o0 0:0 10 30 10 bit 20 3: 207 Nov. | 2907 ei fas B42 26:9 10-4 29:998 1497 6 oe 81 10 2-0 i) 20 30 70 0'0 £0 1-0 ane | 1857 et eed 410) 43:1 is 50:0) 376 38:2 392 aa D803 sis 1 337 50 30 a is 63 ae 50 60 20 20 190 11807 | Noy, | 281:3 43:7 43:3 | f 2 33:2 | 37:2) 109 }116 int ‘ble 10 24 2 3" 10 0 I 255 8D ve ma 2" 14s anny b 39-2 50: 29°707 | 29868 1-270 | 1: 210 90 Sy 20 30 15 20 54 12 ji Noy. | 280:0 3941 Bled 50:0 91 30-115 270 | 1363 i | 13-7| 418) 3:06 y 20 10 30 3:0 6:0 60 - 3:0 1:80 W602 |May | 228-4 rat Fad 405 265 B1 5 1-719 19 a 85 | 86 2-0) 215) 1-0| 2:00) =) £0 £0 6:0 re 3:0 50 " ? : i 2 Y 2 . 01 3° 40 34 131 801 |Teb, | 2281 30:5 i 440 312 1W4 29919 1-641 1 89 90 25 ae 0) 5:17 1-0] 314 20l2e01 | aolso7 0} 30 ‘+0 ‘ Beli ine a wea au 08 2051 ea i 59 ET a io 5 bo 2 50 |a07| gale! | fo/26q | 10/ane | 10am | ay | 22514 491 56:9 ; 61:0 15°3 99.949 : 15 3.39 10 20 3:0 i 2 20 20 mir 5:0) 110 1801 | Nov, | 224°6 38:5 139 41:3 39:0 156 42 1434 9 : 88 20 30 a £0 50 60 . 20 30 ; ane 3 ; 30-070 186 78 , 20 £0 | 6:0 20 2 oi) 224-1 800 iat 33:0 83:4 10:9 Bate 0:937 14 ; 20 2:0 a £0 70 ; 20 12 994 i , pyipes f 1:57 80 i cs 50 40 Py 40 a0 , Mi 2240 56:0 63:4 53:0 53:0 14-1 i 1.295 18 i 4:0 3:0 : 20 50 : 10 9:09 48:7 Ad 30:014 0661 663 87 £0 30 1-0 10 ; 45 25 30 ct 25.71 46:3 526 0 17 29/887 10 187 3:0 20 60 70 50 145 t 2 i 5: a 0-945 : 85 23 ' y 1-0 20 i 4:0 20 ABA 524 33:3 405 36°83 12:0 29) 17 4:31 83 3:0 35 35 70 60 30 118 413 48:7 oh 840 141 30:1 S43) 1-262) 149 ; 20 20 25 an 8:0 55 5 ; 20 236 eee) | | lal) i) | aa) ) [el | fae al a SSRI eel ia eal Rol ey: A aL ie 1808 |Tuno | 2193 58° : 426 47-0 29507 1-430 3:20 80 4:0 or 3:0 20 : : 2 678 295 onl 110 is 8:9. 67-1 * 14-4 99: 22 51 3:0 5:0 i 3:0 40 Y 2.20) 1 J1800 | Juno | 2194 53:0 2 507 47-0 16 29°959 0890 86 10 20 10 5 4:0 3:0 692 118 59! ‘ 4 i 13 F 10 1-0 es 8:0 40 i 118 Doo. | 2157 ris 97 465 275 30/032 0-702 1-66 80 15 i 2-0 30 } 50 3:0 1 | f 9 49:2 , 13:3 29: 12 9 ri 40 B85 oF 8:0 9:0 i 2:33 Juno | 215:0 5-4 cA 407 38:0 9674 1102 2°36 78 0:5 ¢ 45 3:0 : 50 10 f ; ‘ 85 99: 18 ; 10 2 45 25 : 2:64 HIS00.|July | 2148 B78 Hee 460 27°3 13 29-989 1:38 434 85 20 20 30 £0 5 06 20 t : ‘ 2 i : 3:0 ; 70 3 179 | Jan, 0] 214-96 30/940%6 645 5011 309 6 29'733 L074 14 2:37 88 05 i 60 50 40 iN 70 30 5 7 Wg07 |Juno | 2139) 9:5)20:5 44:0 | 5641 84:6 431 Oi ee 29:985 O45 20 3:99 83 ' uid 00 1-0 =i 3:0 20 10 1:86 J ord 66:0 ‘ 40:0 | 396 9-4 | 13-0 ; ee il ‘ esi 10 20 ly 150 5:0 2 1:28 Sopt. | 2108 a6 48.8 66-5 ie 30-065] 29'862 1-241 | 1-163 whee) 83 3:0 2 20 30 60 20 15 ‘ July | 210% Reto 625 49°7 4179 Ne? 30:020 Toso| 14 | 164 2.98] 8:27 86 | 94 sa it 20 £0 30 3d 7:0 60 ti 2:99 58 | May | 2104 ea 651 51-0 5 128 29°852 14 9 279 81 peel 0:5) 2:02 05| 3-03 2:5] 262 a 3:0 60 £0 30 1:67 2 49:5 569 H 46:5 141 an 0+ 15 t 2:0 40 ' SC 8:0 | 2:86) 10:0) 6-72 “0 6:28 087 Oot, | 2104 ; 4241 Pre 29832 0: 3:82 87 5 60 40 8:0) 6:22 4-0) 3:08 102. 46:0 Aled 547 14:8 ‘850 15 . 15 355 StF 3-0 40 25 0 2-12) 2:36 | 1 Oot. | 2080 496 es 40°5 296 29'823 1:339 217 80 (te 35 2.0 a4 { 25 Vb 3:0 86 | 17871 Oot. | 205 558 43:9 17 109 29-784 : 16 281 8 2 10 05 0: a 6:0 Bb Vb 165 Abe 0 . 1:261| u 2:5 i . 5 20 95 0 5:0 R Oct, 44:9 51-0 39:9 11-4 29:803 “ 22 514 87 3:0 30 3:0 95 105 45 1:38 471 53-4 mn 32:9 19:4 ant 1246 16 of 2-0 10 ; 25 65 50 on 20 55 07 32'8 29'892 1-687 2°36 90 15 10 20 +0 ; D 8:0 26 BL | July | 204-4 12 29-620 18 472 30 35 ke 50 5:0 30 a 1:34 4 568 ‘ tes 1872 a 87 22 i 35 3:0 7:0 2:0 om Aug, | 1995 , 63:6 60:0 27-6 19 6:32 88 il 28 21 12 U5 60 15 20 BA Tino | 196-4 poe 659 49.9 a 13°6 29:619 oF 0 0-0 10 30 A (a0 7:0 40 ; 129 9 i) ‘ 2" " 30 90 f 27 1 Sopt, | 1959 a7 640 50-4 Bae 16:0 29-943 Gd 20 394 at 90 3:0 20 By Sopt, | 1946 534 603 4G Be 136 29-961 £008 15 261 10 20 30 ° 2.07 45 ae 2: i a 694 81 - || x F 3:0 £0 m By 38 Hy) [ee] | laa) | | oes ra ee noat i) | feel | fe] [ost | fal | fas) | fas] | [ss vol | |zol | |zel | jaa) | |r ih |e bd : 21 42-4 29'898 099 d 88 ‘ ‘ 40 30 4 3:0 40 July | 192.3 aes 608 48:0 19-7 30°046 7 14 2-30 a4 10 20 3-0 £0 30 3:0 30 0:99 R59 |Juno | 1886 53:8 60-4 47:3 27-1 12:8 30:575 0498 4 0:39 05 05 20 0 30 60 50 d 20 0:88 ‘ ‘ 2 ‘ 2 3 i 2 25 6 : 20 4:0 Ost, | 1880/1858 56:6 GL 436 26:2 131 ane 1-080 19 379 d 20 3:0 60 ap 10-0 70 ae 4 0:92 Sopt, | 1895 i) 45°] 543 61-8| 61:21 39:8 | 47 85:3 16-1 eile 0-790 39 5 2-0 1-0 3-0 5 40 4-0 20 i 25 168 lees 4 43:8 | 33: ' 29934 0:652 a 387 83 . 30 20 i 1:0 40 i July | 1813 50.2 671 43:3 33:9 12:0 |13:8) 99-667 | 2: 11 9. 10 10 t 50 80 3 OBL 59) ' 19°842 1-236 | 0+ 2:04 Vis} GH ‘ 20 20 3:0 i ‘ 4:0 30 Avg. | 1787 69:0 662 51 95:0 13:8 298 0-961 14 | 153 4-60) 3: 20 40 50 70 9:0 ' 115 1859 | So 57:8 0) 19 32-4 14. 29'868 1165 318) 89 | 84 3-0 1-58 alae 3:0 20 40 50 10 pt. | 177-7 65:2 50-4 43 30-050 14 192 8 5 30|1-72| |40|300| | 40/288 50 3:0 176 Aug, | 173:1 pas 592 45:5 SG 147 29:8 1088 14 76 7 3:0 20 2:0/328| | 4-0) 6-57 06: : 20 166 . \ ‘ 50 C 2°76 81 4 20 10 i 4:0| 6:33 4-0| 2:64) 3:0 | 94 Oct. | 1794 ort 628 51-9 25:2 13:6 99:729 1167 14 9 10 2.0 : 20 60 t 0)258) | 1-63) 1-84 : ‘ an 722 : 27 80 : £0 20 2: 80 40 20 gf Avg. | 1684 49:5 554 43: 251 11:0 aa Sy ocs 7 f 0-0 00 0 70 80 109 81 |S 56-0 : 7 30:9 : 9774 0797 321 82 00 4 10 10 50 104 20 30 } pt. | 165:0 62:3 49:7 116 29-936 22 6-44 10 2-0 % 00 90 i 144 587 ’ 26: 3y 1201 86 : 30 40 2.0 20 j 59:2 482 ae re 29'885 0944 14 334 90 aa 00 10 10 40 Wey 8:0 20 20 ae 0 29°728 1172 16 3:35 87 Pin BH 20 40 6:0 ey 100 8:0 10 hae 19 527 88 3-0 an 30 BY 30 70 oy vo 30 1:28 so sty 6:0 30 30 ree Ped | fe *: ' 7 : Ps r r : - 76 eaiy rw i} Pa ori : u } ; 2 — w he i a i. ao x er ’ mn | | ! ba ok ‘ asf 7) = " roe Ge = F a 6 . ure ’ a 7 ‘ : | - e— . 42.5 ' -we? » Ae E re 4 F } 7 | moe ¢ An aA Ee ip: = -« a ae + a . Cea + eee v iJ ve bx: id -. F iq 2 . Pe & = - : 4 Ly : a ’ & a Ss SS —- ad rw . j= oe 1857 Ratio of Deaths per 100,000 living at all Ages. 1858 Ratio of Deaths per 100,000 living at all Ages, 108 29°840 1-289 87 Hapa SISO r= BOTOD ICS SSSSRASAK 2:0 29°804 2021 1:0 la ie I CO ER ICS >MOSSOSSSSS @ 10°7 30-065] 29-998 1-241) 1-427 14 6 2°98 (0.2) ior) Qo’. iss) WHR OSwWNW OOH COIS COIS Ed SOS) SSAAAAAAS ~WODDOOCAAAH 11:9 Gil a ASIC COIS CD DAKAAMTAATS oN TABLE B, RepresEntinc THE METEOROLOGY AND THE DEATH-RATE (FROM ALL AND SEVERAL CAUSE April. | May. | June. | July. | Aug. | Sept. | Oct Nov Dec Jan. | Feb. |March.| April. | May. | June. | July. 42°7 1498 |57-4 |58:0 |60:0 |561 |49°6 |43°7 |449 | Mean temperature, .................- 396 |40°5 |43:0 |41:3 |51:9 | 56°65 | 59:0 48'7 1570 |66°0 |65:1 |67-1 |62°5 |55°3 |48:°3 |49-2 | Mean of the highest temperatures,| 44-4 |45:-4 |48-5 |48:'7 |61:7 |64:7 | 66:2 367 |426 |488 |51:0 |53-0 |49°7 |43:9 |39-2 |40°7 | Mean of the lowest temperatures, | 34-8 |35°5 |37°6 |35:2 |421 |486 |51:9 46:0 |47:°0 |66°5 |46°5 |53°0 |47:9 |470 |50°0 | 38-0 Monthly range of temperature, ...,\27-:1 |29:0 |33:2 |39:0 |424 |35°3 |32:4 12:0 |14°4 |17-2 |14:1 |14:1 |12°8 |11-4 9-1 8:5 | Mean daily range of temperature,| 9 6 98 {109 |13°5 |19°7 |161 |143 |e 29:767| 29:959] 30-020] 29:832| 30:014| 29:882) 29-803] 30°115} 29:989) Mean ht. of barom.: sea-level & 32°,| 29-864| 29-709] 29:707| 29-751) 30-046] 29-934) 30-050) 29 1:142} 0:890} 1-039} 0-850} 0661) 1:101] 1-246] 1:719| 1-338] Monthly range of barometer, ...... 1°855| 1:375| 1-270) 1:289| 0:498] 0-653) 1-083 16 ] 9 15 10 15 16 12 14 | Number of rainy days,............... 7. ive 11 15 + 11 14 2:38 | 1:66 | 2:79 | 2:17 | 1:87 | 3:82 | 2:36 | 2:89 | 3:37 | Rain in inches, ..................0000 4:21 | 3:38 | 4:18 | 3-20 | 0:29] 2:04] 2-76 84. 80 81 80 85 87 90 90 88 | Humidity (Sat.=100), ............ 87 88 85 80 vi 78 81 2:0 15 2:0 1195) 2°35 | 1:5 15 25 0-5 Z N. = 1:0 1:0 2:0 40 2:0 2:0 10 30 | 40 | 40 | 10 | 30 | 35 | 30 | 35 | 00 a N.E, s 00 | 00 | 10 | 30 | 30 | 40 | 20 70 8°5 6:0 0°5 Bia) 3°5 3:5 4:5 00 lee E. A 0:0 1:0 1:0 50 6:0 5:0 40 4:0 4:5 4:0 0-5 35 2:0 3°5 35 10 = S.E. = 1:0 2-0 1:0 2:0) 7 50 3:0 2:0 30 | 30 | SORI20 | 30 | 3d | 30 | 2:0 | 30 ed 8. a 30 | 30 | 20 | 10 | 40 | 20 | 2:0 35 4:5 40 | 95 any 6:0 7-0 5:0 |15°0 = S.W. = 11:0 8:0 8:0 30 4:0 40 70 3°5 2:5 2:5 |10:5 4:5 55 6:0 30 8:0 ra W. = |100 8:0 |10:0 40 2:0 5:0 8:0 2:0 | O05 | Meee | 200) 15 | ae ee 220 & NOW. 5 40 | 30 | 50 | 50 | 10°) (30 | 320 2-0 2-0 3:0 2-0 4-0 3°0 2-0 35 15 a \. C.orV. Zz 1-0 2:0 1:0 30 4-0 2:0 3:0 1-18 | 1:79 | 1:65 | 1:55 | 1:04] 1:38 | 1-29 | 1:10 | 2°32 | Force of wind in lbs., ............... 2:95 | 2°67 | 3:19 | 2:33 | 0°84] 166) 1°44 943-6 | 219-3 | 213°3 |210°5 | 224-1 | 210'8 | 208-0 | 231:3 | 215-7 | Deaths from all causes (all ages), | 243-4 |246-9 | 232-0 | 222-7 |193°5 | 188-6 | 1813 234 | 210 | 203 | 202 | 214 | 204 | 198 | 220 | 205 | Do. from all specified causes, ...... 235 | 2388 | 224 | 213 | 187 | 184 | 176 60 48 44 56 65 ae 62 55 43 | Do. from zymotie diseases, ......... 79 69 57 50 4G 41 43 13°8 9:0 8-2 8:8 TCR 89 113:0) 13:8" 12:0. | Dor tronmtyphue, ~........---c0rssse0 86 8:3 SB 75 8:8 6°7 5:8 7:3 6°5 Brit 3°7 7-0 66 82 6:9 Ar4. NM Dos from Scarlatina, .....<.ce.ce-0ssas 204 1150 |11°2 7-0 5:3 5:2 61 4-9 5:0 50 {12:3 |17°9 |25°9 |14:0 6:0 50: | Dostromidiarrhesa, ......2.0-...00css 3-1 3:8 3:3 2-5 Ll 4:0 72 51 45 46 47 43 37 35 40 40 | Do. from tubercular diseases, ...... 38 42 44 47 43 43 42 372 |31:4 |836 |32-4 |279 |238 |24:0 |27:0 |28°4 | Do. from phthisis pulmonalis,...... 268 |30°2 |31:6 |383:3 |31:9 |31:0 | 296 99 Day 25 16 14 13 18 34 35 | Do. from diseases of resp. organs, | 32 38 27 6 22 18 13 1374 | TE 2:0 5:8 56 5:4 86 |18:2 |164 | Do. from bronehitis,................» 176 1/193 |14°8- |13°3 |10:0 68 6:0 10-7 |111 87 6°6 5:3 54 56 8:82 | 11:3" | Do.tfromi pneumonia, (s...-<.e63ees <2 99 |11°4 71 8:4 74 7-6 59 108°6 1100-2 |90°7 |100°3 1114-5 [111-0 |93:-6 1101-4 |94:0 | Do. at 0-5 years of age,............ 125'8 |120:2 11084 197:0 1831 |769 |846 24-1 |22°6 |25-1 9209 1194 |19:1 |99:9 |201 |194 |Do.at 5-20 do. ............ 22°7 \254 |21-6 |23:°5 |234 |208 ise 706 |61:0 |63°4 |566 |59°3 |51:3 157-4 |61:9 |59-4 |Do. at 20-60 do. — ..s.as-..00e 60°7 |61:2 |663 |62:0 |568 |560 |489 41:4 1/353 [34-1 |32°8 [31:0 |380°0 |340 |47-:7 |440 |Do. at 60, &e. do. .........0. 35°6 |40°3 |36:0 |3880 |30°5 |343 |291 April. | May. | June. | July. | Aug. | Sept. Oct. | Nov Dee. Jan Feb. |March.| April. | May June. | July. 43°8 |49°5 |589 |56:0 |579 |54:5 |449 |89-4 |39°9 | Mean temperature, .................- 35:5 |34:0 |384 |41°5 |502 |53:0 |573 51-4 |569 |671 |63-4 |65:°9 |61-8 |51:0 |444 |440 | Mean of the highest temperatures,| 396 |39:2 |44:0 |48:°9 [57-7 |59-7 |645 36-1 |42:1 |50-7 |48-7 |49:9 |47-2 |39:2 |3844 |35°7 | Mean of the lowest temperatures, |31-4 |286 |32°5 |34:0 |426 |46°5 |50-1 61:0 |54:°7 147-0 |44:0 |52°0°155:0 |32°9 |83:3 |25:2 | Monthly range of temperature, .../28:°5 |35°0 |27:0 |32:°2 |35:5 |27:°5 |309 15°3 |148 |164 |14°7 |16:0 |14°6 | 12-4 9°7 83 | Mean daily range of temperature,| 8-1 |10°7 |11°5 |149 |15:0 |133 |145 29-949] 29-823] 30-032] 29:887| 29 943] 29-898] 29-899] 29:956| 29:703) Mean ht. of barom.: sea-level &32°,| 29-529] 29-939] 29:639] 29-978) 29-831] 29:674| 29-988 1:434| 1:339} 0°702) 0:945| 1:003| 0-997) 1:687| 1-872) 1:297| Monthly range of barometer, ...... 1810} 2:079) 1:931) 1°860) 1:228) 1°102|) 074 9 16 12 ile 15 14 18 10 17 | Number of rainy days,............... 1 133 19 10 15 18 11 1:86 | 2°81 | 2°36 | 4:31 | 2:61 | 2-80 | 4:72 | 238 | 4:00 | Amount of rain in inches, ......... 4-56 | 2°69 | 3°52 | 118 | 2:18] 4:34 | 1°82 78 81 78 8 81 84 87 89 90 | etumudity (Sati, = LO0),) s2-cesneene: 89 85 86 82 81 85 83 2-0 2°5 0:5 2-0 2:0 0:5 PP 31 08 Z N. a 3:0 5-0 3-0 40 1:0 2:0 3:0 2:0 | S01 LOR ZO | 15 | 05 | oe | 26 4) 04 . N.E. 3 30 | 20 | 20 | 40 | 20 | 30 | 20 5:0 3:0 2-0 2°5 2:0 2:0 21 493 1-2 Be EK. A 3:0 1:0 10 5:0 50 6:0 4:0 4-0 3:0 SOM 2:0 30 2°5 2) 39 41 s S.E. eS 40 1:0 2:0 30 4:0 5:0 30 2:0 2:5 4:0 2-0 35 Des: 1:5 2°4 4:8 = Ss. R=) 40 2-0 3:0 2-0 4:0 40 | 3:0 5:0 65 7-0 6:0 6:5 |10-0 7:5 sul 89 p S.W. = 50 4:0 6:0 3:0 5:0 4-0 30 4:5 50 70 60 50 7-0 7-0 4:0 64 rs W. 2 40 6:0 8:0 3:0 6:0 3:0 6-0 25 30 3:0 4:5 3:0 2°5 4-0 26 1:9 5 N.W. = 3:0 6-0 50 30 2-0 20 | 40 3-0 2°5 Bh 4-0 4:0 2:5 Or, 3:5 Die oe Chor We 7, 20 1:0 1:0 2-0 2:0 1:0 3:0 1-45 | 1:34 | 1:36] 1:11 | 0:99} 1:68} 1:90 | 1:09 | 1:80 | Force of wind in lbs.,’............... 1-78 | 2:33 | 1:95] 155] 1:42 | 1:28 | 0879708 227-1 | 210-4 | 219-3 | 224-0 | 199-5 | 194-6 | 205:°3 | 266-1 | 250-0 | Deaths from all causes (all ages), | 280-8 |330°6 | 283-2 | 290-2 |240-0 | 219-1 | 2148 |192 214 | 192 | 208 | 214 | 190 | 186 | 193 | 253 | 238 | Do. from all specified causes, ...... 273 | 323 | 276 | 284 | 236 | 214 | 210 19 45 43 56 62 56 61 59 76 77 | Do. from zymotic diseases, ......... 72 66 57 57 45 48 5) 9-0 81 87 8:2 7:0 7:3 7:2 6:9 (Sie | Womromty phUssieeseeceseesneeeees 108 |104 9:2 8-4 81 60 | 50 i 39 2°5 3-4 37 4:9) 10-3) 175 29:6 |26:6 Doe from scarlatinasc.-------cresseee 16:3 |10°5 par 50 58 63 7:2 ee 3:0 3°7 (O) Welle 96 {11:8 5:2 4°8 28) Do. trom diarrhoea wa ceeeeereeseees 3-4 36 25 37 3:4 24 64 | 6. 46 41 45 45 39 36 33 39 4(). | Do. from tubercular diseases, ...... 45 55 52 51 53 49 45 ie 84:5 |28:8 |82°8 |80-1 |23°5 |22°5 |29-2 |28:8 |29:°3 | Do. from phthisis pulmonalis,...... 31:3 [40-4 |391 |381 |39-5 |37-1 |313 294 32 26 20 ES 18 21 29 52 39 | Do. from diseases of resp. organs,| 59 96 63 66 41 30 27 ies 15:5 |11-4 9:2 9°7 28 Ot) | 1218 29-2) sea Dow tromybronchiticeereeeseeeeeess 36-0 |62:0 |41°2 |43:9 |268 |172 |142 | 107 || Sil CO | SS |) oe 88 |12:9 |14:5 |11:5 | Do. from pneumonia, ............... 14:0 |216 |15-0 |133 |109 | 89 | 89 J) 6! 96:5 | 95°8 | 1048 | 111-7 | 105-0 | 105-4 | 111-1 |134:3 | 122-3 | Do. at 0-5 years of age, ......... 131-2 |155-2 |131-2 | 130-4 [103-5 |}911 |1OE6) 86") | 251 |22°3 |20°7 |24:3 |168 |19°7 |19°7 |27°3 |27°9 |Do.at 520 doe, Petrone 27-4 |283 |2969 '268 |23-3 |25:0 |247 |22° 0h 691 |580 |58:2 157-5 |47:0 |466 |47:°9 |60°8 |62:4 | Do. at 20-60 do." peckesiass 791 |861 |76:2 |77:°5 |70:3 |633 |584 153" 3651 1 33:9) |Soma0e 80:2" \29°4 26:0) 43:0 36:8) | Do. ati60) we: dos 9) aeee--ee 428 |607 |484 |55:°2 |429 |39:5 |299 | | 29° a0 im eS =I = , AND FROM ALL CAUSES AT SEVERAL AGES), IN THE CONSECUTIVE ORDER OF THE MONTHS IN EACH YEAR. _ Nov. Dee |} -———_|—_—_— [394 | 34-0 44°5 1383 34:2 | 29-7 26:9 |35°5 10°4 8-7 29:855]| 29-651 | 2129] 1:853 14 15 3:37 | 3:66 89 88 30 | 40 10 | 2:0 2:0 | 2:0 3:0 | 3:0 30 | 30 60 | 60 60 | 40 30 | 40 30 | 3:0 1:31 | 1:67 236-0 | 263-4. 229 | 259 70 69 85 | 85 26:8 | 18-1 33 | 26 36 42 28:0 | 31:7 | 33 51 68 | 28:8 9-4 |12-1 07-8 | 114:4 36 | 23-2 34 |77°3 15 |49-0 Nov. Dec 91 (341 43:1 =| 37:9 B51 | 30-0 65 (408 msl | 81 8419-919) 29-709 611°641| 1:426 B17 17 (}2:°83 | 3:91 190 90 120 | 40 13:0 | 3:0 8:0 | 40 | 16-0 | 7-0 ) 120 | 30 ) 2-0 2-0 ) 120 | 2:0 ) 120 | 3:0 )aB0 | 3:0 4 11-09 | 1:37 4130-0 | 257-7 6 1222 | 250 0171 a ) 15-1 7-9 ) \7-0 | 20:0 3 PS | 2-4 ) 1138 40 i |7-2 | 29:2 134 | 49 LWr7 | 26-0 ) H:2 | 12:8 12.1)9°3 | 121°3 9 | 22-6 ‘9 |71-1 2 1B-7 =| 42-6 1859 ‘SOdY [1B 4B SUrAT] 000‘00T 10d styvaq jo oney 1860 ‘SOSY [18 9B Surry 000‘0OT tod syywod jo orey 1861 Ratio of Deaths per 100,000 living at all Ages, 1862 Ratio of Deaths per 100,000 living at all Ages. Jan. Feb. 363 | 39°5 404 |44-1 329 |349 374 |29°7 8:2 9°3 30°038)| 29°681 1-026) 1-670 14 15 3:09 | 3:32 90 88 2:0 2°0 1:0 2:0 30 2:0 3:0 4:0 4:0 40 8:0 70 5:0 4:0 2°0 2:0 30 1:0 1:33 | 2°22 304-1 | 228-1 298 223 67 54 US ee 14:5 7-0 29 27 45 40 34:8 | 26°7 73 45 46°8 | 29:4 13°5 _| 10:2 125:0 | 111-2 25:39 215 886 |59°8 63°6 | 35:2 Jan. Feb. 88:4 1401 42:0 |444 34:8 |35°8 21-7 + |\31-2 T1 86 29-686) 30:052 1-451) 1:402 21 11 5:32 | 1:88 90 89 2:0 20 1:0 2-0 2:0 4:0 50 6:0 5:0 30 6:0 30 5:0 4:0 30 2:0 2:0 2:0 1:68 | 1:36 296°6 | 251°3 290°6 | 2480 69 60 111 9:0 54 5:8 33 3°4 45 50 311 |366 68 44 47:3 |31:0 98 6:0 13071 | 1169 25:0) 2547 84:5 | 68:0 571 |409 March.} April. 41-1 | 45-4 469 | 52-4 355 | 383 24:2 | 34:0 114 |141 29°507| 30°177 1430) 0-734 22 9 510 | 1:04 86 83 10 3:0 10 30 10 5:0 2°0 3:0 30 20 8:0 30 9:0 4-0 5:0 4:0 10 30 2°64 | 1:13 220°2 | 223°5 215 | 219 48 40 84 | 7:4 61 4-4 1:8 25 47 53 353 | 866 37 37 231 | 22-7 93 97 102-4 | 96:9 24:0 | 26:3 60:2 | 62:8 33°4 |379 March. | April 378 |446 42°50 | 51:5 33°2 |37°8 34:8 | 39°7 93 |13:°7 29-698) 29°881 1322} 1-204 16 14 3°63 | 2:99 88 83 30 30 60 2:0 9:0 2:0 4:0 3:0 2:0 4:0 30 70 20 5:0 1-0 30 1:0 10 1:36 | 1:57 2567 | 250-0 252°5 | 2456 58 50 101 8:7 a7. || 2Xg) 4:0 28 48 50 364 | 35:1 48 45 31:8 | 28:2 90 {101 115°5 | 1156 24°7 | 25-0 721 |65°5 44-8 [44:5 May. | June. 491 |57-2 56:9 | 64:0 413 | 50-4 39:0 | 323 156 |13°6 30-070) 29-961 0:937| 0-694 14 13 157 | 2:35 80 84 40 30 3:0 4-0 3:0 70 10 4:0 1:0 3°0 6:0 3°0 70 30 4:0 2:0 2:0 2:0 118 | 088 225°4 | 196°4 218 | 191 46 40 114 8:2 2°6 2-4 2-7 3°3 47 41 346 |29°8 36 28 22 asso 96 70 102:2 |90°5 251 | 21:4 65:3 | E19 327 =| 32°7 May. | June SL 1 | 52-4 581 | 58:7 44-0 | 46-0 312 |27:3 © 141 |12-6 29°810) 29-733 0845) 1-074 16 20 3°89 | 3:99 84 83 10 30 2:0 1:0 30 2:0 4:0 2:0 5:0 3:0 6:0 6:0 6:0 70 20 5:0 2:0 1:0 1:27 | 1:67 228°4 | 215-0 223°7 | 2116 46 39 91 8-4 2°8 17 4-0 28 50 52 355 | 369 34 32 198 | 20-1 oy |] 7A! 98:5 |93°8 26:0 | 256 67:6 | 62°4 36:0 | 33:5 13-1 29°735) : 0°790 22 1923 189°3 45 Aug. 168°4 165°5 36 Sept. 53°7 59-2 48-2 277 11:0 29°723 1172 1 09 9 O GP OD bo 1-0 Oct. 49°5 554 43:7 309 116 29:936 1-201 11:0 1513 eee Means of the several Years. 1857. | 1859. Mean temperature. .............00665 48:0 |46°7 Mean of the highest temperatures,| 53-9 | 53-2 Mean of the lowest temperatures, |42-1 | 40-4 Monthly range of temperature, ...)49-8 | 33-6 Mean daily range of temperature, {11-8 | 12-7 Mean ht. of barom.: sea-level & 32°,| 29-893] 29-817 Monthly range of barometer, ...... 1:236} 1:289 Number of rainy days (total),......) 163 | 163 Amount of rain in inches (total),...]30°56 | 37:17 Humidity (Sat.=100), ............ 85°6 | 83°3 A N. g {203 | 23-0 a N.E. 3 31:5 | 20°0 & E. A 147-0 |33°0 s S.E. S [845 | 300 ey 8. 2 $s |385°5 | 34:0 a S.W. ee }815 |79:0 rs Ve 4 63°5 |78:0 & N.W. S 24:0 |38-0 a C. or V. 7, 28:0 | 29-0 Force of wind in lbs., ............... 1°52 | 1-92 Deaths from all causes (all ages), | 227-5 | 212-7 Do. from all specified causes, ......]217°8 | 2056 Do. from zymotic diseases, ......... 59°5 | 57:0 Do. from typhus, ..........--.s-see00 NO |) 785) Do. from scarlatina, ................+. 86 |13°7 Do. from diarrhoea, .............0.-+- 9-2 4:4 Do, from tubercular diseases. ...... 42°5 |39°7 Do. from phthisis pulmonalis,...... 29:4 | 28-7 Do. from diseases of resp. organs, |26°2 | 25-3 Do. from bronchitis, ...............+6. 124 /|11:9 Do. from pneumonia, ............... 85 78 Do. at 0-5 years of age,.........--. 106-4 |97°3 Do. at; S=20RGO: oe een ne es 22°1 | 22°6 Do. at 20-60) do. case enaeeee 61:2 | 58-2 Do. at 60; SOMO, nes ewecceee 387°8 | 34-7 1858. | 1860. Mean temperature, ..........sseeeee- 466 |445 Mean of the highest temperatures,| 53:0 | 50-3 Mean of the lowest temperatures, |40°2 |38°5 Monthly range of temperature, .../45°8 | 31-3 Mean daily range of temperature,}12°8 /11:8 Mean ht. of barom. : sea-level &32°,| 29-916} 29-785 Monthly range of barometer, ...... 1:294| 1-444 Number of rainy days (total),...... 161 | 193 Amount of rain in inches (total),...) 33°91 | 37-88 Humidity (Sat. =100),............-.- 83'°8 | 86-0 A N. a {221 134-0 = N.E. s |21:3 | 28-0 g E. A [306 | 43-0 = 8.E. S i) 867 | 41-0 S S. A £/312 |35-0 2. S.W. = &/805 | 53-0 = W. a |689 |64:0 = N.W. © |40°5 | 41-0 2 \ f@hor V. 7 |32-4 |25-0 Force of wind im Ibs., .............5- 1:56 | 1°52 Deaths from all causes (all ages), | 225°5 | 244-2 Do. from all specified causes, ...... 213°3 | 238°5 Do, from zymotic diseases, ......... 55°5 | 59-1 Do. from sty QHUsy snc... 0.0----s0000: 86 | 74 Do. from scarlatina, ..............++++ 95 |13°8 Do. from diarrhoea, .........---se00+ 61 3°9 Do, from tubercular diseases, ...... 42:2 |44°8 Do. from phthisis pulmonalis,...... 29°5 |32°4 Do. from diseases of resp. organs, |31°5 | 43°4 Do. from bronchitis; ......000---.00s. 156 |266 Do. from pneumonia, ............... 07/4} al ito) Do. at 0-5 years of age,.......-.... 108°5 |112°8 Do. at 5-200) do. —S....... 02 -- 22°2 | 24:3 Do. at 20-60) do. aceensevess 59°2 |66°7 Do. at'GO;Gemedo. ~— <--seceoeoee 351 |39°6 1861. 46°9 52:7 29°812 1:218 199 45°29 86'8 22:0 20:0 34:0 43°0 41:0 75:0 700 35'0 25:0 1°45 229°2 225°6 Mean of all the Years. 46°5 O25 —— eae TABLE €, In wares THE CORRESp,, Mean Mean | Mean | yonthly pipe Mean Height pea Number] pj, | Homi sont, | ven. | termpe-| anes | iowest | oft | Hanse | Geseaterey | got | matoy | im | Se ratore. pears Tempe-| perature. reniees and 32°. Seen Days 100. Se rature N. NE EB 157 | 357| 398| a16| 501| 82| 29698 | 194! 16 | 277/ 87 | 35 | 35 | 29) > 1858 | 393] 440| 346| 400| 94| 30065 |1241] 14 | 298) 86 | 15 | o5 | 32 1859 | 396 | 444| 548] 271) 96| 20804 |1809| 17 | 421) 8&7 | 10) oo | o4 Sanuary | 1e61 | 363 | aoe | 329| 374 82| 30038 |1026/ 14 | 309| 90 | 20 | 33] 30 fa 10 | 30 1862 | 384] 420] 348] 217] 71| 29686 |1451| 21 | 532] 90 | 20] 19 | 32 Means 974| 417] 934/ 341] 84| 29813 |1486/ 166 | 582] s81| 15 | 15 | 4. 1867 | 393 | 443| 343] 560| 108) 29840 |1289/ 11 | 154) 89 | 05 | O09 | 19 | > 1858 | 358 410| 305| 490] 107| 29998 |1427| 6 | 113] 83 | 20 | 95 | 4° 1859 | 405) 454] 355 | 290) 98| 29-709 |1375| 17 | 388] 88 | 10] oo | +2 February /| 1860 340] 392] 286] 350] 107| 29932 | 2079| 13 | 269] 85 | 50 | 20 | 30 Y | 1861 | 395] 441] 349) 297) 93] 29681 | 1670| 15 | 332| 88 | 20 | 59] 3° 1862] 401] 444] 358] 312] 86] 30052 | 1402] 11 | 188] 89 | 20 | 30 | 70 Means 982| 431| 352) 383] 100) 29869 | 1540] 121] 292| 870 | 24 | 16] 90 1857 | 392] 440 | 345] 495] 95 | 20802 | 2021) 16 | 294] a6 | 10) 30] 7 | 1858 | 39:5) 45:5 | 336 | 56:0) 119 | 29852 | 1587) 13 | 195] 85 | 30 | 95 | 7.5 1859 | 43:0 | 48:5) 37:6 | 33:2] 109] 29707 | 1270] 11 | 418) 85 | 20] 10 Lo steaath 1860 | 884) 420] 92:5 | 270] 115| 29639 | 1931) 19 | 352| 86 | 50 | 90] 1° 1861 | 411 | 469] 85:5] 242] 114] 29507 | 1430] 22 | 510) s6 | 10] 10 | +2 1862 | 878) 425] 932] 348] 93] 29698 | 1322] 16 | 303] s3 | 30] 60 | oo Means 898] 452] 845 | 873 | 107] 29701 | 1593] 161] 355] 860] 22 | 96] g¢ 1857 | 427 | 487 867) 460] 120] 20767 | 1142| 16 | 233/ 82 | 20] so] ro 1858 | 433.| 514 | 361/ 610] 153 | 29912 | 1434] 9 | 186] 78 | 20) 20] £5 1859 | 413) 437 | 852] 390] 135 | 29751 | 1-280) 15 | 320] 60 | 40] 30 | 20 April 1860] 415) 48:9 | 340 | 322] 149] 29978 | 1-860] 10 | 118] s2 | 40] 40 | 2° 1861 | 40-4] 624) 883] 340] 141] 30177 | 0734) 9 | 104! 83 | 30] 30] 20 1862) 446) O15 | 978] 397] 13-7) 29881 | 1204] 14 | 299) a3 | 30 | d0 | 30 Means 432} 608 | 363] 419] 139) 29016 | 127/122] 211] s17| 30] 28| 4. 1857 | 498 | 57:0) 42:6] 470| 144] 29959 | 0890) 13 | 166) so | v5 | 4 1858 | 495 | 569 | 421] 547] 148] 29893 | 1999] 16 | 981| 1 | a6 | 30 | 8° 1859) 519 | 617) 421 | 494/ 197] 30:046 | 0498] 4 | 029] 73 | 50 | 39) 22 | 30 May 1860) 602) 677 | 426 | 855) 150) 20831 | 1298] 15 | 218| 81 | 10 | 20 | oo | 2° 1861) 491 | 56:9) 41°38.) 39:0) 156] 30070 |0937/ 14 | 157] 80 | 40] 30] 39 | 20 1602 | 511) 081 / 440) 812] 141) a9810 | 0845] 16 | 389] a | 10 | 20| 30 | Lo Means) 503 680 | 424] 416] 156 | 29923 | 0956] 130 | 207] 798| 20 | 28 | 47 | gg 1857 | 57-4 | 66 ; : : ; 4 lineal 12) Ba) et) as] sg aca) gee Joel eae) a [a2] aa | ge) a ; 1809 | 566) 647 | 486 | 853) 161] 29934 | o622| 11 | 204] 78 | 20 | ao | 20 | 8° 2 4 | 323 | 13: 961 | 0694| 13 | 235 i || a IE 524) 687] 460] 273] 126] 99733 | 1074| 90 | soo S #0 Fea LT Means) 659 | G34 | 485) 395] 1¢9| 29802 | 087/198 | 208] s15| 24 | 98 | o7 | as 1857 | 580} 651] 510) 46:5] 141] 998939 | o850| 15 ) noe ‘ 50} 15 217) 8 + y i 15 sat] 268) oa) ter] eo ar) ee [sel ir | aar| @ | 2a] 2 | 98 | Tul 1860 | 673] 645] 501) so9| ace | cleo | 1083] 14 | 276) s1 | 10 | 20) 40] 30 y, 1861] 568 | 636 | 500| ceo | tao | 22988 | 0745) I | 1:82] 83 | 30] 501] 40] a0 Fase aka el) | 2a | eae) Void) 20 || gl) ge || ein || aie || ea SS) EN] is Be eRe | caret onl 2 I caval as |} ay |E aay | GO | I A A A 2" Mean 868) 638 498/ s¢6| 140] 298m |ose5| 165| 314| a9 | 16 epee cee 1857 | 600] 671 | 63:0] sa0 | qa: 18e4 Bro ae rae pa 141 / 380:014 | 0-661] 10 | 1-87] 95 231 30| 35 | 35 1859 | ors | 6r2 | soe | on2| 160} 29943 | 1:03] 15 | 2e1| a1 | 50 | te | oo | 32 August /] 1880| 544] aps | 480] 271 | 138] spore | toes] 2 | 22%] 8 | 00 | oo | 10 | 10 Ol) 97-4! 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By J. Y. Stwpson, M.D., Professor of Medicine and Midwifery in the University of Edinburgh. (Read 6th April 1863.) In the construction of the animal kingdom, Nature shows herself always provident and saving, both in the amount of organic matter which she uses, and in the complexity of the organic structures which she moulds out of that matter. She never employs any superfluous quantity of material, nor any superfluous quality of mechanism. If a low type of structure in an organ is sufficient for the due performance of the given function of that organ, she never resorts to a higher or more complex type. She does not build organs or animals with the higher organic types of nerves, capillaries, lymphatics, &c., when these organs or animals do not require for their function, or for their life, the special physio- logical action of nerves, capillaries, or lymphatics. She expends no unnecessary workmanship upon the vital machinery which she employs, nor does she ever add to it any unnecessary pieces of organic apparatus. The object of the present communication is to show, that in the human subject we have, and that too upon a large scale, a striking and remarkable instance of this great general law, though the example I allude to has never heretofore, as far as | know, been presented in this light, by any of our manifold writers on anatomy and physiology. From an early period of utero-gestation in mammalia, the system of the foetus is organically connected with the system of the mother by the interposi- tion of the placenta and umbilical cord. The remarks which I wish to make upon the type of structure of these interposing organs apply to these organs themselves, as seen in all mammalia. The illustration of the observations which I desire to offer, is much more perfect in some of the lower animals—such as the cow, sheep, mare, cat, &c., which have the placenta fetalis quite distinct through- out from the placenta maternalis—than it is in the human subject, where those two parts are more intimately and organically conjoined. I shall content myself, however, with drawing my evidence principally or entirely, at present, from human anatomy. The human mother and the human foetus may be looked upon as in them- Selves two of the most highly organised beings in existence. Yet during all the latter period of utero-gestation, their two systems are organically tied and VCL. XXIII. PART II. DC 350 PROFESSOR SIMPSON ON THE ANATOMICAL TYPE OF STRUCTURE united together by structures of the lowest type of zoological organisation. That the structures which connect the mother and child in utero, viz. the umbilical cord and placenta, are of such a low type of organisation as I allude to, the fol- lowing observations will tend to show. Let us begin with the type of structure of the umbilical cord. The rope-like formation constituting the funis wmbilicalis is generally stated to consist in the latter periods of pregnancy of the following component parts, Viz. :— 1st, Of one umbilical vein. 2d, Of two umbilical arteries. 3d, Of cellular or areolar tissue surrounding these vascular tubes, and con- taining in its meshes the so-called gelatine of Wharton ; and Ath, Of a single enclosing sheath, formed by an extension of the amnion. At an early period of pregnancy, other structures are included in the umbili- cal cord, as the vitellary and allantoid ducts, and the omphalo-mesenteric vessels ; but these are not connected with our inquiry, and nothing, at the most, but very shrivelled remnants of them remain in the fully-developed cord. In relation to the subject of our present inquiry, it is of more importance to mark the interesting fact, that though by many of our greatest and best anatomists the finest injections have been often thrown into the umbilical vessels, both arteries and veins, no capillaries have ever thus, or otherwise, been traced in any of the component tissues of these tubes. No vasa vasoruwim have ever been de- tected in the walls or structures of the umbilical arteries or veins. On this point, one of the latest and most careful anatomists who has written on the “ Forma- tion and Circulation of the Human Placenta,” viz., Professor ScHROEDER VAN DER Kok of Utrecht, observes as follows :—‘“ That the umbilical cord has no smaller capillaries besides the large umbilical vessels, is universally accepted. Whether this opinion be grounded on a careful examination, I know not; but it appeared to me sufficiently important to make it an object of particular inquiry. By filling with sufficient force the umbilical vessels with very fine injection matter, so that the vasa vasorum, if any be present, must also be filled, I saw, after the cord was dried, moistened with turpentine, and examined under the microscope, that nowhere was there a trace of any vasa vasorum, so that the umbilical cord contains the only example of blood-vessels which receive no vasa vasorum. After an examination for this very purpose, I could as little discover them in umbilical cords in the third month of pregnancy as in others after pregnancy had been perfect.” The statement that the umbilical cord contains in its structure no capillary vessels, or even any vasa vasorum, requires to be qualified with one remark, viz., that the capillaries and vasa vasorum, which within the body of the foetus extend along the umbilical vessels and abdominal walls up to the umbilical ring, or true OF THE HUMAN UMBILICAL CORD AND PLACENTA. 35] foetal end of the cord, pass there onwards, according to the dissections and injec- tions of Scott and Van per Ko kx, for two or three lines, but they do not stretch for any further distance along the track of the cord itself. They exist, in other words, in the short persistent end of the cord, which remains attached after birth to the umbilicus, and which ultimately fills up the umbilical ring, but they are not found in that great mass which forms the deciduous part of the cord, running from the child to the placenta. The same observation holds true, according to Scuort and VALENTIN, regarding the short extension of the terminal twigs of the nerves of the foetus, which pass out of the body of the foetus along with the umbilical vessels through the umbilical ring. Apparently, like the capillaries, they do not pass further than one or two lines beyond that ring. Numerous attempts have been made to trace nerves in the course of the umbilical cord, but no continuous line of nerve tissue has been detected in itstrack. In former times, CHAussiER and Barr fancied that they had found nervous fibres running along it. Anatomists generally hold that these supposed nerves were only the deceptive remains of the obliterated vitelline duct or omphalo-mesenteric vessels. At all events, since the microscope has come to add its great and necessary aid to this inquiry, the search has been diligently renewed, but hitherto in vain. No nervous fibril, or continuation of fibrils, has been detected by it in this structure. Several years ago, my nephew, Dr ALEXANDER Simpson, when writing his Thesis on the Umbilical Cord, set himself assiduously, with the scalpel and microscope, to the investigation of this question of the presence or absence of nerves in the cord. These investigations were kindly overlooked by Professor Goopsir. The result was, that not a trace of a nervous fibril could be detected in this structure. In some observations which I published twelve years ago, on the Contractility of the Umbilical Vessels, I attempted to show that we could generally, after the child is born, produce in the umbilical arteries and veins, by the local appli- cation of mechanical, chemical, or electrical stimulants, local contractions, which did not again relax. But this form of contractility does not prove, I believe, that nervous fibres exist in the walls of the umbilical arteries and veins; for such local phenomena of contractility occur in the lower animals, where no nerve fibres have been found to exist, as in the Actinia, Medusa, &c. Let me add, that one great exceptional peculiarity in the low type of structure of the umbilical cord is the presence of strong and well-marked contractile muscular fibres in the walls of its vessels, though these fibres are totally unprovided with nerves. Lymphatics have been alleged to exist in the cord by various authors, as WRIsBERG, ScHR@GER, and MicHAELts, and especially by Fouman. The umbilical lymphatics were supposed by Fouman to be capable of being injected by quick- 352 PROFESSOR SIMPSON ON THE ANATOMICAL TYPE OF STRUCTURE silver ; and plates of their appearance, when thus injected, were published by him. But it is now, I believe, universally allowed that these mercurial injections were thrown into the areole of the cellular tissue of the cord, and not into lymphatic vessels ; and I know of no anatomist of the present day who gives credit to the existence of lymphatics in that structure. What forms the proper volume of the cord, or, in other words, what forms the material which surrounds the umbilical vessels, and fills up the serous-like sheath of the cord, is usually spoken of as cellular tissue, containing in its delicate meshes a hyaline substance of an albuminoid or mucoid nature, termed the “Gelatine of Wharton.” This cellular tissue closely resembles ordinary con- nective tissue, and is composed of nucleated stellate cells or corpuscles. The external covering of the cord consists of a serous-like blue membrane or sheath, which, after covering the placenta, envelops the cord from the placenta onwards to the umbilical ring, where, by an abrupt line of division, it meets the white skin of the abdomen of the full-grown foetus. At birth, the contrast at their line of union of the white opaque skin of the foetus with the blue semi- transparent covering of the cord is very striking, and gives in itself the impression of a human cutaneous surface connected organically with a structure of a low zoological type. The umbilical cord, as an organic medium of communication between the foetus and mother, is merely as it were a sheath of sarcoid matter perforated with three tubes for the transmission of the foetal blood to and from the placenta; but it contains apparently no lymphatics, no nerves, no capillaries, not even vasa vasorum. It is skinless, and contained within a sheath of serous membrane. It consists essentially of large nucleated cells formed partly into large and loose cellular tissue containing the gelatine of Wharton, and developed partly into tubal forms, constituting the so-called umbilical arteries and veins. The same remarks which apply to the type of structure of the umbilical cord apply to the type of structure of the placenta. Into the maternal surface of the placenta no anatomist has hitherto traced the passage of any nervous branches from the applied surface of the uterus, nor have any nutrient arteries been as yet, at least, shown to pass from the uterus into the maternal substance of the human placenta. But at all events, the feetal portion, which remains throughout in some animals distinct from the maternal, is assuredly of the same type of structure as the cord, with one or two points of difference ; for, 1s¢, it contains no gelatine of Wharton ; and, 2d, its vessels, both arteries and veins, divide and sub-divide, till they reach the very small size in which they appear in the terminal villi; but still neither their coats nor the sur- rounding tissue contain any capillaries or vasa vasorum, or lymphatics, or nerves. The enveloping sheath or lining of the terminal villi contains a new arrange- ment of tissue not seen in the umbilical cord or other parts of the placenta. OF THE HUMAN UMBILICAL CORD AND PLACENTA. 353 For the duplicatures of veins and arteries contained in the terminal villi are surrounded, as was first shown by Mr Goodsir in one of his admirable papers on the placenta, by a thin layer of nucleated cells, probably, as he suggests, for the functions of nutrition and respiration. This new layer of tissue is apparently derived from the decidua or hypertrophied mucous membrane of the uterus, and, along with the lining membrane of the maternal vascular system of the placental blood-cells, constitutes the maternal portion of the human placenta; but neither nerves nor capillaries have been traced into these structures. The mode or modes of nourishment and growth of a structure like the um- bilical cord and placenta, presenting no capillaries nor vasa vasorum, constitutes an interesting problem in physiology ; but my remarks are at present limited to peculiarities in the mere anatomical type of these parts. These anatomical peculiarities, to which I have attempted to draw the attention of the Society, may in conclusion be summed up as follows :— 1. The volume of the umbilical cord and foetal portion of the placenta is formed of nucleated cellular tissue, traversed by the tubes of the umbilical “arteries and vein and their numerous placental subdivisions, and invested by a sheath of serous membrane. 2. Into the composition of these parts, no capillaries, vasa vasorum, lym- phatics, nor nerves, are found to enter. 3. Hence, in human anatomy, we have these organs, forming a large mass, weighing on an average about two pounds, presenting a type of structure re- sembling that of some of the inferior zoophytes. And, 4. The human mother and her child, two of the most highly organised beings in existence, are thus temporarily united together, during the intra-uterine life of the latter, by structures of the lowest zoological type. VOL. XXIII. PART II, aD Oy - (twit Melina m : j : ’ Maehvonds 7 Vaal ade H : fe ad TERPS “ ; ns ae) mt = i ' ~ | etl bi tt ‘ 1] Oh ‘ ee ud] ie : P — . ; 1) ERR Ge ‘ > @ ~ b. } ‘ alge: ie Fd i) Qa! i | | HMR rere’ ( 355 ) XXVII.— On Earth-Currents during Magnetic Calms, and their connection with Magnetic Changes. By Batrour Stewart, M.A., F.R.S. (Read 6th April 1863.) I have already endeavoured*} to prove that Aurore and Earth-currents, far from producing magnetic disturbances by their direct action, are themselves only secondary or induced currents, generated by those small but abrupt changes of the earth’s magnetism which constitute such disturbances. The proof of this statement was in the first place derived in a general manner from the fact that during the notable magnetic storm of August and September 1859, all the ele- ments of the earth’s magnetism at Kew remained for many hours on one side of their normal positions, while, on the other hand, the earth-currents observed during that time by Mr C. V. Waker had their direction reversed every two or three minutes. * In the next place it was shown that the earth-currents, which occurred simul- taneously with a singularly abrupt and isolated disturbance, recorded by photo- graphy at Kew, were of a character which would favour the induction hypo- thesis rather than that of direct action.+ Professor W. Tuomson has likewise found by calculation, that the electro- motive force, induced by variations of terrestrial magnetism, is probably com- parable in amount with that which manifests itself in earth-currents.+ Since the publication of these views, Mr WaLKER has extended his inquiries, and has communicated to the Royal Society of London an account of some earth- currents which he had observed by the aid of a sensitive galvanometer during a period of magnetic calm.{ It is these observations which I propose to discuss in the present communication. _ Mr Watkxer has been extremely careful in determining that all his ob- Served currents were in no sense atmospheric, but were true and proper earth- | Currents, whatever may have been their cause. In order to accomplish this, he had a telegraphic wire of 67 miles in length, connected with the earth at one of | its extremities, the other being insulated. On this wire he made many observa- , tions during various hours of different days, but always failed in obtaining a current unless when both ends were connected with the earth. * Phil. Trans, for 1861, p. 423. f Ibid. for 1862, p. 621. + Ibid. for 1862, p. 208. VOL. XXII. PART Il. DE 356 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, We are thus provided with a mass of apparently unexceptionable observa- tions of earth-currents made during a period when the magnet was comparatively tranquil, and the question arises, What connection have these with the daily changes which take place in the magnetism of the earth ? In attempting to answer this question, it is, I think, necessary to divide the observations of earth-currents into two categories, for the following reason. It has been shown by General Sazine, that magnetic disturbances obey laws of time and place very different from those followed by the ordinary daily mag- netic changes. Now, if we consider that such disturbances, more or less violent, are of very frequent occurrence, we shall see at once the necessity, in magnetical discussions, of separating the disturbed observations from the undisturbed, in order to obtain accurately the laws of both. Let us bear this in mind, and even without speculating on the connection Sonate between earth-currents and magnetic changes, we cannot, I think, expect thata magnetic disturbance of a certain definite type shall be connected in precisely the same way with an earth-current, as an ordinary daily magnetic change of the same type as the disturbance. This will appear evident, if we reflect that although both changes may be of f the same kind here, yet, if we alter our position and go into another portion of — the globe, they may be quite different one from another, since a change of posi- — tion will affect the disturbance and the daily variation according to very different — laws. On any hypothesis, therefore, the disposition over the earth’s surface of that — current which is connected with the disturbance, will be different from that which is connected with the ordinary daily change. For these reasons it would appear to be highly necessary to ascertain which of the earth-currents correspond in time of occurrence with disturbances of greater or less amount, and which with undisturbed observations. I have been enabled to ascertain this, at least approximately, by means of the photographic records of the earth’s magnetism at Kew. The portions of the Kew declination and horizontal force curves, corresponding in time with the observations of earth-currents, have been carefully inspected, and whenever any appearance of disturbance presented itself, this has been noted by the side of the corresponding earth-current observations, and these have by this means been divided into the three following classes, viz. :— Class I. Observations during Magnetic Calms. II. Observations during smaller Disturbances. III. Observations during greater and more abrupt Disturbances. These are recorded in the three following tables, Mr WaLKEr’s notation being adopted :— AND THEIR CONNECTION WITH MAGNETIC CHANGES. SDC TABLE JI.—OBSERVATIONS DURING MAGNETIC CALMS. Column 1. Column 2. Column 3. Pe Tine Dover—London, u.* | Tonbridge—London, u. | Dover—Tonbridge, u. London—Dover, d. | London—Tonbridge, d.| Tonbridge—Dover, d. 1861. ° ° © October 1 9.31 a.m. 16 u 6d 14u ae DADs: 15u 35d 30 u 2.20 p.m 4u 386d 2.35 3u 28d ae Be 2.16 ye 35 d 20 u 2.47 | 0 0 0 Bee Oe 6u | 28d 18 u 3 oN ORee. 19d 38d 20d 10.12 .-. 20u 0 20 u 4 6.25 A.M. 33 d 3u 45d 12.24 p.m. 385 u 29 d 50 u DIG 40 u 55 u 50 u 4.50 ... 10d 20d 2d | 8 11.0 am 20d 10d 3ld t 9 COR PA a 20d 25 u 9.20 35 d 25u 35 d ; 10 6.58 .. 10 u 15d 20 u 14 2.16PM 10u Wal TEL Gl 2.45 . du 25d 15u 15 11.34 a.m 20u 40d 382 u 12.19 pu 18 u 16d 25 u DP SKO) oe 2u 15d 7u OHeaay e 10d 4u 15d Take ee 20ue&d 5u 40to60d | 7 10.52 a.m 22u 10d 380 u WAS) oe 20 u 25d 388 u WAS? er, 26 u 26d 40 u 2.13 P.M 20 u 18d 35 U 3.41 10 u 20d 15u 5.6 10d lod 0 | 18 10.58 am 14 u 10d 28 u 11.87 24 u 10d 34 u 12.30 p.m 40 u 39d 48 u 2.44 Ns Te 18d 34 u 3.39 15 u 124 | 16 u | 19 12.1 12 u 40d | 45 u 21 7.7 am 5d 0 35d | 10.10 -- 28d 15u 32d | 1.42 pm 50 u 10d 50 u DROME 43 u 15d 47 u 22 615 am 0 5d 200 Wels 2 5d 0 25d 93 10) 5d 0 0 1.45 p.m 40 u 0 45 u 3.9 45 u 0 50 u 24 6.20 a.m 0 7 ol Fw 7.5 0 0 2u 26 12.19 pm 0 10u 0 WOO eae 20 u 20d 26 u CO ae 0 5d 0 | * Dover—London, u, means that a stream of positive electricity is travelling (to use railway nguage) up from Dover to London, and a similar rule applies to the other headings. Date. Time. 1861. October 26 28 29 30 31 20 Basie TABLE I.—Continued. Column 1. Dover—London, u. London— Dover, d. Column 2. Tonbridge—London, u. London—Tonbridge, d Column 3. Dover—Tonbridge, u, ‘Tonbridge—Dover, d. 358 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, fo} — SE POD e wcnrodoodoow oc aco QJeaajnkanhagaasm&a 18d a a BeaAakhAanaanaamaamaa& a aes s ee ornRmoonrocoooonndoooooR DAOCOCHKHOCOKNONAIWWOCM Het ae as a bo [I coonroocornra@Ooanntoon ano & ageaa anAaAneaoaaa a Qe 15 u Otodu 0 to 8u 10u Oto4u 10u 5utodd Otodu 5d bo oo bo LS) OOROArRODONAM oH as aes ac ake Ditties. TABLE I.—Continued. AND THEIR CONNECTION WITH MAGNETIC CHANGES. Column 3. Column 1. Column 2, Date. Time. 7 CST Dover— London, u. ‘Tonbridge—London, u. | Dover—Tonbridge, u. London—Dover, d. | London—Tonbridge, d.| Tonbridge—Dover, d. | 1861. ° ° ° Nov. 20 7.387 AM. 10d 3 HOVGOF 23 8u de al El ade aah 0 r lO 1: 5d SSO ger 18u 8: 12.49 p.m. 0 fe 22 ale | AuNne oe 15 u 23 Sale. Ss 10 u ea 25 1.31 P.M. 0 hae 0 £54 1.34 ... hw ai 6.17 a.m. 0 52 Galo. ar 10u lp 7 ae 10d ; 15d 12.32 p.m. vie 5d 16d Fre SRS) a5, 17d 3u 28d 28 6.15 a.m. 0 we 0 3 Gullit: au 5 u sit BN) G20) 7. 0 Nae 5d 6.24 ... 5u Bee an Grae ae , 5d 30 Geil ee 5d AL 10d aes G.LF Mi 10 u es Dec, 2 49: 23 u 8d 34 u S32 2.24 P.M. 15 u ay 22u 3 6.13 a.m. aes 0 18d Je 6.24 ... 15d 18d 4 GHloy ay. 5d a 0 aes Geli ee 15d ee 5 G20 a. 0 ae 0 mye 6.24 ... Wee 0 Fate fi: 12.34 p.m. 7 40 u 6 6.20 a.m. 0 aoe 0) 13 6.40 ... 10u 0 10u fee CAO. a l0u 14 6.30 . 5d Bee 15d #5 6:30 -.. 10 u 10u 15d ty O.1f24: 10d ‘ 10d GOO sce 5d ue a8 GroOleee Sara 10d 18 GullGie 15d ache 10d a): C2200 2. pee 10d te Pall 6.18 ... 0 Ane 10 u ws G22... soe 28d Be 26 6.25 ... 20u sre 25u GK) Ane 10d aor coe 6.34 ... a aon 25 u ih Gro eer 10u 10d 15 u 8 6.34 ... Dike 0 eae 28 Gali 0 Poe 0 age Gu 1 ws 5 0 or 31 Gly bee 25d _ 30 d P38) ee 0 VOI, XI, PART UL. 359 ~ 360 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, TABLE II]—OBSERVATIONS DURING SMALLER DISTURBANCES. Column 1. Column 2. Column 3. Dee a ie Dover—London, u. | Tonbridge—London, u.| Dover—Tonbridge, u. London— Dover, d. London—Tonbridge, d.| Tonbridge—Dover, d. 1861. ° °° ° | October 2 9.34 a.m. 9u 4d llu | ahd ree 12.24 p.m. | 93 u 26.d° 42u | 3 7.2 AM. 1 35d | 5d 20d Ana Wihetek 2 32 u 14d 38 u 8 12.56 p.m. 20 u 1b u 15u ee 45 u 10d | 50 u 11 10.25 a.m. 0 380 u 0) 12 UES toe 5u 40d 40 u Chath Ole as 20d 20u 40d 14 FOS ee 10d 10d 10d 12.52 P.M. 25u 30d 35 u 15 123). 8u 80d 20 u | 16 6.37 aM 10d 5u 35 d 7.44 5d 35 u 35 d | 12.18 p.m 40u 50d 45 u 18 6.35 aM 30d 0 35d Thole 35d 25 u 45d | 8.36 35d 50 u 32d 12.57 p.m Dat 15d 30u 1.36 ... 20u 25d 40 u 19 7.12 a.m. 25d 10u 388d 21 1.24 p.m. 50u 22d 2.21 55 u | 23 d 52 u 3.30 45 u 22d 50 u ripe 7.57 5d 0 5d 23 6.13 am 0 du 0 Te@lbnc 5d 10 u 30d 24 fe ee 10d 20d ou 25 6.14 . 15d du | 30d Oo": 40d 10u 30d LON. 16d 13 u 380d | 4.50 p.m 20 u 20d 30 u ee OF omeee 25d 1bu 40d *26 6.10 a.m. 20u 25d 30u 7.32 20d 35 u 20d 7.44 25d 40 u 40d G00) 2: 0 5d 0 10.54 ... 21d 15u 40d 12.57 p.m 0 0 0 1226 0 8u 0 A 9.45 ... 0 10d 0 28 10.19 a.m. 0 20d 8u 10.35 23d 15 u 32 d LED) 5d 24d 0 WS: pee 16d 18 d 12d a ey Gee 20d 10 u 35 d 12.57 p.m. 23d 0 26d * The declination needle was on this occasion considerably to the west of its normal position, AND THEIR CONNECTION WITH MAGNETIC CHANGES. TABLE Il.— Continued. Column 38. Column 1. Column 2. Bate anne. Dover—London, u Tonbridge—London, u. Dover—Tonbridge, u. London—Dover, d. London-——Tonbridge, d. | Tonbridge—Dover, d. 1861. ° ° ° Oct. 28 2.50 P.M 10d 3 u 14d 10.10 20u 15d 15 u 10.30 5d 10d od 10.40 ou 25d 20u 11.10 0 10d 3u 11.20 15 u 18d 20 u 11.30 Sa”) ee Bu 11.40 36 d 42u 52d 11.50 25d 22u 385d Ae AO eae 18 d 0 20d 29 12.40 a.m. 22d 8u 36d 2.0 18d 10 u 13 d 2.20 23d 19 u 138d 2.30 18d ay 20d 2.40 10d 15 u 12d 9.20 4d O0tol10u od 5.30 0 Otoliu 0) 6.40 du 0 8u 6.50 5u 10 d 25u TATA ie 10u 7u 10 u 12:2 Pom: 8u 40d 28 u aae sae 12,25 0 10d 0 Nov. 15 12.34 18d Ms 1.56 . 24d 16 10.53 a.m sic 50d mee 21 11.46 10d 6u 20d 23 ey ee 10d 25 2.47 P.M. Be du no 3.23 16 u ee 14 u by 3.24 .. 23 u 26 6.34 aM 10d 12 6:35) .. aA 35 u a, 3.24 PM 5u 10 u 27 2.38 18d 26d oa Wy) 1183 Hes 17d Dec. 4 12:9 20u leu 1.24 34 u aoe 40 u 1.29 ae 16d aa iene 2°40 ... 20u 16u 6 6.39 an. 0 - du i 6.20 16 u 5d 25 u 9 toll 15 u fee 20 u ae 7:16 ne 0 Be 19 6.20 0 fs 0 dais 6.21 hae 10d Wits 20 0 25d ou 361 362 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, TABLE III.—OBSERVATIONS DURING GREATER AND MORE ABRUPT DISTURBANCES. Column 1. Column 2. Column 3. | Date. Time. < Dover—London, u. Tonbridge—London, u.| Dover—Tonbridge, u. | London—Dover, d. London—Tonbridge, d.| Tonbridge— Dover, d. | 1861. ° ° ° Oct. 45 7.A4 AM, 35 d 50d 45 d 8 | 3.12 P.M. 48 u 50 d | 55 u | 10 3.14 ... 30 u 50 d 50 u ) | % 10... 55 d 5u 10d | 11 6.25 a.m. 55 u | 50d 55 u ay aed SHO! G56 55 d 35 u 50 d Ree: Bee es 20 d 20u 20 u ee a fp eee 15 u 99 d 35 u : 3:207%.. 45d 25u 50 d | par 55 d 45 u 55d | Oe... | 30 d / 15 u 43d Uae 0 12d 8u LEA ees 13 d 25 u 38 d 12.29 P.M. 0 15d 0 ee re DAN se 22 u 55 u 15u | se =. 2.44 ... 55 u 50 u 50 u Bao 55 u 13d 55 u 4,23 ... 7u 35 u 0 a. 14 DiGi vce “38d 32 u 40d 25 6.42 a.m. 50 d | 20u 55d 28 Malolos 0 15 u 0 12.13 P.M. 20d 4u 27d ae ne Ue I Ae 30d l4u 40d Dec. 19 BIS 2.) (1 bs hd 55 d With the exception of the two cases noted, the declination and horizontal _ force needles were in no instance very far from their normal positions. : Let us now return to Table I., and endeavour by means of it to find the normal values of the earth-currents for each of the three lines, corresponding to the various hours of the day. And here it is necessary to remark that the strength of the current is not strictly proportional to the angle of deflection noted in the table, but rather to its tangent, which Mr WatkeEr has kindly informed me will, in the case of his galvanometer, approximately represent the value of the current. Taking therefore the tangents of the angles, and averaging the results for each hour, we obtain the following tables, in which the sign + denotes an up, and the sign — a down-current. ; > * The declination needle was on this occasion considerably to the east of its normal position. AND THEIR CONNECTION WITH MAGNETIC CHANGES. 363 TABLE 1V.—Houruty MEANS OF THE EARTH-CURRENTS OBSERVED ON THE LONDON AND DOVER LINE DURING MAGNETIC CALMS. a : Ob. | 15, | 2b. |) 3h.) 4h, | 55.] 6b.) 7b.) Sb. | Oh, | 104.) 114.) 124,} 13h.| 14, / 152, 16%,| 17», 182, 19»,| 20, 21h, 22h, | 230, ‘ nh SSI aaa ae A ig fe | ca eal i (ae a (ania ber of ob- 9 Hacone, 27 | 3 GB) alge 3 3 1 2. 3 2 5 4 4 6 5 24} 13) 8 2 3 4 a value of A 9 s | isa E +34) +50) + 29)4+ 19) + 15) —23 0 +14] — 27) — 29) — 23) — 28 = a ga aia ee +3/4-18)—20]) +4)/+17 ABLE V.—Hourty MEANS OF THE EARTH-CURRENTS OBSERVED ON THE LONDON AND TONBRIDGE LINE DURING MAGNETIC CALMS. 6h. | 72. | 8b. | 9b. | 108.) 112.) 125.) 13h.) 144. | 152.) 16h.) 175.) 184.) 195. 20%, 213,| 29h,| 238. | 4-10 —9| +3/—20)/—12) —6| —7| +3] +7] —3] +1] +2 aaa ead bp | ‘ABLE VI—Hourty Mmans oF THE HARTH-CURRENTS OBSERVED ON THE TONBRIDGE AND DOVER | LINE DURING MaGNETIC CALMS. ax, | an] an.| on, | ox, | 7m. 8x, | 98, ]20,|115.|120,]238, |14»,]150,|168.|17»,]188,|19%,| 20.) 216,| 29%, | 290, a SS en a ea a fe |i s3) 3 2 Fulecaece ames ca lh ieeel tech esl co | aa ok al _ a 4+-68|+39|+32/+26/418/-13] |—63 0 |—29|-34|—29|—36|—27|-29|-25 =8| —2| +2)—17| +7]+32 Mi, . + It will be seen that each of these tables exhibits a daily period, and that in each the values of the currents for the hours of the day are greater than those for the hours of the night. : Also we may regard the means for 0", 2", 3", 18", 19 ",as being best determined. Let us employ the following method as perhaps the best in our power for | exhibiting the characteristic difference between the three classes of earth-currents. Let us represent in a tabular form the departures from the means above given of | the individual observations of each of these classes. VOL. XXIII. PART II. oG 364 MR BALFOUK STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, TABLE VII—DEPARTURES FROM THE MEANS IN TABLE LV. OF THE INDIVIDUAL EARTH-CURRE} = (a OBSERVED ON THE LONDON AND DOVER LINE. + 28) Cuass I.— Observations during Magnetic Calms. Ob, | 1B Qn, gh, | 4h 5h, | 6h. |] 74.) 8b.) 9b.) 1OB. | 114.)126.)13h,)145,| 15h. 16%.) 17%. 18h, | 19», | 20h, | 214, | 290 Eqiaeal 22\— aah Bla 0 + 22/4 o1—11|— 9]— 41411/— 6 of — 58\4 1sle~ 9|— Solna 4+36|— 14/4 l|— 19|/4+ 12/4 5 — 23; Ol4+11/+ 5/+ 7/— 7| o|— 2] + 28/— 12/4 9/4 50) +50/— 20)— 11;— 9 — 15)4+ 5 = 9 + 54+ 1l/— 3)4+ 4/— 2) + 7/— 12)— 18 49 a 26 16 = 4)— 4) 2 sah ob a) 2) cea 299 + 55)/— 16 + 2 — 4/4 2 Oj-— 3 415 + 90\— 37 l+ 4| + 12 +10 — 29/4 21 | + Toa = — 59l+ 74 - Gime ~34 = 24 si + Tae ==) — 37 + 7+ 15 —52 bela = i + 8 | + 7\+ 14 / + 7+ 14 | = 2 | | — 20 | x 2 > + £7 + 7 ae ol — 20 + 7 + 43 ei = 210) Cuass Il.— Observations during smaller Disturbances. + 8|— 14/4 71/— 37|/+ 85| +59 — 14|/+18]+38/-—17/— 4|/—12 + 9) + 7i— 73\— 27|/— 16)e eos Sle, Vila + 12|4+35|—44 —14|+ 2 — 20/4 6/— 27/—. 50h —52)— 36)+114/— 10 +27|/-18 *+4+ 438)/— 21)— 86/4 20)— +50)/— 10 = il +54/— 3 + TFW— 73\— 54 —70\+ 69 + 7 + 35/— 61/— 64 —20|/— 50 +) 71860 =—34/— 50 + 7\+ 6 —52|— 92 + 6 + 2+ 17 + 15 — 3 : me | Cuass III.—Observations during greater and more Abrupt Disturbances. —57|—108 + 92)4-128/4+18 t—lov 4-150|—122)—=. ssi=gs “34 ie 39|— 3 | | —. 3|— 54|— 80) —70 + 21 + 9 pee eae oa | | * ‘Nhe declination needle was on this occasion considerably to the west of its normal position. } The declination needle was on this occasion considerably to the east of its normal position. AND THEIR CONNECTION WITH MAGNETIC CHANGES. TABLE VIII.—DEPARTURES FROM THE MEANS IN TABLE V. OF THE INDIVIDUAL EARTH- CURRENTS OBSERVED ON THE LONDON AND TONBRIDGE LINE. Ciass I1—Observations during Magnetic Calms. Oh, | 1, | 2h.) 3h, | 4h, | 55, | 6,] 78, | 8h,/9n.] lO. | 11.) 12h, /13h,]14%,/155,]16».]17%.] 18h. | 19%,| 20%, |21h,/29n,) gn, m0|— 41) 49|— 37/14/4189, | —1 # 19|—91|— 20|=" dl" 3i4- 7 "si 4) 4 8i—asi— | ol golt a6) =o af 25|—19|—46/4. 16)+- 1/—13 Jey — 9+ 6+ 20 Oj— 3)/—11/—10)— 4) —33/— lj/— 2)—27)|+11 0 f173/+35)+ 3— 37|+14/— 4 415 ees ol eel 8 =O aol lee Obl eal erg! == 30 m54/+17/— 3,— 31 +2 + 7= 6-2 —99|— Ii 0 0 meil+ Si— 8+ 23 = Peta Sie Olek fe gil - 19 ePyGl— 16 +1 uG rela + 12 +24;— 11 + 3/417 - ig +45|+ 16 + 6/+35 + 48 +29)+ 37 — 6417 - 60 te By + 21/—10 . 16 20\—. 1 | eS e7 +12/—19 4+12!—19 | +-20|— 1 + 3 —24 + 3 = @ b —15 . —50 Seek fo8 1 Cuass Il.—Oéservations during smaller Disturbances. 19/4+44/+ 6/4 21)-18/-13 — 9/—21)+110| + 23/4 23/434 + 2| +12/—10/+ 68/+18|—23/4 44 5)—41|- 23/4 25 —18/—50/+ 60 +40 +12/—85/+ 16/440/4+42|— 27 “19\—41/-18/+ 58 —21/+ 20 *_444 8|— 38/-97)4+ 21— 15 89|—10!—20 3h epile |elleeGe —52|—102 48/23 —14/4+46|4 82 + 44 64/417 — 6/417 12|431 ic 40|417 —44)—19 15 +11 p12 aie = il CuAss II].—Obdservations during greater and more Abrupt Disturbances. —103/— 1/485 Wee —116|+35|—121)4+52|\4+84)— 4 —103|+92 4+26/4+ 34/4+29)+11 +159 = 42 + | a | * The declination needle was on this occasion considerably to the west of its normal position. t The declination needle was on this occasion considerably to the east of its normal position. TABLE IX.—DEPARTURES FROM THE MEANS IN TABLE VI. OF THE INDIVIDUAL EARTH-CURRE 366 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, OBSERVED ON THE TONBRIDGE AND DOVER LINkE. on, | 1%, | 2m.| 3h, | 4h, | 58.) 6b.) 72.) 8b.) 9b.) OB, }17./12h./13.) 14h.) 15% |16h.|17h.) 18>. | 19»,| 208, | 21h, i— 104+ 10+ 4|— 14-4 9|—28 —56 + 36+ 8— 6+ 6/ O-+ 9— 71+ 6 — 92-4 384 34\— 53/4 18 4 51/+ 14,—51|\— 264 11/410 +156 — 18\— 7+ 7+ sit 2) 0|+20/4 4| 4+ 55\— 68+ 95/4 53\— 69 + 51|\— 684+87\+ 6\— 18/413 — 18 — 2— 7\— 2\— 74 si— 2) 4 11/— 45|— 11 + 31 _— 64 45/+6s\+ 1 —i7| oO 2 5) of + 204 2— 49 + 2 pT ago) =a —5—7]— 14 56 + 16 —85|— 53 —7 + 5+ 2 Be + 8+ 41 —7 + 8— 7 ml + 81 + s— 12 + 43 + 93 ;+ 8+ 2 B32 — 55 | — lol-+ 29 S=hgg — 58 — 2— 7 + 10 | + 26+ 20 Shige 4. Sis = a] 1 — lj— 25 — 10\— 25 — 24|— 16 — 2414. 49 + 8l-+ 29 | + 8 | “sg — 10 | — 10 + 26 + 55 | 8 | — 50 / | | CuAss II.—Observations during smaller Disturbances. + 22\— 12\487|— 51\+4-101/471 0|4-20|-42'—44|-13|— 9 16) si— 34172) = 167 4 + 10+ 31/+52\— 1 +27|-+65|—94 +13/+ 6 — 50\+ 86\— 60\— 45|\— — 86j— 3 +96— 7 +34|—36 4 66— 684+ 74 17\— | + 32+ 19) |— 75 +65\— 2 + si— 6\— 38 ++ —138\— 39) + 8 + 55\— 98\— 86 SE ee + sr 26 — 68|— 69 + 17+ 16 —104|-+ 44 + 49 — 45|— 88 + 20 + 72 | + 11 + 38 Cuass III.—Observations during greater and more Abrupt Disturbances. —146|—123 +117/-+-125|—71 t—18 +151|+ 2|—102\—102 — a3 + 93— 18 | | —141)4+ 34/—102|—1 —119 + 1 + 68 | | | BS | Cuass 1.—Observations during Magnetic Calins. * The declination needle was on this occasion considerably to the west of its normal position. + The declination needle was on this occasion considerably to the east of its normal position. , AND THEIR CONNECTION WITH MAGNETIC CHANGES. 367 A cursory glance at Tables VII., VIII, IX. is sufficient to show us that the values of the departures for Class 2 are greater than those for Class 1 ; and that in like manner those for Class 3 are greater than those for Class 2. But since it may be objected that the means in Tables IV., V., VI., are not in all cases thoroughly determined, I may likewise remark, that the range of the departures follows the same rule as their absolute values. Indeed, the great characteristic feature of the disturbing force is the large range which it causes between the different values of earth-currents observed on the same line, and during the same hour of the day, while at the same time the departures are perhaps as often to the one side as to the other of the normal values, as far as this may be gleaned from a somewhat limited number of observations. That this peculiar action of disturbances on earth-currents does not depend upon the absolute amount of the disturbing force, magnetically measured, will, I think, be rendered probable from the following considerations :— lst, In the two cases in which the declination needle was considerably de- flected from its normal position, there is no evidence from the corresponding earth-currents to show that these depend upon the absolute amount of the mag- netic deflection. 2d, For all the other disturbed observations of earth-currents, neither magnet was far from its normal position. While, however, there is no evidence in favour of the theory which ascribes magnetic disturbances to the direct action of earth-currents, there is much to favour the induction hypothesis in the great range towards either side of their normals apparent in the values of those earth-currents which correspond in point of time with magnetic disturbances. For it is evident that such a range from side to side would be produced if earth-currents were induced currents, due to those small but rapid changes in the magnetism of the earth, which are repre- sented by the peaks and hollows of the disturbance curves. Another remarkable feature of Tables VIL, VIII, IX., is the tendency of the undisturbed observations in juxta-position with one another, to exhibit departures affected with the same sign; and if we reflect that the order given ‘in these tables is that of time, we shall, I think, be disposed to conclude with Mr Watker, that meteorological conditions in all probability influence the values of the currents observed. If this be the case, there would thus appear to be three independent pheno- mena which affect these values :— lst, The daily magnetic change. 2d, Magnetic disturbances. 3d, Meteorological conditions, probably those which alter the conducting power of the superficial strata of the earth’s surface. If we reflect on this, and bear in mind that we have as yet obtained only a VOL. XXIII. PART II. oH 368 MR BALFOUR STEWART ON EARTH-CURRENTS DURING MAGNETIC CALMS, limited number of observations of earth-currents, and that only at one place, it is surely too soon to endeavour to trace quantitatively the connection between such currents and magnetic phenomena. I have therefore confined myself to a kind of qualitative analysis, which perhaps may help roughly to determine the nature of this connection. I shall be excused if I here call attention to some remarks on the subject of this paper made by the Rev. Dr Lioyp of Dublin, with the view of showing that the facts noticed by this eminent physicist may be explained on the induction hypothesis. These remarks occur in a paper “ On Earth-Currents and their — Connection with the Diurnal Changes of the Horizontal Magnetic Needle,” which is published in the Transactions of the Royal Irish Academy.* The author says,— ‘* When we examine the curves, in which Mr Bartow has represented the course of the galvanometric deflections caused by the earth-currents, we observe that the regularity of that course is continually interrupted by rapid recipro- cating movements, in which the needle oscillates from one side to the other of the zero alternately. These movements are similar to those of the magne- _ tometers with which we are familiar; but they are much more rapid, and bear a larger proportion to the regular changes. . . . . . . The frequency and magnitude of the deflections may both be taken into account, by adding together the alternate changes, without regard to sign, and dividing the sum by the regular daily changes. I have selected for this calculation the obser- — vations made during the six hours, commencing at 3 a.m., on May 29, 1848, — that being a period of comparative disturbance. The sum of the changes of the — galvanometer needle during that period, on the Derby and Rugby line, was equi- — valent to 571 divisions of the instrument,—the mean daily range for the entire week being 11:4 divisions, and the ratio =50. The corresponding ratio for the galvanometer of the Derby and Birmingham line is somewhat smaller. The sum of the changes of the Greenwich declinometer during the same period was only 57 minutes, the mean daily range being 12-4 minutes. In like manner, the sum of the changes of the horizontal force (in parts of the whole) was ‘0158, the mean daily range being ‘0034. The satio is accordingly the same for the two magnetic elements, and its amount is 4°6, or less than one-tenth of the corresponding ratio in the case of the galvanometric changes. We learn, therefore, that the rapid changes of the earth-currents are much greater in proportion to the regular daily changes, than the corresponding movements of the magnetometers.” The fact noticed by Dr Luoyp in these remarks is quite in accordance with the induction hypothesis, and is indeed only another way of expressing the truth already stated, that the action of disturbances on earth currents is to increase the *, Nol. xxiv ps alild, on = AND THEIR CONNECTION WITH MAGNETIC CHANGES. 369 range of the latter, and that this does not depend on the absolute amount of the disturbing force, magnetically measured. A single glance at the Kew disturbance curves will show any one adopting the induction hypothesis why the range of the earth-currents observed during disturbances is so very great. The chief characteristic of a disturbing force will then be seen to consist rather in abruptness than in absolute amount of change ; and it may safely be affirmed that the abruptness of a disturbance exceeds that of the ordinary daily variation to a very much greater extent than the absolute amount of deviation from the normal caused by a disturbance exceeds the ordi- nary daily range. But, on the induction hypothesis, the values of the earth-currents observed during disturbances will depend upon the abruptness of the latter—change in one direction producing positive, and that in the opposite direction negative currents; hence the range of such currents will be very great. Dr Luoyp again remarks,—“ The calculated curve is for the most part above the observed, especially in the Derby and Birmingham line. . . sa 8 may probably be accounted for by the fact, that the zero from which dine meenetis deflections are measured is not the true one, corresponding to the absence of deflecting force. As we have no means of determining the latter, we are accus- _ tomed to take the mean position for the entire day, or the mean of the readings taken at equal intervals, as the point from which the deflections are measured. But there is reason to believe that this is not the true position of rest, corres- ponding to the absence of all disturbing force. The comparative quiescence of the magnets during the early hours of the morning seems to indicate that they are then near their true positions of equilibrium ; and this indication is confirmed by the galvanometric curves, the zero line, which corresponds to the absence of current, dividing the area of the diurnal curve unequally, and being nearer to the night observations than to those of the day.” The following is the explanation of this fact afforded by the induction hypo- thesis :——“ During the early hours of the morning, when the magnets are com- paratively quiescent, and there is hardly any magnetic change, there will con- sequently be hardly any induced current, and hence the observations during these hours will approach very near to the zero of current. The results of this investigation may be briefly stated as follows :-— lst, The earth-currents observed during periods of magnetic calm follow a well-marked daily law, one feature of which is the small value of those currents | eollected during the early morning hours ; and this admits of being readily ex- | plained on the induction hypothesis. 2d, These observations are probably influenced by such meteorological con- ditions as affect the electrical conductibility of the upper strata of the earth’s crust. 370 MR BALFOUR STEWART ON EARTH- CURRENTS, ETC. 3d, The values of the earth-currents collected during periods of magnetic dis- turbance are chiefly remarkable for their great range, with frequent change of sien. This also admits of a simple explanation on the induction hypothesis. 4th, This hypothesis would therefore appear to be sufficient to account for all the earth-currents hitherto observed. (8720) XXVIII.—On the great Refracting Telescope at Elchies, in Morayshire, and its Powers in Sidereal Observation. By Professor C. Piazzi SMYTH. (Read December 1862 and March 1863.) PART A.—InstRUMENTAL DErarts, . : : : . Pages 371-380 PART B.—OBsERVATIONAL PARTICULARS, - ; : i 380-413 PART C.—GexyeErat Depuctions, A : : ; ; 413-418 Part A.—1. Introduction to Instrumental Details. The following pages contain an account of a few double-star measures which, by the kind permission of J. W. Grant, Esq., of Elchies, in Morayshire, I was enabled to make there in September 1862, with his large and equatorially mounted refracting telescope; and as that instrument is altogether the best and most powerful of its kind which has hitherto been erected in Scotland, such a trial of its capabilities, and the first which has been published, will undoubtedly have a peculiar interest for the Royal Society of Edinburgh. The object-glass of the telescope is 1] inches in diameter, or rather its clear aperture, for the glass discs themselves may be a little more; while the next largest in Scotland, that recently acquired by the Glasgow Observatory, under its present able director, Professor Grant, is not more than 9 inches; and the chief object-glass of the Royal Observatory of Edinburgh, or that of the Meridian Transit Instrument, only 64 inches aperture. The light, therefore, of the Elchies telescope is, comparatively,* transcendent; and to enable this feature to be em- ployed with the best effect upon his favourite stellar pursuits of earlier years in India, where extreme accuracy of measurement was always one of his chief desiderata, Mr Grant spared no expense in securing for the Elchies instru- ment an unusually efficient and well made equatorial mounting, fully provided with clockwork motion and micrometrical apparatus. The order for the construction of this instrument would appear to have been given about the year 1849, a period when Mr Grant, though still in India, was just about to bring to a close his long service of forty-four years of continued Official residence there: and it seems to have been commenced immediately ; .* It would not be right to ignore that both England and Ireland have object-glasses of 12 inches _ in diameter ; that the Russian Observatory of Pulkova has possessed for a quarter of a century, and used with great profit to exact astronomy, an object-glass of 15 inches in diameter; and that, in addition to Paris, the astronomers of the United States have now in employment one of the same size, and also one even of 18 inches in diameter, the normal size for a new generation, with similar advantageous results. ~ VOL. XXIII. PART II. ol 372 PROFESSOR C. PIAZZI-SMYTH ON THE for, in 1851, the equatorial mounting, in its chief parts, was exhibited by Mr ANDREW Ross, the optician employed, as his so-called “trophy” in the eastern half of the Nave of the Great Exhibition building of that year, with the effect of gaining for him one of the highest medals awarded. But after that event, lamentable delays took place in finishing the instrument; and before they were all concluded, Mr Grant’s health, too long tried by an Indian climate, unhappily broke down altogether. Hence it eventually occurred, that this fine instrument,— with the assistance of which, as the character of the work he had already exe- cuted in India with a smaller telescope sufficiently demonstrates, its owner would soon have risen to the first rank of acknowledged double-star observers in this country,—remained nearly unused until my going to Elchies in September 1862. I had only intended on that occasion to pay a passing visit, as one of respect to the founder of the largest astronomical equatorial in Scotland; but Mr Granvt’s hospitable notions, and his ideas of the importance of anything at all promising to be useful in practical astronomy, prevented my quitting his mansion until three weeks of observation had been secured, or something more than a mere amateur idea of what the telescope was capable of doing; and as he gave up the Observatory to me for the time entirely, and as I worked these alone, I can answer, and indeed am answerable, for whatever was done in it during that period, especially for any errors or shortcomings of my own. A.—2. Present Condition. . The patrimonial estate of Elchies lies on the banks of the Spey, about 8 miles below the junction of that river and the Avon, in Lat. N. 57° 28’, and Long. — W.3° 15’ nearly. The house, which is on a considerably elevated plateau, stands, together with the observatory a few yards from its south-eastern corner, on a broad lawn surrounded by well-grown trees. There is an ornamental portico to the observatory, decorated, not at all inappropriately, with Egyptian emblems, carved in native stone, and also a small transit room; but the chief bulk of the whole structure consists of the large circular equatorial room, about 25 feet in diameter, and furnished with a metal-covered conical dome. This dome has attached to it wheels of one foot in diameter; and, for motion, is revolved on them, while they roll on a fixed circular rail attached to the wall; impulse being communicated by means of toothed gearing and a hand-crank, which acts sufficiently easily. The shutters of the dome, four in number and arranged in two pairs, an upper and a lower one, open to the sky right and left. This they do by sliding on and off the opening of the dome in a peculiar, and as far as I know, a novel manner, with a sort of parallel motion movement in their own plane; each shutter being carried by two pivots, formed in the ends of two strong iron arms, which again work on their own fixed centres on the dome, and GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 373 have counterpoise weights beyond. These shutters were always most satisfactory and true in their movement, opening and closing with facility, and either offering a very large and broad view of the heavens, or keeping out both wind and wet with perfection. The equatorial mounting is of that character usually known as the German- variety in form, though in this instance it is constructed in the stronger manner of English engineering work; and has been so abundantly described already in print—Ilst, in the Jury reports of the Exhibition of 1851; and, 2d, in the Royal Astronomical Society’s Monthly Notices for November 1862—that little more need be said of that part of the subject here. Though indeed it is proper to record, considering the great size and weight of the instrument, that I found the hand- ling and working of it by myself alone, far more easy than I had expected; ex- periencing too, throughout the whole of the observations, a remarkable freedom from tremors either of tube or mounting; a consequence, without doubt, of the superior weight, and very massive construction of all those larger parts, which the optician, Mr Ross, had wisely confided to the hands of the well-known manu- facturing firm of Ransomes and May, at Ipswich, to execute for him. A.—8. Preparations for Observing. These preparations consisted in little more than cleaning the instrument from old and hardened oil, cleaning both outer and inner sides of object-glass, but with- out separating the lenses; removing paint from, and brightly polishing, the outer surface of the metal dew-cap; reddening the lamp illumination of the field of view, determining the magnifying power of the eyepiece employed throughout (and found to be 397),* testing the equatorial adjustments and micrometer values, chiefly by daylight observations on known stars, and then in preparing the list of objects to be examined. These were, for the most part, selected from the | double and compound stars which I had begun to observe on the Peak of Tene- | riffe in 1856, but had had no opportunity of reobserving since then. It was part of the preparation also to endeavour to form some idea of the quality of the object-glass about to be employed ; an object-glass which, though furnished. by Mr Ross, is said to have been actually constructed in the optical factories of Munich. There are many small bubbles in the material, but no percep- | tible strize ; and the discs which are given to the stars when in focus are extremely | small,—so small that the two stars B and C of y Andromede, stars of the fifth and sixth magnitudes respectively, and 0:6 of a second apart, were on one occa- * This high power could be kept constantly on, without inconvenience when first picking up ‘any small star, owing to the luxurious furnishing of finders to the large telescope, for it had no less _|than three such appendages ; whereof the first had a 4-5-inch object-glass, and a magnifying power of 56 times ; the second, a 2°2-inch object-glass, and magnifying power of 28 times; and the third. _\a1-7-inch object-glass, and magnifying power of 17 times. 374 PROFESSOR C. PIAZZI-SMYTH ON THE sion seen completely separated, well-formed, and with dark sky between them ; a decided advance on what I have ever witnessed with 7 and 9-inch object-glasses elsewhere by celebrated makers. The larger luminous discs also, which the Elchies object-glass gives to stars, on being thrown much out of focus,—and a Lyre was the one principally experi- mented on,—were pretty regular in their circular formation and strength of illu- mination, though they had a disagreeable feature of colour; for when the eye- piece was pulled outwards from the focus, the disc was greenish, with a violet border or fringe; but when pushed inwards therefrom, there appeared a small central disc of violet, with an annular surrounding space of green ; and when set exactly to the focus, the central part of the star was white. or slightly yellowish, astonishingly brilliant, and surrounded with rays that showed an intense violet colour towards their outer ends. These effects, as I presume, are chiefly those of the ‘“ residual spectrum” of the object-glass, a defect that must exist to some extent in every so-called achro- matic, but varying in character in each case with the judgment of the optician and the nature of the glass at his disposal. In the Elchies object-glass, as the outstanding defect seemed chiefly centered in the violet ray, which contains but a very small portion of light, its consequences may not be of moment in most of the ordinary optical observations, though it may become of importance in any attempt to use the telescope photographically, and did seem to prejudice the eye- estimations of the colours of some few stars. For instance, when a Lyre entered — the field, the eye was so excited by the splendour of the great star, a real first magnitude, and by the glory of its violet halo, that the small companion star, which is only of the eleventh magnitude, and has appeared to me in other tele- scopes of a blue colour, assumed in this one a reddish look, apparently from the complementary effect of the dominant violet of the larger. This case, however, is an extreme one, and when the stars under observation were below the third magnitude, little, if any, of the violet halo was ordinarily noticed. A.—4. Identification of Objects Observed. For the large stars, so few in number, their mere names, as every one knows, are quite enough to identify them; but for the constantly increasing hosts of the small stars that are dealt with by modern astronomers, no system of names has ever proved sufficient. In such case, reference has first been tried to their numbers, as they stand in some numerically arranged catalogue; and if every observer was to refer, or could refer, to one and the same catalogue, that might form a practicable method. But this is not done, and for many various reasons; recourse being had instead to the numbers in a variety of catalogues, one man making one catalogue his standard of reference, and another, another. GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 37d Hence considerable confusion has crept in, where a mere number-reference is employed, and great loss of time is experienced in tracing the measures of any one star, through the catalogues of different observers arranged and indexed merely according to their own separate independent and peculiar numbers, which numbers too, in no case indicate the precise point of the sky to which a telescope should be directed in order to find the star. Some natural method therefore should evidently be made to over-ride all these artificial systems ; and none seems better than a statement of the Right Ascension and Declination at a given epoch: I have therefore been much more particular in designating each of the stars in the Elchies list by that method, than by reference to any name or catalogue number. One of these is, indeed, usually given as an approximate step to begin with, but is always followed by the place for 1862, as brought up from the “Cycle,” the chief book of reference employed. Identification, however, thus by place and epoch, has its limits when stars are very close together; especially as the pointing of an equatorial may often be in error, from an accumulation of causes, to the extent of 1, 2, or 3 minutes of space. In such case, recourse must evidently be had to such further natural features as may be presented by the objects in the field of view; and which features do indeed form the chief portion of an equatorial’s work to ascertain and record, viz.,— Magnitude, or brightness. Colour. Relative position angle, when more than one star is concerned ; and Distance, under the same circumstances, This consideration is evidently not new, though it has not been by any means so generally employed as it might have been with advantage to science; for with stars, at first thought nearly similar, most manifold physical peculiarities have been found on closer study. I have endeavoured, therefore, to take more account than has usually been the case, of all the prominent characteristics of every star “Observed; and have not only arranged all my own results in that manner, but those of other observers referred to for comparison, as well; setting down each person’s work in order of date, to the end that any large cosmical progressive change in any of the elements may be instantly manifested. When the cosmical change, however, is small, or the previous authorities Scanty, and the Elchies observation simply shows a difference from what had been expected, then comes the all-important question, as to within what limits can we depend on an Elchies observation; for on the answer given thereto will it rest, whether the difference noted may most probably be put down to mere error of observation ; or, quite certainly assumed as showing a cosmical change in the objects observed. A formal inquiry into these conditions will be all the VOL. XXIII. PART II. 5K 376 PROFESSOR C. PIAZZI SMYTH ON THE more proper in the present case, and respectful from myself to older observers, seeing that double-star measuring is one of the most refined and difficult branches — of practical astronomy, where few persons succeed without much longer expe- rience of it than has fallen to my share; and in which, from the nicety of the micrometrical apparatus employed, it is always possible to read off an observa- tion, and record it on paper to very many more decimal places than it can really be trusted to. A.—d. Probable Error of Observation. Now these errors in my work at Elchies I believed were always large, not only for the reasons given above, but also because the number of nights that any object was observed was seldom more than two or three, and sometimes only one; and because, too, the definition of the atmosphere was almost invariably, on every occasion that I looked through the telescope, so extraordinarily bad, — that every star, instead of appearing like a proper typical stellar point, was blurred into a more or less, and often exceedingly large, and therefore corre- spondingly faint, nebulous patch or wisp of light.—(See Royal Astronomical Society’s Monthly Notices for November 1862, p. 3, and p. 13.) Whereas, therefore, most observers assign to their best measures a weight of 10, and to their worst a weight of 1 only; I, while keeping to their upper limit for an ideal best, have often in practice found it expedient to go lower still than — their lowest, and to divide their 1 into tenths. These numbers will accordingly be found set down against every Elchies observed quantity ; and it is expected that any astronomer who hereafter may use the quantities for purposes of his own, will duly refer to the numerical weight — attributed by their observer. Yet the numbers, after all, indicate only an opinion or marked impression, which may be biased either way; and the number — of observations of each object is too small to allow of estimating the degree of probable error on any rigid mathematical basis, with a logical prospect of prac- tical success ; something else therefore, and more suitable to the case, is absolutely required ; and with the view of attempting to furnish such a desideratum, 1 have compared my Elchies observations, in each of the four features above enumerated, with the mean determinations brought up from the “Cycle,” and other standard authorities; 7.¢., whenever the stars concerned appeared to be i y relatively fixed and constant, or very nearly so, in order to avoid being misled by — any large change, sop on time. a | affairs of siarometeie measurement with all available accuracy, ee: had moni care bestowed upon them. GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. CoRRECTION—TABLE [. 377 BMS fh 15) 6 MAGNITUDE. CoLour. Star Group. Com- ponent. | Standard| Elchies Standard Elchies authority.| observed. authority. observed. neat A 6 6 pom | B 8 8 Peace PPO Vu 65 Piscium A 6 6:3 Pale yellow (?) | Bluish white B 7 7:0 Pale yellow Faint yellowish white By Fiseiam A 55 5:0 Silvery white Yellowish white ’ B 5°5 5:5 Silvery white Bluish white ae (les 4:5 4:8 Bright white Greyish white Y 0 i] B 5:0 4:9 | Pale grey Slightly reddish white a elis A 55 5:3 Yellowish white} Yellowish white rk B 8:0 8:8 Blue Light blue : A 3°5 (?)| 3 Orange Coppery orange Sen + | B 5° (?)) 5 Emerald Greenish ae by 4:5 5 Topaz yellow Yellow rep hraehi, | Bro | el evaranle ae fe Cypni Ja 30 3°0 Topaz yellow Yellow Yen B 7°0 7:0 Sapphire blue | Bluish green Delohini A t 4:5 Yellow Pale yellow ii maid B "i 7-0 | Light emerald | Slightly greenish 1 Peoasi A 4 4:5 Pale orange Yellowish Se B 9 9-0 Purplish Grey CoRRECTION—TABLE II. (See Note to p. 415.) POSITION. DISTANCE. g G Approx. | Approx. Oe ara Position. |Distance. Corrections | No. of Supposed Corrections | No. of Spaced Bil] Sights Ef se His | Nig [PEE 36 Piscium, AGRA) Mole sO Mea Mio 2 | +003 | 2 1 VY’ Piscium, 160 30 0 0 2 2 —0:28 2 1 ¢ Piscium, . 63 23 +0 9 2) 3} — 0-20 2, 1 y Arietis, 0 OPO oon Boe ti ha | n020) | 98 2 y Andromede, . 62 11 +0 3 2 2 + 0°69 1 0°3 32 Eridani, 347 7 —0 10 1 1 + 0:08 1 05 a Herculis, . 119 5 —0 10 33 2 + 0:07 2; 0:8 e Herculis, . 310 4 0 0 2 1 — 0-05 yy 0-8 | 95 Herculis, 261 6 —0 20 2 1 —019 2 06 6 Cygni, 55 35 +0 3 2 2 —010 2 1 @ Sagittee, 313 9 —0 40 3 2 —0:16 3 1 y Delphini, . 273 12 +0 30 2 1 +025 2 0°5 Mean, according to signs, 14 0 48 + 0:08 Mean disregarding ct 14 0 16 | 0-19 | 378 PROFESSOR C. PIAZZI SMYTH ON THE A simple inspection of the first of the two previous tables may be considered to show, that in magnitude or brightness, an Elchies observation is not likely to be in error more than 1 magnitude on the “Cycle,” which follows very nearly the Herschelian scale; and in colour, though the estimation was rude, and based entirely on my own independent ideas of colours, yet the Elchies difference from the same standard authority is always comprised within some small variety of one and the same tint, indicating, therefore, the non-existence of chromatic error or — equation, personal, instrumental, or geographical, to any large or sensible amount. t Similarly the second table may be held as exhibiting, that there are hardly any errors of a constant order worth noticing, on either position angles or dis- tances,* as observed at Elchies, while the occasional errors, + and —, are con- fined within a degree for “ positions,” and a second for “ distances,” over cases varying in absolute distance from 4” to 35”. These limits of occasional possible error, though they include some cosmical uncertainties in the progress of the stars themselves, may appear rather large when compared with the many decimal places adopted by some few single observers in recording their observations; but will appear more moderate when we come presently to compare the results of many such first-rate observers inter se; and will even in the end be found very small, compared to the important : natural changes which have undoubtedly been undergone by some of the stars since the last previous observations that have come to my knowledge. A—6. Stars observed. The following table contains a condensed list of the stars or star-groups observed at Elchies, and arranged in order of Right Ascension :— Approx. R. As- | Approximate De- Approx. R. As-| Approximate De- Name. cension for |clination for 1862, Name. cension for |clination for 1862, 1862, Jan. 1. Jan. 1. 1862, Jan, 1. Jan. 1. h. m § = ae ae hk. mm rep we “ 35 Piscium, . On 7 52 este. Bikes mn Serpentis, . | 18 14 11 | — 2 56 36 65 Piscium, .| 0 42 28) +26 57 31 a Lyre, . .| 18 32 14 | +36 39598 ’ Piscium, 0 58 17 | +20 44 1 28 Aquile,. .| 19 13 14| +12 7 22 @ Piscium, 1 6 87 | + 6 50 44 6 Aquile,. .| 19 18 31 | + 2 50 26 y Arietis, . 1 45 58 | +18 37 61] 128 Anseris, .| 19 20 26 | +19 37°22 2. SATIOUMS, «soos 1 50 15 | +22 55 20 P Cygni, . .| 19 25 9} +27 40 20 222 Arietis, . 1 51 56 | +20 23 14 @ Sagitte,. . | 19 42 52 | +18 47 57 a Piscium, 1 54 54 | + 2 5 46 a Aquile,. .| 19 44 2) + 8 sO y Andromede, 1 55 25 | +41 40 38 y Delphini, . | 20 40 17 | +15 37 54 32 Eridani, : 3.47 24 | — 3 21 52 | 452 Cygni, . .| 20 57 4] +38 58 O @ Uerculis, 27) 17) S20 |) ie on, on 1 Pegasi, . .| 21 15 43 | +19 12 56 e Herculis, .| 17 18 56 | +387 16 35 3 Pegasi, .'°. | 21 30 61 | + Gite 95 Herculis, .| 17 55 88 | +21 35 55 | 312 Pegasi, . .| 21 45 6/| +19 10 53 (0 Ophiuchi, ..).17 08 26h) - 32 32 = 2841, . .| 21 47 46 | +19 "2a * The reading of the equator on the position circle of the Elchies micrometer was obtained — every observing night, in the usual manner, by equatorial stars being made to “thread” alonga . : GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 379 A, 7.—Proper Motion Effects. Though the list of stars observed at Elchies was small, yet it contained not a few instances where previous observers were more or less uncertain, whether the group should be classed as a physical and real, or only as an optical and unreal or apparent, double star. Some of these cases have been affirmatively settled by the Elchies micrometrical observations exhibiting proofs of orbital movement, and others by the test of “ proper motion.” This latter, however, being applied in rather an extreme manner, I propose to introduce at this point a tabular view of the data, and trust that it will be found a convenient and important reference throughout the next section of the paper. The “ proper motions” employed, are those of the British Association Cata- logue, where they are given in their annual amounts, generally for the larger component only of each star group. If in any particular instance, the smaller members of the group form a physical system with the larger, evidently they will experience the same amount of proper motion,—whether real from their own movement, or apparent from our sun’s,—and their relative “ positions and dis- tances” will not be altered thereby. But very different results will follow, if the members of any star-group are not physically connected together, and only the larger component be endued with the British Association Catalogue recorded amount of Proper Motion; and if the accumulated effects of such motion can be traced through a considerable period of time. Now, the greater part of the “ Cycle” references being about thirty years earlier than the Elchies work, I have multiplied the British Association proper motions by that number, and then computed their effect in altering the relative positions and distances of the members of each star-group concerned, on the hypothesis of their being in apparent proximity to each other only. The result is usually an alteration so greatly exceeding the bounds of probable error in an Elchies observation, that, according as it, the alteration in position and distance, is or is not borne out and reproduced by, and in, these observations, we are enabled to state with great confidence (subject only to the truth of the said British Association Catalogue proper motions), whether the group belongs to the one or other leading variety of double stars. wire. The value of the micrometer screw in seconds of space was derived from transits of the pole- star, measured with a sidereal pocket chronometer, kindly lent by Dr Lee of Hartwell to the Edinburgh Royal Observatory for many years, and brought northwards on this occasion. VOL. XXIII. PART II. aL 380 PROFESSOR C. PIAZZI SMYTH ON THE Ghai TL Ne Relative State rudely Proper Motion. Aaa Gy oa nia ily Sri on Sie Gaur P Observed in 1832. |Computed for 1862. R. A. N. P. D. |Position.|Distance |Position. | Distance. 35 Piscium, . . .| +010 | +004 | 150] 11:5] 162] 9-2 65 Piscium, . . .| +0:08 | —0-03 | 299] 45]| 282| 6-2 te +015 | +0-02 ) Piscium, . . | oH ooslateietae } 160 30:0 | 162 | 30-0 imp +020 | +0-06 Co Piscum.. | +028 | 40-02 63 | 23°5 60 | 23:5 » Arietis, el OP ggg 0-00 | 46] 37:0] 48] 385 y Andromede, . .| +0:06 | 40:04 62 | 10-0 52 9:5 32 Eridani, . . .| +0-10 0-00 | 347| 65] 325| 7:8 w. Hereulis, . «|. |. -0-03. | —OOn 119 4:7 140 5:0 e Herculis, . . .| 40:06 | —0-02 | 310] 36] 292] 4:5 90) Hercaliss 5 s:,..:|\ 1-002 —0:06 262 6:0 248 7:0 n Serpentis,. . .| —0:56 | +0°65 71/1330 | 66 | 155-5 a Lyre, . . . .| +030 | —0-298 | 139] 43-2} 153 | 46-5 @ Aquile, +.) hohe OD e001 260 | 96:0 259 | 104°5 128 Anseris, . . .| —0:03 | +0-06 43 | 22-7 42 | 24-6 B Cygni,. . . .| +003 | —0-02 55 | 35-0| 55 | 34-0 % Sagitte, . . .| +010 | —0-07 | 318/ 86] 292| 9-8 a Aquile, . . .| +051 | —0:38 | 820/155-0 | 313 | 157-0 y Delphini, . . { ‘digits ion } 27s 11:8] 280 | 12:5 1 Pegasi, . . .| 40:18 | —0-09 | 311] 37-0| 303 | 39-6 a Part B.—Observational Particulars. The Stars, as observed and compared, arranged in order of Right Ascension. (1.) 35 PISCIUM, Approx. R.A. 08 7m 52s; Decl. +8° 3’ 14” for January 1, 1862. sete es Colour. Position. Distance. Date. Authority. . AB 148 54 12:50 178350 Hi}, we AB 151 6 11-28 182193 «. Rial AB 150 46 11:17 182191 H? and §. eeeeee piaee AB 150 6(w8) 11:60(w7) 183204 Cycle. te Be We We BP BP G22 Whither. inanctnn deena. WO) VW LLIGG ata scaaeaence eeee AB 149 52 11:58 1832-67 C:Sivie hel en yee SO aati: Weciae AB 149 21 11:66 1886:74 & GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 381 Part B.—Observational Particulars. 35 PISCIUM—continued. Com- Magni- ponents. tude. A 6 Raterwhtt@ a ssccs-sesscs Colour. Position. Distance. Date. Authority. Mee 8 Violet tint... 0c... 0. AB 149 30(w7) 11°90(w7) 1887-89 Oycle. A Welllowislit.. asics cece cies. < B wy, 9 edi ZALES Fe ara PR SI a BR es 18448 Sestini. A REE ia aes titeks .7.\2.-c.s0.. B Sriimualeverey:|....o653 :70i..4 AB 63 48(w9) 23:-4(w9) 1839-05 Cycle, 386 PROFESSOR C. PIAZZI SMYTH ON THE Z PISCIUM—continued. Boe ah out Colour. Position. Distance. Date. Authority. A Bin: MMONOW 7 abo dain’ « seaut et, : B ain coin VEMOW! ot ceassceede. | | Maerua oa 18448 — Sestini. A a ee, 28 Bite ee le WL aoece: AB 63 18 23:1 1846-89 Spec. Hart. A WOME ocx sPitet oon cue B Greyieh' |, cn S:cwpurseeres | SWmeRees ae 18497 — Spec. Hart. A Welowisle( 2) "cus donmase B Warm-prey(2).-.--.scc0. | Mealaee oe 1856-68 Alta Vista. Te pal — 5S ee ee ee eee | ee eS ee ary AB 62 54 22°8 1857:93 Spec. Hart. eA CU) 2 Yt ee whe as AB 64 2 me 1861-02 SA Ce ae eae RES om 23-744 1861:74.] | “ae A 5°5(1) Yellowish white (8) ..... B _7;5.(1) sGreenish grey-(S) «..*.0.. AB 63 20(w2) 23:42(w1) 1862:72 Elchies. In Magnitude, variable through rather more than one magnitude. In Colour, also sensibly variable. In Position and Distance, nearly stationary, much in accordance with the difference of the proper motions attributed to either star in the British Association Catalogue. These proper motions are absolutely very large, and their non- appearance on the relative places of the stars, indicates them to be, In Character, slow binaries. Since writing the above, I have become acquainted with the observations of Dr A. Auwers, taken with Brssex’s celebrated heliometer, and now inserted i years, and will command great weight. As such, it is singular to observe how | they strengthen the character of the Elchies observations, of position and dis- tance, making them appear nearly a mean between the best German and the best — Unfortunately for impartial scientific knowledge freed from the bias of national — | forms of instruments and modes of observing, the whole of the learned Doctor’s — case, it is instructive to observe that the variations of the German results inter se, though depending on large numbers of observations, are not less than what was — deduced as the broadest limits of possible error for the Elchies scanty observa- Fi GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 387 tions, compared with other and various authorities, Dr Auweks’ table standing thus * :-— Dect Position. 29:24 63 55 8 62 6 48 63 50 8 64 43 20 63 16 33 64 2 20) 0 el (5.) y ARIETIS, R.A. Com- Magni- ponents. tude. Colour. ee eee eres ee re nnece See ensene weet tense Full white............ Faint blue............ Se Yellowish white (2) . ot igual RUA? De We WP BP Pe ee ee ee ee Pl em Very white .......... 4:4. Wery white .......... 4°5 Bright white.......... 5 PAICNOTOY aais cinsicicn vine Yellowish white (2) . 4-8(3) Greyish white ....... 4-9(3) Shghtlyreddishwhite(3) AB 0 36 (w 3) 8:61 (w2) 1862°73 Elchies. @ PISCIUM. Distance. Date. Authority. 23-364 1830-90 Bessel. 23°740 1834:82 Bessel. 23-499 1842-08 Schliiter. 24°200 1853-82 Peters. 23:145 1855:58 Luther. eee 1861:02 A 23-744 1861-74 DER: 15 45™ 58s, and D.+ 18° 37’ 6”, January 1, 1862. Position. Distance. Date. Authority. AB 356 5 10-17 177968 H}, AB 356 54 8-97 1821-91 «. ', AB 359 59 8-63 183084 5, AB 35948(w9) 88(w9) 1837°93 Cycle, } Bien wy) mis 1644-008 | Sestini. AB 358 54 (w 8) 8:7 (w6) 1849:12 Spec. Hart. \ docmest wih |) | s60g.060 1850°7 Spec. Hart. AB 358 19 8:87 1855:95 4H. Luther. a 1856:68 Alta Vista. AB 359 15 (39) 1861-01 AB nee ee 8628 (22) aay Auwers. oe One of the oldest known of telescopic double stars; in Magnitude, nearly constant. * Astronomische Nachrichten, No. 1393, p. 10. VOL. XXIII. PART II. 388 PROFESSOR C. PIAZZI SMYTH ON THE In Colour, some slight variations, chiefly in the smaller component. In Position and Distance, nearly constant, but with a certain slow oscillation. apparently of a perturbative character, and with no differential proper motion; therefore In Character, a slow binary. (6.) 2 ARIETIS, R.A. 1 50™ 158; D.+22° 55’ 20’, January 1, 1862. Com- Magni- ponents. tude. Colour. Position. Distance. Date. Authority. A Sean aoe Ul (oe AB 5342 2-25 nay _ bee AC 165 36 36-2 i dois taka ce BMG 25 0 lk AD 136 182:5 \ yA ol hed ea ne Seema ( 2) BiG (2) iii. (OU de 1862:96 Lilburn Bac (2) Blue(2) casecccsdesns .. BC 167 32(w 0:5) 36:24(w 0-5) Tower. ey (2) Yellow(2) .......0..+. BD 1 23 (w 0-4) 181-12(w0-3) Some remarkable changes in magnitude, colour, position, and distance, have occurred in this group, according to the authorities. A great writer has indeed asserted, since the Elchies observation was published in the Notices of the Royal Astronomical Society, that the magnitudes and colours assigned to A and D in the Cycle, should be read vice versd for what they are put down. (See Monthly Notices R. A. S. for December 1862.) Tf this point can be proved, it will greatly alter some of the changes believed to have been experienced ; and instead of the Elchies observation, as well as that at Lilburn Tower being interpreted to show that “ A” was missing, and “B” only left outstanding, we may then consider that both A and B were seen on each occasion, but indistinguishable the one from | the other, by reason of disturbed aerial vision ; in which case too, in place of the other positions and distances being entered under the letters BC and EBD, they B ae Should rather be registered under ate C, an - D. But granting that alteration, and also the demanded inversion of the ae magnitudes and colours for A and D, there still remain as notanda in the group,— 1st, The decrease of distance in the last thirty years of A and C; 390 PROFESSOR C. PIAZZI SMYTH ON THE : 2d, The increase of position angle of A and D; : 3d, The increase of distance of A and D; and, ; 4th, Most strange of all, the colour of A, as assigned by Srruve; for he, as $ well as the Cycle, makes it yellow; and either his recorded colour must be repudiated by the repudiator of the Cycle, or the modern change in that star’s f colour must be allowed to be real. 3 The observations now given under the head of Lilburn Tower, are some : which I was kindly allowed to make when on a visit last December to my friend, 7 : Mr E. J. Cottincwoop. His observatory, planned and erected by himself, is a model of perfection in everything which it contains, and is furnished, among other instruments, with an equatorial, whose object-glass, a Munich 6-inch, had : 4 been purchased from the late CHARLEs May, C.E., and by him procured from Mr ; Dawes, under the statement of its having come out of long and very severe trials for defining power, with the most remarkable success. The mounting is by Sums, with some fittings by DoLuonp, in excellent style. Nothing, therefore, was wanting to enable good observations to be made, at least my best, excepting good atmospheric definition. Now both the nights that I observed the object at * oe Lilburn Tower, were stormy in the extreme, and the definition as bad as on the i two when I observed it at Elchies with Mr Grant’s larger telescope ; and I have © described over and over again how bad it was there, in the November Monthly — ‘ Notices, see pages 3 and 13, as well as indicated the same in the small weights 7 a attached to the measures (weights giving much below the smallest weights ever — assigned by most other observers to their worst measures). In such a state of — atmospheric definition, two small, and very close, blue stars, as A and B are ; now asserted to be, might easily have been confounded together; and I would © not have undertaken to decide on the question in that shape at that time i. e., either at Elchies or at Lilburn. But it was not then in that shape to me; for, with the Cycle in my hand, a crowned book, stating, and having stated un- questioned during eighteen years, that the group is “ an exquisite object,” and “an admirable test to try the light and definition of a telescope ;” and describing its three closer members, or A, B, and C, thus:—viz., a large yellow star, A, with one small blue one close to it, and another small blue one a moderate distance off; and then, looking into the telescope, and seeing no trace of a yellow star of any size, big or little, in that place, and only two faint blue burred images there, at just about the distance apart of the two small blue stars, B and C, of the Cycle, —I thought, and still think, myself justified in publishing, that no large yellow star now exists, where the Cycle stated that such a one existed in its day. So far, too, as the subsequent discussion at the Royal Astronomical Society has elicited, the Elchies observation was the first to announce that fact,—a most notable one surely in reference to a “ telescopic test object,” whether originating in a mistake in the Cycle, or a cosmical change in the starry heavens. i } . ; GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 391 As to the subsidiary question, of whether the faint blue burr seen in both telescopes, in the united place of A and B, might have been really composed of two small and close blue stars, it is no slur on the Elchies telescope’s defining power, that that point was not settled then. For, even granting for the moment with the most extreme objectors, that A and B now are, and always have been, these two diminutive and close, blue stars, the power of separating and seeing them as such depends, not only on the defining power of the object-glass, but also on the atmospheric definition at the time and place, as well as on the parti- cular observer’s eye. There is no need, however, of confining ourselves to gene- ralities, as there are already recorded in this very case, three sets of observations, all made by one and the same observer, viz., myself; 2. ¢., the Teneriffe, in 1856°68, with a 7-2 object-glass ; the Elchies, with an 11-inch; and the Lilburn Tower, with a6-inch. Of the transcendent defining power of the latter there can be no question, in a good atmosphere; yet, the atmosphere having been as bad at Lilburn Tower as at Elchies, only a single star was, as at Elchies, suspected to exist ; but in Teneriffe, 10,000 feet above the sea, where the atmospheric definition was exquisite, two stars were perceived at the first glimpse. The same eye therefore, and a medium size of telescope between the other two, joined to a quality which, though good, could hardly have been superior, but a decidedly better atmospheric definition, pro- duced instantly such superior results. What, therefore, might not be the advantage to astronomy of having a large telescope always mounted in an equally well de- fining atmosphere to that of the Teneriffian Alta Vista; for evidently five minutes there, on the showing of the objectors themselves, are, for this purpose, better than four whole nights in a worse atmosphere. (8.) a PISCIUM, R.A. 1" 54™ 548; Decl. + 2° 5’ 45”, January 1, 1862. Bons i aa) Colour. Position. Distance. Date. Authority. Aes: AB 337 23 5-12 177980 HB, ye ' AB 333 0 a 1802-08 Ht. Tron AB 335 33 5-43 1821-93 Hand 8. 48 fii AB 336 54 3-42 1821:96 6 eeeeee base AB 332 59(w24) 3-775 (w 24) 1830:93 Bessel. BIGGS Fee tactacsnnucs wee AB 335 43 3°64 L63tl6: -3. meade MRED bie Lo. AB 3381 58 (w 4) 3°760 (w 4) 1834°85 Bessel. VOL. XXIII. PART II. 50 Be ee ee yp we we WP i) oo 392 PROFESSOR C. PIAZZI SMYTH ON THE a PISCIUM—continued. Com- Magni- ponents. tude. Colour. Position. Distance. Date. Authority. Diy. Shaler preen cr heer. pn * a 6 IDIMCHL. ooo hee eee one AB 333 24 (w9) 3:8 (w 9) 1838:87 Cycle. mene AB 332 46 3-690 1843-04 Schliiter. Wintte +2 a 1) Coppery orange (4). 1) Greenish (4)......... tudes. VOL. XXIII. PART II. Position. AB 116 6 AB 118 28 AB 120 23 AB 118 34(w 30) AB 120 20(w 12) AB 119 6 AB 119 16(w 9) AB 118 40(w 40) AB 118 42(w 9) AB 123 32(w 12) AB 118 23 (w 26) AB 119 24(w 7) AB 117 22 (w 34) AB 116 15 (w 28) AB AB 119 30(w 2) Distance. 472 4:65 4:85 4-994 (w 30) 4-980 (w 12) 4:94 5-084 (w 9) 4-955 (w 40) 4-5 (w 9) 4-99 (w 12) 4-52 (w 15) 4:8 (w 5) 4-41 (w 17) ecoeee 4-71 (w 0°8) Date. 1822-2 1829-63 1830-62 1830-92 1833°53 1834-58 1835-77 1842:53 1842:57 1854-61 1856-08 1856-68 1857-63 1858-04 1861-06 1861°57 1862°72 395 Authority. 6. 2. Dawes. Bessel. Selander. R. Sheep- [shanks. Bessel. Schliiter. Cycle. Luther. Jacob. Alta Vista. Spec. Hart. Jacob. } A, Auwers. Elchies. In Magnitude, both stars are known variables through one or two magni- In Colour, they are brilliant, well understood, and constant; a small chromatic equation being allowed for Struvz’s estimate or ideas of blue and green. I have, 5P 396 PROFESSOR C. PIAZZI SMYTH ON THE indeed, heard of a colour-blind friend—of the orthodox order, which cannot per- ceive any difference between the brightest red and the most brilliant green—say of another who mistook between some shades of b/we and green, “ how extraordi- nary! what a stupid fellow* he must be; now, if he had mistaken ved and green there might have been some excuse for him.” Yet the sentiment of the world at large I conclude will be, notwithstanding, that certain varieties of blue and green are very easily mistaken for each other when viewed under varying contrasts — with other colours. q In Position and Distance, these stars are a caution; and in Character, who shall say what they are, though, too, they have been so abundantly observed. “ Fixity,” relative, from the earliest time, has been strongly claimed for them by some good judges; but in that case, what becomes of the reputed accuracy of the great double star-measurers; and what is the advantage of their occasionally publishing their position angles to the :}sth of a minute, and the distances to the rsot00 of a second,—when a discrepance of no less than five whole degrees in position, and half a second in distance, is shown, by thus bringing together various records of a Herculis, to be a very common error for a long and well weighted series of observations. What, also, at this rate, is likely to be the value of a double-star orbit, computed on a small number of observations extending over no more than a very moderate portion of its periodic time ? . Granting, however, for argument, the imputed relative fixity, these stars would become, under the B. A. C. proper motion test, “ slow binaries;” seeing that their “ position’’ should otherwise have increased twenty-one degrees in the last thirty years. But then, again, other authorities have challenged the truth of the B. A. C. proper motion in this case, which they considered extremely erroneous; and the late Captain Jacos, when at Madras, undertook a series of most carefully conducted equatorial observations, to ascertain whether the group was, in cha- racter, optical or physical. These observations have been fully printed by the Royal Astronomical Society, and resulted in showing with remarkable force, in as far as the agreement of the observations, inter se, could make it, that the group was not only optical, but that the annual parallax of one member upon the f fifth of the difference between his mean of measures and that of Dr LurHER taken — at nearly the same epoch; while Dr A. Auwers, on the mean of four observations | | on each night, has in the year 1861 a difference, reaching, in the short space of four parallactic effect. * It was not M. Srruve, nor indeed any astronomer whatever, who was thus referred to. a5 ile GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 397 Had these several able and learned astronomers observed in the pure, trans- parent, and definition-favouring air of the upper parts of the Peak of Teneriffe, or a similar air in any other part of the world,—I feel sure they would not have racked all men with anxieties, and covered the nature of this star with the confusion arising from such impossible numerical quantities. (12.) ¢ HERCULIS, R.A. 17" 18™ 56s, and D, + 37° 16’ 35’, January 1, 1862. Com- Magni- ponents. tude. Colour. Position. Distance. . Date. Authority. . , ees iit ‘ 0 re AB 300 21 2:97 Wife. 00) EE. A 06, ieee B ee te tet ns snes AB 306 0 3°97 1822-4 6. A 4. Greenish white...... B 5‘1 ‘Greener,.............. AB 307 18 3°60 1830°35 > A 4 Bluish white...... .. B Boo) Paleemerald:........ AB 308 54 (w 9) 3°7 (w 9) 1839°74 Cycle. A Be CW OW ool. on es ecweee : B penetrance outa. cee Wade, Bion, OUIE ue 2 ali! aera AB 274 9 11:82 1779:74 H-. AGRE Ne Meee tee peme 0 hee a eer AB 2738 0 13:50 1800 PR TAGE NE RAY Lateran UBL a) Stn a A ae han AB 278 26 11:83 1823°34 «6 Pie anil peel aS B wen AB 273 43 12°31 1823-68 HandS, | GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 409 y DELPHINI—(continued). Com- Mag- ponents, nitude. Colour. Position. Distance. Date. Authority, tt Sree sdipagth jy ln aes AB 273 20 12-02 1830°57 Dawes. A OGRE vc eben asic snes B Bluish Green......... AB 273 45 11-90 1830-89 &. ose RE leas AB 272 53(w28) 12:016 (w 28) 1830:89 Bessel. canes : aes AB 273 7(w24) 12°045 (w 24) 1834:'76 Bessel. » A + Meloy 2.5 Bike ae st &B 7 Light emerald ...... AB 273 18(w8) 11°8 (w 7) 1839-71 Cycle. = ggg) nes ee eee AB 272 48(w40) 11:943 (w40) 1842-63 Schliiter. - A OPAC ck nasties. » 3B CRU eekly Mie Rastns or alvcteletera 1844-45 Sestini. L Ss A Golden yellow ...... » 8B ioe mre. cps. way Sec kcad |) (4 My ten 1850°7 Spec. Hart. Se ee ee AB 272 55 (w4) 11°530 (w 4) 1853-83 Peters. er B AB 273 8(w20) 11:521 (w20) 1856:52 Luthers. A Cadmium yellow (1) : . B Greenismetmpe(l Re GA> sce ME Waein, 185668 Alta Vista. mA 8 3-4 B 4-9 aie AB 272 #5 (WSO) UA Le 1861-07 i 11-806 (w 22) 1861-38 \Auwers. A 4-5 (2) Pale yellow (2)...... , 5B 7 (2) Slightly greenish (2) AB 272 45(w1) 11:15 (w03) 1862°72 Elchies. - In Magmiude, not quite constant. In Colour, both A and B seem to undergo yellow pulsations. In Position and Distance, there is much still unsettled. Srruve expressly says, : no alteration in angle: and the Cycle, decides on “ fixity.” But Dr A. AUWERs daims a small decrease of distance; and I think that he is not only right there (though the Elchies observation is probably a very bad one), but that the same change has been taking place in Position. In the British Association Catalogue, proper motions to a considerable extent, and nearly in the same direction, are attri- buted to either star ; this looks like a binary connection, and if the difference of | those proper motions is not exactly borne out by the Positions and Distances observed, we can at least say, that the whole proper motion of one most assuredly 410 PROFESSOR C. PIAZZI SMYTH ON THE does not display its effect on the other, as though it were distant and in optical connection only. Hence, In Character, this pair is probably a slow binary, and with its orbit viewed at a small angle. (24.) 452 CYGNI, R, A. 20" 57™ 4s, and Decl. + 38° 58’ 0’, January 1, 1862. a ef vee Colour. Position. Distance. Date. Authority. A 7 Deep yellow ...... ice x, Ba Let Emerald hue ...... AB 297 0 (w 3) 17°0 (w 1) 1832°87 Cycle. A 6(2) Reddish orange (2) B 10(2) Greenish (2) ....... AB 300 33(w 2) 19°39 (w 1) © 13(2) Bluish (2) ......... AC 86 58(w1) 98:87 (w0-4) 1862-73 Elehies. D 15°5(2) Bluish (2) ......... AD 138 54(w1) 54°76 (w 02) Further observations should be accumulated before any conclusions are ven tured on, as to the character of this group. At present it merely offers example, by the two additional stars introduced, of the happiness of reobserv: ing an ancient stellar object with a larger telescope than before employed upon i (25.) 1 PEGASI, R.A. 21" 15™ 43s, and D. + 19° 12’ 56’, January 1, 1862. Com- Magni- ponents. tude. Colour. Position. Distance. Date. Authority. A aes Sadan Wiz inde Soar 4 Baad hees, BOMNe teosnet AB 308 19 37°10 1'780'69 oa. A ge ae B 9:5) > ROBART... ..2 AB 310 0 (Aé 24°70) 1823-87 «. A 4 Pale orange ......... B 9 Purplish 3.50 icc.. AB 310 48 (w 8) 36:4 (w5) 1833:95 Cycle. A 4-5 Strongly yellow...... B Sar A ees |. AB 311 15 36°20 1835°86 &. A a0!) Otange) ccc: eee B tow) UARERE Aaa. Sw. 25%, Ct Cee eet see 1844:5 — Sestini. A Deep yellow ......... B Talwe* biter ic. secese eee ee eee 1851:4 ~— Spee. A Rich yellow (2) ... B Purplish Dhue (@) 5.0"; wkeceees 1), sa adenten 1856-68 Alta Vis A 4:5 (2) Yellowish (3) ...... B 9°0 (2) Grey (3) cores aaaeee AB 311 16 (w 2) 37:09 (w0°5) C 14:5 (2) Blue (3) .........e AC 22 59 (w 1) 80°73(w0'3) 1862-72 Elchies. In Magnitude, nearly steady. In Colour, the same. GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 411 In Position and Distance, showing some binary character, which is confirmed by the B. A. C. proper motion test. This should, however, be confirmed equa- torially by future measures of the Elchies star C. (26.) 3 PEGASI, R.A. 215 30™ 51s, and D. + 6° 0’ 2", January 1, 1862. I ons. ania Colour. Position. Distance. Date. Authority. A ees ece ° é MU _ -«\e Epler AB 352 48 34°72 178276 H,. PE Oh cilainnsan ———-r — ...... AB 350 48 36:90 1800-00 P. Pe ee acne AB 350 30 39°21 1821°54 o. 0 - | eee AB 348 58 39°52 1823-79 MH, and §. A 6 White B Pee IVC icc gascpenees AB 349 26 39°15 1834-91 3%. A 6 White : no Palle: blae? o.y..6).4. AB 349 30 (w8) 39'3 (w 8) 1837°81 Cycle. A White B WS IIGA SAO Gn ie a oa ae OT ces Aire 1844:5 — Sestini. A Flushed white B CHRO © EES Pe OM Vee” mae 1850-5 = Spec. Hart. A Whitish (1) B Biemmmnipeney (Cl grasp erat eaiart) jini) eal) akan 1856:68 Alta Vista. 'A 6 (8) Greyish green (3) nb B 7°3 (3) Lilac tinge (8) ...... AB 350 19 (w 1) 41:69(w0°3) 1862:73 Elchies. In Magnitude, steady. In Colour, A nearly steady; but B, very variable. In Position, nearly constant, but in Distance, undergoing a sensible increase : more observations are however needed to confirm the conclusion. (27.) 812 PEGAST, R.A. 21" 45™ 65; Decl. + 19° 10’ 53”, Jan. 1, 1862. eons. ae Colour. Position. Distance. Date. Authority. A eee NV BCs tact ctu a, i meee 4-0 §©=s Blue.....5.......... AB 95 0(w1) 15°0 (w 1) 1838:66 Cycle. A 7 (2) Yellowish (1)..... mee to 62) Bluish (1)......... AB 92 28(w1) 20°49 (w 0°5) ey? (2) Bluish:(1)/.i00..: AC 323 34(w0-5) 21:94 (w 0:3) DY 15-5(2) Bluish (1).......5. AD 193 48 (w0°4) 81°66 (w 0:2)} 1862-74 Elchies. Suet? (1) Bluish (1)......... AE 355 52 (w 0:2) 128:40 (w 0-1) See. (1) Bluish’ (1)....00. AF308 52 (w 0:2) 107-00 (w 0:1) VOL. XXIII. PART TI. 5) an 412 PROFESSOR C. PIAZZI SMYTH ON THE The Elchies telescope was turned upon this object, because the description in the Cycle seemed so pointedly to define when the Cycle telescope stopped in making out small stars,—viz. decidedly below Sir Joun HeErscuHet’s 20-foot re- flector,—that it seemed an excellent opportunity for ascertaining whereabouts the Elchies telescope, worked by an eye very probably much inferior to both the others, would come. The Cycle describes the group as ‘‘a most delicate double star im a barren jield ; and that it “is No. 947 of H’s 20-foot sweeps, and classed triple, having a minute comes in the np, of the 17th magnitude. But this I ‘(Cycle)’ could not manage to get a sight of, notwithstanding the coaxings exerted.” The Elchies telescope, however, not only showed the above double-star, but also Sir Joun HerRscuE’s C, still existing in the relative place which he pointed — out; and in addition to that, several other and previously unrecorded stars, as the D, E, and F of our list; and the truth of their finding has been since testified to in an uncomplimentary, but, for the truth of a scientific fact, a most unexcep- tionable manner, by the Rev. W. R. Dawes, in the Astronomical Society’s — Monthly Notices for December 1862, page 79, paragraph 3. (28,) 2841 3, ReA. 21" 47™ 46s, and Decl. + 19° 2’ 53’, Jan. 1. 1862. Com- Magni- ponents. tude. A 65 Conspicuously yellow.. sale k e SiON SBlneoeectcncnceeeewe- AB1l11l 2 22°21 1829°46 3%. Colour. Position. Distance, Date. Authority. B RY GaN eliow (8) onccacd Ae oe a Bat SO ge), Siilac(a howe ee AB 110 58 (w 2) 22-46 (w1) 186273 Elchies. The previous star, No. 27, the penultimate of our list, gave some fair indi- cations of the abundant light-transmitting power of the Elchies telescope; and the present star, the ultimate member of the same list, happens curiously enough to close our little record of the trial of Mr Granv’s large telescope, with data having reference possibly to the power of accuracy or agreement with standard authorities in each of the four telescopic phenomena usually noted with every considerable double star. | The case would of course be infinitely more satisfactory, if there had been i several observations by earlier authorities to refer to, and prove thereby whether | this was a stationary or changing group; but I knew of none such at the time, and did not even know of this one until after I had left Elchies, and had communi- — cated my own measures to my friend, Professor Grant, of the Glasgow Observa- — tory,—and he discovered that they must apply to Struve’s star, No. 2841. 4 The whole case occurred in this manner. I had been so long one evening writ- _ ing down some of the particulars observed about the star 312 Pegasi, that when — I went back to the telescope the equatorial driving clock had run down, and the — star was gone. But on looking through the chief finder, lo! there was in its place GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 413 a different and a conspicuous double star near the boundary of the field; and on bringing this stranger into view with the great telescope, it proved quite a splendid object, which I measured, as recorded above; and was much surprised to find that there was no mention whatever of its existence in the “ Cycle,” which was my only book of reference at the time. I wrote, therefore, to Professor GRANT, when on my road home from Elchies, sending him these observations, and saying that the star was new to me, and foreign to the “ Cycle,” but so brilliant and richly coloured, that it could hardly have escaped all former observers. But then it was, that the Scottish historian of astronomy soon identified the star for me with Srruve’s 2841; and assisted in establishing, in as far as two observations alone can establish, that an Elchies measure whether in magnitude, colour, posi- tion, or distance, is not unworthy to stand side by side with an equally small fragment of the noble work of the great Russian astronomer, the maker of Dorpat’s fame, and the founder of Imperial Pulkova. Part C.—General Deductions. Parr C.—1. Instrumental Qualities. When the recorded particulars, of what was done with the Elchies telescope during my period of trying it, extend through so many pages as the preceding, a few words on the final results of the whole may not be out of place. Now, firstly, and most conspicuously, it was by general consent a big tele- scope,—viz. with an object-glass of 11 inches in diameter. Was it found, then, to possess optical advantages commensurate with that size? This is an important question to many parties; for mere size, without other | advantageous qualities, will only prove a drawback, and of a very positive and | incommodious character in the use of any instrument; and while size and its | expected power form the chief point upon which the general public desires to be | informed, it is also one where amateurs are often exceedingly sensitive; for many a man who has in his day provided himself with one of the largest object-glasses of that period, is not particularly delighted when a dear friend, only a few years afterwards, profiting by the manufacturing progress of the age meanwhile, is enabled with ease greatly to exceed him. It has recently been said too, by a gentleman who has had possession for /Many years past of an 8'5-inch object-glass, and with reference to this present testing of the 11-inch telescope of Elchies, that you can always,—without any looking through at the heavens, and by merely measuring with a carpenter’s rule the area of any big object-glass,—compute quite near enough what is the smallest isolated star it will show, if its composition be but decently good; that actual ‘jastronomical observations to such an end, are therefore idle and useless; and 414 PROFESSOR C. PIAZZI SMYTH ON THE \ finally that, as to the small stars picked up by the Elchies instrument, in a trial of that kind, round about 312 Pegasi, No. 27 of our list, he, the objector, had : since quite rapidly identified them all with his 8:5-inch glass. ) The mere measure, however, of the area in inches does not satisfy every one . thus easily, as to each of the many varied star-showing properties or failings of a — large object-glass: and the identification quoted above, leaves perfectly untouched — two most important data in the problem, viz., 1st, The different quality of the two — observers’ eyes in the two cases, and they may be most extraordinarily different — in vigour, sharpness, sensibility or other important optical bearings; and, 2d, The fact that the one observer discovered and micrometrically measured the objects, while the other merely identified them from these measures when printed, and placed in his hand. Much is also due on every occasional trial, to the light-trans- | mitting and defining power of the atmosphere at the place; whence, a long — series of observations, giving a general mean, should be more convincing than some one special and particular attempt. 7 Now in the “ Cycle,” there is a grand mass of evidence of what a good eye was — enabled to do, on the average of many years, in an English atmosphere, with a 59-inch object-glass ; that book, therefore, 1 make my honoured point of reference in the three following cases :— . First, with a 3°6-inch object-glass I have worked for many nights at the ‘* Cycle” objects in the clear atmosphere of Mount Guajara, but could not, with all my pains, and with all the advantages of that pure and well-defining atmosphere, see all, or by any means all,.that the Cycledescribed. © Second, with a 7°25-inch object-glass, I have similarly worked away at the same subjects, and saw without difficulty, anomalies excepted, every feature described in the Cycle; but I hardly saw anything more. . Third, with the Elchies 11-inch, in the bad Elchies atmosphere, I similarly | saw, not only without difficulty, but with ease, whatever, even most minute, was described in the Cycle ; and beyond that saw and measured, in not a few cases, (I) do not say that they were well defined or adapted for making good measures,) — other small stars that had neither been described in the respected pages of the © Cycle, nor seen with the 7:25-inch object-glass in the purer climate of Alta Vista. Here therefore is proved, and in an intensely practical manner, the advantage of size generally; also, that together with its superior dimensions, the great Elchies Telescope really has increased optical power proportioned worthily — thereto, for distinguishing small isolated stars, whether their existence has been — already recorded or not; while the pleasure and satisfaction its use on that account alone imparted to me, is what only an ardent, and previously often foiled, — observer can fully appreciate. What would such an instrument not have done 4 in absolute stellar discovery, if the sharper eye of him with the 8°5-inch objedtl glass, had been employed in utilizing its admirable manifestations! GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 415 The next question will be, as to the defining power of the telescope. This I believe to be good, though the atmosphere was almost invariably so disturbed, that I never could try any very severe test. On one, however, of the only two occasions on which there was good atmospheric definition, I was look- ing at y Andromedee, and had most admirable proof that the smallness of the discs of the stars was just as it should be, with an excellent quality of object-glass of the given size; for, while the Cycle 5:9-inch just barely notched the oblong spot of light formed by the two close stars B and C; and while the Pattinson 7:25-inch on Teneriffe showed them separate, with a black line between them, but yet with their discs mutually compressed on the adjacent sides, and without which com- pression they must have touched,—-the Elchies 11-inch showed them completely separated, and perfectly round; the distance apart of the two stars being about 0”-6, and being believed to have been constant through the three observations. To these optical advantages, depending on size accompanied by excellence, the Elchies telescope also realized, and showed that there is great satisfaction to the observer in fully experiencing the mechanical advantages of greater steadi- ness of motion, freedom from tremors, or disturbance by wind, and constancy of zero points,* as necessarily imparted by a large and heavy instrument, than trifled with by all the smaller and lighter ones ever used by the same observer. Part C.—(2.) Cosmical Results. The series of these Elchies observations is too small to expect much from them of this order in the present very advanced condition of sidereal astronomy; but still I do trust that faithful labour with so powerful an instrument has not gone altogether unrewarded. Beginning with the first of our four telescopic observed quantities, viz., Mag- * The instances in Correction-Table II., p. 377, having been further examined for the often reputed effect of absolute position angle in biasing more or less the estimation of any observer in both position and distance, have given some indications of a small correction of that nature, varying with the position, being required as below; the distances having been first corrected for a probable residual error, both of run of micrometer and method of measuring, amounting at a distance of 5” to +°04”, at 10” to +-01%, at 15” to —-03”, at 20” to —-08”, and at 25” to —-13”. Position Correction in Position Correction in Bastien Correction in Angle. Position. | Distance. Angle. Position. | Distance. Angle. Position. | Distance. 0 48, 07 120 4 eco 240 Ths aes 20 — 9 +:07 140 +4 —°02 °260 — 3 —'02 40 — 4 +:06 160 +3 —'03 280 — 6 ‘00 60 0 +04 180 +3 — 04 300 —10 +°02 80 + 2 +°03 200 +2 — ‘04 320 —138 +04 100 + 38 +01 220 +1 —°03 340 —15 +°06 120 + 4 — 01 240 0 — 03 360 —13 +°07 These corrections, though regular, are so small, compared to the ordinary error of individual observations, that they have not yet been applied in any case. VOL. XXIII. PART I. ' 5 u 416 GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. nitude, No. 18, 6 Aquilee, discovers a change of magnitude in its B; No. 7, 222 Arietis, if not the same in its A, at least rectifies a standard book on a test star ; and the new small stars found around Nos. 3, 17, 20, 21, 24, 25, and 27, promise to form useful points of reference, touching proper-motion determinations by equatorial observers, such as are much required towards the full understanding, or for the due classification of those stars, according to character. In Colour something more has been done; for variations of colour in several stars have been shown to be real and extensive, sometimes affecting both mem- bers, and sometimes one only, of a double-star; and in No. 13, the changes are regularly periodical. This case is new, and, if true also, must be of extraordinary importance even in days of “spectrum analysis.” It is new, for putting on one side the changing colours of those strange isolations, the temporary stars, and certain degrees of change in tint of stars variable in brightness at the time that they are varying,—the best astronomical writers, from Sir Joun Herscuz, downwards, seem to allude to the colours of stars as so many “ statical” facts; things to be — once well determined by eye or by spectrum, and then stored away in classified lists, or printed in books for permanent reference like the colours of minerals or precious stones. But with our No. 13, or 95 Herculis, its two stars are neither temporary nor variable in magnitude, and yet they change and change exceed- ingly in colour; their contrasted colours are not the effect of the light of one powerful star dominating that of the other to the eye as a complementary tint, —because the two stars are almost exactly of equal brightness; and again the bluer colour of one is not an effect of greater distance, because the stars are ‘proved, and now proved for the first time, to be binary. Hence, take them all in all, the two stars of 95 Herculis, do seem to be really periodical changers of cosmical colour from causes inherent in themselves, or connected with their own region of space; appearing thereby to indicate the propriety, both of a date being attached to every future observation of star-colour when made, and, on the strength of the analogy between all true stellar orbs, a record of spectrum analyses of the light of our own sun being kept up regularly, as a check upon periodical or secular variations in the quality or material of his light.* * Some further inquiries may also be subserved by the Elchies colour observations; which, if — unusually few in number, have been more than usually attended to touching the character of the | double stars concerned, or the difference of the distance of their members from our system. 5 There is undoubtedly an ether filling space, say most scientific men; well then, if so, what is its colour by transmitted light ? Star observations are peculiarly adapted to this end, and the colours which we recognise in all stars may partly belong to this medium, whose colour, too, and composition | may be varied in particular regions. First, then, let us ascertain if there is any constant feature of | colour dependent on distance. Now the two nearest well-determined stellar systems are those of @ | Centauri and 61 Cygni; and Sir J. Herscuer has remarked their strong yellow colour, stronger in the small, than the large, component in either case; if, then, those stars are really white, but appear yellow to us, they give in so far a quadruple proof of the medium which extends between them and ourselves, being yellow by transmitted light; by no means an extraordinary result, if, according to — recent mathematicians, the atmosphere of the earth thins away and extends indefinitely into the planetary and stellar spaces. GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. 417 In Position and Distance, the tabular results of observations for each star-group so often giving a mean between distinguished but conflicting observers, as in Nos. 1, 35 Piscium; 4, 2 Piscium; 11, a Herculis; and some others, will prove that useful results have been recorded; though their degree of merit will only be capable of being fully judged at some future day, when impartial computers may, or may not, employ them in orbital calculations. And finally in Character, much is believed to have been cleared up for many of the stars, either by the above measures, or the “Proper Motion” test as now applied; in some instances too with singular success, of which Nos. 13, 95 Herculis; 21, 2 Sagittz; and 22, a Aquile, may serve for example. In conclusion, then, I trust that these pages have now shown that the Elchies But when we pursue our inquiries further still, and beyond the limits of sensible stellar parallax, and merely employ the broad assumption that the smaller that stars do appear, the further off they must be on the whole,—then arises the anti-terrestrial result, that the greater the depth of the distant medium through which stars are seen, the bluer they become; for all very small stars are bluish. The smaller members also of most double stars, whether optical or physical, and of unknown distance from us, are, as a whole, bluer than the larger members; appearing thereby to imply, though there may be other concurring causes to be mentioned, that the medium filling the more distant realms of space is in a positively different physical condition from that in which we are _ moving at present under the control and guardianship of our sun. It is even possible that there are more restricted regions of speciality still, and that floating cos- mical motes may exist in interstellar space, capable of playing very peculiar parts on the light trans- mitted through them from more distant bodies. Cosmical clouds have been suggested by both the _ Herscuets to explain observed changes in telescopic stars and nebula; and such clouds, not very far too from our own system, may be strongly suspected, some might even be inclined to say are found, to exist, from the many variable stars whose periods have been ascertained to be almost exactly 365 days. (See Spec. Hart., p. 269.) On the other hand, our case of 95 Herculis, even if there had not been any thing else of the same 3 order, establishes the point, of colours and changes of colours peculiar to, or arising in, the stars them- 4 selves. That instance forms an extreme case; but the forces at work there are probably in exist- _ ence elsewhere as well, and not improbably in our own sun, and even in our own earth. Let me explain the hasty g Beara ion, which, in the absence of lgeage anything else, may at least incite to % farther observation. The changing tints of the members of 95 Herculis are eminently auroral, i.e. _ of the character of an Aurora Borealis when its displays are intense, such as we see them in the northern sky once in half a century only, and when fiery pink and vivid green streamers alarm the “country ; and they are auroral also in their indications of fitful flashes and pulses, like the changes ‘of lustre in periods of a few seconds noticed by Mr Norman Pogson in the star U Geminorum. (Spec. _ Hart. p. 107). Again, the pink prominences seen at total eclipses around our own sun, and at times or in parts varying to other bluish colours, as established by Orro Srruve, with the appro- Dation of Mr Airy in 1860, have likewise been analogised by Mr Batrour Sruarr to terrestrial “auroras. Something then of the same character that produces the immense effects observed on “the orbs of 95 Herculis, may, and apparently does, exist on the surface of our own sun; following too, in its luminous and coloured manifestations, such active and impetuous changes of short period (for the eclipse red prominences have never feen seen twice alike), that some noni maxima, from the occurrence of secular periods, capable of reacting on the climate of our earth, may at times be looked for. Thus the subject of the colours of the stars becomes one, not only of great astronomical, but also . of terrestrial, interest and extraordinary complication ; and it is possible that spectrum analysis combined with eye estimations, may enable us to separate the colour produced by transmission through intervening cosmical clouds from the colour of the star itself, by reason of the small differ- ence in the dark lines of the spectrum effected by any colouring material at a low temperature. Soa 6} 418 GREAT REFRACTING TELESCOPE AT ELCHIES, IN MORAYSHIRE. telescope not only has remarkable powers for accurate stellar observation, but has — effectually made some small contribution to the furtherance of our knowledge of | the heavens; and also, that Mr J. W. Grant of Elchies,—in conceiving the idea, ordering the execution of, and then erecting that fine instrument in the north of Scotland, on a scale so greatly in advance of whatever had been done in the } country up to his own, and even the present time,—deserves extremely well of — the members of the Royal Society of Edinburgh, and of all scientific men in the land; whose only regret must be, and their sympathy will accompany their regret, that the failure, and nothing but the failure, at the last moment, of Mr Grant’s long Indian-tried health, prevented him from being the first to use his own telescope, and to communicate possibly important discoveries for the promo- tion of science. . CTA) XXIX.— Description of the Lithoscope, an Instrument for distinguishing Precious Stones and other bodies. By Sir Davip Brewster, K.H., F.R.S. (Plate XTX.) (Read 18th January 1864.) In examining the light reflected from the surface of calcareous spar, when in contact with different fluids, | observed several phenomena, both of light and colour, which led me to make the same experiments on the natural and artificial surfaces of the precious stones and other minerals. In these experiments, the in- tensity of the reflected pencil varied, as might have been expected, with the refractive power of the fluid; but I was not prepared for the curious fact, that when the reflective power of the surface was reduced almost to nothing, the sur- face was no longer able to reflect white light, but reflected pencils of different colours, depending on the approximation of the refractive power of the fluid to that of the solid. When the crystal had much double refraction, the colour of the reflected light varied with the inclination of the plane of reflection to the plane passing through the axis of the crystal. In making these experiments, a drop of fluid is placed upon the surface of the body to be examined, and upon this drop is laid the broad surface of a rectangular prism of glass. A parallel film of fiuid will thus be formed between the crystal and the prism, and any luminous image reflected from the two combined surfaces will consist of two images superposed, one reflected from the common surface of the crystal and the fluid, and the other from the common surface of the fluid and the glass. By a slight inclination of the prism, the two images are separated, so that we can examine and compare them, the pencil from the prism and fluid sur- face being a standard light, with which the pencil reflected from the common surface of other crystals and the same fluid may be compared, in reference to colour and intensity of light. By the use of fluids, therefore, of known refractive power, we can distinguish precious stones and other minerals, the standard of intensity and of colour being the invariable pencil reflected from the prism and fiuid surface. A continuous Scale of refractive power, embracing a great variety of minerals and other bodies, may be obtained, by mixing fluids in different proportions. The fixed oils com- bine readily, not only with one another, but with many of the volatile oils; and the aqueous solutions of alcohol and sugar, will to some extent, be useful auxi- liaries in reducing the refractive power of the surfaces on which they are placed. This method of distinguishing bodies is not limited to those which are solid. By standard prisms of crystals, or of different kinds of glass, we may distinguish fluids of a// kinds, because the range of refractive powers from tabaheer to VOL. XXIII. PART III. Sp.¢ 420 SIR DAVID BREWSTER’S DESCRIPTION OF THE LITHOSCOPE. diamond and chromate of lead, is much greater than from water to oil of cassia. - In this case, a standard pencil will be obtained from a standard fluid of a known refractive power, placed on a surface of the same glass as the prism, as will be presently explained. Impurities in oils and other substances may be thus detected, and specific gravities approximately ascertained. In order to make these experiments easily and correctly, I contrived the instrument now on the table, which was constructed for me many years ago by the late Mr Dottonp, and which may be called a Lithoscope, from its application to the discrimination of precious stones. It consists of a rectangular prism PR, mounted as shown in Plate XIX., where AB is a pillar, carrying the horizontal and vertical branches CD, CE. The prism turns vertically round a joint at E, and may be lifted round that joint by the hand, from its horizontal position, or raised slowly by the milled-head F of a screw FG, resting at G upon the branch CD. A small circular plate H, at the top of a screwed rod I, is made to rise or fall by means of the milled head KL; and © has also a motion of rotation round the top of the rod. Two steel rods de, cf, — carry two small aperture tubes ¢, f, through one of which, 7 the incident pencil — falls nearly perpendicularly upon one side of the prism, and at an angle of 45° — upon its base. These rods, with their tubular apertures, slide through short tubes — at mand , in order that they may receive the incident and reflected pencils. Bottles containing oil of cassia and other standard oils are placed at 4, 8, c. In using the Lithoscope, the mineral upon whose surface the observation is to — be made is attached, if necessary, by cement or otherwise to the plate H. A drop — of the proper oil is then put upon the surface of the mineral, and the prism — brought into a horizontal position. If it does not touch the oil, it is brought into contact with it by the milled head KL, which raises the plate H. A plate or film of oil, with parallel surfaces, is thus formed between the mineral and the prism; and if we now view the image of the sun or of a small bright flame, transmitted through the aperture /, reflected from the film, and reaching the eye through the aperture e, we shall see one image consisting of two coincident images, the one reflected from the surface of the prism and the oil, and the other from the surface of the oil and the mineral. In order to separate these images, the prism is- slightly raised round the joint at E, by turning the milled head F. The prism: image will then appear at the right hand of the other image; and by a compari- son of the colour and intensity of these images, we obtain the information we- desire. ‘ It was by an apparatus of this kind, furnished with a graduated circle, thatI discovered the influence of the doubly refracting force in polarising common light in planes inclined to the plane of reflexion. These experiments were published in the “ Philosophical Transactions”’ for 1819, and have led several distinguished mathematicians—Professor Maccuttacu of Dublin, M. Seeseck of Berlin, am SIR DAVID BREWSTER’S DESCRIPTION OF THE LITHOSCOPE. 421 - Professor NEuMANN of Konigsberg—to important extensions of the Undulatory Theory. I shall have occasion, in another paper, to submit to the Society a series of experiments on the influence of the doubly refracting force in turning the planes of polarised light out of the plane of incidence and reflexion ; but at present I confine myself to the consideration of the intensity and colour of the reflected pencils. The following observations were made chiefly with oil of cassia and oil of anise seeds, on account of their great refractive power, and will be sufficient to show the use and application of the Lithoscope :— With Oil of Cassia. Diamonp.—The colour from the crystal is yellow, and the intensity of the pencil four or jive times greater than that of the pencil from the prism. The Diamond may therefore be easily distinguished from Quartz and from Glass of very high refractive power, for which it is often mistaken. Zircon.—The colour from the crystal is white, and the intensity of the pencil two or three times greater than that of the pencil from the prism. Rugy, Oriental_—The colour from the crystal is yellow in artificial light, and the intensity of the pencil nearly double that from the prism. CHRYSOBERYL, Cymophane.—The colour from an artificial face in candle-light is yellowish, and the intensity of the pencil greater than that from the prism. Beryu.—The colour from the crystal is slightly blue, and fainter than the pencil from the prism. BuvE Toraz.—The colour from the crystal is a brilliant lilac, approaching to blue, when the plane of reflexion passes through the axis of the prism, and the surface is artificially polished. On the same face, and in a plane at right angles to this, the colour of the pencil is bluish pink. The intensity of the pencil is two or three times less than that of the pencil from the prism. Upon a natural face, the colour of the pencil is bright blue in every azimuth. Above the polarising angle, the reflected pencil consists of polarised red light and of unpolarised blue light. Topaz from Brazil, colourless.—The colour from a cleavage plane is a brilliant blue, in every direction. Topaz, yellow, from Brazil.—Upon natural and artificial faces, the colour is a | faint red, and the image scarcely perceptible. On another specimen, I found the colour to be a bright pink, the intensity being much less than that of the pencil from the prism. : Cinnamon Stonr.—On an artificial surface of this variety of garnet, the colour . of the pencil was yellowish red, and its intensity less than that from the prism.. GARNET, precious.——The colour of the pencil is reddish yellow, and its intensity a little greater than that from the prism. 422 SIR DAVID BREWSTER’S DESCRIPTION OF THE LITHOSCOPE. Garnet, from Elie, in Fife.—The colour of the pencil is reddish yellow, but the intensity very much less than that from the prism. Prripot.—tThe colour of the pencil is brownish yellow, and its intensity much less than that from the prism. Euctase.—The colour of the pencil is brilliant yellow, and its intensity less than that from the prism. Preunite.—The colour of the pencil is d/ue, but brighter than that from topaz. Quartz.—The colour of the pencil is a faint blue, both on natural and artificial faces, and its intensity less than that from the prism. AmeEtuyst.—The colour of the pencil is a faint blue, as in quartz, and its intensity less than that of the prism. DicurorTE.—The colour of the pencil is a d/we, fainter than in quartz, and its intensity less than that of the prism. Brack TourMALine.—The colour of the pencil in a plane perpendicular to the axis is a brownish yellow in candle-light, and its intensity much less than that from the prism. AuaiTe.—The colour of the pencil, in candle-light, is yellow, and its intensity less than that from the prism. ) SULPHATE OF BarytTes.—The colour of the pencil is brick-red, less faint than in topaz, and the same at all incidences and in all azimuths. The intensity of the pencil is very much less than that from the prism. SutpuHaTE or Leap.—The colour of the pencil, in candle-light, is brillant yellow, and its intensity twice as great as that from the prism. LEELITE.—The colour of the pencil is greenish blue when the oil is warm, the intensity of the pencil increasing with the incidence. JeT.—The colour of the pencil is a very faint yellowish red. and the same at all incidences. | The following experiments were made with Oil of Anise Seeds, a less refrac-— tive oil than O2/ of Cassia :-— Quartz, on a face of the prism. When the plane of reflexion passes through ~ the axis, the image of a candle is just perceptible, and of a brick-red colour. In sun-light the colour is due, of little intensity, but pink when the oil is first put on! , When the plane of reflexion is perpendicular to the axis, the image of a candle is distinctly visible, and of a brick-red colour. In sun-light the colour is red, but yellow when the oil is first put on. . On a face perpendicular to the axis of the crystal, the colour in sun-light is” blue. On a face of the pyramid, the colour is pink in a plane passing through the axis, but ight red in a plane perpendicular to the axis. SIR DAVID BREWSTER’S DESCRIPTION OF THE LITHOSCOPE. 423 AmeEtTHyst.—The colour of the pencil is a jine blue at all incidences and in all azimuths. Dicuroirze.—The colour of the pencil varies from reddish yellow, when the oil is warm, to a b/wish colour when the oil is cold, the intensity being the same at all incidences. Opats, Common and Precious.—The colour of the pencil a pale yellow, but bright. BioopstoneE.—Colour of the pencil lemon yellow. LerLite.—Colour of the pencil purple, becoming bluish at great incidences. LABRADOR FELDspaR.—Colour of the pencil sky blue. Rock Saut.—The colour of the pencil blue, at all incidences. The following experiment was made with Sulphate of Lime :— With Balsam of Capivi the pencil was colourless, and faint at all incidences. With Castor Oil, the pencil was colourless at all incidences. The following experiments were made on Quartz with pencils of polarised light, O and E, polarised in planes + and — 45° to the plane of reflexion :— On the face of the prism, and in a plane passing through the axis of the crystal, with Canada Balsam, E was orange yellow, and not so bright as O, E being polar- ised at a greater incidence than O. In a plane at right angles to this O=E, and both vanish together. On the face of the pyramid, and in a plane passing through the axis of the crystal, O is bluzsh and E a straw yellow, O being much brighter than E, and both vanishing together. In order to reduce the reflective power of the quartz, | mixed Oil of Sassafras and O11 of Anise Seeds, in such proportions that the combination had nearly the same refractive power as the mineral. The image of a candle placed a few inches from the reflecting surface was scarcely visible. In sun-light, however, and on a face of the prism in a plane passing through | the axis, the pencil E was a bright greenish blue at incidences below the polarising | angle, and it consisted of two pencils of different colours, the one a bright blue, | polarised in the plane of reflexion, and the other a yellow, polarised in a plane | perpendicular to it. In a plane perpendicular to that paeaing through the axis, the colour of E | was a bright purple at various incidences. On the face of the pyramid, the colour was blue in the one plane, and pu Aus in the other. The use of the Lithoscope, in distinguishing both solids and liquids, may be ' extended in two ways— VOL. XXIII. PART III. DY 424 SIR DAVID BREWSTER’S DESCRIPTION OF THE LITHOSCOPE. 1st, By dividing the reflecting surface of the prism into two, three, or more parts, by means of grooves, so that two, three, or more oils may be used at once; and, 2d, By using a prism composed of two, three, or more gc of glass with different refracting powers. By either of these means, or by the two in combination, the experimental results may be more readily and accurately compared. In the preceding experiments our attention is called to two different pheno- mena—the intensity and the colour of the reflected pencil. When the pencil is colourless, which is generally the case when one of the surfaces is that of glass, its intensity depends on the index of refraction of the surfaces in contact, which is always equal to the quotient of the greater index of refraction divided by the lesser. The phenomena of colour produced by feebly reflecting surfaces, and first described in my paper of 1819, already referred to, arise from two different causes— : lst, In doubly refracting crystals, from the influence of the doubly refracting force in turning through different angles the planes of the plone of the differently coloured rays; and, 2d, In the same class of bodies, and in those which have no double refraction from the different dispersive powers of the surfaces in contact, and also from the irrationality of dispersion, in consequence of which the coloured spaces in different spectra have not the same proportion to each other. To the subject of crystalline reflexion in which the phenomena of colour are exhibited, I shall have occasion to direct the attention of the Society in anothet paper. When the colour is produced by difference of dispersive power, or by irrationality in the spectra, it is easily explained. In a combination, for example of flint glass and oil of cassia, the index of refraction for red light is the same it both bodies, but different for all the other colours. The ved light, therefore, in ¢ perfectly colourless beam, will pass through the surface of the oil and the glass, without suffering reflexion ; and, consequently, the light reflected must be bluish while the transmitted light will be yellowish. As there is no reason for believing that in any two bodies, whether gaseous, fluid, or solid, the dispersive powers are exactly the same, or the coloured spaces exactly proportional, we may assert that when pure white light is either transmitted by, or reflected from, bodies perfectly colourless, the transmitted and reflected pencil must be coloured, how: ever inappreciable the colour may be.* * See “ Memoirs of the Life and Writings of Sir Isaac Newton,” vol. i. p. 163. Second edition 4 i) z t pes a : R gak , ? PLATE XIX. Royal Soc. Trans. Edir MMMM MMO] a is ( 425 ) XXX.—On the Agrarian Lans of Lycurgus, and one of Mr Grote’s Canons of Historical Criticism. By Professor BLACKIE. (Read 4th January 1864.) The History of Greece, by Mr Grote, perhaps the most notable production of modern English scholarship, is characterised, amongst many great virtues, by what has always appeared to me, in a historian, a great fault—a tendency to undervalue traditional authority, and to over-rate the importance of conjectural ingenuity, in the reconstruction of the past. One of the most remarkable instances of this tendency which has fallen specially under my view, is his treat- ment of Lycureus and his legislation, as it occurs near the end of his second ‘volume. The fallacies which seem to me to lie in this treatment, it is the object of this paper shortly to set forth. Mr Grote’s views with respect to the Spartan laws and customs are sufficiently indicated by his general proposition, vol. il. p. 515, that ‘“‘ Lycurcus, or the indi- vidual to whom this system was owing, whoever he was, is the founder of a war- like brotherhood, rather than the lawgiver of a political community ;” and by his special assertion (p. 524) that “ the idea of Lycurcus as an equal partitioner of lands, belongs to the century of Acis IV. and CLEomENgs ;” that is, to the middle, and towards the end of the third century before Christ, and is to be regarded altogether as a political fiction, not as a historical fact. Now, by what method of inquiry does the learned gentleman arrive at this conclusion’ His statement of his method, on the first blush, seems remarkably fair and reasonable. On examining the witnesses for this alleged historical fact, he has discovered that all the weighty authorities who live nearest to the event are silent on the subject, or even directly contradict the current modern belief, which can in fact be traced to only two of the most recent and least reliable authorities. The canon implied in this method of historical criticism is no doubt, taken broadly, perfectly just. But all such canons, in their application, are liable to be seriously modified by various considerations. In the first place, with respect to the fact here disputed, we must bear in mind that anything like authentic | cotemporary evidence is altogether out of the question; and so far as nearness to the time in which the alleged fact took place is concerned, ARISTOTLE is a witness not a whit more reliable than Potysrus. According to the lowest calcu- _lation, that of Tuucypies (i. 18), Lycureus flourished 400 years before the end of the Peloponesian war, that is about 800 years B.c.; and if, as the historian asserts, | the Lycurgean laws remained in force during this period, their character at the . VOL. XXIII. PART III. 5 Z 426 PROFESSOR BLACKIE ON THE AGRARIAN LAWS OF LYCURGUS, time of their original institution, as contrasted with any changes which, in the declension of Spartan influence, they afterwards suffered, could no more be known as an existing fact by ArisToTLE than by Poiysius, who lived nearly 200 years later. There was no such destruction of books and documents in the period intervening between these two great political writers, as to put the one in a more favourable position with regard to written testimony than the other; nay, so far as parchment documents were concerned, from the accumulated stores of the Alexandrian Library, Potysius had, in all likelihood, much more ample means of information at hand than AristoTLe. Potystus, therefore, who* along with PLuTarcH, in his Life of Lycureus, is‘the principal direct and positive authority for the Agrarian laws, as a part of the Spartan constitution, is, so far as the lapse of time is concerned, a witness by no means to be postponed even to the Stagyrite. As little in respect of any other virtue of a historical authority can any such inferiority be maintained. There is, indeed, no historical author among the ancients, after THucyDIDEs, whose political sagacity and penetration is more generally acknowledged ; and the book in which his remarks on the Spartan con- stitution occur is expressly directed to the comparison of different forms of civil _ polity ; besides, as a native of Megalopolis in Arcadia, and living in the age imme- diately succeeding the great Agrarian movements of Acis and CLEomENES, he had the most ample means of being locally well informed as to the characteristic — points of the Spartan constitution. As to PLuTarcu,} though I may not deny that his account of the Spartan institutions is tinged strongly with rose colour, yet I can by no means share in the light temper of those who habitually talk of the wise old Cheronzean as an amiable, indeed, but superficial and ignorant writer. I think it plain, on the contrary, that his writings everywhere bear the stamp of good sense, of just discrimination, of honest research, and various reading. His” point of view, if not always leading to a perfectly just appreciation of his object, was the point of view of the ancient world generally ; and on no occasion, so far as — my reading goes, can he be suspected of having lightly committed himself to a Le - serious historical assertion. But whatever may be the particular weak points of — this most agreeable and most popular, and now most undeservedly neglected writer, we must bear in mind, that, in reference to such a matter of old historical _ belief as the Spartan constitution, what he does give us, is not to be regarded as his opinion merely, but as the condensed and concentrated result of all the historical testimony that had come through his hands; and as he constantly quotes — * Ths pev 64 Aaxedaupoviwy roXureias tdvov eval pact, TpPOTov pev Td. wept TAS eyyaious KTHGELS, Gy OvdEVE , Xx Lal iA / \ VE »” ” 5 lal a r. a , . 45 pereott TActov, GAAG mavTas TOUS ToAtTas icov Exew det THS TOALTUKHS Ywpas.—VI. 40. , De an , , \ , ca ka Ay a 5 roo» a x ¥ by, f Acdrepov dé tv Avkovpyou Todirevpdtwv Kai veaviKwTaTov 6 THs ys dvadacpos éoTt. Aewys yap ovens > rN ‘ AXG > / \ > , > yi A aN a 8e i , , > FIVE -— 8 dvwpaNias Kat 7oAAGy aKTnPOVwY Kat Gmropwy éemupepoumevwv TH TOAEL, TOD O€ TAOVTOV wavTaracw €is OALyOU a / 4 , AN \ s ovveppunKkoros, UBpw Kat pOdvov kal xaxoupyiay Kal tpudyv kal Ta ToUTwY ert mpEaPUTEpa Kal pciLw voona / lal XN 4 > U 4 ‘\ , 7 > , la > > aA > 4 p. woNiteias, TAOUTOV Kat Teviay, eeAaivwr, CUVETELE THY XWOpaY arracay cis pecov Oevras e& apyns avadagacGat KaL Gav per’ GAAnAwY Grravras Guadets Kat iaoxAyjpous Tots Biows yevouevovs.—Vit. Lye. vill. AND ONE OF MR GROTE’S CANONS OF HISTORICAL CRITICISM. 427 ARISTOTLE, it is not to be doubted, that in composing two such important Lives as those of Lycurcus and Soton, he had before him that very book of corrcim, or political constitutions, in which the Spartan polity was fully discussed, but of which now, unfortunately, only a very few fragments remain. So far, therefore, as direct positive evidence is concerned, I consider that we have in Potysius and PLuTARCH, two independent witnesses of as good faith and authority as can be adduced for any historical fact of similar antiquity. And let it be remembered, that the fact here in question is not a small incidental matter, or a piece of personal gossip, which might easily have been ignored altogether, and with equal ease have been blown into existence out of nothing; it is a grand central fact with regard to the social condition of a people who played, in ancient Hellenic life, a part equally prominent and peculiar, and which, if true at all, must have been as well known to the ancient Greeks, as the aristocratic refinement of the Episcopal, and the democratic plainness of the Presbyterian Church are to modern Chris- tendom. On the basis of these two authorities alone, therefore—one of which, by the way, the Edinburgh Reviewer of Mr Grote’s work, with a characteristic itch for sceptical novelties, most superficially ignores (Edinr. Review, vol. Ixxxiv. p. 371,)—on the testimonies of PoLyBius and PLuTarcu alone, I see no reason why we ‘should hesitate to receive the famous Agrarian laws of LycurGus as one of the most reliable traditions of the ancient world. Of course, Ido not mean to say, that, while accepting this general fact on the testimony of two such writers, I mean to adopt along with it all the dressings and trappings with which it has been tricked out in the course of time. Every one conversant with historical _ evidence knows that the fact is true in a hundred cases—witness the story of Mac- beth,—where the decorations of the fact are fabulous. I build, therefore, as little as Mr Grotz on the details of these Agrarian laws as given in the Life of Lycur- Gus; but while willingly with him tearing away the ornate frippery, and striking off the painted gauds that envelope the old sacred image, I deny his right to con- clude that the piece of fine old carved wood which lies beneath the dress is a mere fiction and a phantom. But let us now consider those more ancient witnesses, in deference to whom only, as he would have it appear, this distinguished writer | has thrown the valuable testimony of PLurarcu and Potystus aside. Of these, the most formidable, indeed the only important one, is ARISTOTLE, who, in the second book of his master-work (chap. ix., Bekker) on Political Science, has described some points of the Spartan polity with considerable detail, and among | others, in alluding to this very matter of the distribution of landed property, not only does not confirm what the other two authorities say about the equal dadaoudc of the lands, to them so striking and essential a fact—but actually asserts the _ direct contrary ; among other views of the Spartan polity, enumerating as one of | the chief, the diminution of small proprietors, and the accumulation of immense landed properties in the hands of afew persons, especially women. Thisis no doubt 428 PROFESSOR BLACKIE ON THE AGRARIAN LAWS OF LYCURGUS, a very startling assertion to a reader coming fresh from the somewhat Utopian descriptions of Spartan simplicity, equality, and fraternity, in the kindly pages of old Prurarcy. But this is not the only startling assertion about Spartan things and Spartan persons that presents itself in the same important chapter ; for, whereas Srrapo informs us (x. p. 449) that there was a common proverb current in Greece, “ A horse from Thessaly, a woman from Sparta, and a man from the banks of the ~ fair flowing Arethusa,” whereby the best article of the several kinds was expressed, the Stagyrite, on the other hand, here allows the famous Spartan mothers no characteristic qualities, but three of the worst,—great luxury, unbounded extra- — vagance, and, what no Athenian could tolerate for a moment, even in conception, an unwomanly mastery over their husbands. These strong statements, coming from a man generally so calm and cool and judicially impartial, naturally suggest to the thoughtful student that the great father of Encyclopzedic science is be- trayed for a moment into a little fit of amiable human weakness, and is speaking, - not as a philosopher altogether, but partly also as an Athenian. But more than this. What ArisToTLE here says with such decision was no doubt strictly true, — for it is not for us to pretend to find him nodding as to a matter of fact,—but it is not the whole truth. Wecan only explain his strong, one-sided, and, as it appears to the reader, extremely prejudiced language, by supposing, what is no doubt the fact, that he is speaking only of the Spartans of his day, not of the days of Lronrpas or of Lycurcus, and is no more to be considered as giving a general portraiture of Sparta and the Spartans, than a THackERAy of the time of Tacrrus — would have had his sketches of Roman life under the Emperors taken for the living counterfeits of the Catos, the Scrrios, and the Fasn of the Punic wars. And this view of the matter will appear the only natural and just one, so soon as the reader has taken up the position and attitude of the great author of the Politics, in this second book, as distinctly enunciated in the very first sentence of this section of the work.* The intention of the work, the author declares, is to ascertain tentatively, and by approximation at least, the best polity, or, as we would phrase it, the ideal commonwealth; but as it might appear impertinent to attempt this if the best form of government had already been realised, the philoso- pher thinks it only reasonable that he should preface the exposition of his ideal plan by showing that the most bepraised commonwealths already existing, so far from being perfect models, are bristling with glaring defects, which a passing glance may readily discover. ARISTOTLE, therefore, by the very conception of this book, has put himself into the not very philosophical position of a systematic fa It- * “Enel dz woaiegweda. bewejous wegl rig xowaving rg TodiTIxXNS, | xeuriorn Taoav Tors Ouvomevors CH manera nar’ svyny, Oe nal Tag HAAaS emsoxepauclus TorITEIAS, AIS TE YeAVTAl TiEG THY ToASwY TeV edvOMElE 4 aN a Ae up S \ ~ > , ~ e Ae my” ” , a) ~ wy Aeyouévay, xaY Ef TIVES Eregas Tuy hyo Ud miVeW Eignwevas na? OonEoas xAADS Exes, Iva rd r delds exo xal rd yenouov, ez1 Oe ro Cyreh ri Tag airas Eregov ur Oox7 weivrwg eivar oopiCecdas Psrouevay, CAR Oi 70 [at nadag tyen rabras reg viv image sons dick r8ro ravryy doxduev exiSudeobas r7v .£00dov.—Pol, il. mit. AND ON ONE OF MR GROTE’S CANONS OF HISTORICAL CRITICISM. 429 finder; his scheme in this introductory chapter does not in any wise require that he should give a perfect account of the rise and growth, and complete development of the Spartan commonwealth, but only that he should show how, in the result, it has found itself very far removed from the model commonwealth, which XENOPHON, PLATO, and other anti-Athenian laudators upheld it to be. “ By their fruits ye shall know them.” Ifthe harvest has brought forth rotten apples, the spring may have been geniai,—we are not careful to inquire about that; but there must have been something wrong somewhere, either in the seed or in the summer. And not only does the philosopher content himself with indi- cating what time has shown to be rotten in the Spartan constitution, but he incidentally drops a remark, which receives its full significance only on the sup- position of an original state of things altogether different from that which he is criticising. For, while discussing the point of the undue accumulation of landed property in his time, he blames the legislator for forbidding or discouraging the sale of lands by the hereditary holder, while at the same time, he allowed them freely to pass from family to family by testamentary conveyance—a liberty by which his prohibition was rendered in a great measure nugatory. Now, this remark plainly implies the existence, in ancient times, of a state of things in which every Spartan citizen, like the old Hebrew yeoman, had his own ancestral allotment of a certain moderate size—for there is no need of supposing mathe- matical equality—which, through the operation of an ill-regulated law of succes- sion, as ARISTOTLE thought, had in the course of time produced the monstrous accumulation of property in a few hands which he considers so pernicious. The evidence of the great Encyclopedic philosopher being thus placed, as it is hoped, in perfect harmony with the testimonies of PLurarcu and Potystus, the other witnesses, on whom the English historian founds his sceptical views, may be shortly dismissed. Their weight in the present question in fact amounts to nothing more than this, that certain authors, who might have been expected to allude to the Agrarian laws of Sparta, say nothing about them. But this sort of evidence, or rather want of evidence, in the case of writers who are not writing | formal treatises on the Spartan polity, proves nothing. A modern writer, for instance, might say many true things of the social state of modern France, and yet not once allude to the very important matter of the compulsory division of | landed property in that country after the demise of the holder. Not a few things in ancient writers about ancient matters are not mentioned, simply because they | Were so well known as not to require to be spoken about. A striking proof of | this occurs, I think, in the Panathenaic oration of IsocratEs, which contains a detailed comparison of Sparta and Athens, but where the Agrarian laws are | alluded to only incidentally in a single clause, which Mr Grors has somewhat | Strangely overlooked; nay, rather he quotes a passage from the oration which, next to the evidence of ARISTOTLE, seems to make most in favour of his sceptical VOL. XXIII. PART IIT. 6A 430 PROFESSOR BLACKIE ON THE AGRARIAN LAWS OF LYCURGUS, position. For, towards the close of the discourse (p. 287) the orator makes one of the advocates of Spartan usages say, ‘‘that whereas every one of the other states of Greece had been disturbed by frequent aristocratic and democratic revolutions, in Sparta alone no one could point out either mutinies or massacres, or unjust banishments, or confiscations of property, or violations of women, or abolition of debts, or change in the form of the constitution, or Agrarian laws (yi dvudaquods), OY any of the incurable diseases to which bodies politic are subject.” True; but this means only what we have already heard from THucypipzs, that the constitution, as settled by Lycurcus, had remained stable in its great supports —a remarkable phenomenon in ancient Greece—for four hundred years, undis- turbed by violent changes and sudden revolutions in the ownership of property ; but that the Spartan land, at the great Dorian immigration, was originally divided into equal lots, is incidentally asserted by the orator in a previous part of his dis- course, p. 270 (ris x wens Ks Teoonxey “sgov “ervey exaorov), with which passage the more vague language of Pato in the laws (III. 684 D.) is perfectly consistent. The silence of XENoPHON on the subject of the Spartan Agrarian laws might appear, at first sight, more difficult to account for. In a special treatise, such as the little book seg) Auxedapoviov wodureiag Unquestionably is, a characteristic feature of national life so prominently mentioned by PLurarcu and Potysius, might naturally have been expected to find a place. But when the extremely slight and flimsy character of this treatise is considered, and when the special fact is also borne in mind, that, though professing to give some idea not only of the Spartan education, but of the Spartan political constitution, the existence of the ixxansia OY Congregation of the Commons, is not even mentioned; and when we consider farther, that the inequality of land in Lacedzemon, so glaring to the eye of ARISTOTLE, must already, in the days of XENoPHON, have become so great as to render the Lycurgean legislation on this point a matter more of historical learning than of present social .significance, we must hold the silence of this writer on this particular point to be a matter of the smallest moment, certainly not of sufficient weight to countervail the positive and distinct testimony of such a grave and judicious writer as PoLyBivs. So much for the authorities, or what theologians call the external evidence. As to internal probabilities and presumptions, however our modern British ideas may incline us to look with a certain suspicion on all accounts of social equality in the tenure of land, it is quite certain, not only that the ancients generally held a land-tenure essential to citizenship, but that a certain equality in this respect was looked on as the sign of a healthy condition of the body politic. The whole history of Agrarian laws amongst the Romans was only a violent exposition of one of the oldest principles of ancient citizenship, that the land which had been — acquired by the exertions of common brothers in arms, should be possessed by — the co-ordinate ownership of equal citizens. But in the case of the Spartans it AND ON ONE OF MR GROTE’S CANONS OF HISTORICAL CRITICISM. 431 seems to me further, that their position as a small band of privileged nobles—for the proper Spartans were in fact a body of nobles, with exclusive privileges, as set against the great mass of the population—this difficult and slippery position, I say, rendered it in the highest degree perilous that any divisions should arise within the principal body; and such dissensions would naturally arise in those days, and in a country where landed property was the only valuable property, if the small section of the country originally occupied by the invaders had been absorbed by a few of the more powerful families, while the great mass was left with small allotments, which, by the action of well-known social laws, would have a tendency constantly to diminish. It is to dissensions of this kind, I conceive, that both PiutTarcn (chap. 2) and Isocrarss (p. 270) allude, when they talk of the period of disorder and confusion which prevailed in Sparta before the final settlement of the constitution by Lycureus; and we may justly conceive the mission of that legislator to have consisted in adjusting this matter by an Agrarian law, as SoLon effected a similar compromise between the claims of debtor and creditor two hundred years later in Athens, or as Baron Srein, after the battle of Jena (in 1808), under the pressure ofa great national calamity, deprived the Prussian nobility of a great part of their landed property, and created a race of independent peasants from the appropriation. Of course, I do not mean to say to what ex- tent the principle of absolute equality in the possession of the national acres might have been systematically carried out by the great Lacedzemonian lawgiver. Of that we can know nothing. All we can say is, that in accordance with the general spirit of ancient citizenship, and as a measure absolutely necessary for the security of a small body of nobles so situated, he would insist that every citizen, | qua citizen, should have his sufficient allotment; and as in those early times, | before the conquest of Messene, the amount of really valuable land in Lacedeemon | was not large, it seems impossible that any very large properties could have been allotted; and thus the very necessity of the case would dictate a practical ) equality, which historians, writing in times of monstrously accumulated wealth, | might easily work up into a sort of mathematical marvel, to a British critical | intellect in the nineteenth century after Christ altogether incredible. These are the views to which, after much consideration, I have arrived on this | interesting subject ; and I feel a strong conviction that they are the views, which with the sound practical intellect of the British people, constitutionally averse to all conjectural novelties, however brilliant, will ultimately prevail. In the meantime, | Ishall not be surprised if the authority of Mr Grore’s name in matters where he | 18a safe guide, shall lead the majority astray for a season in matters where he is | most unreliable. Generally, with regard to his whole method of estimating the } contents of early historical tradition, I consider him to be unsound. As concerns the special matter of the Agrarian laws, I shall conclude here by protesting | against the new canon of historical criticism, which he enunciates formally while 432 PROFESSOR BLACKIE ON THE AGRARIAN LAWS OF LYCURGUS. discussing the matter (vol. ii. p. 532). His words are as follows: —* It appears to me that the difficulties connected with this matter are best obviated by adopt- ing a different canon of historical interpretation. We cannot accept as real the Lycurgean land-division described in the life of the lawgiver ; but treating the account as a fiction, two modes of proceeding are open to us. We may either consider the fiction, as it now stands, to be the exaggeration and distortion of some small fact, and then try to guess without any assistance what that small fact was; or we may regard it as a fiction from first to last—the expression of some large idea and sentiment, so powerful in its action on men’s minds at a given time, as to induce them to make a place for it among the realities of the past. Now the latter supposition, as applied to the times of Agis IV., best meets the case before us.” In regard to this new canon, I object, in the first place, to the lan- guage which states that as altogether a guess, which is merely the acceptance of a well-attested fact, the details of which only are a matter of exaggeration and conjecture. The only guess in the present case which touches the nucleus of a fact, is Mr Grore’s, who, following the evil example of the Germans, has here smuggled into the sober pages of history an ingenious but altogether baseless con- jecture, for the solid foundation of old authority. In the next place, | would lay it down as one of the most important principles to be borne in mind in the inter- pretation of all tradition, written or unwritten, to use the emphatic language of Professor DunckEr, that “historic fantasies are not wont to arise without historic realities;’’ and the bare fact that Acis and CLEOMENEs in the third century before Christ based their famous but unfortunate schemes of reform im Sparta on alleged Agrarian laws of Lycurcus made five hundred years before, is to me a strong proof that such laws did once actually exist. A reforming king, who, as a last resource, rouses the social conscience of a nation against th e usurpation of an aristocracy, or a bureaucracy, must appeal, not to a pious dream or a brilliant imagination, but to a living record imprinted from genera- tion to generation in the fleshly tables of the popular heart. Only by the touch of what is living can a living virtue be imparted to the dead. . ( 433 ) XXXI.—On the Limits of our Knowledge respecting the Theory of Parallels. By Professor KELLAND. (Read December 21, 1863.) The subject of this paper is a very old one, and may to many appear to be "sufficiently worn; but I venture to hope, that there are some to whom a glimpse _ of the successive approaches of the human mind towards the right understanding of a question of pure logic, may have an interest,—even although the problem solved be an abstract one, and the conclusion a negative conclusion, having little eel application. Like the kindred problem of the quadrature of the circle, or the metaphysical problem of ‘“‘ Knowing and Being,” the theory of parallels has been attacked in various directions, and although it is true that no one ever Teached the goal he aimed at, yet it is not the less certain that great and posi- tive results have followed in the history of human attainment. If no other lesson has been learnt, this at least may have been: that in reasoning it is necessary to ‘look warily around and abroad at every step, seeing that admissions, the most Obviously inadmissible, or evasions the most palpable, have foiled generations of thinkers, whilst those who have detected their errors have fallen into others _ of an equally destructive character. | It is not my intention to give an account of the successive failures of different geometers in their attempts on this problem. That has already been done by Colonel THomrson, in his “ Geometry without Axioms.” My object will be rather to show what has been successfully accomplished, and by going over in a positive form the ground which is forbidden to those who attack the problem directly, to ‘indicate as clearly as I can the limits within which future research may be confined. _ Isay I am going over the negative limits of the discussion of the problem in a Tead me. I am much mistaken if those who give themselves the trouble to ‘examine the argument do not find it both interesting and instructive. So far as I know, it has never yet been developed in this country, although the circumstance ‘that for the last seventeen years [ have made it the repeated subject of Lectures and Essays in my Class may possibly take from it some of the appearance of VOL. XXIII. PART III. 6B 434 PROFESSOR KELLAND ON THE LIMITS OF OUR KNOWLEDGE novelty which it would otherwise present. In truth, many of the following pro- positions are due to my students. For the sake of clearness, I shall divide the different steps of the argument into propositions. LeGENDRE, in the 12th volume of the Memoires del’ Institut, proved,— Prop. I. The sui of the angles of a triangle can never exceed tivo right angles. Prop. IT. Lf the angles of any one triangle can be proved to be equal to two right angles, then the angles of every triangle can. These two propositions reduce the difficulty to the very narrow requirement of proving that some one triangle has the sum of its angles equal to two right angles. As a limit, it is evidently true. Forif CD be perpendicular to CA; and if CD be very great and CA indefinitely small, the angles of the triangle CAD approach two right angles as their limit. But this, as we shall see presently, proves nothing. . For although they approach two right angles when CA is in- definitely diminished, they may, for anything that appears, approach a right angle and a half, or any similar magnitude, when CA is indefinitely increased. Further, Mr Merxe has proved in the 36th volume of the Edinburgh Philo-— sophical Journal— Prop. II]. Trvangles which have their areas equal have the sum of their angles the same. We shall consider these three propositions as established beyond question, and _ refer to them in the order here given. . Some years ago, there appeared in CrELLE’s Journal, a notice of a work entitled ‘‘ Imaginary or Impossible Geometry,” viz., a discussion of the conclusions which would follow from the assumption as an axiom, of the hypothesis that “the three angles of a triangle are together less than two right angles.” I have never met with any statement of the propositions which the author deduced from this hypo- __ thesis ; but I have been accustomed, from time to time, to draw conclusions from _| the same hypothesis, and to induce my students to follow my example, so that, from one source and another, I believe I am in possession of most of those — conclusions which are likely to bear on the theory of parallels. And as these conclusions are both curious in themselves, from their connection with the properties of the circle, and appear to point to the limits of our knowledge of the — doctrine of parallels, I have thrown them together in the form of a sequence tag 4 the three propositions above enunciated. It must be premised, that all the definitions and axioms of Eucuim are retained, ae cee RESPECTING THE THEORY OF PARALLELS. 435 so far as they are logically correct, and make no use of the hypothesis of paral- lelism. As a matter of convenience, it is best to define a straight line, with PiayFair, in the following way :—“ If two lines are such that they cannot coin- cide in any two points without coinciding altogether, each of them is called a straight line ;” for Euciin’s definition has no significance in a logical system. It is never referred to by Eucrip himself, nor indeed, could it be, seeing that it expresses nothing. The real characteristics of straightness are contained in two postulates, or, as Simson designates them (and it is as well to refer to Simson), axioms. They constitute Smuson’s 10th and 11th axioms, thus breaking into three parts—a definition and two axioms—what Puayrarr has reduced to one. Evciiv’s definition of a square must of course be rejected. It is essentially vicious, involving both a superfluity and a want of necessary consistency. It is equivalent to the assumption, that the angles of a triangle are together equal to two right angles, or the alternative, which is demonstrably false, that a triangle may have its angles together greater than two right angles. It is further premised, that all the Propositions of Huciip, up to the 28th inclusive, are correctly demonstrated, and are clear of any assumption relative to the angles of a triangle, or to the doctrine of parallels. In the 29th Proposition, Kucuip has to convert the 27th and 28th, or, in other words, to show the conse- quences of starting with the hypothesis that two straight lines do not meet. The difficulty consists in deducing positwe consequences out of negative premises. And the difficulty is further increased by the fact, that straightness is only known from the necessity that two lines do meet, whilst parallelism is only known from the necessity that they do not meet. This difficulty renders it imperative on Evciip to make some additional assumption. His assumption or postulate is What Siuson calls the 12th axiom: “Ifa straight line meets two straight lines, so as to make the two interior angles on the same side of them, taken together, less than two right angles, these straight lines, being continually produced, shall at leneth meet upon that side on which are the angles which are less than two right | angles.” The object of all that has been written on the subject of parallels has | been to get rid of this assumption. I shall not even allude to the history of this | Subject. I am concerned only with that form of the argument which depends on the sum of the angles of a triangle. It has been stated above, that LEGENDRE has | Narrowed the requirements to the discovery of some one triangle, for which the angles shall be together equal to two right angles, by having proved that, if this be true, the same holds good of every triangle. It may perhaps be as well to add that this, once established, leads directly to Huciin’s 12th axiom. The following appears to be the most simple and satisfactory manner of estab- lishing this conclusion :— 436 PROFESSOR KELLAND ON THE LIMITS OF OUR KNOWLEDGE Prop. IV. Given that the angles of every triangle are together equal to two right angles, to prove Euclid’s 12th axiom. Let AB, CD make with EF the angles BEF, EFD less than two right angles; — AB, CD, shall meet, if produced, towards B, D. Let EFG be not greater than a right angle. Draw EG perpendicular to FD. Set off equal distances along EB, viz., EH, HI, &c., and draw HK, 10, &c., perpendicular to EG; and HP per- pendicular to IO. The angles BEG, GEF, EFG, are less than two right angles, but GEF, EFG, make up a right angle; therefore BEG is less than a right angle. Now EHK and HEK make up a right angle, and EIO, IEO make up a right angle, therefore EHK=EIO; and the triangles EHK, HIP, are equal (Euvc. I. 26), therefore HP =EK; but the triangles KHO, HOP, formed by joining HO, are equal (Evc. L. 26), therefore KO=HP=EK. It follows, therefore, that as we advance by equal distances along EB, we also advance by equal distances along EG; so that by going far enough along EB, we must at last advance beyond G; hence there is some point in EB produced, from which, if a perpendicular be drawn to EG produced, it shall cut EG produced beyond G; AB, therefore, meets CD, towards B, D. Let us now examine the consequences of assuming as true the following Axiom. The three angles of every triangle are together less than tivo right angles. : It may be remarked, that it would have sufficed to have assumed that the three angles of some one triangle are together less than two right angles. For, that being admitted, the axiom as enunciated follows at once; inasmuch as no triangle can have the sum of its angles greater than two right angles (Prop. L), neither can any triangle have them equal to two right angles, for then the same would be true of every triangle (Prop. IL.) Cor. 1. The exterior angle of every triangle is greater than the sum of the two interior opposite angles. _ Cor. 2. The angles of a quadrilateral are together less than four right angles. We shall designate the deficiency,of the angles of a given triangle from two right angles by the term angular defect of that triangle; and shall abbreviate the phrase “angular defect of the triangle ABC” by SABC : hence SABC =180°— (A +B+C.) RESPECTING THE THEORY OF PARALLELS. 437 Prop. V. Jf tio triangles have two angles of the one equal to two angles of the other, each to each, but the side adjacent to the equal angles of the one greater than the side adjacent to the equal angles of the other, then the other sides of the triangle which has the greater adjacent side are respectively greater than the other sides of the other triangle, but they contain a less angle. Let=ABC=DEF,and_ACB=DFE, but BC+EF, then is BA>ED,and AC>DF. Cut off from BC, BH=EF; and make the angle BHG=EFD or BCA; HG shall cut BA in G; for if it do not cut BA it must cut CA, and make with HC and CA a triangle, having the exterior angle equal to the interior opposite angle, which is impossible. Now (Eve. I. 26) BG=ED, but BA>BG ... BA7ED. Similarly AC >DF. Alsotheangle BAC is less than EDF. vat For BGH+ BHG+AGH+CHG = four right 6 \ 2 angles; but GAC+ ACH + AGH +CHG are less “a : | ve than four right angles (Axiom Cor. 2); there- A ANG E 6 fore BGH=>BAC, and BGH = EDF, therefore EDF>BAC. — Prop. VI. Jf from two points without a straight line, on the same side of it, the two perpendiculars drann to the line are equal, the straight line which joins the points is parallel to the given line. Let AB be the given straight line, C, D the given points without it on the same side, from which the two equal perpendiculars are drawn to the line, viz., CE, DF; CD is parallel to EF. Join CF, ED meeting in G; and through G draw GH perpendicular to AB, and produce HG to meet CD in K. The triangles CEF, DFE, are equal in every respect, therefore CF=DE, and—CFE=DEF: hence the triangles GHE, GHF are equal (Euc. I. 26), therefore EG=FG, and — = and make EF= AE, and so on. The 7 ; angles ADB, AEB, AFB, continually 5 D E . a diminish (Euc. I. 16). And by proceeding far enough a line may be drawn making. with the given linean angle less than any assignable angle. RESPECTING THE THEORY OF PARALLELS. 439 For —ADB>DAE+ DEA >2AED, because AD=DE: that is, AED=3 ADB. Similarly, AFB=}AEB<1ADB; and it is evident that by proceeding in the same way a line may be drawn from A to BC which shall make with BC an angle less than any assignable angle. Prop. IX. Through a given point without a straight line there may be drawn an infinite number of straight lines all parallel to the given straight line. Let A be the given point, BC the given straight line; from the point A there can be drawn an infinite number of straight lines all parallel to BC. Draw AB perpendicular to BC, and AD perpendicular to AB. Take any number of points HE, G, &., in BC, and join AE, A . AG, &c. \ iF The angles BEA and BAE are less than a right yeh : angle; but the angles DAK and BAE are equal to & §— & C aright angle; therefore DAE>AEB. Cut off FAE=AEB. Again, FAE=FAG and GAE; but FAE=AEB>AGE andGAE. Take away GAE, and FAG>AGE. _ Cut off HAG=AGE, &c. The straight lines AD, AF, AH, are all parallel to BC (Eve. I. 27), and it is evident that their number is unlimited. Prop. X. [fa straight line be perpendicular to each of tivo parallel straight lines, it is the least distance between them; and of all other perpendiculars drawn from one of the parallels to the other, that which is nearer to the least 1s less than one more remote; also two equal perpendiculars can be drawn, one on each side of the shortest line. Let AB be parallel to CD; and let EF be perpendicular to both; EF is the shortest distance between them. From G, any point in AB, draw GH perpendicular to CD : GH, and therefore (Euc. I. 19) any line drawn from G to CD is greater than EF. =| K A eee ee adel B If GH is not greater than EF, it is either equal to it DKDaX or less than it. ci NS NY N_, First, Let, if possible, GH=EF; the triangles EFH, GHF, are equal in every respect; therefore EHH=GF;; and the triangles EFG, | EHG, are equal in every respect; therefore ~GLM. Now, we can prove, exactly as in the former case, that if LM=GH, HLN; but HLN is greater than a right angle, because HLM is less than a right angle, therefore HNL is greater than a right angle, which is absurd: LM is therefore greater than GH. Next, if EP=EG, FQ=FH, PQ will be equal to GH, and will make equal | angles with the parallels towards the same side. For PF=FG, and =EF, therefore LG>KE. Also, since E, F, and H are right angles, LGE is less than aright angle, and therefore LGR greater than a right angle. Cut off the right angle LGI; then the triangles LGI, KEP have two angles of the one equal to two angles of the other, but the side LG adjacent to — equal angles in the one greater than KE in the other ; therefore LI is greater than KP (Prop. V.), but LR>LI .:. LR is much greater than KP, and RS>PQ. Prop. XIV. If through the middle point of the common perpendicular to two parallel straight lines, a straight line be drawn perpendicular to it, this line will biseet at right angles all lines drawn so as to make equal angles towards the same side with the given parallels. Let EF be the common perpendicular to the two parallel straight lines AB, CD. Through X, the point of bisection of EF, let XY ; be drawn perpendicular to EF, meeting GH in Y. i ae 1 r : bisects GH perpendicularly. For the triangle EXY= ; = FXY; therefore EY=FY, ~XEY=XFY and =EYX= ° F a 8 FYX: hence ~YEG=YFH, and triangle YEG=YFH ; therefore GY=HY, that — is, GH is bisected by XY. 7 It is also bisected perpendicularly; for m 6ABC >two right angles; which is absurd. "Hence, the angles of a triangle cannot fall short of two right angles. -_ | It must be remembered that this is not put forth as a demonstration : it is merely exhibited to shew what more will suffice to render the demonstration possible. a Cor. \tis evident that the area of a quadrilateral is proportional to its angular defect from four right angles; and that, with this understanding, everything which has been here demonstrated of triangles is applicable to quadrilaterals. Prov. XVIII. Lf from tivo points in one straight line the perpendiculars drawn to \ i. «ate another straight line are equal, so that the lines are parallel (Prop. VI.), and a straight line be drawn from one of the given points to a point in the given line produced on the side towards which the point hes, the exterior angle which this line makes with the line joining the points exceeds the interior opposite angle which it makes with the other line, by the angular defect of the quadri- lateral formed by these three lines and the common perpendicular. Let CE=DF in the figure of Prop. VI., and let any point B in EF produced be ined with D and let BD be produced to . —CDL exceeds FBD by the angular defect of KHBD. For 90°—CDF = 16CEFD (Prop. XVIL., Cor.) = OKHFD (Prop. VL., Cor. 2), Ba CDL+CDF+ FDB = 180°; therefore CDL—FBD=90°—CDF +90°—(FBD + FDB) = dKHFD+6DFB —OKHBD. VOL. XXIII. PART III. 6E 446 PROFESSOR KELLAND ON THE LIMITS OF OUR KNOWLEDGE Prop. XIX. Jf two triangles have the three angles of the one equal, each to each, to the three angles of the other, the triangles are equal in every respect. : Let ABC, DEF, be two triangles, which have the angle A=D, B=E, and C=F, the triangles are equal in every respect. For their areas are equal (Prop. X VIL) If, therefore, AB be greater than DE, AC must be less than DF. From AB cut off AG=DE, and produce AC to H, making AH= DF; the triangle AHG is equal in every respect to DEF; therefore, =03ABC. It follows, therefore, that for the addition of every new triangle equal to ACB, the angle in advance suffers a diminution of more than half the angular defect of the given triangle. It will therefore be reduced to zero, or a negative quantity, by taking a finite multiple of the triangles; after which no point can be found in BC produced which will yield another triangle equal to the original triangle. x Again, let ACB be a triangle of which C is an obtuse angle; and let AX be | drawn perpendicular to BC produced ; then, since both the triangles ABC, AC i are finite, a finite multiple of ABC will exceed ACX. Let ACY be the first | multiple of ABC that exceeds ACX ; ARY the last of the triangles, each equal to ABC, which constitute their multiple. Then the triangle ARY may be treated — as the triangle ABC is treated above; and the conclusion is general: that only . a finite multiple of a given triangle can be formed by joining the vertex with succes- sive points in the base produced. This very curious result is important, as maintaining the consistency of the / results mentioned in Prop. XVII., and it serves as a strong caution against hasty | inferences. | To retain Euclid’s definition of a parallelogram, it is requisite to combine wi th . H RESPECTING THE THEORY OF PARALLELS. 449 it some special definition of the particular parallels which form the parallelogram. For example, we may define a parallelogram as a four-sided figure, of which the opposite sides are parallel, by making the alternate angles with one of the diagonals equal. It will thus be asymmetric figure. Evctip’s definition of a square is at any rate vicious. To alter it consistently with Evciiv’s construction (I. 46), reading it simply as an equisided quadrilateral that has one angle a right angle, becomes an impossibility on our hypothesis. We may adopt the following Definition.—A square is a four-sided figure, which has all its sides equal and all its angles equal. Prop. XXII. The opposite sides and angles of a parallelogram are equal to one another. Let ABCD bea parallelogram ; AC the defining diagonal. 5 The triangles ABC, DCA have the angles CAB, ACB respec- yf if tively equal to ACD, DAC and the diagonal common; there- ; oe ws fore they are equal in every respect; whence the truth of the proposition. Prop. XXIII. The alternate angles which the sides of a parallelogram make with both diagonals are equal. The triangles ABD, CDB are equal in every respect (Euvc. I. 8); whence the truth of the proposition. Cor. Either diagonal bisects the parallelogram. Prop. XXIV. Parallelograms upon the same base cannot be between the same parallels, For if they could, the diagonals of the two parallelograms drawn from the ‘Same point in one of the parallels would make the alternate angles equal; which is impossible by Prop. VII. | Prop. XXV. The point of intersection of the two diagonals of a parallelogram is the | middle point of the common perpendicular to each pair of parallels, which con- stitute its sides. For if from this point a perpendicular be drawn to each of the opposite parallels, there will be formed two triangles equal in every respect (Evc. I. 26) ; and consequently the perpendiculars will be in a straight line. VOL. XXIII. PART III. 6F 450 PROFESSOR KELLAND ON THE THEORY OF PARALLELS. Definition. The point of intersection of the two diagonals is the centre of the parallelogram. Prop. XXVI. Parallelograms upon equal bases may be between the same parallels only when they have the same centre. For if other parallelograms were upon equal bases, the perpendiculars through their centres on one of the parallels would also be perpendicular on the other (Prop., XXV.) which is impossible (Ax. Cor. 2). Prop. XXVII. Upon a given diagonal to describe a square. Let AB be the given diagonal ; it is required to describe a square on AB as diagonal. = Bisect AB in C; draw CD perpendicular to AB, and pro- duce it, and make DC, CE, each equal to AC. ADBE is the square required. The triangles are all equal (Euc. I. 4), whence the con- clusion is obvious. Cor. A square is a parallelogram. ~XXXU.—On the Temperature of certain Hot-Springs in the Pyrenees. By R. E. Scorrsspy-Jacxson, M.D., F.R.C.P., Lecturer on Materia Medica and Therapeutics at Surgeons’ Hall, Edinburgh. (Read 18th January 1864.) Having determined to spend my autumn holiday in the Pyrenees, it occurred - to me that I might add a link to a very interesting chain of observations which was begun by one of the Vice-Presidents of this Society in the year 1885. Twenty-eight years had elapsed since Principal Forpes made his careful obser- vations of the temperatures of certain of the Pyrenean hot springs ; and I thought that if | could repeat his experiments after so long an interval, the results might not be without some interest.* A visit to the Pyrenees in the year 1835 was so far uncommon as to make a description of the places through which the traveller passed a source of enter- tainment to the general as well as the scientific reader ; but now such description would be tedious. Then, too, some remarks were necessary touching the geolo- gical features of the localities where the springs existed; but it is unnecessary to repeat them now, for I am not aware that the explorations into the rocks in search of new springs, or of a more abundant supply of water from the older “springs, have altered the relations as described by Principal Forses. Therefore, respecting the natural aspect of the country, beautiful though it be, and its geo- logical features, I shall have nothing to say; and as I have no new theory of the ‘cause of thermal springs to propound, I need not repeat the speculations with which we are familiar. The temperature of thermal springs is interesting in a variety of aspects. The geologist and the chemist are alike concerned in it, and to the physician it is a question of no slight importance. In the treatment of diseases by mineral waters, temperature is a cardinal element; indeed in many instances the thermal feature appears to be that by which alone the water is characterised as a medi- cine. Physicians who frequent the bathing places during the season when in- valids resort to them, and who have unusual facilities for witnessing the effects of mineral waters, have great confidence in the curative power of heat. In esti- * See Principal Forzes’ paper “ On the Temperatures and Geological Relations of certain Hot Springs, particularly those of the Pyrenees” —Philosophical Transactions, Part II. for 18386. VOL. XXIII. PART II. 6G 452 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE mating the influence of mineral waters three elements are to be considered,— — the water itself, the substances dissolved in it, and the temperature. ANGLADA — has remarked, that water alone, with the aid of certain temperatures, is capable of producing the diversified effects of a crowd of medicines. Thus, he says, the same liquid which, at a temperature of 35° to 37° Cent. may be used as an — emollient, becomes powerfully excitant at from 39° to 41° Cent., and is trans- formed into an energetic irritant from 42° to 45°,—a temperature which the body — can support only for a few seconds (Op. tome ii. p. 381, e¢ seq.) M. Fonray, medical inspector of the waters at Bagnéres-de-Luchon, divides the action of thermal mineral waters into two parts; an emmediate or physiological action, due to the temperature of the water, and a mediate or therapeutic action, due to its mineral ingredients. He remarks that the springs which enjoy the highest and | most enduring reputation are those whose temperature approaches nearest to that of the human body, and is constant. He declares, that by means of different temperatures alone he can, by the use of mineral waters, either allay the nervous susceptibility of a Belle, or excite a very Hercules.* M. Ourcaup, the medical inspector of the waters at Ussat, amusingly describes his establishment as a thermal gamut, having a note, that is, a degree of temperature, for every phase — of disease. But from whatever point of view the subject of the temperature of thermal springs may be regarded, it cannot but be interesting to know whether the tem- perature be constant or variable. “It is a singular fact,” Principal Forses remarks, “that we are not only unacquainted with the progressive variations of temperature in springs during long © periods of time, but even with the diurnal or monthly changes to which many thermal waters are probably subject. The usual statement of the constancy of the’ heat of such springs at all seasons is abundantly general, but perfectly vague.” This statement, made in 1835, does not seem to have induced any regularity of — observations. The same general but unsupported assertions of the constancy ) of the temperatures, from season to season and year to year, were made to me at * “Je crois que l’on doit tenir compte avec beaucoup d’exactitude des températures auxquelles on t administre les eaux thermales, et je suis persuadé, pour ma part, que les mots fortes et faible, que 3 Yon prodigue, sans examen, 4 telle ou telle eau, sont appliqués le plus souvent d’une maniére irreflechie quant a la composition de cau. Que si Von entend par forte la propriété immédiatement excitante d’une eau thermale, elle doit étre bien plutot entendue de sa température que des propor- — tions chimiques des substances qui y sont contenus. Je me chargerais, pour ma part, de calmer Ja susceptibilité nerveuse d’une petite-maitresse avec un bain d’eau de la Grotte de Bagnéres-de-Luchon _ —appliqué 4 + 32 ou + 33 Cent., et d’exciter un Hercule avec la source de la ‘Preste ou du Pré de Cauterets 4 la température de 444° et de +47° Cent.”—Recherches sur les Eaux Minérales, — p. 188. ya + “Dou il résulte que ces bains, disposés successivement comme les touches d’un clavecin, — offrent une série de températures decroissantes, entre 37 et 31 degrés centigrades, qui forment une sorte de gamme thermale modulée selon les divers besoins de la therapeutique.’—Précis sur les Eaua Thermo-Minerales d’ Ussat-les-Bains. OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 4538 most of the thermal stations in the Pyrenees. The utmost that I have met with in the form of a continuous record is contained in work (Eaux Minérales "des Pyrénées) by Professor Firnon of Toulouse. At page 97 of his book, M. Finnon has given a table of observations made at Bagnéres-de-Luchon, at irre- gular intervals between Ist August 1849 and 15th April 1853; but during that period there are only eighty-six days of observation. It is to be regretted that, from one so highly respected and so eminently fitted to undertake the task, we have not a longer and more connected series of observations. But, far from charging M. Fituot with lack of zeal, we owe him a large debt of gratitude for the labour which he has bestowed on the subject, and for his very valuable record. The value of the table is enhanced by the facts that the observations are all made by the same person, exactly at the same points of each spring, with the same instruments, they being verified on several occasions. 'There- fore, as the observer justly remarks, no doubt can attach to his results. From his laborious personal observations, M. FinHo. is convinced that the temperature of springs—even those best regulated and most protected from water of infiltration—7s not absolutelg invariable. With respect to the variability of their temperature, he divides the springs of Bagneres-de-Luchon into two groups. In the first group he places those springs which do not vary more than a few tenths of a degree at the season of snow-melting, when the level of surface water in the galleries is unusually high; and in the second group those springs whose temperature is more variable, the changes being evidently in relation with the height of the surface water. In the latter group, with a change of temperature, there is generally a corresponding change in the volume of water, a lower tem- perature being observed with an increase in the abundance of water. But this is not uniformly so. The increase in the volume of water of a spring, at the season of snow-melting, is not always due to water of infiltration. Occasionally the volume of water is increased without any diminution of temperature ; more than that, there is sometimes a diminution of temperature with a diminution in the volume of water.* M. Fituot believes that springs with a high temperature are less susceptible of variations than those of a low temperature.+ * A diminution of temperature does not always follow the increase of surface water: Dr Garicov, of Ax, says :—“ Plusieurs sources sont, en effet, penetrées par les eaux pluviales ou par Peau des torrents a l’époque des fortes crues, et en méme temps que leur volume augmente, on peut Suivre l’abaissement de leur température et une diminution dans leur richesse en sulfure. Pour deux sources, cependant, j'ai pu, pendant l’hiver, 4 l’époque de la fonte des neiges, constater une élévation de température bien évidente. Pour l’une de ces sources, celle du Rossignol supérieur, la tempéra- ture s’est élevée de 0°7; et pour la seconde, la source Hardy du Breilh, augmentation dans le calorique a été de 1°.” Etude Chimique et Médicale des Eaux Sulfureuses d’ Ax. ’ Tt “Je crois avoir remarqué que les sources les plus chaudes sont celles qui éprouvent le moins de variations ; c’est ainsi que la source Bayen a oscillé, dans l’espace de trois ans, entre 67° 25, et 18:10.”—Op. cit., p. 96. 454 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE M. Ernest Bauprimonv made a series of observations at the Grande-Grille, Vichy, to ascertain what changes mineral waters are subject to in their compo- sition from day to day. At the same time he recorded the temperature of the ~ water, and on several days in September 1850, he notes it as follows; showing an extreme range in eleven days of ‘80 Cent.= 17:44 Fahr.* Day of Month Temperature, Centigrade. Day of Month. Temperature, Centigrade. 3 33°33 y 32°80 5) 33°33 12 33°25 vk 30 14 33°60 Whenever I had an opportunity I put the question, whether the temperature — of the springs varied from day to day, from season to season, or from year to year. — The answer that I received was almost without exception a negative. When I~ asked the question of one of my professional brethren, the reply was often a little modified, ¢7zvzal variations being generally admitted : but when I put the question to an ouvrier attached to any of the establishments, he invariably betrayed — his sense of the importance of uniformity of temperature by a most emphatic denial. The prevailing opinion in the Pyrenees touching the variability of tem- perature of the springs is precisely what has been stated by Dr LAmsBron, in his comprehensive work (Les Pyrénées, et Les Eaux Thermales Sulphurées de Bagnéres-de-Luchon.) He says :—'‘ The variations of temperature to which well secured (bien captées) thermo-mineral springs are liable are generally so trifling (de 1 a 2 degrés), that we may consider the temperature which they bear from the interior of the earth to be constant; and we may attri-- bute the variations to fortuitous causes, operating either in the interior of the globe (as earthquakes), or far more commonly near the surface, as by the infiltration and admixture of surface water. And these variations are so transient, that at the end of a few days, their normal temperature is” restored”’ (p. 414). Suppose it were commonly admitted, however, that slight variations of tem- perature do occur from season to season, important as that may be to the physicia n and his patient, still the larger question, as to a regular and permanent loss or increase of temperature remains to be answered. M. Firnon remarks, that the changes of temperature are not always in one direction; he found the same springs to be sometimes a little above, sometimes a little below their normal temperature. It is possible, therefore, that temperatures taken at long intervals may differ, to a certain extent, without there being any really permanent change. If one observer record the temperature when the spring is abnormally low, and another when it is abnormally high; or one in winter and another in summer, a2 difference of several degrees may be obtained, without the water having per- * Annales de la Société d’Hydrologie Medicale de Paris, t. 1. p. 261. OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 455 manently changed its temperature, but merely having oscillated between these extremes. One advantage derived from a comparison of my observations with those of Principal Forses is that we both observed at the same time of year— namely, in or near the month of August. There are certain circumstances calculated, if not satisfactorily explained, to cast discredit upon the results of an investigation of this kind: they respect the character of the instruments employed; the scrupulosity of the observer; and certain local conditions. 1. Instruments.—One of the difficulties that we have to contend with in com- paring observations made at long intervals, is that of ascertaining the nature of the instruments employed by former observers. Unless the errors of the instru- ments are recognised and corrected, it is quite possible that what may appear to be a change of temperature may be nothing more than the fault of a ther- mometer. Principal Forbes has been most minute in describing the means adopted for the verification of the instruments which he employed; and M. FitHor has also been at great pains to check the errors of his instruments. Knowing that accuracy of result depended greatly upon the character of the instruments employed, I applied to one of the first houses in Edinburgh, request- ing them to make for me four thermometers of the best description, two going to 140° Fahr., and two to 212° Fahr. These were marked respectively, A, B, C, and D. They were tested by Mr Bucuan, the acting Secretary of the Scottish Meteorological Society, who having examined them and compared them with the Society’s standard thermometers, pronounced three of them perfectly accurate, and the fourth very slightly faulty. The latter was rejected. All the instru- ments are very sensitive, the mercury rising in the tubes very rapidly when heat is applied. As thermometer D was used at every spring, returned uninjured. and was again tested by Mr Bucuan and found perfect, I need only describe it. For convenience of carriage, its length is only (from the extreme ends) thirteen inches. It is a simple glass tube without mounting, the scale being marked on the tube, and containing eighteen degrees Fahr. to an inch. The degrees are not subdivided ; but I had no difficulty in estimating the parts of a degree. _ 2. The Observer.—Having obtained trustworthy instruments, the next fear of error was from carelessness in using them. Any error from this source | was particularly anxious to avoid, and fearing that—from the awkward positions in which many of the observations were made—I might, in the reading of a figure or otherwise, make a mistake, I always endeavoured to associate myself with some person of local reputation who would accompany me to the springs, and make an observation with his own thermometer at the same time. After the observa- tion at each of the springs was made and entered in my book, the Centigrade ‘degrees of my associate’s thermometer were reduced to those of Fahrenheit; if the observations accorded, or were within one or two-tenths of a degree, we ‘VOL, XXIII. PART III. 6H 456 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE were satisfied; if they differed more than that, we repeated the observations, — sometimes three or four times; but often failed in the end to bring the two nearer than within two or three tenths of a degree. Both observations are inva- riably given in the descriptive remarks and in the tables. When the tempera- ture was taken at a buvette, or other running stream, a large tumbler was placed under the stream ; the water was allowed to flow into and over it for a minute or — two, until the glass assumed the temperature of the water as nearly as it could — be made to do; the thermometers were then placed in the tumbler, and allowed to remain for a short time, and were then read; the water all the time flowing over the tumbler. When the temperature was taken at the source (to arrive at — which, we usually entered into a gallery or drift, in the floor of which the springs are secured), we dipped our thermometers into the spring, moved them — about from place to place to find the hottest part, and read them whilst immersed. When it was practicable, we plunged the thermometers so low as to bring the © summit of the mercurial column on a level with the surface of the water, but we — could seldom read them in that position, being obliged to raise them a little to — bring them to the level of the eye (the head stooping to the floor of the gallery). Sometimes it occurred that the water was so far below the level of the floor of the gallery that we could not get near the thermometers to read them — whilst they were immersed. In such cases we got a wine bottle, placed the ; thermometers in it, tied a cord round its neck, and lowered it into the water. It filled with the water, and we allowed it to remain some minutes, then hauled it — up and read the instruments as quickly as possible. Sometimes we were placed — in very inconvenient positions, sprawling upon the floor of the gallery, with the head and limbs awkwardly twisted, encumbered with a candle and a thermo- meter, and exposed to an atmosphere resembling that of a Turkish bath; but we never left a spring without carefully repeating our observations several times we when necessary. I most cordially express my thanks to those gentlemen who so I shall have occasion to mention hereafter. We often found it very difficult t record an exact temperature when there was an escape of gas from the waters, or where the water rushed up with force. In these cases, the rippling of the water caused the mercury to oscillate in the tube so rapidly, that it was difficult te read the instrument; but we always endeavoured to catch the highest point. __ have in many instances succeeded in observing at the precise place occupied by Principal Forbes in 1835. In most instances, my observations have probably been made nearer the actual origin of the springs, because at most of the spas OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 457 Ax, I believe the position of observation is identical, for no alterations appear to have been made there since 1835; the place answers exactly to Principal Forses’ description. In my remarks respecting each of the places visited, I have endea- voured to mention these local peculiarities. In describing the points where I have made my observations, I frequently use the word griffon. I must explain the meaning of the expression. It is used rather vaguely to express a near approach to the point where the spring emerges from the ground; but I have used it to signify the point where the water passes from the fissures in the rock into the artificial apparatus constructed for its reception, _where it is, for the first time, securely cut off from all external influences. This securing of the water is termed captage. At this point the water usually issues by several thin streams from the ground, and it is possible that these may have i different temperatures. Care is therefore to be taken in immersing the thermo- meter, to move it about in order to ascertain whether such differences exist. I frequently found that when my companion’s thermometer was placed at a little, even two or three inches, distance from my own, different temperatures were ‘recorded. Usually, it is not until the water has become well mixed, at a little distance from the place where it emerges from the rock, that it acquires a uniform temperature. All my observations were made in the month of August 1863. f EAUX CHAUDES. Here I had the kind and able assistance of Dr PRosPeR DE PiETRA-SANTA, : physician to the Emperor, who resides during the bathing season at Eaux Bonnes. ‘He kindly accompanied me to Eaux Chaudes. The thermometer employed by M. “Prerra-Santa was made, I believe, by Fastr& of Paris, and was, as I understood, quite accurate. I measured it with my pocket tape, and found it to contain eh degrees of Centigrade to an inch, or forty-five degrees of Fahrenheit, Which on my own thermometer (D) occupy a space equal to two inches and The thermal establishment which existed in 1835 has since been pulled down, d the waters are now administered in a handsome building, constructed in the rs 1848-50 by MM. Francois and Larapie. The new establishment is built upon the right bank of the Gave, at a distance of only a few yards from the ‘site of the oldone. This change of position, however, must necessarily affect the mperature of the water at the place where it is employed by the invalid, the distance between the bwvetics and the griffon of certain of the springs being as much greater now than it was in 1835 as the distance between the old and the Tew establishments. The effect of this change of position, I was informed, was decidedly injurious to these springs, whose waters are now conducted a greater distance in pipes. 458 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE Of the six springs in use at Eaux Chaudes, three are conducted into the estab- — lishment, and these are they which are affected by the change of position. They are named Le Clot, L’Esquirette, and Le Rey. The other three are employed at the several points at which they rise ; they are called Baudot, L’ Arressecq, and Mainvielle. Le Clot.—This spring is received, at its point of emergence, into a reservoir which is hermetically closed. From this reservoir the water is conveyed by two conduits to the establishment—the one leading to the baths, the other to the buvette. The water, doubtless, loses a certain quantity of heat during its passage from the actual source to the buvetie ; and I was told, moreover, that, in spite of every effort to preserve it from decomposition, the amount of sulphuret of sodium — in the water is much less at the baths and the buvette than at the griffon. The loss of temperature at the buvette | was unable to ascertain, as I had no oppor- tunity of testing it at the griffon. The actual temperature observed by me at the buvette was 94:00 Fahr. At the same time, M. pr PreTra-Santa read his ther- mometer at 34°50 Cent. = 94°10 Fahr. L’Esquirette.—This spring has been divided into two parts by a recent explo- — ration into the rock ; they are termed respectively hot and temperate. ‘The hot. stream is conducted to a buvette in the establishment, and supplies also, in com- bination with the temperate stream, the baths and douches. The distance between — the griffon and the buvette of this source, I was told,* is 30 metres, equal to 98°427 English feet. The temperature observed by me at the griffon was 93:80 Fahr. M. pe Prerra-Santa recorded 34°20 Cent. = 93:56 Fahr. At the buvette I found the temperature to be 92°40 Fahr.; M. DE PierRa-Sanva, 33°50 Cent.= _ 92°30 Fahr. :. Le Rey.—This spring rises on the site of the old establishment, and is im- . mediately received into a reservoir, whence it is conducted to the new establish- j ment. The distance between the grigon and the buvette I did not ascertain. Thetemperature recorded by me at the reservoir was 91°40 Fahr., M. pz PieTRa- Santa at the same time recording 33:00 Cent. = 91:40 Fahr. At the bucette I recorded 90:00 Fahr , and M. bE PieTra-Santa 32:00 cent. = 89°60 Fahr. ; Baudot.—The temperature of this spring was taken at the buvette, close to its 4 point of emergence from the granite. My thermometer marked 77-00 Fahr. ; M. ry DE PIETRA-SANTA, 25:00 Cent. = 77:00 Fahr. - L’ Arressecg—The temperature of this spring was also taken at the point ‘ where it leaves the granite. My thermometer marked 74:90 Fahr.; M. pz Prerra- Santa, 24°00 Cent. = 75:20 Fahr. J Mainvielle—The temperature of this spring was taken at the buvette, which is * The distances mentioned throughout are such as were told me by the gentlemen who accompanied me to the several springs. I had no opportunity of measuring them. OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 459 placed immediately in contact with the grzgon, or point of emergence, at the foot of a block of granite. The temperature recorded by me was 51°80; M. DE PIETRA- Santa recorded 11:00 Cent. = 51:80 Fahr. The following table shows the temperature of the springs at Eaux Chaudes, as recorded by different observers at various periods. I give the Centigrade as well as the Fahrenheit reading of the temperature. : L’Esquirette. Le Rey vame ever, Le Clot. A a ze : E Baudot. L'Arressecq. Mainvielle. meee ervation. eas (Griffon.) (Buvette.) (Griffon.) (Buvette.) ore epee aes F. C. F. Cs F. C. 1, C. 195 C. F. C. F. C. Ihe C. orbes (July 1835), . | 94:60 | 34-78 | ... ee | e405 1938:00) |) en. ... | 92:00 | 83°35 | 80-20 | 26-78 | 76:30 | 24-62 tan (Sept. 1835), . | 97:07 | 36:15) ... ... | 89°60 | 32:00 Pe ... | 92°57 | 33°65 | 81:05 | 27-25 | 77-18 | 25:10}... Boe itan (Sept, 1837), . | 96°80 | 36:00 | ... wee | 00208) (ha: 60). .-- | 98:20 | 34:00 | 80-78 | 27-10 | 77-18 | 25-10 | 52-25 | 11-25 S| 9680 (2600). | ver | ee | us Pee Peon (OR BON8H00) ct fo Pea | we) ae | sor Filhol (1850), . | 93°38 | 34:10| ... eteu |p etort= aan onc ... | 94:64 | 34°80)... Scie Ace nee 6 ze monnier (1860), . | 97°16 | 36:20 | 95-00 | 85:00]... ace 92°30 | 33°50; ... --- | 77-00 | 25:00 | 76-64 | 24-80 | 52-70 | 11:50 Pietra-Santa (1863), | 94°10 | 34:50 | 98:56 | 34-20 92:30 | 33-50 || 91:40 | 33-00 89-60 | 32-00 | 77-00 | 25-00 | 75-20 | 24-00 | 51-80 | 11-00 | resby-Jackson(1863),| 94:00 | 84-45 | 93-80 | 34-33 | 92-40 | 83-56 | 91°40 | 83-00 | 90-00 | 32-22 | 77-00 | 25-00 | 74:90 | 28-85 | 51-80 | 11:00 | EAUX BONNES. At Eaux Bonnes, also, I had the able assistance of M. pe Pimrra-Sanra. There are several springs, but three only were available for my purpose, the rest being mixed in such a manner as to prevent the temperature of each being taken separately. The springs whose temperature I tested were La Viewlle, Source du Bois, ou Source Froide, and Source d’ Orteich. Both the griffon and the buvette of La Vieille Source are within the thermal establishment, and are within four feet of each other, being separated only by a wall, through which the water is conveyed by a short pipe. At the griffon, the temperature was not easily taken. The chamber in which it is situated was gloomy, so that we could not read the thermometers without the aid of a candle; and even with that aid we could not read them whilst immersed in the water, the opening into the spring being very narrow, and the column of mercury, when the bulb was immersed, being below the level of the opening; that is, below the fioor of the chamber. Even*with my face touching the floor and close to the opening, Tcould not read the thermometer without raising it several inches, and when I did see the column it was subsiding so rapidly that I could not be certain of having seen it at its highest point. To obviate this difficulty, we placed the thermo- meters in a wine bottle, which was then lowered into the water, filled, and allowed to remain until the bottle assumed the temperature of the water. It was then withdrawn, and the thermometers were read whilst yet immersed in the water. The temperature recorded by me was 91:20 Fahr.; that by M. pz Pietra VOL. XXIII. PART III. 61 460 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE Santa, 32 75 cent.=90°'95 Fahr. The temperature was taken also at thebwvette, and was found to be, as nearly as possible, the same as at the griffon. Source du Bois, or Source Froide.—The temperature of this spring was taken — at a little reservoir (about 6 feet by 3) at the point where the water issues from the rock. My thermometer recorded a temperature of 54:80 Fahr., M. pz PrerRa Santa, 12:80 Cent.=55:04 Fahr. Source @ Orteich.—This spring arises in the Vallée du Valentin, where an establishment is now building. The temperature was taken at the buvette, which is placed immediately over the griffon, and was recorded by me at 72°30 Fahr., and by M. bE Pretra-Santa at 22°50 Cent.—72°50 Fahr. The following table shows the temperature of the springs at Eaux Bonnes, as recorded by different observers at various periods :— Name of Observer and Date of Observation. 5 La Vieille. Froide. ; Orteich. Fahr. Cent. Fahr. Cent. Fahr. Cent. Professor Forbes (July 1835) . . . | 91:40 | 33:00 | 54-40 | 12-45 M, Hentan: (Oct, 1839). (= sags Si. 92:03 | 33°35 | 55:04 | 12°80 M. Fontan«(Sept:.1837) . 46 9s 91°96 | 33°32 | 55:40 | 13:00 Mid Ginttvac (MOAI Nec oy aay yal Be be 91°76 | 33:20 | 55-40 | 18:00 Professor Filhol (1850) . . .. . 89:96 | 32°20 | 53:96 | 12-20 Professor Filhol (1861) . . 90:95 | 32°75 | 55°94 | 13°30 MM. Francois and Pietra-Santa (1862) 90:95 | 32°75 | 55:04 | 12°80 M. de Pietra-Santa (Aug. 1863) . . 90°95 | 32°75 | 55:04 | 12°80 Dr Scoresby-Jackson (Aug. 1863)... 91:20 | 32°89 | 54:80 | 12°67 CAUTERETS. At Cauterets I was kindly received by Dr Buron, and had some conversation with him; but he had been for some time, and was then, suffering from severe illness, and was consequently unable to assist me in my researches. He wa good enough, however, to introduce me to his friend Monsieur bE LALANDE, a gentleman who has travelled extensively, and has had great experience in chemistry and engineering; and also to Monsieur Broca, an experienced phar- macien, who has made himself thoroughly acquainted with the mineral waters of measuring See The mineral springs in the vicinity of Cauterets are numerous, and are dinall dd according to their position relative to the town, into two groups, named respec tively Southern and Eastern. The eastern is the northern group of some autho and occasionally the springs of Za Raillére are separated into a group by them- OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 461 selves, called Central. Commonly, however, and sufficiently for our present pur- pose, they are divided into southern and eastern groups. Southern Group. The springs of this group emerge from the granite. We visited them in the following order :— La Raillere—The water of this spring is conducted into an establishment constructed at its source. We took the temperature first at the buvetie, where my thermometer marked 101-30 Fahr., at the same time the thermometer of MM. ve Latanve and Broca marked 38°70 Cent.=101:66 Fahr. We then passed to the back of the building and observed the temperature at the griffon, which is five and a half metres (=18°044 English feet) from the buvette. Here I found the temperature to be 101:80, whilst MM. p— LALANDE and Brooca gave it as 39:00 Cent.=102:20 Fahr. Mauhourat.—There are two drinking places to this spring,—one at a distance of two metres (= 6°562 English feet) from the griffon, and the second at a dis- tance of 260 metres (=853:034 English feet). The buvette at the latter point is known as the Petit Mauhourat. and was constructed for the convenience of in- valids who may find it too fatiguing to go to the principal buvette near the griffon, the Petit Mauhourat being 260 metres nearer Cauterets. The water is conducted from the source to the more distant buvette by means of pipes. The temperature recorded by me at the distant buvette (Petit Mauhourat) was 117-150 Fahr., that by MM. pe Lauanpe and Broca 47°50 Cent.=117'50 Fahr. At the principal buvetie, near the source, my thermometer marked 121-00 Fahr., that of MM. pr LALANDE and Broca 49 50=121:10 Fahr. Les Gufs.—We observed the temperature of this water at three points,— namely, at the griffon; at the buvette 300 metres (=984-270 English feet) distant from the griffon (nearer Cauterets, and in the same building as Petit Mauhourat) ; and again 1400 metres (=4593°259 English feet) below the latter point (or 1700 metres from the griffon) at the Pont de la Raillere. It is intended to carry the | water of Les Hus into Cauterets by means of pipes, the operations for which had been conducted only as far as the Pont de la Raillére, hence I had an opportunity | of recording the temperature of the water there. The distance still to be accom- | plished, from the Pont de la Raillere to Cauterets, is 1200 metres (=3937:079 English feet). The temperature of the water at the several points of observation | was as follows :— Thermometer D. MM. de Lalande and Broca. Griffon, ‘ : ‘ : 131:00 Fahr. 55:00 Cent. = 131-00 Fahr. Buvette 300 metres from griffon, 128:00_,, 33/50) 5 -==128°30'" -, Escape 1700 metres from griffon, 119-00 _,, 48700) 7s = 119°30 Le Pré.—The temperature of this water was taken at the buvette, which is 462 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE constructed at a distance of 15 metres (=49 213 English feet) from the griffon. The temperature recorded by me was 117:40 Fahr., that by MM. pr LALANDE and Broca 47°50 Cent.=117°50 Fahr. Petit St Sauveur.—The temperature of this spring was taken at the griffon. — I found it to be 93-00 Fahr. MM. pe Latanpe and Broca recorded 34:00 Cent.= | 93°20 Fahr. Eastern Group. These springs issue from metamorphic schist. lowing order :— . César.—We observed the temperature of this water at three points,—namely, — at the griffon ; at the buvette in the building near the source (distance of this buvette from the griffon 60 metres =196-854 English feet); and at the buvette of the establishment in the town (distance of this buvette from the griffon 350 metres =1148-350 English feet). The temperature of the water at the several points of observation was as follows :— We visited them in the fol- Thermometer D. MM. de Lalande and Broca. Griffon, 117-40 Fahr, 47-50 Cent, =117:50 Fahr. Buvette near the oriffon (60 metres), LIG:30 \,, 47:00 , =I166o Buvette at the establishment (350 metres), 114:00 _,, 45°60. , =11¢080 Espagnols.—The temperature of this spring was observed only at the griffon, where I found it to be 115°50 Fahr., and at the same time MM. pr LaLanpeE and Broca recorded a temperature of 46-60 Cent.=115°88 Fahr. a Pauze.—The temperature of this water was observed at two points,—at the grifon, which is not more than 80 centimetres from the griffon of Espagnols ; and again at the buvette, which is distant 10 metres (=32°809 English feet) from 1 the griffon. The temperature recorded was as follows :— MM. de Lalande and Broca. 43:25 Cent. =109°85 Fahr. 39°15 = 102°47 Thermometer D. 109-75 Fahr. 102:30 ,, Griffon, Buvette, . 2? Pe The following table shows the temperature of the principal springs at Cau- terets, as recorded by different observers at various periods :— Name of Observer, Railltre. Mauhourat. Gufs. Petit St Sauveur.| Pauze-Vieux. César. an, a . Buyette of 4 £ wy : Date of Observation. Griffon. Griffon. Griffon. Griffon. Griffon, Griffon. ine (G. 1 C. F, (OE F, Ge 1 C. F, M. Arago (1826), . {101-12} 38-40 |121-28 | 49-60 te ce: 1138-00 | 45:00 |117-68 Professor Forbes (Aug. 1885), . |101-90| 88-80 |121-70 | 49:80 |180-10 | 54:50 | 90-60 | 82°50 |110-30 | 43:50 |118:10 4 M. Fontan (Sept. 1835), 102:65 | 89-25 |121-37 | 49-65 91-40 | 33-00 |1138-00 | 45-00 {118-49 | 4 M. Fontan (Sept. 1837), . he 122-00 | 50-00 vee ine M. Gintrac (1841), 101-80 | 88°50 {122-00 | 50-00 |1381:00) 55-00 118-40 Professor Filhol (1850), 102-20 | 89-00 |120-20 | 49-00 |181-00 | 55:00 119-30 epee in we \ (Aug. 1863), [102-20 | 39-00 |121-10 | 49-50 [131-00 | 55-00 | 93-20 | 34-00 [109-85 48-25 [117-50 Dr Scoresby-Jackson (Aug. 1868), |101-80 | 88°78 |121-00 | 49-45 |131-00 | 55:00 | 98:00 | 83-90 |109:75 43-20 |117:40 ON CERTAIN HOT-SPRINGS IN THE PYRENEES. 463 ST SAUVEUR. There are several mineral springs at St Sauveur, but only two of importance, namely, La Source des Bains, and La Hontalade. As the water of the latter is nearly cold, I did not think it of importance to test the temperature accurately. Unfortunately, I had not the advantage of a good second thermometer at St Sauveur. M. CHARMASSON DE PUYLAVAL, to whom I was indebted for some atten- tion, showed me a broken thermometer with which he had carefully taken the temperature two years previously. I believe the instrument was made by either SALLERON or F'asrre& of Paris, and appeared to have been such as that used by MM. pz LALANvE and Broca at Cauterets. In company with M. pr Puyuavat, I visited the establishment which is sup- plied with water by the Source des Bains. This spring is now isolated from the rest, and has been traced for several yards into the rock, whence it is led by means of a pipe into the establishment. I tried the temperature at the bath and douche nearest the source (according to M. pe PuyxaAvat, 10 or 12 metres from the actual source). I found the tem- perature to be 93°50 Fahr. M. pe PuyLavat tried the temperature with a common bath thermometer, and found it to be 34:50 Cent. (=94:10 Fahr.) and stated that it corresponded exactly with his previous observation made with the now broken thermometer. I then tested the temperature in the bath-room furthest from the source (about 35 metres distant from the actual source, I was informed), and found it to be 93:00 Fahr. With the bath thermometer, M. Puy- LAVAL stated it to be 33°80 Cent. (=92°84 Fahr.), and that it corresponded with his previous observations. Lastly, I obtained permission to enter into the excavated rock, and tried the temperature at a robinet, which I understood was within two metres of the actual source, where I found the temperature to be 94:00 Fahr. M. pre Puyiavat had never taken the temperature at that point, and did not accompany me into the gallery. The observations made by Professor Forses upon the temperature of the ‘spring which supplies the establishment were not satisfactory. He says,—‘* We have stated that there are reservoirs belonging to the thermal establishment of ‘St Sauveur. The consequence is, that the temperature perpetually varies. Ihave Tepeatedly tried it at the ‘ Buvette.’ Thus on the 20th of July 1835, I found it to be 90:2; and on the 24th, only 88:8.” The temperature observed at the Ltobinet de la Douche by various observers at different periods is given in the following table :-— Centigrade. Fahrenheit. M. Fontan (September 1835), . : ; : 3450 = 94:10 M. Fontan (September Se : , : : 34:50 = 94:10 M. Gintrac (1841), ; - : ; 3450 = 94:10 Professor Filhol (1850), . : : 34:20 = 93°56 Dr. Scoresby-Jackson (August 1863), J : 3417 = 93-50 VOL. XXIII. PART III. 6K 464 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE BAREGES. I visited Baréges after leaving St Sauveur, and on the same day observed the temperature of the springs at both places. At Baréges I had the able and cordial assistance of Dr Le Bret, the medical inspector of the establishment, and well known as one of the editors of the Dictionnaire Général des Eaux Minérales. The establishment at Baréges is so constructed that the griffons are not approachable. There are no galleries, the water being conducted immediately into the baths, which are built close to the actual sources. The only experiment — which I made at Baréges was on the temperature of the Zambour (called also Grande-Douche). Tobserved the temperature of this spring at the Buvette of the — new establishment, the distance, as I understood from Dr LE Bret, between the point of observation and the actual source not exceeding one metre. I observed — the temperature with thermometer D, and at the same time Dr Lz Bret observed it with his own thermometer, which was a much shorter instrument than mine, — and the Centigrade degrees were closely marked. ‘The result of our observations was as follows :— Fahrenheit. Centigrade. Difference (Fahr.) Thermometer D, ‘ : ? 109:10 = 42°83 1-20 Dr Le Bret, ; : : : 110:30 = 43:50 The difference between our observations could not be reduced by the most careful repetition, and therefore I concluded that the thermometers were at vari- ance. On returning to Dr Le Bret’s house, I placed both thermometers in a tumbler of cold spring water, and having allowed them to remain a sufficient length of time, we both examined the instruments with the following result :— Fahrenheit. Centigrade. Difference (Fahr.) Thermometer D, . : : : 64-40 = 17°83 1-90 Dr Le Bret, : : : - 65°30 = 18-50 By this experiment I conclude that our observations at the spring were both correct, and that between the temperatures 18°50 and 43°50 Centigrade, Dr Lz Bret’s thermometer marks 1:20 Fahr. higher than mine. Dr Le Bret kindly furnished me with the results of observations made by Professor FirHot in 1862; they will be found at length in the Annales de la Société @ Hydrologie Medicale de Paris, tome neuvieme, p. 369. I give them along with others in the following tabular form :— r. ON CERTAIN HOT-SPRINGS IN THE PYRENEES. 465 Tambour or Grande Douche. L’Entree. La Chapelle, Polard. Name ee Spores IR, C; 12, C. 1, C. F. C. F. C. F, C. F, C. 18), C. Means20), =. «| oe ... {111°88 | 44:10 | 99-87 | 387-7 Joo Ih ene as ale a 200 one sce) SB As | Sy7/el! Forbes (July 1835), sles .-. |111°9 | 44:39 104-4 | 40-22] ..,. son |teXerh || SHIRSKOY oRs son || BRO WSS |) one io ntan (Sept. 1835), .| ... ... |112°55 | 44°75 104-55) 40°30) ... cee |) RY) | GLO © ce ay ane .» | 99°18 | 37-30 ntan (Sept. 1837), .| ... ... |112°55 | 44:75 |104-72| 40:40] ... RCO SON Olson wen. ae sate ... |101-40 | 38°55 Beged),...| ... | ... {i1s00}4500) ... | ... |... |... | 8780] 31-00 sor Filhol (1850), .| ... Pee 2 20:45)) 48:608 wa ste 0 | 80-98) | 31-10 3c Ads 98:60! 37-00 sor Filhol (1862), . |109-40| 43-00 |111:38/ 44-10) ... +. {10400} 40:00] .., ... | 91°40 | 83-00 1 Cabinet No Bret (Aug. 1863), . [110-30] 43-50 Ie £ resby-Jackson (1863),/109-10 | 42-83 A ; BAGNERES-DE-BIGORRE. At Bagnéres-de-Bigorre, I had the kind and able assistance of J. MaxweELt- Lytse, Esq., an Englishman of scientific attainments, who has resided in Bagnéres for eleven years. The temperature of the springs was observed very carefully by means of several instruments. I used, as on all occasions, my ther- mometer D. The instruments employed by Mr Lyre were A, a thermometer made by Gremer of Berlin, and sold in London by Horne & Co. of Newgate Street. The degrees on this instrument were marked, both in Reaumur and _ Fahrenheit, forty-five of the latter corresponding to an inch of my pocket tape- _B, a thermometer made by Fasrre& of Paris, with a maximum index; this instru- ment had twelve Centigrade degrees to the inch of,my tape. C, a thermometer (lent for the occasion by M. Souserviz, medical inspector at Bagnéres) by - Fasree of Paris, having eight degrees to the inch of my tape. Before leaving Mr “Lyrtr’s house, we dipped three of the thermometers (we had not then got M. SOUBERVIE’S instrument) into a large beaker, containing cool spring water. The result was as follows :— Fahrenheit. Thermometer D, : ; ; 2 : ; : 5 78°40 Greiner’s thermometer, : ; , : : : 5 77°50 Maximum, 2 : k ; ; : . 25°70 Cent.= 78:26 In the following remarks, I shall speak only of the temperature as recorded by thermometer D and the maximum thermometer, as there was less difference _ between them than between the other instruments and mine; but I have kept a record of the temperature afforded by all the instruments. | We first visited the establishment known as Le Salut, between six and seven _ hundred yards from the town. There we observed the temperature of three Springs, namely :— * See explanation of difference in text. 466 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE 1. Source de la Montagne.—The temperature of this spring was taken at its source in a gallery, excavated at a little distance from the building. 2. Source de (Interieur.—Temperature taken at the luvette in the building, the distance from that point to the actual source, as I understood, being about one metre. 3. Source de la Pompe.—Temperature taken at the buvette in the building, being, as I understood, close to the griffon. The temperature of the three springs was as follows :— Thermometer D. Maximum. Source dela Montagne, . : , 89:00 Fahr. 31°60 Cent.= 88°88 Fahr. La Buvette de l’Interieur, ; : 87°80: ,, 90°90 >, :=87-G2zaan Source de la Pompe, ; : 5 Br00) 1, 3040 , =86-72— Afterwards, accompanied by a workman to remove the coverings, we visited the sources of the springs which supply the principal establishment situated in _ town. We visited the springs in the following order :— 1. Source du Platane.—At this spring we could easily read the thermometers — whilst immersed in the water. 2. Source du Foulon.—Here the water was too far below the floor of the gallery to permit of our reading the thermometers accurately whilst in the water. We therefore placed the instruments in a quart bottle, which was lowered by means of a cord into the water, filled, and allowed to remain several minutes. It was then raised, and the thermometers were immediately read before their re- moval from the bottle. ; 3. Source du Dauphin. —At this spring we could readily read the instruments whilst immersed in the water. : 4. Source de la Reine.—The approach to this spring is not so easy as to tk as others. We were able to read the instruments distinctly whilst immersed in the water. We also took the temperature of the water of La Reine at the buvette in the establishment; the distance between the latter point and the actual sour where we had previously observed it, being, as I understood, about 100 metres (328 English feet). q 5. Source de Salies.—This spring rises in the open space, about twenty paces | from the right-hand corner of the establishment (the observer looking at the front of the building). At present the spring is open, half a dozen steps leading down to it; but it is proposed to extend a wing of the establishment over it. The temperatures observed were as follows :— Thermometer D. Maximum. Source du Platane, . 4 : 92°30 Fahr. 33:40 Cent. = 92°12 Fahr. Source du Foulon, . : . 95:00 _,, 35°00 _,,. = 95:00) 058 Source du Dauphin, . 2 Ligs-40 ', 48-40" ,, =T19- 12am Source de la Reine (griffon), 5 115-00)" ,, 4600 . =1148008 (buvette) : 110:40 ,, 43°50 , =110°300m Source de Salies, : : : 123-00... 50°45 ,, =122: dhe OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 467 The following table shows the temperature of several of the springs at Bag- néres-de-Bigorre, as recorded by various observers at different periods :— Foulon. Dauphin. La Reine. Salies. me = Pere ha Otservation, Griffon. Bath Griffon. Conduit. Griffon. Conduit. Buvette. Griffon. F, C. F C. 185 (OF F, C. 12% C. F, C. iB C. Ee C. ) (1826), . 5 ae ... |114:80] 46:00] ... ae 122-90 | 50°5 bes (Aug. 1835), . 93-20)/34-00 119-0 | 48°33 114-0 | 45:6 | 95:54'35-30 ; Moet 1836),. .) .. | ... | {Rorsnot. } [122-00 | 50-00 115-88 | 46°60 125-24 | 51:80 n (Sept. 1837) , Bile 94:10/84:50 |118-94 | 48-30 11570 | 46-50 12398 | 51:10 Filhol (1861),. . | 95:90 | 35-50 119-75 | 48°75 115-70 | 46:50 a ... [123-44] 50-80 ll-Lyte, Esq. (1863),| 95-00 | 85:00 119-12 | 48-40 11480 | 46:00 110°30 | 48-50 |122°81 | 50-45 by-Jackson (1863), | 95:00 | 35:00 119°40 | 48:55 115:00 | 46-11 110-40 | 43°55 |123:00 | 50°55 af BAGNERES-DE-LUCHON. ; I spent several hours in the galleries at Luchon, and observed the tempera- ture of many, but not of all, the springs. My notes of the temperatures are before me now, but I scarcely think they are calculated to fulfil the present - object of determining whether the temperature of these springs be constant or “not. So much engineering skill has been spent upon the excavations at Luchon ‘that I suppose Principal Forzes, who visited the place in 1835, would scarcely _ Tecognise the places where he dipped his thermometers; and, as still further exploration is determined upon, probably in a short time the places where I made Sy observations will be obliterated. Another reason why I am not anxious to pub- lish my observations made at Luchon is, that I had no second thermometer whereby to check the reading of my own. Unfortunately Dr Lamsron, from whom I re- ceived much attention and kindness, had left his thermometer in Paris; and M. Fontan, the talented inspector, from whom I also received much kindness, had in ke manner left his thermometer at his winter residence. I was accompanied “into the galleries by an intelligent workman, who afforded me all the assistance ‘in his power ; but I am not sure that he clearly apprehended my questions, though he never failed to make a very spirited reply. For the temperatures of the springs ‘Imust refer to the works of M. Fontan, Dr Lampron, and M. Frinyot. a I spent a short time at the baths of Ussat (Ariége), and noted the temperature of the springs. I was kindly aided by Dr Ourcaup, the medical inspector, in “whose work will be found a notice of the temperature, and of other matters of interest connected with the mineral water. AX ARTEGE. For determining the question of the variation of the temperature of mineral VOL. XXIII. PART III. 6 L 468 DR R. E. SCORESBY-JACKSON ON THE TEMPERATURE springs, Ax was in some respects the most interesting of the places visited in the Pyrenees. At Bagnéres-de-Luchon, art had been so well applied to render the place as attractive as possible to summer visitors, that no trace of the natural — outlet of the water upon the surface of the ground remained; and even the appointed places for its escape had frequently been changed. But at Ax nature had been left almost undisturbed; the mineral waters were still oozing from their natural crevices, and the Place du Breilh still answered exactly to the diagrams given in Principal Fores’ paper of 1836. At Ax I had the able assistance of Dr Garricou, medical inspector of the waters. He mentioned that he had examined no less than seventy-eight distinct — springs, and that he had since discovered many others. I observed the temperature of several springs; but I need mention only two, — namely, the Canons and Rossignol. That the temperatures of these springs were observed exactly at the same places as they were by Principal Forses in 1835 is almost certain, for there appears to have been no change whatever made in the Place du Breilh. Dr Garricou was decidedly of opinion that the places of obser- vation were identical. The thermometer used by Dr Garricou was made by Fastre& of Paris, and contained eight degrees of Centigrade to the inch of "a tape: I made use of my thermometer D. Canons.—The temperature of this spring was ascertained at the taps (in the Place du Breilh), from which it issues in full streams. The water is utilised at this spot by the inhabitants of Ax, and at the time of our observations (about eight a.m.) several women were at the taps washing vegetables. We borrowed a — large tin vessel from one of them, and allowed the water to fill and overflow it for a few minutes. We then immersed our thermometers, the water from the tap continuing to flow into and over the vessel. We did this at both taps, and carefully observed the temperature several times. The temperature recorded was :— Dr Garrigou, : , : : 74:80 Cent. = 166°64 Fahr. Thermometer D, . : : : Ps 166:20 ,, Difference, 44 Rossignol.—Exactly at the spot indicated by Principal Forses (and, if I re- member rightly, about 20 feet from the taps of the Canons), a large stone — Alinsed our dlisctnem eters at once into the water as it flowed to its chase under the street. The temperature recorded, after several observations, was,— Dr Garrigou, : ; ‘ : 77°50 Cent. = 171-50 Fahr. Thermometer D, . : : : bee 17100" =; Difference, ‘50 OF CERTAIN HOT-SPRINGS IN THE PYRENEES. 469 There is therefore a difference of half a degree of Fahrenheit between our observations in the one case, and of nearly the same amount in the other. I remember that Dr Garricou explained to me that the difference was probably due to a slight alteration in his thermometer. I made a note of his remark at the time, but have mislaid it, and I can scarcely venture to repeat it from memory. But whilst, on the one hand, Ax is one of the best places for testing the con- stancy of the temperature of hot springs, because of the locality not having un- dergone any material change; still, on the other hand, perhaps but little depen- dence can be placed upon the results, in consequence of the exposure of the water in its course to many external influences. Dr Garricou has noticed that the temperature of most of the springs at Ax varies with the season, and he adds: Il west pas étonnant qua Aa, ov les sources sont mal captées, au miliew @alluvions, et dans le voisinage de plusieurs rivieres, on ait observé des variations fréquentes dans les indications fournies par le thermometre. The following table shows the temperatures recorded by various observers at different periods :— Name of Observer and Date of Observation. canons: Rossignol, aps. Griffon. Fahr. Cent. Fahy. Cent. M. Pilhes (1786), . . a ere 168-98 76°10 te pf Professor Forbes (1835), rs 168:0 75'6 161:2 71:8 Bieboman(1835)) -. . wi. es 168:26 75:70 166-12 74:50 Micmac (1841) 2 2. et 167:00 75:00 163°40 73°00 M. Roux (1842), . tie oS ile SEM 168:°26 75°50 166°12 74:50 Professor Filhol (1853), . Syn eee 167-72 75°40 171-50 77°50 Dr Garrigou (1861, summer), . . . 167°36 75:20 170:96 77:20 Dr Garrigou (1862, winter), . . . 167-72 75°40 172:04 77°80 Dr Garrigou (1863, August), . . 166-64 74:80 171-50 77°50 Dr Scoresby-Jackson (1863, August), 166:20 74:55 171:00 0'22 From these observations it would appear that whilst there is, perhaps, in no ‘instance a permanent change of temperature, neither is there in any an undevi- ating temperature. It is probable that the temperatures of these springs in the interior of the globe have undergone no change, and that the changes observable | upon the earth’s surface are due to superficial and evanescent causes,—such as | external temperature, the infiltration of cold surface-water, and the like. Toa | certain extent, an allowance must be made for inaccuracies; for it is scarcely to | be supposed that all the observers dipped their thermometers exactly at the same | points, nor do I know that, in all cases, errors of instruments were recognised and corrected. ‘ ; % fy “i! is -~ TIME 2A 2 2PZ (922008 7whoy SuPLy C: 441%.) XX XIII.—On Superposition. By the Rev. Puiuip Kevxanp, M.A., F.R.S., Pro- fessor of Mathematics in the University of Edinburgh. Part-II. (Continued from Vol. X XI. p. 273.) (Plate XX.) (Read 7th March 1864.) In my former paper on the subject, I selected the following problem :— From a given square, one quarter is cut off, to divide the remaining gnomon into four such parts that they shall be capable of forming a square. The gnomon is, I assume, incapable of being formed into a square by being cut into three parts, and consequently the number of different ways in which it can be so formed, by cutting it into four parts, must be very limited. But, to show the fertility of the method of superposition, 1 exhibited the solution of the problem in twelve different manners. Many of these, no doubt, have much that is in com- mon, whilst, on the other hand, some (such as the 12th) differ in every feature from the rest. I had thoughts of following up my plea for the study of the old geo- metry, by exhibiting the solutions of the 47th proposition of Euclid’s first book in their beautiful variety. I have indeed temptation to do so. The modifica- tion which I gave of the demonstration of this proposition in the notes to my edition of Playfair’s Geometry (edition 1846, p. 273), has had the honour of being exhibited in two different mechanical forms. The first by two rotations without sliding, whereby the two squares on the sides, when placed together, are con- verted into the square on the hypothenuse; the second, by two transpositions (slidings) without rotation, whereby the same change is effected The former is obvious enough, and could have escaped nobody. ‘The latter is described by Professor Dr-Morean in the “ Quarterly Journal of Mathematics,” vol. i. p. 236. I venture, however, to think that the problem before us is still more curious, as an exemplification of the method of superposition, than the 47th of Euclid’s first book. With this feeling | have overcome the hesitation I long experienced In presenting the following twelve additional solutions to the Society. The solu- tions are numbered in continuation of my former paper, and the values of x and a are the same as in that paper. Constructions and Demonstrations. XIIl.—BY=2, EG=a—a. Place (3) and (4) on (1) as in the second figure, they will just fill the diagonal of (1). And since the remaining portion of the first figure is a rectangle, whose sides are a and x—a, it exactly completes the second figure ; hence the conclusion. VOL. XXIII. PART II. 6M 472 PROFESSOR KELLAND ON SUPERPOSITION. XIV. BG and BY are the same as in the last method, whilst a parallel is drawn from Y instead of from G. (1), (2), and (8) will unite as in the second figure. Also, since the sides of (3) and (4) are a and 2—a, the square is complete (by No. XIII.) ; hence the con- clusion. XV. (1) and (3) are the same as in method XIII: (4) is constructed by draw- ing GH equal and parallel to AY, and completing the rectangle. (1), (2), and (3) will unite as in the second figure ; and the conclusion is effected as in XIV. XVI. Cut off BY, BV, each equal to 2, draw VE parallel to BY, join CY and produce it to meet VE in D. (1), (2), and (3) will unite, as in the second figure; and the length of (4) is the same as that of (3); hence the conclusion. The division is, in this case, effected by two cuts. Cor. A modification of this method may be produced by omitting CD, and a triangle equal to CDE out of (3), as in the dotted line. XVII. Make BT=2z; draw TQ parallel to AB; make CR=DQ, and draw FG parallel to AQ through any point F, within the limits indicated in the figure by cutting the points C and T; draw RH parallel to AB. (1), (2), (3), and (4) will unite as in the second figure; hence the conclusion. XVIII. Bisect PC in Q. With centre B and radius BR=a, describe a circle; and from Q draw QR touching the circle in R; produce QR to meet BA in S; make BT=BS, and draw TV parallel to BR meeting DE in V. (1), (2), and (3), will unite as in the second figure, and the side of (4) will be in the same straight line with the sides of (1) and (2) ; hence the conclusion. XIX. Bisect CD in Q. With centre A and radius AR=a, describe a circle; and from Q draw QR touching the circle in R; produce QR to meet BE in H; make ET=a, and draw TL parallel to AB. (1) and (8) unite as in the second figure, so that the longest side of the united figure is 2a, consequently (2) falls upon it; hence the conclusion. The division may, in this instance, be effected by two cuts. XX. Bisect CD in F, draw FG parallel to AB; make AH=AY=2a—a ; join AH, and draw YZ parallel to BE. . The triangle is HGK equal to AYZ, hence (1), (2), (3), and (4) will unite, as in the second figure, and the figure is a square. XXI. Bisect CD in G; draw GH parallel to AB; draw BJ, making an angle of 30° with BH, and AK perpendicular to BJ. (1), (2), and (4) will unite as in the second figure, and AK and BJ are each equal to 2; hence the conclusion. XXII. Bisect CD in G, and through G draw GH parallel to AB, meeting AP in J. Draw GL, making an angle of 30° with CD, and make LO=a. Through PROFESSOR KELLAND ON SUPERPOSITION. 473 O, H, and J draw perpendiculars to GL, produce those through O and J, their own length, to X and Y; and complete the figure. The three perpendiculars are each equal to 4a, and the portions (4) and (iv.), (3) and (iii.), (2) and (ii.), are respectively equal ; hence the conclusion. The division may, in this instance, be effected by two cuts. XXII. Make BY=a2, CH=AY; draw KHO parallel to BE; make EF=KL, and complete the rectangle JCOP; YL, KH, and LJ, JF are the cutting lines. Because PO=CJ =2x=BY; triangle PKO=YLB, also because KO=BE. KH+ OQ =a; and BJ =4BF=4 Qa—EF)=4 (2a—KL) =a—KH=QC; therefore triangle EQO=JBF; hence fhe conclusion. XXIV. Draw AK, making an angle of 30° with AB; make AF=EK, and from ¥, E and H (the fourth corner of the square) draw Deuce gun to AK AK, FG, and JL are the cutting lines. For HL=z, and because AB=2PH, AK =2HJ, therefore BK=2PJ=HJ, and FC=4AF=1EK=3 (2a—BK)=a—PJ=GJ. Again FB=2a—AF=2a—FK= BK=HJ; hence GJHO is equal to (4), and DO=PJ ; DE=AP, consequently DETO is equal to (2); hence the conclusion. The division may, in this instance, be effected by two cuts, as in No. X XII. It will be observed that the angle of section is in all cases either 30°, or are such that the tangent of the angle is a function of /3, and of no other surd. For instance, in No. XVIII. we shall find tan. Risa : I have only to add, that a large number of the solutions are due to various friends, including students, to whom my best thanks are tendered. It would not be easy to fix the authorship of each solution with certainty, on which account [ shall not attempt it. ( 475 ) XXXIV.—On the Variations of the Fertility and Fecundity of Women according to Age. By J. Marruews Duncan, M.D. (Read 2d May 1864.) In 1855, when the systematic registration of births in Scotland was estab- lished, the schedule used exacted from the public a variety of interesting details in connection with each return,—a circumstance which gives to the registers for that year an extraordinary value. For, in consequence, I believe, of numerous complaints regarding the irksome labour of filling up the document, it was dis- continued, and a much less comprehensive schedule has been in use ever since. Tt is from the registers of births for 1855 that I have extracted almost all the data which have yielded the results I am now about to communicate. Similar data cannot be found in the subsequent registers. The great value of these registers has been distinctly pointed out by Dr Srark, the able assistant to the Registrar-General. I must here acknowledge, with grateful thanks, the assist- ance and encouragement I have received from Mr Seron and other officials of the Register-House. The exigencies of time, labour, and expense, constrained me to restrict the number of births to be operated on within moderate limits; and I selected Edinburgh and Glasgow, with their 16,593 children legitimately born in 1855, as the field of operations. It is needless to enter fully upon the reasons of my Selecting the conditions of legitimate birth in Edinburgh and Glasgow; my only Object was to secure as much as possible of accuracy and completeness in the filling up of the schedules. It must be noted, that legitimate births, as registered, include only births of living children at the full term of pregnancy or near it. The well-known difficulty of handling statistics without infringement of the Tules of logic has made me be very cautious in my progress in this investigation, and I am all the more bound to be careful, because it will be necessary, in con- hection with my present topic, to point out great errors made by authors who have entered upon it. But although I trust no fault will be found with my mode of reasoning, I have to admit the existence of some comparatively few and unimportant errors in the details given in the registers. The chief of these will be stated in connection with the tables to be brought forward. So far as I know ' the errors are all in the original registers; in the elaboration of the details thence derived, I have spared nothing that could insure accuracy; and must here men- VOL. XXIII. PART III. ON 476 DR MATTHEWS DUNCAN ON THE VARIATIONS OF THE FERTILITY tion my obligations to the various intelligent and assiduous gentlemen who have assisted me in the work. The part of my investigations which is the subject of this communication is confined to the determination of the comparative fertility or productiveness and fecundity of women at different ages. It is necessary, in order to avoid confusion, here to establish a distinction, which I shall maintain as I go on, between fer- tility or productiveness and fecundity. By fertility or productiveness I mean the amount of births as distinguished from the capability to bear. This quality of fertility or productiveness is interesting chiefly to the statistician or the political economist. It does not involve the capability of every individual considered to bear, nor even the conditions necessary for conception. By fecundity I mean the capability to bear children; it is measured by the number born, and it implies the conditions necessary for conception in the women of whom its variations are predicated. This quality of fecundity is interesting chiefly to the physiologist and physician. . In discussing the subject of comparative fertility and fecundity at different ages, I may incidentally afford means for estimating the degree of fertility or fecundity of different ages ; but I wish it to be distinctly understood, that I have not proposed to myself, in this paper, the consideration of the actual degree or amount of fertility or fecundity at any age, but only the variations of fertility or fecundity at different ages as compared with one another. Cuaprer I.—The Actual Fertility of our Female Population as a whole at Different Ages. The first law which I propose to establish, has reference to the ages of mothers of legitimate children. In Edinburgh and Glasgow legitimate birth form atleast 90 per cent. of the whole born. The law, therefore, regards the ages of the women from whose fertility 90 per cent. of the population a recruited. = | It must be observed, that this law or general statement shows nothing re garding the fecundity of women of different ages, although it has been held as — it first because it is pretty well known, because in my own investigations it was first made out, and chietly because it is essential, before proceeding forthe y 4 of which they fase been made the basis.* The facts or data illustrating this law, with which I am best sequaell ha been derived from reports of lying-in dispensaries, as by Dr GRANVILLE, or fro: & similar accounts of lying-in hospitals, as by Dr Cottins, Drs Harpy and M‘CLin- | * See GRaNvILLE, Transactions of Obstetrical Society of London, vol. ii, AND FECUNDITY OF WOMEN ACCORDING TO AGE. 477 Took, and others. I here present, as an example, the table of ages of mothers of legi- timate and illegitimate offspring, whether born alive or dead, from the “ Practical Treatise on Midwifery” of Dr Conzins, master of the Dublin Lying-in Hospital. The data adduced by Dr Granvit1e in the second volume of the “ Transactions of the Obstetrical Society of London,” are closely similar. Judging from these data, it would appear that most children are born of women at or near the age of 30 years or the middle of the child-bearing period of life; and that the offspring of mothers of ages advancing from the commencement of child-bearing to the age _ of 30 or the middle of the child-bearing period gradually increases; that the climax is reached at this age, and that thereafter the offspring of mothers advancing above 30 gradually diminishes. But while the age of 30 forms the climax, there is not an equal fertility on either side of it; a much larger part of the population being born of mothers under 30 than of mothers above 30. Dividing the number of mothers at 30 years, and adding together those on each side of the division, we have on the side of the younger 12,106, and on the side of the elder women 4279, giving a majority of 7827 in favour of the younger: or, otherwise stated, we have three-fourths of the births among the younger half, and only one-fourth among the elder. The mean age of the mothers in Dr Cotins’s table is 27 years. TABLE I.—Suow1ve tae Acs or £AcH oF 16,385 Women, DELIveRED IN THE DUBLIN Lyine-1n Hospitau. | Age, . ees |Lalve)l7) 187) 19} 20) 21 |) 22 | 23) 24 | 25 | 26) 27 | 28} 29 | 30) 31 a bi TABLE II.—Suow1ne toe Aces or 16,385 Women DELivereD IN THE Dusiin Lync-1n . HospiTaL, ARRANGED IN Periops or Five YEARS. 15-19 | 20-24 | 25-29 | 30-384 | 35-39 | 40-44 | 45-49 | 50 and over. | No. of Women, . 762 | 4862 | 53809 | 3817 | 1210 | 397 22 6 » S| EEE Percentage, . . .| 4:65 | 29-67| 32:40| 23-29| 7-38 | 2-42 13 03 _ The next table which I present shows an arranged collection of data, com- | prising the wives-mothers of living children born at or near the full time in | Edinburgh and Glasgow in 1855. The former table has, regarding the use to be 478 DR MATTHEWS DUNCAN ON THE VARIATIONS OF THE FERTILITY made of it, the advantage over this table of including all mothers bearing children, whether legitimate or not, alive or dead, in the Dublin Hospital. But in every — other respect, this second table presents what I judge to be more reliable data. The former table contains a class of cases selected according to complicated con- ditions which it is impossible to state, but which are the result of the correlated circumstances of the Hospital, and of the class from which in Dublin it draws its patients. In the second table the conditions of selection are fewer and less — important, the chief being the legitimacy, life and maturity, or at least viability, of the offspring. Now the limits of the influence of these different conditions are pretty well known, and the proportional differences between the two tables are too great to be accounted for by these differences. The second table is thus shown to be the more trustworthy. TABLE II].—Suow1ne tHe AGE or EACH OF 16,301 Wives wHosE CHILDREN WERE REGISTERED IN EDINBURGH AND GLAsGow IN 1855. Ages, (1617 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 1338/34 Mothers, | 4 |28] 116 | 228 | 406 | 543 | 828 | 888 |1024/1058)1063)| 925 /1116) 875 |121 | 545 | 825 645/62: Ages, .| 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43] 44 | 45} 46 | 47 | 48| 49 | 50) 51 To al Mothers, | 691 | 594 | 409 | 426 | 287 | 404| 142 | 148/ 80/66 /50|27| 6 | 9 | 4 | - 2|4 1/1680 TABLE TV.—SuHowine tHE AGEs or 16,301 Wrives-Motuers in EDINBURGH AND Guascow IN 1855, ARRANGED IN PErtops oF FIVE YEARS. Ages, . . . | 15-19 | 20-24 | 25- 29, 30-34 | 35-39 | 40-44 | 45-49 | 50-54 | 55-59} Total { Mothers, . . | 376 | 3688 | 5037 | 3850 | 2407] 840 | 96 6 16,301 16,301 | IDOE ns 2 a a fe ! Percentage, . | 2°30 | 22°62 | 30:89 |2361 [1476 | 515] 58 | 03 | — Plenee it appears that 93 births are omitted in the extracts. These omissions were made on account of manifest carelessness and inaccuracy in the registers. To these 93 births, corresponds the number of 92 mothers, one being deducted for a twin case. These 92 mothers have been added pro- portionally to the others, in order to make up the total of 16,393. + The actual number of wives-mothers in Edinburgh and Glasgow in 1855 was 16,393, Thi figure is in the text reduced to 16,386, and seven wives-mothers omitted, because there seven W altogether exceptional, occurring as they did between the ages of 50 and 57, and could only dam the statement of results. AND FECUNDITY OF WOMEN ACCORDING TO AGE. 483 But a more interesting and valuable comparison may be made by taking the same number of 15 years before and after the middle of child-bearing life, a total period of 30 years, which includes the immense majority of child-bearing women. Doing so, we find that of 24,252 wives under 30 years of age, 9152 bore living children, and that of 36,956 wives of ages from 30 to 44 inclusive, 7138 bore living chil- dren. Had the elder women been as prolific as the younger, they would have pro- duced 13,946 children, instead of 7138; that is, the fecundity of the younger women was almost double that of the older. * The table given in this chapter has been prepared (see footnote) so as to give the actual amounts. I found it possible to do this with a near approach to exact- ness, and it is evident that in this way the results derived are not only compara- tive statements, with only relative value, but also statements of actual values. From the data now given I conclude— 1. That the fecundity of the mass of wives in our population is greatest at the commencement of the child-bearing period of life, and after that epoch gradually diminishes. 2. That the fecundity of the whole wives in our population included within the child-bearing period of life, is, before 30 years of age is reached, more than twice as great as it is after that period. 3. That the fecundity of the wives in our population declines with great rapidity after the age of 40 is reached. Some of these conclusions may be stated, with the actual numerical results, as follows :—While of all the wives living in Edinburgh and Glasgow between the ages of 15 and 45, one in 3°8 or 26°3 per cent. bore a living child; of those * The data at my disposal enable me to give the figures for each year of age up to 20. But the numbers are so small, that little value can be placed on the results drawn from them. They seem to me to indicate that the fecundity of the mass of married women is probably highest shortly after the age of 20 is reached. For although the low fecundity of one in 2:57 at twenty years of age, is absorbed in Table VII. in the period from 20 to 24, yet this latter period shows, on the whole, the higher fecundity of 2°4, TABLE VIII.—SHOwING THE COMPARATIVE FECUNDITY OF WIVES AT AGES OF 16, 17, 18, 19, AND 20, IN EDINBURGH AND GLASGOW, IN 1855. eS a 16°" | ee 18 19 20 EE se, ke ss 13 55 232 455 1043 Wyives-Miothers,.. .. . . . 4 28 116 228 405 Proportion of latter to former islin| 3:25 1:96 2:00 1:99 2°57 Bemecriapee se iki es el Gt BOTT 60°91 50:00 50°11 38°83 VOL. XXIII. PART III. 6 P 484 DR MATTHEWS DUNCAN ON THE VARIATIONS OF THE FERTILITY between the ages of 15 and 29 inclusive, one in 2°6, or 38:4 per cent., bore a living child ; and of those between the ages of 30 and 44 inclusive, one in 5:1, or 19:6 per cent., bore a living child. Cuapter IV.—The Initial Fecundity of Women at Different Ages. In commencing the statistical inquiry whose results I am now giving, my object was to discover the fecundity of women at different ages, and I now pro- ceed to address myself to this point. It is not my object to illustrate the subject of the arrival of young girls at the age of maturity, the change of the girl into the fertile woman. In the case of some peoples, facts might be collected regarding wives so young as to be ina large proportion sterile from immaturity ; and their fecundity gradually appear ing as age advanced, might produce a column of mothers from 10 to 20 years of age, shewing a gradually increasing fecundity of the population at these ages Even in our tables derived from the data of wives in Edinburgh and Glasgow, some interesting results are to be found, and allowance must be made for a cer. tain amount of immaturity in the wives of from 15 to 20 years of age. But this question of the arrival of girls at maturity is foreign to the present topic. In it all the women are supposed to be mature, and subjected to the conditions essential for procreation. The fecundity of individual women is known to vary extremely. Some ar very frequently pregnant, and repeatedly, or even constantly, have plural births, and thrive with it all. Under like conditions, other women are absolutely sterile, or a miscarriage or a dead mature child forms the climax of their fecundity, and this little may be effected at the expense of permanent constitutional exhaustion. Between these extremes of great fecundity and absolute sterility, there is an w limited series of varying degrees of fertility. On this interesting aspect of the subject of fecundity, the present research throws little light. It is founded on the result of an aggregate of cases, and can show almost nothing as to individuals. It illustrates the fecundity at different ages of women generally, not the individual fecundity of any. hae , te a The table given in last chapter (Table VII.), affords data which cannot be applied to settle the question of the fecundity of women of different ages. For it is evident that among the mass of wives of each succeeding year, or series of years, are included the wives who were once of the former series or part of them— is, a class of wives whose fecundity has been at least liable to be imerea diminished, or exhausted by procreation, before they have come to form part of the wives in any of the columns after the first. In order to arrive at the fecund of women or wives of different ages, it is necessary to secure that the condi- oat io oe ¥ AND FECUNDITY OF WOMEN ACCORDING TO AGE. 485 tions of the compared women of these different ages be as nearly the same as possible. This is not attempted in the seventh table. TABLE 1X.*—SHOWING THE INITIAL FECUNDITY OF WOMEN OF DIFFERENT AGES IN THE Kirst YEAR OF MARRIAGE. Ages of Wives ae L |15-19 20-24/05-29'30-34 35-39140-44/45-49150-54/55-5960-64165-69, Total, Married, sf [perm dR eet ssl oe teh Rei B32 | No. of Wives newly 700 |1835|1120| 402 | 205 | 110 | 46 | 20 | 6 2 1 |4447 _ Married, . | No.of Wives Mothers | within first year of 96 | 3389 | 1389 | 46 | 19 4 ae ero adie | Naiete ah ae yO nS | Marriage, . | Proportion of fatter 73 | 5-4 180187 |107| 75] ... ack to former is 1 in : os ave dee O00 Meercentage, . . .. 13°71 |18-48 |12°41 |11:44) 9-27) 3°63) ... Sis site ae eee A 46 Table ninth is constructed to show the relative initial fecundity of newly- married women of different ages. By the returns of the Registrar-General we calculate how many women at each succeeding year of age contracted marriage | in 1855, in Edinburgh and Glasgow. My extracts from the register for 1855, | shew how many of these women bore living children before they had been a year _ married. When the two figures are compared for each age, we have the fecundity | at the outset of child-bearing at each age. The table reads as follows :—Of 700 women married between 15 and 19 years of age inclusive, 96 bore a living child before they had been wives for twelve months, or one in every 7:3; and so on. Table tenth is in every respect the same as the former, only it shows the fecundity within 24 months of married life; or the number of women bearing living ‘children before they were two years married is compared with the number of newly married. The observation that the fecundity within 24 months is much More than twice as much as the fecundity within 12 months of marriage, appears to me to give this table more substantial value than the former, as an indication of the actual fecundity of the outset of child-bearing at different ages. | Both these tables show the highest rate of initial fecundity to be between the * The number of wives married at different ages in Edinburgh and Glasgow in 1855, is arrived at in the following manner, The marriages in Scotland in 1855 were 19,680. The marriages in Edinburgh and Glasgow in 1855 were 4447, The distribution of the 19, 680, according to age at Marriage, is given at p. 22 of the Registrar-General’s Annual Report for 1861. This distribution "| Tequires a correction for the number whose ages at marriage were not known. Calculating on the |: ages of the whole 19,680, the proportional distribution of the 4447 married in Edinburgh and Glas- gow is found to be as in the table above. { } | | No. of Wives newly | Percentage, . . . «(43°71 |90-51 (75-80 [62°93 140-97 /15-45/4:35 | ... | ... | ... | ... (718 486 DR MATTHEWS DUNCAN ON THE VARIATIONS OF THE FERTILITY ages of 20 and 24 inclusive, and a gradual declension from that time on either side as age diminishes or increases. TABLE X.—SHOWING THE INITIAL FECUNDITY OF WOMEN OF DIFFERENT AGES WITHIN THE First Two YEARS OF MARRIAGE. s Ages of Wives i 15-19|20-24/25-29/30-34 35-39|40-44'45-49/50-54/55-5 9 60-64/65-69| Total. | Married, SS ee Married, . . No. of Wives Mathers within two years of Marriage, | Proportion of latter to former is 1 in 700 |1835|1120| 402 | 205 | 110] 46 | 20 | 6 | 2 | 1 |4447) 1661| 849 | 253 | 84 | 17 2 ae Sele aes we | 817 ! —— (Jy) x (=) fon) The two following tables (XI. and XII.) show that on the side of the women — younger than 20 years, initial fecundity steadily decreases with age. In regard, however, to these young wives, it may be objected that there is a source of error from immaturity which is certainly very trifling after the age of 20 is reached. And the objection is, theoretically at least, quite just, for it is absurd to attempt to measure the fecundity of women who have not become sexually mature, and the admixture of immature with mature is a source of error, important, directly — according to its amount. It is unsatisfactory merely to allege in answer, that immature girls are not likely to be found among young wives in such numbers as — to form a source of great error. I have therefore taken the following means to ensure that this source of error be completely excluded. 4 TABLE XI—Suow1ne THE INITIAL FECUNDITY OF WOMEN UNDER 20 YEARS OF AGE IN THE FIRST YEAR OF MARRIAGE. | «Apes of Wives newly Marniedyy. | <5 f.) aogeenn 16 17 No. of Wives newly. Miawinied 3 <<. sc hogs eee iis 43 108 No. of Wives Mothers within first year of Marriage, 2 7 Proportion of latter to formerislim. . . . «| 216 154 Proportion after correction for Immaturity, is 1 in 15°5 12°8 Percentages ii.'d | a ho! 280i DP Re ee ee DIG EAS Ferg AND FECUNDITY OF WOMEN ACCORDING TO AGE, 487 TABLE XII.—SHowING THE INITIAL FECUNDITY OF WOMEN UNDER 20 YEARS OF AGE WITHIN THE First TWo YEARS OF MARRIAGE. Ages of Wives newly Married,. . . . . . . 16 17 18 ills) eo..of Wivesnewly Married, . . ... =. . 43 108 225 314 No. of Wives Mothers within two years of Marriage, 4 27 98 Wit Proportion of latter to formerislin .... .| 107 4:0 2°3 1°8 Proportion after correction for Immaturity is 1 in . (7 | one 2-1 1:7 IC mie aveet sir sl alive 8 oo. be 12°90 30:00 46:44 57°84 The commencement of menstruation is generally considered by physicians an indication of the arrival of sexual maturity. It may be true that some are still immature in whom this phenomenon has shown itself, and it certainly is true that some are mature before its appearance. Yet it forms a generally accredited indication of maturity. The following table (XIII.), framed by Dr WuiTEHxEaD, is a large collection of data, showing the age of the appearance of menstrua- tion in 4000 individuals in this country. It is easy to calculate what fraction of the whole 4000 had begun to menstruate at 16, 17, 18, and 19 years of age re- spectively, or, in other words, what fraction was capable of exhibiting fecundity at these ages. This I have done, and have corrected the numbers of wives in tables eleventh and twelfth accordingly, reducing them to similar fractional parts. After making this correction for immaturity, I have calculated the proportions of wives-mothers to wives, and placed the results in the last line. They remain the same so far as to show a steady diminution of fecundity as age diminishes. TABLE XIIIlL—*“ SHowine THE AGE AT WHICH PUBERTY WAS ACCOMPLISHED IN FOUR THOUSAND INDIVIDUALS.” (WHITEHEAD, on Sterility and Abortion, p. 46.) At Age of 10 years 9 first Menstruated. At Age of 19 years 148 first Menstruated, ”) 11 ? 26 ” » 20 EF) 71 ? ee 2 oy 136 a is PA 9 - * is > 5, dol Le ee oe 6 oF ” 14 ” 638 9 ” 23 ” 2 29 » 15 ,, 761 23 2 = ae 1 » ” 16 ” 967 ” 23 25 39 i 99 ” Uy 29 499 ” 29 26 39 1 2° 1G 5, sooo From these data I conclude— 1. That the initial fecundity of women gradually waxes to a climax, and then gradually wanes. . VOL. XXIII. PART III. 6Q 488 DR MATTHEWS DUNCAN ON THE VARIATIONS OF THE FERTILITY 2. That initial fecundity is very high from 20 to 34 years of age. 3. That the climax of initial fecundity is probably about the age of 25 years. At this point my present inquiry is closed. I know of no other way of ad- vancing our knowledge of this subject, than by the collection and analysis of statistics. The only very good quarry for such materials that I know of is the Scottish registers for 1855. The tables adduced might be improved by going over a larger field, and increasing the numbers analysed. But I do not see how the matter in the registers could be turned to more account, without encroaching on another topic which is at the same time closely connected with that under discus- sion,—viz., the fertility of marriage. Or, as marriage is scarcely admissible as a term in physiology, I should give this subject the title of ‘sustained fecundity,’ the degrees of fertility which women of different ages, beginning to live with men, continue to exhibit during the child-bearing period of life. In the meantime]! shall summarily state, that, so far as I have advanced in this new topic, the evi dence gained shows that, speaking generally, young women after the outset of child-bearing continue to exhibit a fecundity greater than is sustained by those married when comparatively elderly. The fourteenth table exhibits some of these results. It reads as follows :—Wives of from 20 to 24 years of age exhibit in the fifth year of marriage a comparative fecundity of 1 in 3:0; wives of from 25 to 29 years of age exhibit in the fifth year of marriage a comparative fecundity of 1 in 14:5; and so on. The table shows that at the fifth, the tenth, and the fifteenth years of marriage, the mass of women youngest married continue to show the greatest fecundity. The mass of younger women not only are more fecund at the outset of child-bearing, but after that time is past, they continue more fecund than older women who have been married the same number of years. TABLE XIV.*—SHOWING THE FECUNDITY OF WIVES IN EDINBURGH AND GLASGOW, — AFTER THREE DIFFERENT PERIODS OF CONTINUANCE IN THE MARRIED STATE. Age of Wives,. . . . . . . 2 « «© . © | 20-24 | 25-29 | 30-34 | 35-39 | 40-44) Fertility in Fifth Year of Marriage, . . . . .| 30 | 145 | 59:9 | 202-4| 6982 Fertility in Tenth Year of Marriage, . . . . «| os. 4:0 | 23-2 | 95:5 | 4049) © Fertility in Fifteenth Year of Marriage,. . . .| ... nae 65 | 44:3 340-0! I have made various other inquiries with a view to throw light on the topic of this paper. They refer to variations in sex, size, and weight of newly-born child * This Table is not prepared so as to show anything more than is described in the text. Espe- cially the figures in one horizontal line should not be compared with those in another horiza tal line. To permit this, the table requires large corrections for deaths. AND FECUNDITY OF WOMEN ACCORDING TO AGE, A489 according to the age of the mother, also to the frequency of twins and triplets according to the mother’s age. But the results of these investigations have been so imperfect or unsatisfactory that I do not now describe them. The views hitherto entertained regarding the influence of age on fecundity have been various. “In regard to age (says Burpacn*) fecundity is diminished in the first and last portions of the continuance of the aptitude for procreation. The elk. the bear, &c., have at first only a single young one, then they come to have most frequently two, and at last again only one. The young hamster produces only from 3 to 6 young ones, whilst that of a more advanced age produces from 8 to 16. The same is true of the pig. This rule appears to be general, since it applies also to the entomostraceze ; according to Jurine, the number of the young of the Monoculus pulex is at first from 4 to 5, afterwards rising gradually as high as 18. We scarcely ever encounter the births of 3 or 4 children, except in women who have passed the thirtieth year. Precocious marriages are not only less fertile, but the children also which are the result of them have an increased rate of mortality. According to Sadler, every marriage in the families of the peers of England yields 4:40 children when the woman was married below 16 years of age; 4°63 from this age to 20; 5:21 from 20 to 23; and 5:43 from 24 to 27.” The notions here expressed by BurDacu are in the main correct; but it is evident that they are very indefinite. They are to be regarded, also, more in the light of happy guesses than of well-founded opinions. Burpacu evidently places chief reliance on the evidence afforded by the numbers at a birth. From many quar- ters I have received corroboration of BurpAcu’s statements regarding the increase and subsequent decrease of the number produced at a birth by pluriparous animals, and I have received similar information regarding bitches, guinea pigs, the fertility of hens, &c. When I first paid attention to this subject, the plural births of women appeared to me to form a simple key for the determination of the fecundity of women at different ages. But I soon became dissatisfied with the materials | quickly collected. Woman is not a pluriparous animal, neither does she produce So regularly, or according to season, as the animals with which she is compared. In her the occurrence of twins and triplets is an exception to the normal rule, and the number of children born by her cannot be so simple and sure a test of fecundity, as in the case of animals having multiple litters at stated periods. Indeed, it is apparent that the evidence derived from plural births alone in women may positively mislead, for a woman may be more fertile bearing one child at a time frequently than another bearing twins or triplets more seldom. In this | place I shall only say, that the numerical study of twins, in reference to the age of the mother, yields interesting results, which do not confirm Burpacu’s statement | regarding them, yet are not hostile to the conclusions of this paper. Burpacu, in his work, describes an annual rise and fall in the fecundity of some pluriparous * Physiologie, tom. ii, page 117. 490 ON THE FERTILITY AND FECUNDITY OF WOMEN, ETC. animals. This annual variation forms a series of wavelets in the course of the great wave running from youth to old age, and culminating in middle life. This annual rise and fall of fecundity he attributes to the influence of cold. In his “ Treatise on Man,” M. QuETELET has, with some care, collected the statistical materials available at the time for advancing the settlement of the question of the relation of age to fecundity. He does not allude to the opinions of Burpacu, probably because they have no sufficient foundation, but he refers to Mitng, Mattuus, SADLER, GRANVILLE, Frntayson, and several foreign authors, who have more or less directly tried to throw light on the topic. QUETELET’S whole chapter on the influence of age on the fecundity of marriages is very un- satisfactory. It is at least difficult to reconcile with one another the conclusions arrived at in various parts of this chapter, and I shall not attempt to doit. It is only fair to say, that he seems conscious of the numerical deficiency of data sufficient for a basis of any conclusion, and as an example of the state of matters, the table of SapLer, which he and Burpacu both quote, may be mentioned ; in it — the number of marriages analysed is under 500, and they are all selected accord- ing to extraordinary conditions. The final conclusion which M. QuETELET an- — nounces is, that it is before the age of 26 years that we observe the greatest — fecundity in women. 4 The last writer on this topic whom I know of is Dr GRANVILLE, who, in an interesting paper in the London Obstetrical Transactions, returns to the descrip- tion of his former labours in the same field. In this paper, production or fertility is confounded with productive power or fecundity, and the table to which J] ~ have alluded in Chapter I. he describes not as showing the fertility at different — ages of the industrial classes of the metropolis, but erroneously, as showing the alternations in the productive power of women at different ages. 4 In this paper, then, I have, znter alia, shown that the great majority of the population is recruited from women under 30 years of age; but that the mass — of women in the population, of from 30 to 40 years of age, contribute to the general fertility a larger proportional share than the mass of women of from 20 to 30 years of age :— v Further, that the wives in our population, taken collectively as a mass, show a gradually decreasing fecundity as age advances; but that the average individual — wife shows a degree of fecundity which increases till probably about the age of 25, and then diminishes. a The fertility of the average individual woman may be described as forming a wave which, from sterility, rises gradually to its highest, and then, more gradu- — ally, falls again to sterility. ( 491 ) XXXV.—On the most Volatile Constituents of American Petroleum. By Epmunp | Ronaups, Ph.D. (Read 15th February 1864.) Crude American petroleum evolves, at ordinary temperatures, a quantity of combustible gas, which takes fire on contact with flame, and, when mixed in certain proportions with air, produces an explosive mixture. It is in consequence of this property that it has been thought necessary to pass a very stringent law, known as the Petroleum Bill, with a view of preventing accidents from the incautious storing and handling of the oil. The more volatile liquid products obtained by distilling the crude oil are still more highly charged with combustible vapour, which, when these liquids are again distilled, escapes condensation even by the most powerful freezing mixtures. The liquid constituents of petroleum have now been carefully studied by Messrs PeLouze and Canours, and some of them also by Mr ScHoRLEMMER. These eminent chemists have shown that the oil consists essentially of a mixture of the homologues of marsh gas, having the general formula, Ci Hony1, H. It was during the collection of the more volatile of this series of compounds with a view to their analysis, in which object I have now been forestalled, that my attention was drawn to the large quantities of incondensible gas which escaped at each successive fractionation, and it appeared desirable to ascertain whether the gaseous ingredients of the oil belonged also to the same series, or were accompanied by other hydrocarbons. With this object in view, and still waiting the arrival of some specimens of oil collected and secured in hermetically sealed vessels, direct from the oil wells, I was enabled by the kind permission of Mr Suanp of Stirling, to collect the gas which floated over the surface of the crude oil in the barrels in which it is imported into this country. I also obtained from the same manufac- turer some of the very first products of the stills employed in refining the petro- leum on amanufacturing scale. The gas floating over the surface of Pennsylvanian oil was collected at a tem- perature of — 1° C., and was observed to contain combustible ingredients. It took fire instantly on being brought into contact with flame, burning with a very faint, |bluish light, but without explosion. From Canadian petroleum, which is of much \thicker consistence, no combustible gas was obtained at that temperature. The gas was collected over water by simply removing the original wooden VOL. XXIII. PART III. OR 492 DR EDMUND RONALDS ON THE MOST VOLATILE bung of the casks and inserting immediately a cork bung furnished with a tube, for the delivery of the gas, and a long shanked funnel tube, through which liquid petroleum was poured. Thus obtained the gas was of course a mixture of air and hydrocarbon; it was not affected by fuming oil of vitriol, nor was bromine water discoloured by it. It was hence inferred that no perceptible quantities of the olefiant series were present, and the temperature of collection is sufficient guarantee for the absence of any known members of the benzole series. The gas was treated over mercury, with solid potash and pyrogallate of potash successively, when it yielded— 1:27 per cent. of carbonic acid, and G58" ~ ay, oxygen. The residue, analysed eudiometrically, gave the following results :— Gas collected from the surface of Pennsylvanian Petroleum at a temperature of —1°C., freed from Carbonic Acid by Potash and from Oxygen by Pyrogallic Acid. Corrected vol. Gret | Pegee | miagaon ee Gash) agree Roaticctie” fei 1331 03099 9°. 39-934 Dosscaitirie Ae eye es coy lane fee 1s 392°8 0:5666 a: 215°47 Do-bde.foxypen, «fox -.- « 465°6 0-6391 8:2 288-92 Afteryexplosion, se h« \.%m 3% 421°3 0:5940 10: 245:09 After absorption of CO,, . . . . 383°4 0°5515 8: 205:23 After addition of hydrogen, . . . 474°3 0°6395 38 299-15 Afterexplosionysicay A: style ia cfs 346°5 05062 4: 172°86 Deducting the nitrogen, or 23:4 vols.=54 per cent. of the original gas, we have here a relation of hydro-carbon to condensation and carbonic acid, as— 16°534 : 43-83 39:86 or, 100 : 265 : 241. The oxygen consumed amounts to 67°16 vols., or 4:06 times the volume of , the hydrocarbon. The members of the olefiant He benzole series being absent, it may fairly be inferred that the hydrocarbon resembles in constitution the liquids with which it is associated ; and if this be the case, the gas must be a mix- ture of the hydrides of ethyl and propyl, the former of which requires a relation of hydrocarbon to condensation and carbonic acid, as— i ; 25 : 2 while the hydride of propyl requires a relation of 1: 3: 3. By calculation A CONSTITUENTS OF AMERICAN PETROLEUM. 493 from the numbers above, it can be shown that the gas analysed must have con- sisted of a mixture of these gases in nearly equal proportions, or of— C,H,, Hydride of Ethyl 7:94 C ie Hydride of Propyl 8:01 358? —the correctness of whichis confirmed by the amount of oxygen consumed being about the mean of the quantities required for the combustion of these hydrides separately. Hydride of ethyl requires 3-5 times its volume of oxygen. Hydride of propyl requires 5: times its volume of oxygen. The gas floating over the surface of the petroleum is therefore composed of— Carbonic acid, . , ‘ , ; : : , 1:27 Oxygen, . : ; : ' ; ‘ ; k 6:58 Nitrogen, ¥ , : L : . : oa gO! Hydrocarbon ; { C,H, } 38:15 Ae : : ‘ ‘ C.H, In this condition the gas is not explosive, and would only become so on being mixed with a large volume of air. The most volatile liquid obtained by slaw the very first runnings from the stills employed in the process of refining petroleum has a specific gravity of 0°666. It is not sensibly affected by nitric acid, by oil of vitriol, or by bromine. When distilled, it commences to give off bubbles of gas in abundance at about 25° Cent., but after a few minutes all appearance of boiling ceases, although large quantities of gas and condensible liquid continue to pass over up to 65° or 70° Cent., and the whole liquid is evaporated below 100° Cent. This liquid resembles very closely the kerosolene or kerosoform which an American physician of New York has introduced as an anesthetic agent; and I am indebted to Dr Simpson for the opportunity of comparing it with a specimen of the latter. The specimen lent me by Dr Simpson was quite indifferent to the above reagents. It had a specific gravity of -6336. It began to boil at 28° Cent., and was nearly completely volatilised at 70° Cent., so that it must have been composed almost exclusively of a mixture of the hydrides of amyl and hexyl, | while the crude volatile product from the manufactory contained, in addition to these hydrides, some incondensible gaseous products, and a considerable quantity of the hydride of hepty]l. The incondensible gases dissolved in this most volatile liquid were expelled by gently warming a large quantity (about two gallons) of liquid, and passing the gases, before collecting them over water, through a long metallic worm, surrounded by a freezing mixture composed of ice and salt; the whole apparatus ‘having been filled previously with carbonic acid to expel air. The first two portions which were collected showed, after separating carbonic 494. DR EDMUND RONALDS ON THE MOST VOLATILE acid and oxygen, little difference in composition from that already analysed, and which had been collected from the surface of the crude oil. I omit the details of the analyses of these two, and submit only the results, which correspond in both cases with a mixture of the hydrides of ethyl and propyl. Gas. Condensation. Carbonic Acid. I 8289 c 22:°947 g 19:045 ‘ 100 a it | 249 Oxygen consumed 32°338. TI 7275 4 20°70 : 17:586 : 100 : 280 : 240 Oxygen consumed 31:07 The gas coming over a little later from the same liquid was found to approach nearer in composition to pure hydride of propyl, as is shown by the following analysis. This portion was treated with potash before being introduced into the — eudiometer, but the oxygen which it contained was not separated before combus- tion, but was estimated in a separate experiment, and found to amount to 2°44 per cent. of the gas burned. Oreet Pressure. | Temperature. a rears i pressure, Gas nae Seubieger Scene a Brea 39°723 0:2817 15:1 10:604 After addition of oxygen, . . . . 160° 0:3939 16: 59°548 After addition of ait, 4) 2) 3-4 5 260°128 0-4917 14:5 121-46 After, explosions .0i08 iy ‘se deuresiles 236°386 0:4680 16°5 104°33 Ader SDS ORPHOM, | cy ce 5 enw cory oe | os 204-386 0:451 15: 87:376 After admission of hydrogen,. . . 357161 0602 14 20453 Atfter explosions. caf yah) piles pattie! (4 231:225 0°4643 13°6 102:29 Deducting the nitrogen and the 2°44 per cent. of oxygen contained in the gas, we have here the ratio of hydrocarbon to condensation and carbonic acid, as 5'984 : 17:13 : 16:954 100 : 286 : 283 Hydride of propyl C,H, =2 vols., requires a ratio of 1: 3: 3. The quantity of oxygen consumed by the hydrocarbon is 4° 67 times” i s volume, while pure hydride of propyl would require 5 times its volume. | The gas collected at a still later period from the same liquid was free from carbonic acid, oxygen, and nitrogen gases, and agreed in composition with a mixture of the hydrides of propyl and butyl. . CONSTITUENTS OF AMERICAN PETROLEUM. 495 Gas, After addition of oxygen, After addition of air, After explosion, . After absorption, Gheered | Pressure 43034 0:2821 151-465 0°3857 life 0°6439 372644 06038 : 321: 0°566 After addition of hydrogen, 405: 0649 353'032 0°5846 After explosion, . Corrected vol. Temp. Cent, | at 0° +1 m. pressure. 19-5 11°335 9:9 04°464 20:6 249-70 INO) 212:05 15:2 72411 sa 247°45 15:2 195°52 The relation here of hydrocarbon to condensation and carbonic acid is as— 11-335 100 37°65 302 39:94 352 The oxygen consumed is 5°88 times the volume of gas burned, while hydride of butyl alone requires 6°5 times its volume of oxygen for combustion. The gas evolved on warming the light spirit of petroleum, as it is prepared for sale, after having been kept, however, for some months in a vessel not her- metically sealed, was found to be a mixture of nitrogen and oxygen, with nearly pure hydride of butyl. After separating by potash the carbonic acid which had been allowed to occupy the space above the liquid, the gas was analysed ; the oxygen which it contained was estimated by pyrogallate of potash in a separate experiment, and amounted to 15°37 per cent. ae After addition of air, After addition of oxygen, . After explosion, . After absorption, After explosion, . Observed Volume. After admission of ee 5 73:2 273'3 334° 288°5 228°5 330° 317°5 Pressure. 0:2399 0:4366 0:-4976 0:4523 0:3995 0°5022 0°4799 Temp. Cent. 7. 5:2 57 6:4 10:2 13° 12-2 | tion of hydrocarbon to condensation and carbonic acid as,— 39°502, or as 9°64 100 VOL. XXIII. PART III. 35°32 366 409 Corrected vol. at 0° + 1m. pressure. 17:25 Lead 162°82 127°5 87-998 158-2 145°86 Deducting the nitrogen and oxygen contained in the gas, we have here a rela- 496 DR EDMUND RONALDS ON THE MOST VOLATILE Closely corresponding to the relations in hydride of butyl, which are,— 1: 3:5): 4: This gas was therefore composed of— 28:74 nitrogen, 15°37 oxygen, 55°89 hydride of butyl, and it would appear from this experiment that the light volatile liquids absorb and retain oxygen in greater proportion than that element is contained in atmo-— spheric air. : The liquid condensed by the freezing mixture during the collection of these gases, and that obtained by subsequently heating the large body of liquid from which they were expelled to a higher temperature, not exceeding however 30° Cent., or the boiling point of hydride of amyl, was redistilled. It commenced to boil at 0° Cent. ; a considerable portion passing over between 0° and 4° was col- — lected separately; another fraction between 6° and 8° was also collected apart ; the remainder nearly all distilled below 15° Cent. The liquid distilling between 0° and 4° Cent. is nearly pure hydride of butyl, which has not yet been described. It is a perfectly clear, colourless, very mobile | liquid, having an agreeable sweet smell, but eluding, by its great volatility, the sense of taste. It is insoluble in water, but dissolves in alcohol and ether, and alcohol of 98 per cent. absorbs between 11 and 12 times its volume of the vapour at a temperature of 21°°5 Cent. It burns with a yellow, not very luminous flame. Mixed in the gaseous state with twice its volume of chlorine, liquid chloride of butyl is formed, and the original 3 volumes become condensed into 2 volumes of hydrochloric acid. The specific gravity of the liquid at 0° Cent. is 0°600. It is therefore the lightest liquid at present known. The vapour-density determined by Dumas’ method, the vapour being absorbed by alcohol, gave the following results :— Temperature of air, . . 138. Temperature of sealing, . 40° C. Barometer,’ . 9a. . > ‘7615 m. Capacity of globe, . . . 185°6 ce. Empty globe, . . . . 80°577 grms. Ai bubble, . . .... = jjemem Globe and substance, . . 30:°788 grms. Temperature of alcohol, . 14° C. Hence vapour density=2°11. Hydride of butyl, C,H, requires by calculation 2:006. 4 The liquid, analysed eudiometrically in the gaseous state, gave the following — numbers :— ’ CONSTITUENTS OF AMERICAN PETROLEUM. 497 Analysis of Butyl Hydride. Corrected vol. Ob d : Temperature 5 Value ExeSSules Cent. ashe (S38, 0 oe a rc a 39:04 0:1944 M. 5° C, 6°691 After addition of oxygen, . . . . 326: 0°4810 4°38° C. 164-11 Memerexplosion,.. . . . . . . 294:'8 0:4507 4° C. 130-95 After absorption of CO,, . . . . 2569 0:4215 9° C. 104:°83 Hence we have,— Gas. Condensation. Carbonic Acid. 6-691 23°16 26:12 or, 100 346 390 Hydride of butyl requires— 100 : 3900 i 400 The liquid collected between 6°+8° Cent. is not very different from this last. It is, however, a mixture of hydride of amyl with hydride of butyl. Its sp. gr. at 0° Cent. was found to be ‘6004. The vapour density was 2°178, and the com- position in the gaseous state is shown by the following numbers :— | | Giperet | Paes, | Teuyertere "aro a 15:3 0:4392 19:3 9:39 | BP ORV CM | i ey | 2645 0°6912 19:3 | 185:22 Bueereexplosion, . .°. .» . . . | 223 0-6509 17:9 149:12 Seeerapsorption, . . « . ... 166°8 06154 19°5 106-78 Hence we have,— Gas. Condensation. Carbonic Acid. 9°39 P 36:10 : 42°34 or, 100 : 384 : 450 Hydride of butyl requires,— 100 : 350 400 It was not to be expected, from the manner in which the gases were collected, . that any single portion would correspond exactly in composition with any member of the series, and some attempts which were made to separate the gases from 498 DR EDMUND RONALDS ON AMERICAN PETROLEUM. each other by washing with alcohol, did not yield more conclusive results than those already obtained with the mixtures. with the oil at the springs. ( 499 ) XXXVI.—On Sun-Spots and their Connection with Planetary Configurations. By Barour Stewart, Esq., M.A., F.R.S. (Read 18th April 1864.) In pursuance of an idea which occurred independently to Professor Tarr and myself, a careful examination has been made of the solar autographs, taken at Kew and Cranford, under the superintendence of Mr Warren DE ta Rue. This was done with the view of detecting, if possible, some reference to planetary con- figurations in the behaviour of sun-spots, and in this undertaking, much aid was derived from a remark once made by Mr Brcxey of Kew, when taking pictures of the sun, to the effect that, for a considerable period of time, he did not observe any spots in the act of breaking out on the visible disc of our luminary. A few words may not be amiss regarding the nature of the scrutiny to which the solar pictures were subjected, and also the value of this as a test of planetary action. In the first place, let us bear in mind, that by the rotation of our luminary, the different portions of his surface are successively presented to each planet in turn. Now, if the bodies of our system have any appreciable influence of this kind upon the sun, it is natural to expect that this should differ for any given portion of his surface, according as this portion is presented to the influencing body, or with- drawn by rotation, so that the sun’s diameter is interposed between it and the planet. We should therefore expect to find that, for a given date, the spots ‘should all begin to break out into visibility at or about the same ecliptical longi- tude. Similarly with regard to their healing up; and, generally, all spots on the sun’s disc at a given date should behave in the same manner as they pass a given ecliptical longitude. It is needless to conceal the great difficulty, if not impossibility, of a complete “and final examination of sun-pictures after this method; but, on the other hand, very little consideration is required to show us its great value as a test of the fact ‘of planetary action. For if it once be proved (which may easily be done by means of sun pictures), that all the spots on the sun’s disc at a given date behave in the same manner, as they pass a given ecliptical longitude, we are then compelled to resort to planetary action as the only conceivable explanation of such a phenomenon. In the sun pictures taken by the Kew Heliograph, a vertical line denotes a north and south line through the sun’s disc-—that is to say, such a line denotes a section of the sun’s surface, by a plane passing through the earth’s axis; and therefore perpendicular to the plane of the equator. When this plane passes also through ' the pole of the ecliptic, which it will do twice a year, the vertical diameter of the picture will denote a line of ecliptical longitude; but in the following very VOL. XXIII. PART III. 6 T 500 MR BALFOUR STEWART ON SUN-SPOTS AND THEIR approximate investigation, this line has been used as denoting sufficiently well an ecliptical longitude at all seasons, and the behaviour of the spots has been examined with reference to it. This difference is of less consequence, when we reflect that solar spots occur in a zone extending not very far on either side of the solar equator; and therefore also not very remote from the plane of the | ecliptic. . The motion of the spots, owing to rotation, is in these pictures from left to right, and the earth or point of view from which the phenomena are observed, is of course in that longitude which passes through the centre of the picture; so 4 that if any planet were 90° to the left of the earth, it would be opposite that por- tion of the sun’s disc corresponding to his left limb; and if 90° to the right, if would be next the right limb. The motion of the planets is also from left to right, so that Mercury and Venus gain upon the earth, while on the other hand, the superior planets all behind to the left. : In making this examination of sun-spots at Kew, it was soon seen both by Mr Becxey and myself, that if the sun’s disc be filled with spots at any period, and if one of these begins to heal up before passing the central line, another does the same; if again, the disc be empty of spots, and one breaks out on the right- hand side of the disc, another spot will break out on the same side, and not on the left. a So marked is all this, that | have been enabled to construct the following table, from which it will be seen, that the same behaviour of spots often lasts for a considerable period of time. In this table, the planets of which the action is investigated, are Mercury, Venus, and Jupiter,—the first of which, although small, is very near the sun; the second, although farther from the sun, is much larger than the first; while the third is far off, but extremely large. 4 The pictures (which comprise all those at Kew available for the purpose) ) were examined by myself, and the result obtained was confirmed by a separate examination by Messrs BeckLey and WuippLe of Kew Observatory. From groups (1), (2), (4), and (5), we find that when Venus is at or nea E opposition, there are a good many spots, and their tendency is to increase in size up to the centre, or somewwhat past it, and then decrease. Again, for groups (3), (6), (7), (8), Venus is at or near conjunction, and there . are few spots; while for group (8), where both Venus and Jupiter are in conjune- tion, we observe a tendency towards the breaking out of spots on the second half f of the disc. As far, therefore, as may be gleaned from this record, Venus is espe- cially influential in promoting the formation of spots for that portion of the sun's surface, which is receding from her, and in arresting this formation for that Pol tion which is approaching her. qj 501 CONNECTION WITH PLANETARY CONFIGURATIONS. ‘006 ULY} Ioyvord st syoursd om oY} Jo apnyzLsuo] jeodrpo oyy uosajog apsue oy} ‘yYF11 04 yo] WoIy Yyae oY possed sulavy snua,A 4e ‘qYSII oy} 0} YonT ‘uorjtsoddo avoyy ‘uomtsoddo 0} Sursseg “WT OY} OF 08 ‘WOT OY} 0} OTT VW “4Y.OII oY} 07 001 qnoqe 4sv] ye st pue ‘uoy -1soddo ysnoryy pessed seyy Pear eu 0} pulyoq s]jey pavasoye ‘ET Youey uo uorjounluoo yw ‘JYSI oY} 07 Yon! ‘FYSIL oY} 0F YON ‘royidnp Jo uorts0g ‘JYSII OY} 0} 0G 10 , ‘JYSIL 043 03 .O€ ‘USI 043 03 sessed pue dq ‘WOT OU} OF Gh NOGY “391 OT} 07 You | ‘read oy} JO pud oy} ynoqe sure}ye 4 YOM SuOTIIS -oddo 03 34614 oy} W014 8004 ‘VYSII oy ) 0} uoyounfuos ysno«yy ye, oy} woz possed Taal ‘uontsoddo rea Ny 4 WYSE oY} 0} POUT | ‘snmeA JO UOTISsOg ‘uorztsoddo aeayy PL yy oF yong ‘YSIL OY} OF, | ‘sassed puv ysvy ye dn soutoo ‘JOT OY} 0} YOnTE ysay 4W ‘FYSIt ay} 0} [ap poos W | "yywes oy} yjta uorounfuoo ut 4180 yy “AMMOoIOT, JO WOrpIsog ‘Iap1og st[} 0} OS Sulop onuy -U0d puL “YSTUIWUIp 01}U90 oY} SUTYOVaL arojoq Ayqeqord ynq say ye osvoro “Ul Yyorya ‘odaey autos ‘syods o10q ie peed? J9A0 Suissed ut ysturutp 0 Louspuay, ‘sjods moz L104. ‘puooes oY} UL YStuTWUIp pure Yyey 4ysary o4y UL OSvoaIOUL 0} Tayyea AOUapus} v 2q 0} savodde a10Y} pur ‘s}ods jo Aytorvosyeoid ® st ary} A[ng yo Suruurseq ayy Ul ‘a.1,U00 OY} ysvd 03 sjods jo osvaaour [e1oues VW ‘asva.oap wou} pue “y148vd 10 91309 a4} 0} osvaso -ur 0} Aouepue, ‘syods Auvur poos y ‘OPIS JYSLC 04} spavaroy ATTe~odsa ‘no yeorq 0} Aouspue, ev pur ‘sjods mag ‘aUl]T [eIyUI0 oY} ysed yeyMoulos 0} oesvorour ‘syods Auvpy ‘OUI [VI} WED aq} eTOJoq YSTU -1wiIp 0} Aouepuey v pur ‘sjods Cuvpy ‘sjodg jo mmorvyeg CARS Gh ee ee “O8I uvyy SSo] pue ne 0% oung ‘Lg “990 og SURE 6981 ‘gt Avy 0} 2 “qa, ‘ZOST ‘¢ “PO 03 91 “3dog "6S8I ‘g ydog 0} ¢g ‘sny "6981 “ope q} ‘suvom sIyy, x, eee xj (0) ay 5D ate ie a ac fo fs } } “MdLIdN ff GNV ‘SANTA ‘AUNOUAJ AO SNOILISOD AHL ALIA AAUVANOO SI SLOdQ-NOG JO YAOIAVHGG AHL HOIHA NI ‘ATG VL oe - . 502 MR BALFOUR STEWART ON SUN-SPOTS AND THEIR With respect to Jupiter, these records do not enable us to come to any con- clusion; perhaps the reason of this may be, that the diameter of the sun is very insignificant compared with the great distance of this planet, and that we ought rather to look for its influence in some change produced on the sun’s surface, as it passes from perihelion to aphelion. In the interesting volume on Sun-Spots, — recently published by Mr CarrineTon, we have a comparison of this nature, the results of which are embraced in the following table :— CoMPARISON OF THE DATES OF GREATEST AND LEAST SUN-SPOTS, WITH THOSE OF THE - GREATEST AND LEAST RADIUS VECTOR OF JUPITER. (Rom Mr CARRINGTon’s CuRVES.) Greatest Maximum Least Minimum Elongation. of Spots. Difference. Elongation. of Spots. Difference. 18630 — 18607 = } 2:6 1845'1 — 1843-2 = + 19 1851-1 — 1848:9 = 4 272 1833:°2 — 1833°5 = — 03 1839:°2 — 1837-4 = + 18 1821-4 — 1823:0 = — 1:6 ISA ee Ue PA8)27/ eS 1809'4 — 1810:0 = — 06 1815:4 — 1816-8 = — 1-4 1797-7 — 17980 = — 03 1791:9 — 17886 = + 3:3 1785:9 — 1784-4 = + 1°5 178070 — 17795 = + 05 1773'9 — 17752 = — 13 1767°9 — 1770°5 = — 2:6 1762:0 — 1766-2 = — 49 1756-2 — 17616 = — 5-4 1750°'1 — 17685 = — bat 1856°8 — 18559 = + 09 On this subject, also, Mr Carrincton makes the following remark. “ It wi l be seen that from the year 1770 there is a very fair general agreement between maxima of frequency and maxima of Jupiter's Radius Vector, and between minima and minima, with such an amount of loose discrepancy, as to throw grave doubt on any hasty conclusion of physical connection. In the two periods” which precede that date, there appears to be a total disagreement ; and although the data for frequency are less certain for those years, yet the general form of the curve of Professor Wo xr, is probably too well established to admit of any- thing like reversion, by the addition of other observations which have not yet come to hand.” Now, every one must agree, that caution is very requisite in a generalization of this nature. On the other hand, lam tempted to think that the behaviour of sun-spots, to which allusion has been made in this paper, is very conclusive as to the fuct of planetary action, and if this be allowed, it must < the recession of Jupiter from the sun is favourable to the breaking out of spots, and his approach unfavourable to their production. Coupling this with what I a) tavourable to spot production, while the recession from the sun of a heavenly body is favourable to the same. ) Let us now see what support this conclusion derives from the phenomena — of CONNECTION WITH PLANETARY CONFIGURATIONS. 5038 variable stars ; but before doing so, I would remark, that when the sun’s disc has many spots on it, we probably derive less light from it than when it is free from spots. This is not altogether self-evident, for each spot is accompanied by faculze, and it has been observed by Mr Warren Dea Rue and others, that these faculze, when near the sun’s limb, are much brighter than the neighbouring surface of the disc, but when in the centre they are not sensibly brighter than the neigh- bouring surface. When, therefore, a spot occurs near the limb, the loss of light which it implies may possibly be replaced by the faculee which accompany it; but in this position, both spot and facule are much foreshortened, and present but a small field of view. On the other hand, the same spot, when near the centre of the disc, fills a much larger field of view, and the loss of light which this implies is not made up by any superior brightness in the accompanying faculze beyond that of the neighbouring disc. On the whole, therefore, we have a loss of light occa- sioned by spots. Against this it may perhaps be argued, that when the sun’s disc is full of spots the general luminosity is greater than during those periods when there are comparatively few spots; but we have no proof for such an assertion. Assuming, therefore, that a disc full of spots is deficient in lumino- sity, let us now turn to the phenomena of variability presented in other stellar systems. Without entering into details, it will be sufficient to mention the hypo- thesis which many astronomers believe in as serving well to represent these pheno- mena, I allude to that of rotation on an axis, where it is supposed that the body of a star is from some cause not equally luminous in every part of its surface. It is in the last clause of this sentence that the deficiency of such an hypothesis as a physical, and not a mere formal explanation, consists: for it is exceedingly diffi- cult to conceive a body, one part of which is permanently luminous, and another part permanently dark. If, however, we conceive of a variable star as a sun round which a planet of some magnitude revolves at a small distance from its primary, and adopt the law which probably obtains in our own system, we shall have a state of things phenomenally equivalent to a body partly dark and partly bright. For as the planet moves round its primary, that portion of the disc of the latter next the planet will be brighter than that which is more remote, and this appearance will move round as the planet itself moves. It still remains to discuss the case of a planet with a very elliptical orbit. Such a body would for a very long period of time be far removed from its primary, and for a short period of time extremely near it. We might therefore expect, according to the above law, a long period of comparative darkness in the primary, followed by a short period of brilliancy, corresponding to the perihelion of the planet. Now, this is precisely the appearance presented by temporary stars. These bodies emerge from comparative obscurity, become suddenly bril- liant, and thereafter very soon begin to fade, darkness being their normal state, while their brilliancy is short-lived and exceptional. VOL. XXIII. PART III. 6uU 504 MR BALFOUR STEWART ON SUN-SPOTS. The hypothesis herein advocated appears, therefore, to be capable of explain- ing, we may say, all the phenomena both of sun-spots and double stars, so far as these are at present known. In conjunction with Professor Tart, the author would beg to make the follow- ing suggestion before concluding this paper:—These phenomena,* appear to lead to the conclusion, that when celestial bodies approach each other, there is an evolution of light. Let us compare this with the analogous fact, that when atoms approach each other we have the same result; and we are conducted to the belief, that one great law acts in all these cases, although its modus operandi is no doubt circumstantially different in each. (Added 9th April.) We may also be permitted to state our impression, that in the case of atoms, as in that of systems, it is perhaps the largest body which radiates most, for when metals of which the combining equivalent is generally large, unite with oxygen for instance, which has a small equivalent, it is the vibration of the metallic particle, and not of the oxygen, which give a character to the light emitted. Possibly the following may be the explanation of this fact :— The idea of the constitution of ether, which involves the fewest assumptions, is that which makes it a medium by means of which a body in motion parts with 3 its motion to neighbouring bodies, and the phenomena of percussion perhaps entitle us to assume, that this property which a body has of stopping the motion of a neighbouring body depends on the size of the former, and its distance from the latter. ) When, therefore, a small body is in violent motion near a large one, the pre- j ferential radiation of the motion of the former towards the large body above its _ radiation to the surrounding bodies will be very great. But when this motion has once been absorbed by the larger body, and taken to a great extent, the shape — of heat since energy as well as momentum must be preserved, the preferential radiation of this towards the small body, as compared with its radiation to neigh- 4 bouring bodies, will not be great, but it will radiate nearly equally on all sides. The large body will thus, as it were form a reservoir into which the motion — of the smaller body is emptied, and from which it is distributed nearly equally — in all directions. * And the behaviour of comets ? te . ( 505 ) XXXVII.—On the Freezing of the Egg of the Common Fonl. By Joun Davy, M.D., F.R.S., Lond. and Ed., &. (Communicated by Professor MacLaGcay.) (Read 2d May 1864.) In the Transactions of the Royal Society for 1778, Mr Hunter has given an account of some experiments which he made on the freezing of the egg of the common fowl, from the results of which he inferred,—“ That the fresh egg has the power of resisting heat, cold, and putrefaction, in a degree equal to many of the more imperfect animals, . . . . and that it is more than probable, this power arises from the same principle (a living principle) in both.” Mr Pacer, in the Transactions of the same Society, the volume for 1850, has described how he repeated and added to these experiments of HuntEr, but whilst admitting their general accuracy, the conclusion he drew from them was different, viz‘ That it is not by the power of a vital principle that eggs resist the influence of cold,” but is owing to the viscidity of the albumen,—to use his own words,—“ That the property which enables fresh albumen to descend below 32° Fahr. without freezing, is its peculiar tenacity or viscidity, by means of which the water combined with it is held so steadily, that the agitation favourable or even necessary to the freezing, at or near 32°, cannot take place.’”* The manner in which Mr Hunter and Mr Pacer conducted their experiments was similar. They both used strong freezing mixtures, and consequently there was a rapid cooling of the eggs, which were subjected to the cooling process; thus, in the experiments of the latter, fresh eggs placed in temperatures varying from zero to 10° Fahr. were frozen on an average in 26 minutes. In neither of their experiments does it appear that the time of the exposure of the eggs was prolonged much beyond half an hour. Considering the importance of the subject in its physiological bearings, and reflecting on the circumstances under which their experiments were made, it appeared desirable to repeat them with some modifications. This I have done. The chief differences have been, that instead of an artificial mixture for cooling the egos, and a rapid refrigeration, the eggs, in the trials I have made, have been exposed to the open air, and have been cooled more slowly. 1. An egg, a fortnight old, was placed on grass and left out fully exposed to * Mr Pacer assigns for the freezing-point of the egg a temperature of 32°, or between 31° and |, 32°, and supposes that it cannot fall below that, unless at perfect rest; he says,—“ That the egg should be unmoved, and that its albumen should be not even so much disturbed as by the intro- duction of the thermometer.” My results, as will be seen, nowise accord with this. VOL. XXIII. PART III. 6x 506 DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. the sky, on the night of the 22dof February, when a register thermometer, placed alongside of it, was 19° at its lowest. On the following morning at 10 a.M., it stood at 22°. The egg was now found fractured and frozen, the fracture of the shell proceeding from the small end towards the large end, containing the air- vesicle. With a strong knife, a section of the egg was made with some difficulty, so hard it had become. The albumen was white and crystalline, and most dis- tinctly towards the surface. The yolk had much the same appearance it would have had had it been boiled ; it showed no appearance of change of structure, none of crystallization ; it was easily indented, and was softest at the centre, where its colour was orange-yellow, and was strikingly contrasted with that of its including or outer portion, which was pure yellow. During the thawing, some of the yolk became diffused in the white, seeming to indicate, at least, a partial rupture of the membrane of the former. From what is mentioned of the yolk, it is evident that in the cutting of the egg, the resistance encountered was most in the albumen. 2. On the night of the 22d of the same month, two eggs were similarly exposed, one laid that day, the other of a large size—double the ordinary size—and, as was afterwards ascertained, containing two yolks; it had been kept about six months, — and during the whole time had been exposed to the air within doors. At 8°30 A.M., next day, the thermometer close to them was 25°; I am not sure that it had been lower at night. The fresh egg was fractured, the fracture proceeding from the small end, and reaching halfway towards the large end. A little of the albumen had exuded, and was seen as a white frozen froth. The shell was — removed with care, leaving the whole egg entire in its frozen state. It was of a pure lemon yellow, centrally darker, from the colour of the yolk transmitted through the translucent albumen. Portions of the shell removed had attached — to them a thin layer of albumen, which showed distinctly a cellular or areolar — structure. After thawing, the egg for some time retained its form, exhibiting the ¥, structure just mentioned; gradually, however, as if from gravitation and the con- traction of the cells, the albumen separated, leaving the yolk, in its proper mem- brane, entire. The albumen was unusually thin, 7. ¢., less tenacious than when ~ retained in the structure described.* The large egg was not fractured, but when — opened, it was found to be frozen. There was a great deal of air in the large end, a circumstance which may account for the freezing without rupture. A thermo- meter placed in the white close to the shell fell to 27°; in the yolk, to 275°. The appearance of the two parts was much the same as that of the preceding. 3. On the 24th of the same month, two eggs laid the same day were exposed: _ one was smeared with a solution of gum, allowed to dry; nothing was done to — * From such observations as I have made, this filamentous cellular structure of the albumen a 1 differs but little from fibrin; it appears to possess the same contractile quality. (See the authors — ** Physiological Researches,’ p. 422.) DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. 507 the other. During the night, the thermometer was as low as 24°: 3; at 8°30 A.M. on the 25th, it was at 25°. Both eggs were found ruptured, the fracture extend- ing from the small end towards the large; if there were any difference, the gummed egg was most ruptured. The shell removed, the albumen of each pre- sented the same crystalline and cellular appearance as that of the day preceding. The yolk of one egg was 27°5°; the white 31°; of the other, the gummed, the yolk was 29°, the white 31°. These temperatures were ascertained when the temperature of the open air had risen to 35°. 4. On the night of the 25th, two newly laid eggs were exposed, one of them smeared with butter. During the night the thermometer was as low as 19°. At 8°30 4.m., on the 26th, it was at 20°. Both eggs were found fractured, the smeared one, at about equal distance from both ends, the other at both ends. At 11:15 a.m., when the thermometer in the open air had risen to 30°, the tempera- ture of the smeared one at its surface within the shell was 31°5°; deeper, 31°; that of the other, in the albumen, just within the shell, was 30°5°; deeper, 30° ; it was more firmly frozen than that smeared with butter, and this throughout. These two trials were made on the idea (not supported by the results), that the coating of one of the eggs might greatly retard or prevent its freezing. 5. On the 26th, two eggs were exposed, one taken from lime-water, where it had been kept about twelve months; the other, laid the same day; ‘both sank in water. Their temperature, ascertained before exposure by a thermometer intro- duced through a small hole, made about midway between the two ends, in the newly laid was 45°5°; in the other 46°, this within doors. At 10°3° a.m., they were placed on moss in the open air, the thermometer close by 26°. At 10:24 A.M., when the open air was 32°, that of each egg was 39°. At 10°40, the air 34°, that of the fresh ege was 35°; of the other 36-5. At 1:10 p.m., when the open air was 44°, that of the fresh egg was 40°, that of the other 38°5. These results do not appear congruous, I give them as obtained. They may at least tend to show the obscurity of the subject. 6. On the night of the 26th, other two eggs were exposed, one from lime- water, the other newly laid; both sank in water. Most of the time the sky was overcast. At 8°30 a.v., on the 27th, the thermometer was 31°. Both eggs were free from fracture, and it may be inferred were not frozen. All the while, from the 22d to the 25th, a calm prevailed, and the sky at night was unusually clear. The newly laid ege which had been exposed in the last experiment to a tem- perature of 31°, on the 27th was put under a hen that had been sitting since the 19th of February. On the 10th of March, when most of ten eggs were hatched (six out of nine), the egg in question was taken from under her and examined. _ The foetal chick was found well-developed for the period, and was evidently alive when removed warm from the nest.* * The foetus, well detached from the vitellus and the membrane, weighed 27°3 grs. The allantois 508 DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. 7. On the night of the 9th of March, two eggs were exposed to the open sky, one newly laid, the other from lime-water. The thermometer close to them fell as low as 20°. At 830 4.m., the following morning it had risen to 31°. There had been a fall of snow, and the eggs were found buried in the snow, as was also a glass of water, the water about equal in volume to that of an egg; the water was frozen to the depth of about an inch. Both eggs were found fractured longi- tudinally. The newly laid egg was easily cut in two by a knife, both the albumen and yolk being comparatively soft. The former had a crystalline appearance, and was of a light-yellow colour. The yolk was marked with concentric lines of different hues of yellow and orange, the latter most conspicuous towards the centre. The thermometer at the centre was 30°5°; next the yolk in the albumen it was 29°5°.. The two parts not being firmly frozen were easily separated. The ego from lime-water was as easily divided. Its albumen exhibited much the same appearance as that of the newly laid. Its yolk was of an orange colour at centre, but not concentrically marked, like that of the preceding. Its temperature at the centre was 30°, that of the albumen, close by the yolk, was 29°75". The newly laid egg was somewhat the largest, its long diameter being about 4th of an inch in excess of that of the other ; their shorter diameter was the same. Besides the preceding, I have made other trials on change of temperature of the two kinds of eggs; the newly laid, and those long kept in lime-water. This was done by putting them alternately into hot and cold water, accompanied by others of the same kind which had been boiled hard. I have observed no differ- ence in the rate of increase and diminution of temperature, except a slight one, and that, as well as I could judge, depending on the difference of the weight of the eggs used. Even between the eggs hardened by boiling and those not so hardened, the augmentation and increase of temperature hardly appreciably differed.* or membrane next the shell, was highly vascular, as was also the vitelline membrane, +their vessels conveying red blood of a florid hue. The red corpuscles were, for the most part, of the form of those of the adult fowl; some were circular and yet nucleated; these were of a larger size. The fluid be- tween the allantois and the yolk was slightly coloured reddish, from blood corpuscles suspended in ~ it, from the rupture of some vessels. It was limpid, very dilute, contained little or no albumen. When heated to the boiling point, it was not coagulated, nor did it become even milky, merely a minute portion of greyish matter subsided, no more than might be referred to the blood corpuscles. It had a strong alkaline reaction. 28-2 grs. of it, evaporated to dryness, left only ‘3 gr. of solid matter, or 1-06 per cent., consisting chiefly of common salt and an alkaline carbonate. Contiguous to the yolk, and contained within its vascular membrane, there was some very tenacious transparent albu- men, of faint alkaline reaction. By heat it was coagulated ; the coagulum was milk-white, unusually _ dense andfirm. 57 grs. of the viscid matter, evaporated to dryness, afforded a residue of 14:7, or 26°8 s per cent. The yolk consisted of a thin and thicker fluid, both of which showed a faint alkaline reaction, __ A mixture of the two-was of the sp. gr. 1022; of the thin kind, 33:9 grs., evaporated to dryness, — were reduced to 8°6 grs., or 25°3 per cent. of the thicker kind; 30-4 grs. evaporated to dryness were _ reduced to 9:3, or 30°6 per cent. The eyes of this foetus were fully formed; the lens of each, resting _ on the crystalline humour, was :133 of an inch in diameter, a perfectly transparent sphere. : ; * The appearance of the yolk of the newly laid egg, and of that from lime-water, kept about — oe . twelve months after being boiled, slightly differed ; that of the latter was of a paler and less bright % - * is DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. 509 As the results of the foregoing experiments seem to show that there is no well- marked difference as to freezing between the newly laid egg and the egg which has been kept many months, nor any well-marked difference as to their rise or fall of temperature, they appear to support Mr Pacet’s conclusion, that the egg is not protected under these trials by a vital principle, as supposed by HuntsEr. There are other experiments which I have made, which seem to have the same tendency. These have been on the freezing of the different parts of the ege by ether, and a freezing mixture in a thin glass tube. The advantage of this method is, that what occurs is seen, and one is thus better acquainted with the particulars. Owing to the peculiar qualities of the contents of the ege, the subject is obscure and difficult, and it is not easy to arrive at consistent and altogether satisfactory results. My first object was to endeavour to ascertain the temperature at which the several contained parts freeze. From many trials, I am led to infer, that the | freezing point of the thinner albumen is 31°75°, of the thicker 31:50°, and of the yolk 31:25°; and that comparing those of the newly laid egg with those of the egg long kept in lime-water, there is no well-marked difference. Whether such results might be expected, I hardly venture to form an opinion, not knowing to what extent the two differ in composition. That there is a difference, has already been noticed in the appearance of the yolk, and in the quantity of air contained ; and another slight difference I have observed,—viz., that whilst the yolk of the newly laid egg has an acid reaction, that of the long-kept egg is neutral. Owing to conflicting results, and many repetitions in consequence, it would be tedious to give the particulars of the many experiments which I have made. One or two examples I shall offer, and this chiefly with a view to show the variability of the freezing point. The trials were made in a tube ‘7 inch in diameter of thin glass. The ther- mometer, a very delicate one, was introduced with the fluid, and was often moved. As the results with a freezing mixture were least unsatisfactory, I shall confine myself to them. In the yolk of a newly laid egg the thermometer fell to 20° without freezing occurring. It was taken out freed from adhering yolk, and again immersed ; it fell to 28°, presently freezing began at the circumference, the thermometer in the centre continuing at 28°, where the yolk was still fluid; pretty rapidly it rose to yellow. In both eggs, between the yolk and the white, there was a greyish discoloration. The quantity of air that was disengaged from the egg long kept was remarkable. I supposed that it raight be carbonic acid or azote; but from one examination I made of it, it appeared to be merely , Common air. Owing to this circumstance, eggs thus kept, or kept long otherwise, crack, and some- times with a little explosion, when put into boiling-water ; the newly laid, which contain very little or no air, not being subject to the same effect,—the exemption may be held to be characteristic. VOL. XXIII. PART III. 6Y 510 DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. 30° and 31°, the freezing making progress. When the greater portion was frozen, the thermometer, where the freezing had not reached, showed the temperature — last mentioned. The experiment was repeated on another portion of the same yolk. In it the thermometer fell to 22° without the occurrence of freezing; it was taken out, wiped, and returned; it fell to 28°, and continued at that degree several minutes, the yolk remaining liquid. It was again taken out and wiped, and returned, it fell to 30°, and almost immediately freezing took place at the circumference, whilst in the middle the yolk was still fluid, though the thermometer there stood at 28°, after that it rose to 31° and to 31:25". With the yolk from an egg kept in lime-water, the thermometer fell to 20° before freezing began at the circumference, it then rose as the freezing proceeded to 31:25°. Another portion of the same yolk fell to 28° before freezing began; the ther- mometer then rose rapidly to 31:25”. The albumen, whether thick or thin, showed the same irregularities in freez- _ ing. On what they depend I hardly venture to offer an opinion; perhaps the strength of the freezing mixture is most concerned, yet the trials made to endea- vour to determine this were nowise satisfactory. . In all the experiments which I have made on the freezing of the contents of the egg by a freezing mixture and by ether, the congelation, as might be — expected, always began at the circumference, gradually extending towards the centre; it was remarkable, unless the freezing mixture was powerful, how slowly ; it proceeded, the centre being often soft, whilst the surrounding part was hard ; and from the circumstance that concentric rings were often seen in a portion of — yolk entirely frozen, as noticed in the instance of the egg, it seems probable that ; the congelation was in a manner paroxysmal. The moving of the thermometer, — even to active stirring, in the fluid, seemed to have little or no effect in hastening _ the freezing, even at 20° or below 20°. * Mr Pacer lays stress on the low degree of temperature which the egg bore q in his experiments before its freezing took place, a result with which mine, con- ducted in the open air on the entire egg, hardly accord. He, as already remarked, is disposed to attribute this resistance of the egg to the peculiar viscid and tena- al cious state of the albumen. That this viscous state, and more especially the cel- e lular filamentous tissue in which the albumen is retained, and to which the following experiments may be mentioned in proof :— om The thick albumen of an egg was plunged into a freezing mixture; congela- tion took place at the bottom and sides, there the thermometer was 31:5", whilst — DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. O19 towards the surface and middle, which the congelation had not reached, it was 33°5°: and more remarkable still, when the albumen was frozen hard below, above, where it was still liquid, it was 35°, a difference this strikingly illustrative of the impediment offered to the mobility of the fluid by the tissue in question. Another experiment with the thinner portion of the albumen of the same egg, one which had been kept in lime-water upwards of twelve months, may be worthy of notice in the way of further illustration. In this instance, after freezing, when thawing was going on, and the albumen was perfectly liquid below, there the thermometer was 32°5°, whilst towards the surface it was 31:75°, a difference, owing, it may be inferred, to particles of ice ascending in the act of thawing. In this trial congelation did not begin until the temperature of the fluid had fallen to 20°. Besides the quality just mentioned, there is another, which probably has much to do in retarding the freezing of the egg,—viz., the composition of its several parts, and especially their saline elements, on the presumption of the well- ascertained property which the soluble salts have in lowering the freezing point of water, and how in aqueous solutions containing salts, such as common salt, by augmenting the cold, a gradual concentration may be effected, a strong brine may be obtained in contact with frozen water, or mingled with it. In some of my experiments the appearance of the frozen albumen, in a soft state, at a tem- perature below 32°, much resembled sea-water suddenly frozen. I have mentioned in a preceding note the fluids contained in the egg in an advanced stage of development. These, with the foetal chick, I subjected to the action of a freezing mixture. The results obtained seemed in accordance with what has been just stated. The very thin fluid next to the allantois or outer vascular membrane, froze partially at 30°5°; it was not completely frozen at 21°, a portion was still fluid at ‘the centre. The thermometer, as the freezing proceeded, rose to 31:5’, and it continued at that temperature whilst thawing. The very thick viscid fluid fell to 23° before freezing began, though it was stirred ; when the freezing took place, it rapidly rose to 31°25. The thin portion of the yolk fell to 23° before it began to freeze, then it pretty rapidly rose to 31:75; when the thermometer was kept in this central, more fluid part, it was 31°. The results with the thicker portion did not differ materially. The foetus fell to 20°, and remained at that temperature some minutes without | freezing. Whatever may be the cause or causes on which the resistance of the egg to | freezing depends, its possessing this property must be acknowledged to be a | _ happy circumstance in the animal economy, and an adequate security for the ‘ preservation of its life, or of that of the germ which the fertile egg contains, and on which its after development into the chick depends, 7.¢, under the ordi- 512 DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. nary conditions of incubation, taking the season of the year into account, the habits of each kind of bird, and the kind of nest it forms. But whether it belongs to the egg of the common fowl, to the extent which Mr Pacer infers, seems to me somewhat doubtful; and also somewhat doubtful whether the | freezing of the egg is compatible with any ufter development. In the following . passage the first is stated, the second is inferred. Speaking of the peculiar pro- perty of the albumen, he says:—‘‘The purpose or utility of this peculiar pro- perty of the albumen of eggs is manifest in the defence which it provides for the eggs exposed to a temperature below 32°. If an egg be frozen, the damage sustained by its structure is such that the germ cannot be fully developed; but mere cold, however intense, if freezing does not take place, does not prevent the complete development of the young bird.” In proof, he adds, “ L placed three eggs in a freezing mixture, varying from zero to 5° Fahr., one of them froze, and its shell was cracked from end to end; another froze, and when it thawed, its yolk was burst and mixed with the albumen. In incuba- tion, two spots of blood were developed in the former, and an enlargement of the cicatricula ensued in the latter of these eggs—sufficient indications that the intense cold and freezing had not killed them, though it had spoiled their struc- ture.* But in the third egg, which had been exposed for nearly an hour to a temperature below 5° Fahr., perfect development took place in incubation. Even this degree of cold had neither killed nor frozen the egg, though, according to the average rate at which eggs part with heat, its whole substance must have’ been for half an hour at a temperature between 5° and 10° Fahr.”’ These, it must be acknowledged, are very remarkable results, especially the last. But, it may be asked, is it certain that in the two eggs, in which incipient development was found to have taken place after apparent freezing, the yolk was frozen, or that the part of it containing the cicatricula was structurally damaged? Moreover, is it certain that there was no mistake as to the egg: which was hatched after having been exposed to so a low a temperature? The the freezing of the several parts begins. One experiment in such a matter, when the result is anomalous, is hardly to be relied on. The experience of the breeders of poultry is not in favour of eggs bearing any considerable degree of cold with impunity. It is well known to them that the tendency of eggs to * Are, it may be asked, the above indications sufficient 4 In two instances I have found specks of blood on the membrane of the yolk of the newly laid egg. In that of the last, I examined the blood, and found it to contain well formed, elliptical nucleated corpuscles similar to those of the adult fowl ; the inference made was, that the blood was derived from the oviduct in the descent of the yolk. As to the enlargements of the cicatricula, its evidence seems less open to objection; and yet, without a large comparison, can it be said with certainty, that the size was the result of increase from development? I have found the cicatricula of a newly laid egg that had been frozen, ap- parently a little enlarged. DR DAVY ON THE FREEZING OF THE EGG OF THE COMMON FOWL. 513 abort, is much greater in the early spring, in cold weather, than in the advanced spring and in summer. Very lately an example of this kind occurred. On the 26th of January thirteen eggs were put under a hen, a good sitter; on the 16th of February six of these were hatched ; the chickens produced were strong and healthy ; of the other seven—the aborted—one only was found in a state of advan- ced putrefaction; in three of the remaining there were embryos from ‘6 to ‘7 inch in length, and in the other three, though no embryo could be seen, there was an appearance of vessels containing discoloured blood.* During the period of incu- bation for many days there was severe cold; but then, even in the open air, exposed to the clear sky, the thermometer never fell below 18° Fahr. The hen’s nest was under cover. Whether the germ can exist, retaining life without vztal action of any kind, even at a temperature below the freezing point, is a physiological question, I need hardly observe, more easily asked than answered, and yet surely a question deserving of consideration. If, as some distinguished inquirers maintain, there cannot be force without action, can there be life without it? or, to quote the words of Mr Pacer, giving them in the form of a question, Can there be ‘a vital princi- ple in organized bodies, such as may enable them, even when inactive and dis- playing no other sign of life, to resist passively the influences of physical forces 2”’ Another question, of no less difficulty, is, Whether the germ can resume vital action after having been frozen? I will only remark, that the mere act of freezing does not necessarily imply inaction, at least the absence of chemical charge, for I have found ammonia in an unmistakeable manner evolved from the fresh egg when frozen. And further, provided the structure of the parts— that of the yolk and germ for instance—be not materially altered. and from freezing, the structure of the yolk, we have seen, has not been apparently changed | is not the condition of the germ similar to that of the ear of the rabbit and the wattles of the cock, which Hunter found could be frozen without mortifying.} * In one of these only, were there marks of incipient putrefaction. It is noteworthy, that in three of these, the albumen was firmly coagulated, as if it had been boiled; it was quite white, and showed its usual alkaline reaction. The yolk was also coagulated, but less firmly. Mr Hunter states (op. cit. p. 29) “that if an egg was not hatched, that egg became putrid in nearly the same time with any other dead animal matter.”” This does not accord with the results just mentioned, nor with others which I have obtained. In many instances I have found the aborted eggs free from putridity after incubation ; whether an embryo could be detected or not, there was commonly a blending of the yolk and white, and the formation of a fluid, almost entirely destitute of viscidity. Such an admixture is certainly favourable to the putrefactive change. } Phil. Trans., for 1778, p. 34. Lesxetu How, AMBLESIDE, March 17, 1864. VOL. XXIII. PART III. 6 Z CubES a) XXXVIII.— On the Morphological Relationships of the Molluscoida and Coelenterata, and of their leading Members, inter se. By Joun Denis Macponatp, R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” (Read 21st December 1864.) Few departments of zoology have recently suffered more remarkable changes, both in classification and accepted views of structure, than the Polypi or Ceelen- terata, and their immediate allies in the ascending scale, the Molluscoida,—greatly depending upon the more extended study of those animals of late years. We have been thus enabled to discover natural affinities: which prima facie evi- dence would scarcely ever have indicated, as well as intrinsic differences which the same kind of evidence has hitherto been incapable of revealing to the mind. Leading from the Protozoa to the Mollusca proper, the Coelenterata and Mol- luscoida constitute an unbroken series of animals forming a considerable section of invertebrata, distinguished from the Protozoa by the development of true ova, and from the Mollusca by the property of gemmation developing compound ex- amples of the principal types. Furthermore, the motion of the blood, or its equi- valent, is effected either by ciliary action or by a propulsive organ; but when the latter occurs it is unfurnished with valves, so that the course of the circulation may be reversible in the same canals. The study of the different stages of development of a certain organ in the same animal comes within the pale of ordinary physiology: but when we pry into the progressive advance of any organ or function, taken in the abstract, we _ enter upon a more comprehensive branch of science, which not only embraces the common physiology of each particular animal, but its combined import in all. On comparing the relative parts of two distinct animals, one unaccustomed to a study of this kind could scarcely doubt that the mouth of one was anything more or less than the exact equivalent of the mouth of the other; but it may be clearly ‘shown that mouths acting as such, so far as simple function is concerned, may nevertheless exhibit a remarkable difference, homologically speaking, in animals constructed on different types. It was formerly believed that the branchial and cloacal orifices of the Asci- dian were homologous with those of the siphonal tubes of Lamellibranchiata ; but this very natural error has been pointed out by Professor Huxiry, and it can- not be doubted that the orifice of ingress is in reality oral in one, while it is simply . pallial in the other. In the Ascidian, moreover, the inner or commonly recog- nised mouth is but the cesophageal opening, though it is critically answerable to VOL. XXIII. PART II. va 516 MR J. D. MACDONALD ON THE MORPHOLOGICAL RELATIONSHIPS the mouth of the polyzoon. It may be assumed that the prominent mouth of the Hydrozoon (in which, in truth, there is no stomach homologous with that of the higher types) is equivalent to the everted internal gastric opening of the Acti- nozoon; or, conversely, that the stomach of the Actinia is but an inversion of the oral projection of Hydra, still preserving a communication with the somatic cavity, but necessitating the formation of a new oral orifice. In the same way, the ten- — tacula encircling the mouth, in some of the lower forms of animal life, are not in _ all instances homologous organs. Thus, the branchial tentacula, as they occur in — the Ascidiozoa, are found in none of the other members of the series now under > consideration; and in the passage from the tubularian Polyp to the Actinozoon, the oral tentacula of the former (with a single exception, so far as known to me) are suppressed in the latter; while the outer or somatic set remains, and even becomes more numerous or densely crowded as a general rule. The true nature of the Aggregate Tunicata was first made known by Savieny. and they were with great propriety removed from the zoophytes, with which they had been formerly confounded. To M. Mitne-Epwarps is due the credit of having elevated the Polyzoa from their low estate, and ranked them with the 4 Tunicata in his Molluscoid group. Professor Huxtery again, from his compre-— hensive view of the subject, saw the propriety of associating the Brachiopoda with the Molluscoida, but more immediately with the Polyzoa, as exhibiting the ‘‘neural” intestinal flexure, in connection with many very striking points of homology which had never before been conceived.* The delicate membrane surrounding the base of the tentacula in the Polyzoa ~ Hippocrepia is considered by Professor ALLMAN as analogous to the membrane of the respiratory sac in Zunicata ; but Mr Busx says that this has not yet been detected in any marine Polyzoon, though I may add that it is distinctly present in the Brachiopoda; and he further considers that the membrane surrounding th base of the tentacula in Pedicellina is not homologous with it, having an entirely different import. If ever a Polyzoon resembled a Tunicary, it is the said Pedi- cellina, more especially when its two dorsal bends are in course of development, and a zealous observer might be very readily deceived as to the true nature of certain parts in one bearing a striking but delusive resemblance to those in the other. Yet, without going farther into the refinement of the subject, it would not be far wrong to assume, in round terms, that the pharyngeal respiratory system of the Zunicata is represented by the oral tentacula of the Polyzoa.t The epistome of the Polyzoon, moreover, is regarded by Professor ALLMAN aS homologous with the languet of the Twnicata. employed by Pr ofessor Hux ey, more eat poe with reference to the Cetera + See Professor Artman’s remarks on this subject, in his valuable work on the fresh-water Polyzoa. Published by the Ray Society. 3 OF THE MOLLUSCOIDA AND CQLENTERATA. 517 The property of gemmation in a marked manner distinguishes the JJollus- coida from the Mollusca proper, on the one hand, while it associates them quite as obviously with the Colenterata on the other. We know nothing of a process of this kind as occurring in the so-called Ctenophora, including the families Cal- haniride* and Beroide ; but the organisation of these animals, first rightly con- sidered by Frey and Levukarrt abroad, and by Professor Huxtry at home, referred them to the higher section of Coelenterata, namely, the Actinozoa. Yet, the more I have studied Cydippe, the more it has appeared to me to hold a position be- tween the Actinozoa and the Polyzoa, linking the two by characters which it exhibits in common with either, or both. Indeed, in any other place it would seem to be not only friendless but intrusive. A view similar to this has, I believe, been already expressed by M. Voet, but I regret that I have not access to his observations on the subject. | It is curious to observe the progressive development of the digestive system, _ proceeding from the Hydrozoon onwards through the Actinozoa, Ctenophora, and Polyzoa, to the Tunicata. The important part taken by the Ctenophora as a link in this beautiful chain, is represented in the accompanying series of diagrams. Moreover, certain points in the structure of these animals, are even made more tangible to our philosophy by the light which is thus shed upon them. The stomach of Cydippe is connected with the walls of the body by two vertical septa, with two interseptal loculi. The ccecal tubes forming the lining of these loculi run forwards as far as the mouth, and are at once diverticula of an alimentary system and of a somatic cavity. We observe here, as in Actinia, a well defined internal gastric opening, bounded by two crescentic folds, determined by the persistence of the before-mentioned loculi. These latter communicate below with the rudimentary intestine which is _ yet little more than a central tubular narrowing of the somatic cavity, from the _ gastric end of which also pass off the two dichotomously-branched tubes, which terminate peripherily in the fusiform sinuses,} corresponding with the ciliated | bands. All this affords usa more distinct idea of the mode in which the intes- tinal tube is formed. Thus, instead of arising simply as an extension of the proximal end of the stomach, the whole gut is at first but a tubular process of endoderm, inclosing a portion of the somatic cavity. In Cydippe, the intestine is perfectly straight and axial, reaching the posterior extremity of the globose | body, where it exhibits a small, but distinctly marked bifurcation, and the little | heryous ganglion, with its otoconical sac, is received into the intervening recess. * This family name is objectionable, as having been chosen from a supposititious genus founded }, upon a mutilated specimen of Cydippe, indifferently drawn. t Would it be too far-fetched to suppose that these sinuses are, as it were, retrospective of the tentacula of Actinia ? 518 MR J. D. MACDONALD ON THE MORPHOLOGICAL RELATIONSHIPS The end of each division is well rounded, and closely applied to the ectoderm on either side of the ganglion, but I have always found it difficult to detect the so- called anal openings, though I have once or twice observed the escape of matters from within the tube at this part. The least I can say, however, is, that they are by no means so definite in nature as they are represented to be in figures and descriptions. Professor Huxuey first pointed out the striking original difference in the in- testinal flexure in Brachiopoda and Polyzoa, as compared with that in Tunicata. Thus, in the two former, the intestine is simply flexed forward (7.¢., towards the - nervous ganglion or ‘‘neurally”), while in the latter it is at first flexed backwards (z.e. towards the heart, or heemally), and subsequently turns forward to terminate neurally in the “atrium.” In Cydippe, therefore, the intestine is straight; in the Polyzoon and Brachiopod, it is once flexed (forwards), and in the Tunicary it is twice flexed (backwards and forwards). The nervous ganglion appears to hold some relation to the conditions just noticed ; thus, it is nearly midway between the branchial and cloacal openings in the Tunicary, between the oral and anal orifices in the Polyzoon, and at the posterior termination of the intestine in Cydippe. The homologies of the ciliated bands and tentacula of Cydippe have not yet been satisfactorily determined, though it does not appear improbable that the former organs represent the tentacula of the Polyzoon or of the Brachiopod having become retroverted, and connate as it were with the body, as next in order of suppression. The configuration of the genus Cestwi is strongly in favour of this view, and if the possibility of such be admitted, then the retractile racemose tentacula may be regarded as pallial. If, on the other hand, the position here supposed in relation to the ciliated bands of the Ctenophora be doubted without valid reason, I can only say that it is not at all more remarkable than the modifications of the — ambulacra in the Echinodermata, passing from Asterias to Spatangus for example. The branchial tentacula in the Zuntcata may be regarded as ecclusory and perhaps prehensile, while respiration is effected by their pharyngeal apparatus, and the same office is probably also exercised by its homologue the oral circle of tentacula in the Polyzoon, and the so-called cirri of the Brachiopod. In the case of the latter, however, it may be subserved also by the pallial sinus system, which is ciliated within, and thus enabled to circulate the contained corpusculated fluid. The renewal of the water passing over it is of course chiefly brought about by. the action of the vibratile cilia clothing the double row of tentacula (“ cirri’). There is apparently, to my mind, but a short step from these latter organs to the ciliated bands of Cydippe, in which they are both locomotive and respiratory, being in close relation with the aquiferous system; and it must be remembered, that this, like the pallial sinus system of the Brachiopod, is not only lined with OF THE MOLLUSCOIDA AND C@HLENTERATA. " 519 a a circulating a corpusculated fluid, but also contains the reproductive organs. Finally, the tentacula in the Celenterata are in most cases both prehensile and respiratory, while in many they are also locomotive. The accompanying series of diagrams will show more distinctly the relation- of the various organs and parts in the five groups so imperfectly glanced at A. An Ascidian. E. Tubularia, B. A Polyzoon. F. Clava. - C. Cydippe. G. Hydra. ‘D. Actinie, fixed and free. ‘The numerals have a corresponding signification in all the figures. a y outer oral, or branchial tentacula of T'wnicata, which do not appear again in any of the inferior types. x conjoined summits of the tentacula of ee 3. The branchial chamber or respiratory pharynx of Tunicata, to which the tentacula of Polyzoa and the ciliated bands of Cydippe may offer an equivalent; being thus pharyngeal in the first, oral in the second, and somatic in the last. It is, moreover, altogether absent in the other sections of Celenterata. 4. The inner or esophageal opening of Tunicata, and the proper mouth of Polyzoa, Ctenophora, and Actinozoa. 5. Pyloric orifice of the stomach, leading into a closed intestine in T'unicata and Polyzoa; and into an intestine communicating with the somatic cavity in Ctenophora ; and solely into the somatic cavity in the Actinozoa. Probably, also, in the everted state forming the oral orifice in Hydrozoa. Anal extremity of the intestine in Molluscoida and Gheneotaaen ]. Position of the nervous ganglion in the same. 8. The oral tentacula in Actinozoa, probably equivalent to the outer or somatic tentacula of the _ Hydrozoa, always occurring on the outer or proximal side of the reproductive organs, J. The oral tentacula of Hydrozoa, always on the distal side of the young gemmules. In accord- ance with the views here expressed, it may be assumed Jee the inner circle of Tubularia is homologous with the single series of Hydra, &c. Regarding Cydippe as holding a middle position in the foregoing series, the VOL. XXIII. PART IL. 7B 520 ~ MR J. D. MACDONALD ON THE MORPHOLOGICAL RELATIONSHIPS theoretical passage of the type upon which it is constructed into higher and — lower types is effected in the tentacular system by addition, and in the alimen- _ tary system by modification, and these are, of course, either progressive or retro- } gressive, as they tend to the higher or lower forms. Thus, the tentacula of the Polyzoon, and the branchial tentacula of the Ascidian, are progressive additions, — while the oral tentacula (so-called) of the Actinozoa, and then the oral tentacula of the Hydrozoa, are retrogressive additions, however contradictory the phrase may appear.* On the other hand, the insulation and simple flexure of the in- testine in Polyzoa, and the perfect looping or double flexure of the intestine in — Tunicata, are progressive modifications, while the simplification and central e - largement of the somatic cavity, abolishing the intestine in Actinozoa, and, finally, the virtual eversion of the stomach in Hydrozoa, are retrogressive modifications. — To make the principles here expressed more intelligible, I have arranged them in — a tabular form, thus,— Conversions of the Cydippean Type. il MODIFICATIONS AFFECTING THE ALIMENTARY SYSTEM. * Progressive. Complete insulation of the intestine from the somatic cavity. a. Primary type, with simple neural flexure—Brachiopoda and Polyzoa. b. Secondary type, with primary hemal and final neural flexure—Ascidiozoa, ** Retrogressive. a, Primary type. Stomach more completely insulated by the abolition of the intestine— Actinozoa. b. Secondary type. Eversion and consequent abolition of the true stomach—Hydrozoa. it ADDITIONS AFFECTING THE TENTACULAR SYSTEM. * Progressive. a, Primary type. Oral tentacula of Brachiopoda and Polyzoa. b. Secondary type. Branchial tentacula of Ascidiozoa. ** Retrogressive. a. Primary type. Oral tentacula* of Actinozoa. b. Secondary type. Oral tentacula of Hydrozoa. Two suggestions present themselves in this mode of considering the subject,— / viz., first, that the Brachiopoda and Polyzoa should be taken together as a group — pound forms; and, secondly, that the Ctenophora should be received within the | pale of the Molluscoida, perhaps as a pelagic section representing Salpa, Doliolum, Lucernaria, while they are the sole prehensile organs of Coryne and Hydra. OF THE MOLLUSCOIDA AND CQALENTERATA. + 521 c., amongst the Tunicata. In accordance with these views the following classi- ication may be given :— ' With primary hemal Intestine insulated from ) and final neural flexure. Ascidiozoa. — Molluscoida (including } the somatic cavity, . With simple neural \ Brachiopoda the Ctenophora), . . flexure, / 70: and Polyzoa. Intestine straight, and communicating with the Ct " somatic cavity, © . SLO) EO Intestine Gulitenated ; Broach communicating with ee Celenterata (excluding ) the somatic cavity, . a SISOS the Ctenophora), . . True stomach obliterated, its office ‘being ‘answered Hyd by the'somiatic cavity, Ye.) .fo 1, ot Aue A aed _ * These are probably 1 in ordinary cases truly somatic, for, in some instances, an inner and geatinet set exists, more worthy of the name of oral, homologically speaking. Shs _ Goes) XXXIX.—On the Great Drift Beds mith Shells in the South of Arran. By the Rev. Rosert Booe Watson, B.A., F.R.S.E., Hon. Mem. Nat. Ver., Liineburg. (Plates XXJ., X XII.) (Read 4th January 1864.) Tue Sourn or Arran IN GENERAL. Conciusions—(continued.) CHARACTER oF THE DriFr-BeDs THERE. 5. Boulder clay contains land-formed beds. DESCRIPTION OF THESE IN DETAIL. 6, e deposited as land was sub- 1. Auchinreach Burn. siding. 2. Glen Ashdale. 7. Subsidence extended to 1100 or 1200 ft. 8. Torlin Burn. | 8. - was continuous, not oscilla- 4. Cloinoid Burn. tory. 5. Slaodrigh Burn. | 9. a was gradual. 6. Crogeréver Burn, reney + was it rapid ? 7. Clachan Glen. ; | 11. No general glaciation since re-emergence. ConcLusIoNs :— | 12. Boulder-clay beds of all ages of glacial 1. Boulder-clay derived from land glacia- epoch. tion, 13. Drift and Boulder-clay contemporary. 2. Ice covered the land till submerged. 14. Relation to sea-line, a test of age. 3. Boulder-clay deposited in the sea. 15. No material change on the basement- 4, compressed by ice, We. rock since glaciation. Summary. The whole southern part of Arran forms a field by itself, and whatever may be the deeper connections of the agencies that have fashioned the north and the south of the island, the result is a trappean area to the south, as distinct as if it lay in another hemisphere from the north, with its granitic nucleus, and encom- “passing rings of stratified rock. This district is little visited, and is almost, if not quite, undescribed ; it pre- sents, however, much beautiful scenery, and for the geologist, problems of extreme difficulty and interest, which deserve more attention than they have got. oe It may be divided into two belts of tilled land and moorland, above which | are the hill tops. This division corresponds roughly to three regions, the lowest | chiefly of sandstone, the middle where felstone prevails over the sandstone, and. | the highest of greenstone. _ From the sea, the land rises in a precipice, of from 50 to 200 feet in height. In general, for some two or three miles up the valleys, the rock is sandstone with- out fossils, and of doubtful age, but probably Permian. It is soft, fine-grained, often shaley, thinly laminated, chiefly bright red or purple, and much intersected though not much disturbed by dykes of igneous rock—large isolated masses of Which also occur. This sandstone region extends from the coast to a hcight of \from 300 to 500 feet. Its rising slope towards the interior is extremely gentle both in the valley bottoms and in the hill sides above. VOL. XXIU. PART Ul. (Re 524 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS From the sandstone region, the rise is generally a steep one, and marked in the burns by a waterfall. This is the edge of the felstone district, where the sandstones, though present, and often considerable in depth, occupy but a small superficies. Here the land rises in faster slopes, to a height of 1200 or 1500 feet. The felstone varies very much. In the south-east it is generally a grey yellow or pink felstone, very friable, disintegrating to soft sand with great rapidity, some- times columnar, sometimes also amygdaloidal, and frequently markedly lami- nated, a quality plainly due to the unequal cooling of the mass while in motion. In the south-west again, this felstone is sparingly present, and the prevalent ioneous rock is a very beautiful felstone porphyry, with a matrix of close-grained compact felstone, sometimes approaching in texture to hornstone, pinkish and yellowish, but most often grey in colour, and containing large crystals of white orthoclase and irregular rounded granules and lumps of crystalline quartz. Above the felstones rise tabular masses of greenstone, which occasionally reach a height of 2000 feet. They are of no great extent, but have been largely eroded. The combined result of these features is a table-land with long slopes and rounded contours, rising in hummocky elevations in the distance, and much in- tersected by valleys. Over the whole of this table-land lie clays and sands. Superficial sand-beds are not common, but occur here and there, from 50 to 570 feet above the sea. Stratified gravels and clays are to be found in the basins which occur in nearly all the valleys. . . Markedly distinct from these two classes of superficial beds, is the great deposit of coarse red boulder-clay, which swathes hill and valley in a dense mantle, and gives its characteristic feature of rounded outline to the scenery. (Pl. XXL fig. 1.) It may be found on the very edge of the beach. It lies deep over the terrace which rises steeply from the shore along the coast line, and is only absent where this terrace towers up in a great precipice of igneous rock, as at Leac-a-breac, Benan-head and Dippin. From 50 to 300 feet above the sea, it reaches its greatest development, pre- senting banks in the water-courses from 80 to 140 feet high. On the hill slopes, as might be expected, it is shallower, and in the valleys too, as they rise into the uplands, the banks of boulder-clay become smaller. Even there, however, they are still considerable, and at a height of 520 feet, I found one face of the boulder- clay 110 feet high.* The greatest measured height at which I ascertained the presence of the * JT need hardly say, that the sections formed by the burns are transverse to the bedding of the boulder-clay ; and, therefore, that the above measurements do not give the true depth of the deposit, but only the height of the sections. IN THE SOUTH OF ARRAN. 525 boulder-clay was 1100 feet, or a little more (Aneroid barometer), but I remember to have seen it 100 or 200 feet higher, and I have no doubt, patches of it may be found a good deal above this, but I had not time to seek them. From all this it will be obvious, that the boulder-clay has not been piled up in immense irregular masses, like glacier moraines, but conforms, on the whole, to all the contours of the rock surface. Even in the valleys, where, of course, it has accumulated in masses disproportionally great compared with those on the hill faces, and where therefore the contour of the surface ceases to conform strictly to that of the rock below, there are indications, in the separate beds of the boulder-clay, of the modifying influence exercised upon them by the form of the ground on which they have been deposited,—the line of the valley forming the synclinal axis of the beds. Where wide basins exist in the valleys, which is often the case above some transverse stream of igneous rock,* the boulder- clay lies equally round its whole margin, and follows the slope of its banks. The importance of this agreement between the lines of the boulder-clay and of the rock below is, that in glacier moraines, there is no such regular disposi- tion of beds, and still less would such be found in the scattered droppings of floating ice. . Great irregular masses of material, resembling moraines, I only observed high : up on the face of the hill, between Kildonan and Benan-head; and again, at the head of Glen Cloy, where there is a huge moraine.t The form in which the boulder-clay beds present themseives in the burn- courses is as steep slopes thinly grass-grown,—occasionally, where water oozes over them, the face of the beds is steeper, more broken, and covered with con- fused heaps of stones and mud. The best view of their composition is generally to be got where the burn has cut in to the underlying rock, and the bank rises precipitously above. In general character, the boulder-clay of the south of Arran is a coarse, red, sandy clay, full of stones, both striated and water-worn, and of all sizes, from boulders 4 or 5 feet in diameter downwards. It varies a good deal in texture, being sometimes loose and gravelly, at others dense and hard, so as to stand up in nearly perpendicular precipices, dotted over with projecting stones so firmly * One is apt to mistake mere erosions of the boulder-clay for true basins in the basement rock, but where there has simply been an erosion, there is of course no such agreement as that spoken of between the contours of the surface of boulder-clay and the basement rock, + I do not think this moraine has been noticed. It lies near the head of the glen, and rises to a height of 800 or 900 feet above the level of the sea. Where the glen contracts there are, on the : south side, immense heaps of huge blocks of rock tumbled down in the wildest confusion,—the same f appears on the north side of the valley, and all the valley bottom is obstructed by heaps of gravel , and stones. The cup formed by this is about half a mile long, and above, on all sides, the hills rise | perpendicularly to a height of 1100 or 1200 feet. These moraine masses extend down to the foot of | Glen Dhu, more than half a mile, and in this glen, also, is some appearance of smaller moraines. In the lower part of the Glen Cloy moraine granite boulders become frequent. 526 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS fixed, that in the water-worn gullies one may often climb far up the steep bank by holding on to them. On the whole, it is perhaps less compressed and homo- geneous than boulder-clay often is; it is also occasionally traversed by bands of stones or beds of sand and clay. Towards its upper surface it is often somewhat disintegrated, and less dense than below. At times it passes upwards into a dense, fine gravel. In some places it is to be found resting directly on the rock below; but at the lower levels it is often separated from the rock by a bed of sandy clay, while at a higher level it is, in at least two instances, underlain by a very hard, densely-packed, angular gravel or coarse sand, with large striated boulders, which seems to have lain directly under a glacier. Shells occur occasionally in considerable quantities, both in the boulder-clay and in the sandy clay (not in the glacier gravel) below, at various heights, from 80 to 320 feet above the sea. No general principle explanatory either of the presence or absence of the shells is obvious, except that they seem uniformly wanting in the beds of large stones. In the boulder-clay they are very much broken. In the Jaminated beds, both those which rest on the rock and those which traverse the boulder-clay, the shells, when present, though of more delicate type, such as Ledas Naticas &c., were less destroyed. At first, from the broken state of the shells, I thought the whole deposit must have been formed on the beach; but more careful observation showed that the inference was drawn merely from bits washed out by the rains, these being by far the most abundant. If carefully dug for, the shells may often be found, crushed indeed, yet with each fragment in its own place—two-shelled species with their valves united. Some of the large speci- mens of Cyprina, though unbroken, are indented as by a sudden violent blow. In short, the whole condition of the shells suggests that heavy stones have been dashed down on them, or that they have yielded in the bed where they lay to the weight of sand and stones more quietly piled over them. Of species there are sixteen determined and one doubtful, besides many frag- ments which do not seem to belong to any of these, but are too minute for re- cognition.* As to their habitats, they belong distinctively to the coralline zone, or to even deeper water. Of the sixteen species which have been determined, seven, so far as they are known on our coasts, are never found in water shallower than 150 feet (25 fathoms); and except one, all the others, though found at a less depth, are also found in very much deeper water. The single exception was the Litorina litorea, but of it I found only two fragments. In character, Mr SEARLES Woop, who was good enough to examine them for me, pronounces them decidedly boreal. All the species, except Turritella communis (which is common in the Norwegian drift-beds), extend to the arctic province. * For list of these see end of paper. IN THE SOUTH OF ARRAN. 527 Three—Pecten islandicus, Astarte arctica, and Cryptodon Sarsii (if it be really distinct from the sinwosum), are distinctively arctic, a character further indicated forthe whole collection by the prevalence of astartes, which, both in species and individuals, greatly outnumber all others. Vegetable remains, apparently heather stalks, were present at two places in the boulder-clay. In general, the material of the boulder-clay is derived from the rocks of the particular glen in which it lies.- Still foreign materials are not wanting. Thus, in Cloinoid Glen, I found pieces of syenite, which must have crossed the water- shed between that glen and the Torlin Glen to the ‘east, in which the syenite rock lies. In the same glen also were pieces of a very peculiar (carboniferous) sandstone, which must have come down across two water-sheds, from the Clachan Glen to the north. Fragments, too, have been brought down from the Silurian shales in the north-west, and from the granite in the north ; and one bit of impure coal I found, which must have come either from the little patch of coal in the ex- treme north-east, or from the mainland opposite. All these wanderers have pro- bably been brought by floating-ice. The red colour of the boulder-clay shows how largely it is indebted to the friable red shales of the district. Hardened knots of this shale, which are always striated, are frequent ; but by far the largest proportion of the stones which it contains are derived from the igneous rocks. The soft laminated felstone, in- deed, which prevails in the south is not common, from its proneness to disinte- gration, but felstone porphyry and greenstones abound. The absence of striations on the stones from the felstone porphyry is very striking. This, however, is apparently due merely to the texture and colour of the stones, and is equally true of the whitey coarse-grained variety of greenstone. At the lower levels the surface of the underlying rock is rarely to be seen striated, a fact partly owing to its texture, which is very soft and friable, and * partly to the difficulty of getting a surface at once sufficiently exposed, clean, and unweathered. On the shore between Brodick and Lamlash, however, there are some very well-marked striated surfaces. _ Ihave made these general remarks as full as possible, in order to avoid repe- tition in detail of features common to the whole boulder clay, and will therefore now only refer to individual places, in so far as they strikingly illustrate previous statements, or otherwise present something peculiar. Below the bridge over the Auchinreach Burn, above Whiting Bay, 70 fect above the sea, the boulder-clay is 40 feet deep. It rests directly on a bed of ' friable shales. The stones in it are much striated; small granite boulders are frequent. At 50 feet above the sea this bank is 50 feet high, but it is only the lower 15 feet that are boulder-clay. The underlying rock is not seen here. The re VOL. XXIIl. PART III. {D 528 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS boulder-clay is very hard. Through it there runs a stratum of fine clay 3 or 4 inches thick. Above the boulder-clay is a great bed of sand, in some places 35 feet thick, but diminishing rapidly in depth as the bank slopes downwards to- wards the sea. ; At the mouth of Glen Ashdale, the boulder-clay beds lie deep over the whole hill side to the north. They are also present, but in a very ruinous state, on the south. Between Whiting Bay and the Torlin Burn they are everywhere to be seen, but I did not examine them minutely. In the Torlin Burn, and especially in the Cloinoid branch of it, they are im- mensely developed, and present the best sections I have seen in Arran. The beds also contain shells. At the farm of Torlin, on the edge of the sea cliff, the boulder-clay rises from the beach to 110 feet above the sea. On the road above Lag, at the schoolhouse, it is 150 feet above the sea. This is just above the edge of the great red banks, which rise steep and broken from the burn, and run on uninterruptedly for a couple of miles. The first place where I found shells in these banks was on the east side of the burn, 120 feet above the sea (Plate XXI., fig. 1), and about 15 or 20 feet below the top of the bank, which is here 50 or 60 feet high. Just below the Church of Kilmorie, the burn is crossed by a little wooden bridge. Immediately below the bridge, on the west side of the burn, 80 feet above the sea, is an extremely interesting section. The bank is 100 feet high, but is much obscured by sludge. The boulder-clay, however, can be made out in detail nearly to the top of the bank. At the edge of the burn course, the sandstone is laid bare. It is very considerably hardened by a greenstone dyke, which lies here ~ in the burn course. The face of sandstone slopes quietly up from the level of the burn for 4 or 5 feet. If it was ever striated, the burn has effaced the markings, the whole surface having been evidently exposed for a considerable time. Its upper edge is perpendicularly broken off on an irregular line; and at the. back of this edge, the curious succession of beds shown in the accompanying sketch can be made out. (Plate XXI., fig. 2). The impression which they produced on my mind was, that the under beds to No. 6 or 7 had been formed by running water under a glacier, and had been jammed in at the back of the rock by the ice moving downwards, not directly in the line of the present burn course, but obliquely across it from the north-west, while the other beds above, from No. 8 onwards, were deposited in the sea. In any case the presence of the sea during the formation of beds Nos. 10 and 11 is certain, from the presence of shells in both of them. In No. 101 found a few unbroken Zedas in pairs; and in No. 11, besides fragments of Ledas two broken 7urritellas, anda small bit of a Litorina litorea. This last bed is harder and darker than No. 13; and the stones, which are well striated, are fewer and smaller, but both beds are distinctly boulder-clay. Bed No. 10 seems to dip IN THE SOUTH OF ARRAN. 529 under No. 11 to the west, at an angle of 75°; but the dips in all these clay beds are very deceptive. Above the church there is a flat open space in the bottom of the valley. In the centre of this flat a bank slopes out from the hill side above, and breaks abruptly in the middle of the field, presenting a face 20 feet high. On the top is seen coarse water-rolled gravel—below is fine clayey sand. This seems to be the wreck of the superficial deposits, which had once covered the whole flat. Just below this, in the burn course, I found, resting on the boulder-clay, a layer of fine clay, buried beneath sand and gravel, and containing dead equisetum roots, which Ihave no doubt are modern; but the depth to which this plant penetrates is often very deceptive. These beds seemed to form a lower member of the super- ficial deposits mentioned above. In the centre of the field a boss of felstone porphyry projects above the flat. Tt has the form of a roche moutonnée, but I could not satisfy myself that it was striated. Above this the boulder-clay banks are of great size, but I did not examine them carefully. In the upper part of the valley, at 450 feet above the sea, and near the path leading over to Lamlash, I found a well striated face of greenstone. Further on, at the same height in the burn course, is a bank of boulder-clay, rising to 40 feet above the burn, but the lower part of the bank, for 20 feet, is formed of the friable shale rock of the district. Close by, however, the boulder- | clay has fully this depth, and is hard, firm, and flakey in texture. This is just | below the farm of Stragael. In the valley bottom here is a flat, where the | boulder-clay is covered with gravel. At 570 feet above the sea, just above the farm of Stragael, is a great bed of sand with a fewstones. At 800 feet above the sea, the boulder-clay banks beside the burn are still 30 feet high. At 1100 feet it is 10 feet thick; but at 1130 it is thin and sandy, and the shales appear in broken angular fragments close to the surface. On the hill-side, north from this, at 100 or 200 feet higher, it again lies thicker, but I could not examine this locality minutely. At 1250 feet there are well striated bosses of felstone. The Cloinoid Burn is a branch which joins the Torlin Burn from the N.N.E., about a mile, or rather less, from the sea. Between the burns the land swells up in a rounded back, which is, however, very little higher than the edge of the great boulder-clay banks which line the burns. The valley is very narrow in its lower part, and the banks high and steep; but they are much obscured by debris, sc that the details of the boulder-clay can seldom be followed for any distance. ‘The best section of them occurs about a mile above Lag, from 160 to 200 feet above the sea, the top of the bank rising from 240 to 340 feet above the sea, or from ‘80 to 140 feet above the burn. This section extends, with interruptions, for several hundred yards. It may best be considered in two parts. The first part (Plate XXI., fig. 3), is about 80 feet high and 200 yards long. At the 530 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS bottom is exposed a small face of soft friable sandstone, above which is a dense sandy clay apparently about a foot thick, but very little of it can be seen from the debris. It is best seen at the south end of the rock, and its lamine corre- spond to the slope of the rock. About 20 feet above this the face of the boulder- clay is crossed by a band 2 feet thick of big stones, some of which are 2 feet long and broad. This bed runs downwards across the bank till it sinks to 8 or 10 feet above the burn. Ten feet above this is a less marked bed of stones, which, on the whole, keeps its relative position to the other, till, at their point of lowest depression, they seem to run into one another. As the centre of this section is obscured for 100 yards by a grassy bank, of course there is no certainty that these stone beds are the same throughout; they seem however to be so. If they are their dip is probably due to the fact that they were deposited on the slope of the hill side, and that the section which the burn has made is not in the line of their strike but transverse to it,—as indeed is obviously the case from the exposure of the rock where they are highest, and its concealment where they sink lower. The irregularity of the two beds relatively to each other is no more than might be expected. A close examination of these beds is impossible from the steepness of the bank, and the view of them from below, or from the other side, is unsatisfactory, owing to the debris, the irregularity of the surface, and the similarity of the colour throughout. Above this bed of stones is a layer of clay a few inches thick. Little bands of clay and sand traverse the boulder-clay, and about half-way up the bank is at one point (Plate XXL., fig. 4), a bed of stratified sand, overlaid by a stratum of boulder-clay, which last is separated from the mass of the boulder-clay above by a parting of sand. The sand-bed contained a few fragments of shells. The layers of sand curve sharply over upon themselves, as if they had been thrust forwards under a heavy weight from behind, and forced to over-ride one another. The boulder-clay resting on this sand seems to have shared in the thrust, but being less easily bent has merely swelled out into a club-shaped mass. Between this and the next good section a considerable mass of felstone porphyry appears in the burn. Above this is by far the finest section of all (Plate XXL, fig. 5.) It is from 200 to 300 yards long, and the bank is 140 feet high. It pre- sents two or three broad perpendicular faces, intersected by deep hollows channelled out by the running of water. The lower 20 feet or so is a debris talus. Just above this the rock crops out through the bank at one place. It is a soft, crumbly shale. It is covered by a bed much more sandy, and with fewer stones, than the rest of the deposits. It was in this bed that I found Naticas quite unbroken, but so fragile that they could not be got out uninjured. In it I also found a fragment of Litorina. The boulder-clay above the sand shows a tendency to bedding. A very marked line, apparently of large stones, crosses the whole face of the bank from 25 to 50 feet up, rising as it goes down the IN THE SOUTH OF ARRAN. dol burn to the south. It is very likely one of the beds of stones which we saw in - the last section. There are also other indications of water-sorting in the beds both above and below. Shells were most abundant near the rock, and also high up the bank to the south end of the section. Above this a great mass, 30 to 40 feet high, of laminated felstone, in a very shattered and rotten state, crosses the valley. The channel cut through this is only the breadth of the burn, and in this narrow passage are a few old rounded, but not striated surfaces; but elsewhere I could see none, so completely is the whole rock in a splintery state. The boulder-clay lies over the top of this rock, and comes down to the burn both above and below it. I unfortunately neglected to measure the height to which this rock barrier rises above the burn,— a point so far of importance that the rock, if it really cross the valley, as it seems, must have formed a dam behind which the glacier ice, coming down from the hills above, would be checked and embayed in the basin above. Of course it may have accumulated till it rose high enough to overflow the barrier, but the narrowness of the passage, obviously cut by water, indicates plainly that through it the ice found no egress. Above this barrier is an open basin half a mile long (Plate XXI. fig. 6.), round which the boulder-clay lies deep. The curve of the bank all round faintly suggests a water-formed terrace, but I did not attempt to ascertain how far it keeps the same level. The lower end of the basin is about 300 feet above the sea, the upper about 330. It was in the boulder-clay bank, about 20 feet up from the burn at the lower end of this basin, that I found the last fragment of shell I met with. Plate XXI. fig. 1, gives this bank. The lower part of the bank consists of a singularly hard, dense, dry, gravelly clay, derived from felstone porphyry rather than from the sandstones. It looks as if it had been jammed in dry against the felstone rock, to the east and south down the burn, by the glacier when in motion. In it are several large, well striated greenstone boulders. Above this hard gravelly clay, to the left, the red boulder-clay rises to the top of the bank. To the right this boulder-clay has been stripped off, and over the surface of the underlying bed is a stratum 2 or 3 feet thick of water-rolled boulders. This bed merely laps up on the edge of the red boulder-clay as it thins out on the flat. The relation of the two is indeed very difficult to make out from the debris and turf which conceal their junction in the corner at the rise of the bank; but it is better seen at the other end of the section of their junction-line, where it is ex- posed about 100 yards up the burn, and this is shown in Plate XXII. fig. 8. Here, as before, the hard yellow gravelly clay, about 6 feet thick, lies in the burn course, and, resting directly on it, is the bank of red boulder-clay. To the left, cut ’ off by the burn, is seen the projecting edge of the valley flat. Here the yellow clay seems to have been eroded and buried under a thicker mass of rolled stones and | gravel, which becomes thinner as it is followed down the edge of the bank to the VOL. XXIII. PART ITI. 7E 532 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS former section. In the angle of the bank and the flat, this bed of stones is over- laid by the remains of a bed of sand. Both of these beds seem to be superficial deposits of a later period, when the basin was occupied by a loch or inland sea- bay, the currents of which had deeply eroded the red and yellow clays. Elsewhere in the flat other superficial beds besides these can be made out,— not indeed all at any one spot, yet distinctly enough, to a thickness of 8 feet: 1. At the bottom coarse water-worn gravel, what this rests on is not seen; 2. Above this fine clay, with equisetum roots apparently of the period of the clay, but this is not certain; 3. Sandy gravel; 4. Coarse gravel; 5. Sandy clay; 6. Loose coarse gravel, or small rolled stones. In this last bed nearly every stone, both greenstone and felstone, was so thoroughly disintegrated that the whole bed seemed at first to be merely sand. At the very head of this basin a burn goes off to the west or north-west, in which a deep section of the boulder-clay is given; and between this burn and the Cloinoid Burn, just to the east of the clachan of Cloinoid, is a deep land-slip in the boulder-clay, which strongly conveys the impression of how deep the clay is. The boulder-clay banks press closely in on the burn above this, and at 520 feet above the sea is a waterfall over the edge of a great bed of felstone porphyry, and from the foot of the fall the boulder-clay rises 110 feet perpendicular; but above this the valley rapidly opens out to a mere depression in the contour of the hill, and the boulder-clay thins out more and more. The next great glen to the west is that of the Scoradale Burn or Slaodrigh Water, in which, and all its tributaries, the boulder-clay banks are very large. Up one of these tributaries I found a bank of the clay 130 feet high at 310 feet above the sea, and in the main burn they seem even larger. I examined them carefully, however, only in the Croghcréver Burn, which joins the Slaodrigh Burn from the north-west, about a mile above the sea. At the junction of the burns, 50 feet above the sea, one gets a very good view of the mass of the beds, which are here from 90 to 100 feet high. Just above the junction is a steep but some- what ragged face of the boulder-clay (Plate XXII. fig. 9). Here the soft shales at the bottom rise on the left to about 15 feet, but diminish in height down the stream. Above the rock are ten or twelve feet of coarse gravel and sand plainly stratified. Above this is boulder-clay 50 feet, with traces of bedding, and perhaps somewhat looser than usual. I found a few fragments of shell about the middle of the bank. They had been washed out by the rains, and I could not trace them to any particular spot. The nature of the bank prevents a very close examination of it in detail. Just above this is a bank which a year ago presented a remarkably fine section. Being very deeply channelled by water-courses, its details were well shown, and it was also remarkably rich in shells. Scarcely a trace, however, now remains of it, so completely has it been washed away or buried in its own IN THE SOUTH OF ARRAN. 599 ruins. The soft sandstone rock here appeared about 40 feet above the burn, and over its face lay a dark bed of fine clay, in which shells were both abundant and remarkably fresh and unbroken, the bivalves being in pairs, and retaining both their ligament and epidermis. Above this is a long, narrow gorge, about 60 feet deep and half a mile long, cut through the soft shales in the line of their strike, which is north-west. The houlder-clay lies down the dip of the strata on the north-east. (Plate XXII, fig. 10.) At about 130 feet above the sea the gorge turns a little more westward than before, and in the angle it expands and forms a small basin, with huge boulder-clay banks 120 feet high on the north-east side. About 60 feet up, the bank is crossed by a dense bed, a few inches thick, of dark brown clay, very hard, with small gravel in it, and very rich in shells, especially Zeda in pairs, and Balanus valves. Above the gorge is a great stretch of laminated felstone, which occupies both sides of the burn-course. It is this felstone which seems to have protected the shales lower down the burn. The phenomena of the clay-beds for half a mile above this point, which is from 250 to 300 feet above the sea, are extremely instructive and interesting, but very difficult to explain. (Plate XXII. fig. 11.) Cut through by the burn is a bank, 7 feet high, of intensely hard yellow clayey gravel, resembling that which I have described in Cloinoid Glen, and like it, chiefly made up of felstone porphyry. Like it, too, it has all the appearance of having been travelled over by the glacier, so compressed and yet so dry and in itself incoherent is it. The upper surface of this bed seems to be quite uncon- formable in its slope to any of the other contour lines, either of the rock below, or of the beds above, for it dips to the westward, while the whole land is rising in that direction. It seems, in short, just like a bank that had nestled in be- hind the edge of the rock, and was thus preserved from the abrasion of the glacier. | On this back slope of the yellow gravel lies the much redder and somewhat softer common boulder-clay, in which I found a fragment of shell. (Plate XXII. fig. 12.) Horizontally overlying this, and abutting unconformably against the yellow gravel, is a ten-foot thick bed of coarse sand, on the top of which is a ) layer, 3 feet thick, of very large stones. Above this is some 6 inches of fine light- coloured sand, and over all is earth. On the east side of the burn, this bed of yellow gravel (Plate X XIT. fig. 11) nestles in behind a strangely isolated mass of the felstone, close above which is another rock of rotten felstone, round which the | old burn-course lies. The new channel is 3 feet deeper than the old one. Some | very large and well-striated boulders of greenstone lie in the yellow gravel bank | opposite this point, as shown in Plate XXII. fig. 12. Just above this, in the burn-course, there appears on the west side, a long face of felstone, which rises 4 or 5 feet above the burn. It seems glacier-worn 534 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS from its rounded form, but its whole exposed surface is utterly shattered, while its junction with the overlying clay beds is entirely concealed by debris. (Plate XXII. fig. 13.) Resting directly on it, is a confused dark-coloured bed of gravelly clay, with large angular stones crushed rather than ground, some of them striated. In this, a year ago, I found quantities of heather-stalks, but this spring, on revisit- ing the place, I found it a good deal more concealed by debris, and I could only find one bit of heather-stalk about an inch long, which I fairly dug out of the clay among the hard pressed fragments of stone. ‘The discoloration of the bed, which is very marked, may be partly due to the vegetable matter, but it seems much more owing to the disintegrated greenstone and pitchstone fragments which abound. I had great difficulty in satisfying myself what this bed was, but was -ereatly helped by finding it again further up the burn. It is just the hard yellow gravel formerly described, and the red boulder-clay which (Plate XXII. fig. 12), along the burn, intervenes between it and the yellow gravelly clay, must be just a tongue of the boulder-clay, lying in a depression of the surface of the yellow clay. For some way up the burn, the felstone rock forms one side, and the boulder- clay the other of the water-course; aud no doubt, the yellow gravelly clay lies hidden under the debris between, for it reappears a little higher up on the opposite (i.e. the east) side of the burn, and there it distinctly underlies the boulder-clay. It is intensely hard, and all the stones in it are angular. From the point where it reappears, it can be followed more or less continuously for a long way, some- times on one sometimes on the other side of the burn, but never, I think, occupy- ing both sides at once, so that it seems to be thin. At one place, on the east side of the burn, it actually seems to underlie a considerable mass of the red and yellow soft shale rock which unexpectedly makes its appearance amidst the felstone. At the north-west corner of the mass where alone I could get a good view of their relations, the edges of the shale strata distinctly lay upon and pro- jected over the yellow gravel beds. On the whole, the shale rock seemed either a mass projecting amidst the felstone, and into the foundations of which the yellow gravelly clay had been violently forced, or more probably a loose mass of the strata which has either slipped or been pushed over the top of this yellow clay- bed, yet without being upset or indeed very violently disturbed. Higher up again, the yellow gravelly clay is seen directly overlaid by the red boulder-clay. Just above this, at 280 feet above the sea, the clay banks are 100 feet high. From this point, a great shallow circular basin opens up on the hill face, and all around its margin, the boulder-clay banks go sloping down into it.* * Just where the burn escapes from this basin, the section of the strata shown in twenty yards of the burn-course is most curious. Descending the burn, one first reaches the junction of the fel- stone porphyry and the underlying sandstone. The felstone porphyry crosses the burn to the N.N.W., and unconformably overlies the sandstone from which it is parted by a greenstone dyke. The sandstone is considerably hardened. A little lower down the burn the sandstone laps up on IN THE SOUTH OF ARRAN. 539 Between Glen Scoradale and the Great Black Water Valley there are immense beds of boulder-clay, and also of water-rolled gravels but, I only marked their presence without examining them in detail. In the Clachan Glen, the great boulder-clay beds extend from the bridge at its mouth at 190 feet above the sea upwards for a mile and a half or two miles. At 220 feet above the sea, felstone rock appears in the burn-course, but it is all so shattered on the surface and buried in debris, that no striations can be seen. At 250 feet above the sea, the shales reappear. Here, in the open and flat valley- bottom, a bank rises 20 feet above the burn which presents the section shown in Plate XXII. fig. 14. The lower part is entirely concealed by a talus of debris, above which the shales rise perpendicularly on the left. These are partly over- laid by 2 feet of dense gravel, very hard pressed, which belongs to the boulder- clay series. Above both the shales and the gravel-bed are 3 feet of large loose stones, and 2 feet of fine sand, with earth over all. The two latter beds, that, viz., of stones and that of sand, seemed to me to belong to the class of later superficial deposits thrown down when the boulder-clay was eroded by the action _ of a lake or bay of the sea. A little way behind this on the north, the boulder-clay banks rise 120 feet high, while 100 yards east, or further up the burn, they reach 170 feet. The upper part of this bank consists of hard stratified gravels, less dense than usual in the boulder-clay, and the surface below the turf has three inches of fine hard clayey sand. : By far the best sections of the drift are to be seen on the other (the south) side of the burn; for there, though hardly more continuous, they are somewhat more perpendicular and less obscured by debris than on the north side. - Unfortunately, however, they are so far obscured and interrupted, that the beds which they present cannot be traced continuously for any distance. At 290 or 300 feet above the sea is certainly the best and most interesting view that can be got of them, the whole bank being cleared from the burn upwards for 90 feet. (Plate XXII. fig. 15.) At the bottom is some 15 feet of hard gravelly clay; above this a layer of 4 or | 5 feet of great stones and gravel; then 15 feet of dense finely laminated clay With fine sand, becoming more sandy towards the top. In the uvper part of this, almost at its junction with the overlying bed, I found some smal! broken twigs of exogenous wood, crushed flat. They were lying well into the hank, between the undisturbed horizontal layers of the sand, and beyond a doubt belonged to the period of the formation of the bank. Next is a bed 8 feet thick of dense hard pressed boulder-clay, more gravelly and sandy than usual. Then follow 5 feet the back of a mass of the laminated felstone, the lamine of which are parallel to the junction-line with the sandstone, but turn sharp round at an acute angle, where they abut against another green- stone dyke, which here occupies the opposite or left side of tke burn, and which cuts through the | Sandstone from S.H. to N.W. VOL. XXIII. PART III. TE 536 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS of very coarse big stones and gravel, much water-worn, and over this 30 to 40 feet of boulder-clay; the materials of which are less coherent than in any of the other glens I examined, having less clay and more stones than elsewhere, and this is a characteristic of the boulder-clay throughout the whole Clachan Glen, a peculiarity obviously due to certain specialities of the valley itself, affecting the disposition of the boulder-clay. At 20 feet above this section, the beds are again well shown; and there the creat bed of clay is either buried under the talus of debris, or is absent altogether. At this point a prodigious stretch of the banks is displayed, but too much ruined to afford much information. Most of the stones are much water-rolled, but many of them still retain traces of striation. By far the greatest number of these are greenstone and felstone porphyry, but the latter, as usual, scarcely ever show striations. Out of 105 stones distinctly striated, which I counted in this bank, there were,— Greenstone, : : : 28 = 27 per cent. Knots from the soft red shale, ‘ ‘ : 28 ee Laminated felstone, : : ; : 4 = 4s Felstone porphyry, : : : : 3 = Tae Soft sandstone, ‘ ‘ 19 ==! Loy ees Green conglomerate, from the altered carboniferons strata, 9 ee bes OP Hard, purply, aml slatey shale, . ; : 9 See Syenite, : 5 =) (Dog die 105 100 About two miles above the bridge, at 300 feet or so above the sea, is a deep narrow gorge in the valley, where the drift banks are enormous, rising 200 feet high. The gorge is formed by a great felstone dyke, and the shales which it has protected. These have made a kind of dam across the mouth of the upper valley. Both the felstone and the shales crop out in the boulder-clay banks on the south side of the burn, at various points, at 100 or 120 feet above the burn. The shales seem to be overlaid by a mass of laminated or banded felstone, which apparently has spread out from the dyke. ‘This is best seen in a precipice on the south side of the gorge. The greatest. mass of boulder-clay lies on the north side; and the top of the bank here, for 3 feet, looks like water-sorted clay and sand, beneath which are some large stones, and below this is boulder-clay. The boulder-clay banks extend up both the main valley and a side branch, which opens to the south-east, above the gorge; but they lose there the huge proportions they have below. Before concluding this examination of these beds, I think it may be well to explain why I have so definitely spoken of them throughout, as being composed of boulder-clay. Of course, I am aware that exception may be taken to this application of the name, on the ground that these beds present traces of stratifi- cation, and contain shells. But this objection could at most only apply to the * if ss IN THE SOUTH OF ARRAN. 537 particular portion of the clay which is stratified or shell-bearing, and cannot be held to exclude the great mass of the beds, which, in their heterogeneous stiff clay mixed with striated stones, present—if not in high development, yet beyond a doubt—all the characteristics of true boulder-clay. If parts of the beds, then, must be classed undoubtedly as boulder-clay, the whole must be so called, and the elevation of mere stratification and the presence of shells into crucial tests of what is not boulder-clay must be rejected. But, besides this, these beds belong un- questionably to the glacial period, as is proved by the striated surfaces of. the rock and of the stones, and by the boreal character of the shells. Now, failing any evidence of the submergence of Arran during the glacial epoch, we may con- clude that boulder-clay must have been deposited on the island; and unless it were true, as it is not, that the boulder-clay has been entirely remade, and that the existing beds are the mere wrecks of that deposit—then these must just be the boulder-clay beds of the glacial period. Such, then, are the facts here presented to us; and with these facts before us, it is obvious that we have, to some extent, a record of the history of the land. How far can we decipher the record ? Let us start from what we know. In geologically recent times there has been a glacial period. The existence of roches moutonnées, of striated surfaces and of scratched boulders, proves the action of ice on the land. The presence of marine shells and of water deposits is evidence of the submergence of the land to a con- siderable depth. Its present state implies its re-elevation. Of these phenomena enough at least exists in the south of Arran—in the boreal shells, the striated | stones, and the hard chaotic clay—to justify the belief that this district formed | no exception to the general condition of the country; that any differences here are due to local circumstances; and that we may fairly bring the general infor- mation gathered elsewhere to eke out our knowledge of this district. Assuming, therefore, that in Arran, as elsewhere, the land was gradually covered by ice, let us try to conceive the result. At first snow would accumulate on the hill tops, creeping thence as glaciers down the valleys. As it grew in depth, it would spread further and further on the slopes till the whole land was swathed deep in ice. The fact that in our country all the rock surface at all elevations. with mere local exceptions, is striated, indicates such an existence, not of glaciers merely, but of a massive ice- cake, more universal than even in Southern Greenland now. Beneath this ice- cake the soil, and all of life it supported, would be gradually harried away to the sea, any traces of it left being nests of debris nitched into corners, ground over and disturbed in every conceivable way by the ice above. Loose blocks would be ' carried off, corners would be rounded—the rock faces and the scrubbing-stones would be striated—quantities of stones, gravel, sand, and mud would be ground promiscuously together, and the tendency of the whole mass would be down- 538 REY. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS wards, ever by the steepest and the fastest descent it could find, towards the valleys and the sea. At the shore the ice-cake would still sink, crushing down, and yet partly resting on, the debris which lay beneath it, until at a depth pro- portioned to its thickness it would at last be floated up, forming that flat terrace along the land known among Arctic travellers as the ice-foot. Beyondt he ice-foot, we know what occurs in Greenland, and some of the main features are familiar even to Norwegian travellers: floating icebergs, laden with debris, driven about by winds and currents,—masses of ice floating up with a thaw, and bringing up rocks to which they had been frozen, often dropping these again at a far higher level than their parent bed,—turbid fresh water, ice cold, flowing out to sea in a shallow stream, destructive of all animal and vegetable life. At the edge of the ice-foot, a steep bank of tumultuous debris,* shelving down precipi- tously toa great depth; beyond this, gravel, sand, and mud irregularly distri- buted, according to the currents, but in the main a fine mud always present at a distance ; seaweeds rare, or only locally frequent; while, from the very edge of the debris bank, animal life in abundance, but in the tumult of the debris bank itself only exceptionally present. Such are the phenomena more or less to be found along all glacial coasts; and-such, no doubt, were the phenomena of our own shores in the glacial period. This then being so, we are entitled to say— 1. That the material of the boulder-clay is the result of land glaciation. The enormous debris torn from the abraded surface of the basement rock must have gone somewhere—the huge boulder-clay heaps must have come from somewhere. Do not the two fit each other, as the broken masses of a land-slip in the valley fit the bald rock-face on the hill above ? But besides this, the shells associated with the boulder-clay are decidedly boreal in character, and indicate just such a glacial climate as the ice-covered land implies. The shells, therefore, show that the boulder-clay in which they are found belongs to the glacial period. 2. The ice covered the land till it was submerged. This certainly implies a great severity of cold, and an enormous snow-fall, and yet this seems actually to have been the case. Had it been otherwise; had the ice-cake begun to waste off the land at the lower levels before these were covered by the sea, we should probably have found traces immediately on the rock of the debris with which a glacier is charged, and which, in melting, it would have left behind it. The ice * I have repeatedly lain on the edge of such a bank, at the mouth of glacier rivers in Norway —particularly at the Skars Fjord glacier, where nothing but warps would hold us, the face of the bank on which our anchor lay being too steep to afford any hold. Our bows were almost grat- ing on the shingle, while we had 70 fathoms under our stern, and 83 fathoms, with a fine mud bottom, at 100 yards distance. The surface water was filthily turbid, bitterly cold, perfectly fresh, and not above 8 or 9 feet deep, if so much; below was the clear salt water, sensibly warmer, and swarming with animal life, both fish and mollusks. IN THE SOUTH OF ARRAN. 539 seems rather to have been actually floated off by the sinking of the land; and the first deposits thrown down on the bared rock are marine and shell-bearing. 3. The boulder-clay was deposited in the sea. With the moving ice the debris entangled in it and under it must have been in constant progress seawards, and could never permanently have come to rest till thrust out into the sea under the ice-foot. From this consideration alone we might have inferred the deposition of the boulder-clay under water; but we have more direct evidence, for in Arran, as in some other places, the boulder-clay contains marine shells in considerable numbers, and in circumstances indicating that the animals lived and died in the bed where they now are. Obviously, therefore, the clay in which these are found was deposited under water. Corroborative proof of this fact is further found in those beds of stratified sands and clay which are, comparatively, so frequent in Arran, and which are seen elsewhere wherever an extensive section of the boulder-clay is visible. These plainly imply the action of water, but of them- selves, and without the shell beds, would still have left it doubtful whether the ‘water-action might not have been temporary and lacustrine. The two combined confirm each other’s testimony to the deposition of the boulder-clay in the sea. 4. Though deposited in the sea, the boulder-clay has been compressed by ice. At the edge of the ice-foot there must have been a growing bank of debris, on which fresh heaps were constantly emptied. Ona free and open slope, in such circumstances, the mass of course simply rises in height, till, the angle of slope become too great, the face of the bank breaks, and the upper part slips forward over the lower. But in the case of the boulder-clay, the massive shelf of ice above would prevent the free growth of the bank, which, partly under its own weight, and partly under the pressure of the ice, must constantly have been sub- siding, to some extent undergoing compression, to some extent yielding inter- nally and bulging out in front, so as to undergo a complete disarrangement and confounding of all its component parts, which is one of the characteristic features of the boulder-clay, and of which we may regard the bed shown in Plate XXI. fig. 4. as an unfinished and transition example. There the pressure has evi- dently been at once from behind and above, so that the beds have bulged out for- wards, but the pressure had not been long enough maintained to work the various beds into one another. The influence of the massive ice-foot, in working utter confusion in the bank which lay below it, must have been all the greater from the different conditions it must have assumed under the ever varying change of the seasons, and those slower oscillations of rain-fall and temperature. which extend throughout years. At times it would crush the oozy mass below with an enormous weight, till the ‘ sludge was compressed almost to the solidity of stone. Again, it would be floated off, and leave space below it for the deposition of stratified sands and clays, in which even molluscan life might thrive, till a rush of debris, brought down by a VOL. XXIII. PART III. 7G 540 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS warmer summer, buried them, or a series of wetter and colder years swelled the mass of ice so that it rested again with its full weight on the bank, crushing down its surface, and, as it ground its way over the resisting mass, producing those ‘‘striated pavements” which are well known as one of the striking features of the boulder-clay. 5. The boulder-clay contains beds which seem to have been formed on the land. Such beds as those I have described at pages 528, 531. and 533 certainly give the impression of their having had a glacier lying directly upon them, and the nature of the position in which they lie confirms the impression of their having been thrust into an angle of the strata by the glacier. But whether it be true, as I believe, for these cases or not, it is obvious that instances of the kind must have occurred, and are to be looked for in all such corners, and other places of the basement rock, as could give shelter. 6. The boulder-clay was deposited as the land was subsiding. Of this fact, the proof which appeals to our senses is the sequence of thebeds. From thesea- level to 1200 feet they can be followed uninterruptedly, with quite enough of stratification to leave no doubt that the beds higher above the sea are also higher stratigraphically, and rest on those below. The other proof, though not so direct, rests on even a broader and less fallible basis of fact. The mere presence of the boulder-clay, from the sea-line up to the mountains, implies its deposition during the subsidence of the land; for let us suppose the contrary, and imagine that at some period of the glacial epoch the land previously submerged began to rise. As each zone of the land successively came to the surface it would be subjected to the ice and glaciated. So long as the glaciation went on, every particle of soil would be stripped off the rock and accumulated at the sea-line; and when the glacial period passed away, it would have left our land like a bleached and ghastly skull projecting from the grave. This obviously is not the case. The whole country more or less, except only the higher mountains, is covered with soil, the boulder-clay itself rising to 1100 or 1200 feet at least; and this is exactly what would occur under the other supposition, that the glaciation of the country, and the deposition of the boulder- clay, went on as the land was subsiding ; for thus, as Hucm MILLER has some- where shown long ago, the sea would protect the boulder-clay from the ice, while the ice-foot would shelter it from the surf, and only when the ice was gone would the higher level beds be so far wave-beaten and eroded as to supply a coating of soil to the bare rock of the hill tops, and the higher mountain summits alone would be left in the nakedness of broken and weathered rock which characterises them. And here, if adaptation of means to an end be a proof of design, we have a marked evidence of the work of God preparing the earth for man’s habitation. 7. The subsidence extended from the present sea-level, and ultimately reached IN THE SOUTH OF ARRAN. 541 1100 or 1200 feet at least. The striated surfaces (indicative of ice) at the pre- sent sea-level prove that the land, during the boulder-clay period, stood at least no lower than it does now, and the presence of the boulder-clay—a sea deposit as we have seen—proves that to a height of 1100 or 1200 feet the sea rose over the land. There is indeed some evidence that during the glacial period the land stood higher than now, and still better proof exists, in Wales especially, that the depression extended to not less than 1400 feet ; but I confine myself now to the evidence afforded by the Arran beds. 8. The subsidence was probably continuous not oscillatory. Of course there may have been oscillations here, as there have been, in recent times, at Naples and elsewhere; but, so far as I know, no evidence exists of such oscillations occurring during a protracted and long-sustained process of subsidence and upheaval: and certainly no trace of such irregularity has yet been found in connection with the movements of our country during the glacial period. At the same time it is not very obvious by what evidence such oscillations, during the deposition of the boulder-clay, could be established. Still, in the absence of any strictly analogical case, we may consider that the subsidence of the land here was continuous. 9. The subsidence was gradual. As this opinion is opposed to that which I held when I read this paper to the Society, it is right that I state somewhat fully the grounds on which it rests. The depression of the land might take place by a succession of sudden jerks or leaps, with long intervals of rest, or by a slow, steady subsidence, as is the case at present in Greenland.* In the former case, the ice-cake would be floated off the land as it sank, and between the top of the boulder-clay bank on which it had been resting, and the new ice-foot, there would be a zone of bare rock perpendicularly equal to the amount of the subsidence, but which, in the flatter districts, would be of con- | siderable extent horizontally. Along the upper edge of this zone, at its junction with the ice, the boulder-clay bank would again begin to form, but all its lower expanse would lie too remote from the supply of debris to be thus covered. The | glacier streams, however, floating out to sea on the surface of the salt water, would gradually drop on it the detritus with which they are always charged, and a bed of stratified sand and clay by degrees would overspread the bare rock, | till the growing mass of boulder-clay buried it. Now in Arran, as I have men- . tioned, I found several cases of just such a bed resting directly on the rock, and buried beneath the boulder-clay; and the inference seemed to me a fair one, that _ these beds indicated a sudden subsidence of the land at that point. I still believe them to indicate the remoteness of the ice-cake at the time of their deposition, * Such jerks must of course be supposed considerable, since, if minute, the subsidence in this way would practically be slow and steady as in the other. 542 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS but I no longer think that remoteness of the ice due to sudden subsidence. Had it been so, the basement-bed of sand and clay would have run round our whole | coast pretty much at the same level. But this is not true, even for Arran. The stratified beds, therefore, on the basement rock must, where they exist, be accepted merely as local phenomena, and be therefore explained by local causes, connected probably with those banks of eruptive rock which lie across the valleys, and which must have interfered with the free motion of the ice. Thus, in the absence of any evidence of a sudden depression we accept the other alternative of steady gradual subsidence, during which each separate level must in turn have formed the shore line and lain at the edge of the ice foot, and have received the glacial detritus—the coarse red clay and stones which the ice and its accompanying streams were bringing down—while the finer detritus would be spread as stratified sands and gravels over the boulder-clay beds already deposited. 10. Was the subsidence rapid? A question I rather ask than answer. If the mass of the boulder-clay suggest long-continued formation, the comparative rarity of interstratified beds, and the merely local development of the overlying beds of sand and clay—though perhaps capable of explanation on other grounds —still seem to point to such a steadiness of climate and of currents as is hardly compatible with a very lengthened duration of the glacial epoch; and in this case the huge mass of the glacial debris would be the result of an enormous development of the ice-cake, which tallies well enough with various known facts. On the whole, this point must be considered doubtful, and its determination is’ probably to be sought from a careful examination of the larger shell-beds, the layers of life in which may indicate the duration of their development. 11. There has been no general glaciation of the land since its re-emergence. Had glaciers existed on the land after it rose from the sea, they would certainly have cleared the upper valleys at least, of boulder-clay, and left nothing but great transverse moraines, as is the case in Norway. (See Kjerulf on the glacial phe- nomena of Norway in the Edinburgh New Phil. Journal for July 1863, p. 8.) Instead of this the boulder-clay thins out gradually upwards, and fringes the upper valleys as a beach terrace. 12. The existing boulder-clay must represent all ages throughout the whole glacial epoch ; for so long as the ice-cake was present on any part of the land the manufacture of boulder-clay went on. 13. There must be drift-beds of sand and clay resting on the boulder-clay, but truly contemporary with the boulder-clay of a higher level than that on which they he. It may not be easy or possible to determine which of these answer to one another; but it is obvious, that while the coarser debris from the land was forming boulder-clay under the ice-foot, a deposition of the lighter detritus must have been going on from the fresh-water currents that were setting - : : : IN THE SOUTH OF ARRAN. 543 seaward, and scattering, first the sand and ultimately the mud, with which they were charged, on the boulder-clay already spread over the lower levels. Thus these two beds, the boulder-clay formed under the ice-foot, and the stratified sands and clays deposited in deeper water, though so different in texture, would be really strictly contemporary. Of course the determination in any particular ease, of which are the corresponding beds, is now the more difficult task, from the erosion of the beds at certain points, and their remaniement or remanufacture in others. 14. We may determine, approximately at least, the relative age of the drift- beds. Superposition, of course, implies subsequence in time, but this principle is of very limited application, and will not avail for the comparison of the boulder-clay in different districts. If, however, the boulder-clay was deposited under the ice-foot as the land was subsiding, the sea-level affords us a standard of comparison for the boulder-clay beds over the whole country. Allowing for possible differences in the thickness of the ice-foot, which would be deeper of course in the valleys than on the hill faces, and deeper also in a mountainous than in a flat region, all boulder-clay beds are contemporary which rest on the basement rock at the same level above the,sea; and of two beds at different levels that is the older which lies on the rock nearest the sea-level. 15. Since the boulder-clay period there has been no material change of any kind on the basement rock of the country. Such changes might have occurred in three ways. In the process of subsidence and re-elevation the whole face of the land might have been remodelled, and hill and valley have changed places. Such a change, or something like it, has been asserted even by so eminent an authority as the great German geologist NAUMANN. (See Geognosie, vol. i. p. 249.) But in our drift-beds we have casts made of our valleys as they sank under the sea, and these casts show that what are valleys how were valleys then; in other words, they assure us that the subsidence and re-elevation of the land has not been accompanied by any such protrusion of one part of the coast above another, or of the interior above the coast line, as to affect the relative contours of hill and valley. _ Another form of change is that on the river beds, the erosion of which is generally attributed to existing streams; whereas in Arran we find that the burns are only now beginning to lay bare the rock which underlies the boulder- clay. If, then, making all allowance for the slight erosive power of such small Streams, they have yet done so little here against sands and clays, how much : less elsewhere against solid rock. They seem, in fact, to be only now beginning to occupy the old river-beds formed long ago under the ice, and in part even earlier. The third change which has been often asserted, consists in the erosion of the older and present coast-lines by the sea, upon which calculations have even VOL. XXIII. PART III. Cu 44 REV. R. B. WATSON ON THE GREAT DRIFT-BEDS WITH SHELLS been founded to determine the length of time during which the sea stood at the forty-foot terrace-line, and so on. Now, admitting the obvious fact of the destruction of the rock at many points of our present sea-line, it yet appears that on the whole the influence of the sea in modelling the land in recent times has been very small. In a great many cases it has not so much as penetrated the — boulder-clay ; and even where that has been washed away, as in the coast of the Little Cumbrae, figured and described by Mr Smiru of Jordan Hill, in his ‘‘ Newer — Pliocene Geology,” p. 144, the striations of the rock remain with wonderful fresh- ness. From all this it is obvious that the terrace lines of the basement rock are not due to the action of the present sea, but were given to it previous to its sub- mergence. In short, we find that all the latest geological changes, with their accompani- ment of river and sea-action, have not materially modified the face of the country —the rock skeleton of which was moulded finally under the glacial epoch.* o List OF THE SHELLS FOUND IN THE ARRAN BEDS, WITH THE DEPTHS AT WHICH THEY LIVE ON OUR OWN AND THE NorWEGIAN Coasts, AS GIVEN BY ForBES AND HANLEY, AND BY DANIELSEN. 4 Name. British. Norwegian. - Balanus crenatus, Deep water to 50 fathoms. =—S— Panopoea norwegica. Deep water to 90 __—, Not known living. Tellina balthica, (a brackish variety of Seidel) Shore. 20-60 fathoms. Cyprina islandica. 5-80 x 20-40, Astarte elliptica. - 10-40 A 20-60", arctica. &0 (dead) = 10-80 me compressa. 7-70 ps 10-40, striata (avariety of compressa.) i ss pte: * I cannot let this paper go without expressing my obligations for much information and many suggestions to my friend Mr Gzrxte’s valuable paper on the Phenomena of the Drift. I am grati- fied to agree with liim on the land origin of the material which constitutes the boulder-clay, and on the subsidence of the land during the formation of the boulder-clay. On some other points, too, I think we are not very far from an agreement, though I fear we differ fundamentally on many of the most important. , + I only found one specimen of this species. The shells were partially crushed, but the two valves were united, and retained both epidermis and ligament. Mr Szartes Woop, who was good enough to examine it for me, says it is one he does not recognise. Mr §. P. Woopwarp, who has” also taken the trouble of looking at it, considers it an unusually large 4. compressa of the variety striata. It is one-third larger than even the excessively large specimens of the species from the Red Crag, figured by Mr Szartzs Woop in his Bivalves of the Crag.—(Pal. Soc. Pub., vol. ii. p. — 184, pl. 16, fig. 8, a and c.) — e IN THE SOUTH OF ARRAN. igi i 545 é , List OF THE SHELLS FOUND IN THE ARRAN Bens, &c.—Continued. ’ Name. British. Norwegian . Syn. Lucina. e } Cryptodon | Ca eae } Si Jt s ae ie lm ance 20-180 fathoms. Modiola modiolus. 0-60 fathoms. Shore. Leda (syn. Yoldia) pygmza. 25-40 30-140 ,, pernula. : { eo = ee \ “5 10-140 _,, Pecten opercularis. 5-100 pe 30-50, islandicus. 35-100 (dead.) a 10-60°' | Litorina litorea. Shore. a Shore. Turritella communis. 4-100. a 10-30 ,, Natica. Species not determinable. _...... Description of Plates. Pruate XXI. of the land, the clothing of boulder-clay, and the way in which the burn-course is cut through it. The banks in the burn-course are from 60 to 120 ft. high. (P, 524-528.) Fig. 2. Bed of various clays, &c., in the Torlin Burn, below the church. (P. 528.) found here, 5 or 6 feet. 12. Layer of large stones and coarse gravel, 1 foot. , 13. Boulder-clay. g. 3. Great shell-bearing banks in the Cloinoid Burn-course, 80 to 100 feet high. The upper part grass-grown. The centre being obscured by debris is omitted. (P. 529.) y. 4. A bed of sand overlaid by boulder- mak The whole subjected to a forward thrust under pressure. (P. 530.) . 5. Immense boulder-clay bank on the Cloinoid Burn, 140 feet high; in many places perpendi- cular; with shells. In the centre of the bank, the rock crops out. (P. 530.) ‘Fig. x. pe should go together, as they show the same beds, and are nearly continuous, 100 yards | Fig. 8.{ only intervening. They both occur at the lower end of the basin, shown in fig. 6 6. Fig. 1. Lower part of Torlin Water seen from the east, 450 ft. above the sea, to show the contours 1. Small gravel and minute angular stones, 3 inches. zi ae clay with angular stones in upper corner, 2 inches. All this is purply and red . Sand, 3 inches. like th ine 4. Clay with stones, 3 inches. ae oe : y ta the district 5. A nest of gravel, 3 inches, . 6. Sand, 4 inches. 7. Fine yellowish sand, 3 inches. 8. Fine reddish sand and clay, without stones, 6 inches. 9. A nest of gravel, 3 inches. 10, Sandy clays distinctly laminated, and slightly varying in texture; dipping under next bed, No. 11 at 75°; shells found in this, 8 inches. ; 11. Very dense, dark, coarse boulder-clay, with few stones, and slightly stratified ; shells Fig. 6. Basin in the Cloinoid Burn-course, to the contours of which the boulder- clay conforms. (P. 531.) - ‘es 546 REV. R. B. WATSON ON THE DRIFT-BEDS IN THE SOUTH OF ARRAN. Fig. 7. Shows at the bottom a bed formed under a glacier. To the left it is overlaid by the boulder- _ clay, which to the right has been eroded, and the glacier-bed here is overlaid by a layer of — large stones. (P. 531.) Priate XXII. Fig, 8. At the bottom, the same glacier-formed bed overlaid to the right by boulder-clay ; to the left, both the glacier-formed bed and that of boulder-clay seem to have been eroded, an¢ a mass of stones and gravel, like that in fig. 7, but thicker, lies on the hard glacier-bed. (P. 532.) Fig. 9. Bed, 100 feet high, in Crogeréver Burn-course, just above its junction with the Slaodrig Burn. (P. 532.) Fig. 10. Gorge in Crogeréver Burn, the west side being formed by the rock, the east side by the — boulder-clay lying down the dip of the strata. (P. 533.) Fig. 11. Bed of hard yellow clayey gravel, lying in behind a barrier of felstone. The burn has — partly cut in between the rock and the bed, but in the distance in the fig., has turned to — the right, and cut through the bank. (P. 533.) Fig. 12. The same bed further up the burn, with overlying beds. (P. 533.) 1. The hard yellow clayey sand or gravel, with a huge striated greenstone boulder sticking in it. This bed is laminated, but not stratified on its upper surface to the left. 2. Overlying 1. Red boulder-clay, with a large boulder sticking in it, but projecting above its surface into , 3. Coarse sand, 10 feet thick in parts. 4, Very large stones, 3 feet. 5. Fine light-coloured sand, 6 inches. 6. Earth. Fig. 13. The same bed still further up the burn, and just below the felstone rock. To the left, i the burn-course, is boulder-clay. Underlying this is the hard yellow clayey gravel much discoloured, and containing heather stalks. Above this is debris, with boulder-el: showing atop. (P. 534.) Fig, 14. Beds in Clachan Glen, 20 feet high. At the bottom is a talus of debris. Above this, t the left, a face of. the shale-rock, 2 to 3 feet high. Lying up on this to the right, 2 fee the dense gravel. Overlying this bed, and to the left lying directly on the shales (whiel have been stripped there of the dense gravel), 3 feet of large stones; then 2 feet fine sand Earth atop. (P. 535.) Fig, 15. Great banks in Clachan Glen. (P. 535.) 1. Hard gravelly clay, 15 feet. 2. Looser stones and gravel, 4 feet. 3. Dense finely laminated clay with fine sand, becoming more sandy towards the top, containing twigs, 15 feet. A . Dense hard boulder-clay, 8 feet. . Big stones and gravel, 5 feet. . Boulder-clay or drift, 30 to 40 feet. Oo Plate XXI. WH MS Farlane, Jith® Edin™ Soc. Bdin® Vol. XXIII. Plate XXII. W.HM Farlane, Litht Edin® ( 547) XL.—On the Principal Deities of the Rigveda.* By J. Murr, Esq., D.C.L., LL.D. (Read 7th March 1864.) wel Ya St". In the paper which I had the honour to read before the Society last winter, I _ stated the reasons, drawn from history and from comparative philology, which - exist for concluding that the Brahmanical Indians belong to the same race as the - Greek, the Latin, the Teutonic, and other nations of Europe. If this conclusion _ be well-founded, it is evident that at the time when the several branches of the great Indo-European family separated to commence their migrations in the - direction of their future homes, they must have possessed in common a large ‘stock of religious and mythological conceptions. This common mythology would, in the natural course of events, and from the action of various causes, undergo a gradual modification analogous to that undergone by the common language which had originally been spoken by all these tribes during the period of their union; and, in the one case as in the other, this modification would assume in the different races a varying character, corresponding to the diversity of the influences to which they were severally subjected. We shall not, there- ‘ fore, be surprised to find that even the oldest existing mythology of the Indians _ differs widely from the oldest known mythology of the Greeks, any more than _ we are to find that the Sanskrit in its earliest surviving forms is a very different | language from the earliest extant Greek, since the Vedic hymns, the most primitive remains of Sanskrit poetry, date from a period when the two kindred races had been separated for perhaps above a thousand years, and the most ancient monu- "western branches of the family; while, at the same time, we should, of course, expect that such traces of common religious conceptions would be more distinctly _ * This essay contains the substance of a series of papers either already communicated, or in- tended to be communicated, to the Royal Asiatic Society of Great Britain and Ireland, in which the Same subject is treated in greater detail, and with numerous references to the original passages of the gveda. For further information on the gods of the Veda, reference may also be made to Profes- “sor H. H. Wilson’s prefaces to the three volumes of his translation of the Rigveda; to Professor Budolph Roth’s papers, “Die Sage von Dschemschid,’ and “Die héchsten Gétter der Arischen Vélker,” in the Journal of the German Oriental Society, vols. iv. and vi.; to the paper by the same _ author “On the Morality of the Veda,” and the account of the “main Results of the later Vedic Researches in Germany,” by Professor Whitney, in the third volume of the Journal of the American _ Oriental Society ; and to Professor Max Miiller’s “ History of Ancient Sanskrit Literature,” and his “Essay on Comparative Mythology,” in the Oxford Essays for 1856. The sketches of Rudra and Vishnu given in this paper are abridged from the fuller accounts of those gods in my “Sanskrit Texts,” vol. iv. VOL. XXIII. PART I. (a 548 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. perceptible in the older than in the more recent literary productions of the several peoples. And such, in point of fact, turns out to be the case. The mythology of the Veda does exhibit in some points a certain similarity to that of Homerand Hesiod, and the mutual resemblance between the religious ideas of those ancient works is, upon the whole, greater than that existing between the later Indian and the later Greek pantheons. I say that, upon the whole, the older Indian mytho- logy coincides more nearly with the Greek than the later Indian mythology does. But, on the other hand, the later Indian system presents some points of resemblance with the Greek which the Vedic system does not exhibit. I allude to the fact that we find in the Indian epic poems and Puranas a god of the sea, a god of war, and a goddess of love, who are unknown to the oldest parts of the Veda, and yet correspond in a general way to the Poseidon, the Ares, and the Aphrodite of the Greeks. Personifications of this sort may, however, be either the product of an early instinct which leads men to create divine representatives and superintendents of every department of nature, as well as of human life and action; or they may arise in part from a later process of reflection which condue iS to the same result, and from a love of systematic completeness which impel a people to fill up any blanks in their earlier mythology, and to be always adding to and modifying it. Resemblances of this last description, though they are by no means accidental, are not necessarily anything more than the results of similar processes going on in nations possessing the same general tendencies and char- acteristics. But the older points of coincidence between the religious ideas of the Greeks and the Indians, to which reference was first made, are of a different character, and are the undoubted remains of an original mythology which wa S common to the ancestors of both races. This is shown by the fact that, in the cases to which I allude, it is not only the functions, but the names, of the gods which correspond in both literatures. But the value of the Vedic mythology to the general scholar does not consist merely in the circumstance that a few religious conceptions, and the names of two or three deities, are common to it with the Greek. It is even more important to observe that the earliest monuments of Indian poetry, consisting, as they do, almost exclusively of hymns in praise of the national deities, and being the pro- ductions of an age far anterior to that of Homer and Hesiod, represent a more ancient period of religious development than we discover in the Greek poets, and disclose to us, in the earliest stages of formation, a variety of myths which a few centuries later had assumed a fixed and recognised form.* It is also to be noticed that, from the copiousness of their materials, the hymns of the Rigveda supply us with far more minute illustrations of the natural workings of the human mind, in the period of its infancy, upon matters of religion than we can * See Professor Max Miiller’s essay on “‘ Comparative Mythology,” in the Oxford Essays for 1856, p. 47. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 549 - find in any other literature whatever. From their higher antiquity, these Indian _ hymns are also fitted to throw light on the meaning of a few points of the Greek system which were before obscure. Thus, as we shall see, the Indian Dyaus (sky, _ or heaven) explains the original meaning of the Greek Zeus, and the Sanskrit _ Varuna gives a clue to the proper signification of Ouranos. As in my former paper I stated the grounds on which the Vedic hymns are i assumed to have been composed at a period considerably more than a thousand years before our era, I shall here take their great antiquity for granted, and pro- _ ceed to give some account of their cosmogony and mythology. ‘ To a simple mind, reflecting in the early ages of the world with awe and _ wonder on the origin of all things, various solutions of the mystery might naturally present themselves. Sometimes the production of the existing universe would be ascribed to physical, and at other times to spiritual, powers. On the a hand, the speculator, perceiving light and beauty emerge slowly every - morning out of a gloom in which all objects had, shortly before, appeared to be A confounded, might conceive that in like manner the brightness and order of the world around him had sprung necessarily out of an antecedent night in which the elements of all things had existed together in undistinguishable chaos. Or, on the other hand, contemplating the results effected by human energy and design, and arguing from the less to the greater, or, rather, impelled by an irresistible instinct to create other beings bearing his own likeness, but endowed with higher powers, he might feel that the well-ordered frame of nature could not possibly have sprung into being from any blind necessity, but must have been the work of a conscious and intelligent will. In this stage of thought, | however, before the mind had risen to the conception of one supreme creator and | governor of all things, the various departments of nature were apportioned '; etween different divinities, each of whom was imagined to preside over his | own special domain. But these domains were imperfectly defined. One blended ‘with another, and might thus be subject in part to the rule of more than one deity. Or, according to the various relations under which they were regarded, These several provinces of the creation might be subdivided amongst a plurality of divinities, or varying forms of the same divinity. These remarks might be illus- | trated by numerous instances drawn from the Vedic mythology. In considering t. literary productions of this same period, we further find that as yet the differ- | ence between mind and matter was but imperfectly conceived, and that although ' im some cases the distinction between some particular province of nature and the | deity who was supposed to preside over it was clearly discerned, yet in other instances the two things were confounded, and the same visible object was at different times regarded diversely as being (1) either a portion of the inanimate universe, or as (2) an animated being and a cosmical power. Thus in the Vedic hymns the sun, the sky, and the earth are severally considered sometimes as 550 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. natural objects governed by particular gods, and sometimes as themselves deities who generate and control other beings. The varieties and discrepancies which are in this way incident to all nature- | worship are, in the case of the Vedic mythology, augmented by the number of the poets by whom it was moulded, and the length of time during which it con- tinued in process of formation. The Rigveda consists of more than a thousand hymns, composed by successive generations of poets during a period of many centuries. The authors of these hymns give expression not only to the notions of the supernatural world which they had inherited from their ancestors, but also. to their own new conceptions. In that early age the imaginations of men were peculiarly open to impressions from without; and in a country like India, where the phenomena of nature are often of the most striking description, such specta- tors could not fail to be overpowered by their influence. The creative faculties of the poets would thus be stimulated to the highest pitch. In the starry sky in the dawn, in the morning sun scaling the heavens, in the bright clouds floating across the air and assuming all manner of magnificent aud fantastic shapes, in the thunder, lightning, rain and tempest, they beheld the presence and agency of different divine powers, propitious or angry. In the hymns composed under any such influences, the authors would naturally ascribe a peculiar or exclusive importance to the deities by whose energy the phenomena appeared to have been produced, and would celebrate their praises with proportionate fervour. Other poets might attribute the same natural appearances to the action of other deities, whose greatness they, in like manner, would extol; while others again would devote themselves to the service of some other god, whose working they seemed to witness in some other department of creation. In this way, while the same traditional divinities were acknowledged by all, the power, dignity, and functions of each several god might be differently estimated by different poets, or, perhaps, by the same poet, according to the external influence by which he was awed or inspired on each occasion.. In such circumstances, it need not surprise us if one particular power or deity is in one place put above, and in another place sub- ordinated to, some other god; is sometimes regarded as the creator, sometimes as the created. This is illustrated in the case of the first Vedic divinities, to whom I shall refer—viz., Heaven and Earth. a Dyaus and Prithivi. It has been observed by a recent French writer, that “the marriage of Heaven — and Earth forms the foundation of a hundred mythologies.” * According to the ~ Theogony of. Hesiod (116 ff.), the first thing that arose out of chaos was “‘t. broad-bosomed Earth, the firm abode of all things.” She in her turn “ produc the starry Heaven (Ouranos), co-extensive with herself, to envelope her on every _ * Albert Réville, Essais de Critique Religieuse, p. 383. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 651 part.” From the union of these two powers sprang Oceanos, Kronos, the Cyclopes, Rheia, &c. (132 ff.); and from Kronos and Rheia again were produced Zeus, Here, and other deities (453 ff.). The Rigveda (which is, as I have already intimated, the earliest source of infor- mation regarding the religion of India) contains no uniform or consistent system of theogony or cosmogony. But in numerous passages Heaven and Earth (Dyaus and Prithivi) are spoken of together as the parents of all things; and several separate hymns are dedicated to their honour. They are characterised by a pro- fusion of epithets, not only of such a kind as are suggested by their various phy- sical characteristics, vastness, breadth, profundity, productiveness, but also by others of a moral or spiritual nature, as innocuous, or beneficent, promoters of righteousness, and omniscient. In the Veda we are not told, as we are in the system of Hesiod, which of the two, Heaven or Earth, was the older. On the contrary, one of the ancient poets seems to have been perplexed by the difficulty of this question, as at the beginning of one of the hymns (i. 185) he exclaims, _“ which of these twain was the first, and which the last? How were they pro- “duced? Sages, who knows?” Besides being described together in the dual as the “parents,” Heaven and Earth are separately spoken of in various passages, the ‘one as the father, the other as the mother, as in vi. 51, 5—‘“‘ O father Heaven, | penignant mother Earth, brother Agni, and ye Vasus, be gracious to us.” I must here remark, by the way, that the words which stand in the original of this verse for father Heaven, or rather Heaven father, viz., Dyaush pitar, answer exactly to the z:b¢ rar4g of the Greeks, and the Diespiter of the Latins, though, as ‘is well known, Zeus is not in the Greek mythology, as he is in the Indian, iden- ‘tical with the primeval Heaven, the father of all things, but is his grandson ; while again, the Indian god, who corresponds in name, and also in some points in | character, with the Greek ’ovgaréc, is Varuna, who, however, as we shall by and by ‘see, differs from *ouzaés in various respects. The word Priturvi, on the other hand, which in most parts of the Rigveda is used for Earth, has no connection with any Greek word of the same meaning. It seems, however, originally to have been merely an epithet, meaning “ broad;” ‘and may have supplanted the older word go, which stands at the head of the earliest Indian vocabulary, as one of the synonymes of Prithivi (earth), and which closely resembles the Greek ram or rj. In this way Gaur matar may have once corresponded to the rj wArne OF Anujrne Of the Greeks. _ This designation of the Earth—the prolific source of all vegetable products, and the home of all living creatures—by the epithet of mother, is perfectly Natural, as is proved by common usage. This is remarked by Lucretius in _ Various passages,* (referred to by Professor SzLLar in his “‘ Roman Poets of the * De Rerum Natur, ii. 991 ff.; 998 ff; v. 793 ff.; 799 ff.; 821 ff VOL. XXIII. PART II. aK 552 MR J. MUIR ON THE PRINCIPAL DEITIES IN THE RIGVEDA, ' Republic,” pp. 236, 247, 276), in which the poet says, that the Earth “ has de- servedly received and retains the name of mother.” The Greek poets also, as Hesiod, Aischylus, and Euripides, speak in like manner of the Earth as the uni- versal mother and nurse.* In like manner Tacitus (Germania, 40) tells us that certain of the German tribes ‘“ worshipped, in common, Ertha,} that is, mother earth, and imagined her to interfere in the affairs of men, and to move about among them in a covered car.” And the conception of the Heaven as the father of all things is also, though in a less degree, a natural one, and is noticed by Lucretius where he says (ii. 992), that ‘‘ We have all the same father, the Heaven, from whom the bounteous Earth receives that moisture by which she is rendered fruitful.” The same idea may be obscurely implied by Diodorus Siculus (i. 7), where he says, that, in the opinion of some speculators, ‘‘ heaven and earth had, accord- ing to the original constitution of things, but one form, the natural properties of the two being blended; but that afterwards, when the body of the one had become separated from that of the other, the world assumed that regular order which we now witness.” And further on he adds: “ And in regard to the nature of the universe, Euripides, who was a disciple of Anaxagoras, the physical philosopher does not appear to have differed from the views which have been stated. For in his Melanippe he lays it down that ‘The heaven and the earth were of one form; but when they became separated from each other, they produced all things and introduced them into the light,—trees, birds, beasts, the offspring of the deep, and the race of mortals.’” But the Rigveda regards Heaven and Earth as the parents not only of met but also of the gods, as appears from the epithet deva-putre, viz. “ the twain whe have gods for their children,” which is applied to them in various passages. On the other hand, however, these two divinities, Heaven and Earth (as I have above intimated), exemplify the general remark already made, that the Vedie deities are constantly appearing in opposite characters,—sometimes as supreme and as creators, at other times as subordinate and created. In many place Heaven and Earth are said to owe their existence and support to the gods, some- times to one, and sometimes to another.{ In one passage (i. 160, 4) it is said * Hesiod Opp., 561, y% révrwy wqrne. Zischylus, Prom. 90 raupyroe re vi; Sept. cont. Thebas, 16, yi re wnrel, GiAréry ro0p@. Kuripides, Hippol., 601, & yaiw wijree qriov r dvaxruyai. Compare also the name of the goddess Demeter, an old form of Ge meter. (See ‘“ Liddell and Scott’s Lexicon,” s Diodorus, 1. 12, says that the Egyptians, ‘* conceiving the earth as a sort of receptable of things! course of production, had designated her as mother; and that the Greeks had, in like manner, called her Demeter, the form of the word being slightly changed through time; since she wa ancient times named Gé Métér (Earth Mother), as Orpheus testifies when he says: ‘ Earth (om ‘ the mother of all, Demeter, the wealth-bestowing.’” } Ertham is Ritter’s emendation, the common reading being Nerthun. (Compare Ritter’s 1 no! ote on section 9 of the Germania.) t In Rigveda, x. 54. 3, Indra is said to have created the father and the mother (Heaven and Earth) from his own body. ; MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 053 (and though the words seem to be meant as eulogistic of Heaven and Earth, they also affirm their creation), “ He was the most skilful of all the skilful gods, who produced, who meted out, Heaven and Earth, and established them with unde- _eaying supports.” In other places, Heaven and Earth are said to bow down, to tremble, to be disturbed, at the presence of particular deities. In several hymns we find various speculations about their origin. One as to their respective priority _ has been quoted above. In another passage (x. 31, 7), the poet asks—“ What was the forest, what was the tree, from which they fashioned Heaven and Earth?” a In another hymn (x. 81, 3), the creation of the worlds is ascribed to the sole § agency of the great Architect Visvakarman, who is also (x. 82, 3) called the father, the generator, the disposer, who knows all spheres and worlds, and gave * names to the gods; but here, too, the same question is asked, as to whence the wood came of which Heaven and Earth were constructed, and other ques- ‘tions are put, which show the sense of awe and mystery with which the poet was i oppressed. __ Elsewhere (in a hymn, x. 129, quoted in the paper which I read before the "Society last year), it is said that formerly there was neither non-existence nor "existence, neither death nor immortality, neither night nor day. Nothing existed ‘but the One, in whom love or desire arose, which was the first germ of mind,* and led to all further development. ‘“ Who can tell” (the poet proceeds) ‘“‘ whence - this creation arose? The gods are subsequent to its production: Who then knows whence it sprang? He who in the highest heaven is its ruler, he knows, or per- haps not even he.” i- 1a The Vedic Gods in general. ‘The gods (to whom I now pass) are sometimes said to be thirty-three in “number, eleven belonging to each of the three spheres into which the universe is | usually divided in the Rigveda, Heaven, Earth, and the region intermediate be- tween thetwo. Aswe have already seen, these deities are occasionally described as being the progeny of Heaven and Earth; and in the passage just quoted, they are expressly affirmed to have come into existence subsequently to the creation of the orld. In the Rigveda they are constantly spoken of as immortal ; but in the later mythology, at least, their immortality is regarded as merely relative, since * The part here assigned to love or desire (Kama), in the creation, corresponds, as the classical ‘scholar will have noticed, to the position of Eros in the Greek mythology. Hesiod (Theog. 120) | makes this deity coeval with Gaia and Tartarus, and prior to Ouranos. (See “‘ Smith’s Dict. of Greek and Roman Biogr. and Myth.” under the art. Er os, and the passages of Aristotle, Plato, and Avristo- phanes, there referred to.) In the Satapatha Br ahmana, and other similar works, the creative acts | of Prajapati are constantly said to have been preceded by desire. In the Atharva Veda, Kama is distinctly personified as the god of desire in general, and as of love in particular; and his darts are ‘there spoken of (iii. 25, 1 ff.) just as they might be by a Greek, or by a modern, poet: “I pierce | thee in the heart with the terrible arrow of love (Kama). May Love pierce thee in the heart, having bent his shaft winged with anxiety, pointed with desire,” Sc. 554 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. they are considered to perish, as far as regards their corporeal organisation, at — every periodical dissolution of the universe. Their souls, however, like those which animate all other living creatures, from Brahma to a plant, are, according to later theories, imperishable. In the Rigveda a specific origin is ascribed to many of the deities, as, for instance, to the important class called the Adityas, including Varuna, Mitra, and others, who are all regarded as the sons of Aditi. Indra, too, is in several places spoken of as having both a father and a mother. In the Brahmanas, the gods are regarded as having been originally mortal, — and many discrepant stories are told of the way in which they acquired the pre- — rogative of immortality. Aditi. It is not very easy to define the character of Aditi, the goddess whom I have just alluded to as the mother of Mitra, Varuna, and the other Adityas. | In the old Indian -vocabulary, the Nighantu, she is identified with Prithivi, the — earth; and some of the epithets assigned to her in the Rigveda, such as “the widely-extended,” ‘“‘ the supporter of creatures,” “the friend of all men,” would i agree with this supposition. Some others of her designations, however, as “the y luminous,” appear to be more appropriate to the sky; and in various passages Aditi seems to be distinguished from the earth. Perhaps she may best be con- e sidered as a personification of universal nature, with which, in the following é remarkable verse (i. 89, 10), she is in fact identified : “‘ Aditi is the heaven; Aditi a is the intermediate firmament; Aditi is mother, and father, and son; Aditi is all _ _ the gods, and the five tribes of men; Aditi is whatever has been born; Aditi is” a whatever shall be born.” In another verse (v. 62, 8), she is thus mentioned, along — with another goddess, Diti :— ig “ Ye, Mitra and Varuna, ascend your car, and from thence ye behold Aditi and Diti,” From her name, and the manner in which she is introduced, the latter goddess — must be held to stand for something antithetical or supplementary to Aditi. The two together are meant to represent the whole creation, though it is not very clear what is the separate idea which each is intended to convey. In a hymn of the tenth book of the Rigveda, supposed, from its position in the collection, and from its contents, to be of comparatively late date, the process of creation is described with greater minuteness than in most other passages, and the share which Aditi took in it is declared, though not in a very intelligible way —Rigveda, x. 72. 1, ‘“ Let us in chanted hymns celebrate with praise the births of the gods, any one of us who in this later age may behold them. 2. Brahmanaspati blew forth these births like a blacksmith. In the earliest age of the gods, the existent sprang from the non-existent. 3. In the first age of the MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. DDD gods the existent sprang from the non-existent. Afterwards the regions sprang from Uttanapad. 4. The earth sprang from Uttanapad ; from the earth sprang the regions. Daksha sprang from Aditi; Aditi sprang from Daksha. 5. Aditi was verily produced, she who is thy daughter, oh Daksha. After her the gods were born, blessed, partakers of immortality. 6. When, oh gods, ye moved, in _ agitation, upon those waters, then a violent dust issued from you, as from dancers. 7. When, oh gods, ye, like heroes, replenished the worlds, ye drew - forth the sun, which was hidden in the (ethereal?) ocean. 8. Of the eight sons of Aditi, who were born of her body, she approached the gods with seven, and cast out Marttanda, the eighth. 9. With seven sons Aditi approached the former generation. She again produced Marttanda for birth as well as for death.” It will have been observed, that in the fourth verse of this hymn, Dakshais said to have sprung from Aditi, and reciprocally, Aditi from Daksha. The old Indian expositor Yaska (Nirukta, x. 23), thus attempts to explain this circum- stance, which had struck him as very strange :—‘ Daksha is, they say, a son of Aditi, and is celebrated among the sons of Aditi. And yet Aditi, on the other hand, is the daughter of Daksha, according to the text, ‘ Daksha sprang from Aditi, and Aditi sprang from Daksha.” How can this be possible? In this way, viz., that they may have had the same origin; or, in conformity with the nature of the gods, they may have been born from each other, and have derived their substance from each other.” Varuna and Mitra, _ The most famous of the sons of Aditi are Varuna and Mitra, who are very f equently associated with each other in the Rigveda. I have already stated above, that Varuna corresponds in name to the ’Ovgas of the Greeks.‘ Uranos,” as Professor Max Mutter remarks,* “ in the language of Hesiod, is used as a mame for the sky; he is made or born that ‘he should be a firm place for the blessed gods.’} It is said twice that Uranos covers every thing (v. 127), and that ‘when he brings the night he is stretched out everywhere, embracing the earth.t ; This sounds almost as if the Greek mythe had still preserved a recollection of the symological power of Uranos. For Uranos is the Sanskrit Varuna, and is derived from a root var to cover, &c.” Irepeat, however, what I have said above, that | th e parallel between the Greek Uranos and the India Varuna, does not hold in all * Oxford Essays for 1856, p. 41.. { Hesiod. Theog. 126,—Tatu 6¢ ror redirov wey eyeivaro ioov suur7 “Ougavov doregotvd’, ive wey reel sdvTa naAvaror, | "Ope in wandeecot becis 00g dopurzs cel. t Ibid. v. 176,—7Abe 6: Nour’ emdywn weyas ’Ovgavis. duo de Tain jwciony Oidornrog extoxero nal ‘oe eraviodn Then VOL. XXIII. PART III. “I | 556 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. points. Not to insist on the fact, that Varuna is a far more important deity in the mythology of the Veda than Uranos is in that of Hesiod, there is also this special difference between the two, that in the Indian mythology there is no rela-_ tion between Varuna and Prithivi, the earth, as husband and wife, as there is between Uranos and Gaia in Hesiod; nor is Varuna represented like Uranos as the progenitor of Dyaus or Zeus, except in the general way in which he is said (like many of the other Indian deities) to have formed and to preserve heaven and earth. The original identity of the two gods, however, appears to be not the less undoubted. Varuna is also, in the opinion of certain writers,* connected, at least, in- directly, with the Ahura Mazda of the old Persian mythology ; and in support of this it may be alleged,—(1.) That the name of Asura, the divine being,+ is fre- quently applied to Varuna, as an epithet; (2.) That the class of Indian gods, called Adityas, of whom Varuna is the most distinguished, bears a certain analogy to the Amshaspands of the Zend mythology, of whom Ahura Mazda is the highest ; and, (3.) That a close connection exists between Varunaand Mitra, just as Ahura and Mithra are frequently associated in the Zendavesta, though the position of the two has otherwise become altered, and Mithra is not even reckoned among the Amshaspands. Other scholars, however, think that there is no sufficient proof of Varuna and Ahura Mazda being connected with one another. The common origin of the Mitra of the Indian and the Mithra of the Persia a mythology is, however, placed beyond a doubt by the identity of their names Accordingly, the late Dr F. WinpiscHMann, in his dissertation on the Persian Mithra,{ regards it as proved that this god was common to the whole primitive Aryan race before the separation of its Iranian (or Persian) from its Indian branch; though the conception of his character was afterwards modified by Zoroastrian ideas. That Mithra was worshipped in Persia in the age of Hero- porus is, as WINDISCHMANN remarks, established by the currency of such Persian names as Mitradates and Mitrobates. Hrroporvs himself (i. 131) speaks of Mitra not as a god but as a goddess. But XENopHoN describes the Persians as swearing by the god Mitra. And PLuTarcd, in his treatise on Isis and Osiris, chapter xlvi. tells us that Zoroaster conceived of Mithra as standing between the deities Oromazes, the representative of light, and Areimanius the representative of dark- ness and ignorance. I need not further refer to the Persian Mithra, the ultimate introduction of whose worship into the west, in the time of the Roman Empero S, is matter of history. * Roru in the Journal of the German Oriental Society, vi. 69 f.; Wuuitnery in the J ournal of the American Oriental Society, vol. ii. p. 327. ij A name identical with the Zend Ahura, as the letter s of Sanskrit words is always represented by A in Zend, + Abhandlungen fiir die kunde des Morgenlandes. Mithra, ein Beitrag zur Mythengeschichte des Orients. Leipzig, 1857. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 557 I return to the Mitra and Varuna of the Rigveda. The frequent association of these two gods is easily explained, if the Indian commentators are right in determining that Mitra is the sun, or the deity who presides over the day, while Varuna is the god who envelops everything in darkness, and rules over the night. In one text of the Rigveda, it is said of the latter that he ‘‘ embraces the nights, and by his wisdom establishes the day, and does every thing perfectly.” On this Indian interpretation, Professor RotH makes the following ingenious remarks :*—‘‘Though such representations, as expressed in Indian exegesis, are far too narrow and one-sided, they nevertheless contain a certain amount of truth, and we may guess by what process they are to be developed. If Varuna is, as his name shows, the Aditya whose abode and whose sphere of authority is the bright heaven, in whose bosom is embraced all that lives; and if, therefore, he forms the remotest boundary, beyond which human thought can seek nothing further, then is he also one who can hardly be attained either by the eye or the imagination. By day the visual power cannot discover this remotest limit; the bright heaven presents to it no resting place. But at night this curtain of the _ world in which Varuna is enthroned, appears to approach nearer, and becomes _ perceptible as the eye finds a limit. Varuna is closer to men. Besides, the _ other divine forms which, in the clouds, in the atmosphere, and in the rays of light, filled up the space between the earth and yonder immeasurable outermost sphere, have vanished. No other god now stands betwixt Varuna and the mortal beholder.” Varuna is, notwithstanding, represented in the Veda as being sometimes visible ina bodily shape. He then assumes a luminous aspect, or is clad in golden armour. He sits in his abode exercising sovereignty, surrounded by his spies (or angels); and in two passages he is described as the joint occupant with Mitra of a vast palace, supported by a thousand columns.}+ Again, these two deities are described as ascending their chariot, which shines with a golden radiance at the break of day, and at sunset assumes the colour of iron. Seated in this car, and soaring in the empyrean, they behold all things in heaven and earth. The ‘sun is in one passage denominated the golden-winged messenger of Varuna; in other places he is said to be the eye of Mitra and Varuna. Both of these deities, but in particular Varuna, are celebrated by a variety of epithets, as exercising sovereign authority and universal sway, as possessing a spiritual nature, and divine wisdom. The grandest cosmical functions are ascribed to Varuna. Pos- | sessed of illimitable resources, this great being has meted out, created, and | upholds heaven and earth. He dwells in all worlds as sovereign: indeed the | three worlds are embraced within him. The wind which resounds through the 4 firmament is his breath. He has placed the sun in the heaven, and opened up = * Journal of the German Oriental Society, vi. 70 f. + Compare Ovid. Met. ii. ff. : «« Regia Solis erat sublimibus alta columnis,” &c. 558 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. a boundless path for it to traverse. He has hollowed out the channels of the rivers. It is by his wise contrivance that, though all the rivers pour their waters into the sea, the sea is never filled.* By his ordinance the moon shines in the sky. and the stars which are visible by night disappear on the approach of daylight. Neither the birds flying in the air, nor the rivers in their sleepless flow, can attain a knowledge of his power or his wrath. His spies (or angels) behold both worlds. He himself has a thousand eyes. He knows the flight of birds in the sky, the path of ships on the sea, the course of the far-sweeping wind, and per- ceives all the hidden things that have been or that shall be done. No creature can even wink without him. He is a witness of men’s truth and falsehood. His power and his omniscience are thus celebrated in the Atharva Veda (iv. 16, 1-6): (1.) “The Great Ruler of these (worlds) beholds, as if he were close at hand. When any man thinks to do aught by stealth, the gods know it all; (2.) and (they perceive) every one who stands, or walks, or glides along secretly, or withdraws into his house, or into any lurking place. Whatever two persons, sitting together, devise, is known to Varuna the king (present there as) a third. (3.) This earth, too (belongs) to King Varuna, and that vast sky, with its far distant limits. The two oceans (aérial and terrestrial), are Varuna’s loins; and he dwells in this small pool of water. (4.) He who should flee far beyond the sky, would not there escape from Varunatheking. His spies (or angels), descending from heaven, traverse this world; thousand-eyed they look across the whole earth. (5.) King Varuna perceives all that is within, and all that is beyond, heaven and earth. The winkings of men’s eyes are numbered by him. He handles (all) these (things) as a gamester his dice. (6.) May thy destructive nooses, which are cast sevenfold and threefold, ensnare the man who speaks lies, and pass by the man who speaks truth !’?+ * Compare Ecclesiastes i, 7—‘ All the rivers run into the sea; yet the sea is not full; unto the place from whence the rivers come, thither they return again.” + Then follow two verses containing imprecations. After giving a German translation of this hymn in his “ Dissertation on the Atharva Veda’ (Tiibingen, 1856), Professor Ror remarks :— “There is no hymn in the whole Vedic literature which expresses the Divine omniscience in such forcible terms as this; and yet this beautiful description has been degraded into an introduction to an imprecation. . But in this case, as in many other passages of this Veda, it is natural to conjecture that existing fragments of older hymns have been used to deck out magical formulas. The first five, or even six, verses of this hymn might be regarded as a fragment of this sort.’ I have attempted to transfer this hymn into English verse as follows :— “The mighty Lord on high our deeds, as if at hand, espies : The gods know all men do, though men would fain their sins disguise. Whoever stands, whoever moves, or steals from place to place, Or hides him in his secret den,—the gods his movements trace. Wherever two together plot, and deem they are alone, King Varuna is there, a third, and all their schemes are known. This earth is Varuna’s, and his those vast and boundless skies ; These oceans are his loins, and yet in that small pool he lies. Whoever far beyond the sky should think his way to wing, Yet could not there escape the hand of Varuna the king. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 559 The attributes and functions assigned to Varuna impart to his character a moral grandeur and sanctity far surpassing that ascribed to any other Indian deity. He is supposed to have unlimited control over the destinies of mankind. He is continually supplicated to drive away evil and sin. He is entreated not to steal away, but to prolong life; and to spare the suppliant who daily transgresses ‘his laws. With his bonds or nooses he seizes and afflicts transgressors. Mitra and Varuna conjointly are said to be armed with many nooses for entangling liars. And Indra and Varuna are described as binding men with bonds not formed of cords. On the other hand, Varuna is said to be gracious even to him who has committed sin. He is the wise guardian of immortality, and a hope is held out to the good that they shall behold him reigning together with Yama in - blessedness in the world to come. I shall add some specimens of a hymn (Rigveda vii. 86) already translated by " Professor Max Mixxer, in which Vasishtha, the rishi, or seer, who appears to be the author, expresses his sense of Varuna’s displeasure, and implores the restora- tion of his favour. I begin with the third verse :—‘‘ Seeking to know that sin, O Varuna, I inquire; I resort to the wise to ask. The sages all tell me the same; it is Varuna who is angry with thee. 4. What great sin is it, Varuna, for which thou seekest to slay thy worshipper and friend?* Tell me, O unassailable and self-existent god; and, freed from sin, I shall speedily come to thee with adoration. 5. Release us from the sins of our fathers, and from those which we have committed in our own persons. O king, release Vasishtha like a robber who has fed upon cattle; release him like a calf from its tether. 6. It was not our will, Varuna, but some seduction, which led us astray,—wine, anger, dice, or thoughtlessness. The stronger perverts the weaker. Even sleep occasions sin.” The following touching hymn (vii. 89) has also been already translated by His spies descending from on high glide all this world around, And thousand-eyed their gaze they cast to earth’s remotest bound. Whate’er beyond the heaven and earth, whate’er exists between, That too by Varuna the king is all distinctly seen. The ceaseless winkings all he counts of every mortal’s eyes: He wields this universal frame, as gamester holds his dice. Those knotted nooses which thou fling’st, O god, the bad to snare,— All liars let them overtake, but all the truthful spare.” With this hymn compare Psalm exxxix, 1-10, passim; with verse 2, compare St Matthew ‘Kyiii. 20; and with verse 5, St Matthew x. 30, . * Tn another place (vii. 88, 4, ff.) the same seer alludes to his previous friendship with Varuna, and to the favours formerly conferred on him by that deity, and inquires the reason of their cessa- tion, “ Varuna placed Vasishtha on his boat; by his power the wise and mighty god made him a rishi, to offer praise in an auspicious period of his life, that his days and dawns might be prolonged. 9. Where are those friendships of us two?* Let us seek the harmony which we enjoyed of old. I _ have gone, O self-existing Varuna, to thy vast and spacious house with a thousand gates. He who was thy friend, intimate, constant, and beloved, has, O Varuna, committed offences against thee. ) Let not us who are guilty reap the fruits of our sin, Do thou, O wise god, grant protection to him | who praises thee.” * Compare Psalms lxxxix. 49, and xxv. 6. VOL. XXIII. PART III. 7M 560 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. Professor Max MiLuer :—“ Let me not, O king Varuna, go to the house of earth. Be gracious, O mighty god, be gracious. 2. I go along, O thunderer, quivering like an inflated skin; be gracious, &c. 3. O bright and mighty god, I have trans- eressed through want of power, be gracious, &c. 4. Thirst has overwhelmed thy worshipper when standing even in the midst of the waters; be gracious, &e. 5. Whatever offence this be, O Varuna, that we mortals commit against the people of the sky (the gods); in whatever way we have broken thy laws by thought- lessness, be gracious, O mighty god, be gracious.” Indra. Professor Roru* is of opinion that Varuna belongs to an older dynasty of the gods than Indra, and that during the Vedic period the high consideration which originally attached to the former god, was in course of being transferred to his rival. However this may be, there is no doubt that Indra is, as Roru remarks,} the favourite deity of the Aryan Indians. More hymns of the Rigveda are dedi- cated to his honour than to the praise of any other divinity. Although, however, his greatness is celebrated in the most magnificent terms, he is not, as I have already noticed, regarded as an uncreated being, but is described in numerous” passages as having a father anda mother. Thus it is said of him (Rigveda iv. 17, 4) “ Thy father was the parent of a most heroic son: the maker of Indra, he who produced the celestial and invincible thunderer, was a most skilful workman.” And again (x. 134, 1): “A divine mother bore thee; a blessed mother bore thee.” In one place only is his mother’s name mentioned, and she is there called Nishtigri. This word is treated by the commentator as a synonyme of Aditi; but though Indra is regarded as an Aditya in the later mythology, and appears to be addressed as such, along with Varuna, in one passage of the Rigveda (vii. 85, 4), he is not, as far as I am aware, described as such in the other parts of that | collection. Indra is the regent of the atmosphere or intermediate rgion, the Jupiter Tonans and Jupiter Pluvius} of the Vedic Pantheon. He is the most martial of all the deities. Even as an infant he is said to have manifested his warlike dis- position. ‘As soon as he was born,” says one text (vill. 45, 4, 5) the slayer of © Vrittra seized his weapon and asked his mother, ‘Who are they that are re-_ nowned as fierce warriors?’” He leads the armies of the gods in their assaults” on the Asuras or Titans, destroys all the superhuman enemies of his worshippers, | and grants them victory over their mortal foes. .% A great variety of laudatory epithets are lavished upon Indra. He is styled * « Jour, Germ. Orient. Society,” vi. 73; “ Sanskrit and German Lexicon,” s.v. Indra. + ‘‘ Sanskrit Lexicon,” s.v. t See Srrazo, xv. 1, 69, p. 718; quoted by LassEN, Indische Alterthumsk. ii. 698; Aéye 0: nai radra wage ray ovyyeacéwv, Ori céPovras wev Tov ouPgiov Ala or Ivdol, xal rov Teyyny woranti cel rous Fy welous Sunniae MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 561 youthful as well as ancient, undecaying, strong, agile, heroic, martial, all-conquer- ing, lord of unbounded wisdom and irresistible power, wielder of the lightnings, &c., &e. He has vigour in his body, strength in his arms, a thunderbolt in his hand, and wisdom in his head. He assumes the most beautiful forms, and is invested with all the splendour of the sun. The Vedic poets have described a few of the features of his personal appearance. The epithet which is most constantly applied to him is Sws¢pra or Siprin,—in the interpretation of which the Indian commentator wavers “between god with the handsome cheeks or nose,” and “the god with the shining helmet or turban.” He is also called “the ruddy- _ cheeked,” the “ruddy-haired,” the “ruddy, or golden-hued.” He wears a ruddy, or golden beard, which is violently agitated when he puts himself in motion. He is also called the “iron god,” which the commentator explains to mean that he wears a coat of iron mail. But his forms are endless; he can assume any shape he pleases. Holding in his hand a golden whip, he is mounted on a golden car, which moves more swiftly than thought, drawn by two ruddy or tawny steeds, _ snorting, neighing, and irresistible, with flowing golden manes, hair like peacock’s feathers, and tails like peacocks. He is also said to be borne along by the horses of the sun; or, by a natural and obvious image, by the horses of the wind (Vata). He is armed with a thunderbolt, forged by Tvashtri, the Indian Vulcan, which is variously described as of gold and of iron, as four-angled, as ending in a hundred, ; and a thousand points. He is elsewhere said to carry a bow, and to discharge arrows with a hundred points, and winged with a thousand feathers. Invoked by his mortal worshippers, he speedily obeys their summons, and arrives in his chariot to receive their offerings. He finds food prepared for his horses, and large libations of the juice of the soma plant \Asclepias acida, or Sarcostemma “viminale) are poured out for himself to quaff. All the gods, we are told, hasten eagerly, when invited, to partake of this beverage, but Indra is particularly addicted to the indulgence, and seems to be dependent upon it for all his valour and energy. His mother gave him this juice to drink on the very day of his ph. Exhilarated by copious draughts of this elixir, and fortified by the encouragement both of gods and men (who are even said to place the thunderbolt ‘in his hand), Indra hurries off, escorted by troops of Maruts or Winds, and some- times attended by his faithful comrade Vishnu, or by Agni, or by Vayu, to encounter the hostile powers in the atmosphere, who malevolently shut up the liquid treasures of the clouds. These demons of drought, who are called by a great variety of names, such as Ahi, Vrittra, Sushna, Namuchi, &c., &c., and who, on their side, also, are armed with every variety of celestial artillery, vainly attempt to resist the onset of the god. Heaven and earth quake with affright _at the crash of Indra’s thunder, and even Tvashtri himself, the forger of that ‘thunder, trembles at the noise of his own handiwork, and at the fury of the impetuous deity by whom it is wielded. The -enemies of Indra are speedily 562 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. pierced and shattered by the very sound of his iron bolts. The waters, released from their imprisonment, descend in copious streams to the earth, fill all the rivers, and roll downward in torrents to the ocean. The gloom which had over- spread the sky is dispersed, and the sun is restored to his position in the heavens. Constant allusions to these conflicts between the opposing powers of the atmo- sphere occur in nearly every part of the Rigveda, and the descriptions are some- times embellished with a certain variety of imagery. The clouds are represented as mountains, or are variously characterised as the autumnal, moving, iron, or stone-built cities of the demons of the atmosphere, which Indra over- throws. He destroys his enemies when he discovers them on the aérial moun- tains, or hurls them back when they attempt to take the sky by escalade. One is a monster with ninety-nine arms: a second has three heads and six eyes; a third he pierces with ice, or crushes with his foot; the head of a fourth he strikes off with the foam of the waters. | The growth of much of the imagery just described is perfectly natural and easily intelligible, especially to persons who have lived in India and witnessed the phenomena of the seasons in that country. At the close of the long hot weather, when every one is crying aloud for rain to moisten the . earth and cool the atmosphere, it is often extremely tantalizing to see the : clouds collecting and floating across the sky, day after day, without discharg-— ing their contents. And in the early ages, when the Vedic hymns were | composed, it was quite in consonance with the other ideas which their authors — entertained, to imagine that some malignant influence was at work in the atmo- . sphere to prevent the fall of the fertilizing showers of which the parched fields — stood so much in need. It was but a step further to personify both the hostile — power and the beneficent agency by which it was at length overcome. Indra is q thus at once a terrible warrior and a gracious friend, whose shafts deal destruc- tion to his enemies, while they are the instruments of deliverance and prosperity to his worshippers. The phenomena of thunder and lightning almost inevitably suggest the idea of a conflict between opposing forces: even we ourselves, in our more prosaic age, often speak of the war, or strife, of the elements. The other appearances of the sky, too, afforded abundant materials for poetical imagery. The worshipper would at one time transform the clouds into the chariots* and horses of his god, and, at another time, would seem to perceive in their piled-up masses the cities and castles which he was advancing to overthrow. The power and glory of Indra are characterised by the grandest epithets. Thus, it is said of him in different texts: “ His greatness transcends the sky, the earth, and the atmosphere. He who fixed the quivering earth, who gave stability to the agitated mountains, who meted out the vast atmosphere, who propped up * Compare Psalm civ. 3. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 563 the sky, he, O men, is Indra. Not all the gods are able to frustrate the counsels of Indra, who established the earth and this sky, and, wonder-working, produced the sun and the dawn. Through fear of thee, Indra, all the mundane regions, however steady, begin to totter; heaven and earth, mountains, forests, all that is fixed, is afraid at thy coming. Indra is not to be overcome, Sakra (another name of Indra) is not to be overpowered; he hears and sees all things. At the birth of thee, the glorious one, the heavens trembled, and the earth, through fear of thy wrath. Heaven and earth are not sufficient for his girdle. All the gods yield to him in power and force. The two worlds are equal to but the half of him. Which of the poets who were before us have found out the end of all thy greatness? seeing that thou didst produce at once the father and the mother _(i.¢., heaven and earth) from thine own body.” These passages afford a fair specimen of the strains in which Indra is most commonly celebrated in the hymns. It will be observed that the attributes which are assigned to this deity are chiefly those of physical superiority and dominion over the external world. In fact, he is not generally represented as possessing the spiritual elevation and moral grandeur which are so strikingly characteristic of Varuna. There are, however, many texts in which his close relations with his worshippers are described, and a few in which an ethical char- acter is attributed to him. Faith in him is confessed or enjoined in various passages; the reality of his existence and power is asserted in opposition to sceptical or faithless doubts. He is the friend, and even the brother, of his pre- sent worshippers, as he was the friend of their forefathers; but he desires no friendship with the man who offers no oblations. He is reminded that he him- self has friends, while his adorers are friendless. His friend is never slain or conquered. It is he almost exclusively who is invoked as the patron of the Arian Indians, or civilized invaders of Hindostan, and their protector against their barbarous aboriginal foes, or their unseen and supernatural enemies. He is invoked by men as a father; he is embraced by the hymns of his votaries as a husband is embraced by his wives; his right hand is seized by suppliants for riches; his powerful arms are resorted to for protection, and he is a deliverer easy to be entreated. He isimplored not to slay for one, two, three, or even for many sins. Destruction falls upon the man who offers him no libations, while he richly rewards his faithful servants. Yet he is sometimes naively importuned to be more prompt in his generosity, and is even given to understand that his worshipper, if in his place, and possessed of his means, would be more liberal. He is supplicated for all sorts of temporal blessings, and, among the rest, for victory in battle. As a man, in walking, puts first one foot forward and then ’ the other, so Indra, by his power, changes men’s relative positions ; he subdues the fierce, and puts others in the foremost ranks; he is the enemy of the WOle XXII. PART Iit. 7N 564 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. prosperous and ungodly man, while he protects his own servants, and leads them into a “large room,”’* into celestial light and security. Vayu and the Maruts. Vayu, or the Wind, who, as we have seen, is often akeouaied with Indra, does not occupy a very prominent position in the Rigveda. But few epithets are applied to him. He is called beautiful or conspicuous, and handsome in form. He is thousand-eyed, and swift as thought. Like other deities who have been already passed under review, he rides in a shining ‘golden chariot, drawn by ruddy or purple steeds, and his team is sometimes said to consist of as many as a hundred, or even a thousand horses. Indra frequently rides by his side. In one of the latest hymns (x. 168), the phenomena of the wind are picturesquely described. His chariot rolls along, resounding, and rending all it encounters. He drives before him, as he advances, the dust of the earth. He never ceases to — move along the paths of the atmosphere. The poet then asks, in phrases some of which are almost those of St John (iii. 8), “ In what place was he born ? whence has he sprung? Soul of the deities, source of the universe, this god wanders — where he lists; his sound is heard, but his form is not (seen).” 1 The Maruts or Rudras, deities of the storm, receive in the Rigveda a much — more frequent and enthusiastic celebration than Vayu. They are the sons of Rudra (who will be noticed below) and Prisni. Numerous hymns are dedicated to their 7 honour, in which they are described by a great variety of picturesque epithets. _ They are compared to blazing fires; they are free from soil, and of sun-like e brilliancy. In one place they are thus apostrophised :—“ Spears rest upon your Z shoulders, ye Maruts ; ye have anklets on your feet, golden ornaments on your breasts, fiery lightnings in your hands, and golden helmets on your heads.” They — shatter the demon of drought into fragments; they are clothed with rain; they distribute showers over all the world, and alleviate the burning heat; they shake the mountains, the earth, and both the worlds; they overturn trees, and like wild elephants, they consume the forests; they have iron teeth; they roar like lions, and all creatures are afraid of them ; they are swift as thought; they ride, with whips in their hands, in golden cars, with golden wheels, drawn by ruddy, tawny, or speckled horses, with which their chariots are said to be winged. The Maruts, as we have seen, are frequently described as the attendants of Indra; but they are the subjects of celebration in many separate hymns in which that deity is never mentioned. Rudra. Rudra, who, under the name of Siva, or Mahadeva, and as the third person * This is a phrase of frequent occurrence in the Rigveda. Compare the very similar expres- sions in Psalms xvi. 19, xxxi. 8, and exviii. 5. f a: a MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 565 of the Indian triad, the Destroyer, is one of the three great gods in the later Indian mythology, is a deity of but subordinate importance in the hymns of the Rigveda. Like most of the other gods, however, he is designated in those hymns by a variety of magnificent epithets. He is self-dependent, the strongest and most glorious of beings, the father of the world, cognisant of all the doings of gods and men. He is described as seated in a chariot; as being himself brilliant as the sun; as arrayed in golden ornaments, and wearing braided hair; as wielding a thunderbolt ; as armed with a bow and arrows, a strong bow and fleet arrows. His shafts are discharged from the sky, and traverse theearth. He is called the slayer of men. His anger and his destructive bolts are frequently deprecated ; but he is also represented as benevolent, gracious, easily entreated, as the source of health and prosperity to man and beast. He is often described as the pos- sessor of healing remedies, and is characterised as the greatest of physicians. Rudra is also designated in various texts as the father of the Rudras or Maruts, the class of deities last described, who rule the winds; and from this relation we might expect that he would be represented as still more eminently than they, the generator of tempests and chaser of clouds. Except, however, in a small number of texts, there are few distinct traces of any such agency being assigned to him. The numerous vague epithets which he constantly receives would not suffice to fix the particular sphere of his operation, or even to define his personality, as most of them are applied to other deities. While, however, the cosmical function of Rudra is thus but obscurely indicated, he is, as we have seen, described as possessing other marked and peculiar characteristics. There can be little doubt, though he is frequently supplicated to bestow prosperity, and addressed as the possessor of healing remedies, that he is principally regarded as a malevolent deity, whose destructive shafts—the source of disease and death—the worshipper strives by his entreaties to avert. If this view be correct, the remedies which Rudra dispenses, may signify little more than the cessation of his destroying agency.* Vishnu. Vishnu, who, at a later period, was considered as one of the class of gods mentioned above, the Adityas, and who, as the second deity in the great Indian triad, has cast al] the other gods except Rudra, or Siva, into the shade, was not, as compared with Indra or Varuna, or perhaps even with Savitri, a very promi- nent object of adoration in the Vedic age. There are, however, a few hymns in which he is celebrated, sometimes singly, but mostly in conjunction with Indra, | and also a good many detached verses in which he is mentioned. The charac- | teristic function by which he is repeatedly distinguished from every other god,} * See Sanskrit Texts, vol. iv. p. 339, f. { Only Indra is associated with him in two passages (vi. 69. 5; and vii, 99. 6) as taking vast | strides, 566 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. is that of striding across the heavens in three paces. These three steps are explained by one of the ancient interpreters as denoting the triple mani- festation of light—as fire on earth, as lightning in the atmosphere, and as the sun in the sky; and by another, as designating the three stages of the sun’s daily movement—his rising, culmination, and setting. From this difference of view prevailing between two of the oldest expounders of the Veda, it appears that these three steps of Vishnu must, from a very ancient period, have been regarded as something enigmatical. Some of the highest divine functions and attributes are also assigned to Vishnu in the hymns. Thus he is said to support alone the sky and the earth, and to comprehend all the worlds with his three vast strides. No one, even the soaring birds, can attempt to follow his third and loftiest step. He alone is acquainted with the highest sphere. No one born, or yet to be born, can in thought attain to the furthest limit of his greatness. The pious enjoy celestial bliss in his abode. Varuna and the Asvins do homage to his power. But we are not, therefore, to imagine that he was regarded as superior to the other deities; for Indra is associated with Vishnu even in some of the hymns in which the latter is most magnified. Nay, in one place, the power through which Vishnu takes his three strides is said to be derived from Indra; in two other texts Vishnu is represented as celebrating Indra’s praises ; and, as described in various other passages, the former appears to play a secondary part as compared with the latter. Besides, the same high functions and awful attributes whieh are ascribed to Vishnu, are in other and far more numerous texts assigned to Indra, Varuna, — and other deities.* Sirya and Savitri. The great powers presiding over day and night are, as we have seen, sup- posed by the Indian commentators to be personified in Mitra and Varuna. But these two deities, and especially Varuna, are far more than the mere representa- tives of day and night. They are recognised as moral governors, as well as superintendents of physical phenomena. There are two other deities who are far more direct representatives of the solar orb—viz., Surya and Savitri, who are in a few passages described as belonging to the same class of gods as Mitra and Varuna—viz., the Adityas. It is under these two different names that the sun is chiefly celebrated in the Veda, according, perhaps, to the different aspects in which he is viewed, or the functions which he is conceived as fulfilling. Different sets of hymns are devoted to his worship under each of these appella- tions; and the epithets which are applied to him under each of these characters are for the most part different. Surya is described as moving through the heavens on a car, which is some- * See my Sanskrit Texts, vol. iv. Preface iv. ff., and pp. 54-101. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 567 times said to be drawn by one, sometimes by several, sometimes by seven, horses. His path is prepared by the Adityas, Mitra, Aryaman, and Varuna. The god Pishan goes as his messenger, with his golden ships, which sail in the aerial ocean. Surya is the preserver, the soul, of all things, moving or stationary; the vivifier of men; the upholder of the sky. He rolls up darkness likea hide. He is far-seeing, and by an image common, I suppose, to most literatures (and which we find in Homer and Aischylus),* he is said to be all-seeing, beholding all worlds, and the good and bad deeds of men. He is the eyet of Mitra and Varuna. In many passages, however, his dependent position is asserted. Thus, he is said to have been produced, or placed in the sky, or caused to shine, by Indra, or by some other deity. Ushas, the Dawn, is in one place said to be his wife. In another passage the Dawns are, by a natural figure, said to produce him. The name Savitri is derived from a Sanskrit root su, to propel, stimulate, or inspire; and may therefore be taken to denote the sun in his character of stimulator orinspirer. This signification of the name is frequently referred to in the Veda, and is coupled with the constant use, in various other forms, of the verb from which. it is derived, to denote the functions attributed to this god. As described in the Rigveda, Savitri is pre-eminently the brilliant and golden deity. He is go!den- eyed, golden-handed, golden-tongued; he is surrounded by a golden lustre; he mounts a golden car, drawn by radiant horses; he stretches out his golden arms, which infuse energy into all creatures, and reach to the utmost ends of the sky. He is also called broad-handed, beautiful-handed, beautiful-tongued. He beholds all things ; he illuminates the atmosphere and all the regions of the earth. His | ancient paths in the sky are said to be free from dust. He is called a divine | spirit (aswra). His will and independent dominion cannot be resisted, even by | Indra, Varuna, Mitra, Aryaman, Rudra, or any other being. The waters fall and the winds blow by his ordinance. His praises are celebrated by the Vasus, by | Aditi, by the royal Varuna, by Mitra, and by Aryaman. He is the lord of crea- | tures, the supporter of the world and of the sky. In one place he is even said, whether literally or figuratively, to bestow on the gods the gift of immortality. It would appear to result from all this, that Savitri was at one time the object of avery enthusiastic adoration in India; and in fact the holiest text in the Veda (iii. 62. 10), that which is called par excellence the gdyatri, is addressed to him. This verse is thus rendered by Mr Colebrooke (Misc. Ess. i. 30)—“ Let us meditate on the adorable light of that divine ruler (Savit77): may it guide our intellects.” | Professor H. H. Wilson translates it thus: ‘‘ We meditate on that desirable light of the divine Savitri, who influences our pious rites.” Professor Benfey, in his | * liad, iii. 277, xiv. 344 f.; Odyssey, viii. 270; and Asch. Prom. 91. Compare Ovid. Met., Same i71 f.; 195 fF. t Compare Hesiod, Opp. et dies: rdévra idav Aids dpbarwds nai mévran vonous. xT A VOL. XXIII. PART III. O Low A ( 568 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. “Sama Veda’ (ii. 812), gives yet a different rendering: ‘“‘ We receive this glorious brightness of the generator, of the god who will prosper our works.” In the hymns Savitri is sometimes expressly distinguished from Sirya. To explain this circumstance, the Indian commentator asserts, that before his rising, the sun is called Savitri, and at his rising and setting Sarya ; and in another place — he says, that though the godhead of the two deities is identical, they may yet, from the diversity of their forms, be spoken of as separate agents. Yaska,amuch _ older writer, says, that ‘‘ the time of Savitri’s appearance is when darkness has ; been removed, and the rays of light have become diffused over the sky.” But — it is scarcely consistent with this explanation, that in one text Savitri is said to — exercise his influence after the rising of the sun. In other passages of the Rigveda, the two names appear to denote the same deity. E Tvashtri. Another god who, in the later mythology, is regarded as one of the Adityas, — but who does not yet bear that character in the Rigveda, is Tvashtri, the Vulcan _ of the Indian pantheon. He is represented as the most skilful of all artizans, and | as versed in all admirable contrivances. He sharpens the iron axe of Brahmanas- pati, and forges the thunderbolts of Indra. It is his peculiar function to fabricate forms: he gives shape to heaven and earth; he bestows generative power, moulds all structures, human and animal, out of the seminal germ; forms husband and wife for each other in the womb. He gave his daughter Saranyu in marriage to ~ Vivasvat, the sun, and is thus the grandfather of Yama; and he is also described as the father-in-law of Vayu, the god of the wind. Agni. Agni is the god of fire, the Ignis of the Latins. The word, as all scholars ; know, has been lost in Greek. He is one of the most prominent deities of the | Rigveda, since nearly as many entire hymns are addressed to him as to Indra, _ and more than are assigned to any other divinity. Agni is not, like the Greek — Hepheestus, or the Latin Vulcan, the artificer of the gods (an office which, as we — have just seen, is in the Veda allotted to Tvashtri), but derives his importance almost exclusively from his connection with the ceremonial of sacrifice. He — is an immortal, who has taken up his abode among mortals, as their guest, their friend, and their domestic priest. He is a sage, intimately acquainted with all rate human functionaries. He is a messenger moving between heaven and earth, and commissioned both by gods and men to maintain their mutual communica-— tions, to announce to the immortals the hymns, and to convey to them the offer- MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 569 ings, of their worshippers. On the part of men, he invokes the gods, invites them to attend the ceremonies instituted in their honour, arrives with them seated in the same chariot, and receives them with reverence and adoration. In other places, he is somewhat differently described as the mouth, and the tongue, through which both gods and men participate in the sacrifices. He is the banner, symbol, or outward manifestation, the father, guardian, protector, lord, and king, of sacrifice; the lord of the house; the lord and king of the people; and the father, mother, brother, and son, of his worshippers, some of whom claim with him a hereditary friendship. In the descriptions of the Rigveda, the element of fire is frequently, and almost inevitably, confounded with the deity who is supposed to be its representa- tive,—many of the epithets applied to the latter being quite as appropriate, if not more appropriate, to the former. Thus, although Agni is often said to have been generated by the gods, or to be the offspring of heaven and earth, or to have been brought from heaven by Matarisvan; he is also constantly alluded to as having been first kindled by Manu, or some other ancient sage, and his birth is _ described as resulting from the homely process of rubbing together two pieces of % stick ; which are spoken of as his parents,—parents, whom their infant offspring _ afterward unnaturally devours. This infant is, however, like the wriggling brood of a serpent, very difficult to catch ; but when seized, he is nourished with oblations of clarified butter. This nourishment is alluded to in the epithets “butter-haired,”’ | and “butter-formed.” The following are some of his other appellations; ‘‘smoke- | _ bannered,” “‘ black-pathed” (this alludes, of course, to the way in which fire 1% chars the wood which it consumes); “ brilliant-coloured,” “ brilliant-flamed,” | “flaming-haired,” “ golden-haired,” “ golden-bearded,” “‘ golden-formed,” “ sharp- | weaponed,” “ sharp-toothed,” “ golden-toothed,” ‘ four-eyed,’ ‘ thousand- | ‘ eyed,” and ‘‘ thousand-horned.”’ His flames roar like the winds, like the waves of the sea, like a lion, like a bull; he envelopes the woods, and blackens them | with his tongue; he shears the hair of the earth; he shaves the ground, as a | barber a beard. He rides on a chariot of light, or of lightning, or of a brilliant | or golden colour, drawn by fleet horses, of a ruddy or tawny hue. In some passages, Agni appears to be identified with light in general, as where it is said (Rigveda, x. 88, 6, 10, ff.) “ Agniis by night the head of the earth; | from him is produced the sun which rises in the morning... . With a hymn ‘the gods, through their power, produced in the heaven Agni, who fills the world. ‘They made him to exist in a threefold character... . . When the adorable gods | placed him in the sky as the solar orb, the son of Aditi, then they beheld all the worlds.” The ‘threefold character” here alluded to, means, according to an old commentator, the three forms of fire upon earth, lightning in the atmosphere, and the sun in the heavens.* — y * See Nirukta, vii. 28, and xii. 19; and my Sanskrit Texts, vol. iv. p. 55 f. D70 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. Although Agni is not in general celebrated in the same lofty strains as Indra and Varuna, there are yet a few passages in which the attributes of creator and preserver of the universe are assigned to him by the Vedic poets. Thus, he is said to have produced the two worlds; to have meted out the regions of the air, and the heavenly luminaries; to have spread out heaven and earth, like two skins ; to have propped up the sky; and to exceed the universe in greatness. All the deities fear and reverence him. He delivers them from evil. His ordinances are not violated. He knows the races of the gods, the recesses of heaven, and the secrets of men. He beholds all worlds. He is celebrated and worshipped by Mitra, Varuna, the Maruts, and the 3339 divinities. Through him Varuna, Mitra, and Aryaman triumph. He is sometimes identified with other gods, such as Indra, Vishnu, Varuna, Mitra, Aryaman, Tvashtri, Rudra, and is said to compre- hend them all within himself, as the circumference of a wheel surrounds the spokes. He is also at times associated with some of the other deities, especially with Indra, in several of whose functions, such as that of thunderer, slayer of Vrittra, and destroyer of cities, he is said to participate, and of whom he is in one place said to be the twin brother. The votaries of Agni prosper. He is the friend of the man who entertains him ~ as a guest, and he bestows protection and wealth on the worshipper who sweats to bring him fuel, and wearies his head to serve him. He has it in his power to bestow many kinds of blessings, and to avert many species of misfortunes, and — is therefore supplicated to grant his favour and protection, and to be an iron wall ; with a hundred ramparts to shield his votaries. He is master of all the treasures in the earth, the atmosphere, and the sky. All blessings proceed from — him. as branches from a tree. . In one passage, the worshipper naively says to Agni,—“If I were thou, and thou wert I, thy aspirations should be fulfilled on the spot; and again,— ~ “ft, Agni thou wert a mortal, and I an immortal, J would not abandon thee to wrong, or to penury. My worshipper should not be poor, nor distressed, nor miserable.” The blessings which this god is solicited to bestow are almost entirely of a | physical character; but in one or two places, he is asked to forgive sin. He & ee by of the righteous. The Asvins. The Asvins seem to have been a puzzle even to the oldest Indian commen a tators, one of whom, YAsxKa, refers to them in the following terms (Nirukta, - xii. 1): —“ Now come the deities whose sphere is the heaven. Of these the two Asvins are the first in order. They are called Asvins (from a root as), because MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 571 they pervade everything—the one of them with moisture, the other with light. AURNABHAVA says they are denominated Asvins, because they have horses (asvath). But who are these Asvins? ‘Heaven and Earth,’ say some. ‘ Day and Night,’ say others. ‘Two kings, performers of holy acts,’ say the legendary writers. Their time is subsequent to midnight, whilst the break of day is de- layed.” It may seem singular that two gods of a character so little defined as that of the Asvins should have been the objects of so enthusiastic a worship as appears, from numerous hymns in the Rigveda, to have been paid to them in ancient times. But the reason may have been, that they were regarded and hailed as precursors* of the return of day, after the darkness and dangers of the night. According to one of the hymns in the tenth book of the Rigveda (xvii. 1, 2), they appear to have been regarded as the twin sons of Vivasvat and Saranyu. They are also called the grandsons of the Sky, and the offspring of the Sea—whether this means the terrestrial or the atmospheric ocean. ‘The time of their appearance is the early dawn, when they yoke their horses to their car, and descend from heaven to receive the adorations and offerings of their votaries. In one place their sister is mentioned ; and the Indian commentator considers that Ushas or Aurora is meant.+ Their chariot is of a singular formation, being three-wheeled, trian- : gular, and triple in some other parts of its construction, which are not very easy toexplain. They are also fancifully requested to bestow a number of different sorts of blessings thrice. Their chariot is further described (like those of other gods) __ as golden, as swifter than thought, or than the twinkling of an eye, as thousand- _ formed, and decorated with a thousand banners. They are sometimes said to be | drawn by a single ass,+ but more frequently by fleet and winged horses. The Asvins themselves are represented as young, beautiful, radiant, of golden | form, wearing many shapes, and decked with lotus garlands, agile, fleet as thought, | skilful, profound in wisdom, strong, awful, overthrowers of pride, armed with terrible and golden spears. They are also described as physicians, and restore the blind, sick, and emaciated to sight, health, and strength. In several hymns the numerous succours of various kinds which they had in former times granted * Roru says of them (Journal Germ. Orient. Society, iv. 225), “The two Asvins, though, like the ancient interpreters of the Veda, we are by no means at one about the conception of their character, hold yet, according to their signification, a perfectly distinct position in the entire body of the Vedic deities of light. They are the first bringers of light in the morning sky, who in their chariot rapidly precede the Dawn, and prepare the way for her.’”” Compare Professor Max Miituer’s “Lectures on _ the Science of Language,” 2d Series (which have just been published as this paper is passing _ through the press), pp. 489, ff. + The passage alluded to is Rigveda, i. 180, 2. In another text, i. 123, 5, Ushas is said to be the sister of Bhaga and Varuna. t See Have’s “ Aitareya Brahmana,” vol. il. p. 273. ‘‘ The Asvins were winners of the race "|: with a carriage drawn by donkeys; they obtained (the prize). Thence (on account of the excessive efforts to arrive at the goal) the donkey lost its (original) velocity, became devoid of milk, and the slowest among all animals used for drawing carriages,” &c. The race alluded to is one which the | gods ran to settle a point in dispute between them. See p. 270 of the work just quoted. VOL. XXIII. PART III. CP 572 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA, to their worshippers are enumerated, and among them a few cures are specified. They are frequently supplicated for various kinds of blessings; they are implored to prolong life, and even to forgive sin; and their hereditary friendship with the worshipper is sometimes appealed to. Soma. I have already alluded to the important share which the exhilarating juice of the soma plant (Asclepias acida or Sarcostemma viminale) assumes in bracing — Indra for his conflict with the hostile powers in the atmosphere. This juice, or rather the plant from which it is extracted, is personified in a god Soma, who is, or rather at one time was, the Indian Bacchus. The whole of the hymns in the ninth book of the Rigveda, 114 in number, besides a few in the other books, are dedicated to his honour. It is clear, therefore, as Professor Whitney remarks,* that his worship must have been at one time remarkably popular. The soma sacrifice, in fact, formed an important part of the old Brahmanical ritual, as well as that of the ancient Persian worship.t But with the decline of the Vedic rites, and the transformation of the old, or the introduction of new, deities, the early popularity of Soma has long since passed away, and his name is familiar to those learned Brahmans only who, in a few places, maintain the old tradition of the Vedic observances. The hymns addressed to Soma were intended to be sung while the juice of the plant from which he takes his name was being pressed out and purified.t{ They describe enthusiastically the flow- ing forth and filtration of the divine liquid, and the effects produced on the worshippers,§ and supposed to be produced on the gods, by partaking of the eer ys hen Ps * Journal of the American Oriental Society, i. 299. . + See Dr Have’s Aitareya Brahmana, i. 59, ff. ; and Wrnpiscumann’s ‘‘ Somacultus der Arier ;” % as well as my “Sanskrit Texts,” vol. 11. pp. 469, ff., where the most important parts of this dissertation . are translated or abstracted. See also the extract there given from ‘‘ Plutarch de Isid. et Osir.” 46, — where the soma plant, which in Zend is called haoma, is mentioned under the name of tways. - { Wurryey, Journal of the American Oriental Society, as above: “Sanskrit Texts,” vol. ii. p. 470. § These effects are thus described in a verse (Rigveda, viii. 48, 3) which may be freely trans- lated as follows :— ys Ue « We've quaffed the Soma bright, and are immortal grown: We’ve entered into light, and all the gods have known, «© What mortal now can harm, or foeman vex us more ? Through thee beyond alarm, immortal god, we soar.” Compare Euripides, ‘‘ Cyclops,” 578, ff.,— 6.0 dugavds wor Gumpmemirywevos ones 7 vn pegeodus. ro Aréc geo) Ego Asboow rd riiv re Ocesovey cryvov o&Pas. I subjoin a free translation of the 119th Hymn of the Tenth Book, in which Indra himself is sup- posed to express his sensations when in a state of exhilaration :— J ‘* 1, Yes, yes, I will be generous now; and grant the bard a horse and cow, ‘ I’ve quaffed the soma draught. 7 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 5738 beverage. ‘The juice itself is called an immortal draught, and a medicine for the sick. The god, too, is said to cover whatever is naked, to heal whatever is diseased; through him the blind sees, and the lame walks. The most magnificent attributes and functions are assigned to him. He is the friend, the ally, and the soul of Indra, whose vigour he stimulates, and whom he renders triumphant in his conflicts with Vrittra. He rides in Indra’s chariot; he is armed with sharp and terrible weapons; and he is, like Indra, the destroyer of hostile demons, and the overthrower of their cities. And not only so, but he is also declared to be the father of the gods, the creator of the sky and the earth, of Agni, of Strya, of Indra, and of Vishnu. All creatures are in his hand; he is the king of gods and men, the upholder of the heavens, and the sustainer of the earth; he destroys darkness, and causes the sun to rise. He is thousand-eyed, beholds all worlds, and strikes down the impious into the abyss. He is the possessor of all resources. He bestows immortality on gods and men; and it is worthy of remark that in a passage (ix. 113, 7 ff.) where the joys of paradise are more distinctly anticipated and described than in most other parts of the Rigveda, the deity from whom this _ future felicity isasked is Soma. Two of the verses of this hymn are as follows :-— * Place me, O purified god, in that everlasting and imperishable world, where there is eternal light and glory. O Indu (Soma), flow for Indra. Make me im- mortal in that world where King Vaivasvata (Yama) lives, where is the innermost sphere of the heaven, where those great waters flow. O Indu, flow for Indra,” Sc. «© 2. These draughts impel me with the force of tempests in their furious course. I’ve quaffed the soma draught. «3, They drive me like a car that speeds when whirled along by flying steeds. I’ve quaffed, &e. «4, Not fonder to her calf the cow than that fond hymn which seeks me now. I’ve quaffed, &c. “6, I turn it over while I muse, as carpenter the log he hews. I’ve quaffed, &c. “6. The tribes of men, the nations all, I count as something very small. T’ve quaffed, &c. “7, The sky and earth, though vast they be, don’t equal even the half of me. I’ve quaffed, &c. “8, The heavens in greatness I surpass, and this broad earth, though huge her mass. I’ve quafted, &c. 6e 9 Come, let me as a plaything seize, and put her wheresoe’er I please. I’ve quaffed, &c. “10. Come, let me smite with vigorous blow, and send her flying to and fro, I’ve quaffed, &c. “11, My half is in the heavenly sphere; I’ve dragged the other half down here. I’ve quafted, &c. “12. How great my glory and my power! Aloft into the skies I tower. I’ve quaffed, &e. CaS, Yr m ready now to mount in air, oblations for the gods to bear. I’ve quaffed the soma draught.” 4 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. Or is | Yama. Yama, the son of Vivasvat and Saranyu, is the ruler of the world to come. In the later mythology he becomes distinctly the Indian Pluto, the judge of the dead, who in a future state recompenses the good and bad according to their deserts ; but he is there depicted principally as an object of terror. The awful side of his character is not altogether unrecognised even in the Rigveda, where he is said to have two insatiable dogs with four eyes and wide nostrils, which guard the road to his abode, and wander about among men. They are evidently regarded with dread, and the spirits of the departed are advised to hurry past them. The bonds or nooses of Yama are also mentioned in one place along with those of Varuna, and he is, in another passage, identified with death, and described as sending a bird as a forewarner of doom. Ina text of the Atharva-veda, death is said to be his messenger. But in the Vedic hymns he is most commonly represented as the sovereign and guardian of the blessed. In a text already quoted, the wor- shipper prays to be admitted to the abode of Yama, in the innermost sphere of heaven. In another place the souls of the departed are desired to proceed by the path which their fathers had trodden before, and which would introduce them to the vision of Yama and Varuna dwelling together in blessedness. Pro- fessor RotH has pointed out that Yama was sometimes regarded by the Indians © as the first man, the first who departed to the other world and became its ruler.* Thus, in one text of the Rigveda, he appears to be spoken of as the sole existing — mortal; and in another place he is described as having been the first to discover — the way to heaven. This is still more distinctly expressed in a verse of the Atharvaveda, which runs thus: “ Worship with an oblation that King Yama, the son of Vivasvat, the gatherer together of men, who was the first of mortals that z died, the first who departed to this [heavenly] world.” In another verse of the — Rigveda he is described as carousing with the gods under a leafy tree. . It is quite clear from all this that towards the end, at least, of the Vedic age, — the Indians had a distinct belief in a future state of rewards. The following are some of their other ideas regarding the future destinies of men. When the remains of the deceased have been placed upon the funeral pile, and the process — of cremation has commenced, Agni, the god of fire, is besought not to scorch or consume the departed, not to rend asunder his skin or his limbs, but after the flames have done their proper work, to convey to the fathers the mortal who has been presented to him as an offering. The eye of the dead is bidden to go to the sun, bis breath to the wind, and his other members to the sky, the earth, the waters, or the plants, according to their several affinities. As for his ‘unborn part,” Agni is supplicated to kindle it with his heat, and putting on his most uv " * Manu, Yama’s twin brother, is, however, far more frequently mentioned in the Rigveda as the first man or the progenitor of the Indians. See my paper on Manu, in the 20th vol. of the Journal of the Royal Asiatic Society, pp. 406, ff. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. 575 _ auspicious form, to convey it to the world of the righteous. Leaving behind it here below all that is evil and imperfect, and traversing the vast abyss of dark- ness which separates this world and the third heaven, the spirit soars in a car, or - on wings, on the undecaying pinions of Agni, wafted by the Maruts, and fanned j by delightful zephyrs, to the realms of eternal light, recovers there its ancient _ body, now invested with celestial radiance, meets with the forefathers who are dwelling in festivity with Yama, is recognised by that god as one of his own, ob- tains from him a delectable abode, and enters on a new existence and more perfect - life, which is passed in the presence of the gods, and employed in the fulfilment of their pleasure. In a passage of the Atharvaveda, an expectation that the family ‘relations will be maintained in the next world is expressed in these words: “Conduct us to heaven; let us be with our wives* and children.” In the verses ~ which follow those I have already quoted from a hymn addressed to Soma, the happiness of heaven is said to consist in the fulfilment of all desires, and the unrestrained enjoyment of a variety of gratifications, the nature of which is not explained, but which yield complete satisfaction. These pleasures are probably to be understood as being of a sensual character, as in a passage of the Atharva- veda (iv. 32; 2, 4) a promise is held out to those who offer up a particular oblation that their sexual appetites shall be abundantly gratified in paradise, and that they shall there be able to revel in milk, curds, butter, honey, and wine. _ Virtuous men of different classes,—the faithful worshippers of the gods, the per- formers of austerities, the brave who have fallen in battle,} the bestowers of liberal gifts,—are all said to be dwellers in that higher sphere. These glorified Saints, who ride in the same chariots with the gods, are supposed to be capable | exercising an influence over the destinies of their descendants, to have the | power of hearing their prayers, and of granting them protection and riches. ~ | ee | the Atharvaveda speaks in one place of the nethermost darkness, and in another text of hell. _ Inregard to Yama, see Professor Roru’s paper in the “Journal of the German Oriental Society,” iv. 426 ff., which refers to all the principal texts on the subject; and the same author’s article, in the third volume of the “ Journal of the American | Oriental Society,”’ on the “ Morality of the Veda,” pp. 334 ff. See also Professor | _ * The later Indian writings hold out to the widow who burns herself on her husband’s funeral _} pile, the hope of rejoining him in heaven. See Coxesrooxn’s “ Misc. Essays,” i. 116, f. { In the Mahabharata (xii. 3657) it is declared that “ thousands of beautiful nymphs | (Apsarases) hasten to meet the hero who has been slain in battle, exclaiming, ‘Be my husband.’” Again, at v. 3667, it is said: “ Behold, these shining worlds, filled with daughters of the Gand- | harvas, and yielding all manner of delights, belong to the brave.” VOL. XXIII. PART III. LQ 576 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. Max Muturr’s article, on “The Funeral Ceremonies of the Brahmans,” in the volume of the first-named journal for 1855, pp. xiv. ff, where many of the texts 3 which I have referred to are translated into German. I may now add the same author’s new volume of “ Lectures on the Science of Language,” 2d Series, pp. 513, ff, where he combats some of Roru’s conclusions. Goddesses of the Rigveda. Of the female divinities occurring in the Rigveda, some have been already noticed—viz., Prithivi, the Earth, the wife of Dyaus; Aditi, the mother of the Adityas, with Diti her counterpart ; Nishtigri, the mother of Indra; Pris‘ni, the mother of the Maruts; and Saranyu, the mother of Yama and the Asvins. Of the other goddesses, the most important is Ushas, the ’Has, ’A%s, or ’Avds of the Greeks, and the Aurora of the Latins,* to whom twenty separate hymns, and numerous detached verses, are dedicated. Of one of these hymns, some of which are very beautiful and imaginative, a specimen was given in the paper which read before the Society last year. | Sarasvati also is a goddess of some, though not of any very great, importance in the Rigveda. She is primarily, ifnot throughout, a river deity,} as her name, “ the watery,” clearly denotes; and in this capacity she is celebrated in a few separate hymns, as well as in a number of detached passages. In one of these texts, as well as in later works, allusion is made to sacrifices being performed on the banks of this river, and of the Drishadvati; and the Sarasvati, in particular, seems have participated in the reputation of sanctity which, according to a passage in the Institutes of Manu (iii. 17 ff.), attached to the whole region lying between these two.small streams, and situated to the westward of the Jumna. The Sarasvati thus appears to have been (though in a less degree) to the early Indians what the Ganges (which is only twice named in the Rigveda, and was not then regarded with any special veneration) became at a later period to their descendants. When once the river had acquired a divine character, it was perhaps not unnatural tha in, she should be regarded as the patroness of the ceremonies which. were celebrated — on the margin of her holy waters, and that her direction and blessing should e invoked as essential to their due performance and success. The connection int a which she was thus brought with sacred rites may have led to the further step y of supposing her to exercise an influence on the composition of the hymns which — formed an important part of the proceedings, and of identifying her with Vach He (the Latin Vox), the goddess of speech. Sarasvati is frequently invited to the sacrifices, along with several other god- — desses, 11a, Bharati, Mahi, Hotra, Varutri, and Dhishana, who were not, like her, a * See Benrey’s “ Griechisches Wurzellexicon, i. 27, and i. 334, + In the Brahmavaivartta Purana she is said to have been changed into a river by an impreca tion of the Ganga, See Professor Aurrucut’s “ Catalogue of the Bodlean Sanskrit MSS.” p. 23. MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. BY mE river nymphs, but (most of them, at least) personifications of some department of religious worship, or sacred science. In many, or in most, of the passages where Sarasvati is praised, her original character is distinctly preserved,—as, where she is mentioned along with other streams, or characterised as the divinest of rivers, or as one of the seven rivers, or as the mother of rivers, or as flowing pure from the mountains to the sea, or as wearing away the hills on her banks with her impetuous and resounding current. But she is also described as a purifier, as unctuous with _ butter, as stimulating, directing, and favouring the prayers of the worshippers, as riding on the same chariot with the oblations and with the sainted forefathers, as _ bringing prosperity and riches, as the source of life, as affording perfect protec- tion, as sheltering her votaries like a tree, as conquering enemies, or delivering - from them, as the wife of a heroic husband, as carrying a golden spear, as a slayer of foes or of Vrittra, and as filling the terrestrial and intermediate regions. __ In the later mythology, Sarasvati became the wife of the god Brahma, and is “regarded as the goddess of eloquence, in which capacity she is frequently invoked, “much in the same fashion as the Muses were by the Greeks. __ The other goddesses of the Veda are not of much consequence. We have, indeed, a Varunani, an Indrani, and an Agnayi, who were regarded as the con- sorts of Varuna, Indra, and Agni, and a Rodasi, who is said by Yaska to be the wife of Rudra, all of whom might therefore have been expected to occupy posi- _ tions corresponding to the rank of their respective husbands. Such, however, is | notthe case. They play no such important parts as Juno and Minerva perform in “classical mythology. They are rarely mentioned; except Indrani, they are never | associated with their husbands,* and no distinct functions are assigned to them. We meet also with a few personifications, such as Sraddha, of religious faith: ‘Nirriti, of evil; Aranyani, of sylvan solitude, &c. &c. | __ Though it thus appears that in the Vedic age there was no female divinity of “much importance, the case has been far otherwise in later times. Passing over the consorts of Vishnu, and of his incarnate representatives, Rama and Krishna, . sl need only refer to the spouse of Mahadeva, who, under the names of Uma, Par- ‘Yati, Durga, Kali, &c., has held a prominent place in Indian mythology ever since the age of the great Epic poems, who still continues to be one of the principal objects of popular terror and adoration in all parts of India, and who is identified _ by some of the Brahmanical sectaries with the great divine Energy from which the creation of the universe is declared to have proceeded. nit * Jn ii. 53, 4 ff. Indra is thus addressed :—‘ A wife, Indra, is one’s home; she is a man’s dwell- ing : therefore let thy horses be yoked, and carry thee thither. But whenever we pour forth a libation of soma, then may Agni hasten to call thee. Depart, Indra; come hither, brother Indra; in both quarters thou hast inducements. Whenever thy great chariot halts, thy steed is unharnessed. Depart, Indra, to thy home; thou hast drunk the soma; thou hast a handsome wife, and pleasure in thy house, Wherever thy great chariot halts, thy steed should be unharnessed.” 578 MR J. MUIR ON THE PRINCIPAL DEITIES OF THE RIGVEDA. a From the above review, it is clear that there are but few of the Vedic gods who can be certainly identified with any deities of the Greek and Roman mytho- logies, by the double correspondence of names and functions. Of the numerous divinities who were originally common to these three branches of the Indo-Ger- manic family, the greater part became soon so extensively modified by one or other, or all, of these races, after their separation from each other, that at the _ dawn of history only two or three survived in such a form that we can without: hesitation affirm them to have preserved, in some measure at. least, their original character from the earliest times. These, as we have seen, are the Dyaus or Dyaushpitar, the Varuna, and the Ushas of the Veda, corresponding with the Zeus and Diespiter, the Ouranos, and the Eds or Aués, and Aurora of the Greeks and Latins. The Indian Agni, too, is evidently the Latin Ignis; but 1am not _ aware that any trace exists in Latin literature of the element of fire having ever been worshipped under this name; and the adoration of Agni may, perhaps, have originated with the Indians and Persians after they parted from their kindred tribes. I need scarcely allude to Mitra or Mithra, who, though common to the Indian and Iranian mythologies, was unknown in the West till his worship was introduced from Persia. Several of the remaining deities of the Veda, such as Indra, the thunderer, Surya or Savitri, the sun, Vayu, the wind, Yama,* the god of the dead, corre- spond in their functions with the Jupiter, Apollo, AZolus, and Pluto of the classicz writers; but as the names of these parallel divinities do not coincide in the dif- ferent literatures, the resemblances in their offices scarcely suffice, perhaps, establish any traditional connection between them, or to prove anything more than a similarity in the mental processes by which these gods were severally created. Between different systems of nature-worship, especially between the systems prevailing among cognate races (even though they may have been long separated), we may reasonably expect a general resemblance, as the great physical objects and phenomena which are common to all countries, are also those to which the process of personification is most naturally applied. But it is not merely the primitive deities of the earliest Indo-European race which have undergone modification. The gods of the Veda themselves were soon subjected to a similar process, the most eminent among their number being, i the course of time, reduced to a subordinate rank, while others, originally less distinguished, were raised to the highest position. In the later mythology Varuna, the noblest of the Vedic divinities, was stripped of his attribute of supreme dominion, as well as of all his moral grandeur, and was only regarded as the god C mini ee « * Yama’s brother, Manu (who, as I have mentioned above, p. 573, note, is most commonly represented in the Rigveda as the first man, or progenitor of the Aryan race), resembles in name the Greek Minos, and the Mannus of the early Germans. See my paper on this subject in the “ Journal of the Royal Asiatic Society,” vol. xx. pp. 429 f. ' MR J. MUIR ON THE PRINCIPAL DELTIES OF THE RIGVEDA. 579 of the ocean. Indra continued, indeed, to be looked upon as the chief of the Indian Olympus, but he became the monarch of the subaltern gods and goddesses alone. Vishnu, who in the Rigveda is far less prominent than Indra, soon began to eclipse his ancient comrade. In the systematic mythology of the Puranas, he is the preserver, the second of the three persons in whom the divine nature is represented, while his own special votaries identify him with the Eternal Spirit. In like manner Rudra, who plays a subordinate part in the ancient hymns, be- came, in later ages, the third person in the Hindu triad, and was exalted by his own sectaries to the same supreme dignity which they allege is erroneously claimed for his rival, Vishnu. ___Note.—The passage regarding the original union, subsequent separation, and consequent fecundity of heaven and earth, which I have quoted from Dioporus SICULUS, i. 7, in p. 552 of the preceding paper, finds a curious illustration in the following extract from the “ Aitareya Brahmana,” which I cite according to Dr Have’s translation, p. 308 :—“‘ These two worlds (heaven and earth) were (once) J oined. (Subsequently) they separated. (After their separation) there fell neither Tain, nor was there sunshine. The five classes of beings (gods, men, &c.) then did not keep peace with one another. (Thereupon) the gods brought about a re- conciliation of both these worlds. Both contracted with one another a marriage “according to the rites observed by the gods.” VOL. XXIII. PART III. TR XLIL—The Law of the Volumes of Aeriforms extended to Dense Bodies. By Rev. J. G. Macvicar, M.A., D.D., Moffat. (Read 18th April 1864.) It is certain that the unities which constitute aeriform media, when they have been fully separated from each other by an adequate temperature, and relieved from excessive pressure, are all equal to each other in volume, whatever the aeriform may be, either singly or in couples, or in pairs of couples, double pairs of couples, &c., giving such ratios as 1: $: 4: 8, &ce. More than this cannot be affirmed, except by hypothesis or convention. But this is a great deal. By this, many formule justly entitled to the name of rational (for they are representative of the molecules of bodies, both as to quality and quantity), become probable. But the construction of such formule is limited to such molecules as can be raised into the aeriform state. And the discovery of some such law in reference to such bodies as are permanently dense, is at this moment a great desideratum in science; for the doctrine of atomic volume, as insisted upon by some distinguished chemists, is beset with endless embarrassments, and is, besides, plainly wanting in that simplicity and breadth which belong to all laws which are really those of nature. What the author here proposes is to show, that the same law which has been discovered in reference to aeriforms holds good also in reference to dense sub- stances—viz., that the molecules of which they consist, whatever the dense body may be, are all equal to each other in volume, either singly or in couples, &c. The method which he here adopts to prove this is, jist, To construct out of the least chemical units, or the aeriform elements of bodies, such molecules as have the highest intrinsic verisimilitude in their favour; and, secondly, To show that these molecules, as measured by their atomic weights, give the specific gravi- ties as found by the balance,—the argument being the same in form as that which has settled the question as to the volume of aeriforms. By intrinsic verisimilitude, is meant the probable reality arising from that fact which forms the basis of all demonstrated science—viz., that nature is a dynamical system, or system of applied or concrete mathematics. But to begin: In having to do with molecules, we have obviously to do with structures in which the constitutive forces are in a statical condition. This suggests at once, as the forms of molecules, the regular polyhedra of geometry, towards ’ an adequate discussion of which all Euclid’s labours and the ancient geometry aspired, and may I not say the modern geometry now again aspires. They are only five in number, which, beginning with the most perfect, stand thus :— VOL. XXIII. PART II. C8 582 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS The icosahedron, : : : : : 20 trigonal elements, The dodecahedron, . : : : : 12 pentagonal elements, ] The octohedron, ; ‘ ; ; ; 8 trigonal elements, > or facets. The hexahedron, 5 ; , : 6 square elements, The tetrahedron, : : ‘ : i 4 trigonal elements, | But it is with the more perfect, the two first named, almost exclusively, that we shall have to do when treating of the primary molecules of bodies. When, indeed, the elements forming into molecules are very volatile, then, instead of the icosahedron (or icosatom), which is the form of culmination, but which demands the simultaneous concurrence of 20 elements to construct one molecule, we have the octohedron and tetrahedron, whose elements are the same as those of the icosahedron, but which demand the concurrence of only 8 or 4. As to the hexahedron, its sphere of development is not among the primary molecules of bodies, but among those highly composite molecules, where crystallisation begins. It must be added also, that the cosmical element of aq or HO, which is here (as is usual) taken as unity for specific gravities, is assumed to be (as indeed ag and HO indicate) dimorphous; as is also its molecule of culmination, or that which constitutes a particle (or unit-volume) of water; the architectural element of the latter, when it adopts the form of one of the regular polyhedra (the dodecahedron), being not one but three atoms of HO. In other words, our unit-volume of water consists of 36 atoms of steam or vapour, while most other substances consist of 12 only, or 20 at the most. Hence, our constant divisor for specific gravities is ag,,, which we may write AQ. and whose weight on the hydro- gen scale is therefore 9 x 36=324.* Adopting the letter X, then, to represent any chemical unit whatever, and Y and Z to represent dissimilar units, we immediately obtain as the molecules of dense bodies X,, and X,,, and occasionally, among volatile substances, X, and X,. But here the grand law of chemistry, the law of differentiation, presents itself to our regard. Dissimilars only unite chemically; and the condition of molecular stability or repose in the interior of a mass or medium is, that it be duly differentiated internally. Hence, given X as material for molecular constructions, we shall not only have X,, or X,,, but as often as possible, and that in the same * That an unit-volume or particle of water consists of three times the number of chemical units or elements or minims, which other molecules in general consist of, is shown by the numbers of aeri- form volumes which it and they respectively give. Thus, a volume of cold water gives from 1700 to 1728 volumes of steam, according to estimate, of which the third part is from 567 to 576. A volume of alcohol, when its vapour is heated up to the temperature of steam, gives 570 volumes. A volume of ether, supposing its aeriform units of volume to be dedoubled so as to assimilate it to water and alcohol, gives, at the same temperature, 2 x 285-9572 volumes. And so in other cases, where at first sight there seems no relation. Thus, oil of turpentine gives, of the same tempera- ture, only 193 volumes. But the formula of the unit of that liquid is C,,H,,=4(C,H,). It requires, therefore, to be multiplied by 3 to bring it up to the dodecatom, and render its vapour- volume comparable with the others. Now, 3x 193=579, near enough the others. Good experi- ments in this field would be very valuable. - SAMIR tran . ~ = Anat cd dk ee oe, et ee EXTENDED TO DENSE BODIES. 083 mass or medium, both of them either adjusted to each other binarily and most stably as X,,X,,, or inscribing and circumscribing each other as X,,. For the same reason, X,, or X,,, when they are forbidden to differentiate each other, may both of them be differentiated by the addition of some dissimilar unit or units on two opposite points of their forms to develope poles, and thus to impart unity of direction in the functioning of the molecules; for both the dodecahedron and the icosahedron of geometry are in themselves isometrical. We thus obtain a series of molecules of which we may tabulate the leading members (for the sake of subsequent reference) as follows, adding the corresponding numbers in the authorised chemistry, which always draws, and often quarters molecules, as our forefathers did traitors, till one of the molecular constituents is reduced to a single element. Authorised Numbers. Examples. Type (a.) aX: Ope hs cen pa Xen anf Od (6) a XG BO eh ERX lod gt 8 Py.) I AeA Nein LELX Ir ie Seu Ole TI THEY cc Co) ete, OG) oe Oe Ie AS 2 Ep eee Vex 2. 10x oY foxy to.” ClO, BN 8 CGN ARs 0 LAK OR ys TR 1.10, or (a) perpe VV 1 IOX AY Yee CIO. e .) YXZ XK, ZXY Xi VEO 7m GV FSI GHATS, These are the principal members of the first or lowest series of molecules. But of ‘i others are composed according to the same laws. Thus we have (X,,).» & Buch v views will not be thought altogether strange with regard to organic molecules, the established formulze of many of which already give as many, nay | very many, more atoms as their constituents. But they will be thought very | Strange in reference to merely chemical, metallic, and mineral bodies. I know of no reason, however, to call for a break in the economy of nature in this respect between one class of molecules and another, or to explain such a break, if it really existed. And as the view here advanced is in favour of the unity of nature and the simplicity of science, it can have nothing against it, except its novelty or its inadequacy to explain phenomena. To see how it stands in this respect, therefore, let us give a specimen of specific | gravities, deduced a priori by its aid, and compare them with the experimental results obtained by the balance. And to anticipate the charge of special selection of such as alone would serve my purpose, let us take the most familiar and | notable substances, whether of the laboratory of nature or of the chemist, some | undecomposable bodies non-metallic and metallic, some acids, some salts, and some stones. The reader is only requested to bestow his critical eye specially ‘upon those that are abundant in nature in the concrete state, and respecting whose specific gravity there is no doubt. 584 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS Undecompo sable Bodies. Oxygen, 16; Sulphur, 832; Selen. 80; Tellur. 128.* Of these the three last, as is well known, are most closely allied, and to all appearance isomorphous. But they differ remarkably in weight. Hence, of the three, S, the lightest, alone can attain completely to the icosatom. The heaviest, Te, can attain only to the octatom. While that which is intermediate, Se, give both. — S,, 32x 20 7: Pane ages =a : Sulphur . GAG F 394 =1:975. . Expt. 1-98. F Te,. 128 x8. «. : Tellurium . C= AG + ieee =—orowe Expt. 6 3. Se 80 x 20 20 _ ef 2AQ 648 eee : Se, 80x8 Selentum . G= sag iene | Expt. 4:3... 48) Se, Se =4:44. | 20 = Se, Se,, Se, =421. ‘ Oxygen does not belong to the same category as these three substances, — Oxygen is, in reference to sulphur, what fluorine is in reference to selenium. { Ozone, which is a name for oxygen in every state except that in which it — exists in the atmosphere (and probably for more), shows by the disappearance of — volume when it is generated, that oxygen is capable of the molecular or dense — state, though it cannot be thrown into this state by mechanical pressure. From carbonic acid we may infer what the molecular form and specific gravity of 4 similarly condensed oxygen would be; for all the habits of fixed air, compared with those of oxygen, and all the relations between oxides and carbonates in nature, lead us to infer that carbonic acid is not only isovoluminous with atmo- ; spherical oxygen, and, like the latter, contains a couple of atoms of oxygen in one normal or atmospherical unit, but differs from it only by carrying an atom 4 carbon as a nucleus between the two atoms of oxygen (whence, of course, its physiological relations must be completely changed). Now, with regard to carbonic acid which has been condensed, the dodecatom gives— f (CO) nee zs oP Petr Expt. at zero, ‘803. Carbonie Acid . G= AQ 304 * J have here taken the atomic weights of this group of bodies as it stands in the unitary nota- tion. But I must here add, that our molecular theory gives these numbers, not as atomic, but as” molecular weights, proper to the smallest regular polyhedron, viz., the tetrahedron, so that the S, Se and Te of the unitary system are in ours, S,, Se, and Te,, while the O of the unitary: system, which is — truly an unit of oxygen gas, is in ours a coupled molecule=@©), or O,. Sulphur as §S, exists free, and unites with hydrogen and metals; and, in a word, functions as O. As S, on the other hand (being the alternate or reciprocal form of O), it unites with O, and when by itself forms an icosatom S.9 which is of course also the nucleus of (S,),,; but S,, differs from (S,),,, at least when secularly consolidated, in possessing metallic lustre, and in being very stable, if not undecomposable. Its existence as a separate substance has only been obscurely detected. But for the sake of rela it may be called Sulphurium ; its symbol $,,=8 x 20=160. — 4 é EXTENDED TO DENSE BODIES. 585 Similarly condensed oxygen would therefore be only about ‘6. The molecule of ozone appears to be the dodecatom and icosatom one=O,, =4 vols. Fluorine, 19; Chlorine, 35:5; Bromine, 80; Iodine, 127. Our theory of molecular structures is here at war with current atomic weights. In our theory every atomic weight consists of five times as many units of weight as there are units of number in the hydrogen scale ; and the elements of the same substance from different regions of nature, and probably after different manipu- lations in the arts, are apt to vary somewhat in the number of units of weight of which they consist, their full weights being generally somewhat heavier than those most recently adopted in chemistry. Thus the full weight of Cl is believed to be = 36, and of 1,=128. But that by the way. This difference tells but very slightly on specific gravities. Cl, 36% 125... Chlorine. G=F AO 324, 5, = 1:33, Expt. 1:33, : a Bry, _ 02a, : Bromine .G= AQ = 324 =2'99. Expt, 2:99. : slo SAAT vs ee Todine G=nO7 ane 74, Expt. 4:94 2 If the experimental determination in the case of iodine be correct, it indicates that some of the molecules are differentiated. (See type (y), p. 583.) Phosphorus, 31; Arsenic, 75; Antimony, 120. We may here take phosphorus last, in order to follow it by carbon, with which it has many both physical and physiological relations. : AST ec OrX Lan ; ; Arsenic CNG = 162 ent URGE OHS GOR 5, BG) : Sb, ,Sb 120 x 144 22 ep Seo She ees = 66. GEG. 6 * Antimony G= PAO ME: 648 6:6. Expt. 66 6-7. _ It may be shown that when both an icosatom, either single, such as X,,, or With poles, as X,,, forms from the same element, such as P or C, which element also forms dodecatoms, then the icosatom is much more open (as for instance to the attacks of oxygen, and therefore far more combustible) than the dodecatom. Hence, with regard to , 31 x 20 Most combustible . ae nea = ona Jisa Expt. 19. 12 31 x 12 2S) Phe ee) 2 % Phosphorus / Least combustible .G=- TAQ™ 162 29. Bxpty 24.9 sme 22, PP 81 x eel White (natural) .G@= OHNE + GLE aia 1:53, Expt. 1-52. * The dodecatom and icosatom, when both are differentiated, that is X. X,,X, X X,,X=36X (the number of elements in AQ), gives, when divided by 2AQ, the same specific gravity A ihe com- pound dodecatom (X,,),,=4 x 86X when divided by 8AQ. VOL. XXIII. PART III. 77 586 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS Carbon. Like phosphorus carbon is an eminently allotropic substance, giving specially these three forms (independently of those which are proper to organisation and charcoal, which I shall not touch upon); jst, the diamond; secondly, an in- — combustible or less combustible residuum when diamond is burned; and, thirdly, 4 coke and graphite. According to what has been stated, the diamond being a mature product of nature, eminently stable, ought to have for its molecule a — structure differentiating itself, such as C,,C,, or C,,. The more combustible part ought to be the open or circumscribing icosatom, C,,, leaving C,, as the residuum. The icosatom ought also to be the molecule of coke and perhaps graphite. : — (Cy2Cooig 12x 72 +120 _ P Diamond . CG — 2AQ => eee a ae 56. Expt. 3°56. ; —(Cyo)ig_ 12 X72 _ : Unburnt Residuum G = Q@ = 324 =2°67. Expt. 2°67 (Jacquelain.) _(Coohig_ 12 x 120 _ ‘ 3 Coke. ‘ G=5 Q 648 = 222. “expe PO's - 2° 2d: Liepic has proposed as the formula of Newcastle coal C,,H,,0. This is obviously a dodecatom of CHC = C,H, moistened all over by an atom of HO on each of the twelve points of the periphery. It is a good molecular formula; — but coal is not an individualised substance. Detach the moisture, however, to — obtain a pure hydrocarbon, and then impart to it stability in the current of che- mical action by bestowing an atom of oxygen gas,—.e., 20, on each pole, or O — merely when O=16, and we obtain two of the most eminent products of the dis- tillation of coal, our formule being as usual the doubles of those usually given. C,H 144412 Benzene oie 3AQ 169 963. Expt. ‘956 (solid.) dy Go Op ed ee ae 1-065 . Carbolic acid — ree 162 =1:16. Expt. 65. P But these calculations are on the supposition that the entire mass or liquid consists of homogeneously constructed molecules, of which there is but little chance. _ By simple additions of its own elements, CHC = C,H, instead of oxygens on the ~ poles, Benzene gives Toluole, &c., . . . Cymole. And it dedoubles into naphtha — (CH),,=C,, H,,, or with H omitted on the poles, C,,H,,. The element CH being the same in all, and the liquid differentiated to the full, there may be,— (CH),,__ 140 TAQ 7 ewaen Naphtha G= CO ae a = 0 Mean ‘86, Expt. 86... -90. y (CH eae y oo -§ EXTENDED TO DENSE BODIES. 587 Every sort will soon proceed to differentiate itself, in spite of every process which aims at obtaining it in a homogeneous state. The products of the most careful fractional distillation probably continue to be what they are found to be only for a short time. Some of these give exquisitely constructed molecules, as for instance the distillate lately obtained by MM. Canours and PEtoussE from the rock-oil of America. Its formula is C,,H,,, which doubling, we obtain C,,H,,, plainly indicating, a dodecatom whose body is composed of naphtha with double walls, and whose poles are atoms of marsh gas. Whence we can understand the permanency of rock-oil in the presence of moisture and oxygen; for it is on the poles that chemical action mostly takes place; and marsh gas (for a reason which may be shown) is in all natural conditions secure from the attack of oxygen. Moreover, this beautiful hydrocarbon seems to have succeeded in the hands of its discoverers in gaining its way up to icosatomic molecules, each occupying no less than 16 normal volumes. Thus,— (C,H, (C,H,)!°C,H,),, _ 2880+ 560__ 2. ='664, Expt. -669. Distillate of Rock-oil . G= 16AQ r= eileen Many may be the molecular types developed by the reduction of the naphthas, especially by the departure of hydrogen in greater quantity than car- bon, and the introduction of nitrogen and oxygen instead. The most highly parti- tioned, and the last which admits of being raised into the aeriform state, and thus separated from the carbonaceous residuum and brought before the chemist, is an element consisting of a single atom of H surrounded by five of C with an atom of H on one pole, to carry it up. Its elementary formula is consequently C,H,. But it is dissymmetrical. And in the aeriform state, with a normal or atmo- spherical volume it must be C,,H,; and with a double volume, like most com- pounds, it must be C,,H,. It is therefore the naphthalinic element. As the terminal of one pole is H and of the other C, we may well infer that it is capable both of the icosatom and the dodecatom. These give,— C,H,),, 360+ 24 iN it 824 Naphthaline .G= Mean 1:035., Expt. 1:048 (Ure.) (CeHy)a9 600440 gp 2AQ 2x 324 =1:183. Expt. 1-153 (Reichenbach.) If heat were gently applied and sufficient time given, and means of purification existed, it looks as if, between naphtha and naphthaline, there might be obtained the essential oils ; for their element is a combination of the type of marsh gas | with that of naphthaline with omission of the atom of H on the pole of the latter, | which causes its dissymmetry. Or, the essential oil element is marsh gas CHH,C = C,H, with (CH),, substituting H,. But 3CH may be variously applied so as 588 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS to give five elementary types, all different from each other, and the compounds may be numberless. The first molecule is the tetrahedral (C,H,),=C,,H,,. This, with half a normal or aqueous volume, or the octohedral molecule with one such volume, or the icosatom with two, gives,— C,,H,, _120+16 2016 TAQ’ = 12 = 84 Expt. 84. . . 86. Essential Oils wt [Ss 600+ 80 9AQ 2% 324 =1:05. Mean ‘945. Expt. -94. But when, in order to continued existence, greater stability is required (as in drenching with chlorhydric acid) the dodecatom in some cases is constructed. Thus, of cubeb camphor, the formula is C,,H,,ClLH=(C,H,),ClH, a very usual formula. When expanded, it gives type » (p. 583). Andcalling C,H,=X, and CIH=Y we obtain, — YXY (X),,YXY.=X,,Y, or X,Y, or X,Y. C O 120+16+16 (C,H,0,),,__ 60x 12 = =1° Pee lid, 2AQ 2% 324 iit; Expt. 1°1. Soli = Bed) Nese If ek an . Camphor G = { 1 oe 162 ='94. Expt. -99. Wl ERROR ener ey how: ime ; 3 Sugar ey Tg E158. Expt. 156... 16. ‘ % (C,H,0,)ap_ 80x 20) _ oo a AAO Koo . Acetic Acid G = Mean 1:068, Expt. 1:063 .. 1:065. Liquid. nad This implies that the melted crystals of acetic acid consist of dodecatoms and | icosatoms in equal numbers—a complete differentiation, which also appears in | F (C,H,O,)o9 46x20) ogy ; 4AQ 4% 324 5 Alcohol G = Mean ‘796. Expt. *796. mi (C,H,0,),. 46x12 | _ p90 2AQ 2x 324 Ether is an eminently mobile liquid, and, when alone, seems to be constructed : like the essential oils. (C,H,O), 87x4 | Ko! = 1a = 913. Ether G = Mean -742, Expt. ‘736. (C,H,0)9)_ 37x20 _ poy 4AQ 4x 324 Metals. We may here take the leading metals in the order of the simplicity of their molecules. EXTENDED TO DENSE BODIES. 589 I. Metals—Molecule the dodecahedron, either without or with the poles marked X,, or X (X),,X the latter giving the specific gravity uniformly 4th heavier than the former. Li(Li), Li 748447 Lithium TAO 1, 1G =*60, Exp. :59. : Na (Na),,Na_238+2764+23 Sodium AQ oe 304 =="99. . Exp. “97. his K (K),,.K 89+ 4684+39 Potassium WO Oe 84, Exp. 86. : (Mg),._12x12_,, : Magnesium Bags "61 = 176.) *Exp.71:74. ( (Ca). _ 20x12 _ 145 } | oe DA Ora os LOD har | alcium Mean 1°57. Exp. 1:57. Cal(CayCa). 2014 ee Caer emus «162 -ames wea Mercury. One of our two icosatoms, though marked as differentiated, and consisting of : twenty-two elements, is completely isometrical, and in its atmosphere spherical. | It is therefore suitable for the liquid state at any temperature, as might be shown, | but for the necessity of avoiding here all morphological exposition. Hg (Hg),,Hg _100x 22 TAQ) = 19 = 13°58. Expt. 13:59. Mercury G— * The relation between the atomic weights of these eminently active or basilous metals to each other and those of the principal constituents of the crust of the earth is very interesting. Thus, esti- | mating their functioning by their respective attractions to the earth (their weights), the first, Lithium, . ea. by doubling and doubling again, gives nitrogen, aluminium, and iron, disregarding fractions in atomic weights, and taking the integers immediately above them,— € 2li=2x7=14=N, Si and Al 4hi=4x7=28= Fe, and its companions. Then the sulphide or deutoxide of each gives the metal in the series immediately above,— iD fig neem Gree Li0, =Na=7 + 16=28. d NaO,=K =23+16=39. Purther, if we take Na at 24, and K at 40, which may be the primeval unreduced or full weights of these elemental bodies, then, by dedoubling, we obtain weights to complete the series,— Na 24 = == Meg. K 40 a ae ea Thallium, in our theory, comes out a composite metal, of the type X X,,X. The body being sulphu- rium, the poles sodium, all locked together. T1=Na S,,Na=23 + 160 +23=206, or 208. VOL. XXIII. PART III. ~T 590 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS Let cold be urged so as to reduce the open icosatoms to the more compact dodecatoms. Then,— Hg,,__ 100 x 12 4AQ”81 Solid Mereury. G= =148. Exp. 14-4. II. Metals.—Molecule the icosahedron without or with the poles marked X,, and X 9 ». & é (Sn),, 69x20 , Tin FAQ — 162 = 728. / Nxpt 29. Cu(Cu),,Cu 32x22 . Copper fA tele 8-6. Expt. 8:9. Tron oe Gorse ss =7°6.. Exp. 7-7. The formule here, however, are equivocal, because the fine symmetrical com bination X,,X,,4),=2% 5%. (Pb,5)12__ 104 x 144 ' Lead 1RQ,, wees i115." Tixp. £14 (Fito Ok Oe eee : : Zine SAQ — 2324 af22, Mixp. G9... aki Here, too, they are equivocal, thus (X,,),,=4(X X,,X,X X,,X); that is,z combination of dodecatom and icosatom both differentiated. Bi, Bi,, 208 x 12 + 20 Bismuth i DAO = : 2 0). apa 10:3. Expt. 9°8. But this metal, in our molecular synthesis, comes out as composite. some others; the metallic atoms in symmetrical relation, and locked into each other by that structure which renders so many metals in the mass tenacious: and ductile. Our synthesis also presents some fine metals, which have not ye same relation that zinc does to sulphur. The metallic molecules are of the type X X,,X, or rather Y X,Y. Cadmium, . . . . Mg(Zn)Mg=12432+4+12=Cd 56, Tin, . .. . . « Al(@Zn) Al=14432414=S8n 60. Lead,. . . . . . Mg(Se)Mg=12+80+12=104 Pb. Silver, . . . . . Al (Se) Al=144+804+14=108 Ag. avoiding fractions in atomic weights. = EXTENDED TO DENSE BODIES. 591 Noble Metals. Ill. Metals.—Already differentiated by their molecular structure, and there- fore not urgently in need of oxygen or other element :— Type X,,X,). Silver Ga “Big Be — ae -eeo #20 f0-@ Expl 10s. Gold Ge ate ees “ ee 19-1. Exp. 19:2, Platinum @= a ee pe ee =20°66. Expt. 20:8. pee Shar lap 1D x LEO Oe ent 286 8. . 2-67. 4AQ — 162 The construction of molecules might often be simplified by introducing the doctrine of substitution supposed to take place in the act of reducing the metal from its ore. Thus the element of ore in reference to the last is Al,O,. Suppose that as fast as every atom of O (or Cl, or be what it may) is expelled, one of Al takes its place, and we have as the metallic unit Al,. C= (Al,) po 13°75 x 60 AQ ayia The Three Eminent Acids. ° ‘The glacial sulphuric acid shows its individualised character by its aptitude for crystallizing. ; ; 2HO 40 +18 x20 _ Glacial Sulphuric acid, Ge TAO Joo — “ =1:790. Expt. 1-785 at 15°C.Playfair. In the strongest oil of vitriol of commerce, MM. Gay Lussac, Marianac, and Breau found always ;1,th more than one atom of water. This indicates (SO sH0),, + HO _ 12x 40+9+9 324 Strongest Sulph. Acid, G= = 1-843. Expt. 1-842. The number of true hydrates, or symmetrically constructed molecules of oil of vitriol SO,HO, or, as our notation gives it, SaqS (the least element of sulphur being S=8, and the unitary equivalent a tetratom S,) is very great, the most _ dilute being similar in structure to a particle of sea water or animal water, viz., one atom if symmetrical as C,H, N,0,, or SaqS, or a couple of atoms if dissym- 592 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS metrical as ClNa as a nucleus, in a molecule of water of the type X X,,X, viz., AQ AQ,,AQ which gives about 1 per cent. of oil of vitriol. The next hydrate is when we have a particle of water on each pole only, AQSaqSAQ, which gives about 7 per cent. of oil of vitriol. And this forms spontaneously in a damp atmosphere. In hydrosulphuric acid we have 8, the tetratom, with H on each pole; condens- able under great pressure. Sulphydric acid, Eda Se 1:09. Forced Expt. about -9. AQ 2x324 In sulphurous acid we have S, partitioned as in sulphuric acid, giving as the product of combustion of sulphur the element SO, heteropolar, and capable both of the dodecatomic and icosatomic molecule; also condensable only under pressure. a ($0)ip(80) ao 16 x 12416 x 20 Sulphurous aci 304 =1:58. Forced Exp. 145. Resembling sulphurous acid in the dissymmetry of its element is chlorhydric acid, HCl. But its weight is greater and its volume larger, the icosatom as is most usual having double the volume of the dodecatom. Chlorhy- ele (HCl) ,5_ 86:5 x 12 36-5 x 20 dric acid, AQ 9AQ ~ 3294 + 2x324 = 1:369 + 1:126. Mean1:247. Expt. 1-247. The most stable hydrate, that into which both weaker and stronger acids resolve themselves by boiling, has for its authorised formula CLH + 16aq. Doubling as usual, we obtain 2C1H + 32aq, or 2ClHaq + 30aq, 7.¢., 10(OHaqHO), leading to” the construction of the fine dodecatom, ce =1:111. Expt, 1-111. aqHCl (OHaqHO),,ClHaq_9 + 87+ (27 x 10) +3749 AQ 304 The formula of nitric acid NO,HO when doubled, gives also a dodecatom. But all its constituents are so bent upon the aeriform state, that the icosatom cannot be constructed till the molecule is loaded with aq, as by continued boil- ing. And even then it is so tender, that the discordant results of chemists indicate a differentiated liquid, or a liquid struggling for stability by differen- tiation. But the tetrahedron or octohedron is decided. Thus, taking the usual formula,— Nitric Acid (Oa eaey Bf epee ue AQ Souue 1°55. Expt. 1°55. Ou Nal (Su) EXTENDED TO DENSE BODIES. A Few Common Salts. cabie sare N80 yo_ BEBE 12 AO 394 =2°16, Expt. 2°15. Kopp. with full atomic weights, it comes out 2°22. Expt. 2°22. (SO,Na0),, 40481 x12 AOE Sulphate of Soda 304 =2'62. Expt. 2°63, Glauber’s Salt is a fine molecule, the body composed of (aqHO),,, the poles SO,NaO ; formed into a dodecatom occupying 8 volumes, G=1:49. Expt. 1:47. _ f(80,KO),, 40+ 47 x20 Sulphate of Potass G= { ae ae =267. Expt. 2°66, 2x 824 (OKO) 1.97 nao. . c= Mean 2:08 Expt. 2:07. with poles marked =2-18 QO MONA).» 14g -Nitrum Flammans .G= Mean 1:62, Expt. 1-7. with poles marked 1:75, F : = (CIH,N),, a6 : Salammoniac . G= ZAQ cio, ixpts 15: Ammonia, in our theory, in one of its forms is isomorphous with aqaq, or _ double vapour, and affects the molecule am,,, like aq,,. A Few Common Minerals. | ‘ As the attempt to show the structure of highly compounded molecules in “common writing is necessarily difficult, let us here take the shortest symbols | possible for the common mineral constituents, as for instance, S for SiO,, A for | Al,O,, F and i for FeO and Fe,O,, and H for HO. §(8),.S_ 1430 sq 162 Quartz G= = Oss Expt 2a. + 2°83: The dodecatom with A instead of '$, gives G=3'82. Expt. 3°87, But as developed by nature, it may be,— Sapphire G= =3°824+4:44 Mean=412. Expt. 4-08. But the same specific gravities are obtained by the finer molecule of the form q eg And such molecules we are not to regard as too large, as is clearly VOL. XXIII. PART II. Gax 594 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS shown by the very small percentages sometimes occurring in the analysis of minerals. It is indeed usual to regard these small percentages as accidental ingredients. But that will not do. Thus, prase is represented as quartz, with about 2:9 per cent. of protoxide of iron as an accidental ingredient. But on constructing that molecule, which seems to be the most prevalent in the crystal- line world, viz., the compound dodecatom with marked poles, which, to show all its constituents, may be expanded on the paper thus:— | x (X)oX(X (X)oX )roX (X), 2%, 2-9 per cent. of protoxide of iron just gives four atoms, one to differentiate each of the two poles of the two polar dodecatoms, that is, to take the place of the sepa- rate atoms of X in the above formula, F(8),F (S (8),28),F (S)aF- Nay, half this quantity, or 1°5 per cent. might enter into the symmetry of the molecule. And so it may possibly be with Ti in rose quartz, as found by Fucus. But let us look to the grand products of nature. The quartz molecule will tend to be differentiated more effectually than by an element of its own kind on each pole of the dodecatom. And more especially, we may expect 4. and K, or Na, or both performing this function and giving, Ril ees ot eer —K,0,.Al,0,.128i0,. KSA(S),,ASK. (See Type 6) which last is the formula for orthoclase, in Wart’s Chemical Dictionary (the atomic weights of O and of Si being here halved.) (See Art. Fe/spar). But both the ratios of ingredients and the specific gravities show that, in order to explain nature, we must rise from the simple dodecatom to the compound dodecatom. Thus, the purest felspar or adularia gives, (KA(S),,AK),. C= BAQ =2:59. Expt.2°53 ... 2°58. Theory. Berthier. 144810, 4320 64:5 64:20 Aastra} 24A1,0, 1248 18:6 18:40 ; from St Gothard. 24KO 1148 16:8 16:95 G= 8x324 )6716( 2°59. Expt. 253... 2:58. But in order to show the substitutions which take place during further differ- entiation and development, the above formula requires to be written out, KA(8) AK(K A(8),, 4K), .K R(S), AK. Thus, let us substitute Na for Ke in the polar dodecatoms, and we obtain, — Na (8), Na(K AS), a K),,Nadl( S),2 A Na. EXTENDED TO DENSE BODIES. 595 Theory. Abich. ( 144Si0, 4320 65°14 65°72 24A1,0 1248 18°82 18°57 Felspar 20KO ~ 940 14-17 14-02 from Baveno. 4NaO 124 1:85 1:25 G=8x 324 )6632( 255, Expt. 2°5552. (See Millar’s Mineralogy, p. 367.) the felspathic, is when we have S instead of K or N a, with only one atom of Li on each of the twelve parts which constitute the compound dodecatom. This gives,— Theory. Plattner. Petalite 24A1,Q3 1248 20-4 13:36 } rom a. 12Li0 PEdy sage ee Mma eet wkEaston.)) j ' J | On the other hand, the smallest amount of differentiation that is possible on G=8 x 324 )6108( 2:39 Expt 23-8... 24, But in all the felspars, the silica greatly overmatches the alumina. Instead ‘of a molecule of silica with an atom of alumina on each pole, the balance of nature is rather the reverse of this, or at least, instead of ACS), jz it is SAS. _ Thus, the clay which results from the unremitting application of the atmosphere _ to the hard compounded rocks, and advances nature towards a vegetable kingdom, has, for its element HSASH = Al,0,2Si0, +2HO. We may, therefore, look in nature for some abundant mineral in which the element of the body of the mole- cule, instead of being S merely, shall be SAS. But such a molecule over all its periphery must be wholly non-metallic, like quartz itself. Let us, therefore, | differentiate it by introducing more fully metallic matter of the same form. We | thus obtain the molecule, — KSK (SAS),,K SK Theory. H. Rose. 26Si0, 490 492 Common Mica 12A1,0, 39:2 39:0 from Kimito. 4KO 11°8 98 Arragonite G= = 430934 | Expt.2:992 92°. 0". (Ca0CO,),, 28+ 22 x 20 RGane wee 304 ut as greater stability is urged, or spontaneously acquired, the icosatom must end to the dodecatom. Hence, a series of structures, giving G=2:47 to 2°77, of 596 DR MACVICAR ON THE LAW OF THE VOLUMES OF AERIFORMS which the most complete is, as usual, the compound dodecatom, which closely written is, — 28 + 22 x 144 : _(Ca0CO,), ee Calcite or Marble . G= BONA oe ae \ 2277, Expt. 2°6: .. eis Limestone, as chemically conceived, seems a singular combination. But if we could dedouble alumina and peroxide of iron, as we can dedouble limestone into a protoxide, and a deutoxide, that singularity would disappear. Thus, written according to the law of symmetry or union by difference, carbonate of lime is OCaOCO similar in structure to OAIOAIO, and OFeOFeO, &c.; and for mineralo- gical notation it might be written CaC like A and 32. The fully differentiated phosphate (see type ®) gives, Bone Phosphate P Ca P (Ga), PCa p = 4(P0,3Ca0). the usual compound dodecatom occupying 8 volumes. Written with the usual formula, we obtain for this substance, Gg — (P0;80a0),._ 71 +84 x 12 2AQ 2 x 324 = 2°87. And with poles marked 3:35, Mean 3-11. Expt. 3°1. 3°2. Purely magnesia minerals are rare, but as a mineral constituent, none is more interesting or important than magnesia. Theory. Walmsted. TRAN e coals ayer 148i0, 420 402 401) 4) Olivine FSF (MgSMg),, FSF = 24Mg0 480 459 4425 « i 4FeO 144-0 38 es = 324 )1044( 322. Expt. 3:3... 3-4, It is not the symmetrical or septary element MgSiMg, however, but the quinary combinations MgSi and CaSi, 2.c. the sesquiform, so great a favourite with nature, that are the great mineral constituents. They seem generally to form into dodecatoms, the poles marked by the application of molecule to molecule, or by the omission of an atom of the basic element, or by substitution of Fe for Mg or Ca. Of these, the simplest symmetrical structure is that in which 2Fe serve to unite 3 dodecatoms, the central consisting of CaS, and the lateral of MgS. (MgS ),.F (CaS ),.F (Mg $),, omitting from the six poles (Mg+ Mg) (Ca+ Ca) (Mg + Mg); | or written out,— S (MgS),,8,F, 8 (Ca8),,8, F, S(MgS),,8. Theory. Bonsdort. S6S10,-2 “1080, 59-0 *507—> 20Mg0 AO 2182 Nee [ fcfitnee 10CaO 280) i Glo aula f SO eae 2FeO 72 3-9 3-9 G=2'*324 L882) 92-82 O ixpt. 2oteeeise Hornblende EXTENDED TO DENSE BODIES. 597 In talc, when most simple, the sole genetic element is MeSi: molecules differ- entiated by Fe. But here differentiation is too active for easy study, until the elements settle into serpentine, to represent which a very interesting molecule presents itself; the body, a sesquicombination of magnesia and silica, and the whole surface hydrated magnesia, except the two poles, which are iron oxide. F (aqH MgS Mg S Mg),, F. Theory. Kerstin. 36MgO 720 417 41:5 Genpenine 24810, 720 41:7 40°3 from 24HO 216 12:6 12-9 Swartzenberg. 2FeO 72 4:2 4-] G=2x324 )1728/( 26620 Mxpty 2-470. 26) And here | may close, conscious that these constructions are but the merest approximations, and the rudest representations of the exquisite structures of nature. Still, it will not be denied, that to any one who has given his mind to the preceding pages, they supply much for men of science to think about; for in this paper the specific gravities of between sixty and seventy of the most eminent . substances of nature and the laboratory have been deduced a@ prior2, have been shown to be proportional to certain molecular numbers which are suggested by pure geometry (and the law of differentiation), the same being supposed to prevail all through nature. It is true that our molecular numbers imply that the formulze of mineral chemistry, and indeed of chemistry generally, are sub- multiples (halves, quarters, or lesser elements) of the molecules of nature, as nature is here conceived And this will necessarily be against the study of them for a time; as also the too short statement of them in this paper. But let the thing be seriously looked into, and there can be no doubt as to the ultimate issue. VOL. XXIII. PART III. cy ( 599 ) XLIIl.— Biographical Sketch of Adam Ferguson, LL.D. F.RSL., Professor of Moral Philosophy in the University of Edinburgh. By JouHn Smauu, M.A., Librarian to the University. (Read 18th April 1864.) The Memoir now submitted to the Society, while it details the chief events in the life of a man who occupied a distinguished place in the literature of Scot- land, at a period when it had attained a high reputation, cannot claim to be so complete as might be desired. His life was prolonged for several years after nearly all of his early friends had passed away; and since his death many papers have been destroyed or have fallen aside, which would now be of the greatest interest. Whilst in this way much has been lost that might have given greater com- _pleteness to these pages, still, the recent publication of the Diary of his friend Dr CaRty_ez of Inveresk, has furnished many additional details, and afforded further evidence of the estimation in which he was held by his literary associates. Several letters selected from the lives of his distinguished friends, and from the Manuscript Collection of the University, in addition to information derived from the short notices of his life already printed, have afforded the materials for ‘preparing this sketch of one, whose career was more varied, while his public labours and literary connections were not less important and extensive, than those of any of his contemporaries. _ Dr Ava Fereuson, son of the Rev. Apam FEreuson, minister of the parish _ of Logierait, Perthshire, was born in the manse of that parish on the 20th of ‘June 1723. His father was descended from an old and respectable family in Athole, to whom the estate of Dunfallandy yet pertains; and his mother was the ‘daughter of Mr Gorpon of Hallhead, in the county of Aberdeen. In the female line Fercuson traced a connection with the noble family of ARGYLL, thus referred | to in a letter addressed to him by Dr CartyLe of Inveresk: “I am descended from the Queensberry family by two great-grandmothers—much at the same distance as you are from that of ARGYLL.’”* | ApAm was the youngest son of a numerous family. His father had been minister of Crathie and Braemar from 1700 to 1714, and was long remembered with gratitude for having sheltered in his manse of Crathie some of the unfortu- nate Macdonalds on their flight from the treacherous massacre of Glencoe. Just before the Rebellion of 1715 he was translated to Logierait, where he passed the * MSS., University of Edinburgh. VOL. XXII. PART III. CZ 600 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. remainder of a long life, discharging his ministerial duties with exemplary piety and firmness. Although the parishioners were at the period of his induction almost universally hostile to Presbyterian principles, he speedily secured general respect, which he retained till his death in 1754. FERGUSON received his earlier education partly at home under the tuition of his father, who had soon discovered his son’s superior abilities, partly at the parish school of Logierait. He was afterwards sent to Perth, where he attended the classes of Mr JAmes Martin, rector of the grammar school, a distinguished teacher, who had numbered amongst his pupils the great Lord MANSFIELD. There he was committed to the charge of his relation, Wi1it1Am FERGUSON, a merchant, and at one time chief magistrate of that city. At the Grammar School of Perth Fercuson excelled in classical literature, and especially in the composition of essays; and we learn that his themes were not only praised at the time, but were long preserved, and shown with pride by Mr Martin, who declared that none of his pupils had ever surpassed the writer. In 1738, when he had just entered on his sixteenth year, FERGUSON was enrolled at the University of St Andrews, where he studied Latin under Pro- fessor Younc, and Greek under Professor Prineie. The classes were then ably superintended by Principal TULLIDELPH, to whom FERGuson had the advantage of being recommended by his father’s friend and namesake, the minister of Moulin. At the commencement of the session, FERGUSON gained by competition one of the foundation bursaries, which are tenable during the curriculum in the Faculty of Arts, and which entitled him to maintenance at the College table. This he owed to his previous excellent training in Latin. His attention was now given to the study of Greek, of which, hitherto, he seems to have had little knowledge; and that so successfully, that at the end of his first session he read Homer with considerable ease. During the summer recess he resolved to read one hundred lines of the [liad daily, and in this way perused the whole poem. He obtained his degree of M.A. on the 4th May 1742, when he had nearly completed his nine- teenth year; and thus finished his curriculum in arts with the reputation of being one of the best classical scholars, and perhaps the ablest mathematician and metaphysician of his time at the University. ' Having been intended by his father for the church, FErcuson entered the Divinity Hall at St Andrews in 1742, under Principal Murtson and Professors Saw and CAMPBELL ; but shortly afterwards he removed to Edinburgh, and con- tinued his course under Professors Gowpie and Cummine. There he joined a number of young men who afterwards attained to eminence—amongst whom were JouN Home, author of ‘ Douglas;’ Witt1am Rosertson, afterwards Prin- cipal of the University ; Hucu Barr ; Mr Weppersurn, afterwards Lord LoueH- BoRoUGH; and Dr CarLyLe—in forming a debating society. This club after- MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 601 wards became merged in the Speculative Society, which still exists in unimpaired efficiency. Fercuson, while not neglecting the study of divinity, applied himself less to it than to those subjects of philosophy for which he showed special aptitude, and in which he was afterwards to become so celebrated. In 1745, when he had attended divinity classes for two only, out of the full period of six, years—the time then required before obtaining license to preach—he was offered the ap- pointment of deputy chaplain to the 42d regiment, or “ Black Watch,” by Mr Murray (brother of Lord Exrzanx), who was principal chaplain. For this appoint- ment his knowledge of the Gaelic language was an important qualification. The rules of the Church allowed Gaelic students to be taken on trials after four years’ attendance at the Divinity Hall; but it was necessary, in FERGuson’s case, to obtain from the General Assembly a still farther dispensation. The Assembly, in consideration of his good character and high testimonials, granted special authority for his ordination, and he was ordained by the Presbytery of Dunkeld on the 2d of July 1745. A few days after this he joined his regiment, then serving in Flanders; and ina short time he obtained, on the retirement of Mr Murray, the rank of principal chaplain. We are informed by Dr Carty ez, that it was through the influence of the Duchess Dowager of ATHOLE that FERGuson obtained his appointment as chap- lain to the 42d Regiment. ‘“ Her son, Lord Jonn Murray,* had obtained the colonelcy of that regiment when he was not more than twenty-two years of age; and the Duchess had imposed the very difficult task upon FERGusoN, to be a kind of tutor or guardian to Lord Joun,—that is to say, to gain his confidence, and keep him in peace with his officers, which it was difficult to do. This, however, he actually accomplished, by adding all the decorum belonging to the clerical character to the manners of a gentleman; the effect of which was, that he was highly respected by all the officers, and adored by his countrymen, the common | soldiers.” Shortly after FERcuson joined his regiment, the battle of Fontenoy took place, in which he behaved with the greatest bravery. In that battle, according to the account of the French themselves, “ the Highland furies rushed in upon them with more violence than ever did a sea driven by a tempest.” FERGUSON went into action at the head of the attacking column, with a drawn broad-sword in his ; hand, and could with difficulty be persuaded to retire to the rear.} Colonel | Davin Stewart, author of the “ History of the Highlanders,” remarks, that he continued with his regiment during the whole of the action, in the hottest of the * Lord Joun Murray—son of Joun Duke of Aruotz by his second marriage—was appointed colonel of the Royal Highlanders on April 25, 1745; major-general in 1753; lieut.-general in 1754; and general in 1770. + Sir W. Scorr’s Miscellaneous Prose Works, vol. xix. p. 331. 602 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. fire, praying with the dying, attending to the wounded, and directing them to be carried to a place of safety. The Colonel further remarks, that FerGuson, “ by his fearless zeal, his intrepidity, and his friendship towards the soldiers (several of whom had been his schoolfellows at Dunkeld); his amiable and cheerful man- ners, checking with severity when necessary, mixing among them with ease and familiarity, and being as ready as any of them with a poem ora heroic tale, acquired an unbounded ascendancy over them; and while he was chaplain of the corps he held an equal, if not in some respects a greater, influence over the minds of the men than the commanding officer.” * While he was connected with this regiment, he published a sermon, which was his first contribution to literature. It is entitled— A Sermon preached, in the Ersh Language, to His Majesty’s First Highland Regiment of Foot, commanded by Lord Joun Murray, at their Cantonment at Camberwell, on the 18th day of — December 1745, being appointed as a solemn Fast. Translated into English for the Use of u« Lady of Quality in Scotland, at whose desire it is now published.+ This sermon, printed at the request of the Duchess Dowager of ArHotz, with . whom FERGUSON was a particular favourite, is more remarkable for the vigour of its patriotic exhortations than for the elegance of its language, and contains strong denunciations of the attempt made in the year 1745 to seat Prince CHARLES on the throne of Britain. With this gallant regiment Fercuson served during the whole of the cam- paign in Flanders; and on the peace of Aix-la-Chapelle, he obtained leave of — absence, and visited the scenes of his youth, where he spent much of his time in wandering amongst the Perthshire mountains. Writing to an intimate friend at a subsequent period, he says, “ If I had not been in the Highlands of Scotland, { might be of their mind who think the inhabitants of Paris and Versailles the — only polite people in the world It is truly wonderful to see persons of every — sex and age, who never travelled beyond the nearest mountain, possess them- selves perfectly, perform acts of kindness with an aspect of dignity, and a perfect — discernment of what is proper to oblige. This is seldom to be seen in our cities, — or in our capital; but a person among the mountains, who thinks himself nobly born, considers courtesy as the test of his rank. He never saw a superior, and ~ does not know what it is to be embarrassed. He has an ingenuous deference for those who have seen more of the world than himself; but never saw the neglect © of others assumed as a mark of superiority.” | With a desire to obtain a more permanent and more congenial sphere of use- fulness, FerGuson applied for the living of Caputh, a beautiful parish near Dun- keld, in the patronage of the Duke of ATrHotze. He was not, however, in all | * Hist. of the Highlanders, vol. i, p. 292. + Lond., 1746. 8vo. t MSS. Univ. of Edin. ST a ee ee MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 603 respects qualified for discharging the duties of a Scottish clergyman. Although, by his polished manners and his great abilities, he took a prominent part in pri- vate society, he was deficient in the gifts necessary for the popular preacher. His sermons were elaborate disquisitions, showing more acquaintance with systems of philosophy than with the wants of common hearers.* He was unsuccessful in his application for this living; and when the death of his father (whom he had hoped to succeed) took place shortly after this disappointment, he abandoned all intention of undertaking the duties of a parochial charge. He continued to remain attached to his regiment, during its service in Ireland, till about the year 1754, when he resigned his commission. The knowledge of military affairs thus acquired by his service in the army enabled him to give so much distinctness and liveliness to his descriptions of war in his ‘ History of the Roman Republic, that it is remarked by Car Lyte, that he was excelled, in this respect, by no historian but Potysrus, who was an eye- witness of so many battles. His military service also proved beneficial to him by opening up a wide field for the observation of human character, and gave him enlarged opportunities of studying the political phenomena of the period. | After resigning the chaplaincy of the 42d Regiment, Frrcuson spent some | time in Holland with his friend Mr Gorpon, and resolved to give up all thoughts | of further exercising the clerical profession. Writing to Apam Srrx from Gron- ingen, in October 1754, he concludes by requesting a reply to be addressed to him | at Rotterdam, “ without any clerical titles, for I am a downright layman.”?+ Shortly after this, Ferncuson returned to Edinburgh, where he renewed his | acquaintance with the friends of his youth. As Davin Hume had at this time ‘given up his appointment of Keeper of the Advocates’ Library, he became a candidate for the office, and was appointed Hume’s successor as Librarian and | Clerk to the Faculty on the 8th of January 1757. | While he was connected with that Library, FErcuson became a member of | the Select Society, which had been instituted in 1754 by Mr Atuan Ramsay, | the eminent artist. The meetings of the Society were held weekly in one of the ‘inner apartments of the Library, and were for the purpose of literary discussion, -_ * The following anecdote illustrates their character :—“ Sometimes he lent or presented a sermon | to his friends. One of them one day preached a very profound discourse on the superiority of per- sonal qualities to external circumstances, that showed a very thorough acquaintance with the doc- ‘tines of Plato and Aristotle. Mr Bisser (his father’s successor), in whose church the gentleman _ delivered this sermon, was at first greatly surprised at hearing such observations and arguments from a worthy neighbour, whom he well knew to be totally unacquainted with the philosophy of Plato, or any other, ancient or modern. When service was over, he paid the young man very high encomiums on his discourse—that it very much exceeded the highest expectations he had ever enter- _ tained of the talents of the preacher; who told him very honestly that he knew very little about _ these things himself, but that he had borrowed the discourse from his friend ApaM Frrcuson,”— Histor. Mag. (1799) vol. i. p. 44. + This interesting letter is in the possession of the Rev. Mr Cunnineuam, Prestonpans. VOL. XXIII. PART III. SA 604 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. philosophical inquiry, and improvement in public speaking. This Society exer- cised an important influence in diffusing a taste for letters in Scotland, and it has been remarked, that “the classical compositions of Hume, Ropertson, Surry, and Fercuson, the writings of Joun Home, of Professor Wiukiz, of Lord Hames, Lord % Monsoppo, Sir Jon Datrymp.e, the elder Mr Tyrier, all members of the © Select Society of Edinburgh, have thrown a lustre on that institution, as marking the commencement of a literary era, which it is doubtful if the succeeding times have yet seen surpassed.” * Frercuson, shortly after entering on his duties in the Library,} was solicited to undertake the education of the sons of Lord Burts. Huvmg, in aletter to GimperT Exot, of Minto, states, that he had some scruples with regard to accepting this 5 appointment, as he was to have the charge of more than one boy, and adds, “ I hope Lord Bute will conform himself to his delicacy, at least if he wants to have a man of sense, knowledge, taste, elegance, and morals, for a tutor to his son.” Having arranged satisfactorily the terms of his engagement with Lord Burs, — Fercuson seems to have left his office of Librarian rather abruptly, for, — according to the Minutes of the Faculty of 3d January, 1758, “it was repre- — sented to the Dean and Faculty that Mr Apam Frreuson, who in January last ? had been constituted Library-keeper and Clerk to the Faculty, had gone from this — place some time ago, and had left behind him a letter demitting said offices, so that the Faculty had now neither a Librarian nor a Clerk; by whatever omission or neglect, it happened that the said letter of demission had neither been pre- sented to the Dean nor laid before them. And the same thing being affirmed by divers members, after reasoning on the matter at good length, the Dean and — Faculty declared the said offices to be vacant, notwithstanding that the said . demission had never been presented.” : Frercuson was succeeded in this office by Mr Wizt1AmM WALLACE, advocate, — elected at the meeting above referred to. Zz Before giving up his. connection with the Advocates’ Library, Frercuson — attracted considerable attention by a pamphlet which he wrote in defence of JoHn” - Home, author of ‘ Douglas,’ who had incurred the censure of the Presbytery of — Edinburgh by the publication of his celebrated tragedy. This pamphlet, entitled — The Morality of Stage Plays seriously considered,t was published anonymously, , and was admitted on all hands “to be the only piece on that side that was . written with any tolerable degree of discretion.”” Homz was one of FERGUSON’S — most intimate friends, and it is not surprising that Fercuson was led into ye 3. an active part in the controversy which the publication of ‘ Douglas’ occasioned. Home had at this time resigned his parochial charge, to avoid the persecution to * Life of Lord Kamgs, vol. i, p. 175. + Like his predecessor Hume, spare enjoyed the moderate salary of L.40 per annum. t Edinburgh, 1757, 8vo. 2 ee Pa te aR tas MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 605 which he was subjected by the Church, while his tragedy was received on the Edinburgh stage with the most enthusiastic applause. Along with Principal Rosertson, Davip Hume, and Dr. Buarr, Fercuson had taken a deep interest in the attempts of Home to have his ‘ Douglas’ properly brought before the public, and it has been stated that it was privately rehearsed by these gentlemen, in the lodgings of Mrs Saran Warp (one of DiccEs’ company), in presence of some of the most distinguished literary men of Scotland.* From his friendship with Davin Hume, and Apam Smiru, then Professor of Moral Philosophy in the University of Glasgow, who were well aware of his extraordinary accomplishments, it was now proposed that FERcuson should be promoted to a Chair in one of the Scottish Universities. At this time the in- fluence of Lord Mizron,} the political agent of ArcurpaLD Duke of Argyll, was ‘paramount in the patronage of almost every office of emolument and dignity in Scotland. Even in the exercise of the patronage of the Chairs in the University of Edinburgh, so jealously guarded by the Town Council, the influence of Lord Mitton was so strong that Provost Drummonp, one of the most meritorious and public-spirited benefactors of the community over which he presided, did not find himself at liberty to promise any preferment at the disposal of the Town Council, without Lord Mitron’s consent being obtained.t Under such a system, it is not surprising that Professorships might not only become matters of private arrangement, but, as it would appear by the following letters, even attainable by the payment of considerable sums of money. From the terms of these letters, preserved in the Royal Society,§ it was accordingly contemplated to transfer Apam SmitH to the Chair of the Law of Nature and Nations in the University of Edinburgh, then expected to become vacant by the retirement of Professor ABEr- OROMBY, and to appoint FeRGcuson to the Chair occupied by Smirx at Glasgow. “ Hume fo ADAM SMITH.” * 8th June 1758. “ Dear SmituH,—I sit down to write to you, along with JoHNsToNE;|| and as we have been talking over the matter, it is probable we shall employ the same arguments. As he is the younger lawyer, I leave him to open the case, and *The following was the cast of the piece on that occasion :—“ Lord Randolph, Dr Robertson | (Principal); Glenalvon, David Hume (Historian); Old Norval, Dr Carlyle (Minister of Mussel- burgh); Douglas, John Home (the Author); Lady Randolph, Dr Ferguson ; Anna (the Maid), Dr | Blair (Minister, High Church).” “The audience that day, besides Mr Dicczs and Mrs Warp, were the Right Hon. Patrick Lord Exreanx, Lord Mitron, Lord Kames, Lord Monzoppo (the two last were then only lawyers), the Rev. Joun Sreeve and Wintiam Home, ministers.”—Edinburgh Weekly Chronicle, 21st January, 1829. Dr Cartyze corroborates this statement so far in his Diary, p. 311. + It has been stated that in 1742 Fercuson was Secretary to Lord Mitton, and lived with |him in that capacity for some time, at Brunstain House, near Edinburgh.—Chambers’s Journal, | No. 60, 1855. t Sommervill’s Life and Times, p. 380. § ‘Hume's Life by Burton, vol. ii. p. 45. | Afterwards Sir Witu1am Putteney. 606 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. suppose that you have read his letter first. We are certain that the settlement of you here, and of Fercuson at Glasgow, would be perfectly easy by Lord — Mixton’s interest. The prospect of prevailing with AsERcromsy is also very — good; for the same statesman, by his influence over the Town Council, could oblige him either to attend, which he never would do, or dispose of the office for the money which he gave for it. The only real difficulty is then with you. Pray, then, consider that this is perhaps the only opportunity we shall ever have of getting you to town. I dare swear that you think the difference of place is” worth paying something for, and yet it will really cost you nothing. You made above L.100 a-year by your class* when in this place, though you had not the character of Professor. We cannot suppose that it will be less than L.130 after you are settled. JOHN STEVENSON ;{ and it is Joan STEVENSON makes near L.150, as we are informed upon inquiry. Here is L.100 a-year for eight years’ purchase; which is a cheap purchase, even considered as the way of a bargain. We flatter ourselves that you rate our company at something; and the prospect of settling Frercuson will be an additional inducement. For, though we think of making him take up the project if you refuse it, yet it is uncertain whether he will con- sent; and it is attended, in his case, with many very obvious objections. I be- seech you, therefore, to weigh all these motives over again. The alteration of these circumstances merit that you should put the matter again in deliberation. I had a letter from Miss Hepsurn, where she regrets very much that you are settled at Glasgow, and that we had the chance of seeing you so seldom. I am, &c.” *« P.S.—Lord Mitton can with his finger stop the foul mouths of all the roarers against heresy.” i “ Hume to the Rev. Joun JARDINE.” Without date. “ Rev. Sir,—I am informed by the late Rev. Mr Joun Home that the still Rev. ADAM FeErGuson’s affair is so far on a good footing, that it is agreed to refer the matter to the Justice Clerk, whether more shall be paid to Mr ABERCROMBY than he himself gave for that Professorship. Now, as it is obvious that in these of the person are to be considered, I beg of you to inform my Lord of the true | 3 state of the case. FERcuson must borrow almost the whole sum which he pays |) for this office. If any more, therefore, be asked than L.1000, it would be the most ruinous thing in the world for him to accept of the office. I am even of |) ments if the case were mine. * Situ had lectured on Belles Lettres in Edinburgh in 1748. + Professor of Logic. =a MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 607 “ If the Justice Clerk considers the matter aright, he will never agree to so unreasonable a demand as that of paying more; and I hope you will second these arguments with all your usual eloquence, by which you so successfully confound the devices of Satan, and bring sinners to repentance.—I am, Rev. Sir, your most obsequious humble servant.’’* The negotiations above referred to were unsuccessful, and Mr ABERcROMBY was succeeded in the Chair of the Law of Nature and Nations by Mr Roper ‘Bruce in 1759.+ The long wished for opportunity of obtaining for FEercuson an academic appointment soon after occurred, for a vacancy took place, in 1759, by the death of Dr JoHn Stewart, Professor of Natural Philosophy in the University of Edinburgh. The Town Council, who were the patrons of this Chair, after consultation with the ministers of the city, appointed FErcuson on the 4th of July of the same year. Frercuson immediately began to prepare his lectures, so as to be ready to conduct his class when the University session was opened in October. Notwith- standing the shortness of the time at his disposal, he was so successful in his teaching, that “ Davin Hume said Fercuson had more genius than any of them, as he had made himself so much master of a difficult science,—viz., natural philosophy, which he had never studied but when at college,—in three months, so as to be able to teach it.’’t In 1760, FERGUSON was instigated by Dr Cartyzez to publish a little volume, | to which the following quaint title was given,—The Mistory of the Proceedings | in the Case of Margaret, commonly called Peg, only lanful sister to John Bull, Esq.§ The object of this publication, which went through two or three editions, was to turn into ridicule the opposers of the Scotch Militia Bill, which had been rejected in the preceding session of Parliament. The Act of Parliament by which the militia of England was constituted did not apply to Scotland, as, on account of the Rebellion of 1745, and the still existing jealousy of the Jacobites, Govern- ‘ment had felt alarm at the proposal to extend to the sister kingdom a measure which should put arms into the hands of those who might turn them to revolu- tionary purposes. This jealous feeling towards Scotland was the cause of con- * Hume’s Life, by J. H. Burton, vol. i. p. 47. + It may here be mentioned, that the Professorship of the Law of Nature and Nations—the patronage of which was vested in the Crown—was then a sinecure, and was abolished in 1832. It _ has, however, been again revived as the Chair of Public Law, by the Universities’ Commissioners of 1858. + Carlyle’s Diary, p. 283. § Lond, 1760, 12mo,—It may be interesting to those who possess this curious little volume, _ which (from its having been published anonymously) has sometimes been attributed to Swirt, to have the following key to the principal characters referred to in it:—John Bull, England; Sister Peg, Scotland; Nurse, Lord Hardwicke; Jowler, Mr Pitt; Hubble Bubble, Duke of Newcastle; Boy George, George Townshend, Esq. ; Bumbo, Lord President Dundas; M‘Lurcher, The Highlanders ; ‘Sir Thomas, The King; Gilbert, Sir Gilbert Elliot, Bart.; Squire Geoffrey, The Pretender ; Small | Trash, Charles Hope Weir; Lick Pelf, Earl of Hopetoun; James, James Oswald, Esq. ; Suckjist, General Watson. * VOL. XXIII. PART III. 8B 608 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. siderable agitation in Edinburgh, and called forth several pamphlets, none of which, except that of Fercuson, are now deserving of attention.* Fereuson and the other members of the Select Society, which had been insti- tuted in 1754 for the promotion of philosophical discussion, but which was now in a declining state, in 1762 revived it in a different form, as a means of agitating the militia question, and keeping alive the flame of patriotic feeling. To this new society was given, at the suggestion of FeERGuson, the name of the “‘ Poker Club,” which numbered among its members nearly all the literati of Edinburgh and its neighbourhood.t This Club continued in existence till 1784, when from various causes it dwindled away, without achieving the object for which it was instituted,—viz., the extension of the Militia Bill to Scotland. It was not till 1793 that the Government agreed to place Scotland on the same footing as England in regard to an establishment so essential for the safety of the country, As the salaries allowed at this time to the Professors in the University of Edinburgh were very small, it was not uncommon for them to receive into their families the sons of noblemen and gentlemen while they attended the University. From the reputation which FEreuson had now obtained, he was, in 1763, en- trusted with the education of the Honourable Cuares and Rosert GREVILLE, the — sons of the Earl of Warwick, whose eldest son, Lord GREVILLE, had been educated under the care of Principal Rosertson. These young gentlemen remained with him for some years, and always retained a lively sense of the benefits they received under his care. The connection thus formed was of great service to FERGUSON, as it brought him more immediately to the notice of many persons of rank, and the fame he acquired shortly afterwards by his writings greatly ex- tended his influence among his contemporaries. Whilst these young noblemen were residing with him, Fercuson employed — me of his most promising students, who afterwards became a very distinguished _ nan, to aid him in superintending their studies. This was Joun, afterwards Sir 1 Joun M‘Puerson, Governor-General of India, who always acknowledged that it : 4 was to his intercourse and co-operation with Fercuson that he owed most of his knowledge and success in life. Fercuson also took a warm interest in James M‘PHERsON, the translator of Ossian, who, in 1760, had anonymously published his “ Fragments of Ancient — Poetry, collected in the Highlands of Scotland.” A curious incident which : occurred about this time, with reference to the Onsignic Poems, will be subse-_— quently noticed. * An account of the manner in which this singular work was written is given in Cori lea Diary, page 407; and an interesting letter of Hume, in which he avowed himself as its author, is” given in his Life, by J. H. Burton, vol, ii, page 88. t See Carlyle’s Diary, page 419. + Along with Patrick Lord Enrpanx, Principal Roszerrson, Dr Brain, and J. Home, Furaus MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 609 He continued Professor of Natural Philosophy for about five years, and con- ducted his class in a manner which gave universal satisfaction. By adapting his lectures to the capacities of his students, he contrived to render his subject more attractive than it had been hitherto considered, and he also published for the use of his class a short analysis of his Course. The study of Ethical and Political Philosophy, however, in which he had dis- tinguished himself as a young man, had always a greater attraction for FERcuson than the physical sciences, and on the transference of Professor BALrour, of Pilrig, to the Chair of the Law of Nature and Nations in 1764, Fereuson was elected his successor as Professor of Pneumatics and Moral Philosophy. About ten _ years before this, when Mr Ciecuorn, the predecessor of Mr BaLrour, was on his deathbed, he urged Ferauson to apply for this office, for which he conceived him to be particularly qualified. “ Mr CLEcHorN, after expressing his regret at not having influence with the patrons to secure such an arrangement, added, as Frrcuson sometimes related with much emotion, ‘I can only say of you as Hamlet did of Fortinbras, He has my dying voice.” * On being appointed to this Chair, which had long been the object of his am- bition, Fercuson applied himself to its duties with the greatest activity, and his lectures were attended not only by the regular students, but by the most dis- tinguished men of the country. Within little more than a year after his appointment he published his Zssay on the History of Civil Society,+ which contributed to raise him still more in the estimation of the public. This celebrated work, a portion of which had been written several years previously, had been, in 1759, submitted in manuscript to the critical opinion of Davip Hume, asa ‘ Treatise on Refinement.’ Hume gave it his approval, and stated that with some amendments it would make an admirable book, “ as it discovered an elegant and a singular genius.” The ‘Essay’ was again submitted in its finished state to Humr, who now | recommended Frreuson’s friends to prevail on him to suppress it, as likely to be injurious to his literary reputation. Hume had heard an opinion expressed, by the French philosophers HreLvetius and Saurin,{ with which he at the time concurred, that the fame of MonrsEsquizv’s ‘Esprit des Lois’ would not be lasting. As Frercuson’s Essay may be regarded to a certain extent as a com- _Mentary on Montesquieu, Hume, perhaps, hastily adopted the same opinion with regard to the work of his friend. When he found that the general opinion was favourable to the work, he heartily joined in the congratulations which Frreuson now received. son made zealous efforts to induce M‘Puerson to promote his further researches for the discovery of ‘ ancient Gaelic Poetry, and he took part in a meeting convened by Dr Brair, in 1760, to provide funds for the purpose of enabling M‘Puzrson to do so.— Browne's Hist. of the Highlands, vol.i. p. 43. * Encyc. Brit. Suppt. vol. iv. art. FEReuson. + Edinburgh, 1766. 8vo. +t Hume's Life, by J. H. Burtoy, vol. ii. p. 387. 610 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. Writing to the author, in February 1767, he says:—‘ Dear Ferauson,—I hap- pen’d yesterday to visit a person three hours after a copy of your Performance was open’d for the first time in London. It was by Lord Mansriztp. I accept the omen of its future success. He was extremely pleas’d with it; said it was per- fectly well wrote; assured me that he would not stop a moment till he had finished it, and recommended it strongly to the Perusal of the Archbishop of York who was present. Tho’ I set out with reluctance, I do not repent my journey. Direct to me at Miss Extiot’s, in Brewer’s Street. I have not seen SmitH; Judge of my hurry.”* In another letter to Ferauson he says, that he had ‘met with nobody that had read it who did not praise it. Lord MANSFIELD is very loud to that purpose in his Sunday Societies. I heard Lord CuesTerFietp and Lord LyTTLEeTon ex- press the same sentiment; and what is above all, CappELL, I am told, is already projecting a second edition of the same quarto size.” + Writing to Dr Biatr, Hume further remarks,—“I hear good things said of Frreuson’s book every day. Lord HoLpERNEss showed me a letter from the Archbishop of York, where his Grace says, that in many things it surpasses Montesquieu. My friend, Mr DopweELL, says, that it is an admirable book, elegantly wrote, and with great purity of language. Pray tell to Ferguson and to others all these things.” + Writing to Principal Ropertson from London, on the 19th March, Hume makes the following interesting statement :—‘‘ Fercuson’s book goes on here with great success. A few days ago I saw Mrs Montracur§ who has just finished it with great pleasure. I asked her, Whether she was satisfied with the style ? Whether F it did not savour somewhat of the country? ‘O yes,’ she said, ‘a good deal; it seems almost impossible that any one could write such a style except a Scotchman.’ ” || . Dr Beattie of Aberdeen, writing to the Poet Gray, on 30th March, states,— — “ A Professor at Edinburgh has published an Essay on the History of Civil Society, 5 but I have not seen it. Itis a fault common to almost all our Scottish authors that they are too metaphysical. I wish they would learn to speak more to the *. heart and less to the understanding; but alas, this is a talent which heaven only 4 can bestow; whereas the philosophical spirit (as we call it) is merely artificial, and level to the capacity of every man who has much patience, a little learning, and no taste.”’4] * His hurry was so great that he apparently had not time to sign the letter. It is inthe pos- session of D. Laine, Esq. “a + Encyce. Brit. Suppl. vol. iv. art. Ferguson. { Life of Hume, by Burton, vol. il. p. 386. § The elegant author of an Essay on the genius of SHAKESPEARE. || Stewart’s Works, vol. x. p. 2238. ~ -_ {| Gray’s Works, vol. ii. p. 296. —. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 611 Gray, in reply to Brarrisz, thus refers to the Essay of FErcuson :—“ I have read over (but too hastily) Mr Fercuson’s book. There are uncommon strains of eloquence in it ; and I was surprised to find not one single idiom of his country (I think) in the whole work. He has not the fawlt you mention ; his application to the heart is frequent, and often successful. His love of Monresaquieu and Tacitus has led him into a manner of writing too short winded and too senten- tious, which those great men, had they lived in better times and under a better government, would have avoided.”* Besides the interesting letters relating to the publication of this valuable work, which are to be found in the lives of Hume and Lord Kamgs, the following letter from the Baron D’Hotsacu to FERGUSON is very characteristic :— “ Sir,—I receiv’d with the deepest sense of gratitude the undeserv’d favour of your kind letter dated the 3d of March; tho’, your valuable work is not yet come to my hands according to the orders you were so good to give your Bookseller in London, I shall expect the favour you intended with thankfulness, and even with patience ; having had the good fortune of getting the perusal of a copy belonging to an acquaintance of mine. I found it answering completely to the high opinion _ I had conceived of your great abilities and ingenuity, by the testimonies given of you by Mr ANDREW Stewart, Colonel CLERK, and several other gentlemen from your country, with whom I have had the pleasure of conversing in this place. Tho’ you don’t seem to set a high value on theory, it must necessarily precede practice, and I think that given in your grand performance, by enlightening the human mind, may contribute to render their practice better; for I don’t despair of the perfectibility of mankind: I believe they have been mere children in matters the most important for them. I am of opinion that the greatest part of our distresses arise from our ignorance, and give me leave, Sir, to tell you sincerely, that I am persuaded that your valuable work is, and will be, very able to dispel the foggs that hang over our understandings. We are always indebted to great men for _ useful inventions, that are the fruits of their invention and theory. What they have found out with a great deal of trouble, becomes by and by popular; and by degrees truth, when become general, influences the general practice, even in spite of those who think it their interest to keep mankind in the dark. As to the virtues that preserve nations, or at least put off long their decline, I believe they - must be the effects of learning; when morality shall be clear’d, or rescued from the hands of those who have made it their study to render it obscure. I think every individual will be more virtuous, and even the powerful movers of men will find it their own interest in governing according to the rules of reason. I have the honour to be, with the highest consideration, Sir, yours, &c., “ Paris, 15th of June, 1767.+ ** DT’ HoLBAcH.” * Gray’s Works, vol. ii, p. 295. + MSS. University of Edinburgh, VOL. XXIII. PART III. 8c 612 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. The praise with which this Essay was received was well deserved, as it was the result of a great amount of research into the history of ancient and modern times, and of a remarkable knowledge of the springs of human action. The author considers the condition of man, under various forms of government, at different periods, and traces him through the several steps from his first rude efforts at civilization and arts, to a high state of politeness and refinement. The gradual efforts of the human mind, rising from the simple perceptions of sense to the heights of moral and political knowledge, are delineated in elegant and classical language. Dr Re had about two years previously published his ‘ En- quiry into the Human Mind;’ a work which was the first systematic attempt to carry out in the study of human nature the same plan of inductive investigation which had conducted NEwTon to the properties of light and to the law of gravita- tion. FERcusoN was the first to applaud Rern’s success, and his Essay on Civil Society is to be regarded as one of the earliest applications of the same method of research to the development of society and to national policy.* FERGUSON was of opinion that mankind should be studied in groups, and that all speculation as to their progress should relate to entire societies, and not to single individuals. In this point of view, he discusses the subjects of self-preservation, war and dissention, — | intellectual powers, moral sentiments, happiness, and national felicity. In the treatment of these important subjects, FeRcuson particularly endeavours to in- culcate that the happiness of man consists in the exercise of his faculties as a member of society, and with the view of promoting public utility ; that the power of states depends principally on the national character and public spirit, which are counteracted and sometimes annihilated amongst modern nations by selfishness and by the spirit of commerce. Adopting the views of Montesquieu, he ascribes to climate and situation a great influence on the literature, commerce, and policy of nations; and justly observes that man has always attained to the principal honours of his species under the temperate zone. He further considers the laws — which ought to regulate political establishments, and is of opinion that these, while they may vary according to the diversities of character and circumstances, — should not interfere with that firm and resolute spirit, with which the liberal — ; mind is always prepared to resist indignities, and that the power of restraint should be exercised in an inverse proportion to the general knowledge and virtue of a people. The enthusiasm of his own nature may be traced in his opposition to despotic governments and to political slavery. He viewed with solicitude the tendency to — despotism which characterised some of the military governments of the continent, and he expresses his fear of a renewal of those revolutions so frequently described, which out of the ruins of several nations form those colossal powers always fatal to liberty and to the wellbeing of man. * Stewart’s Works, x. p- 261. >. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 613 On the whole, this Essay must be regarded rather as an exposition of general principles, than an application of these principles to particular instances. It is defective in so far as the subject of religion, which in every age has had so con- siderable an influence on society, has been omitted. But, notwithstanding its defects, it must be admitted that the disquisitions which it embraces have as ‘much interest at the present time as they had one hundred years ago, because they trace the same affinities between man and man, generation and generation, im the delineation of common passions, affections, and desires. To say that human society is modified by our present circumstances, and affected by the pro- “gress of modern civilisation, is only to render it still more amenable to those laws of moral and intellectual symmetry which regulate the destinies of our species, -and which Frerecuson has with much ingenuity attempted to evolve. _ The fame which Frercuson had now acquired, and the connection he had formed with many persons of influence, led to suggestions of higher preferment. The following letter from his friend Colonel (afterwards General} CLERK, brother | _of Sir James CuerK of Pennicuik, shows that at this time he was regarded as a | suitable person to fill some political office. The Colonel had pressed him to dedi- “cate his Essay to Lord SHELBURNE, but this was declined, and the book appeared | without any dedication :— i” To Apam Frrcuson, Esq.—R. CLERK.” “ London, October 10th,1766. | 4 “1 have not wrote you for some time. I suppose that your book is printing. | Lord SHELBURNE told me one day that he supposed Governor JoHNson would not | perhaps return to West Florida, as he is coming home, and sayd, that he saw no Treason why he should not offer the government of it to you. I answered that I hould write to you of his kindness for you long before it should be an object of | deliberation, but that I thought you would be happier in your present situation, | and more independent, for the other was uncertain, though, in the common way of thinking in the world, it wasa great favour. Besides, I thought that you was Of more service to mankind where you was. He laughed at me. We shall have time to consider of this. However, it shows Lord SHELBURNE’s kindness for you, and good opinion of you. You asked my opinion upon a subject which I shall | give you when at leisure.— Yours affectionately.” In 1766, Frrcuson revisited Logierait, and delighted the villagers by his re- ci llections of themselves and their kindred, while they, in their turn, were no | less proud of the distinction attained by the son of their former pastor. This was also the year of his marriage to Miss KATHERINE BurNET of Aberdeenshire, the | amiable niece of Professor JoserH Buack. This union was one of unmingled hap- : piness to both, till it was broken by the death of Mrs Frrauson in 1795. Among the many allusions to FERGuson, contained in the Diary of his friend Dr Car.y_z, we learn that he and Fercuson had, about ten years before this. 614 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. paid, their addresses to the same lady, but without success. CarLyLe has not favoured us with the name of the lady, who must have possessed many attrac- — tions; but he remarks, that “ after having rejected rich and poor, young and old, to thenumber of half a score, she gave her hand, at forty-five, to the worst tem- pered and most foolish of all her lovers, who had a bare competency, and which, ~ added to her fortune, hardly made them independent. They led a miserable life, — and parted, soon after which he died, and she then lived respectably to an ad- a vanced age. ; In December 1766, FreRGuson received the honorary degree of LL.D. from the ; Senatus Academicus of the University of Edinburgh. / He also published, in the same year, a short syllabus of his lectures, entitled, Analysis of Pneumatics and Moral Philosophy. For the use of the Students in the College of Edinburgh. This work was afterwards enlarged, and published as the Institutes of Moral Philosophy,—a book which was found so useful, that it was translated into French, German, and Russian, and was made a text-book in — several foreign universities. It exhibited a clear outline of his Course. About the close of the year 1773, Fercuson was solicited to undertake the charge of the education of Cuar.es, Earl of Chesterfield (nephew of the celebrated Earl), by his guardians Lord Srannope,* Mr Hewirt, and Sir GzorGE SAVILLE. © The offer of this appointment was made by Lord Stanuyopre in the most compli- mentary terms on the recommendations of Dr Apam SmituH,}+ who endeavoured with great earnestness to induce Fercuson to accept of it. The young Earl was then in his nineteenth year; and it was proposed that he should travel on the Continent for several years, under the charge of FERGcuson, who by his care was expected to make up for the neglect of the Earl’s previous instructors. . At the present time it may seem strange that such a proposal should have been seriously entertained by any one holding a Professorship in the University ;_ o& * Editor of Dr Rozerr Simson’s posthumous works. + Writing to Smiru with reference to this appointment, Fercuson alludes to Brarrin’s cele- brated Essay on Truth, and the corpulence of Hung, in the following letter, Bzarriz’s “ Essay on the Nature and Immutability of Truth in opposition to Sophistry and Scepticism,” was so popular a” work, that in four years five large editions of it were sold off. It was first published in 1771; and the letter of Ferguson refers to the 3d edition, which appeared in 1773 :— “* Edin. Sept. 2d, 1773. ‘My Duar Sir,—I am told that Dr Beary, or his party, give out that he has not only refuted — but killed D. Hume. I should be very glad of the first, but sorry for the other; and I have the pleasure to inform you that he is in perfect good health; if he had been otherwise I should have certainly mentioned it in some of my letters. He had a cough, and lost flesh, soon after you went from home, which we did not know what to think of, but it turned out a mere cold, and it went off — without leaving any ill effects; he has still some less flesh than usual, which nobody regrets, but in point of health and spirits I never saw him better. You seemed to doubt whether I should not — write to Lord Stannore. I had inclination enough, but was not so decided as to send my letter to himself without putting it in your power to withhold it if proper, and therefore I stayed for a frank; what is disagreeable is, laying him under the obligation to make a ceremonious answer, and, if he be — gone, subjecting him to Continental postage, so you will judge. [ have not seen J. Fercuson, but — he must acquiesce.—I am, dear Sir, most affectionately yours, Apam FEreuson.” MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 615 but the emoluments from his Chair were at that time so small, and the terms offered by the Earl,—an allowance of L.400 a-year during the Earl’s minority, and an annuity of L.200 for life—were so tempting, that FERcuson, not without ‘some hesitation, undertook the responsibility. His reasons are fully given in the following letter to his friend ADAM SmiTH :— “ Hdinburgh, January 23d, 1774. “MY Duar Friznp,—It has given me great pleasure that you have avoided ‘doing anything that might tend to urge Lord Srannope farther than he has _ already gone in the proposal respecting Lord Cursterrietp. If I had known the 7 ‘part he took in that business, I should certainly at first have either frankly accepted of the offer made me, or declined it in a way that could not imply an ‘intention to raise the terms. This is certainly the only alternative that is now left me. I have revolved the subject all night and this morning, and the possi- bility of my becoming a burden on Lord Stannope’s family weighs much, but the ‘odds on Lord CHESTERFIELD’S life is so great as very much to reduce that consi- -deration. My place here, a few years ago, was worth about L.300 a-year, but | this and the preceding year it has fallen considerably short; and while the pre- en alarm of the scarcity of money, and the expense of education at Edinburgh, “continues, it may not rise again to its former value. To this I must add, that in ease of debility or old age, I shall probably be reduced to my salary, which is no ‘more than L.100a-year. For these reasons I think that I can fully justify myself % my family in accepting of L.200 a-year certain, with the privilege of choosing “my place and my occupations; and if my Lord CuEsTERFIELD’s guardians should | be of opinion that he ought, when he comes of age, not only to relieve my Lord | SS of his engagement, but likewise, in case I shall have acquitted myself f ithfully and properly, to make some such addition to my annuity as I men- * I shall then likewise think that I can justify my conduct to the world, st Biiject to correction. JI mean to read your letters, and this I am writing to one | or two of my friends. If they approve, it shall go to you; and if you agree with I e, be so good as intimate my resolution to the guardians of my Lord CHEsTErR- FIELD; or, if you have any objections of moment, delay it till I shall have heard from you. My own present feeling is, that I should be to blame if I omitted putting myself and family under the protection of persons so worthy and so respectable, when I have an opportunity of doing it without any real hazard to ‘|my interest But TI shall not enter on this subject, my heart, indeed, being too \ full, especially with respect to Lord Sranuore. Jam, &c., ApDAm FEeRguson.”* | Having, through ApAm Smiru, arranged satisfactorily the terms of his engage- * MSS. University of Edinburgh. VOL. XXIII. PART III. SD 616 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. ment with Lord CHESTERFIELD, FERGuson prepared for his travels on the Con- tinent. He accordingly, in February 1774, wrote to the Town-Council, as Patrons | of the University, requesting permission to name persons to teach his Classes — during the remainder of the session, viz. Dr James Linn, for the Natural Philosophy Class,* and Professor Bruce for that of Moral Philosophy. The Council, however, — refused to consent to this arrangement, and ordered that Ferauson eucnia teach — in person during the remainder of the session. Notwithstanding the refusal of the Town Council, Fercuson joined his pupil 4 in London at the close of that winter session of the University, in the belief that — the Provost and the greater part of the Council would be disposed to sanction his . absence for the subsequent session. When that session, however, commenced in the following October, the Council — appointed Professor BrucE to conduct the class of Moral Philosopy, and took steps to punish the contumacy of his colleague. Accordingly, in April 1775, they passed the following act :—‘‘ The Council, considering that upon the 16th of February 1774, they had refused an application of Mr Apam Fereuson, Professor of Pneumatics and Moral Philosophy in this city’s University, where he requested that he might be allowed to substitute proper persons in what remained of his business in the College that winter; and also considering, that notwithstanding thereof he has deserted his office, and come under engagements incompatible with his discharging the duties thereof; and the act of the 23d of May 1764, electing Mr Apam FeErcuson into the said office being read, the Council did, and hereby do, rescind the said act of Council, with all that has followed thereupon and declared the said office of Professor of Pneumatics and Moral Philosophy in the University of this city vacant.”+ Whatever may now be thought of the propriety of this step of Frreuson, still it had not been without precedent in the history of the University. His friends in the Senatus Academicus gave him their support, and he took measures vindicate his conduct, and to stay the somewhat arbitrary proceedings of the Town Council. The following notes for his defence, drawn up by his friend Dr Buair, are interesting, as showing his warm sympathy with his colleague :— “ Mr Fercuson, on his going away, engaged one of his colleagues, Mr Bruce — lately elected Professor of Logic, to supply his place in teaching this winter. “He wrote a letter to the Town Council, begging leave of absence for one | season, and proposing Mr Bruce to be allowed by the Council to teach in his place. This letter, indeed, was not delivered ; because the member of Council [o whom it was addressed, upon its being mentioned to him, advised, as more for — Mr FERGuson’s interest, that it should not be presented. * On the death of his relation Mr Russerx, Ferevson had undertaken the additional duty of teaching the Natural Philosophy class during sessions 1773, and 1774. } Dauzet’s Hist. of the University of Edin., vol. 11. p. 445. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 617 “ But by a minute of the Town Council in the beginning of winter, Mr Bruce was appointed to teach in Mr Frreuson’s. place. As this gave the sanction of the Council to the substitute whom Mr Frereuson proposed, it was considered by him and all his friends, as equivalent to giving him leave of absence for this session, and he had not the smallest apprehension of any intention to deprive him of his office, without at least giving him warning of his danger. “ On Wednesday last, 5th April, just upon the close of the session, the Town Council, upon a motion made by the Provost concerning the impropriety of pro- fessors in the College strolling through the country as governours, found the office of Professor of Moral Philosophy vacant, and were desired to have their thoughts on a proper person for filling it up ; and this without any summons given to Mr -Fereuson to attend, or any intimation whatever made to him or any of his friends. “The Professor of Moral Philosophy, by his Commission from the Town Council, holds his office ad vitam aut culpam must not the culpa, therefore, be first pro-: perly found, and the Professor summoned to see what he can say in his defence, before he can legally be deprived of his office ? “ The words of King James’ Charter respecting the power which he gives the _ Magistrates over the Professors are,—‘ cum potestate imponendi et removendi ipsos sicutt expediverit.” Do these words authorise every arbitrary and wanton exer- cise of power over the Professors? Or does the clause sicutc expediverit restrain it to what is profitable, and expedient, and fit ? “Do not the words in the charter which immediately precede these ‘ avisa- mento tamen ministrorum eorum,’ connect with the words before quoted, and was not the avisamentum necessary to have been taken on this occasion ? “ Mr Ferauson has not only for many years, ever since he was elected Pro- fessor, regularly discharged all the duties of his office, but in the session imme- | diately preceding this, when the Chair of Natural Philosophy became vacant in | the beginning of the session, taught both the classes of Natural and Moral Philosophy. « Sir JoHN PRINGLE, who was a predecessor of Mr Frrcuson’s in the same | Chair, went abroad when in that office as physician to the army, and for a year | (or for years, uncertain which) taught his class by a substitute without quarrel, | until he thought proper to demit. “‘ The Professor of Mathematics has been absent for two years, and taught his class by his son without quarrel. **« Dr DrumMonpD was elected two years ago by the Town Council, Professor of , the Theory of Medicine, and has never appeared to discharge any of the duties of his office, which for two sessions have been discharged by substitutes without quarrel, and no step taken for finding the office vacant. “ When Mr Ferrcuson. after being absent only for five months, is suddenly 618 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. deprived of his office, without any requisition given him to attend, without any communication previously made to the Principal, or any members of the Univer- sity, but the intention of depriving him kept profoundly secret till the moment of its execution, does not this plainly indicate that the Town Council did not seek — to bring back Mr Ferecuson to the discharge of his office, but had formed a design to turn him out with a view to bestow his office on another? and can such — violent and unjust proceedings towards an eminent Professor and a respectable University be warranted by law ?” * F These grounds of objection to the harsh measure of the Town Council were embodied by FERGusON, in an application to the Court of Session for a bill of suspension of the sentence of deprivation,} which had the desired effect of causing the Council to rescind their act, and restore the Professor to the peace- able enjoyment of his office. | The tour which Fercuson made with his pupil Lord CHEsTERFIELD through ~ France and other parts of the Continent, although it brought about this disagree- able quarrel with the Town Council, proved highly advantageous to his improve- ment. In a letter to his friend Apam Smiru, he thus describes the pleasure which his appointment afforded him. es Fee rarae ett ‘“* Geneva, June \st, 1774. - My Dear SmitH.—You see I have taken full benefit of the time you allowed me to form my opinion of this situation, and have the pleasure to inform you it is in most material circumstances very agreeable. I was received with great politeness, and continue to be treated with sufficient marks of regard. I have found-not only vivacity and parts as I was made to expect, but likewise good — dispositions and attachments, servants all of an old standing, and become friends _ without any improper influence or disorder that I have yet observed. I was + made to expect great jealousy of control, and set out with a resolution to ony no other than what a sense of my great regard might give me. It is likely that a person of a different character was expected, and the disappointment, I believall 3 has had a good effect. My journey hither furnished no adventures worth — relating. My Lord Stanyorr’s being at Paris gave me access, for the few days I ig stayed, to some very respectable and agreeable company, in which I was,ques- tioned concerning you, particularly by the Duchess D’ENvILLE, who complained — of your French, as she did of mine, but said that before you left Paris she — had the happiness to learn your language. I likewise met with your friend, Zz Count SarsFIELD, to whom I had great obligations, and if you write I beg that — you will thank him, &c. &e. ApaAM Fercuson.”$ Fercuson, and his pupil Lord CnrsterFIExp, after residing for some time at — Geneva, returned to London in the Spring of 1775, and the following interesting — dat * MSS. University, Edinburgh. + Ably drawn up by Inay Campsert, afterwards Lord President. . + Ibid ‘4 + . » x - MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 619 letter addressed to Dr CarLyLz, gives an account of their proceedings while on the Continent :— * Blackheath, April 29th, 1775. “My DEAR CaRLYLE,—In answer to the two or three letters which you have written to me, I can give you five or six which I had written in my own mind to you, before I received any of yours. The first was from Geneva, where, having had the advantage of lodging in CALVIN’s own house, and having access to some of his most secret manuscripts, I thought myself, without vanity, qualified to give you some light into the more intricate recesses of our Church. My second was from Ferney, the seat of that renowned and pious apostle, VoLTAIRE, who saluted me with a compliment on a gentleman of my family who had civilized the Russians.* I owned this relation, and at this and every successive visit encouraged every attempt at conversation—even jokes against Moses, Adam and Eve, and the rest of the Prophets—till I began to be considered as a person who, tho’ true to my own faith, had no ill humour to the freedom of fancy in others. As my own compliment had come all the way from Russia, 1 wished to know how some of my friends would fare, but I found the old man in a state of perfect indifference to all authors except two sorts—one, those who write Panegyrics, another who write Invectives on himself. There is a third kind, whose names he has been used to repeat, fifty or sixty years, without knowing anything of them—such as Locks, Boyz, Newton, &c. I forgot his competitors for fame, of whom he is always either silent, or speaks slightingly. The factis, that he reads little or none, his mind exists by reminiscence, and by doing over and over what it has been used to do. Dictates tales, dissertations, and tragedies; even the latter with all his elegance, tho’ not with his former force. His conversation is among the pleasantest I ever met with; he lets you forget the superiority which the public opinion gives him, which is indeed greater than what we conceive in this Island. But he is like to make me forget all the rest of my letters. The third was from the face of a snowy mountain in Savoye, higher than all the mountains of Scotland piled upon one another, and containing more eternal ice | in its recesses than is to be found in all Scotland in the hardest winter. The bottom of this ice is continually melting in the valleys, like the bottom of a roll of butter placed on end in a frying pan. It is perpetually creeping down from | the mountain, where fresh snows continually fall in snotters. Masses come down _| from the mountains sometimes, and shake all the rocks with a force that nothing | but an earthquake can imitate, and drive the air out of the narrow valleys with | the force of a hurricane, that roots up trees on the opposite hills. I wrote you _| this letter in the full belief that you are a great natural philosopher, and disposed * Fereuson’s ‘ Institutes of Moral Philosophy,’ having been translated into Russian, was | used as a Text-Book in the Russian universities. VOL. XXII. PART III. 8E 620 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. to believe every word I say. My fourth letter was written from the innermost parts of Swisserland, on a Sunday afternoon, when I saw the militia exercise. They have uniform clothes and accoutrements all at their own expense, which is not a great hardship, for it is their only public burden. They appear to me to be a very effective military establishment, and as they were the only body of — men I ever saw under arms on the true principle for which arms should be carried, I felt much secret emotion, and could have shed tears. But to conclude, my fifth and last letter was from the neighbourhood of this place, where everything, from a pair of snuffers to the Venus of Medicis, and the great — Diana of the Ephesians, is better provided than anywhere else; where every one is busily enjoying, and no one thinks whence it came nor how it is to be kept. I thought to have finished all my letters here; but as a frank will carry another sheet, I shall take room, at least, to sign my name. As I have already written you five letters, and this new sheet may pass for another, you will please to observe that you are, at least, four letters in my debt. Jam much obliged to you for your goodness to my wife and my bairns. [If I live to return to them, we shall not part so easily again. You may believe! was much surprised at the attempt of the Town Council to shut the door against me; but am obliged to them for opening it again. I may bea great loser; but the end for which I am persecuted cannot be gained while I have it in my option to return. I have been much obliged to the general voice that was raised in my favour, as well as to the ardent zeal of particular friends. I_tay Campprti has given me proofs of friendship which I can never forget. _PuLTENEy has behaved to me in everything, as he would have done at the beginning of the Poker Club. I have always been - an advocate for mankind, and am amore determined one than ever; the fools and knaves are no more than necessary to give others something to do. I saw J. Home in town yesterday morning, he goes on as usual. Mac* is listening to” the reports of his History. I do not live among readers, and am really ignorant of the general verdict. I have been living here above three weeks. A charming villa, in a magnificent scene, sed guis me sistat gelidis in montibus Pentland ; and H this I do not say on account of the hot weather, tho’ it has been for three dayay : the greatest I ever saw in this country. : ‘* Remember my blessing to Mrs CarLyLE and your young ones, of whose — thriving state 1am happy to hear. Tell Epgar, when you see him, that I have lately a letter from CLERK, and shall write to him—meaning Ep¢ar—soon. I am, dear CARLYLE, yours most affectionately, Apa Frereuson.”t The engagement which Frerauson had with Lord CumsTERFIELD terminated — rather abruptly shortly after this; and on returning to Edinburgh, he continued — his literary pursuits with renewed activity. 2 * James M‘Puurson (Ossian). + MSS. University, Edinburgh. — MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 621 The following interesting letter, addressed to ADAm SmitH at this time, has reference to the publication of the ‘ Inquiry into the Wealth of Nations ’— “ Edinburgh, April 18th, 1776. “« My DEAR Sir,—I have been for some time so busy reading you, and recom- mending and quoting you, to my students, that I have not had leisure to trouble you with letters. I suppose, however, that of all the opinions on which you have any curiosity, mine is among the least doubtful. You may believe, that on fur- ther acquaintance with your work my esteem is not a little increased. You are surely to reign alone on these subjects, to form the opinions, and I hope to govern at least the coming generations. I see no addition your work can receive except such little matters as may occur to yourself in subsequent editions. You are not to expect the run of a novel, nor even of a true history; but you may venture to assure your booksellers of a steady and continual sale, as long as people wish for information on these subjects. You have provoked, it is true, the church, the universities,* and the merchants, against all of whom I am willing to take your part; but you have likewise provoked the militia, and there I must be against you. ‘The gentlemen and peasants of this country do not need the authority of philosophers to make them supine and negligent of every resource they might have in themselves, in the case of certain extremities, of which the pressure, God knows, may be at no great distance. But of this more at Philippi. You have heard from Brack of our worthy friend D. Hume. If anything in such a case could be agreeable, the easy and pleasant state of his mind and spirits would be really so. I believe he will be prevailed on at last to get in motion, and to try the effect of Bath, or anything else Sir Jno. PRINGLE may recommend. I have said more on this subject to Mr Giezon, who, if you be found at London, will communicate to you. If not, | hope we shall soon meet here. And am, &c. ‘“¢ ADAM FERGUSON.” + For several years Ferauson had meditated the publication of a History of the Roman Republic; and he now began with greater perseverance to collect his materials for the projected work. He was also stimulated to bring his labours on this subject to completion, as Gibbon had, in 1776, begun the publication of his ‘ History of the Decline and Fall of the Roman Empire;’ and the following correspondence is valuable, as showing the friendly relations which existed _ between these eminent men :— ; ‘“« Edinburgh, March 19th, 1776. “ DEAR Sir, —I received, about eight days ago, after I had been reading your History, the copy which you have been so good as send me, and for which I now trouble you with my thanks. But even if [had not been thus called upon to offer you my respects, I could not have refrained from congratulating you on the * See ‘Wealth of Nations,’ book v, chap. i. part 3, art. 2. { The original letter is in the possession of the Rev. Mr Cunnineuam, Prestonpans. 622 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. merit, and undoubted success, of this valuable performance. The persons of this place whose judgment you will value most, agree in opinion, that you have made a great addition to the classical literature of England, and given us what Thucydides proposed leaving with his own countrymen, @ possession in perpetuity. Men of a certain modesty and merit always exceed the expectations of their friends; and it is with very great pleasure I tell you, that although you must have observed in me every mark of consideration and regard, that this is, never- theless, the case, I receive your instruction, and study your model, with great deference, and join with every one else in applauding the extent of your plan, in hands so well able to execute it. Some of your readers, I find, were impatient to get at the fifteenth chapter, and began at that place. I have not heard much of their criticism, but am told that many doubt of your orthodoxy. I wish to be always of the charitable side, while | own you have proved that the clearest stream may become foul when it comes to run over the muddy bottom of human ~~ nature. I have not stayed to make any particular remarks. If any should occur on the second reading, I shall not fail to lay in my claim to a more needed and more useful admonition from you, in case I ever produce anything that merits your attention. And am, with the greatest respect, dear Sir, your most obliged, and most humble servant, ApDAM FERGuson.” * GripBon’s reply to this letter was as follows :— * Bentick Street, April the 1st, 1776. “ Dear Sir,—I shall not pretend to deny that your approbation, and that of your literary friends at Edinburgh, has given me very great pleasure. I am not proud enough to be above vanity; and I have always looked up with the most sincere respect towards the northern part of our island, whither taste and phi- losophy seemed to have retired from the smoke and hurry of this immense capital. Your good opinion, in particular, I should wish to cultivate; and am pleased to understand from some passages in your letter that you are engaged in a work, which I am convinced will stand in the same proportion to my imperfect essay, as the Roman Republic may be considered to have done, if compared with the lower ages of the declining empire. * What an excellent work is that with which our common friend Mr Apam Smitu has enriched the public!—an extensive science in a single book, and the most profound ideas expressed in the most perspicuous language. He proposes visiting you very soon; and I find that he means to exert his most strenuous endeavours to persuade Mr Hume to return with him to town. Iam sorry to hear that the health and spirits of that truly great man are in a less favourable state than his friends could wish; and I am sure that you will join your efforts in convincing him of the benefits of exercise, dissipation, and change of air. * Gibbon’s Miscellaneous Works. By Lord Sheffield, vol. i. p. 499. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 628 « If I were not afraid of being too troublesome, I would desire you to inform me by a line of the particulars of his present condition, as well as of his inten- tions. Iam, dear Sir, your most faithful and obedient servant, EH. Grspon.’’* To this letter of Ginpon, FERGUSON returned the following answer :— “ Kdin., 18th April 1776. * Dear Str,—I should make some apology for not writing you sooner an answer to your obliging letter; but if you should honour me frequently with | such requests, you will find that, with very good intentions, I am a very dilatory _ _and irregular correspondent. I am sorry to tell you that our respectable friend, Mr Home, is still declining in his health; he is greatly emaciated, and loses | strength. He talks familiarly of his near prospect of dying. His mother, it seems, died under the same symptoms; and it appears so little necessary or proper to flatter him, that no one attempts it. I never observed his understanding more clear, or his humour more pleasant or lively. He has a great aversion to leaving the tranquillity of his own house, to go in search of health among inns and hostlers. And his friends here gave way to him for some time; but now think it necessary that he should make an effort to try what change of place and air, or anything else Sir Jonn PRINGLE may advise, can do for him. I left him this morning in the mind to comply in this article, and I hope that he will be prevailed on to set out in a few days. He is just now sixty-four. + * Dalzel’s Hist. of the University of Edinburgh, vol. i. p. 22. + It was principally at the desire of Fercuson that Davin Hume, a few days after the date of this letter, was induced to undertake a journey to London, to try the effect of change of air in Mitigating the severity of his disease. Frrcuson had also written to their mutual friend ApAm SmirH, giving him an account of Humn’s critical state at this time; and thus describes his condition — Davin, I am afraid, loses ground. He is cheerful, and in good spirits as usual; but I confess that my hopes from the effects of the turn of the season towards spring have very much abated.” Th consequence of this letter, SmirH and Joun Home set out from London to visit Hume at Edin- burgh, and accidentally met him at Morpeth on his way south. Home returned to London with Home, and preserved a diary of the journey, which has been printed in his life, by Macxenziz. In _ this diary is the following interesting entry :— i= “ Newcastle, Wednesday, 24th April. “Mr Hume not quite so well in the morning,—says that he had set out merely to please his friends ; that he would go on to please them; that Ferauson and Anprew Stuart (about whom we had been talking) were answerable for shortening his life one week a-piece: for, says he, you will allow Xenophon to be good authority ; and he lays it down, that suppose a man is dying, nobody has a right to kill him. He set out in this vein, and continued all the stage in his cheerful and talking humour. It was a fine day, and we went on to Durham—from that to Darlington, where we passed the night.” The illness of Hume, feelingly alluded to in the above letters of Gippon and Frreuson, was the cause of his death on the 25th of August in the same year. The following interesting letter (belonging to Mr Davin Laine), dated at Edinburgh, on the 9th of July before his decease, is very characteristic of the cheerfulness which he displayed up to his last moments. It is addressed to “ Joun Hume at Kilduff, near Haddington :”— “* My pear Joun,—lI offered to give you a letter along with you, informing you how I should be on Tuesday thereafter, viz., weaker and more infirm than when you saw me. This, indeed, would | have sav’d postage; and I can do no more at present than confirm the same truth, only that the matter seems now to proceed with an accelerated motion. I had yesterday a grand jury of phy- sicians who sat upon me, the Doctors Cunzen, Brack, and Home. ‘They all declare the opinion of VOL. XXIII. PART III. oF 624 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. “Tam very glad that the pleasure you give us recoils a little on yourself, through our feeble testimony. I have, as you suppose, been employed, at any intervals of leisure or rest I have had for some years, in taking notes or colle ing materials for a history of the destruction that broke down the Roman Republic, and ended in the establishment of Augustus and his immediate succes- sors. The compliment you are pleased to pay, I cannot accept of, even to my subject. Your subject now appears with advantages it was not supposed to have had, and I suspect that the magnificence of the mouldering ruin will appear more striking than the same building, when the view is perplexed with scaffold- ing, workmen, and disorderly lodgers, and the ear is stunned with the noise of destruction, and repairs, and the alarms of fire. The night which you begin to describe is solemn, and there are gleams of light superior to what is to be found in any other time. I comfort myself, that as my trade is the study of human nature, I could not fix on a more interesting source of it than the end of the Roman Republic. Whether my compilations should ever deserve the attention of any one beside myself, must remain to be determined after they are farther advanced. I take the liberty to trouble you with the enclosed for Mr Surru,* whose uncertain stay in London makes me at a loss how to direct for him. You have both such reason to be pleased with the world just now, that I hope you are pleased with each other. I am, with the greatest respect, dear Sir, your most obedient and humble servant, Apam FEreuson.” } — The progress of his labours, in collecting materials for the History of Rome was, however, interrupted by circumstances which turned his attention for a time to other inquiries. The Revolution in America had now drawn more general attention to the affairs which were passing on that great continent. It is unnecessary here to relate the different steps which led to the institution of the American Congress in 1773. It is sufficient to remark that the Congress had, in 1776, assumed the functions of sovereignty, and required all persons to abjure the British Govern- ment, and swear allegiance to the Congress itself. + the English physicians absurd and erroneous. They owna small tumour in my liver; but so sm mM and trivial, that it never could do me any material injury ; and they say that I might have li twenty years with it, and never have felt any inconvenience from it ; each of them has had patients who have had tumours in that part ten times larger without almost complaining for years together. They have thoroughly persuaded me to be of their opinion ; and, according to their united senti- ments, my distemper is now a hemorrhage as before, which is an illness that I had as lief dye of any other. The first part of the text being now discuss’d, we proceed to the second, viz., the which I leave to another opportunity. I send youa letter which my nephew opened by mis but finding, after he had read a few lines, that it was not meant for him, he proceeded no further. - Yours sincerely, Davin Hume.” In token of the long friendship which had existed between Hume and Fereuson, Home be- queathed him a legacy of L.200. * Dr Apa Smirtu. ‘t Gibbon’s Mise. Works. By Lord Sheffield, vol. ii. p. 501. { Frreuson was in the habit of discussing from time to time in his correspondence ¥ ' vith General Cuerx, Mr Jounstone (afterwards Sir Witt1am Puttenegy), and other friends, the variou us " ; —_ a hi i lies MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 625 The endeavours of the Americans to throw off the yoke of the British Govern- ment, and to assert their independence, were warmly defended by Dr Ricuarp Price, a dissenting clergyman in London, well known as the ingenious author of a ‘ Review of the Principal Question in Morals,’ and of some works relating to the theory of annuities, and the finances of the country. Price had, in 1775, published his ‘ Observations on the Nature of Civil Liberty, the Principles of Government, and the Justice and Policy of the War with America.’ This work took up the ground, that from the nature of civil liberty one country could have no power over the property or legislation of another which was'not incorporated with it by a just and adequate representation. It drew, in contrast to this country, the most flattering picture of America, where, as its author observes, “ we see a number of rising states, in the vigour of youth, inspired by the noblest of all sentiments, the passion for being free, and animated by piety—/Here we see an old state, great indeed, but inflated and irreligious, enervated by luxury, encumbered with debts, and hanging by a thread. Can any one look without pain to the issue? May we not expect. calamities that shall recover to reflection (perhaps to devotion) our libertines and atheists?’’* It concluded by prophesying ruin to England, through the addition of many millions to the national debt, unless some plan of reconciliation were speedily to be carried out. The publication of these views, which had the greater weight from their author's reputation as a sound financial writer, created an immense sensation both in England and America. In the course of a few months 60,000 copies of this book were disposed of; and while Prick was lauded by the friends of American free- dom, he was subjected to abuse and misrepresentation by those who supported measures of repression. Along with other writers of note, FERGUSON sympathised in his views with Government, and he communicated his objections to the pamphlet of Pricz in a letter to Mr Grey Cooper, one of the Secretaries of the Treasury. Mr Cooper was so much pleased with the observations of FERGuson, that he sent the following letter in acknowledgment :— *< Parliament Street, March 23, 1776. « Sir,—It was my duty to have thanked you sooner for your letter, and the very masterly and judicious paper which accompanied it, and which I have read political changes which were taking place at this period. The following extract from a letter addressed by General Crerx to him when he was at Geneva, in 1775, with Lord Cuesrerrizxp, is interesting in connection with recent events in America, The General says: ‘‘ When I saw you at Paris, you said that the American Colonies would end in military governments, You astonished me, and though I contradicted you, I had not patience to discuss it at that time, as it required the clearing up of so many points of which you and I had different opinions. However, I never doubted of its being a very disagreeable affair for us, and I think now that it has the appearance of being as bad as ever I imagined it.” —MSS. University of Edinburgh. * 4th ed. p. 98. 626 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. with great attention and pleasure. Dr Pricr’s pamphlet has been circulated with the same zeal that the Methodists circulate their manuals and practices of piety. Like base coin struck in times of disorder and confusion, it has had a value and a currency in the world which no other times could have given it. In that respect he deserves and demands what neither the weight of his arguments or the accuracy of his knowledge entitle him to expect—an answer from a good and able writer. I have ordered the observations to be printed by Mr Srranan, without its being known who is the author of them. Iam happy of having this opportunity of corresponding with Professor Fercuson ; and if zdem sentire de republica be the basis of friendship, I can very fairly pretend to yours; for I entirely concur with you in your noble sentiment, that the great object is to lay the demon of discord on both sides of the ocean; and I am, dear Sir, with great regard and esteem, your very faithful, humble servant, Grey Cooper.” * The reply of FeRGuson was accordingly published anonymously as Re- marks on a Pamphlet lately published by Dr Price, intitled Observations on Civil Liberty, &c.; and was acknowledged to be written with less invective and with more moderation than the publications previously issued on that side of the American question. FErcuson contended that, although the Colonies were by their charters and original compacts bound to submit to Parliamentary taxation, their altered circumstances now required a change of policy; and suggested that, — as Commissioners were to be appointed to settle all differences, negotiation should speedily take place. He was led, however, into various positions of a question- able nature, that weakened the effect which his conciliatory views would other-— wise have had upon the public mind. The British Government, which had at first treated the disputes in America with contempt, now began to take measures to vindicate their authority, and sent reinforcements to their army in that country. At the same time they appointed General Howe and his brother, Lord Howr, Commissioners, to settle all disputes in an amicable manner, as the feeling indicated in FERGuson’s pamphlet began to gain ground, that measures of conciliation should be attempted. : The Americans, however, flushed with several advantages gained over the 4 British troops and by the promise of assistance from France, were determined that no proposal for reconciliation should be entertained except upon the footing — of a treaty between two independent powers. 4 In 1778, Gzorce IIL, who throughout the whole of the American disputes had inflexibly opposed pacific measures, began, when too late, to yield to a iif more liberal policy. In that year two bills for effecting a reconciliation with — America were introduced into Parliament by Lord Nortu. Commissioners were > again to be sent over to treat with the Congress; and as it had been — * MSS. University of Edinburgh. 4 Ay j MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 627 that the powers of the former commissioners had been unduly restricted, the new commissioners were expressly authorised to discuss and settle every point in dispute between Great Britain and her colonies. The commissioners were the Earl of CARLIsLE; Mr EpEn, one of the Commis- sioners of Trade, and Under-Secretary to Lord SuFFoLK ; and GrorcGE JOHNSTONE, originally a captain in the navy, and at one time Governor of West Florida. With these three commissioners were conjoined Lord Hows, and his brother General Sir Witt1Am Howe, the members of the commission formerly appointed. The three newly appointed commissioners met at Portsmouth in April 1778, and proceeded to open their instructions, after which they embarked at Spithead on board the Trident, and arrived at Philadelphia, on the 5th of June 1778. The appointment of a Secretary was one of their first acts on reaching America. They had expected that Mr Henry Srracuey, the Secretary to the former com- missioners, would continue his services to the new commission, but they found that as he had already returned to England a new appointment was necessary. By virtue of their powers they elected Frercuson as their Secretary on the 6th of June, having special confidence in his ability for discharging the difficult and delicate matters intrusted to them. The commissioners, on proceeding to business, found many unforeseen circum- stances of discouragement in an undertaking which had never been very hopeful. In consequence of the expected war with France, orders had been sent from England in March for the British troops to evacuate Philadelphia and retire to New York, and these orders, of which no previous intimation had been made to the commissioners, were in process of execution when they landed. The treaty between the Colonies and France, concluded by FRANKLIN on the 6th of February, had also arrived in America, and was the occasion of great rejoicing to the American people. Nothing daunted by these untoward symptoms, the commissioners proceeded to open negotiations with General WasuineTon and the Congress. They inti- mated to the former that it was their intention to send FerGuson with despatches to Congress, and requested that he might receive the necessary passport for that purpose. They then drew up a letter to that body, in which they stated their powers, and expressed their desire to concur in every just arrangement for the cessation of hostilities and the restoration of free intercourse between Britain and the Colonies. This letter was ordered to be delivered to Congress by Fer- GUSON in person. On reaching the outposts of the American army with this letter, Frrauson was met by the officer commanding the piquets, who informed him that he ’ could not be allowed to proceed to headquarters without a passport, and that the application for this document previously made could not be granted until the pleasure of Congress was known. In order, however, that the object of the com- VOL. XXIII. PART III. 8 G 628 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. missioners might not suffer from unnecessary delay, it was determined to send the letter by the ordinary conveyance of the military posts, and it was accordingly delivered on the same day to the American piquets by Lord CatTucart. The commissioners, while awaiting with considerable anxiety the reply of Congress to their conciliatory letter, in which they proposed concessions of the most liberal nature, gave an account of their proceedings to Lord Grorcr Grr- MAIN, Secretary of State for the American Department. In this letter they plainly informed Government of the difficult position in which they were placed by the unfortunate order for the evacuation of Philadelphia. They also admitted that, in consequence of the state in which they found the country, they had offered terms to the Americans of a more liberal nature than their instructions allowed. These papers of the commissioners caused some dissatisfaction to the ministry, and were not at the time made public. The following letter, addressed by Sir WitL1am PuLreney (brother of GEorGE ~ JOHNSTONE) to FERGUSON, is interesting, as showing the state of feeling in England with reference to these proceedings of the commissioners :— “* London, 4th August 1778. Dear FEerGusoN,—I was much obliged to you for your letter of the 19th June, which arrived a fortnight ago, and was delivered by Mr Mackenzie. I enter entirely into your sentiments, and those of my brother, concerning the unfortunate order of the 24th March. I have done all I can in consequence of the despatches ~ I have received, and I have hopes that I have not laboured in vain. I have wrote a long letter to my brother, which will give you all the information that seems to me material. Firmness, wisdom, and exertion were never more wanted — for any country than now. I approve much of the letter to Government, and the letter to the Congress, and J believe they will meet with general approbation, though the ministers do not, I guess, relish the first, and neither have been given . to the public.—I am, dear Fercuson, most affectionately yours, “ WILLIAM PULTENEY. ‘{ think it right to suggest to your private ear an observation or two. 9 Though I am not surprised at the heat with which the commissioners took up : the concealment of the order and the order itself, yet I have my doubts whether it was prudent to let it transpire in America that they disapproved of the measure, or that they were ignorant of it till they arrived. I can see many advantages which might have resulted from their appearing satisfied, but none from the contrary. It is true, the misery of the departed inhabitants and their complaints A must have made it next to impossible for the commissioners not to vindicate themselves from having had any hand in the measure; but I think it right to — make this observation with a view to the future. — } MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 629 “ [ also think it would have been as well if the opinions of the commissioners had been communicated by letter to fewer persons here, because I think it was apiece of knowledge which ought to have been withheld from the American Deputies at Paris, and the Court of France. By communicating only to a few proper persons, every good end of this communication might, I think, have been attained without the disadvantages. I make this observation with a view to the future. «7 have some reason to think that Dr Franxutn has acted a double part. From some facts I have heard, I suspect, that notwithstanding his solemn pro- mise to me that no use should be made of what passed between us, he did from the first make use of it to urge the French Court to a further immediate treaty, to be put over and to be ratified before the commissioners should arrive, from a fear that the Americans would certainly accept our terms. The date of the last treaty will throw light upon this, when compared with the dates of my conver- sations with him. He was told of my arrival in Paris, and my errand on Thursday the 11th March. I saw him first on Saturday the 13th, and again on Sunday the 14th. The declaration of the French ambassador here was made on Friday the 12th. I saw him again on Sunday the 29th, and Monday the 30th, and for the last time on Saturday the 5th April. “Tam informed by ANDREW Stewart, that Da. Hume told him the follow- ing remarkable fact:—Hume went to visit Mr Oswatp of Dunnikier, then, I believe, a Lord of Trade, soon after Dr FRANKLIN came to England, which was ‘in 1758; and as he entered the room Dr FRANKLIN was coming out. Hume took notice that FRANKLIN, who was just gone, was a very ingenious man. OswaLp said he had been with him on business relating to the Colonies, and added these Temarkable words,—: He is certainly a man of genius; but if I am not much ‘mistaken in characters, that man has more of faction in his mind than is sufficient to embroil any country in the world.’ ” * _ The commissioners, after despatching the letters above referred to, and feeling ‘discouraged by the effects of the order for the evacuation of Philadelphia, re- embarked on board the vessel which had carried them to America, and set sail for New York. | While in that city they received a communication from Congress, intimating | that the only ground on which they could enter on a treaty would be an acknow- | ledgment of the independence of the States, and the withdrawal of the British | force from America. | The commissioners then issued a proclamation, calling upon all persons in | America to aid them in bringing the unhappy quarrel to a speedy termination. After some correspondence with the Congress relative to the performance of i * MSS, University, Edinburgh. 630 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. the stipulations contained in the convention of Saratoga, the commissioners found at length that the decision of the American disputes was to be left to the sword. They accordingly set sail from America about the end of November, and reached Plymouth on the 19th December 1778. The time for which they had been ap- © pointed expired on the Ist of June 1779, when they formally demitted office. They had the honour to receive a formal intimation of the royal approbation of their services, through Lord Grorce GERMAIN, who also expressed his regret that his correspondence with them, from which he had received so much infor- mation, had come to a conclusion. On his return to Edinburgh in 1779, Frercuson resumed the charge of his class, which had been conducted during his absence by Mr DuGaLp Stewart, and continued the preparation of his ‘Roman History.’ But before that work made its appearance, a serious illness befell its author. Towards the end of 1780, Frercuson had an attack of paralysis, probably occasioned by his free manner of — living. His recovery from this illness is still quoted by medical authors as one of - the most remarkable on record. Under the treatment of his distinguished relative Dr Buacx,* the symptoms — gradually became more favourable, and FErGuson was able, after some months, to undertake a journey to Bath. But he did not receive so much benefit from the use of the waters there as from the Pythagorean course of diet which he adopted, and which brought about a complete restoration. During the long period of thirty-six years that elapsed between his paralytic attack and his death, FrrGuson enjoyed remarkably good health. The occasional ailments he had seem to have been in no way connected with the disorder from which he made so wonderful a recovery. $ Of his many sympathising friends, no one was more sincere than Sir JoHN M‘PuERsoN, now about to proceed to India as a member of the Supreme Council. — The following letter expresses his feelings on this occasion :— . ; si st asec “ Kensington Gore, 13th January 1781. «¢ My Dear Frienp,—Though your illness has not filled me with despondency, — the first reports I had of it took away the happiness I should naturally have had in announcing to you my India appointment. The truth is, I was so little dis- posed to mention that event to any of my friends in Scotland—while I under- * The resemblance between this case and the attack which ultimately proved fatal to M. DE Saussure in 1799 rendered that eminent French philosopher anxious to learn the mode of treat- ment employed by Dr Buack, under which Frrevson had recovered. Dx Saussure’s physician, Dr Oprer, accordingly requested Dr Marcer, then a student at the University of Edinburgh, to obtam — from Dr Buack the desired information. Dr Marcet, accompanied by Professor Ducatp STEWART, waited on Dr Buacx, who, after a long and interesting conversation, delivered to him, in writing, _ for transmission to De Saussure, an account of the case and its treatment, which has been printed in the ‘ Medico-Chirurgical Transactions’ (vol. vil. p. 230), and is the more interesting, as it is, perhaps, the only existing memorial of the medical practice of that distinguished chemist. - a MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 631 stood you were in a situation not to communicate it to them first—that I never wrote to any person here of it; and the only correspondence I have had with your capital of late, is an answer which I thought myself obliged to send to the Duke of Gorpon. I have likewise written to the Duchess this night. “ Dr CaRrLyYLe’s letter of to-day has set my mind more at ease. You have naturally a good constitution; and I place every hope in your Highland stamina, your philosophy, and knowledge of nature. _ My friend CaruyLe has written me, with an interest in your welfare, and all that belongs to you, that adds, if possible, to my attachment to him. There is a circumstance which, with all his love for you and me, he is not fully known to—it is that I met you when I lost my father, and that your children and I are of but one family.—Farewell. May the power of affection be a power to give health and happiness! If you do not recover your health before I leave this country, I leave it with half my spring of satisfaction and soul—Yours ever, . JoHN M‘PHERSON.” * The intimate friendship between FERGuson and Sir JoHn M‘Puerson has already been mentioned. It began in 1763, when the Honourable CHAr.zs and RoserT GREVILLE, sons of the Earl of Warwick, were attending the University. Sir JouNn was son of the minister of Sleat, in Skye, and, when a student, had been private tutor to these young noblemen while they lived under Fercuson’s care. A circumstance occurred at that time (1765) which singularly enough gave rise to a controversy in 1781 between FEercuson and the celebrated Dr Prrcy, | Dean of Carlisle, afterwards Bishop of Dromore. The occasion of this contro- versy was the keen discussion regarding the authenticity of the poems of Ossian, ‘which the most eminent literary men were at this time engaged. As is well known, James M‘Puersoy, the translator of “ Ossian,” first published his “ Fragments of Ancient Poetry” in 1760, The work was anonymous; but as it professed to give a specimen of a great amount of ancient Celtic poetry | still existing in the mainland and isles of Scotland, it was received with the utmost enthusiasm. M‘PHERsoN made a tour to obtain further materials, after Which he gave to the world ‘Fingal,’ an ancient epic poem in six books; shortly afterwards followed by ‘ Temora,’ in eight books, with other poems | of ‘ Ossian.’ These productions caused an immense sensation, and were translated into several European languages, while M‘PHERson was hailed as the preserver of | these relics of ancient culture. A few years later, however, a suspicion began to be entertained that these poems were not authentic, and their genuineness |,became the subject of as warm a controversy as ever was waged in the annals | of literature. * MSS. University of Edinburgh. VOL. XXIIl. PART III. 8H 632 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. From James M‘Puerson’s friendship with Fereuson, Buarr, and Principal Rosertson, and from the high approval which these eminent men bestowed on — his labours, they were subjected along with M‘PHERson to various attacks and misrepresentations. In particular, Fercuson and Buair were, in 1781, charged by Dr Percy with having perpetrated upon him a practical joke relative to the poems of Ossian, when he visited Dr Buarr at Edinburgh in 1765. The immediate cause of this matter being revived so long after the time when it happened was the publication, in 1781, of ‘ An Enquiry into the Authenticity of the Poems ascribed to Ossian,’ by Witt1AmM Suaw, the author of various Gaelic works. . From the several letters written on the occasion, we learn that in October 1765 Dr Percy, when travelling in Scotland, had been for a few days the guest of Dr Buair, at the time an enthusiastic admirer of the Ossianic poems. Bua, according to Percy’s statement, carried him to FerRcuson’s house, that he might have an opportunity of hearing some of the original Gaelic of the poem of Fingal recited to him by a native of the Highlands. After the recitation took place, Dr Percy was called upon by BLair to mention in print this circumstance, as a proof of the genuineness of the Gaelic poetry of Scotland. The Doctor, who was then preparing for the press the second edition of his famous ‘ Reliques of English Poetry,’ accordingly inserted the following paragraph :— Concerning the bards of Gaul . . . no remains of their poetry are now extant; but as for those of Britain and Ireland, they have been more fortunate. . . . For an account of the Irish bards, the curious reader may consult O’Connor’s ‘ Disserta- tions on the History of Ireland,’ Dublin, 1776; Spencer’s ‘ View of the State of Ireland,’ &c. &c. But no pieces of their poetry have been translated, unless their claim may be allowed to those beautiful pieces of Erse poetry which were lately given to the world in an English dress by Mr M‘Puerson; several fragments of which the editor of this book has heard sung in the original language, and translated viva voce by a native of the Highlands, who had at the time no oppor. tunity of consulting Mr M‘Puerson’s book.’* In 1781, when the controversy regarding the genuineness of Ossian was at the Poems of Ossian.’ In this dissertation the author stated, that “ amidst the general wreck to which our traditions and poems have fallen for some time back, many pieces of Ossian are still remaining, and are found to correspond with the translation. A Highlander may perhaps be suspected of partiality in making this assertion ; but several gentlemen of candour from other countries have made * « Reliques,” 2d ed. ; vol. i. p. 45. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 633 the experiment, by causing such as had never had any access to see the transla- tion, to give the meaning of those pieces which they repeated ; and they declare that, on comparing the Gaelic and the English, they were entirely satisfied with the justness of the translation. Mr Percy, in his preface to ‘ Reliques of old English Poetry,’ tells, that he himself had often done this, and found the inter- pretation which he had got extempore correspond with the English translation, with which they had no access to be acquainted. Either these persons were ‘inspired, or Ossian’s Poems are authentic.”* In the bitter attack on M‘PHERson by Suaw, that writer refers to this state- ment of Smirx as follows ;—“< Mr Smira mentions Dr Prrcy’s ‘ Reliques of An- cient Poetry,’ in which he says the Doctor confesseth, that he himself heard pieces of it recited ; and being compared with the translation, exactly corresponded. Dr Percy does not understand a syllable of the Erse, and therefore could be no judge. The truth is, Dr Buatr and Professor Fercuson, when Dr PERcy was at Edinburgh, took care to introduce a young student from the Highlands, who repeated some verses, of which Professor FEReuson said, such and such sen- tences in Fingal were the translation. Mr Smitu, if he looks into the second and third editions of the ‘ Reliques,’ will find the observations there no longer; and that Dr PErcy, on reflection, had just reason to suspect that this young student had previously been taught the part he recited, and the lines might as readily be any common song as the original of Fingal ; for they knew it was impossible for an Englishman to detect it.” + This treatise gave FERGUSON some annoyance, and on the 21st of July 1781, _ he gave a formal denial to SHaw’s statement, in the public prints. In his advertisement, he quoted the passage from SHAw, and added, “ to pre- vent any inferences which might be drawn from my silence, I think it material to declare that the above passage, so far as it relates to me, is altogether false ; and that I never was present at the repetition of verses to Dr Percy by a young student from the Highlands.” When the pamphlet of SHaw and the advertisement. of Frrcuson were | brought under the notice of Dr Percy, he also wished to vindicate himself. _ Being, however, at a distance from his papers, he could only trust to his recollec- tion at the time, and wrote the following letter to De Buatr, enclosing the draft of an advertisement which he proposed to insert in the newspapers. “ Alnwick Castle, \7th August 1781. “ Dear Sir,—lI have at length gained a few moments of leisure, and will now endeavour to give you a full and true account of what may have occasioned the indecent liberty which has been taken with our names in the pamphlet you . Mention. “In autumn 1765 I spent a week with you most agreeably at Edinburgh, * Gallic Antiquities, p. 96. } Shaw’s Inquiry, p. 25 634 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. when, among other kind instances of your friendship, you introduced me to many worthy and ingenious men, and among the rest to Mr Professor Fercuson. I believe you mentioned to him, that I had entertained doubts of the authenticity of Ossian’s Poems, to remove which, he sent for a student that was a native of the Highlands, who told me he had heard lines of the original sung by the servants and country people there; and being asked if he could repeat any lines himself, he recited some passages in Earse, which being then translated to me, contained part of the description of Fingal’s Chariot (a part of the poem of which I had — entertained the greatest doubt). You then desired me, in a future edition of my ‘ Reliques of Ancient Poetry, &c., to testify what I had heard. To this I could not reasonably object, and accordingly, in my second edition, 1767, I related in a note what had occurred. Some years after, I became acquainted with a gentle- man, who is also intimately so with Mr M‘PurErson; but whose name I will now never mention, because I will not expose him to the inconvenience of being dragged before the public, as I have unfortunately been myself. This gentleman, in the most solemn manner, assured me (as one perfectly well informed) that the Poems of Ossian were almost all the productions of Mr M‘PuErson’s own genius ; that what was really original hardly exceeded in quantity our ballad of Chevy Chase. When I urged to him the transaction, at which I myself had been present, he assured me I had been imposed on, and advised me to suppress the note in my next edition, which accordingly I did in my third impression in 1775, ‘silently and quietly, never intending to enter at all into the controversy concerning the — genuineness of Ossian’s Poems, of which I was so incompetent a judge from my utter ignorance of the Earse language. ‘* From the positive repeated testimony above mentioned, together with some other observations, which I occasionally made myself, I own I began to believe them to be modern, but no less brilliant, proofs of Scottish genius, equally tending to do honour to the country that gave birth to their author. But as I never intended to publish one word on the subject, I fondly hoped I might have gone out of the world without having my name ever mentioned in the controversy. ‘* This, however, was unluckily not to be my fate, for Mr Saw having called on me just before he set out for the Highlands, when he assured me he would inquire with the utmost impartiality into the genuineness of the poetry attributed to Ossian. To him I unreservedly expressed my sentiments on that subject, without concealing anything I knew or believed concerning it, not intending to influence his opinion (which would have been absurd in one who knew so little © of the matter), but to spur his diligence to remove my objections. “T accordingly related the transaction at which I had been present, and the positive assurances I had since received from Mr M‘Puerson’s friend, that I must have been deceived. I also urged the suspicious circumstance of the wolf being — MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 635 never mentioned, or alluded to in these volumes. But this was not my own observation, it had before occurred to others;* only that I have occasionally in my researches found abundant proof that the wolf existed in England long after the Norman Conquest, and much later in Scotland; and in Anglo-Saxon poetry, I find such reference to the wolf, as would naturally happen in a country where it abounded, and was the only animal of terror. * Little did I imagine that this writer would quote my name at length, and assign whole sentences to me, without ever asking my consent, or allowing me to revise what I might have inaccurately let fall in conversation. Yet this he has done, and till I saw his pamphlet in print, I never knew or suspected that I was to make such a figure in it. «Thus the matter stands: I never in my life had the most distant suspicion that you were privy to the imposition, if it was one; and as for Mr IeRGuson, he may also have been free from any share of the deception, which may have origi- nated only from the reciter himself; but the lines were certainly recited in his presence, as I perfectly well remember, although he may have entirely forgot the occurrence. «Thus far I had written, before I saw the advertisement published by Mr Fereuson. As he hath committed himself to me, I am now compelled to give my testimony to the public. I perfectly well remember the transaction, though Mr FPerecuson may have forgot it ; we may both be sincere, though my recollection may, in this case, have been better than his. ‘“« As I have been unwillingly forced into this controversy, I shall desire to get out of it as soon as I can; and if not again attacked, it is not my intention to push the matter any farther. Upon the whole, I hope you will think the adver- tisement which follows is written with temper and decency, and such as may have a tendency to compose the dispute, so far as I am engaged in it. * As for yourself, my good friend, I hope it will make no breach in our friend- ship. I know your generous and enlarged heart can extend its regard to persons who may differ from you in points of the most sacred importance; éven (as our Liturgy expresses it) to all Jews, Turks, Infidels, and Heretics. And though, on this question, I may have the misfortune to be one of the /atter, yet I hope you will still allow me to subscribe myself, your ever affectionate friend, “ Tuomas Prrcy.” « P.S.—Pray write to me without delay, under cover, to his Grace the Duke of NoRTHUMBERLAND, at Alnwick Castle, in Northumberland. Mrs Percy joins with me in respects to you and Mrs Buarr. “ P.S.—I have some notion that the student who was produced to me by Mr ' FerGuson was (the Indian) Mr Macruerson, then (I believe) his pupil. Perhaps * See Johnson's Life by Boswe xt, vol. 11. page 303. VOL. XXIII. PART III. 8 1 636 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. this circumstance may serve and awaken the recollection of you both. Pray, in- form me how Mr or Dr Fereuson is usually styled. Is he called Mr or Dr? * Dr Percy, after some time had elapsed, began to think that he might possibly be mistaken on some points, and wrote the following letter to Dr Buatr, after con- sulting the memoranda which he had made, when on his visit to Scotland :— “* Alnwick Castle, September 10, 1781. “¢ DEAR S1rr,—You will excuse my having remained so long silent since I was — favoured with your last (inclosing the polite letter from Mr Professor Fercuson), when I inform you, that I delayed my answer till I could send into Northamp- tonshire, to have my papers there searched for minutes, which I remembered to have made, of some of the particulars that occurred to me during my short visit to Edinburgh in 1765 ; for, as I have the misfortune to differ about a matter of fact from a gentleman of so respectable a character as Mr Professor Fercuson, I thought it would not be treating him with due regard, to neglect any means of information that could contribute to settle the point between us. After all, I think he would have recollected the recital made to me by the student, as well as he has done some of the other circumstances, at least he would not have been so positive on this head as he appears to be in his letter, if you had reminded him that the student produced to me was his own pupil, Mr Macpuerson, who, I believe, then boarded with him in his house. “ T have, however, recovered a pocket-book, in which I had written down minutes at the time, expressing how and where I spent every day during my short stay at Edinburgh in 1765, where I was only five days; for I arrived there from Stirling on Tuesday, October 8th, and departed thence for England early on Monday morning, October 13th. “ Now by these minutes I find, that on Wednesday, October 9th, Mr Fercuson dined with me at your house; and on the Sunday following, October 13th, after evening service (wherein I well remember to have heard a most eloquent sermon from you), you caused me to drink tea with Mr FEercuson. « At his house it was, during that visit, that Mr Fercuson, I believe, gave me the written specimens of Earse poetry, which he mentions; but very certain it is, that then and there the student was produced to me, who recited viva voce the passages in Earse, as I have related in my former letter. To which I can now add this farther circumstance, that it being Sunday, he could not decently sing the tune, which I had a great curiosity to hear; and as I was obliged to leave Edinburgh early the next morning, and was not likely to see him again, he in the evening, as we were going away, took me aside, and in a low voice, hummed a few notes to me, as a specimen of the old Highland tune. “ This having been the case I can have made no jumble, as Mr Fereuson is pleased te suppose, nor could I possibly confound this with any other occurence, for * MSS, University of Edinburgh. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 637 I not only never heard the sound of the Highland language from any other persons but Mr Fercuson and his pupil, during my stay in Edinburgh; but I do not find that I was ever there in company with any other natives of the Highlands but themselves ; and for this I can appeal to my memorandum-book, which mentions persons (and there were many very worthy and ingenious ones) to whom you then introduced me; and also how and where I spent the whole five days among them. «JT might even proceed further and aver, that 1 never heard the recital of Earse poetry, either before or since, in my whole life; but that I now recollect, I once heard a short song or two from an old Highland soldier, who, travelling home to Scotland, begged at my door, but who I could not find knew anything of the subjects of Ossian’s Epic poetry. On his account I shall suppress the cir- cumstance of my never having heard the sound of Harse poetry, except at that single recital of the student, and, in my intended advertisement, which I shall also, in other respects, shorten as much as possible, for I heartily wish to rid my hands of this foolish business ; and unless Mr FERGuSON is more desirous of com- mitting his name in print than I am, our controversy shall soon be at an end ; for I shall only attribute to him a want of recollection, which surely might happen to the best memory at so great a distance of time. “ In truth, [ cannot but think Mr Fercuson’s name too respectable to deserve to be tacked to slight appeals and rejoinders in the common newspapers; and I must acknowledge I have some reverence for my own; and, therefore, when I have once supported my own veracity in as few words as possible, I hope the matter will drop, and neither of us be ever mentioned more on this subject. But if he still persists in denying publicly the existence of a recital, which at your desire I once mentioned in print (though, upon since reflecting how little I knew of the matter, and for other reasons assigned in my former letter, I have since suppressed it), 1 must then be compelled, much against my will, to produce at large necessary proofs in support of my own affirmation, which yet, I trust, I shall with temper and decency, and still continue to approve myself—Dear Sir, your affectionate friend and very faithful servant, ** Tos. PERCY.” «© P|S.—My Lord Ateernon Percy, who has been here since I wrote to you last, but who is since gone away, could not distinctly remember, as I had at first understood him, that Mr Ferauson was present when Mr MacpHerson repeated the Earse poetry to me; but he remembered that fact better than could have been expected, after six years’ interval, considering too, he was but a boy when it happened. ** The Duke desires his compliments, and pray deliver mine in the kindest _ manner to Mrs Buarir. I am now removing to Carlisle, where I hope to receive your next favour.” * * MSS., University of Edinburgh. 638 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. This letter was sent to Fercuson, who wrote the following answer to Dr BLAIR :— “ Edinburgh, 15th September, 1781. ‘¢ Dear Str,—I return Dr Percy’s letter of the 10th inst., on this disagreeable subject, of the recital of Erse poetry. Iam sorry he has had so much trouble; but cannot blame myself, as I am satisfied the trouble did not originate with me. I have in what is past, and shall continue in what may follow, to confine myself strictly to what is necessary in my own defence. I found it alledged in print, that Dr Percy had a cheat put upon him when at Edinburgh, to which I was accessory. In such cases it is often argued that until such or such assertions be contradicted they must be supposed true; and I did not choose that my character should rest upon that footing. J was free to deny any concurrence in the cheat, and even free to deny my having ever been present at any such scene as that in which the cheat was said to be practised. With respect to the last point, indeed, it may be thought that I could speak only negatively, and deny my having any memory of the transaction; and so it is no doubt of all past transactions. But there are circumstances which entitle a person to be more or less positive. In this case the cheat that is said to have been put upon Dr Percy could not be practised in my presence without my concurrence; and this every feeling of my — mind warrants me in denying in the most positive terms. As I never questioned the fidelity of Mr James M‘Puerson in his publications, I was none of those who busied themselves in finding evidence of it. It has happened to me, indeed, to mention a very few particulars of Erse poetry that were known to myself; and from my knowledge of which I had taken a very early impression of what mere — genius, without the aid of literature or foreign models, may do where the human ~ mind is free and the passions have scope in recital as well as in action. I imagined that evidence of its power might have been found in every country if collected before language and manners had so far changed as to obliterate or efface its productions. There being any remnants of it in the Highlands of Scot- — land, I imputed to the manners and language having changed less than they — have done elsewhere in equal periods of time. Whether or no this be honourable for the people I will not at present try to determine. It appeared to me matter of some curiosity in the history of mankind, but very little as matter of vanity — to one corner of this island, much less of jealousy to any other corner of it. The scraps | showed to Dr Percy had a reference to this idea, not the fidelity of Mr M‘Puersoy’s publications. And I was surprised to find myself, contrary to the ceneral tenor of my feelings, stated as a fabricator of evidence on that subject. I thought myself free to deny in very positive terms my having ever been present at the repetition of verses to Dr Percy by a student from the Highlands ; because I never knew a student who pretended to repeat any part or specimen of Ossian’s © heroic poetry. And the mention of Mr Joun M‘PHeErson’s name does not at al 2 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 639 alter the state of my recollection, for my memory of him is, among other parti- culars in which he is well known to me, that he never appeared to be in posses- sion of any part of Ossian’s poetry. I well remember that he was in some degree asinger, though | do not recollect any particular song but one, which, with a very few words of any meaning, consisted chiefly of a chorus or burden, not more significant than lullabolaro or derry down. If he repeated this or any other song that Dr Percy might hear the sound of the language, it is no wonder that I should forget that circumstance, especially as I have totally forgot Dr Prrcy’s visit with you at my house. But I hope that Dr Percy, now he has seen his minutes, will be sensible that a person may mistake what he thinks he remembers, as well as another may forget what has really passed. What he wrote from his memory ina former letter was, that I had sent for a student to your house. What he writes now is, that he came to the student at my house. Some other very easy mistake in the circumstances, if recollected, might acquit me entirely of any share in the imposition that was put upon Dr Percy. I confess that I was astonished at the ease with which this charge was stated against me in the pamphlet which has given rise to this correspondence. If I had the honour of being sufficiently known to Dr Percy, I should certainly request that he would compare proba- bilities, and consider which is most likely, that I should be accessory to a cheat, or that he should mistake some material circumstance of a story sixteen years old. Although I may not be entitled to employ this plea with Dr Percy, I cer- tainly must be allowed to submit it, in case I am under a necessity of more pub- lications, to persons to whom I am better known. There is certainly hitherto no reason to apprehend from me, as Dr Percy mentions, any improper desire of committing my name in print. J appeared, from necessity, to prevent inferences which might be drawn from my silence against me. Ido not pretend to set up my affirmation against that of any other person ; but as often as occasion is given to the same inference, I must appear again to the same purpose. Dr Percy is _ pleased to say in the letter which I return to you, that if I persist in denying publicly the existence of a recital, &c., he must then be compelled, much against his will, to produce at large necessary proofs in support of his own affirmation. Dr Percy will be pleased to observe, that I do not pretend to know what recitals he may have had made to him. I only deny that I ever was present at any impo- sition put upon Dr Percy by any pretended recital of Erse, and that I ever was present at any such recital. Iam persuaded that there are no proofs to the contrary, of which Dr Percy will not perceive the weakness the more he con- Siders them. At any rate, he must be sensible that if any such proofs are sup- _ posed, I cannot possibly consent to have them secreted. When they appear, I |, hope that I too shall proceed with temper and decency, although I have a little more at stake than Dr Percy, and have my integrity to defend against a most unexpected attack, which it seems is to be carried on against me in support of his VOL. XXIII. PART III. 8 Kk ? 640 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. accuracy in conversation.—I am, with much obligation for your good offices in this business, dear sir, your most affectionate humble servant, ** ADAM FERGUSON.” * This singular dispute about a matter of fact is only interesting from the emi- nence of the persons engaged in it; at the same time, the question of the genuine- ness of the Ossianic Poems given to the world by M‘PHErsov, is still an interest- ing subject of inquiry. The advertisement of Dr Percy, followed by a further statement of FERGuson, duly appeared in the public prints, after which the subject dropped. + There can be no doubt that Buatr, when writing his elegant dissertation on the Ossianic poetry, was an enthusiastic believer in the genuineness of these poems, and that the recitation of Gaelic poetry had taken place at his instigation. On the occasion of this correspondence, he seems to have shown a forgetfulness, or possibly a fear of admitting any statements tending to compromise his opinions, which caused some annoyance both to Dr Percy and Fereuson. From the letters above given, we learn that FERGUSON was a supporter of the genuineness of the Ossianic Poems, as he states that he “never questioned the fidelity of Mr James M‘Puerson in his publications.” { A correspondence with M‘Puerson relative to the publication of the original Gaelic of Ossian will be subsequently referred to. In 1782, Fercuson entered warmly into the scheme proposed by Principal RoseRTSson to institute in Edinburgh a society, similar to the foreign Academies, for the cultivation of every branch of science and literature. The immediate cause of this proposal was the application of the Society of Antiquaries to be in- corporated by Royal Charter. § The Senatus Academicus drew up a memorial to Government, proposing that, ‘instead of granting a charter to the Scots Antiquaries as a separate society, a society shall be established by a charter upon a more extensive plan, which may be denominated ‘The Royal Society of Scotland,’ and shall have for its object all the various departments of science, erudition, and belles lettres. That a certain number of persons, respectable for their rank, their standing, or their knowledge, shall be named by the Royal Charter, with powers to choose the original members of the Society, and to frame regulations for conducting their inquiries and pro- ceedings, and for the future election of members.” || * MSS. University of Edinburgh. t See Shaw’s ‘Inquiry’ for Fercuson’s vindication, Appendix, p. 82. i { See his letter to Mr M‘Kenzie, Secretary of the Highland Society, in that Society’s Report on the Poems of Ossian, Appendix, p. 62. 4 § Smellie’s Account of the Antiquarian Society of Edinburgh, p. 12. || It was due to the persevering efforts of Principal Rozprrtson that the Royal Society was instituted. After memorialising Government, about the end of the year 1782, to the effect above stated, the Records of the ule bear that the Principal, on the 10th of February 1783, ee MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 641 The members of the Philosophical Society, which had long existed in Edin- burgh, were at this time also anxious to be incorporated by Royal Charter. They, however, adopted the views of the Senatus Academicus, and entered heartily into the scheme for the establishment of a society, on the model of those at St Peters- burg and Berlin, for the purpose of cultivating every branch of science, erudition, and taste. The Royal Society was accordingly incorporated in June 1783. The following is a list of the noblemen and gentlemen named in its Charter :—Hrnry, Duke of Buccleuch; Lord President Dundas; JAmzEs Montcomery, Lord Chief-Baron of Exchequer ; Lord Justice-Clerk Miter; JoHn Grieve, Lord Provost; Sir ALEx- ANDER Dick; Sir GEeorcGE CLERK; Principal Ropertrson; Professors CULLEN, Monro, Buarr, WALKER, FERGUSON, DAuzeL, Ropison, MaconocuiE; ILay CAmp- BELL, Solicitor-General; J. Hunter Buarr, and ApAm Situ, Esqrs.; and J. Mactaurin, W. NarirRNE, and RopertT CULLEN, Advocates. Fereuson took a warm interest in the progress of the infant society, and was elected one of the Councillors. His only contribution, however, to its literary labours was a sketch of the Life of his relative, Dr JosepH Biack, published in 1801. them, that as they had the prospect of being in Edinburgh during the recess of Parliament, they had not returned any answer to the letters which the Principal had written to them, in obedience to the appointment of the meeting held on the second day of December last, but that they had laid the Memorial transmitted to them before His Majesty’s ministers, and had good reason to think that what was requested in the aforesaid Memorial would be granted. That in order to obtain this, it would be necessary that a petition from the Principal and Professors of the University, in respectful and general terms, should be addressed to His Majesty, which the Lord Advocate undertook to present.” «The Principal produced a scroll of such a petition, the tenor whereof follows :—‘ Unto the King’s most excellent Majesty, the Petition of the Principal and Professors of the University of Edin- burgh, humbly sheweth—That literary societies having been found by experience to contribute greatly towards promoting useful science and good taste m every country where they have been established, many persons eminent in rank, or in learning, have long expressed an earnest desire that a literary society, formed on the plan suited to the state of this part of the United Kingdom, might be instituted in Edinburgh, being fully persuaded that its labours and researches will be of considerable advantage to the nation. «‘ We, therefore, deeply sensible of your Majesty’s paternal attention to the welfare of your people in every instance, and confiding in the gracious disposition of a Sovereign who has distin- guished his reign by the splendour of his efforts to extend the knowledge of nature, and the liberality of his institutions for encouraging the arts of elegance, are humble suitors to your Majesty, that you may be graciously pleased to establish, by Charter, a literary society, to be denominated, The Royal Society of Edinburgh, for the advancement of learning and useful knowledge, empowering the Members of it to have, as the objects of their investigation and discussion, not only the Sciences of Mathematics, Natural Philosophy, Chemistry, Medicine, and Natural History, but those relating to Antiquities, Philology, and Literature. “ ¢ We humbly request that your Majesty will take our petition into your gracious consideration, and be pleased, as Founder and Patron, to give a beginning and form to this Royal Society, in that mode, and under those Regulations, which to your Royal wisdom shall seem most proper.’ «¢ Which being maturely considered by the Senatus Academicus, was approved of, and the Prin- cipal empowered to sign it in their name, and to transmit it to the Lord Advocate and Mr Hunter Buarr, with thanks for their obliging attention to the former application of the Senatus Academicus, and to request that they will still continue to attend to this business, until it be brought to the desired issue.” 642 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. In 1783 FErausoNn gave to the world his principal work, entitled The History of the Progress and Termination of the Roman Republic. This title strictly embraces the period between the end of the early Roman monarchy, and the elevation of Julius Czesar as the first Emperor of Rome. But, in order to bring the narrative nearer to the point at which Gipson begins his History of the Decline and Fall of the Roman Empire, Fercuson continues his work down to the death of Tiberius, the time when the succession to the throne began to be considered as hereditary. Fercuson has thus written the History of Rome from a.u.c. 240 to a.u.c. 790, a period of 550 years, and has given a lucid and compendious account of the leading events of that history. In preparing his work, he of course availed himself of the classical authors, and, amongst modern writers, he made use of the researches of GuazEsst and VesTRINI, the Annals of Picurus, and the celebrated Essay of MonTEsQur£v, on the -Grandeur and Decline of the Roman People. His aim was rather to give in a connected and elegant form a narrative of the great facts of Roman history, than to indulge in discussions of the many matters of controversy which so extensive a subject necessarily involves. He does not enter upon the story of the origin of Rome, or even of the rise of the Republican form of government, but leans to the view previously held by DE Bzaurort, and more fully developed by Sir GeorcE CorNEWaLL Lewis, that the early history of Rome was so involved in fable that no profit could result from such inguiries. In this way Fercuson’s History, ably and elegantly as it was written, does not afford the rich fund of information to be obtained from the more recent works of NiepuHR and Mommsen, who, with infinite skill, have elucidated the early history of Rome by a critical examination of the remains of the classical authors ; and who, by the comparison of their fragmentary details, by the examination of institutions existing in later and more historical times, and by the study of. analo- gous phenomena among other nations, have endeavoured to place that history on a more trustworthy basis. Frrcuson was led to undertake this work from a conviction that the history — of the Roman people, during the period of their greatness, was a practical illustra- tion of those ethical and political doctrines which were the object of his peculiar — study; and he has remarked, that to know the history of Rome well was to — know mankind, and to have seen our species under the fairest aspect of great ability, integrity, and courage. He regarded the great Roman statesmen and warriors during the Republican period, as exhibiting the utmost range of the — human powers; while he reckoned the steps, by which the republican form of government was exchanged for despotism, as well deserving the careful attention of the student of political history and human nature. 7 % As was before remarked, the military experience which he had seen in his youth — MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 6435 was of material service to him in writing his vivid account of the wars in which the Roman people were so constantly engaged; and his knowledge of human nature enabled him faithfully to portray the characters of the principal Roman leaders, and to test them by the laws of a high morality. The many editions of this work which have been published show the estima- tion in which it has been regarded by the literary world.* The errors and omissions of the first edition were subsequently carefully corrected; and Frr- Guson himself, ten years after it first appeared, visited Italy to inspect the scenes of the more important events which his work describes. In 1785, Fercuson, now in his sixty-second year, finding the anxiety at- tendant upon his professorial labours pressing upon his health and _ spirits, resigned the Professorship of Moral Philosophy. That he might retain his salary, he was, according to the custom of the Town Council, appointed to the Chair of Mathematics in conjunction with a junior professor, Mr PLayratr, while Pro- fessor DuGALD STEWART was transferred from the Chair of Mathematics to that of Moral Philosophy. Srewakrt had been the pupil of Fercuson, and owed to his instructions the development of that taste for metaphysical speculation, by which in his lectures and writings he shed so much lustre on the University. As Professor of Moral Philosophy, Fercuson amply sustained the reputation of the institution with which he was so long connected. He was manly and impressive as a lecturer, but at the same time persuasive and elegant. In one particular his mode of teaching was peculiar, and not easily imitated. As he _ had delineated the general plan of his course in his ‘ Institutes of Moral Philo- sophy, he had for many years no written lectures, but trusted to his mastery of the subject for the expression of his ideas on the spur of the moment. When his health gave way in 1781, however, he found it necessary to write out his course, which, during the leisure of his retirement, he corrected for the press and published in 1792. Amongst the many proofs he received of the value of his professorial instruc- tions, none were more agreeable to him than the attentions shown by Sir Jonn M‘Puerson, who had now attained the high position of Governor-General of India. The following letter, which enclosed a munificent gift, is no less creditable to his kindness of heart than to the merits of the veteran Professor :— “ 12th January 1786. ** My pEAR F'r1enp,— When I was but a Company’s writer in the Carnatic, I remember I sent you a small bill, which you told me you accepted with pleasure, as it came from me, and you bought French cloth with it, being then on a visit * It was translated into French by De Meunier and Gibelin in 1784, also into German and Italian. VOL. XXIII. PART III. 8 L 644 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. to Paris. I have been near a year Governor-General of India, and four years a Supreme Counsellor, and I have sent you nothing but a little madeira, yet you are the friend next to my heart, and your interests are dearer tome than my own, as they involve the concerns of a numerous family depending on the state of your health. If 1 have been thus inattentive to your situation, you are your- self the cause, for to you am I indebted for those rules of conduct in my public trusts, which have bound my generosity to your or to my own private interests within narrow limits. You have been occasionally informed of the line pursued by me since I left Europe, the situation in which I found affairs, my labours to retrieve them, and the disbursement of my own income in various attentions to — those who were recommended to me, and whom I could not oblige at the public expense. If the line I have pursued was not necessary from its satisfaction to my own mind, the example of it was a sine qua non to enable me, when affairs devolved upon me, to reduce the expenses of this colony about a million sterling — per annum, and to silence the cries of thousands who might otherwise have just grounds for charging me with partiality and selfishness. ‘¢ | have followed your maxims in the practice of affairs,—upon perhaps the greatest theatre of affairs, if the greatness of affairs is founded in the numbers of men, and the extent of their interests—the concerns to be extricated or forfeited —the wealth that might have been acquired, and the consequences that might ensue to individuals, tribes, and nations. ‘The events that hinged upon my ideas and conduct four years ago were more important than those which I can now influence, though I stand at the head and in absolute charge of all our affairs in India. ‘It is, my friend, one-and-twenty years since I began under you the rudi- | ments of these affairs; and as there is no period of my life that I look to with such a conscious sensation of joy and pride, as that which I passed with you and our noble pupils, so to you is due the account which I can in truth give, and which I am bound to notice to you: It must be interesting to you, and it is for the benefit of our native school, and perhaps of society in general, that I should enable you to know the result, that you might hereafter be the more confirmed ~ in your system. | « T have amply experienced the truth of three of your favourite positions :— “ 1st. That the pursuits of an active mind are its greatest happiness, when they are directed to good objects, which unite our own happiness with that of our friends and the general advantage of society. Hence the first success in the Carnatic; the subsequent efforts in London; the return to India; the visit to Europe in ’77; the intercourse with men in business; the friendships of the ministers ; Lord N.’s * selection of me for my trust in 1778. : «« 2d. I have likewise experienced, that he who has not been in contact with * Lord Norru. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 645 his fellow creatures knows but half of the human heart. But such are the neces- sary taxes of occupation, of business, and perhaps of life. “ 3d. That all that rests with us individually, is to act our own parts to the best of our ability, and to endeavour to do good for its own sake, independent of events, disappointments, or sufferings. “< Under these impressions I have acted and I now act; and if the India Com- pany, the ministers, and the Legislature extend their views to the necessity of affairs, and to the future prosperity of Britain and India, as they stand united ; and if they will adopt the plans I have laid before them, I am steady in believing that the greatest benefits to Britain from Thule to the Land’s End, and to Asia, from Cape Comorin to Tartary, may flow from the practical operation of the commercial and political systems I have opened for the adoption of the empire. _ The outlines are clear and strong, as well as the ground of the operations them- _ selves. Look on the map and see the field of empire marked by the Thibet Hills from Tartary to Chitagong, by the Ganges from its source to its embrace of the ocean, and by opposite chains of hills and of wild tribes from Balasore to ~ the Jumna. | «This empire asks nothing from Britain but protection and some staples ; and it sends to Europe every year about twenty fine Indiamen, loaded with the | industry and the productions of its extraordinary soil. Hach ship is worth _1.100,000, one with another. The improvements made in navigation, and the _ knowledge of climates, and the care of health, enable Britain to carry on this | trade, if she adopted a liberal plan for it, on a footing to employ a fleet in going | and returning, including China and the coasts of the great Peninsula, about seventy | - ships—now equal in size to 50-gun ships, why not to 64 and 74 ? Commerce would then create a navy for Britain, at least such as would command the Indian seas ; and as in King William’s days, the first great operations of our state began ey converting our debts into funds or property by regular payments of the interest ; so we may here employ the present interest of our debts to be a | Sedinm for remitting the whole to Britain in an additional investment of goods. | Upon this system, which necessity forced us to begin here in 1782, by pro- viding what was called a subscription investment, and drawing bills upon the proceeds of the goods, India was saved from the jaws of war and the chains of a little monopolist policy, which forced all remittances to Britain through the | channels of foreign trade, and which paid the tribute of custom to Lisbon and | Copenhagen, at a rate that has turned the exchange from Copenhagen against | England to about 18 per cent. But my system does more; it pours in upon Britain more streams of friend- '} Ship and of aid, which every officer, civil and military, in these colonies wishes to send partially to his relations, and which, in the general remittance and receipt. \ive the British heart on this and your side of the ocean its most delightful 646 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. exercises, and which gladden every village and place, from the cottages of the Isle of Skye to the palaces of London. “T think a still greater scene opens by this commercial intercourse, if our rivals in Europe wished but for a proper share in it. It would embrace much of the repose of the universe, the happy communications of all the inhabitants of the globe from the sources of the Mississippi to those of the Ganges, and from west to east, till the east and the west are united. “ T have at this moment at Calcutta ambassadors from Tidore, in the eastern seas, from Thibet, from all the states of India, and from Timur Shaw, who is crossing the Attock ; and as Manilla is opening her trade, I hope to hear direct from Lima before I leave India, and to make the Incas of Peru acquainted with the Brahmin Rajahs on the banks of the Ganges. ‘“‘ Curious are, besides, the treasures in literature and the oblivious history of nations that are dawning upon us from the researches of Sir WiLu1am Jones and others, in Shanscrit, Arabic, and Persian. Even Anacreon and Euclid’s best and happiest labours may have been long asleep in the translations of this country. And what seems to complete our prospect of elegant and useful information, is that the present Governor of Chinsura, who was for seven vears in Japan, has brought in the wonders of that country. Their Encyclopeedia is in his hands, and in some of the arts of life and of government, those islanders of Asia, those Anglo-Asiaticks, have left all other nations far behind. ‘“¢ While devoting all my moments that are my own to such general consider- ations, I have perused, and am perusing again, your story of the Roman State and their rule of India—Thanks ! thanks! my dear friend, but one ambition remains —it is to converse with you at your town over these affairs. Has life in reserve for us this happiness? or is our expectation of it enough? May I be able to meet you there worthy in every respect of your esteem as of your affection,—and is it possible to go through the remaining acts of my service here with progressive dignity and success. Hitherto all isas you could wish. But all may not be at the farm as you wish.* I know the feu-duty embarrasses you, and the dignitas - without the ofiwm may be there. Receive, then, the inclosed bill upon my ’ masters, the India Company. Let the amount of it be sunk to discharge the annual feu-duty of the farm during your life, Mrs FErauson’s, and the lives of all — your children and their descendants. It will be a future business to buy off the 4 feu-duty altogether; at present I can send you no more. And should fate have de- 4 prived me of the future happiness of knowing that you can be conscious of this little attention, those nearest and dearest to youl must consider as what remains to me of you. To them I address this letter; also, in such event, JoHN FLercaenl Home, M‘Puerson. FeErcuson will keep a room for me, or any remembrance - * Ferreuson, for several years after his marriage, had cultivated the farm of Bankhead, near Currie, at a considerable sacrifice of his private means. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 647 the farm-house. Tell him (for I will not admit the idea that you have left us) that he is my son. His father was more than the father of your ever affec- tionate, * Joun MacPHerson. “ Mind me to Drs Buair, Homes, Ropertson, CARLYLE, BLAck, &c. &e.”’ About the time of the resignation of his University duties, Fercuson resided in what was then a southern suburb of Edinburgh, named “ the Sciennes.” This suburb, which now forms part of the city, was then considered so far distant that his friends used to call his house “ Kamtschatka ;” and there, in the beginning of 1787, an interesting occurrence took place, which shows the pleasure he always took in the recognition of youthful genius. Burns had come to Edinburgh at the close of the previous year, to super- intend the printing of the second edition of his poems. His arrival in the capital had produced a sensation, and he received great attention from many of the literati of the time. FERGuson’s colleagues, Professors DauzeL and STEWaRT, have recorded the feelings of interest which the arrival of Burns excited in the literary society of Edinburgh. Being desirous to converse with so remarkable a man, FERGusoN invited a small party to meet him at his house, amongst whom were Drs Hurton and Buackx, Mr DuGALp Stewart, and the famous aeronaut Lunarpi. Trifling as this incident may seem, it afforded to Sir WaLTER Scor7, then a boy and companion of Fercuson’s sons, the only opportunity he ever had of meeting with Burns. On that occasion also he displayed that wonderful ac- quaintance with poetry for which he afterwards was so remarkable. In a letter to LockHart, ScorT thus describes this interesting meeting :—<“ I saw him one day at the late venerable Professor FERGuson’s, where there were several gentlemen of literary reputation, among whom I remember the cele- brated Mr DucaLp Stewart. Of course, we youngsters sate silent, looked and listened. The only thing I remember, which was remarkable in Burns’ manner, was an effect produced upon him by a print of BunBury’s representing a soldier | lying dead upon the snow, his dog sitting in misery on the one side, on the other | his widow, with a child in her arms. These lines were written beneath :— “ Cold on Canadian hills, or Minden’s Plain, Perhaps that parent wept her soldier slain ; Bent o’er her babe, her eye dissolved in dew, The big drops mingling with the milk he drew, Gave the sad presage of his future years, The child of misery baptised in tears.” “ Burns seemed much affected by the print or rather the ideas which it suggested | tohis mind. He actually shed tears. He asked whose the lines were, and it chanced that nobody but myself remembered that they occur in a half-forgotten | poem of Lancuorne’s, called by the unpromising title of “The Justice of the Peace ;”’ I whispered my information to a friend present, who mentioned it to VOL. XXIII. PART III. Su 648 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. Burns, who rewarded me with a look and a word, which, though of mere civility, — I then received and still recollect with very great pleasure.” * In 1792, Fercuson published his lectures, under the title of Principles of | Moral and Political Science, being chiefly a Retrospect of Lectures delivered in the College of Edinburgh. This work was the first extensive contribution to mental — philosophy which emanated from the University of Edinburgh. Hurcuerson in the University of Glasgow, Reip and Bearrie in that of Aberdeen, had previously laid the foundation of the Scottish school; and FERGuson has the merit of having introduced its doctrines into a new sphere, where they were destined to attain a further development. He also had the advantage of bringing to his specula- - tions a greater amount of historical knowledge, and a much more extended acquaintance with human character. He divides his subject into two parts, the jist of which states historically the most general appearances in the nature and state of man; embracing his descrip-_ tion and place in the scale of being, mind or the characteristics of intelligence, * Life of Scort, vol. i. p. 136. © . Some interesting reminiscences of Fercuson’s son, Sir Apam, who was the life-long friend of Scort, printed in Chambers’s Journal, No. 60, 1855, supply one or two particulars which Scorr’s modesty suppressed. ‘‘ The large black eyes of Burns, which literally glowed when he spoke with feeling or interest, overflowed as he read the above lines, and he turned with an agitated voice to the company, asking if any one knew who wrote them. The philosophers sat mute ; and after a interval, young WatTer said half aloud and very carelessly, ‘ The’re written by one Lancuorne,’ Burns caught the response, and seeming, both surprised and amused that a boy should knoy what all those eminent men were ignorant of, he said to Scorr, ‘ You’ll be a man yet, sir.’ Rather oddly, we have found on an inspection of the print, that the name ‘ LancHorne’ is inscribed below the lines, though in so small a character, that where the picture hung on a wall, it might well have escaped the notice both of Burns and Scort.” In the same interesting article, an amusing anecdote is recorded of Principal Rosen when dining one day at Fercuson’s house :— «« Ferguson, while devotedly attached to Dr Rozgertson, and a great admirer of his works, found reason to complain of the manner in which he conducted himself in private society, particu- larly at dinner parties. It was the worthy Principal’s custom, as soon as the cloth had been re- moved, to settle himself in his chair, and throwing out a subject, commence lecturing upon it to the destruction of conversation, and the no small weariness of the company. By way of giving him a check, Dr Frereuson took his friend Dr Cartyxe of Inveresk into counsel ; and it was speedily arranged between them that, immediately after dinner, Dr Cartyzte should anticipate the ordinary lecture of Dr Rosertson, by commencing a long tirade, in an enthusiastic manner, on the virtues of an article then in the course of being puffed in the newspaper advertisements, namely, patent mustard! FERGuson, in the meantime, had a private conversation with the Principal, in which he took occasion to remark, that he had lately begun to fear there was something wrong with CarLYLES mind ; he was getting so addicted to speak loudly in praise of trivial things,—for example, he was — unable for the present to converse about anything but patent mustard! Roserrson expressed his concern for the case, but hoped it was only a passing whim. The dinner party accordingly assembled at Dr Fereuson’s, and Ropertson was about to commence as nen with one of his long-winded for- ; mal palavers, when all at once Dr Cartye broke in,—‘ This was,’ he said, ‘ an age most notable for its inventions and discoveries. Human ingenuity was exerted on the noblest and the meanest things, and often with the most admirable effects on the meanest. There was, for instance, an article — of a humble kind which had lately been wonderfully improved by a particular mode of preparation, si and he for his part was inclined to say, that patent mustard was the thing above all others which gave a distinguishing glory to this age. In the first place,’—it is needless, however, to pursue discourse further ; suffice it, that Dr Roperrson sat paralysed, and could not afterwards, during t whole night, muster power or spirits to utter more than an occasional sentence.” MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 649 and the principles of his progressive nature. Having laid this foundation of his course in history, FeErGuson proceeds in the second part of his work, to examine the specific good incident to human nature, and to treat of moral law or the distinction of good and evil, and its systematic applications, which are explained under the heads of Ethics, Jurisprudence, and Politics. In the treatment of the metaphysical part of his course, Fercuson declares himself an enemy to the scepticism of Hume, and opposed to the doctrine of ideas as maintained by Hospss, Lockr, and BrrKkeLey, but he coincides in his views with the metaphysical doctrines of ARISTOTLE as revived by Rein. He is also a valuable exponent of the inductive method of observation as applied to the mind, so well laid down by Ret, and consistently recommends the employment of this mode of procedure in all investigations. His metaphysical discussions are also valuable, as showing clearly the characteristics of mental as distinguished from material action, and establishing those primary truths on which all useful philo- sophical speculation is founded. In his moral system, FERGuson was a philosopher of the Stoic school. He avoided, however, the exaggerations and paradoxes into which many of its disciples have fallen, and endeavoured, by selecting what seemed reasonable and just from that and other theories of morals, to enunciate a more perfect system. In opposition to Hutcusson, who confounds the Will with Desire, FERcuson first of all establishes Free-will as the subject and foundation of Moral Science. To the laws which regulate the Will—viz., the Luw of Self-preservation—the Law of Society—and the Law of Estimation or of Progression, FuRcuson refers all moral facts, and all systems of morality. By this theory also he attempts to refute or reconcile the different theories previously promulgated. In supporting his system, FERGUSON was opposed to that of CLARKE, who re- garded the Intellectual principle as the arbiter of right and wrong, and who thus made virtue a matter of mere calculation. He was opposed to Hume, who places the foundation of morals in Utility, and shows, that if utility and virtue often unite to urge us in the same direction, they are often also at variance and mutu- ally contradictory ; and that whilst virtue is that which is most definitely useful, and most certain to promote our happiness, it nevertheless is not confounded in our minds with any idea of private interest. He was also opposed to SmrrH’s theory of Sympathy as the principle of morality ; and proves, that to sympathise with a person, and to approve of his conduct, are two very different things. He thus also disposes of Hutcurson’s celebrated theory of the moral sense :—*“ If,” says he, ‘“‘ moral sense be no more than a figurative expression, by which to dis- tinguish the discernment of right and wrong, admitting this to be an ultimate fact in the constitution of our nature, it may appear nugatory to dispute about words, or to require any other form of expression than is fit to point out the fact in question.” 650 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. Ferguson endeavours to reconcile all these systems of morals, by compre- hending them in his own classification. With Hopses and Humes he admits the power of self-interest or utility, and makes it enter into morals as the law of Self-preservation. HutcueEson’s theory of universal benevolence, and SmitH’s idea of sympathy, he combines under the law of Society. But as these laws of Self-preservation and Society are the means rather than the end of human destiny, they are subordinate to a supreme end, and this supreme end is Per- fection. It was in this [dea of Perfection, then, that FErcuson placed the principle of moral approbation, and considered it as the law which every intelligent being forms to himself, by which to judge of every sentiment of esteem or contempt, and every expression of commendation or censure. The philosophic speculations of Fercuson have been carefully criticised by Cousin, who thus expresses himself with reference to this theory of Perfection :— ‘“‘ We find in his method the wisdom and circumspection of the Scottish school, with something more masculine and decisive in the results. The principle of perfection is anew one, at once more rational and comprehensive than benevolence and sympathy, and which, in our view, places FERGUSON as a moralist above all his predecessors.’’* In treating, in the latter part of his course, on the fundamental law of morality, and its applications and sanctions, FrErGuson observes, that some of these sanc- tions may be enforced, whereas others may be left to operate on the free will of the agent. Obligations and sanctions which may be enforced form the subject of Jurisprudence; those which cannot be enforced, are the applications of morality to the Duties of men. In treating of Jurisprudence, FERGusoN explains the laws relating to peace and war, and follows Grorius in acknowledging the law of self-defence to be the only © just foundation for employing force or stratagem in the case of independent or unconnected individuals. The Duties of men FErcuson divides into two classes,—those which may be considered as prohibitory, forbidding the commission of wrongs, and those which regard conscience, and can only be recommended by way of persuasion. The duties which involve in regard to others the right of constraint or prohibition are the foundations of natural law; and in this way FeRGuson enters upon the last portion of his subject, which is Politics. Fercuson treats of Politics under the heads of Population, Manners, and — Wealth, and Civil Liberty. In this department, he follows Montesquizu and — Hume, and eloquently pleads the cause of well-regulated liberty and free 4 government. His views in 1792 were, however, somewhat modified from those — * Philosophie Ecossaise, 3d ed., p. 512. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 651 he had enunciated in 1769, when he published his ‘‘ Institutes of Moral Philo- sophy.” In that work, when treating of Political Institutions, he had thus ex- pressed himself,—‘“‘ Institutions that preserve equality, that engage the minds of the citizens in public duties, that teach them to estimate rank by the measure of personal qualities, tend to preserve and to cultivate virtue.” The progress of the French Revolution, however, had, by the time when he published his lectures, cooled the general enthusiasm for liberty; and FErGuson, who seems in 1769 to have held extreme views, at length admitted the necessity for inequality in rank, and the expediency of hereditary distinctions and of an aristocracy. * In 1793 Frreauson was elected an honorary member of the Academy of Sciences of Berlin. He was also a member of the Academy at Florence, of the Etruscan Society of Antiquaries at Cortona, and of the Arcadia at Rome. From his knowledge of the Gaelic language, and from his early friendship with James M‘Puerson, he was at this time consulted as to the proposed publi- cation of the original Gaelic of the Poems of OssIAn. M‘Puerson had from the first professed his willingness to satisfy the public as to the authenticity of Oss1an’s Poems, by printing the originals which had come into his possession. At the same time, when urged by the Committee of the Highland Society, he always pleaded want of leisure as his excuse for with- holding them from the world. In 1793, however, a few years before his death, he prepared to comply with the generally expressed desire, but a difficulty arose as to the selection of the character and spelling to be adopted in printing the Gaelic language. It appears from the following exceedingly interesting letter, addressed to Fercuson, that he had resolved to adopt the letters of the Greek alphabet, as more adequately representing the niceties of Gaelic pronunciation. With the view of making a trial of this method, he printed a specimen sheet, containing a passage from the Gaelic translation of the Bible in Greek characters, which he submitted to the criticism of his friends :— “* London, May 21st, 1793. “My Dear Sir,—I wrote you a few lines some time ago, wherein, if I re- collect aright, I promised to send you soon after an answer to your letter of the 8th of April, on the subject of the proposed printing the original of the Poems of Ossian in the Greek character. Having been, at the time of receiving your letter, immersed in a hurry of business, from which I have not, as yet, wholly extricated myself, I desired a gentleman, who has for many years, in conjunc- tion with myself, thought crztzcally, of the Gaelic language, to throw our opinion upon paper, at his convenience, more for your satisfaction than from either a wish or expectation of making converts of others. This he has done accordingly, * Institutes, 2d ed., page 293. The Lectures on Moral Philosophy were translated into | French, and attracted much attention abroad, VOL. XXIII. PART III. ; SN 652 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. as you will find under another cover, which goes by to-morrow’s post. As my friend has left little that is material for me to add, I shall not trouble you with a long letter. ‘«« Our friend, Dr Buarr, I perceive, labours under much want of information on the subject ; for there is not one of the points on which he states his objections founded in fact, and, that being the case, his arguments and reasons require no answer. I cannot conceive what interest, except it was a silly degree of vanity, to give themselves a consequence on account of their knowledge in the Gaelic, those persons who gave the information had in deceiving our friend. “ Mr Davipson writes rationally, but he seems not to know that there is scarce any manuscript to be followed, except, indeed, a very few mutilated ones in a kind of Saxon characters, which is as utterly unknown to the Highlanders as either the Greek or Hebrew letters. With respect to the cheap copy he mentions, if there should arise a wish for having a small edition, there is scarce any common printer but can metamorphose the Greek character into something like it in the Roman. With respect to the splendid edition now intended, it was never my intention to put it up to sale, so that its grandeur will not keep it out © of the hands of those who would enjoy it most. I believe it will appear, from the accompanying observations, that there are not many of those amateurs between — Glotta and Tarvisium. “Mr Davipson should be informed, that neither the Irish nor the Scotch High- landers had ever any alphabet of their own. When they wrote, or attempted to write, they made use of the Saxon characters, which are much more confined than — even the Roman, from which they are derived. “ As I have heard that Mr Davipson is an excellent Greek scholar, he may be — induced perhaps to try the effect of the specimen now sent on the Highland porter or chairman, in the manner recommended in the accompanying observa- — tions. Our friend Mr Home, and even Dr Buarr, who are both good Grecians, — will be able, I trust, to read the original of OsstAn, as it is to be printed in Greek, — in a manner that will be intelligible to such Highlanders as wnderstand their — native tongue. But these, | apprehend, are much more circumscribed in number ‘ than is generally supposed. 5 ‘“« The result of the whole is, that I have resolved to follow the example of the — old Druids, in writing the Celtic language in Greek characters. I shall not, there- — fore, with Dr Brarr, agree, ‘ That it is the opinion of some of the /earned in Harse that must determine the point, and that to them it must be submitted’ Where those learned men are I have never been able to learn. With respect to the — clergy, I would rather take their ghostly advice on matters of religion than accept — of their opinion about the manner of printing profane poetry. I consequently — request, that instead of submitting the decision to them you will be pleased to ; return to me the specimen, already in your hands, at your convenience. And % - MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 653 after having weighed the observations at your full leisure, and at your own time, you will please to put them also under a cover to me. You will easily per- ceive, that this letter is meant only for your own eye; for few men wish to know that they have been so long deceived, on a point which the smallest attention might at once ascertain.—With my best respects to all friends, I am, with great esteem, yours most faithfully, James MacPuHerson.”* The observations on the method to be adopted in printing the Gaelic language in Greek characters, drawn up at M‘PHeErson’s desire, and sent to FERGUSON along with the above letter, were to the effect, that the existing Gaelic ortho- graphy does not give the pronunciation of that language with truth and cer- tainty, for the same letters represent different sounds, and the same sounds are expressed by different letters, and this in a promiscuous manner, according to the fancy of the writer. That in Gaelic a large number of letters are absolutely quiescent, which were probably introduced to represent in a clumsy manner a coarse pronunciation used chiefly in Ireland. That from these irregularities in the use of the letters which are really needful, and from the absurd accumula- tion of those which are useless, confusion has arisen, that renders the writing of the language arbitrary and the reading of it a matter of conjecture. With the view of making an experiment, a Scripture story—the finding of Moses by Pharaoh’s daughter—was copied from the Gaelic translation of the Bible, and on the opposite page the same words were written in Greek characters. This specimen of the proposed system was circulated by M‘PHERSoN among his friends, who were requested to make the experiment of reading the specimens to some illiterate Highlander, with the view of ascertaining which of the two would be best understood. In answer to the objection, that the use of the Greek alphabet would be a great inconvenience and innovation, it was urged, that the Highland gentry do not generally read the Gaelic; that it would be but the labour of a few hours to master the Greek letters, and their use would smooth the way for those who wished to read and write the Gaelic language. It was further expected, that the familiar use of the Greek letters would naturally lead to the study of the Greek language itself, then much neglected in Scotland ; and that it would be “ no degradation of its characters to express the composi- tions of a poet, which the taste and learning of Europe have long since ranked among the admirable works of antiquity.” To the letter of M‘PuErson, and these observations, FERGUSON replied in the following terms :— “ Edinburgh, 30th May 1798. My Dear Sir,—I am glad you are decided on the form in which Ossian is to be recorded. You may expect to hear different opinions on the subject; but if * MSS. University of Edinburgh. 654 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. any one thinks he can do better in a more portable form, or in Roman character, this he can easily accomplish from your standard copy; and I shall cease to reason on the subject. Being but a bastard Gaelic man, my ear is a very uncer- tain rule for pronunciation or orthography. I will, however, mention what occurs under correction of your better judgment. Will it not be proper to prefix an alphabet, with notice of the power of each letter? If so, I think the two sigmas should be distinguished, the one s the other sh. I think the alpha is sufficiently full and broad in the sound without any additional vowel, as (v), for instance ; and I think the upsilon should have the power of the English (v) uni- formly given to it. The modern Greeks always pronounce it so. The (2), falsely numbered with the diphthongs, should always stand for the Italian (w) or English double (00), as in moon or boon, &c. To illustrate these remarks, I have ventured to mark the changes they would make in the specimen. Axzs, I see, you spell with a kappa, to my ear it is rather a (y), gamma; however you know much better. Query, also whether the nasal sound, when the article a precedes a word be-— ginning with gamma or kappa, may not be marked with the double gamma, as in the tale of Pharaoh’s daughter («yy x0p2r) ; so much for remarks which you will not make any use of, as you see cause. [| have conformed to your former injunc- tion exactly in consulting no more persons. There are few persons of any educa- tion in the Highlands, whether clergy or laity, that do not know the Greek — alphabet ; and perhaps will have easier access to your Ossian in that alphabet than they would in the barbarous orthography which few, and I among the rest, never learned to read. I know that this would make many a learned man stare. For there is no persuading people south of Tay, that all the works of the bards are not to be found in booksellers’ shops in Lochaber or Morven the capital — of the country at least. I tryed your experiment on J. Home, and he made it much more intelligible from the Greek orthography than from the Roman. I showed — him in confidence your flagellation of the Edinburgh critics, and he is much diverted. J admire the fair hand and current writing of Greek in your amanu- — ensis.—And am, dear sir, your most obedient and most humble servant, ‘* ADAM FERGUSON.” * M‘PueERson does not seem to have received much encouragement towards — using the Greek characters for his projected edition. He died three years after this, and the Poems of Ossian, which were printed in Gaelic after his death, — appeared in the ordinary Roman characters. le About the end of the year 1793, FERcuson, sdthionph' now in his seventieth : year, finding his health much improved, formed the resolution of visiting Italy, that he might be the better able to prepare a new edition of his Roman History. He accordingly set out for the Continent on his way to Rome, and visited the ;: chief cities of Germany, in all of which he was received with much distinction. eo a i > - * This letter has been kindly furnished by Sir Davin Brewster. os = MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 655 The following letters, addressed to Sir Joun M‘PHERSoN, were written from Frankfort, Munich, and Venice, and are interesting from their allusions to pass- ing events at this memorable period :— “ Frankfort, 25th Sept. 1792. “ My Dear Frienp,—I wrote a line from Ostend, to give notice of my safe arrival on the Continent. Ihave since made out so far of my journey to this place, where I halt a day or two; but do not find that I can venture to go in search of the Marquis Luccuesini, and therefore enclose your letter to him, and consign it to the post, with my regret for not being able todo more. Military matters are well here, a division of French prisoners has just past, a second is expected at night, and a third to-morrow, amounting in all to about three thou- sand men taken in battle lately by the Duke of Brunswicx, but I cannot learn where. You pelted me with letters from the Continent, to which I was not en- abled to make any answer. I should be sorry to return you the compliment exactly. My pelting will be very moderate, and your answers, I hope, will come, though I don’t at present know where to direct them nearer than Rome, to the care of Mr JENKINS, banker, and there, in the name of God, let them come as many, and as soon as possible; that is to say, much sooner than gleich and geschwind, which I have generally found to be as slow as possible. All I have to say for the present is, that travelling even here is certainly a very healthy business, for I thrive wonderfully upon it. I have some inducements to go by Munich, and to take the inland route by Nurenburg, &c., as I know less of it than I do of the other, and the road, I am told, is good. I sometimes torment myself with thinking what is to become of the world; but as I have no commission to govern it, the wisest course is to mind my route, and so I shall do in the best humour I can muster.—Believe me to be yours most affectionately, “ ApAM FERGUSON.”* * Munich, 5th Oct. 1793. * My Dear FrienD,—Here I am at Munich, in a most prosperous course of travelling, waxing in strength and patience. I sent you a line from Frankfort, intimating my intention of sending your letter to the Marquis LuccuesinI, with My regret for not being able to hunt for military quarters in person. I did so in the best French I could muster. The elector of Bavaria said at his levee yester- day that the king of Prussia has declared his intention to winter at Berlin, and to leave his army under the Duke of Brunswicx. There is, I find, a hankering in- clination to censure his Majesty, on a supposition that more might have been | done in the campaign; but I am of the opinion, which I guess is also yours, that to hem in the French, and give them as few opportunities as possible to take * MSS. University, Edinburgh. VOL. XXIII. PART III. 80 656 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. what we call crop to themselves, is the very perfection of conduct. There is a report here that the Emperor is about setting out for Brussels, and that even part of his equipage is in readiness. I surprised James Stuart by meeting him here, and find we shall be much together at Rome, &c. &c. It is now about forty years since I have known him to be one of the pleasantest, naive, and best hearted creatures in the world. I am introduced to Mr Watpote here, and was at a vrai diner d’Embassadeur, all English, at his house yesterday ; but I shall make no stay, being very impatient to get within the precincts of the Old Re- public, and no less impatient to be at some place where I can hope to hear from you, and learn something of what is doing in the world ; for in this way of life we are hood-winked, and know no more than can be seen when the glasses of the sulky are down.—I am, my dear friend, yours most affectionately, “ ADAM FERGUSON.” * « Venice, 19th Oct. 1793. ““ My DEAR FriEnND,—I write merely to let you know what is become of me, and the sum total is that I am well, and have come on as prosperously as a speculative master and a dumb servant could do without any other aid. I wrote a line also from Frankfort or Munich, with an account of what I did with your letter to Count Luccuesint. I see from newspapers since, that if I had stayed but a few days more at Frankfort I should have seen him there; but the secrets of kings who can know? and I should have thought myself in a scrape amidst the scarcity of horses, caused by his Majesty’s motions. In the way I took by Nurenburg and Munich I avoided that distress, came prosperously through the Tyroll, and at Verona began to reap the fruits of my labours. If you remember. the Cimbri or Teutones are said to have performed wonders against Carutus the Roman general in that neighbourhood ; and though it be not of much conse- quence whether that tale be exaggerated or no, yet I was anxious to judge of its credibility on the spot, and got on horseback from Verona for that purpose, and reconnoitred the banks of the Adige for some little way. So far I had come post; but there I fell in with a Florentine veturino, who had brought some travelle 8 Suseee state. 7 told him I should be at Florence soon, though at present I go by Loretto; and if any distress befal me, my point of rallyment will be Floreala being under the special protection of Count MANFreEp1nI, so that Antonio Lopi ni, this veturino, and I are already a sort of compatriots. I languish for news from England. I call for newspapers everywhere, but nothing has yet overtaken me * MSS. University, Edinburgh. : MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 657 more than I knew, and in part witnessed in passing through Flanders. I some- times flatter myself that you will not have waited for accounts of my arrival at Rome, but will have written under care of P. Morr, and JenxKins the banker; if you have not, pour amour de Dieu delay it no longer. I could not pass this place, though it is much too modern to be any object to me; I wonder at it; but am not much delighted. Si je n’avois que soixante et div ans, as VOLTAIRE used to say, I would read its history with great avidity; but that is for the world to come. I went to the opera last night, and was truly entertained with the audi- ence.—I am, my dear friend, yours most affectionately, ‘** ADAM FERGUSON.’ * From the disturbed state of the Continent at the time, owing to the effects of the French Revolution, Fercuson’s stay at Rome was shorter than he anticipated, but he returned to Edinburgh much pleased with his tour. After his return he continued to reside at: his villa at “ the Sciennes,” where he enjoyed the society of his literary friends. Principal Roperrson dwelt in the neighbourhood, at the Grange House, and Mr Cocxgury, father of Lord CockBurn, had his abode in the immediate vicinity, at Hope Park, midway between the houses of the Principal and his late colleague. Lord Cocksurn informs us, in the “* Memorials of his Time,” that he, when a boy, was frequently at the houses both of Ropertson and FrErcuson. He thus gives us his recollection of FERGuson’s appearance :—“ Our neighbour on the east was old ADAM FErcuson, the historian of Rome, and Strewart’s predecessor in our Moral Chair—a singular apparition. In his younger years, he was a handsome and resolute man. Time and illness, however, had been dealing with him, and, when I Bret — him, he was a spectacle well worth beholding. His hair was silky and white ; his eyes animated and light-blue; his cheeks sprinkled with broken red, like autumnal apples, but fresh and healthy; his lips thin, and the under one curled. A severe paralytic attack had reduced his animal vitality, though it left no ex- ternal appearance, and he required considerable artificial heat. His raiment, ‘therefore, consisted of half-boots, lined with fur; cloth breeches; along cloth waistcoat, with capacious pockets; a single-breasted coat ; a cloth greatcoat, also lined with fur ; and a felt-hat, commonly tied by a ribbon below the chin. His boots were black, but with this exception, the whole coverings, including the hat, were of a quaker-grey colour, or of a whitish-brown; and he generally wore the furred greatcoat even within doors. When he walked forth, he used a tall staff, which he commonly held at arm’s-length, out towards the right side; and his ‘two coats, each buttoned by only the upper button, flowed open below, and ex- . posed the whole of his curious and venerable figure. His gait and air were noble; his gesture slow; his look full of dignity and composed fire. He looked ————————————— * MSS. University, Edinburgh. °c 0 658 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. like a philosopher from Lapland. His palsy ought to have killed him in his fiftieth year, but rigid care enabled him to live, uncrippled either in body or mind, nearly fifty years more. Wine and animal food besought his appetite in vain, but huge messes of milk and vegetables disappeared before him, always in the never-failing cloth and fur. I never heard of his dining out, except at his relation, JosepH Buack’s, where his son, Sir Apa (the friend of Scort), used to say it was delightful to see the two philosophers rioting over a boiled turnip. Domestically he was kind, but anxious and peppery. His temperature was regu- lated by Fahrenheit; and often, when sitting quite comfortably, he would start — up, and put his wife and daughters into commotion, because his eye had fallen on the instrument, and discovered that he was a degree too hot or too cold. He always locked the door of his study when he left it, and took the key in his pocket ; and no housemaid got in till the accumulation of dust and rubbish made it impossible to put the evil day off any longer, and then woe on the family. He shook hands with us boys one day in summer, 1793, on setting off, in a~ strange sort of carriage, and with no companion except his servant James, to visit Italy for a new edition of his History. He was then about seventy-two, and had to pass through a good deal of war, but returned in about a year younger than ever.” * ; In 1795, Ferauson received a severe blow to his domestic happiness by the death of his wife, who had been his faithful partner for nearly thirty years. Being now well advanced in years, and taking but little pleasure in society, he began to look about for a spot where he could spend the rest of his days in peaceful seclusion. It happened at this time that the old castle of Neidpath, over- hanging the Tweed, near Peebles, was left untenanted by the Duke of QUEENS- BERRY, and Fercuson, charmed by the beauty of its situation, interested himself to procure a lease of the old castle, and a few acres of ground, from the Duke. The following letter fully shows the eagerness with which this new arrangement was entered into by the veteran philosopher :— “« Edinburgh, 20th May 1795. “My Dear Frienp,—Tho’ the time is now approaching at which I have for some time past flattered myself with the hopes of seeing you here, I take my chance of overtaking you at Brompton with a few lines. The scheme of a country — life, which you proposed to dispute, still remains with me, and I have been look- ing out for some place at which to settle. Among others, I have seen the castle of Nydpath, on the Tweed, belonging to the Duke of QuzensBerry. It has been lately dismantled, or stript of its furniture, and so far destined to become the habitation of bats and owls, or what is little better, such a tenant asl am. The servant who showed the place told me that his Grace has been asked to let it, but declined, which makes my prospect somewhat desperate. I have, neverthe- * Memorials of his Time, p. 48. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 659 less, made proposals in form to the man of business here. And beg the favour that, if you should see the Duke of QUEENSBERRY, you will try to incline his Grace not to forbid any transaction with me. And I undertake to satisfy you that the scheme I propose is the best for my family as well as myself. I am, your most affectionate humble servant, AvAM FERGuson,”’* It was in the month of May that Fercuson had removed his household gods to Neidpath, and during the summer the old Castle was found to be a most desirable residence. “ The woods, the hills, and the river, are Elysian, and the atmosphere all composed of vital air.” These were his expressions in September; but when the cold blasts of winter approached, the Castle was anything but an enviable residence in its existing condition. The following letter to Sir Joun M‘PuErson gives a glimpse of his situation in the winter season there :— * Nydpath, 9th January 1796. “My Dear Frienp,—I have just now received your affectionate letter, with the inclosed commission of business for ADAM the Writer to the Signet, and write merely to get out my breath on this plaguy situation into which I have got, without the accommodation of either town or country. . . . Inowsee the mistake of having thrust myself into this situation before it was cleared for me one way or another ; but I reasoned that I must either occupy the Castle before winter to keep it in repair, or lay aside thoughts of it altogether, to the last of which I was extremely reluctant. I am sensible what I should do now is to wait _the chapter of accidents, but patience, the great virtue for succeeding in any- thing, has been but very scantily dealt to me. Old as Iam, I had rather be doing anything, than wait doing nothing, of which this very letter is a suffi- cient proof; for it certainly will do you no good, nor me any other than employ- ing some minutes of this woful time. I have to wait for some instruction to his ‘man of business from the Duke of Q. ‘So much for one Duke; if ever I have to do with another, I will give them leave to. duck me in the first horse-pond. I am, most affectionately yours, ADAM FERGUSON.” * It has been remarked, that no Stoic philosopher more completely subjected his passions and his feelings to his reason than did Fercuson; but the discom- forts attendant upon his residence at Neidpath were a sore trial for his philosophy. Writing about them, in February, he says, “ if any body think me a philosopher, he is grievously mistaken. I have done nothing but peste and scold inwardly for three or four weeks, not to say months.” The arrangements necessary to get quit of the lease of the Castle were, how- “ever, easily made; and he took up his residence at Hallyards, a farm in the * MSS. University of Edinburgh. VOL. XXL. PART II. Sp 660 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. immediate neighbourhood, where he lived for the next fourteen years,—a longer period than he had ever spent in any of his previous places of abode. During this period he still enjoyed good health, and interested himself in farming with all the ardour of a young agriculturist. It was to an incident which occurred while FERGuson lived at Hallyards, that we owe one of Sir W. Scort’s most characteristic novels. Among the hills near the house lived an eccentric and misshapen dwarf, called Davip Rircut1e, and Scott, then a young advocate, when he came in 1797 to pay a visit to the Ferausons, was taken to see Davin as one of the lions of the district. The strong impression which the interview with the hermit, who was supposed to be possessed of magical powers, made on ScoTt, was never effaced; and the tale of the ‘ Black Dwarf,’ published twenty years afterwards, owed its origin to this remarkable occurrence.* The following letter addressed to Sir Joun M‘PHERsonN, contains FeRcuson’s views as to the epitaph which he wished to be inscribed on his tomb, and also an allusion to the energy which was the distinguishing feature of the character of the late Sir JoHN SINCLAIR. “ Hallyards, 3d July 1798. ‘My Dear Frienp,—My silence is not negligence nor forgetfulness. If I had ten thousand of the best letters that ever were written, you should have them all ; but what can I write from this post, at which my prime consolation is, that I have nothing to do but to wait quietly till my time comes. The French, I trust, although they may teaze, cannot subdue this armed nation; and all speculation on the subject is at an end. I have in my viewa most delightful kirkyard, retired and green, on the bank of a running water, and facing a verdant hill, which in your part of the world would pass for a tremendous mountain; but to me it gives the idea of silence and solitude away from the noise of folly;. and so I fancy myself laid there, with a stone to tell the rustic moralist what he will no understand, because I sometimes project it should be in Greek, as follows :—as yw Tov xoouov eOayuaca, xo ov beaonmevos xaue; but then, again, I wish to explain it, and so it should be, ‘ I have seen the works of God, it is now your turn, do you behold them and rejoice.’ I would speak my verse for agriculture in Greek also,—Avégamou yw yewoyre,—and you may judge of my willingness to write when I put all this on paper to you. I have not stirred from home for many months past till lately, when Admiral and Mrs Nucent being at Edinburgh led me thither to gratify my sense of their kindness to my little seaman. And | am still the more convinced, that NuGEnT is the most amiable, faultless creature upon earth. In that excur- sion I met our friend, Sir Jonn Srvcuare, in the street; this put it in his head to write to me since my return hither, an account of works he is projecting to pro- mote what he calls statistical philosophy. I hinted that his project is too vast; * CuameBers’s Hist. of Peeblesshire, p. 402. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 661 but he tells me that his mind is made up to draw it on a great scale, and on as perfect a plan as possible; and that he never started at any difficulty that could be surmounted, ever since he collected, as far back as the year 1780, one thousand and two hundred men, and in one day’s time made a road of six miles long over a mountain, till then thought impassable. The fact is, that he has got an in- stinct to be doing, which other people ought to know how to employ without turning him out of place. Although I have so many excuses for writing so seldom, I am not willing to allow you any; so I pray, when you are writing how- ever, let there be a scrap for me, even if you should not be able to tell me what is become of Buonapart&. By the by, is that a genuine Prussian paper in answer to the French demands, which we have in the newspapers? It is menacing, and I do not see how the great nation can give way to it, without appearing to be cowed. They certainly meant to gall us, and to secure the co-operation of Prussia against us, by transferring Hanover, &c. &c.—Yours most affectionately, “ Apam FErcuson.”* The following letter, also addressed to Sir Joun M‘Puerson, concerning the purchase of an estate in Peeblesshire for a ward of Sir JoHn’s, contains an allu- sion to ALLAN Ramsay and the Edinburgh writers :— ** Hallyards, \st August, 1798. “My Dear Frienp,—To begin where your letter ends amicus amicissimus indefatigabilis. After having splashed you before with bad Greek, you are well off that there is nothing more now than bad Latin. I do recollect hearing of S. J. E.’s desire to have some land property near his native spot, but at present know nothing more, nor do I know of any fit place at Peebles for your ward, but shall inquire. There is no property in this country you know without a doer, as ALLAN Ramsay used to call the writers when he was angry with them, which he was, indeed, for the greatest part of every hour of his life. If there be any subject on which to make us your doer, we shall not neglect to do what is proper; and for the sequel, if there be any sequel, it must come as God will have it in the whims and inclinations of those concerned. As to the world, I am glad you think BuonaParTEé is gone upon a mere trading or plundering voyage. In that way he cannot be long without having the seas disputed with him, and I patiently wait for the consequence, without supposing that every encounter of ours must be veni, vidi, vici, for even the great JULIUS was a puppy at a time, and more so than has yet appeared of Buonaparrk. A combination of Europe, including Russia, if not properly directed would do us no good. You may possibly remember my bull, that the proper way to make war on the great nation is to make peace with them. In this they are too wise to be caught, I mean their directors; but I think we may make a war as like peace as possible, especially if Europe com- * MSS. University of Edinburgh. 662 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. bine in it, by keeping them at bay,—leaving them no outlet from home, nor ~ goading them with any trifling attacks to keep their attention and animosities directed abroad. There was an expedition to Ostend, and there is one again now, the newspapers say, from Margate, mere proofs that we have not yet learned the character of our enemy or the nature of our contest, but of that no more. I am no oppositionist, and this moment think the nation in a most prosperous state— that is to say, we have men, arms, and spirit, and if we should come to have less wealth we must consume the less, either by having fewer mouths or putting less in them. I was in Edinburgh for a day or two when your last letter came here ~ to Hallyards, otherwise, having now three or four such favours to acknowledge, should have done it sooner. The ‘Roman History’ advances but slowly. The printers have much other work when our law courts are sitting; then much of the business proceeds by a kind of paper war from the press. Five octavo vol- umes are projected, but little more than one is yet printed. I shall be obliged to — your German author for his prolongation scheme, though having annuities and salaries from other people, ’tis like they think I have prolonged enough. I went to Edinburgh to see our friend G. JounsToneE, and was highly gratified —I am, my dear friend, most affectionately yours, ** ADAM FERGUSON.” * In the following extract from a letter, written in 1799, Fercuson thus ex- presses his opinion of the views then published by Sir James MacINTOSH. At that time Mactntosu had been recently called to the English bar, and with the view of bringing himself into notice, he delivered a course of lectures on the Law of Nature and Nations. The introductory lecture was published as ‘A Discourse on the Law of Nature and Nations,’ and it, with the other lectures of his course, received the highest praise from men of every shade of political opinion. Frrcuson states, “I hear very favourable accounts of Mr Macintosu’s per-— formances at Lincoln’s Inn. As I judge only from his pamphlet, his tone, though — perhaps more harmonious, is in unison with mine. He had his reasons, probably, — for not mentioning me, and I am not solicitous about them. He will probably © procure to Moral Philosophy that popularity in England which I wished for, but have been unable to obtain. His taking his ground in the law is not so apt to alarm the Universities and the Church as if he had called his object Moral Philo- sophy, which those authorities sometimes mention among the corruptions of the 4 times.” * . The literary labours of Fercuson were not yet over. In 1801 was published , his already mentioned contribution to the Transactions of the Royal Society, under the title of Minutes of the Life and Character of Joseph Black, M.D. (nit there is * MSS. University of Edinburgh. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 663 given a concise but interesting account of Buack’s discoveries of carbonic acid and latent heat, which entitle him to be regarded as the father of modern chemistry. It was his relationship to the family of JosrpH Buacx,* which was probably the indirect means of forming FrerGuson’s own philosophical views. The father of Dr Buack had been a wine merchant at Bourdeaux, and when residing there enjoyed the intimate friendship of the great MonTEsquigeu, who was the president of the parliament or court of justice of that province. The letters and scraps of correspondence which passed between Montesquieu and Mr Brack, the descend- ants of the latter preserved as though they had been titles of honour belonging to their race. In his own Philosophy, Fereuson has in many places followed the views of Montesquieu, and his ‘ Essay on Civil Society’ may be regarded as an eloquent introduction to the immortal work, ‘The Spirit of Laws.’ The infirmities accompanying advanced life now made FEerGuson desirous of again residing in a town, where he might have more opportunities of conversing with intelligent friends. As St Andrews was the place where he had been educated, his early predilec- tion for that ancient city returned, and in 1808 he retired thither to spend the remainder of his life. He there enjoyed the society of the Professors of the University, and that of the patriotic Grorcz Dempster of Dunnichen, whose endeavours to extend the manufactures of Scotland are well known. Among FeErcuson’s letters, perhaps not the least curious is the following, addressed to Mr CartyLe BELL, in which he expresses his opinion of the ‘ Diary’ _of Dr Cartyte of Inveresk. Carty Le died in 1805, and it was proposed in 1810 by his executors to edit this work, which, however, has only recently appeared under the editorial superintendence of Mr J. Hizi Burton. Had it been published in 1810, in place of 1860, the Diary would not have excited the same interest :— “ St Andrews, 21st July 1810. “My Dear Sir,—lI have received your letter acquainting me that trustees whom you do not name, are now deliberating on the publication of my worthy friend and your late uncle’s manuscripts. Of this you must be sensible that I cannot give any opinion. The small part I saw, or with my impaired sight could decipher, did not appear to me intended for publication; but rather the amuse- ment of leisure in the exercise of a talent in which our friend excelled; the easy and satisfactory detail of familiar occurrences affording a pleasure which his correspondents experienced in every letter he wrote to them. I was so pleased in reading the part you showed me or I could attempt to read, but it related to _ things and persons most of us so obscure as not to be entitled to public notice, * The mother of Fereuvson was aunt of the mothers of JosrpH Brack and James Russei ' Professor of Natural Philosophy. Frreuson was also married to Dr Bracx’s niece. VOL. XXIII. PART III. 8 Q 664 MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. that I should not be willing to exceed what I believed to be the writer’s original intention by publication; and I thought myself the more at liberty to give this opinion that I found my own name repeated with that partial favour which I always experienced from my friend. It was our lot through great part of our time to be neighbours so near as to be frequently together, and the opportunities, I believe, were never willingly omitted by either. We were sociz criminis in the countenance we gave to the first representation of our friend J. Home's tragedy of Douglas, a charge for which I was never called to account. But Dr CarLyLe was more known, and had more enemies, who, by prosecuting him for this offence, declared him innocent of anything more likely to serve their spite. We were also accessory to the formation of a Poker Club, and survived most of its members, and thus had occasions of regret which are but ill repaired in the solitary com- forts of sequestered old age. You cannot doubt my desire to promote the respect which is due to the memory of Dr Carty ez, but how I know not, beyond the testimony, if it were called for, that I never knew a more steady friend or more” agreeable companion, and in this I should have so many concurring witnesses as to make my words of little account. I shall be anxious to know how you proceed, and I beg I may hear from you.—I am, with best respects to Mrs BELL, yours most affectionately, ADAM FERGUSON.” During his residence at St Andrews FERGuson’s mind was almost as vigoro as in his younger days, and his bodily functions, with the exception of his sight, ~ were scarcely impaired by age.* Even in 1815, the year before his death, his health was better than it had been for some years, and his spirits ‘were elevated by the successful termination of the war with France, in which he had always been much interested. About the beginning of February 1816, however, he was attacked by a febrile complaint, to which he had been occasionally subject. This illness, after con- tinuing for four days, proved fatal on the 22d of that month, when he was in the ninety-third year of his age. Fereuson had a family of seven children, four sons and three daughters. His’ * In 1812 Frereuson was requested by Mr Henry Macxenz1se—‘ The Man of Feeling’—to furnish him with some memoranda relative to his early acquaintance with Joun Home, author of ‘ Douglas.” Mackenztx’s last literary effort was a Memoir of Home, which he read before the Royal Society in 1822, and which was afterwards published in a separate form. To that volume an- Appendix is added, containing a remarkable letter, written when Frreuson was in his ninetieth year. Besides referring to his early connection with Joun Home, it contains further information as to his views with reference to the Ossian controversy. There was also published, after his death, a short biographical sketch or memoir of his friend, Lieut.-Col. Patrick Frreuson (second son of JaMzs Fereuson, of Pitfour, one of the Lords of Justiciary in Scotland), which he had written some short time previously. It was intended as an article for the Encyclopzdia Britannica, but it was considered by the editor too long for that work; and as Fereuson declined to abridge it, it was not inserted. A few copies were printed in 1817 from the original sketch, for private distribution. MR SMALL’S BIOGRAPHICAL SKETCH OF PROF. ADAM FERGUSON. 665 eldest son, Sir ApAm,—one of the most genial and kind-hearted of men—was an early friend of Sir WaLTEr Scort, and is frequently alluded to, under the soubri- quet of Linton, in Sir WauTeEr’s Life by Locknarr. His second son, JosEpx, entered the army, and died in India in 1800 as Captain in Lord Szarortn’s regi- ment. His other sons were, James, Colonel H.E.I.C.S., and JoHn, Rear-Admiral, Royal Navy, who survived their father. His daughters, IsAneruA, Mary, and Marcarer are frequently noticed in LockHart’s Life of Scorr, as having, when residing at Huntly Burn, formed part of the delightful circle which Scort gathered around him at Abbotsford. In these Memorials of ADaAam Frercuson, which we now conclude, we renew our converse with many persons of whom Scotland has every reason to be proud, and amongst whom Fercuson deservedly holds a high place. Whether viewed as a historian, a moralist, or a man, FERGUSON was eminently distinguished by a vigour and a simplicity of character which well entitle him, as the last survivor of a galaxy of great contemporaries, to be designated Ultimus Romanorum ! On the monument erected to his memory by his family, within the grounds of the old Cathedral of St Andrews, is the following elegant inscription, from the pen of Sir WALTER ScorT :— HERE REST THE MORTAL REMAINS OF ADAM FERGUSON, LL.D., PROFESSOR OF MORAL PHILOSOPHY IN THE UNIVERSITY OF EDINBURGH. HE WAS BORN AT LOGIERAIT, IN THE COUNTY OF PERTH, ON THE 207m OF JUNE 1723. AND DIED IN THIS CITY OF ST ANDREWS, ON THE 22p DAY OF FEBRUARY 1816. UNSEDUCED BY THE TEMPTATIONS OF PLEASURE, POWER, OR ‘AMBITION, HE EMPLOYED THE INTERVAL BETWIXT HIS CRADLE AND THE GRAVE WITH UNOSTENTATIOUS AND STEADY PERSEVERANCE IN ACQUIRING AND DIFFUSING KNOWLEDGE, AND IN THE PRACTICE OF PUBLIC AND OF DOMESTIC VIRTUE. TO HIS VENERATED MEMORY THIS MONUMENT IS ERECTED BY HIS CHILDREN, THAT THEY MAY RECORD HIS PIETY TO GOD AND BENEVOLENCE TO MAN, AND COMMEMORATE THE ELOQUENCE AND ENERGY WITH WHICH HE INCULCATED THE PRECEPTS OF MORALITY, AND PREPARED THE YOUTHFUL MIND FOR VIRTUOUS ACTIONS. BUT A MORE IMPERISHABLE MEMORIAL OF HIS GENIUS EXISTS IN HIS PHILOSOPHICAL AND HISTORICAL WORKS, WHERE CLASSIC ELEGANCE, STRENGTH OF REASONING, AND CLEARNESS OF DETAIL SECURED THE APPLAUSE OF THE AGE IN WHICH HE LIVED, AND WILL LONG CONTINUE TO DESERVE THE GRATITUDE, AND COMMAND THE ADMIRATION OF POSTERITY. Trans. Roy. Soc. Edin* Vol. XXIII. Plate XXIIL. see p.p.677, 678. Fig. 3. South North LATITUDE MARKINGS AND PASSAGE- PLACINGS BY HYPOTHESIS. Plate XXIV. - Roy. Soc. Edin® Vol. XXII. see p.p. 677, 678, 681, 687. / 1 f / Y, “Lf - ‘ ) iv / ML fis THIN Vi / // “i Le HO nse DIM reel Tas? SS) Uso ts fie Lig Lh fe / ---- = ---------—- —----- - - - ----- ~~ --- - - = ---- -- +--+ --- 4 1 i ' ' r ' X \ , | . ' ; i ' ‘i 80 : : | 1000. 500 0 1000 2000 G000 7000 8000 ‘9000 i] T ] WS 10 20 30 20 130 140 150 160 170 180 a = kings Chamber. 6 = Queens er. © = Subterranean (hamber. MERIDIAN SECTION OF GREAT PYRAMID, | after HOWARD VYSE, | with the principal hypothetical lines of Fr¢.3. marked in dots. 90 80 10 60 78 no 30 20 40 & PLAN. —S = 4030 20 10 100 Cc hes. mouc. dim. Vol. XXIII. ns. Ro Plate XXVI. see p.p. 697, 698, 699. OL FUOsL}2/ 03 0g r= t “sayout “LAT 000€ % B'S sh osye sas "GINYYAd LyayD aHo NI ‘STDNVSSVd-4IWil ZHL JO NOILVWUOd TIVOILLAHLOdGAH GQIWVuAd a0 1004 O% oe 0002 yatvuAnAAO cS oe or O,reyv ob ¢ ¢ Uf SUL, 90 00% O0E 004 009 00k 008 006 0001 0 005 0001 ‘S9YyOUl PIUDIAT JO APIS A 888 ‘SS (OSOT prutv.shy JO LIFUAD L i ' 1 1 1 1 1 ' 1 ' 1 1 ' 1 ' ' 1 ' ' ' 1 1 : |S S i qnog Purqooy aut, panop fq safessed re ayy Suimey aS 10 Isv a & Ai) Wigiieralis. esos sty onewaln W L 1d oud Vol. XXIII f= oOo FY [S) aN SY QQ c AG CN6GZ 2) XLIII.—On the Reputed Metrological System of the Great Pyramid. By Professor C. Prazzi Smytu, Astronomer-Royal for Scotland. (Plates XXIII .—XXVIL) (Read 21st March 1864.) CONTENTS. PAGE PAGE (1.) Circumferential Analogy of the eee 667 (9.) Pyramid Weights and Measures, : 688 (2.) Standard of Length, . : ; 672 | (10.) The Sacred Cubit of the Jews, . , 694 (3.) Figure of the Earth, . : : : 675 | (11.) Time Measures in the Pyramid, . ‘ 696 4.) Latitude Markings, : : ; ‘ 677 | (12.) The Final Argument, . 700 (5.) Unique Interior, . 680 | Appendix 1.—Chronology Seave ae the (6.) The Porphyry Coffer ; its Size ea Nufevial 683 Pyramid, . 700 7.) Why of that Size ? 2 . 5 : 685 | Appendix 2.—Colonel Sire’ s Measure of 8.) Of what Weight? @ : ‘ : 686 the Queen Elizabeth’s Standard Ell, . 702 In the year 1859, a book of remarkable power and originality was published by Mr Joun Taytor, of London, entitled ‘‘ The Great Pyramid, why was it built ?” On first looking into it, I was unfortunately inclined to fear that its results were unlikely to be very sound ; though merely because they seemed to bear, in a hitherto nearly barren, or difficult, and certainly most mysterious field, such a remarkably large crop of rich and promising-looking fruit. But considering after- wards, that that was not the proper frame of mind to be indulged in connection with, and certainly not in place of, strict scientific investigation into the merits of the case,—I read the book carefully, and then searched for the data required to test it, both in the original authors appealed to, and in some others. Without attempting to follow Mr Taytor in all the learnedly copious breadth with which he treats the subject, and which would be quite beyond my powers,—I have endeavoured to submit to a still more searching examination than he him- self has done, such part of his inquiry as I felt myself in some measure pro- fessionally conversant with the general principles of,—and have now to submit the results to the indulgence of the Royal Society of Edinburgh. (1.) Circumferential Analogy of the Pyramid. The first proposition or statement which Mr Taytor puts forward, admitting of scientific examination is, that—“‘ the vertical height of the Pyramid (which rises from a square bed, see Plate XXVII. fig. 7), is, to twice the length of one side 39 of its base, as the diameter to the circumference of a circle:” or, as in fig. 1 on ‘the next page; Where, AC : DBx2 :: Diam. : Circumference DEFB »: : 1 : 314159, &e. VOL. XXIII. PART III, SR 668 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM Now this statement alludes of course to the primitive condition of the Pyramid, 4 as it came out of the hands of its builders nearly 4000 years ago; and to identify, without any doubt, which Pyramid is referred to, we may mention that it is the — largest of the group of stone Pyramids near the modern village of Jizeh, Jeezeh, or Gheezeh, and some 15 miles north of the © ancient city of Memphis; standing there- fore on the western or opposite side of the — river Nile,to that on which the modern city — of Cairo is presently found. Altogether it is the largest, most solidly, and compactly — | built, and most exquisitely finished in its — interior, as well as one of the earliest of — all the Egyptian Pyramids; has generally — been known amongst all nations for ages as “ the Great Pyramid; and has been in later years tried by more theories than — any other, yet without yielding hitherto any fully satisfactory account of its objects or intentions. For nearly 3000 years after its erection, the external surface of the Great Pyramid remained untouched; and would have at that time allowed Mr Taytor’s" proposition to be instantly tested with severity; for the Pyramid was then as beautiful a realisation of the mathematical solid so called, as well could be imagined ; but after that interval, the Arabian Caliphs in Cairo began systema- tically to carry away the whole of the external marble casing; leaving at last only the rude steps of the inner component masonry, which made the new. exterior assume sensibly another figure. These stone steps too, serving unfor- tunately after that, to render the climbing of the Pyramid easy to any one and — every one,—European, as well as other travellers have been for ages past seized with a strange madness to clamber up to the top of the structure, and then begin throwing down some of the uppermost stones, for the ignorant pleasure of seeing | them smashing and thundering down the steep sides of the monument; whence it comes to pass, says the learned “ Description de Egypte” of the French nation, that ‘the area which now exists, in place of the original sharp point, at the top of the Pyramid, is daily growing larger, and the height becoming smaller.” § Hence the original height of the Pyramid cannot now be determined by direct measurement; and though, abstractly, we might compute the proportions — required in Mr Taytor’s proposition,—either, from. the measured axial height and the length of one of the sides of the base,—or, from the angle made by one of the sides with the base, without reference to linear measures at all—yet we ' must in practice confine ourselves to the last method alone; that is, to procuring OF THE GREAT PYRAMID. * 669 accurately the angle at the Pyramid, represented by the angle ABC, in our fig. 1. Now, early travellers, it seems, though attempting many other measures, seldom ventured upon angles; or when they did, mentioned this particular angle of the Pyramid, as being almost anywhere between 30° and 60°; and even Dr Perry in 1743, who was dissatisfied with all previous measures, and found fault with the regularity of the Pyramid also, stating that the angles of every side were different, and ran thus 40°, 37°5, 35°, and 42°:5,—was wofully far from the truth with every one of them. Hence there is no angle observation on record worth any attention, until that of the French savans in the celebrated Napoleonic expedition of 1799; and they, confining their attention chiefly to the Northern face of the Pyramid, or that upon which the one and only entrance into the Pyramid is found, and looking as well as they could along the broken line of the steps of stones as left by the ravages of the Caliphs, made the angle,— Billi! 47 This was in truth an exceedingly close approach, compared to anything that had been previously accomplished ; and it was confirmed by Mr Hamitton, who visited the Pyramid immediately after they had left, or in 1801, and recorded the angle as 51° 23" 46” And though M. Caviexia said the angle, in 1817, was so much as 58;, it is plain that he made no attempt at refinement in his measures. In this state, therefore, the matter remained, until Colonel Howarp Vysz’s all- important discovery in 1839, of two of the original casing stones, well preserved under the hill of rubbish below the entrance into the Pyramid; and he found them still firmly in setw ; that is, cemented securely to the grand and admirably smoothed as well as levelled plateau of rock on which the whole pyramid stands. Colonel Vyse’s three volumes should be carefully read, and some fifty other | authors, to establish the extraordinary importance of this discovery. | The stones were very large and of the most exquisitely truthful workman- | ship: one of them appearing thus in cross section (see fig. 2, on next page). The angle of the sloping side, being carefully measured by Mr Brerret, C.E., | for Colonel Vyst, came out 51° 50’; but on computing the angle from the linear _ sides as given above, in Mr Perrina’s measures, it appears to be = 51° 52’ 30:3’. | There is little doubt of the truth really lying between the two results, for | neither of them is to be implicitly trusted ; not the angle observed, because it is |, exceedingly improbable that the clinometer employed was equal to the unusually | high precision required in this case; and not the angle computed from the sides, | because those sides were not only measured with a rudeness, of merely to “ the 670 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM nearest inch ;’ but because an error of more than an inch may be suspected in — measuring the lower side, or that lying flat on the rock. Fig. 2. Feet. Inches. Its lower side being . 8 3 OULpper ee. cae aoe 3 Fi verueal:s oo one 74s ee » inelined . 6 3 This suspicion arises, from the circumstance of the lower left-hand corner in the section, which should be a right angle, coming out in the computation more than one degree and a half different therefrom ; an amount of error in their easiest angle, which the builders were not likely to commit, when they had arrived within 1 or 2 minutes only, of what was required of them in their most difficult angle. We have therefore as follows, from that unique opportunity of and the mischief-working of curiosity-mongers. By angle direct = 51 50 0 By vertical and inclined sides — 51 62 30:3 Mean = 51 51 15:2 By angle direct = 51 50 0 By vertical and inclined sides = 51 52 30°3 By three measured sides =e 51 50 46°5 Mean = 51 51 96 By angle direct = 51 50 6 By vertical and inclined sides = 51 52 30°3 By three sides = 51 50 46°5 By two sides, and base bes : shortened by one inch ? i oF On eee Mean = 51 51 222 OF THE GREAT PYRAMID. 671 Bl pl. 15-2 51 56 51 51 22-2 By all three means fl = First Mean 51 51 14:3 Hence we may arrange the authors, angles, and the circumferential propor- tion (or 7) which they attribute to the Pyramid, agreeably with Mr Taylor’s proposition, in this manner— é “ 7 Caviglia : : 58 = 2°49950 French Academy : 5119 4 = 320257 Mr Hamilton : 51 23 46 = 319360 Vyse and Brettel ; 51 50 0 = 314393 Vyse and Perring ; 51 50 46:5 = 314268 Vyse and Perring 3. 51 52 30°3 = 3°13922 Vyse and Perring corrected 51 52 12-2 = 313978 Final Mean, V., P., & B. 51 51 14:3 = 3°14159 Now the last result for z, is absolutely correct so far as it goes; and though there may be some doubt about the best way of taking the mean of all the ob- servations, where the observers had such very large probable errors as their measures of the stones exhibit,*—yet there can be none, as to the Pyramid result coming out better and better, in proportion as it is more closely examined into. The Pyramid has in fact proved itself to have been built closer to the truth, than the best and greatest of modern savans from all existing civilised countries have been able to measure it to: and if we are obliged to draw rein in pushing _ on the severity of our inquiry to still further places of decimals, the reason is not _ that the Pyramid fails in accuracy, but that modern observations are not suffi- ciently good to bear more than has been already put upon them. This first result, therefore, of applying an independent test to one of Mr | TayLor’s propositions, has ended entirely in his favour. And if the finding has | depended on the angle, A B C in fig. 1, alone, it may be as well to state here, that | there is nothing in-what remains to us of the original linear proportions of the _ Pyramid that tends in any way to invalidate the conclusion. | There have been, indeed, several ingenious suggestions as to various geometrical | proportions existing between the several parts of the Pyramid, including its | height, and base-breadth ; but it is hardly worth while to allude to them further, |as they are not accurate, and have not been advanced very confidently by any * Though the Vrsz and Perrine observations were so rough, yet they seem eminently honest | and fair: and it must add additional weight to their testimony in this case, that neither of these | gentlemen seem to have had any idea at the time, of what refined results their observations might | eventually be made to bring out, or what indeed the Pyramid itself contains in this direction ; for jin his 2d volume, Colonel Howarp Vysz, enumerating his laborious assistant Mr Prrrine’s conclu- | sions about the Pyramid, says, that its height is to its base-side, as about 5 to 8; which gives no | closer approximation to the value of a, then 3-200. VOL. XXIII. PART ITI. 8s 672 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM one as constituting the intention of the Pyramid; with the exception, however, of one very old statement, treated with much favour by Sir Joun Herscuet in the Athenzeum, April 1860; and asserting, that the area of each of the four inclined sides of the Pyramid equals the square inscribed on its height. Now to do this, the angle at the foot of the Pyramid, requires to be, as he states, 51° 49’ 46"; and — that is an angle which Sir Joun Herscuen declares to be “ practically indistin- guishable” from the angle required by the circular analogy of Mr Taytor, or 51° 51’ 14:3”; and, as Heropotus says that the Egyptian priests told him, that the area of the side to the square of the height was the intention of the Pyramid, —Sir Joun accepts such explanation, and repudiates Mr Taytor’s idea. 4 Answer may be made however, Ist, That the two angles are by no means practically indistinguishable; and that the measures already given, point clearly to the larger angle; 2d, That the Egyptian priests and people, even if inclined to instruct Hrropotus, were ignorant of the full contents and objects of the Great Pyramid; and 3d, That the area analogy can rank merely as an isolated feat, while the circular one is the most essential foundation in all that higher metro- logy, #01 which it may presently appear the Pyramid was actually erected. (2.) Standard of Length. Having in the last section determined only the proportion ‘existing between the height and base-breadth of the Great Pyramid, let us now endeayour to ascertain their values in /ineav measure. The following are actual observations, overlooking some comparatively small differences of French and English feet, Te- ported to have been taken by different travellers at the dates specified :— Present Northern Side of Name. Date A-p. Height in feet. Base in feet. Jean Palerme, ; : : 1581 600 660 J. Greaves, . : ; ) 1638 _ 499 Pen D. Monconys, : ; > 1647 520 682 M. Thevenot, : H 3 1655 520 682 Mr Melton, . , , oe 1661 520 682 M. Vausleb, . : ; : 1664 662 720 : M. Lebrun, . ; ; § 1674 676 704 De Careri, . F é : 1693. 520 682 Egmont, ; : ; : 1709 500 693 Dr Shaw, : , E é 172i 500 670 Or Perry, 7) : : ; 1743 687 789 M. Niebuhr, . 5 ; : 1761 440 710 Mr Davison, . ; P : 1763 461 746 M. Denon, . aoe é 1799 448 _ 728 French Savans, ‘ ; : 1799 nee 763°62 M. Caviglia, . ’ , 1817 ee 756 Howard. Vyse, ‘ - : 1839 nah 764 The list is interesting, as showing how little mere agreement amongst dif- ferent reporters, as in 1647, 1655, 1661, and 1693, can be taken as proving th the truth has been arrived at. On the whole, the height has been exaggerated OF THE GREAT PYRAMID. 673 ‘by bad observers more than the base-breadth ; the latter indeed, measured un- fortunately on the northern side of the Pyramid only, having been apparently shortened as compared with the latest measures: but that is mainly due to the latter being carried on at the real base, or a broader part of the Pyramid than the older observers ever arrived at, and being also increased by application of the computed thickness of the casing stones to either side. The French measure in 1799, and Col. Howard Vyse’s in 1839, are indeed the only returns that can be accepted, because the only ones that really touched the original marks of the workmen; and these they obtained by sinking down through the sand-hills that have silted up all the lower part of the Pyramid for many ages, and then uncovering on the foundational rock-area of the whole structure the peculiar socket-marks of the old N.E. and N.W. corner stones, clearly and deeply cut into firm material. The honour of this very important discovery belongs to the French, and is detailed at length in their great work. The mean of these two most useful French and English measures, gives 763°81 for the breadth of the side of the Pyramid base; and the angle we deduced be- fore, gives with such base, the original vertical height equal to 486'2566 feet. Now these are such extremely awkward fractions to have to deal with, that we may take them as conclusive against any measure like English feet having been employed in laying out the Pyramid. And if we seek on this principle for simpler numbers to give the proportion for the circular analogy, we find 116°5 and 366. They are not exact, as no numbers can be when the proportion itself is incommen- surable; but they are exceedingly close, the change for fuller accuracy being thus, 116°5014 and 366. or 116°5 and 365:9956. The number 366 in this case represents twice the base-breadth of the Pyramid, ~ or what was employed against the height of the Pyramid (116°5) in representing the analogy of the circumference to the diameter of a circle. And as measures of space and time are often considered in company, it is worth while to remind, that 366 is also the nearest even number of days in a year; and more especially, that it is the number of whole turns made by the earth on its axis in the same time, as measured by the sidereal day. A length, therefore, of which 366 would measure the double base-breadth of the Pyramid, has some arithmetical, chro- nological, and dynamical arguments in its favour; in connection with the last of which, it further transpires, that such length has the very peculiar metrological import of being the ,..., of the earth’s axis of rotation; or of the only fully individual and correct reference for lasting national measures which the earth contains, now that its diameter at the Equator has been shown by recent geode- sists to vary with the longitude. ~ To test such a point as this, we require, not only the nominal measures taken 674 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM at the Pyramid, but comparisons of the scales or rods employed there with those used in modern geodetic operations. These unfortunately we have not directly, and in all the cases which I have had an opportunity of examining, there had been a shortening of the scale in a hot, desert country. On a wooden scale, the dry weather might account for this; but on a steel rod where it certainly existed, it seemed only explainable by a slow contraction of the metal, gradually recovering itself from the operations of extension which it had undergone by hammering and rolling at the forge. The French savans ought to have guarded against these sources of error, and their observation is evidently by far the more carefully taken of the two pre- viously cited ; and gives, reduced to inches, for the ,4,th part of the double base- breadth, multiplied by 10 millions, 500,733,000 ; Or, in using the 343.3555, 500,740,000. Howard Vyse’s measure, similarly treated, gives 500,984,000, and 500,990,000. But correcting his measure, by the proportions which his numbers for ‘‘ the coffer” bear to those of Prof. Greaves, and correcting Prof. Greaves’ measures by the French determination of the length of the foot which he engraved in the Pyramid on granite, immediately after measuring the coffer, and which foot is stated by M. Jomard, in the “ Description de l’Egypte,” to be 0°30460 of a metre (of which a whole length is equal to 3937079 English inches), the above quantity should be reduced to 499,915,000, and 499,921,000; and the mean becomes, giving twice the weight to the French measure, as seems at least its due, from the superior care taken with it, 500,528,000, and 500,535,000 ; \ Mean =500,532,000. Now this quantity is quite contained within the variations of modern observa- tions of the earth from each other, even in the best and latest geodetic com-— parisons; for they are given in the shape of different determinations of the — length of the earth’s polar axis in inches, by De Schubert, as varying between 500,560,000, and 500,378,000 ; but with much more inclination toward the former than the latter; and he is not materially differed from by the results of Bessel, Airy, Herschel, and Pratt; the latter, by his last refinements of taking into account the local disturbances at each | astronomical station, making the polar axis equal to 500,523,000 inches nearly ; while the others are all rather under 500,500,000. Wil OF THE GREAT PYRAMID. 675 We can hardly, therefore, do otherwise than conclude, if the supposition of a “lucky accident” be afterwards shown improbable, that the standard of length (=50°05 English inches nearly) in use at the Pyramid was, and was intended to be, in linear value=,,—, of the earth’s axis of rotation; and it is even further identified with the Pyramid in this manner :— Mr Taylor has pointed out that there are reasons for concluding that inches were in use at the building of the Pyramid, and that these inches were slightly larger than ours, so that 500,000,000 of them measured the earth’s axis of rota- tion precisely. Now in the Pyramid, a body mathematically with 5 sides and 5 angles, every- thing may be expected to go by fives; and, accordingly, the inch, the wnt of linear measure, is the one 5-hundred-millionth of the earth’s axis of rotation. The grand linear standard,—for scientific formative purposes, or those wherein the earth has to be alluded to as a whole,—and which we propose to call the “metron,” viz. the ;4,th of the double base, and the one ten-millionth part of the same axis, contains 5 times 10 units. The smaller standard,—for convenient use, and for distance-measuring, wherein the half only of the earth requires to be referred to, because distances should be reckoned from the centre, and not either the nearer or further, surface of a ‘sphere,—is zé;th of one side of the base; contains 5 times 5 units, and is the one ten-millionth of the earth’s radius of rotation. While if a foot do not contain any even number of fives, it likewise is not any integral fraction of the earth’s axis of rotation, is not a scientific standard, and, though tolerated in the base, has not been allowed to enter into any of the interior arrangements of the Pyramid. (3.) Figure of the Earth. If anything further could add weight to the belief of the polar diameter of the earth, so clearly hit by the actual measures of the double base-breadth, having been intentionally referred to for the linear unit of the Pyramid, it might well be the finding that certain other diameters are indicated in the building, and a knowledge of the full figure of the earth, with a purpose, thereby manifested. Without having speculated originally about any such idea, something of the sort appeared spontaneously to me, when engaged in testing two “ size-analogies,”’ which Mr Taylor published for the second time in 1863, in his “Battle of the Standards.” They had been examined by Sir J. Herschel in 1859 or 1860, and declared by him, in the Athenzeum of 1860 for April, to be the only cases he then knew of, where a relation had been made out between the size of the Pyramid and that of the Earth; but he intimated that they were only rudely approximate. By aid, however, of the conclusions deduced from the base of the Pyramid in our ‘last section, we can employ improved values, because the original ones, for both height and base, and therewith repeat the calculation under more favourable cir- cumstances. VOL. XXIII. PART IU. o 676 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM For the height, then, we take 1165 metrons, or 5825 primal inches; for the base-breadth, 183 metrons, or 9150 primal inches; or 762°5 feet, 7.¢. primal or Pyramid feet ; and for the polar axis of the Earth, 500,000,000 of the same inches. Then, the first of Mr Taylor’s two analogies is, in the form chosen by Sir John Herschel,’ “‘ a band encircling the earth, of the breadth of the base of the Great Pyramid, contains one hundred thousand million square feet.” Adapting this statement to our primal Pyramid feet, and to a form of expression suitable to bringing out the diameter of the earth, and in inches, ‘i have 100,000,000,000 762°5 12 This resulting quantity, so much greater than the Polar diameter, may be refe from the encircling-band manner of its derivation, to a mean latitude of 45°. The second of the analogies is, that “‘the height of the Great Pyramid i is a70.000th of the earth’s circumference.” Why, however, that particular fraction? Had it been 3554555 OF souv0o OF even + 900.000: 2-é., anything easily made up of fives and times of five, there wo have been a rude sort of “ Pyramid reason” in it: but for 270,000 I could find no reason. Considering, however, the act of standing by the Pyramid on its base, in this inquiry where its height is to be measured against the earth which it is standing upon, —and finding that the area of its base in hundredths of feet has when thrown into a circular shape, a circumference equal to 270,299,—I presumed ~ that that might be accepted, if not as a reason, at least as an apology, for trying the case with that number. Arranging the expression accordingly so as to bring out the axis in inches, there appears, = 500,946,700 Primal or Pyramid inches. x 3°14159 270,299 sake 3:14159. ~ ’ or 5825: x 86038:901=501,176,400 Primal or Pyramid inches. Pyramid height in inches x This diameter of the earth, obtained so directly from the height and act of standing of the Pyramid on its own base, must, if any one result could do so more than another, refer to the diameter in the Pyramid’s own latitude: and the Pyramid’s position is stated in the French maps, and most of their memoirs, to be, 29° 59’ 6"; but may be assumed in such an approximate case as this, to be 30°. _ Computing next, from a theoretical polar diameter of 500,000,000, the values for latitudes 45° and 30°, with a compression of ;3,, we have the following to compare with the Pyramid deductions :— | Computed Earth Diameters. 2 Pyramid Analogies. Polar, ~ . 500,000,000. Polar, = 500,000,000. Lat. 45° . 500,840,000. 45° = 500,946,700. Lat. 30° . 501,257,000. 30° = 501,176,400. Simple inspection of these numbers will show at once, that by far the grea portion of the whole difference from the Pyramid-base deduction, assumed polar, OF THE GREAT PYRAMID. . 677 is explained by the compression hypothesis, combined with the latitudes 45° and 30°. The amount of difference left outstanding, is indeed much smaller than the limits of errors of observation in the best modern measures of the earth’s polar diameter: so that perhaps we ought therewith to be content. But of course the question will be asked, in which way do the residual differences point, 7.¢., for more, or less, polar compression than that favourite quantity of .3, ? And then comes the answer ; that they indicate the average quantity of $5 to be exceedingly close to the truth ; but accompanied by an irregularity, tending to produce a protrusion near Lat. 45°, at the expense probably of the neighbouring parts; and inclining to give the earth, in meridian section, something of that squarish look, which Sir Witt1Am Herscuex thought that he had detected tele- scopically in the planet Saturn. Mr Matn’s Greenwich observations of Saturn are, indeed, considered in some quarters to have annihilated the Herschelian idea ; and they have proved that there is no very Jarge quantity of such squareness ; but such a moderate amount as what is indicated by the Pyramid analogies, is far beyond the powers of astronomical micrometer observation, in our bad ob- serving atmosphere and even in the present day, to hope to reveal. (4.) Latitude Markings. The grounds on which we have hitherto considered that the latitudes 45° and 30° were intended to be alluded to in the Pyramid, are certainly of a hypothetical character; and therefore, though the hypotheses be ever so sound, they will be improved and strengthened in the opinion of many persons, if proofs of a prac- tical character can be found to support them. Proofs too, of this order, do really appear to exist in the building still; though we must begin with something of hypothesis to arrive at them. In figure 3 (Plate X XIII.), therefore, is a carefully drawn theoretical meridian section of the Pyramid, as in fig. 1, (p. 668); but in place of the large square of the base, there is now a small square, symmetrically placed with it. The size of this small square is 103:246 metrons in the side, and is obtained by computa- tion as being equal to the area of the Pyramid’s meridian section. This small square, in itself, and by some very simple divisions, shown by the dotted lines in fig. 3, enables us to arrive quickly at the placings of all the few chambers and passages in the Pyramid. To prove this important relation, fig. 4 (Plate XXIV.) contains a careful copy of Colonel Howarp Vysz’s large meridian section of the Pyramid, in the Ist volume of his great work ;* and to facilitate the comparison, I have added to it the chief lines of the hypothetical Plate X XIII. fig. 3, in rows of dots. * This section, like most meridian sections published, since the time of Professor GReavss in 1637, agrees to overlook the small distance by which the passages of the Pyramid, though truly in the plane of the meridian, are slightly to the east of the true central meridian section of the Pyramid. See fig. 7, Plate XX VII. 678 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM First, we may remark, of the chambers,—the top of the topmost chamber of construction is on the level of the upper side of the square EF. The floor of the so-called “ King’s chamber,” is nearly on a level with the line LN, or 4 the semi- diameter below EF. The floor of the “‘ Queen’s chamber,”’ so called, is nearly on a level with the line OP, or 2 the semi-diameter below EF; and the floor of the subterranean chamber is on a level with the line C’S, or 4 below the centre; and these are all the chambers known to exist in the Pyramid. Second, of the passages, principal. The entrance passage places itself exactly on our hypothetical line C’*’, until very near its lower termination. The ascend- ing passage, with the floor of the grand gallery, also place themselves exactly on our hypothetical line, in fig. 3, QRL ; and the horizontal passage places itself also on our line, RO. Now, the angular direction of C*’, (QRL being the same angle inverted), is made by construction the same as that of C*; and that again depends on the height of the Pyramid as radius, and the semi-side of the square of area as sine; and = 26°18’ 10". This might be looked on at first as a pure geometrical result, but it depends on the measured height and base of the actual Pyramid; and, further, it agrees unexpectedly with the measured angle of the entrance passage, which has hitherto been universally allowed an astronomical signification ; viz. to point — to « Draconis, the Pole star of 2121 B.c., at its lower culmination, or, according to Sir Jonn Herscuet, 26° 15’ 45"; and inasmuch as the best measures of the — actual angle of the Pyramid passages are anywhere between 25° 55’ and 27°, our hypothesis is as fair as it need be. | That hypothesis next gives the line CE, as at an angle of 45°, of course; but it is further, and architecturally testified to in the Pyramid, according to Col. Howarp Vyse’s plate, by the line of the Southern air-channel being also at an _ angle of 45°; or one of the geodetic indications we are seeking. . The Northern air-channel on the contrary, his plate makes at an angle of 33° _ or 34°, for the drawing is not fully accurate; let us say, then, 33° 42’. If, then, the mean of this and the angle of the entrance passage, the only remaining com- munication from the Pyramid’s interior to the outer air, on the same northern side be taken, it is equal to 30°; or the same as our hypothetical line C’ 30°, which is by construction = to C 30°, and which depends on the semi-diameter of the area-square as sine, and the radius of a circle of equal area to the base of the Pyramid, as radius; and is the other geodetic indication being sought. Strictly computed, with the 116-5 and 183 metrons to start from, this theoretical Goedetic or Latitude angle is 29° 59’ 59-2”, and reminds us that the observed Latitude of the Pyramid in 1799, was less than 30°, and more than 29° 59’. On the one hand, however, it may be said, that, given a Pyramid built to realise + OF THE GREAT PYRAMID. 679 the abstract circular analogy, or Mr Taytor’s first proposition,—an angle C 30° must come out very like what we have educed: no matter in what Latitude soever of the earth such a Pyramid were planted down. That is quite true: but then, on the other hand, we are assured by the observa- tions of the French Academicians, for the azimuth of the sides of the Pyramid, and which they found under 20’ of error,—that astronomy had a most im- portant share in the foundation of this Pyramid: and therefore, when we find appended to the above-mentioned construction-angle of 29° 59’ 59-2” a certain other angle of 26° 18’, which astronomers have already proved before the world, to have been intended for the lower culmination of the Pole star of the Pyramid- building period,—there seems hardly anything else that we may conclude, except that the first angle is astronomical also, and represents the latitude at the time. For the mere purpose of checking a determination of the terrestrial polar compression, the difference of 53”, or less, in the ancient and modern latitude is of no great importance. But is that difference explainable by a slow change of the latitude of places on the earth, insensible from year to year, though notable in 4000 years? Perhapsitis so; for the latitude of Greenwich has been similarly decreasing under its three last Astronomers-Royal, to the extent of almost 2” in 100 years; partly from other known or suspected causes, but not entirely. It may again be objected, that if the latitude of the Pyramid is to be typi- fied, as above, in the proportions of certain of its parts,—there is only one parallel of latitude, where such a Pyramid could be set up, and preserve alike both its geometric truth, and its astronomical and geographical indications. To this, we may say, that the remark is perfectly just, and will prevent other Pyramids in Northern or Southern countries ever competing with the scientific importance, and fullness of meaning of the Great Pyramid ; while if, as we may be presently able to show, the founders of the Great Pyramid were not native Egyptians, but came into Egypt from a country in another latitude, and went back to it again after finishing the Great Pyramid in Egypt, but built no similar | Pyramids in their own country, it would almost appear that they understood | the weight of the modern objection to any other parallel of latitude than that | which they employed, and even went out of their way to seek. In the meantime, we merely conclude this section with a few of Col. Howarp | Vysn’s measures of the Pyramid, to check his drawing, or rather our small repro- | duction of it, before going forward to some more important consequences. Approximate Pyramid Dimensions. By Col. Howarp Vyssz, 1839. Feet. Inches.| Inches. Former base, ; ; ; ; ; : ; . 764 0 9168 Present base, - ’ ; ; : ; 746 0 8952 Present height, vertical, : 450 9 5409 Perpendicular height from base to bottom of entrance, , 49 0 | 6588 Distance of centre of the entrance, eastward from centre of l 24 g | Pyramid, : : ; ; ; J 294 VOL. XXIII. PART III. 8U “ 680 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM Approximate Pyramid Dimensions—continued. Feet. Inches. | Inches. Angle of entrance passage = 26° 41’. Length from beginning of roof to the junction of ascending 63 9 758 passage, : , ; : : From thence to end of descending part, : . fa OD 8 3092 Depth from base of Pyramid to roof of subierranesd chamber, = 90 8 | 1088 First ascending passage, length, : : ; ip = 104, oh 1492 Angle = 26° 18’. Grand Gallery, length, ‘ : 2 156 0 1872 Horizontal passage, length, . ‘ : ; 2 Sime hOOK oacl 1319 Northern and southern air-channels,— ; Inclined height from base of Pyramid, . ; : . = 831 0 3972 Northern channel, length, . A : : . . 233 0 2796 Southern channel, length, : 4 ner 3 2091 From base of Pyramid to floor of King’s Chamber, : Paik 9 1665 Height from floor of King’s Chamber, to roof of Col. Camp. i bell’s chamber, or ‘‘ topmost chamber of construction,” j = 69 3 831 Height from base of Pyramid, to floor of Queen’s Chamber, = 67 4 808 (5.) Unique Interior. Though Pyramids are numerous in Egypt, and may be counted, some say by | hundreds, there is not a second instance, to be found in any part of the land, of — the full interior arrangements of the Great Pyramid of Jizeh. In proof of this remarkable assertion, the reader may be referred either to — Colonel Howarp Vyse’s and Mr Perrine’s very numerous plans and sections of all the principal pyramids in Lower and Middle Egypt, or to the “ theory of pyramid structure’ put forth by Dr Lerstus, and Mr Winp, architect, and testified — to by Bonomi, Guippon, and almost all other modern Egyptologists. The theory is, when abstracted to set forth the subject we are dealing with, that a pyramid is a king’s tomb, built by himself: that he begins on his first accession to the throne, by excavating deep in the rocky soil a sepulchral chamber, reached only q by a descending passage ; and that he then goes on adding masonry every year — round about a nucleus erected vertically over the said chamber, until he dies. — When the upper pyramidal mass has spread at its base, by yearly additions, beyond the descending entrance-passage’s mouth in the rocky soil,—it, the pas- _ sage, is continued upwards, and at the same angle as before, through every addi- — tional layer of masonry. But when the king dies, his body is conveyed down that inclined passage, and deposited in a stone sarcophagus, in the underground — chamber ; after which the entrance to the passage is sealed up, and all the rough — rectangular corners of the layers of masonry on the outside of the pile are bevelled off, in situ, to one, smooth, inclined surface. Now that mere subterranean chamber with a descending passage, which is all the internal arrangement implied in the theory, and all that is found in general Egyptian practice; (except when one king has broken into the Pyramid cellar of another, and made himself a subterranean sepulchre and entrance- OF THE GREAT PYRAMID. 681 passage from a different side, by digging into another’s property; and even then it is still the same order of arrangement),—this one principle or feature, we say. exists also in the Great Pyramid (see fig. 4); and is exemplified in the one descending entrance-passage, and the subterranean chamber marked c. That particular portion, and that portion only, of the internal arrangement of the Great Pyramid, is a common Egyptian institution; and there are proofs in fact that the Romans were once inside that chamber. (Col. Howarp Vysz, 2d vol. p. 290.) But all the upper parts of the arrangements of the interior (see the same ‘ fig. 4), all that is gained by the ascending passages, are absolutely peculiar to the Great Pyramid alone; and there are no proofs whatever that Romans, Greeks. Persians, or the Egyptians themselves, subsequent to 2130 B.c., knew anything whatever about the existence of that part of the interior. Its builders had in fact sealed it up carefully; and their stone-seal remained on, and kept its secret faithfully, until it fell off, of its own accord, or in a manner rather more than accidental, in the time of Caliph Al Mamoun, about 820 a.p. . Then it was that the first symptoms of there being an ascending passage were perceived: It could not, however, be rushed straight into by the eager beholders. because an unliftable portcullis of granite stopped the way; but by breaking a path through the smaller masonry, Al Mamoun and his people succeeded in entering the same ascending passage further on; and from thence pushing forward. fired by the hope of seizing “on the wealth deposited by the antediluvian kings of the earth,” they passed through the “ Grand Gallery,” the little ante-chamber, and then entered the so-called King’s Chamber, evidently the principal chamber of the whole Pyramid, the last of its series of rooms and passages, and the one for which the entire structure had been erected. A magnificent room it was, 34 feet long, 17 broad, and 19 high, formed on every side, floor, walls, and ceiling, of enormous blocks of granite, perfectly flat. admirably polished, and fitting to each other so closely, that the smallest needle could not be introduced into any of the joints. But there was nothing in the chamber! The eager visitors looked about (by torchlight, for all of the interior of the Pyramid, save the entrance passage, is necessarily unvisited by the light of day), and could find absolutely nothing; unless indeed a stone trough, as they called it, or a granite chest; but if a chest, it had no lid and was entirely empty ! The Caliph and his companions were thunderstruck; their treasure theory had | so completely failed ; and though they afterwards quarried holes in different parts , of the exquisite building, they found no jewels of silver or jewels of gold, beyond | the one particular pot of money which Al Mamoun himself had just previously | buried, to encourage the workinen. | Previous to Al Mamoun’s entrance into the Pyramid,-the Arabian writers had | indulged in every kind of rhapsody as to the extraordinary treasures which it | contained ; and soon after his signal failure, they recovered somewhat of their | spirits, and began, in their patron’s praise, to chaunt his astonishing findings : 682 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM but in terms that now prevent their being listened to with patience: while, seeing - that some of them declare that the king’s chamber was admirably sky-lighted, when we know the interior to be absolute darkness; and that its ceiling was covered with inscriptions, when the whole of the finished interior is positively without a stroke of inscription,—shows how little we can trust their statements, either that a dead body having a golden breastplate, was found in the stone box, with a sword of inestimable value, and a carbuncle the size of an egg, shining like the light of day; or, that the said box was full of gold in coin of very large size. Ages passed after Al Mamoun’s essay, European travellers began to look in at the Pyramids, and rather patronised the corpse notion: for the stone chest, or marble hot-bath, or porphyry coffer, as it was variously called, was very much in shape like the lower part of an Egyptian sarcophagus. But then in that case, why was it, the coffer, so entirely without orianicnil why so utterly without inscription, when that would be the precise place where Egyptians would have lavished their inscriptions; why without a cover, and without any fixing places to receive a cover ; and then whoever heard of a corpse being buried above, and so much as 140 feet above, the level of the ground: and, lastly, if the room was intended for a corpse only, why was it so well ventilated, by the two remarkable and effective air-channels (see Plate XXIV.) discovered by Colonel Howarp VyszE? In short, the failings of the sepulchral theory were so many, as of themselves to give rise to the idea with some philosophic minds who weighed everything carefully (such as the French Academicians in 1799, and Sir GARDNER WILKINSON in 1858), that no body of a king had ever been deposited in that porphyry coffer. The Academicians even boldly expressed a belief that the said coffer might pro- bably have been intended for something entirely different ; or, for a standard of linear measure. This idea, however, they were not able to prove; and even the — very memory of it seemed to be lost within a few years after, by reason of the — excessive applause which followed the discovery of hieroglyphical interpretation. Hieroglyphics, however, have done nothing for the explanation of the porphyry coffer, because indeed it has no hieroglyphics, and in the meanwhile Mr TaYzor ~ comes out with a new and striking idea,—* ‘ The porphyry coffer, says he, is a standard measure, not of length, but of capacity and weight; it was the original of all corn measures; the Pyramid itself receiving its name from svg; wheat and ergo measure ; and the so-called ‘‘Quarters, ” in which the British farmer, up to the present day, measures his wheat, are accu- rately quarters of the cubical contents of the porphyry coffer in the King’s Chamber 5 of the Great Pyramid. | * While at press, I am informed of the existence of a rare pamphlet, but have not yet been able to see it. The Origine and Antiquitie of our English Weights and Measures discovered by their near agreement: with such standards, that are now found in one of the Egyptian Pyramids, London. 1706. Anonymous : and reprinted in 1745, with the authorship attributed to Professor Greaves, of Oxford, who died in 1652. I OF THE GREAT PYRAMID. 683 Let us look into the accuracy of this very suggestive statement. (6.) The Porphyry Coffer ; its Size and Material. The following table contains all the printed particulars which I have been able to collect, touching the measured size of the coffer; and it will be seen, not- withstanding the popular impression as to the most accurate admeasurements possible having been repeated again and again on every part of the Pyramid,—that these measures of the coffer are, on the whole, so bad, as to reflect not a little discredit on almost all those modern civilised nations they emanate from; and who, when at home, employed on their own standards, measure them, they say, to seven or eight decimals of an inch, true. Some of the measurements may be in French inches, and therefore require an increase of their number to represent English inches, but that would not much improve the real diversities of the measures by different men. MopERN MEASURES OF THE PYRAMID COFFER. Date EXTERIOR. INTERIOR. AUTHORS. j MATERIAL. a Length. | Breadth.| Depth. | Length. , Breadth.| Depth. Inches. Inches. | Inches. | Inches. | Inches. | Inches. Bellonius, . .{|1553) Black marble | 144: [2k nit P. Alpinus,. .{|1591) Black marble | 144° 60: 60: Ie ta | LOLOL 6 oo ve waisles 84: 47: “ De Villamont, . {1618 Black marble | 102: a 60: Ade bite tae Prof. Greaves, . |1638) Thebaic marble | 87:5 39°75 | 39°75 | 77:856| 26°616|] 34°320 De Monconys, . |1647, ___....... 86° One 40: oe ee oa M. Thevenot, . |1655) Hard porphyry 86° 40: 40: 75:2 29° 4 Misbebrum... .|1674) _—......... 74: 37° 40: me wie M. Maillet,. . {1692 Granite 90° 48- 48: De Careri, . . /1693 Marble 86: 37° 39: tan ae Lucas, . . .{|1699| Like porphyry 84: 36° 42° 74:2 26°14 Egmont,. . .{1709, Thebaic marble | 84: seve 42: 72:2 “or Pére Sicard, . |1715 Granite 84: 42- 36° aes oy Dreshaw, . . 1721 Granite © 84: 36° 42: ea 24:2 Dr Perry, . . {1743 Granite 84: 30: 36° ne oe M. Denon, . . |1799 2 84- 48° 38: Aas ae SA M. Jomard,. . {1800 Granite 90-592 | 39°450 | 44-765) 77:836| 26:694| 37:285 Dr Clarke, . . {1801 Granite 87°5 39-75 | 39°75 he pee Loe Mr Hamilton, . |1801 Granite 90: 42° 42: 78:2 30: 2 sic mrwWhitman, .|1801] __...... 78: 88:75 | 41:5 66° 2 26°752| 32: Meeyilson, . .|1805) 6. ...... 92: 38° oe: 80°? 26:2 34°5 Mescaviclia, .|1817) | - ....0» 90: 39- 42- 78: 2 27° 4 ‘Dr Richardson, |1817| Red granite 90: 39° 39°5 vas we Sir G. Wilkinson,/1831) Red granite 838° 36° 37° a Bie ae ie } BBS] wee ate 90-5 | 390 | 41:0 | 780 | 965. | 34-5 When a note of interrogation has been applied to an interior measure, such measure has been obtained from the exterior one, through means of the thickness as given by the observer in question. VOL. XXIII. PART III. 8 x 684 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM The three chief authorities who, for accuracy, distance all the rest, are Professor GREAVES in 1638, M. JomarD in 1800, And Howarp VYSE in 1839. Yet even on their measures it would be dangerous to speculate on what the out- side dimensions of the coffer may be, to within an inch or two. Fortunately, for a capacity measure, we have not to pay much attention to — the exterior; and the zmszde dimensions are given with less uncertainty. Never- — theless, Howarp Vyse’s are rude beyond toleration in such a case (only to the © nearest half inch); and the French measures are vitiated in the depth element, — by a blunder of nearly three inches; 2. ¢., it seems so to my best judgment. Hence, the ancient Oxford Professor is the only authority left outstanding; — and happy it is that he so far transcended his age’s ideas of accuracy in such — admeasurements; and thought, too, so much more of the interior, than the exterior. There is, indeed, some doubt as to the real value of the length of a foot on the scale employed by Greaves, and that known as the English foot in the present day; and there, the French academicians have done good service; for GREAVES, immediately after his measure of the coffer in 1638, marked off the length of one foot of his scale on the unchanging granite of the walls of the chamber; and these marks being visible in 1799, M. Jomarp measured them and found them =0°3046 of a French metre; whence, on the understanding that one French metre is equal to 39°37079 modern English inches, we have the following corrected statement of GREAVES’ measure, Vviz.— Interior length =77°806 breadth = 26:599 depth =34:298 2 3? and these being multiplied together, yield 70,982:4 English cubic inches, as the observed contents of the Pyramid coffer. If we then turn to the British Act of Parliament defining from the bushel the number of cubic inches in a “ Quarter,” and multiply that by 4, we have, ’ 70,982°1 ; a closeness of approach which is something more than startling. : As to the material of this remarkable vessel, it would be hazardous to venture — from black marble to red granite; but we rather incline, from private informa- tion, to “‘ porphyry;” and, in the event of the metrological character being full; / established, it would be important to ascertain both precisely what sort of porphyry it is, and where it came from. At present, we must rest satisfied, with OF THE GREAT PYRAMID. 685 its having apparently most admirable qualities for a standard measure, viz., extreme hardness, utter unoxidisability, perfect freedom from flaws, small expan- sion from heat and extraordinary great age. (7.) Why of that scze ? Given, agreeably with the observations detailed, that the cubical contents of the coffer are, 70,982°4 cubic inches,—let us inquire, why are they so? or, why was the coffer capacity measure, made of that particular size ? With the linear standard, if a similar reason be asked, the Pyramid answers at once, because that length is the one ten-millionth of the earth’s axis of rotation : but if the question be asked an Englishman, touching his bushel,—he can only say, accident ; and if the modern Frenchman, touching his “ litre,’”—he can only say, that it is the cube of an arbitrary fraction of his linear metre Now it is the intellectual boast of the Frenchman that his linear metre is an integral fraction of a linear proportion of the earth itself, or rather, a quadrant of the meridian; then why did he not try to get a similar scientific merit for his capacity measure, viz., that it is an integral fraction of the capacity of the earth ? But he did not do so; nor did he contrive for his weight measure, that it should be a similar fraction of that all-important physical characteristic, the weight, of the whole earth-ball; whose general figure, and one and only property, as implied by the French metrical system, is. that of being a curved line, like the boomerang of an Australian savage—a flaw, certainly, in the scientific recommendation of the French system. Then how does the same point fare in the Pyramid ? I had been quite at a loss to find out any reason there, for the size of the coffer; until certain features of the Pyramid itself led me to an idea, which was not in my mind before. Over the entrance door into the chamber containing the coffer, are five vertical parallel lines, or, as some say, a space divided into five equal parts. This should have reminded any one of the Pyramid standard, and kept him true to that, as indicating the foundation of what was within. Now 50? = 125000, and that is much more than the cubic contents of the coffer ; besides indicating a rectangular figure for the earth. Three dimensions must be taken, but they belong to a spherical body, or, as the latest geodesists have shown, to an ellipsoid with three axes, viz., the Polar, and the major and ‘minor of the Equator; and this seemed to be intimated by the three curved hollows in the antechamber, described by many authors, and pictured in our Plate XXV. fig. 5. Reducing the cube of 50 to a sphere’s contents, will how- ever not give the coffer’s conteats; it will give the same number of places of figures, but their value is too small. Seeing, however, that weight-measure usually goes with capacity ; and this is typified in the ante-chamber, by the suspended block of granite in the 4th groove, close to the semicircular hollows; and being reminded by the 5 chambers of 686 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM construction above the coffer room, of the fraction representing the earth’s mean density,* I tried applying that to 50°, and got the contents of the coffer at once, though in the form of being multiplied by 10. Striking off, however, one figure,— so as to have the number of places of figures as given by the pure capacity reduction,—then the precise value of the coffer's cubic contents in inches was obtained, to at least this very close degree of approach, viz. : 50 “9 % 5672 = 70,900 ; but 70,900 being Pyramid inches, must be increased to 70,970-2 in order to represent the same in English inches. The measured quantity, in the same terms, it will be remembered, gave 70,982°4; but we shall now use the theoretical determination of 70,970-2 in preference. This then forms a definite metrological quantity, derived thus simply from the one ten-millionth of the earth’s axis of rotation, influenced only by the combined qualities of the earth’s capacity power, and mean density, or weight-power; and has therefore eminent scientific recommendations for the grand standard of ca- pacity and weight measures. (8.) Of what Weight ? The capacity of the coffer is already given at 70,970:2 English cubic inches; but what weight shall be assigned to it ? The best plan is, to fill the vessel of that given size, with pure water, and weigh the contents. Now the Great Pyramid seems to have had in its normal state a deep well penetrating down to lower strata, soaked with and filtering the Nile water: while the so-called Queen’s Chamber, with its peculiar depressed floor and air-tight masonry, served as a reservoir at once large and conveniently placed: water therefore could be had. But then, of what temperature would it be? for water alters its density rapidly on heating or cooling. . The mere mention of this scientific requirement of modern times, seemed at first to threaten ruin to the sufficiency of any arrangement descended from primeval days of the world, to meet the exacting demands of present physical science; but — * The history of the experimental determination of the earth’s mean density, is a very interesting one, and its honours fall almost entirely to Great Britain. It has been tried by the attraction of the plumb line on mountains : by the effect on a pendulum at the top and bottom of a mine, and by the — ‘* Cavendish experiment,” between the parts of a philosophical apparatus; and has varied in the first case from 4°5 to 5:4; in the second from 6 to 6:5; and in the last from 5-4 to 5:8; or in the latest, — and most perfect trial of it, by Francis Baity, from 5°68 to 5-66. His own published mean is 5-675, but uncorrected for some circumstances which he himself thinks should be corrected, and — which we have estimated, in accordance with his numerical indications, at —:003.—Sce further at p. 699. $ é OF THE GREAT PYRAMID. 687 the result of examination has been the crowning of the Pyramid system with some most unexpected features of practical success, and purposed intention. To “correct for temperature,” is a very interesting occupation in Natural Philosophy, whether accomplished by calculation, or by instrumental appliances of compensation ; but in practice, and where extreme accuracy is required, it is found that heat is so excessively subtile an influence, and has so many various actions on bodies, sometimes with a secular, and at others with a periodical effect, —that the safest plan by far is, to reduce the amounts of temperature variations themselves to the lowest possible ebb ; and then only have to deal with the effects of the very small residual quantities of heat'so left. Hence at Pulkova, Paris, Edinburgh, and some of the most accurate Observatories in the world, great advantage has recently been found, by placing the sidereal clock of each establish- ment, though armed with a reputed temperature compensation-pendulum, under circumstances where variations could not happen so easily, quickly, or to so great an amount, as in the open room: and every increased degree of such protection has been attended by better performance of the clock. The simple placing of the clock in a large closet, has been of sensible service ; but much more good has been obtained by establishing it in a cellar, as at Pul- kova; and more still, in a cave 95 feet under the surface of the ground, as at Paris. But at no Observatory in the world have they a room, like that of the King’s Cham- ber containing the porphyry coffer or weight and capacity standard, in the Great Pyramid, protected by nearly 180 feet in depth, of solid stone on every side. In such a room, the semi-annual variations of atmospheric temperature may be cut down from 50° Fahr. to something less than -01 of a degree. Hence the interior Pyramid temperature, must, so far as depends on external natural causes (for of course it is not proof against numerous Arabs inside, with blazing torches), be practically constant from day to night, and summer to winter, and year after year. There is evidently, then, a peculiar temperature to the Pyramid; which, in Metrology would form a valuable constant. What then, is, that temperature? Or, rather, what used it to be, when the building was in its normal state, throwing off the sun’s hot rays from its polished white casing-stones, and having the dryness of its atmosphere corrected by watery vapour effused from its lower, open water-well? see Plate XXIV. As the Pyramid has never been observed by moderns under these circum- stances, we must seek our data from various older quarters; confined however practically to the French alone; amongst whom M. Jomarp states that he and his compatriots, in 1799, noted the temperature of the King’s Chamber to be 22° cent.; of the lower part of the dry-well, 25° cent.; and of certain tombs outside ‘the Pyramid, also, 25°. Now these two last sites are nearly on the same level, and a few feet under the general surface of the ground; it is therefore right that they should have the VOL. XXIII. PART IIL. Sy 688 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM same temperature. But the other station, though inside the Pyramid, is 140 feet — above the ground outside; it is therefore also right that its temperature should be less, perhaps about 22°. : But this temperature was raised unnaturally by the presence of Arabs and their torches, and by the absence of watery vapour. Referring therefore to the — same philosopher’s measure of the temperatures of the great Joseph well in the — citadel of Cairo,—and where there was probably rather too much watery vapour,— : and finding him give that temperature as 17° or 18° centigrade,—we may suspect that the mean between these two and what was observed in the King’s Chamber, at least to the nearest even degree, would be the true result for that chamber under normal circumstances. ; We conclude, therefore, from thence, that the Pyramid constant is 20° centi- grade; or, 68° Fahrenheit. But, the note worthy of remark about that par- ticular point is, that it defines what may be called a temperature of 4th; 22. ith the distance between freezing and boiling, upwards from the freezing point; exhibiting again in the most unexpected manner, the typical division of the Py- ramid. Hence there can be little hesitation in adopting 68° Fahr. ; and inasmuch as one English cubic inch of distilled water weighs 252'458 English grains at temperature of 62° Fahr., and Barometer at 30 inches,—the coffer, measuring 70,970°2 English cubic inches, would weigh 17,917,000 English grains, with the contained water at that temperature. But reducing the weight of the water from its density at 62° to that at 68°, the quantity becomes 17,905,500 English grains. ~ This, therefore, is the total weight of the Pyramid’s grand standard of weight measure; excepting my own possible errors of reduction. (9.) Pyramid Weights and Measures. With the capacity of the coffer, its water-weight, and the linear standard, as already determined, we have now to see what sort of a commercial and scientific system of measures they are capable of affording, and for small as well as for large quantities ; especially, too, in how far such a Pyramid-derived system may agree, and in how far it may differ in the subsidiary items, from what is at pre: sent in use in Great Britain. 4 The chief point of difference will evidently be in the divisors ; for the Pyramid can acknowledge of little beyond fives and times of five ; and they are not found frequently in the British system. Nevertheless, it is remarkable to see in how many instances the two arrangements approach each other; and that in some cases, where a closer approach might have been desirable, it is found by appealing from the “Imperial System” of George IV. to the ancient British weights am measures. OF THE GREAT PYRAMID. 689 Pyramid Capacity Measure. Denomination Seem ee Unit = 1 drop = 0:002836 = 00001 100 drops = 1 dram = 0:2836 = 0:01 10 drams = 1 oz. = 2:836 = 0-1 10 oz. | = 1 pint = 28°36 = 1-0 10 pints = 1 gallon = 283°6 = 10-0 10 gallons = 1 bushel = 2836°0 = 100:0 2-5 bushels = 1 sack = 7,090-0 = 250-0 *10 sacks = 1 coffer = 70,900:0 = 2,500-0 Or arranged in double entry, Drops HOOMssuxdrs 4) 1 1,000 = IQ) =_.0z), 1 10,000 — 100) 10 = pint 1 100,000 = 1,000 = 100 = 10e= “valle 009;000-= .10;000.= . 1,000,=— , 100 = 10 =bush. 1 2500,000 =. 25,000. = 2,500 = 250 = 25 = 2-5 = sack 1 25,000,000 = 250,000 = 25,000 = 2,500 = 250 = 2B ee 10=coffer 1 And compared with the English cubic inches, Imperial system, through the temporary medium of Pyramid Capacity English Cubic British Capacity English Cubic Measures. Inches. Measures. Inches. 1 drop = + 0:0028388 1 drop Apoth. = 00036103 1 dram = 0:2838808 1 dram Apoth. = 0:2066187 1072. = 2838808 1 ounce Apoth. = 1:73295 1 pint = 28°38808 y 1 gallon = 283°8808 1 pint Imperial = 34659 l bushel = 2,838:808 1 gallon Imp. ae O77-274 1 sack fe 7,097 -02 1 bushel Imp. == 7 2,218-192 1 coffer = 70,970°2 1 sack Imp. = 6,a2RD7(6 4 quarters Imp. = 170,982-144 Pyramid Weight Measure. Reference to Reference in Denomination. Pyramid Cubic Inches ‘Terms of of Water. Pyramid Pound. Unit = 1 grain = 00028386 = 0:0001 100 grains = 1 dram = 0:2836 = 0:01 10 drams = oz. = 2°836 = 0-1 10 oz. = lpound = 28°36 = 1:0 10 lbs. = 1 stone = 283°6 = 10:0 10 stone = 1 ewt. =) 205020 = 100-0 2:5 ewt. = 1 wey = 7,090-0 — 250:0 10 weys = 1 ton = 70,900-0 SS Oe _ And we have arranged for double entry, * In place of 10 sacks=1 coffer, there may be used, 2°5 sacks=1 quarter; and, 4 quarters=1 coffer. 690 PROF. C. P. SMYTH ON THE REPUTED METROLOGICAL SYSTEM Grains 100 = dr. 1 OOO) == MOMs Oz9 ah 10,000 = 100 = 1O'= Ib. ft 100,000 = 1,000 = 100) = 10 = st. 1 1:000,000 = 405000-= “1,000, — S100) =. d0%=-) cri 1 2:500,000 =. *20;0G00= "2.500 = -2a0r— Bar 2-5 = wey 1 25,000,000 = 250,000 = 25,000 = 2,500 = 250 = 25:0 = 10 = tonl., And compared with British imperial weight measures, through the temporary medium of English grains, Pyramid Weights. English Grains. . English Grains, : ; 1 grain old English = 075000. 1 grain a 0°71622 { 1 grain modern English = 1-00000 — , 1 dram Avoird. = 26°71875 1 dram = 71-622 1 dram Apoth. = 60:00000 © j 1 ounce Avoird. ani 427°5 1 ounce = 716-22 1 ounce Troy, Apoth. = 480-0 1 pound Avoird. = 7,000 1 pound = 7,162°2 1 pourid old Engl. & Scot.= 7,600 1 stone, meat = 56,000 1 stone = 71,622: 1 stone, coal = 98,000 1 ewt. = 716,220- 1 ewt. Avoird. = 784,000 1 wey = 1,790,550: 1 wey, English = 1,274,000 f 1 ton Avoird. = 15,680,000 1 ton =o Tis, e00 { 1 ton shipping =18,816,000 _ Pyramid Linear Measure. , Denomination, bres re ; : 1 Unit — 1 inch — 500,000,000 1 : = ee. a Se a Earth’s Radi and 12 inches 1 foot 41,606,666°6 &e. 7 - hese: ; 6" = OHO #O-O-H: "= O-O-H. : OOO. 710 DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. Of these the latter only is admissible, for the theory of atomicity taken strictly does not admit of free affinities in a molecule. This formula then must be ~ common to the two acids. 5. In the abstract of this paper, published in the Society’s ‘‘ Proceedings,” the dehydrogenates and the bibromo derivatives of pyrotartaric acid were inadver- tently included in the list of bodies probably absolutely isomeric. From the relation of pyrotartaric acid to propylene, and of the latter substance to FRIEDEL’s alcohol, we may deduce the following formula for pyrotartaric acid :— OOO © 0506-6) If this formula be correct, it is obvious that there may be three metameric dehydrogenates and bibromo derivatives. 6. As the two atoms of hydrogen in the radical of maleic acid are, on the theory of atomicity, in precisely similar positions, it is obvious that there cannot be two metameric bromo-maleic acids. And as KexuLs has shown that there are two acids, bromo-maleic and isobromo-maleic, these must be absolutely isomeric. 7. Two perfectly admissible formulze can be constructed to represent bibromo- succinic acid :— But that these formulze do not correspond to bibromo-succinic and isobibromo- succinic acids is plain from the following considerations. These acids are formed by the direct addition of bromine to maleic and fumaric acids. The bromine must therefore be combined with the two carbon equivalents, which in maleic and fumaric acids are combined together, so that the latter of the two formule given above must be that of both brominated acids. } 8. As the constitutional formula for succinic acid shows no difference as to ** chemical position” among the four atoms of hydrogen in the radical, there can be only one formula for the substance produced, by replacing one of these atoms DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. TAL by the water residue; but we have two varieties of malic acid, active and inactive; these must therefore be absolutely isomeric. 9. The same argument applies to the case of active and inactive aspartic acids; aspartic acid being succinic acid in which one atom of radical hydrogen has been replaced by the ammonia residue NH,. 10. As there are two possible formule for bibromo-succinic acid, there are also two for tartaric, or dioxy-succinic acid. We have not the same reason for excluding either of these in this case as in that of the bibrominated acids ;* but as we have three undoubtedly different varieties of tartaric acid (excluding racemic acid), two of these at least must have one of these formule in common. So far we have been concerned with pairs of substances which seem to be really absolutely isomeric. The remaining substances in our list are more probably metameric. 11. If we consider the various reactions of the ethylene compounds, particu- larly the formation of glycollic acid from glycol, we are forced to the conclusion that the two unsaturated equivalents of the radical ethylene belong to two different carbon atoms. This conclusion may also be arrived at in another. ” perhaps less satisfactory way. As chloride of ethylene is formed by the direct union of chlorine and ethylene, the chlorine must be combined with those carbon equivalents which in ethylene gas are combined with one another; but equivalents of the same atom cannot be combined with one another, therefore in chloride of ethylene the two atoms of chlorine must be combined with different carbon atoms. The constitutional formula of chloride of ethylene is therefore @ @--O-€ © © and that of oxide of ethylene @-O-©--© Ow Again, the reactions of aldehyde, the oxide of ethylidene, lead to the view of its con- stitution first proposed by Koxpg, and now almost universally adopted, a CoO, * It would be interesting to compare the properties of the tartaric acid formed from isobibromo- succinic acid with that from bibromo-succinic, and with the varieties obtained from the grape. VOL. XXIII. PART III. QE (lee DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. in which both oxygen equivalents are combined with the same carbon atom. | The constitutional formula of chloride of ethylidene is therefore ® @ @--©-O-O © © ® @ O25 lala @ - These two series of substances are therefore metameric. 12. The researches of Wisticenus (An. Ph. cxxviii. 1) and LirpMann (An. ” Ph. exxix. 81) prove that lactic acid and paralactic acid stand to one another in a relation similar to that of chloride of ethylidene and chloride of ethylene; that, in fact, the former is a compound of ethylidene, with the water residue and the and that of aldehyde group Gs \ do) ‘and the latter of ethylene with the same radicals. They have a therefore the following constitutional formule, and are metameric :— Sees Olin avai ® O6-O-07 06-06 ORO MCB unre) OPAC © © 13. With regard to the two series of alcohols—the alcohols proper and the hydrates of the olefines—we know, at least, that FRIEDEL’s alcohol is not absolutely isomeric with propylic alcohol, but, as suggested by Kotsz, only metameric. If we consider the relation of these alcohols to their aldehydes—propionic aldehyde, and acetone, the aldehyde of FRiEDEL’s alcohol—we easily see that the formula of propylic alcohol is | DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. 718 while that of FRIEDEL’s alcohol is Ome © ®--©--©--©--@ © © © I | © | Or As FRiEDEL’s alcohol is identical with that obtained by Bertsetot from propylene, it is highly probable that the same difference exists in the case of all the other members of the two series. In the same way the iodide of propyl is 14. As to the aromatic alcohols and the isomeric acids, we know too little of their constitution to speak definitely with regard to their relation. They may, as suggested by ERLENMEYER (Zeitschrift, vii. 12), be absolutely isomeric, or, on the other hand, they may be related to one another as the two series of alcohols last mentioned are. Having enumerated the bodies which may without hesitation be called absolutely isomeric, I shall now consider the bearing which the existence of such substances has upon the theory of atomicity. If we examine the fundamental definitions of that theory, we shall see that there is a point of importance left undecided. We define a multequivalent atom as an atom having two or more equivalents, by means of which it may unite with the equivalents of other atoms, but it is not decided whether these equivalents are similar to one another or not. On the former supposition, there can be only one substance corresponding to each constitutional formula, and absolutely isomeric compounds are impossible. It must therefore be rejected, as such compounds exist. We must then assume that some of the equivalents of at least some multequivalent atoms are different from other equivalents of the same atoms. This assumption may take one of two forms,—1. We may suppose that the difference is an essential and unchangeable one; that, for instance, the two equi- 714 DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. valents of a diatomic atom differ from one another as chlorine does from bromine ; and that the one can no more be changed into the other, than an atom of chlorine can be changed into an atom of bromine; or, 2. We may suppose that such a change is possible. Our knowledge of facts is not as yet sufficiently extensive to enable us to decide definitely between these two hypotheses, but it may be of some use to examine their consequences. The second is, as yet, obviously too vague and indefinite to admit of this, I shall therefore confine my remarks to the first. The principal advocate of this hypothesis is Professor ERLENMEYER of Heidelberg. Professor BuTLERow of Kasan, has also published some speculations in the same direction; and in his paper on Organic Acids in the supplementary volumes of Lrzsic’s ‘“‘ Anna- len,” Professor KexuL& of Ghent treats shortly on the same subject. The only attempts, however, to apply this hypothesis in a definite way to the explanation of particular cases of absolute isomerism are, as far as lam aware, 1. That of © Professor KoLBe, who applies a form of this hypothesis to the case of the isome- rism of oxide of ethylene and aldehyde. I have already given my reasons for be- — lieving that these substances are metameric, and shall therefore not discuss the — point further here. 2. That of BurLerow (Zeitschrift, v. 301), who endeavours by means of it to explain the isomerism of hydride of ethyl and methyl gas; and 3. That of KexuL£ (Ann. Ch. Ph., Supp. b. ii. 111), in his explanation of the — isomerism of maleic and fumaric acids, and of citraconic, itaconic, and mesaconic acids.* I shall examine the 2d and 3d of these examples in detail, and think I shall — be able to show a certain degree of inconsequence in both. Professor BuTLEROw argues, that in methyl gas the two atoms of carbon are combined by two affinities of the same kind (secondary affinities), each being the affinity which in iodide of methyl is combined with iodine. In hydride of ethyl, the two carbon atoms — are combined in the same way as in the other members of the ethylic series, — therefore, probably in the same way as in the members of the acetic series, one — of which is acetonitrile, which is cyanide of methyl, the one is therefore the free affinity of methyl (secondary), the other the free affinity of cyanogen. These — must be different, because hydride of ethyl is not identical with methyl gas. BuTLerow indicates this, by calling the free affinity of cyanogen primary. We have thus in methyl gas two primary affinities united together, and in hyde of ethyl a primary united to a secondary. 8 In this reasoning we have eee assumptions,—1. That the nature of then carbon affinities is unchangeable; 2. That the carbon atoms continue united to-— gether by the same affinities ee a series of chemical reactions, such as the * I do not here notice the remarks of Professor Konsz (Zeitschrift, vi. 13) on the same subject, as his object is rather to prove the metamerism than to explain the isomerism of these bodies. if DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. 715 transition from acetonitrile to hydride ef ethyl; and, 3. That hydride of ethyl is not identical with methyl gas. ) By carrying this argument a little further, and making use of no additional assumption, we arrive at an absurdity,—thus, the carbon radical of the acetic series is the same as that of oxyacetic (glycollic) acid, that again is the same as that of oxalic acid, therefore as that of oxalic nitrile or cyanogen gas; but in cyanogen gas we have the two carbon atoms united by two primary affinities; but we have before proved, that in the acetic series they are united by a primary affinity of the one, and a secondary affinity of the other. It is obvious, then, that at least one of our assumptions is false. And when we closely examine the two general assump- tions (1. and 2.), we shall see reason to believe, that neither of them is rigidly true. It is well known that the replacement of one equivalent in a compound by another, while it leaves the ‘‘ chemical structure,” or ‘‘ chemical position” of the other atoms unchanged, exerts an influence on the intensity of the chemical at- traction, not only of the equivalents directly concerned in the replacement, but of all the equivalents in the molecule.* To see this we have only to compare the nature of the force, uniting H to O in acetic acid, and in Glycocoll, We here see the hydrogen and the ammonia residue NH, exerting a “‘ disturbing” influence on the relation of oxygen to hydrogen through two carbon atoms. Many other examples will at once occur to every chemist. The nature of the equivalents, that is, of the force they exert, is thus seen to be variable, but the facts of abso- lute isomerism force us to admit, that this variation in the character and intensity of the chemical force exerted by the different equivalents of one atom depends upon something else, as well as upon the nature of the other equivalents with which that atom is united. We find, then, that although the nature of one equivalent of an atom does change, as the other equivalents are united with different substances, there must be some original difference between them, which renders absolute isomerism pos- sible. In what this original difference consists, whether it is essential or merely accidental (using the word in its strictly logical sense), we cannot as yet say. We may thus divide the force, uniting any two equivalents, into two com- * Bur.eRow notices this disturbing influence (Zeitschrift, vi. 516) as opposing an obstacle, which he seems to regard as for the present insuperable, in the way of determining whether a difference exist or not among the equivalents of a multequivalent atom. VOL, XM. PART IL, OF 716 DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. ponents, one depending on the structure of the molecule, and the position of the equivalents in question in it, and the other independent of these. For con- venience we may call the first the molecular, and the second the atomic component.* From all that we know of the disturbing effect of an equivalent on the rela- tions of the other equivalents in the molecule, we may safely assume that the molecular component of the force uniting the two carbon atoms to form the hex- atomic carbon radical (C,)", is not the same in any two compounds. And if there be more than one body having the formula C,H,, we are forced to the con- clusion, that in these cases at least, the atomic component is different also. The question in reference to the second assumption mentioned above may now be stated thus,—Does the atomic component of the force uniting the two carbon atoms remain the same through such a series of transformations as that connect- . ing acetonitrile and hydride of ethyl? There is every reason to suppose that it does, if it is always the same for the same pair of equivalents; for there is nothing in any of these transformations which would lead us to suppose that one carbon equivalent has changed places with another. We are then brought to the dilemma, either methyl gas and hydride of ethyl are identical, or a change takes place in the atomic component of the force uniting the two carbon atoms in some of the transformations connecting cyanogen gas and hydride of ethyl. ‘In connection with this, it may be proper to examine shortly the relation between the view of the chemical nature of carbon provisionally adopted by BuTLEROW, in the paper referred to above, and that of KoLBg, as explained in his ‘* Lehrbuch der Organischen Chemie,” and in several valuable papers in LiEsic’s “ Annalen,” and in ERLENMEYER’S “ Zeitschrift.” Professor Ko.be considers carbon (carbonyl=(C,), C=6) as a tetratomic element (as indeed it is now admitted by every one to be), and holds that ina large number of organic compounds, the four equivalents united to the carbonyl atom may be divided into two groups,—the intra-radical and the extra-radical,—so far his view resembles that of BuTLERow; but it differs from it in the following respects :—BuTLEROW assumes that it is an essential property of the carbon atom to combine in this way, that carbon a/ways combines with two equivalents in one way, and with two others in another way. Ko.use only admits this in the case of bodies derived from dibasic carbonic acid. In methylic compounds, for in- stance, he regards the three atoms of hydrogen as precisely similar. When we examine the theories more closely, we see another reason to doubt their identity. If we try to compare them, we find it difficult to decide whether BUTLEROW’S * The term component is, of course, not used here in its strictly dynamical sense, what is meant is, that the total force uniting a pair of equivalents, is a function of two quantities, the one depending on the structure of the molecule, and the position in it of the two equivalents, and the other on the chemical nature of the two equivalents. = DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. fag primary affinities correspond to the intra-radical or extra-radical affinities* of H 0, Kose; for instance, in formic acid,—C- 0” or C, i H _, the Hand the OH (or O: HO) OH ( 0-HO are united to the extra-radical affinities, but by carrying out BuTLERow’s reason- ing, we are led to the conclusion, that the H is united to a primary, and the OH to a secondary affinity, unless we suppose that the free affinity of methyl is different from that of formyl. It is not impossible that such a difference may exist, but till this point is settled, and till we know whether the two free affinities of (CO)” are similar or not, it is impossible satisfactorily to compare the two theories. The other attempt mentioned above to explain cases of absolute isomerism, in harmony with the theory of atomicity, is that of Professor KexuLf.}+ After shortly recounting the principal facts, more minutely described in his admirable researches on organic acids, he says,—*‘ All these facts find, in my opinion, to a ° certain extent, their explanation in the following considerations :—According to the views on the atomicity of the elements which I communicated some time since, succinic acid and its homologue pyrotartaric acid may be regarded as closed molecules, that is, all the affinities of the atoms composing the molecule are saturated by other atoms. Both acids contain two atoms of hydrogen re- placeable by radicals, because two atoms of hydrogen are united to the carbon group by means of oxygen. These two replaceable (typical) atoms of hydrogen may be easily exchanged for metals, because, besides the two atoms of typical oxygen (7.e., oxygen united by only one affinity to carbon), there are other two atoms of oxygen united to carbon by both affinities, which, therefore, in the language of the typical theory, belong to the radical. If these two atoms of hydrogen are represented apart from the rest, as is done by means of the typical formulee,— om H. °.) 0, C, H, o:) 0, 2 or still more clearly by the graphic representations which I have made use of more than once in another place,{ it will be readily seen, that in succinic acid * T use the terms intra- and extra- radical affinities as abbreviations for the carbon affinities, with which the intra- and extra- radical oxygen atoms are combined. t Loe, cit. ; { In order to elucidate this passage as much as possible, I append the graphic representa- tions referred to :-— Succinie Acid. Pyrotartaric Acid. 0 0 Cc mem 5G H t) ) c H?H C 0 0 OO O0OZZZZ 00OG4GGOo OO OO Z@ZZZ OO G@GF@QZGP7 Ww) I0GSOI 00 G9SI 00 OW 09GSO 00GGSS00GSSSGO | # c a Sah iC 0) ) H c BH° ¢c ae C H 718 DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. there are four, and in pyrotartaric acid six, other atoms of hydrogen present. This hydrogen is considered, according to the typical theory, to belong to the radi- cal, according to the theory of atomicity, to be directly united to the carbon, and in such a way that there are always two atoms of hydrogen united to the same carbon atom. If we now suppose, that in the one or the other of these two nor- mal acids two such hydrogen atoms are wanting, we have, on the one hand, the composition of fumaric and maleic acids, on the other, the formula of citraconic itaconic, and mesaconic acids. Now, as there are in succinic acid two pairs of hydrogen united in this way to carbon, we easily see the possibility of the existence of two dehydrogenated acids, as the one or the other of these pairs of - hydrogen atoms is absent. “ Similarly, in the case of pyrotartaric acid, the existence of three isomeric dehydrogenated acids is intelligible, in each of which another of the three pairs of hydrogen atoms directly united to carbon is absent. At that place in the mole- cule where the two hydrogen atoms are wanting, there are two carbon affinities unsaturated, there is at that place, so to speak, a blank.” * There is some difficulty in understanding this last statement. For what can be meant by two affinities of the same carbon atom uniting together? unless the definition of either “ atoms” or “ combination” be completely changed. Or if we take the natural meaning of the sentence last quoted, and suppose two car- bon atoms pushed together, so that two affinities of each previously united to hydrogen come to be united together, the two wanting hydrogen atoms do not come from the same, but from two different carbon atoms.t+ But leaving this preliminary difficulty out of consideration, and also granting the existence in such a molecule of diatomic carbon, a glance at the diagrams is sufficient to show, that this view does not give us two but only one formula for | fumaric and maleic acids, unless a difference be admitted among the affinities of carbon. The pairs of hydrogen atoms, which I have marked a and 6, have per- fectly similar positions, the one being related to one end of the diagram, exactly as the other is to the other end. In the same way the graphic representation of pyrotartaric acid suggests only two formule for citraconic, itaconic, and mesa-— conic acids, there being no apparent difference between the position of the pairs c and ¢.t This explanation is insufficient, not to say unintelligible, unless we suppose a functional difference between the two carbon atoms, with which the pairs of atoms of hydrogen are united ; and if we make this assumption, it fol- lows as a necessary consequence, that there is a difference between the two groups of HO. It is no doubt possible, that such a difference may exist; but it * «Tt may of course equally well be assumed, that the carbon atoms are, as it were, pushed together (zusammengeschoben), so that two carbon atoms.are united by two affinities of each. This is ‘only another form of the same idea,” + See Ertenmeyer, Zeitschrift, vi. 21. s t See Burierow, Zeitschrift, vi. 524. DR A. CRUM BROWN ON ISOMERIC COMPOUNDS. 719 seems very unlikely that such a property of a substance so well known as succinic acid should not have been observed. We thus see, that the attempts to apply to the explanation of particular cases the principle of a difference between the equivalents of multequivalent atoms have failed, not, however, as far as can at present be seen, from any absurdity in the principle itself, but rather from a want of well-observed facts to guide us in its application. These we may expect before long, from the labours of BUTLEROW, SCHORLEMMER, and others, and we shall then be in a position to form a definite opinion as to the form which this hypothesis should assume. VOL. XXIII, PART III. 9G XLV.—On the Theory of Commensurables. By Epwarp Sana, Esq. (Read 7th March 1864.) The general proposition in the theory of commensurables is to determine the conditions under which lines, surfaces, or solidities, connected with prescribed figures or forms, may have their ratios expressible by integer numbers. The attention of geometers must have been drawn to this subject by the con- templation of incommensurable lines: the altitude of an equilateral trigon is incommensurable with the base; the diagonal of a square incommensurable with the side, and soon. And, when the two sides of a right angle are expressed by two numbers, the hypotenuse is, in the great multitude of cases, incommensurable with the sides : thus, if the sides be 5 and 7 inches respectively, the length of the subtense cannot be accurately expressed either in integers or fractions. How- ever, when the sides are 3 and 4 units, the hypotenuse is exactly 5 of the same units. This circumstance seems to have turned the inquiries of geometers at a very early period to the discovery of those cases in which the three sides of a right- angled trigon, are all commensurable; and the computation of Pythagorean numbers was to them a very interesting problem. Many problems of a similar nature may be proposed: thus we may require that the three sides of a trigon, and the line bisecting one of the angles, be all commensurable ; that the four sides and the two diagonals of a tetragon be all expressed by integer numbers, and so on. The methods of solving such problems may be said to constitute the theory of ' commensurables. Section 1.—On the Right-Angled Trigon. 1. If A and B represent the sides of a right-angled trigon, of which the hypo- | tenuse is C, we must have the equation | At BA 62. | and the question is to discover integer values of A, B, and C, which may satisfy | this equation. | When it happens that two of these three numbers have a common divisor, the | third number must have the same divisor; for if A and B had the common divi- | sor n, so that A==na, B=nb, A?+B?, that is C? would be divisible by n”; in other words, C would be divisible by nm, and thus the case A, B, C might be reduced by | division to the lower numbers a, 8, e. And conversely, when we have obtained one solution, as 3, 4, 5, we can thence VOL. XXIII. PART III. 9H 722 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. deduce others, as 6, 8, 10; 30, 40, 50, by multiplication. Hence it is almost enough to consider only those cases in which the three numbers are prime to each other. For convenience we shall indicate that the solution is in the lowest terms, by the use of the small letters; solutions in general being indicated by capitals. 2. Any odd prime number may represent the side of a rational right-angled trigon, but of only one. For the equation A’? + B*=C’ may be put under the form A® =C’—B’=(C +B) (C—B), while A? may be regarded as the product of unit by A*; wherefore we may put =C+B; 1=C—B, whence =} (A2—1); C=} (A? +1) so that if A be an odd number, A’—1 and A?+1 are both even, and therefore B and C both integers. Representing prime numbers by the Greek letters, if a=a, we have b=} (a@°—1); c=} (@’+1), whence the solutions Bd Be 9G TIMNBs -7 Dae Oh: CUCM Rei lice Since a is a prime number, the only decompositions of a’ are a? x1 and — axa. The former of these has just been considered; the latter would give a=C—B, a=C+B, whence B=o, C=a, showing that the trigon has collapsed into a straight line. 3. Any odd number which is the product of two unequal prime factors may represent the side of four distinct rational right-angled trigons: of these two are reducible and two are in their lowest terms. If A be the product of two primes, a, @ (neither of which is 2), we may put A’ as the product of two factors in five ways, viz., a?@’x1; a°@xB; ab’ xa; a’ x 8’; and aG x a@; the last of these can give no trigon, so that there remain the — four solutions b= (a°8"—1) =1(@B-B) | B=4(a#—-a) | b=3(a'-8) =} (a76? +1) =} (a+) =} (aSi+a) | c=} (a?+(%) In the second of these, each side is divisible by @, in the third by a, so that these two solutions are included among those of the aii article: but in the first and last, the sides are all prime to each other. . Hence the solutions 15, 112, 1138; 15, 8,17; 33, 544, 545; 33, 56, 65, &. 4. Any odd composite number of the form a’. @’.y’=A may be the side of half as many distinct trigons as there are units in the product (1+2p) (1+29¢) (1+27r). . . less one. For the continued product 6’=a’?. B°4.y’... &., has, inclusive of unit and A? itself, divisors to the number (1+ 2p) (1+ 2g) (1+ 27)... of which A itself is MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 723 one. Omitting the case A x A, which cannot give a trigon, it follows that A* may be represented as the product of two factors in $ {(1+ 2p) (1+2g) (1+2r)...—l} ways. Each one of these gives a distinct solution, for if A7=P.Q be one of these decompositions, A=/P.Q; B=} (P—Q); C=} (P+Q). Of the total number of these solutions, only those are in their lowest terms in which P and Q are prime to each other. Therefore, if m be the number of sepa- rate primes which enter into A as factor, the number of cases in their lowest terms is 2”-1, and is irrespective altogether of the exponents p, g, 7, &c. 5. No double of an odd number can be the side of a rational right-angled tri- gon in its lowest terms. For if A be the double of an odd number itself prime, or the product of two or more prime factors, a, @, its square is 4 a’ 6’, which can be resolved into un- equal factors prime to each other only of the general forms 4 a’Q’ x1; 4 a’ x 6”, one of which is even and the other odd; wherefore the sums and the differences of these factors are all odd, so that in the solutions A=2a8; B=4(4a?6?—1); C= (4a?6?+1) A=2a8; B=} (40?—6?) ; C=} (407+ 6?) &e. the fraction $ must occur. To remove this fraction we must double all, and then A=4a8; B=4a?6?-1; C=4a?G?+1: A=4a6; B=4e?—-@? ; C=4a7?+? : &e. 6. Any number of the general form 2‘ Ay in which ¢ exceeds unit, A and » being odd numbers prime to each other, may be the side of a rational right-angled trigon in its lowest terms. For A? =2” 2’ »’ and may be resolved into the two factors P=27")n? ; Q=2y’, whence A=2'Ay; B=2*??—p?; C=2** d? + y’, which are all integer and prime to each other. If m be the number of odd primes which enter into A as factors, the total num- ber of cases in their lowest terms is 2”~’. 7. Land m being any two numbers whatever, /’+m?’, 2m and ’—m? repre- sent the three sides of a right-angled trigon. For if A=2/m, B=? —m? and C= +m’, we have A?+ B’?=C’. If 7 and m have a common divisor, A, B, C, can all be divided by the square of that divisor. If / and m be prime to each other and both odd, the numbers in the above solution may be halved ; but if one be odd, and the other even, the solu- tion as given is in its lowest terms. 8. Ofa right-angled trigon in integers, one of the two sides is divisible by 3. In this investigation we may suppose that the trigon is in its lowest terms. In the equation a’?+0’=c’, if the number a be not divisible by 3, it must be of one of the forms 3n+1, 3n—1, so that its square must be of the form 3n +1. 724 MR EDWARD SANG ON THE If now 6 be also indivisible by 3 its square must be of the same form, so that a’ +6* would be of the form 32+2, which cannot possibly be that of a square number. And thus one of the two must be divisible by 3. 9. Of a right-angled trigon in integers, one of the two sides is divisible by 4. The square of every odd number is of the form 82+1, wherefore if a and 6 were both odd numbers, a? +6? would be of the form 8+ 2, which cannot be that of a square ; thus one or other of the two must be even. Now if a be even, 6 and ¢ must be both odd, wherefore a’ being the difference of two odd squares, viz., c’—b’ must be divisible by 8; but no square can be divisible by 8 unless its root be divisible by 4, wherefore the even side a must be divisible by 4. 10. Of a right-angled trigon in integers, one of the three sides is divisible by 5. All numbers not divisible by 5 are of the forms 5n = 1, 5n = 2, the squares of which are contained in the forms 5n+1, 5n—1. If neither a nor 0 be divisible by 5, their squares cannot be both of the form 5z+ 1, nor both of the form 5x—1, for then a+ 0° would be of the form 5x +2, or 5n—2, neither of which belongs to asquare. Wherefore, if @ be of one of the forms 521, b must be of one of the forms 5n==2, in which case a’ +0’ is of the form 5n, and therefore may be a square. Again, if the hypotenuse c be not divisible by 5, c’*=.5n- 1; and similarly, ifd be not divisible by 5, 0°w=>.5n+1. Ifnow 0? =.5n +1 while c’~=.5n—1, the difference c? —b* would be of the form 5n—2; or if b?e=.5n—1 whilec’?=5n+ 1, c’—& would be of the form 5n+2; neither of these can be square. The other two combina- tions Deadn+1, Pwadn+]1, and DP w5n—1, ¢5n—L, both give c’—b’ & 5n which can be a square, and then « must be divisible by 5. 11. The hypotenuse of a right-angled trigon in its lowest terms can never be divisible by 7. For if ¢ were divisible by 7, neither @ nor 0 can be so, as then all three would be divisible by 7. Hence a and 5 must be of some of the forms 721, 7n=2, 7n=3, and therefore their squares must belong to some of the forms 7x + 1, 7” +4, 7n+2. Nowno twoof the remainders 1, 1; 4, 4; 2, 2 can make up 7, and there- fore a’ +6" can never be divisible by 7. The same argument may be used to show that 19, 23, 31, &c., cannot be divi- sors of the hypotenuse of a right-angled trigon in its lowest terms. 12. Lemma. If two numbers be each the sum of two squares, their product may be decomposed into two squares at least in two ways. Let d=s°+?, and e=w’+v’, then, on multiplying we obtain de=s*u? + s?u? + Pu? + tv", which may be put under either of the forms, de=s7u? + 2stuv + t?v? + s?u? — Astuv + Pv? ; de=s*u* — Istuv + Pv? + s?v? + 2stuu + Hu? ; THEORY OF COMMENSURABLES. 725 which are equivalent to de=(su + tv)? + (su—tu)? de=(su—tv)? + (su + tu)? ; and thus the product de is shown to be the sum of two squares in two different ways. Cor. The square of the sum of two squares is also the sum of two squares For if d= S47 @= st + 2s? t?7 + t4 st— 2s? 7 4 t* + 4s? ¢? (s?—@)? + (2st)? ll tl il 13. If a number be divisible into two squares prime to each other in two different ways, it is the product of two numbers, each of which is the sum of two squares. Let c be the sum of s* and 7”, and also the sum of wu’ and v’, that is, let C=s?+?=u? +0? ; then s*—u?=v"* — 2, or stu:vtt::u—t:s—u wherefore the ratio s+u: v+¢ is not in its lowest terms; that is, s+ wand 1+ must have a common divisor, which we may suppose to be ¢, put then s+ w=ez, o+t=ey; and then v:y:: v—t:s—u, so that we may put v—t=/a, s—u=/y. in which f may have the value wnit. We thus obtain stu=ex; vt+i=fa s—u=fy; v—t=ey whence s=} (ea+fy), t=3 (fa—ey) so that s+ P=4 {ea + 2efayt fry? + fra’ — 2efay + e?y?} =3( +f?) (w?+y’) and thus ¢ is the product of two factors, each of which is the sum of two squares. Cor. Hence no prime number can be divided into two squares in more than one way. 14. If an even number be the sum of two squares, its half is also the sum of two squares; and conversely. If the even number 27 be the sum of two squares s’ and 7’, its half x is also the sum of two squares. It is evident that the numbers s and ¢ must either be both even or both odd. wherefore $(s+7) and 4(s—é) must be integers; now (s+)? +3(s—t)?=4(s° + 7) ' =n, therefore n is the sum of two squares. 15. If the successive square numbers be divided by any odd prime a, the re- mainders, including zero, recur in groups of a terms; and of the a—1 terms VOL. XXIII. PART III. 91 726 MR EDWARD SANG ON THE between 0 and 0, the one half is the converse of the other: farther, no two re- mainders in the half group are alike. The import of these assertions may be seen by taking any prime number, as 11, and dividing the successive square numbers 0, 1, 4, 9, 16, 25, 36, 49, &c. by it. The remainders are found to be 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1, 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1, 0, and so on. In reference to the divisor @, the natural numbers 0, 1, 2, 3, &c., belong to the forms na +0 na+0 na +1 na+l na+2 na+4 Coro; na + z aod 1 PEI 5 na+% | of which the | ,,,@—%a+1 2 | squares are ; 4 noe ON glee tne same | na+ a*—2a+1 “ forms with 4 a a?—6a+9 ne =) na 7 Leta ; ee nea0 / \na+0 From which it is obvious that the order of the remainders in the latter half of the group is inverse of the order in the former half. Also the same remainder cannot occur twice in the half group. For if any — two squares, as &* and /’, & and / being each less than 3a, had the same remainder, — their difference /’— /? would be divisible by a. Now both £+/ and £—J, the fac- tors of *— /’, are less than a, and their product cannot possibly be divisible by @. 16. The sum of two squares which are prime to each other is not divisible by — any number of the form 4n—1. q Every composite number which is of the form 4n—1, must have an odd ~ number of factors of the same form combined with some or no factors of the form 4n+1. It will be enough to show that the sum of two squares prime to each other cannot be divided by any prime number of the form 4n—1. . If the two numbers s and ¢ be both odd, s?+# is even, and its half is the sum — of two squares and also odd; and if s*+2’ be divisible by any prime 8, its half must also be divisible by 8. Wherefore we have only to show that the sum of an odd and an even square can never be divisible by 6 = 4n—1. Let us suppose that s=p@ +h, t=g@ +1, then P+ P=(p? +9?) P42 (pk+ qh +h +P i and / being each less than 36. Wherefore if the sum s’+? be divisible by a THEORY OF COMMENSURABLES. (20 prime number @, we can always find two numbers £ and / each less than 36 also divisible by (. In regard to # and / being odd or even, there are only three possible combina- tions; one may be odd and the other even, in which case /’+/? is of the form 4n+1; they may be both odd, in which case £*+/° is double of an odd number, which odd number is the sum of an odd and even square, and still divisible by 6; lastly. they may be both even, in which case we can halve them, and continue to halve, until one of the quotients be even and the other odd, without affecting the divisibility of the sum of their squares by £. Therefore, universally, if the prime number ( be a divisor of s’+72, s and ¢ being prime to each other, it must also be the divisor of 4°+/?, in which / and / are each less than 46, the one being even and the other odd. Now #4+7 being of the form 4n+1, cannot be divisible by any number @ of the form 4n—1, unless the quotient be also of the form 4n—1; but 4’+/7? is less than 46”, wherefore that quotient must be less than $@. And thus if any prime number 6 of the form 4x—1 can be a divisor of the sum of an odd and an even square, some number less than its half, and consequently some prime number less than its half, and of the same form 42—1, must also be a divisor. If it were possible, then, that a prime such as 103 could divide the sum of an odd and an even square, it would follow that some other prime of the same form, and less than 51, would also be a divisor. The greatest prime of the form 4n—1, under 51 is 47; if it, or any prime of the same form less than it, were a divisor of k?+/7; it would follow that some other prime (23 or under) would also bea divisor. In this way we must ultimately arrive at the smallest prime of this form, which is 3. Now there is no even number less than the half of 3, so that 3 cannot be a divisor of the sum of an odd and even square, and therefore we conclude that no prime number, nor any other number, of the form 4n—1 can be the divisor of the sum of two squares prime to each other. It is obvious that, whatever @ may be, it is always a divisor of (@s)’ + (Gt), but then it is also the common divisor of Gs and £t. 17 Every prime number of the form 4n+1 is the hypotenuse of one sole right angled trigon in integer numbers. — Every prime number of the form 42 +1 can be resolved into two square num- bers, one of which is odd and one even, but only into one pair. Let, then Y= (2p)? +¢@°, and a? =16p* + 8p?q? + 9* = (4p? — 9”)? + 4p9q, . wherefore vy is the hypotenuse of a right-angled trigon, of which 4p’—q’ and 4yq are the two sides. Here it may be observed that one of the sides is always divisible by 4. 18. Every product of two prime numbers 7, 0, each of the form 47+ 1 is the 728 MR EDWARD SANG ON THE hypotenuse of four right-angled trigons in integers; of which two are in their lowest terms, and two are reducible by the divisors ‘, 0. For, since every prime number of the form 42 +1 is the sum of two squares, we may put ry? =p? He =r? +8, whence we can form the four equations 720? = (pr+qs)? + (ps—qr)? 0? = (pr—gs)* + (ps+qr)? 720? = yr? i ys? 7202 as 02? ae 029? giving the four trigons pr+qs, ps —4r, yo pr—gs, ps+qr, 0 1 ES Dae Ope wg 450 of which the two first are in the lowest terms, while the two latter are reducible. 19. The product of n primes, each of the form 4r+1, is the hypotenuse of — 2"—' right-angled trigons in their lowest terms. ; For with one prime ‘y we can have one trigon ; with the product of two primes, 6, we can have two trigons. On introducing a new prime factor ¢«, we can com- bine the sides belonging to it with each of the two former trigons in two ways, thus obtaining four cases. With a fourth factor 2, we can obtain two for each of © these four, and thus we proceed doubling the number of trigons at each accession of a new factor. 20. Every power of a prime number of the form 47+ 1 is the hypotenuse of one sole right-angled trigon in its lowest terms. i If a, b, Y, represent the three sides of a right-angled trigon ; that is, let a+ Pay". Also put A, B, y’, for those of a trigon having ‘y” for its hypotenuse, or, A2+B2=7". Multiply these two equations and we obtain A2a?+.A,2b? + B,2a? + B,20? =y2"t2, or (A,a+ B,b)? + (Anb— Ba)? =(y"*)?, or. | - (A,a—B,b)? + (Anb + B,a)? = (y"41), from which it would appear that for every trigon with the hypotenuse " we — have two with the hypotenuse y"t*. One of these, however, is reducible, the other is not. THEORY OF COMMENSURABLES. 29 Taking the operation in detail, we have, on supposing Any Bay Y" ; Anu Boa, yt, &e. to have been deduced in succession from a OLY; we have Anpi=GA,+0B,; Bryi=aB,—dA, - If now we deduce from these, Ayso=GAgiat bBia1s Boye oBn Ani, the results are, Ando=(a? —b?)A, + 2abB, ; B,42 = —2abA, + (a?—b?)B,, which, if A, and B,, be prime to each other, have no common divisor. But if we take the second combination, and put Anpo=GAngi—bBiyis Brpo=aBnyi + bAnt , we obtain Avy (a7 + 67) A,);. Bao =F 0 Das. ft. ; which are all divisible by a’ +0° or Y’, and bring us back to A,, Bn, Y”. And thus we see that in forming the successive trigons A,, B,, y’; A,, B,, y’, &c. from a, b, Y; and confining ourselves to those only which are in their lowest terms, we form only one series. 21. Every number which is the product of 7 primes of the form 4” +1, or of any powers of those primes, may be the hypotenuse of 2”—’ right-angled trigons in their lowest terms. In regard to the obtaining of trigons in their lowest terms, the power ‘y" gives only one as ¥y itself does; wherefore the combinations Y" 6” €’, &c. give just as many cases as the product Yo«, &c. General Scholium. From these propositions we obtain a convenient method of computing and tabulating the cases of right-angled trigons in the lowest terms. We form a list of the prime numbers of the form 4n+1; these are 5, 13, 17, 29, 37, &c., and we decompose each of these into two squares ; thus, 274+ 1°=5; 3°+2?=13; 4°=1’=17, and so on, the general form being p’+9’=Y. From these decompositions we then obtain, according to the formulee a=2pq, b=p*—¢q’, the sides of the trigons of which these prime numbers are the hypotenuses. Having thus constructed, to whatever extent we may desire, the table of trigons with prime hypotenuses, we combine them according to the formule of articles 18, 19, 20, and obtain the cases in which the hypotenuses are composite. VOL. XXIII. PART II. YK 730 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. In table I. are given the roots of the component squares, the prime numbers, and the sides, for all prime hypotenuses under one thousand, and also the factors — of the hypotenuse with the corresponding sides for all composite numbers up to the same limit. Section 2.—On Muarif Angles. 22. If the sine and cosine of an angle be both commensurable with the radius, all other functions, as the tangent, secant, cotangent, cosecant, of that angle are ~ also commensurable. If the sine of any angle, as 6 be expressed by the fraction = a and ¢ being © prime to each other, the cosine of that angle is 2 ize wherefore, in order that the cosine may be rational, c’—a’ must be a square number, say 0”, that is to say, a’ +0’=c’, and thus it appears that all such angles belong to rational — right-angled trigons, so that we may write sin 0=%, cos pee: whence tan ae c c b cot pee sec 0=< cosec O=°. a b a Definition—We shall see immediately that these angles indicate or make known the solutions of many problems in commensurables, and therefore I pro- pose to designate them by the title G>x~, muarif, formed from the same root as — the word tarzf in common use. 23. All the trigonometrical functions of the sum and of the difference of two muarif angles are also rational. If sin b=-, cos e—" while sin ¢ = “ cos p= = we have, according to the 7 fundamental propositions of trigonometry, — aa (0+p) =e? ae (+g) =e re oe (6 ¢)= na a SER (04+¢)= tos which are all rational, and therefore all the other trigometrical functions of the same angles are rational. N.B.—In Table I. the values of the lesser angle of each trigon is given in ancient degrees. ; 24. Every trigon of which two angles are muarif has its altitudes, its woe the radius of the circumscribed circle, and those of the four circles of contact, all rational. 7 & i MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. (oe If the angles at A and at B be both muarif, the sides of the trigons AFC, BFC are commensurable; wherefore the area of the trigon is commensurable with the squares of any of the lines AF, FC, FB, BC, CA, also the trigons ADB, AEB, are similar to CFB and AFC respectively ; wherefore their sides also are com- mensurable. Or in general, all the angles shown in the \ figure are muarif, and therefore all the trigons 4 F 2 have commensurable sides and areas. If a, 6, c, be the three sides of any trigon, and S the surface, the radius of the Cc inscribed circle is — those of the three circles of external contact are ¢ ae 3 a > a -- and that of the circumscribed circle is ov and those, a+b—e¢ a—b+c —a+b+ce 48 obviously, are all rational if 8, @, 6, and ¢ be so. 25. If any straight line be assumed as a base, and if, at each of its extremities any number of muarif angles be made, the sides of these being indefinitely extended, all the distances intercepted on them are commensurable with the base, and all the included areas are commensurable with the square of the base. It is evident that all the angles obtained by this construction are muarif, and that, therefore, the areas of all the trigons formed on the base are commensurable with its square, while their sides are all commensurable with the base itself. Now, all the segments are differences or sums of the sides of these trigons, and all the areas are differences or sums of their areas; wherefore, all of these are commen- surable with the square of the base, and all of those with the base itself. 26. If, at any of the points of intersection of the preceding article, muarif angles be made, the segments and areas so obtained are all commensurable with the base, and with its square. = , 4 The truth of this assertion follows at once from that of the preceding. 27. If, at the point of contact of astraight ‘ line with a circle muarif angles be made, if the extremities of the chords so obtained be joined and continued indefinitely, and if tangents be applied at their extremities, all the intercepted straight lines are com- mensurable with the diameter, and all the ’ areas with the square of the diameter. Since the angles which a chord makes with a tangent at its extremity are equal to those in the alternate segments of the SS 732 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. circle, every angle obtained in this way is muarif, and therefore the truth of the proposition follows. 28. The double of any angle of which the tangent is rational, isa muarif angle. If the two sides AB, BC, of the right angle ABC be commensurable ; that is, if the tangent of the angle BAC be rational, BAD D_ double of BAC is muarif. Since AC bisects the angle BAD, we have BA : AD::BC:CD and AC’?=BA . AD — BC. CD, whence easily BA? — AC’: BA’+AC’?:: BA: AD:.: BC: CD € wherefore AD and CD are both rational, and conse- quently BD is rational, that is to say, the angle BAD is muarif. ; F b : a A B Otherwise if tan 0=-, whence sin O= By : 2 2 __ 6? ; : cos 0=FoBH and sin 20=—5 a cos 20-55; that is both sin 26 and cos (a* 26 are rational. 29. To find a muarif angle which may approximate as closely as may be desired to a given angle. The general solution of this problem follows at once from the preceding theorem; we have to compute the series of fractions which approach to the tangent of the half of the given angle, and from these to deduce the corresponding muarif angles. In particular cases, however, special solutions may be obtained. Example 1. 30. To construct a rational right-angled trigon of which the angle may be © nearly half a right angle. B Having constructed the right-angled isoskeles tri- gon ABC and bisected the angle at A by the line AD, E draw DE perpendicular to the hypotenuse AB, then, as is easily shown, CD=DE=EB, and CD: DB::1 : 4/2; or, CD: AC:: 1: 14/2, that is tan CAD= D ree the Brounckerian approximations to which are — 0D) Soe AND coe soe eee r s 1 0 4 2 5 1220, 50 tpn aoe. 0.1 2B Sy 1 29. 70. e169) 408" Senciae which, by help of the formula A =2aé, B=@—l’, C=a’+0’, give the cases,— 5, esi, 3, 29, 20, . 21, 169, tgs 120, 985, 697, 696 5741, 4059, 4060, &e. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 133 This proposition may also be put in the form “to find two numbers which may differ by unit, and the sum of whose squares may be a square,” Putting B=A+1 in the equation C’=B’+ A’, we have C’=2A’+2A+1, or 2C°?=(2A+1)’+1; thatis to say, we must resolve the indeterminate equation D=/(2C’—1) in integers. For this purpose we put /2 in the form of a con- tinued fraction, and obtain the progression, — We a ! OL Eee oe Pine sin WZ, | AD 9 230 COT L398 & eS 1S 89: 470 G9 408 + O85 T : 1 7 41 . ‘ : of which the alternate terms 7 5 99 belonging to our equation, the interme- diates > a &c., belonging to the twin equation D=/2C0?+1. The former follow the law (—1, 6), that is to say, if the progression of the numerators be D,, D,, D;, ... D,, Digi -. we have D,,.=6D,4,;—D,, and so also of the denomi- nators; the progression thus formed being,— Sigal RA. P39) 1898 8219 Lit RE Sip. By p BO’ MAGN MOSB? qT” Xe. in which the denominator of each fraction gives a hypotenuse, while the integers immediately above and below the half of the numerator represent the two sides. EHaample 2. 31. To construct a right-angled trigon in integers, such that its lesser angle may be the tenth part of a revolution. The tangent of 18°=20° is /1—2/5; or 3249 1969 6232 907, which, when resolved into a chain fraction, gives the quotients,— Spies 6, l, 6, 20," 400 eeloelon ow. ie ly ide. whence the approximations, — oe tg 6 1 1 iO teel e 12. 13), SOMOS wi 08 Olea ua ST 40> Qe ee aig a Ot 79 which give the trigons,— 10, 8, 6, or 5, 4, 3; 1513, 1225, 888; 1769, 1431, 1040; 84829, 68629, 49860, &c.; the third of which gives an angle 36° 00’ 30’. 9 &e. EHzample 3. 32. To construct a right-angled trigon in integers of which the lesser angle may be nearly 23° 27’ 26’, the obliquity of the ecliptic. VOL. XXIII. PART III. IL 734 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. The half of this angle, viz., 11° 43’ 43” has for its tangent ‘207 6118, to which we have the successive approximations, — te Mie ey 5 18 1 ie eawretitan 289° the trigons 17, 15, 8; 26, 24,10; or 13, 12, 5; 601, 551, 240; 2930, 2688, 1166; or 1465, 1344, 583; &c. 33. To find a trigon having its sides rational and its area commensurable with — the squares of those sides, and which shall have, approximately, the shape of a given trigon. The general solution of this problem follows at once from the preceding. We must find two muarif angles approximating to two angles of the trigon, and with these construct a rational trigon. But some of the special cases admit of peculiar solutions. &c., which again give =| & oH | on to is i) | 9 Example 1. 34. To construct a trigon of which the three sides may be represented by three contiguous numbers while the area is a multiple of the square unit. Let a—1, a, a+1 be the three sides, S being the area, then— 16S? = 3a (a—2) a (a+ 2)=3a? (a? —4) wherefore 3(@’— 4) must be a square number, or a’— 4 must be the triple of a square. Let, then, a@—4=38a°. This equation cannot be satisfied when z is odd, for then a also would be odd, and the first member of the equation would be of the form 4n+1, while the second would be of the form 4n+3,; hence both a and x” must be even, or we may put— a=2a, x=2z, whence a? —1= 327; a’ =324-+ 1. Now, when we develope 3 in the form of a chain fraction we obtain the | approximations,— eth (RAY Sy ep ree ee) ig, Ma o: viaq oath 0 na ae aad alipee tp Teyana L Lab hip et Sia eV (15) tly Gey which belong, alternately, to the equations a®=3z?—2 and a?=32°+1; the values of a thus obtained are 1, 2, 7, 26, 97, &c., the next term being four times the last term less the penult. Hence the trigons are— 3, ES? Sl IGS a ze: 270 on | &e 4, 14, 52, 194, 724, 2702, 10084, 5, 15, » Bil) 195, ay 725.) 0S es Loge MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 735 35. In a given circle to inscribe a polygon having all its sides, diagonals, seg- ments, commensurable with the diameter, and their areas with the square of the diameter; and which may approximate to a given inscribed polygon. The general solution of this problem is another variation of No. 29; we have only to seek the muarif angle approximating to the angle at the circumference subtended by each of the sides of the given polygon, less one. 36. If, of a rational trigon, one of the angles be double of a muarif angle, the lines bisecting that angle internally and externally are commensurable with the sides. If the angle ABC be double of a B muarif angle, and if the angle at A also be muarif, the two trigons ABD, DBC, into which ABC is eae divided by the line BD drawn to ,. 5 , , bisect the angle ABC, have all their angles muarif, and so has CBE formed by drawing BE perpendicular to BD. Hence the line AE is cut harmonically and rationally. 37. If, of a rational trigon, two of the angles be doubles of two muarif angles, the six lines bisecting internally and externally the three angles intersect each other and the sides of the trigon produced, so that the segments are all rational, and the 7 areas commensurable with their squares. For, if each of the angles OAC, ACO, be E muarif, their sum FOA must also be muarif, wherefore its complement FBO has all its trigo- nometrical functions rational; so that, all the angles in the figure being muarif, all the seg- ments of the lines must be commensurable, and all the areas commensurable with the squares of the lines. XX 9) C SEctTION 3.—On Co-ordinates. 38. If any system of points have their co-ordinates from two rectangular axes, all rational, their co-ordinates referred to another pair of rectangular axes, making a muarif angle with the former, are also all rational. If « and y be the co-ordinates of a point, when referred to one system of axes, uw and v its co-ordinates when referred to another system with the same origin, and if 9 be inclination of the one system to the other, we have — u=x cos 0—y sin 0; v=a2 sin 0+y cos 6; wherefore, if z and y be rational, and the angle 6 muarif, wand v7 must also be rational. 736 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 39. To construct a tetragon which may have the co-ordinates of its corners and its sides all rational; subject to the condition that its sides have, nearly, given inclinations to the axes. Since the inclinations of the sides of the actual polygon to the axes must be muarif, we must select such muarif angles as may be suitable; and, moreover, we may always transform the co-ordinates, so that one of the axes may be parallel to one of the proposed sides. If, then, /,, /,, /,, 1, be the lengths, and 6,, @ ,, 6,, 6, the bearings of the four sides taken in order, we must have— 1, sin 0,+/, sin 0,+/, sin 0,+2, sin 6,=0 l, cos 0,+1, cos 0,+1, cos 0,+1, cos 0,=0 in which, if we put the appropriate rational fractions for the sines and cosines, we shall form two indeterminate equations, involving four unknown quantities. By placing one of the axes of co-ordinates parallel to (say) the fourth side, we cause the equations to take the form— 1, sin 0, +1, sin 0,+/, sin 0,=1, 1, cos 0, +1, cos 0,+/, cos @,=0 in which we have only to consider the latter. As an example, let it be proposed to construct a tetragon ABCD, such that AB may have about the direction 22°, BC about 74°, CD about 168°, and DA 270°. The muarif angles corresponding to these directions are, — 09-5 Bread 13,0 Dow, B 73... 44 .. 23 an ay 1D 1S nae Alp vel) 270 .. 00... 00 1 ‘eee and thus if 13a, 25d, 41c, and d be assumed as the four sides, we must have,— 12a+7b—40c=0; 5a4+24b+ 9c=d in which, if the values of a, 6, ¢, be obtained in integers, that of d must also be © integer, so that we have only to consider the indeterminate equation 12a+7b— 40c=0 ; this may be put under the form,— 124+ 7b _ 3 40 | that is to say, we have to obtain such values of a and b as may make 12 a+7b divisible by 40. The lowest solution of this indeterminate problem is a=1l, — b=4, c=1; whence the sides are 13, 100, 41, 110. . a By an extension of the same process we may obtain polygons of any number of sides, having all their sides and ordinates commensurable. The area of such , a polygon is also commensurable with the square of the linear unit; but it does’ not follow that the diagonals drawn from one corner to another are rational. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 137 Section 4.—On Trigonal Areas. 40, The only regular figures which can be used to cover surface are the trigon, the tetragon, and the hexagon; and any one of these may be used in the measurement of surface. Thus we may as well say, that the area of a figure is so many trigonal inches, as that it is so many square inches. If we were accus- tomed to it, the one mode of expression would be as intelligible as the other; and by confining ourselves to the rectangular or tessular method of denoting areas, we may fail to discover all the relations of geometrical magnitudes; or even to apprehend the cause of the superior convenience of the actual system. Since the regular hexagon contains exactly six regular trigons, there is no need for considering the trigonal and hexagonal systems separately ; it will be enough for us to assume the surface of the equilateral trigon, constructed on the linear unit as the unit of surface. For the sake of brevity, we shall use the expression frigonal area, as an equivalent for the area measured in equilateral trigons constructed on the linear unit. 41. If one angle of a trigon be 60° or 120°, that is 47 or 27, its trigonal area is expressed by the product of the numbers representing the containing sides. 42. The trigonal area of any equilateral trigon is represented by the second power of the number of units in its side. The truth of these two theorems is apparent; they are merely quoted for reference. 43. If a trigon have one angle 120°, the equilateral trigon, constructed on the subtense, is equivalent to the sum of the equilateral trigons, constructed on the two containing sides, together with the original trigon. If the angle ACB be the third part of a revolution, the equilateral trigon ADB, constructed on the subtense AB, E is equivalent to AEC and CIB, con- structed on the containing sides AC, CB, together with the trigon ACB. For ACF and ECB are straight lines; join DC. Then it is easy to show that the trigon DAC is equal to | BAE, and DBC to ABF, wherefore | the tetragon DACB is equivalent to | the pentagon AECFB, together with the trigon ACB. That is, thetrigon ABD | is equivalent to the pentagon AECEB. If a, b, ¢ denote the three sides of / such a trigon, c being the subtense of | 120°, we have,— “ a’? +ab+b?=c?. VOL. III. PART III. IM 738 MR EDWARD SANG ON THE THEORY. OF COMMENSURABLES. This well-known theorem is easily deduced from the tetragonal system of areas, and is usually given in this form,—‘“ the square of the subtense of 120° is equivalent to the squares of the containing sides, together with their rectangle ;” but it is more consistent to put it in the above form; and we must observe, that @ (the second power of the number a) does not represent the square of the side BC, but the equilateral trigon on BC. 44. The equilateral trigon on the subtense of 60° is less than the sum of those on the containing sides by the area of the trigon. The proof of this assertion is as easily obtained as that of the preceding. If a, b, c be the three sides of such a trigon, c being the subtense of 60° we have,— a* —ab+b*?=c? 45. Every number which is of the form a’+ab+0’ may, unless @ be equal to 6, be put in two ways under the form A*—AB + B’. This arithmetical proposition may also be stated thus,—“ every number which is the quotient of the difference of two cubes by the difference of their roots, is also in two ways, the quotient of the sum of two cubes by the sum of their roots.” The preceding diagram at once illustrates the truth of this assertion, for AB, which is the subtense of 120°, with the containing sides AE, CB, is the subtense of 60°, with AE, EB, and also with AF, FB, for containing sides. Or, alge- braically, a’ +ab+ b?=(a+b)?—(a+b)b +b? =(a+b)?—(a4+b)a+a?- otherwise a—b®? (a+b)?+b? (a+b)?+a° a—b ~(at+b)+b ~ (a+b)+a Hence the solution of the equation a+ab+b?=c? in integer numbers includes that of two others of the form @ —ab+b? =? 46. If any two of the three sides a, 6, ¢, of a trigon of 120° have a common divisor, the third has the same divisor. This is clear. Hence we need only consider those cases in which all the three are prime to each other. A7. If of the trigon a, 0, ¢, having an angle of 120°, the subtense ¢ have a common divisor with the sum of the two sides, the sides themselves have that divisor. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 739 For if AB and AF have a common divisor, FB must have the same divisor. 48. The product of two numbers each of the form a’+ab+0’ may be put, in two ways, in the same form. This theorem (as is also the corresponding one of squares) is only a case of a more general theorem; instead of repeating the arithmetical proof which is to be found in treatises on the Theory of Numbers, I shall give its geometrical illus- tration. Let there be two numbers P and Q, such that P=a’?+ab+0’, while Q=0+a6+(", in which we may suppose b>a, G>4, and also the quotient Oube @ iS to be greater than . A From the point A in any indefinite straight line, measure off AC equal to 6, make the angle ACB one- third of a revolution, and CB equal to a linear units. Join AB, then the second power of the number of units in AB is equal to a’ +ab+0’, that is AB’=P. Also, since AC is greater than CB, the angle CAB is less than 30°. In ABmake Ay equal to @, the angle Ay, 120°, and cut off 78 equal to a, join AB. Then AG’?=a’+a84+@=Q. Also since the ratio Ay: y@ is more unequal than that of AC: CB, the angle yA@ is less than CAB. And this disposition of the parts can always be made, unless the two ratios be identic. The angle CA@ is thus less than 60°. From the line A@ continued, cut off a distance AD to represent the product of the roots /P and /Q, so that AD? may represent the product P.Q: draw DG parallel to BC, and we shall have P.Q= AD?=DG?+ DG-GA+ GA’; therefore the product P .Q will be decomposed as asserted, provided we can show that DG and GA are expressed by integer numbers. Draw DE parallel to @y, EF parallel to BC, Ei parallel to FG, and having cut off IH equal to IE, jon EH. EIH is evidently an equilateral trigon, while HDE is similar to CAB. From the similarity of the trigons, we obtain the six proportions following. with their results :— A®@:@6y:: AD: DE or VQ: a::/7P.Q: DE=ayP AB: Ay:: AD: AE /Q:8::V7P.Q: AE=ByP AB: BC:: AE: EF VP Sao Gy ae Ea G AB: AC:: AE: AF VP Worn) bee Ada AB: BC:: DE: EH VP Ha): yay Py} Eh=oa AB: AC:: DE: DH VP) SOW Eh ba 740 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. But DG=DH+HE+EF ; AG=AF—EH, wherefore DG=ba+aa+aZB 2 AG=bG—aa and P.Q=(ba+aa+aZ)? +(ba+aa+aZ) (bB—aa) +(bB—aay. Again ; make the angle EAD’ equal to EAD, AD’ equal to AD; join ED’, draw G’D'T parallel to GD, EV’ parallel to FG’ and D’H’ to EH; then it is easy to pu that D’V’H’ is Suan” and that ED’H’ is equal to EDH. Now D'G’=EF-—D’'H’ , AV =AF+EH+HD, wherefore DG@=aG—ba ; AG’=bC+aa+ba, and P.Q=(aB—ba) + (ab —ba) (bB +aa+ba)+(bB+aa+ba)?, thus giving a second decomposition of PQ. | By interchanging a for } and a for (, in the above expressions, we obtain other two, viz.,— P .Q=(ba—aB)? +(ba—af) (66 +aB+aa)+ (bB+aB+aa)? P.Q=(aa—b)?+(aa—b8) (ba+aGb+bC)+(ba+aB+bB)? . and at first we might suppose that there are four decompositions: but if we take notice that if ba—a@ be positive in the one it is negative in the other, so that two of the four must belong to the form A?’—AB + B’. If we regard the trigon ABC as analogous to the right-angled trigon of the previous part, we may, taking AB as the unit or radius, consider BC as coming in place of the sine, AC in place of the cosine; and, for the moment, we may call the former the opposite, the latter the adjacent of the angle: that is we may define a as the opposite of CAB =e as the adjacent of CAB; and then we form four theorems for the functions of the sum and difference of — two angles, analogous to the fundamental theorems of trigonometry. These are, putting @ and @ for the angles BAC, @Ay, opp: (p +. 8)=opp. P. adj. 0+adj. . opp. 0+ opp. @ opp. 6 adj. (p+ 0)=adj. db. adj. O—opp. ¢. opp. 6 opp. (b—0)=opp. ¢. adj. @Q—adj. . opp. @ adj. (p — @)=adj. d. adj. 0+ opp. d. opp. 6+ adj. @. opp. @. in which it is to be remarked that we cannot pass from the function of @+ 6, to MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 741 the corresponding function of @—é@ by a change of sign, as we can in orthogonal trigonometry. 49. If a number be of the form a’+ab+0’, its square is of the same form. In order to decompose P* into A*+AB+B’, we have only to suppose that a, G6 of the preceding article are equal to a and 0 ; whence, P? =(a?—b?)? + (a? —b*) (2ab+a2) + (2ab+a2)? =(b?—a?) +(b?—a?) (2ab+b2) + (Qab+b?)? only one of which belongs to the prescribed form, the other belonging to A?—AB+B?’. 50. The number 3 is of the form 17+1.1+71, it is the only number of that form whose square cannot be put in the same form. If we make, in the preceding formule, a=1, }>=1, we obtain 9=0? +0343? 9=07?—0°34+ 3? Our previous demonstration proceeded on the assumption that @ and 0 are prime to and different from each other. In the present case the trigon is collapsed into a line, while the conjugate trigons take the forms 0, 3, 3, and 3, 3, 3, the one being a line and the other an equilateral trigon. 51. When the number P=a’+ab+0’ is multiplied by 3, we have, on substi- tuting 1 and 1 for a, @ of No. 48, 3 P=(2a+b)? + (2a+b) (b—a)+ (b—a)? of which the two conjugate forms are 3 P=(a+2b)?—(a+2b) (b—a) + (b—a)? 3 P=(a+2b)?—(a+2b) (Qatb) + (2a+b)? 52. When the sides of a trigon having one angle 120° are in their lowest terms, the subtense cannot be a multiple of 3. If the subtense were divisible by 3, the sides must necessarily be of the forms 3n +1; these admit of three distinct classes of combinations. First, a and 6 may be both of the form 32+1; secondly, they may be one of the form 37+1, the other of the form 327—1; and thirdly, they may be both of the form 3n—1. In the first case, if we put a=3a+1, b6=3C +1, we have, 9(a? +a8 + 6?)+9(a+B)+3=c? now, no square can be divisible by 3 without being also divisible by 9, therefore this combination is impossible. The same argument applies to the third case, for if a=3a—1, b=3G—1, we have, 9(a? +a8+6?)—9(a+ B)+3=c?. In the second case, if we put a=3a+1, b=3@G—1, the sum of a and 2 is VOL. XXIII. PART III. 9N 742 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. divisible by 3, and therefore the subtense AB and the side AF being both divi- sible by 3, the other side BF must also be so, and consequently the trigon could not have been in its lowest terms. 53. The subtense of 120°, in its lowest terms, cannot be even. For if both a and 6 were odd, we might put a=2a+1, b>=28+1 which give ‘4(a? +a8+ 6?) +6(a+6)+3=c?, which is inconsistent with ¢ being even. 54. If one of the sides of 120° be even, it must be divisible by 4. ; For if we put a=2a, 6=28+1, we have 4 (a? +a8+(")+2a+4@6+1=¢; now, in all cases of ¢ being odd, c’—1 is divisible by 4, wherefore 2a, that is a, must be divisible by 4. 55. The subtense of 120°, in its lowest terms, cannot be a multiple of jive. For if ¢ were divisible by 5, the side @ must belong to some of the forms 5a+1, 5a + 2, while > must also be of some one of these forms. Now if we con- — join the supposition that a=5a+1, with each of the four b=56+1, 6=58+2, b=58+3, b=56 +4, we find that the sum a? + ab+0? is of the form 5n+3 in the first and third case, and 5% +2 in the second case, neither of which is a possible form for a square number; but in the fourth case we find c’ == 5n+1, which is possible; but then a being 5a+1, and b, 58+4, their sum is divisible by 5, so that (No. 49) the trigon cannot have been in its lowest terms. Next, combining the form a=5a+2, with b=56+4 2, 58+3, 5644, we find that the first and last give the forms 5x+2 and 52+3, which are impossible, while the intermediate case gives the possible form 5n—1, but then as a=5a+2, b=58+3, a+b would be a multiple of 5. Combining now the form a=5a+3, with 6=5@6+3, and b—56+4, we find the forms 5x+2, while lastly, combining 5a+4, with 56+4, we obtain the form 52+3, which is impossible for a square number. Hence in no combination of numbers for a and 2 not divisible by 5, can we obtain a form possibly a square, for a? +ab+0’. a 56. If a and 6 be two numbers prime to each other, a*+ab+0? is either divisible by 3 or of the form 62+ 1. In reference to the divisor 6, all numbers leave the remainders 0, 1, 2, 3, 4, 5, and the only possible combinations of two of these, not giving numbers having 2 or 3 for a common division are,— . a=6a+0, b=6641 P & 6n+1 b=6845 P w= 6n+1 a=6a+2, b=66+1 P w= 6n+1 b=68 +8 P «=, 6n+1 b=66 45 P = 6n+3 a=6a+4, b=668+1 P 6143 b=66 +3 P & 6n4+1 b=66 +5 P&S 6n4+1 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 743 a=6a+1, b=66+41 P = 6n+38 b=664+8 P «= 6n+1 b=63+5 Bes Gnd a=6a+3, b=604+5 P & 6n+1 57. The subtense of 120°, when the three sides are in the lowest terms, is of the form 6n+ 1. For, according to the preceding theorem, every number P is of one of the two forms 6n+1, 62+3; now it cannot be of the form 62+3 when the three sides are prime to each other; wherefore, the subtense must always be of the form 6n+ 1. 58. If a prime number a divide any number P of the form a? +ab+0’, a and b, being prime to each other, another number of the same form, but less than a’, may be found also divisible by a. If a and 6 be greater than a, we may put them under the forms a=na*<¢, b=ta +d, in which c and d are each less than the half of a. Inserting these values in the equation, P=a? +ab+b? we find, — P=n?a? +2nca+c? +nta? +ica+nda+cd+t?a? + 2ida+d? wherefore, if P be divisible by «4, c* +cd+d’ must also be divisible by it; now |. cd+d? = 3a’. 59. If a and 0 be prime to each other, no prime number of the form 6n—1 | can be a divisor of a? +ab+b=P. | For if some prime number @ divide P, we may find some other c’ + cd+ a’, | less than 8a’, which is divisible by a. Now, we have shown that c?+cd+4d? is | either divisible by 3 or of the form 6n+1; if it be divisible by 3, its third part is | also of the same form, so that eventually we arrive at a number of the form | 6n+1. But no number of this form can be divided by a x6n—1 unless the | quotient be of the form 67—1; hence if c?+cd+d? =a, the quotient @ less than 3a must be of the same form. By proceeding in the same way, we can show | that some other number 7, less than 36, must be a divisor of some number of |) the form e’+ef+f*; and so we can continue. By this process we must at last | arrive at the number 5, the least of this class: now, we have shown that 5 | cannot be a divisor; wherefore no number of the form 6n—1 can divide the _subtense of 120°. | 60. The subtense of 120°, when the numbers are in their lowest terms, can only be a prime number of the form 6”+1, or the product of two or more of ‘such primes. This follows immediately from the preceding theorem. Hence, in order to \tabulate trigons of this kind, we must decompose the primes 7, 13, 19, &c., linto three parts, a’, ab, b°. Having found, for example, that 7=1+2+4, we lobtain 7°=3*+3.5+ 5° from the formula given in article 49. 744 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. In the appendix there is given a list of all primes of the form 6x+1, under 1000, with their decompositions, and the resulting trigons, as also the values of the lesser angles. Thus there are muarif angles belonging to the trigonal system of measure- ment, analogous to those which we have already seen to belong to the tetragonal system: to distinguish them from those formerly treated of we shall call them trigonal muarif angles, while the others might have been styled tetragonal muarif angles. 61. If two angles be both muarif of the same system, their sum and their difference are so; a right angle being regarded as muarif in the tetragonal and an angle of 60° as muarif in the trigonal system. This has already been shown to be true for the tetragonal system; the proof for angles of the trigonal system is of the same nature. 62. If a trigon be constructed with two of its angles muarif of the trigonal system, its sides are commensurable with each other, and its area with the equi- lateral trigons constructed on the sides. The proof of this is analogous to that already given for the other system. 63. If at the two extremities of a line taken as a base, any number of trigonal muarif angles be made, their sides, continued indefinitely, cut each other into segments commensurable with the base, and intercept areas which are commen-. surable with the equilateral trigon described on the base. This is merely an extension of the preceding proposition. 64 Ifat any of the points of intersection of the preceding figure, other tri- gonal muarif angles be made; the distances intercepted by these new lines are commensurable with the base and the intercepted surfaces with the equilateral trigon on the base. 65. If at the point of contact of a straight line with a circle, trigonal muarif angles be made; if the extremities of the chords so formed be joined, and if tan- gents be applied at the extremities of those chords, all the intercepted distances are commensurable with the side of the inscribed equilateral trigon, and all the areas with the area of that trigon. ee 66. To construct a trigonal muarif angle which may approximate to any given angle. Let it be proposed to compute, in integers, — D the sides of a trigon which shall have one of its angles equal to a given angle BAC, and c another either 120° or 60°. = E "Gi If the given angle BAC exceed 60°, it is impossible to have either of the remaining angles 120°; we shall therefore deduct 60’, or if need be, 120° from BAC, thus leaving bAC less than 60° Having bisected DAC by the line AD, draw EF, making AEF =120°; and deter- MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 745 mine, by the method of continued fractions, or by any other process, two numbers, a and @, which may represent with sufficient nearness the ratio FE: EA; and then compute a, 6, c, the sides of a rational trigon having one angle 120° by the formulze,— c=(a+8)?—a8; b=(a+BP—-H; a=P?—a’, then the angle of this trigon opposite to a is double of not the angle DAC, but an angle sufficiently near to DAC, wherefore that angle is nearly equal to 0AC. This is the general process, analogous to that given for the tetragonal system ; but in special cases we may use peculiar methods. Example 1. 67. To construct a rational trigon having one angle 120°, and of which the containing sides may differ by unit. That is, in other words, to construct a tri- gonal muarif angle approximating to 30°. If c, b, a, be the sides of such a trigon, and if b>=a@+1, we have c’=3a’+ 3a +1, that is to say, c’=3 (a@+4)’+4; or multiplying by 4. (2c)?=3 (2a4+1)?+1, and therefore 2c and 2a+ 1 must be the numerator and denominator of a fraction converging to /3. Now, we have for /3,— (Co ed tiga: ef 5 7 LO Sor Tk. OT & a... 0, ayy [etlinank Wooo) anynsen Ts of which the alternate terms,— iy ee ete i ee oe Et EE ga 1 2 7 26 97 362 1351 5042 , Ceres” tH aE Page M70 “corr satisfy the equation p’=3q’+1. These may be formed by means of the multi- plier — 4. Of these again, the alternate terms have their numerators even, viz. :— —14 -14 -14 —14 2 26 362 5042 70226 aS is + 209°. 291 Voss &e. | and of these, if we put the numerator equal to 2c, and the denominator to 26—1, or to 2a+1, we find the cases,— Cal Widlions diSiie 2521.9 &e, b=1, 8, 105, 1456, &c. a=0, 7, 104, 1455, &. | and it may be remarked, that this progression of fractions may be continued by | help of the multiplier —14. m WOL. XXIII. PART III. 90 746 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. The intermediate fractions which have their numerators odd, give trigons of which the sides differ by 2, thus,— ‘ c=, O1,) ‘1dpl; PLSery, ae, b=5, 57, 781, 10865, &e. a=3, 55, 1779, 10864, &c. Eazample 2. 68. To construct in integers a trigon having one angle 120° and another nearly 45°. In this case the angle FAE is 214°, while AFE is 373°, wherefore the ratio of 6 to a is identic with that of sin 37° 30’ to sin 22° 30’, that is, of 6087614 to 3826834. On approximating to this ratio by the method of continued fractions, we obtain the quotients 1, 1, 1, 2, 3, 1, 14, &c., whence the values,— Le Beye lt Br) Peete ak 0 Ad eta Ree 2 aes LO) FB gle Gg ay Wig es and thence the trigons,— c=7, 19, 43, U477%, 2479, &e. b=5, 16, 35, 1207, 2024, &e. o=3, 5, 12 Ae Lee 69. In a given circle to inscribe a polygon of which all the sides and diagonals may be commensurable with the side of the inscribed equilateral trigon, while the polygon may approximate to a given inscribed polygon. The solution of this problem is analogous to that of the corresponding problem of the tetragonal system. Section 5.—On Muarif Angles in General. 70. Inthe first branch of our inquiry we treated of trigons having one angle right, in the second branch we extended our researches to trigons having angles of 60° or 120°, and in either case we arrived at general theorems analogous to each other. I proceed now to consider whether there may be other classes of muarif angles possessing the same generic properties. If in the figure of article 48 we .suppose that the exterior angle EFG’ is de- — scribed by 6, we have AB’=a’* +2ab cos 6+0’=P, and similarly, AG? =@" + 2a8 — cos 6+ 6?=Q, and all the equalities given on page 739 hold good, with the ex- ception of HI, which, instead of being represented by aa, is now represented by 2aa cos 6, and H’l’, which becomes 26a cos 6, and we obtain AD? =P.Q=(b? + 2ab cos 0 +a?) (0? +2aB cos 6+ a?) DG =a8 + ba+2aacos 0 | AG =0b6 — aa. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 147 If in this we suppose a=a, b=6, we obtain AD=C=? +2a@ cos 0+ a? AG=B=/(? — a? GD=A=2a (+a cos 6), Wherefore, if in a trigon AY, the two sides 0, a, be denoted by integers, while the cosine of the angle AY is rational, the three sides of the trigon AGD having an angle GAD double of yA, will be commensurable. The subject may be presented in another light, thus— Let the cosine of the angle 6 be denoted by the rational fraction = , then e¢, 6, a, being the sides of any trigon having 180°—@ for the angle opposite : we have 2 C= or ab +a? 2s s? P—s7 eee pe + Pp a? 2 =) a? 2 — (6 + : a)? + : or, (tc)? = (tb + sa)? + (t? —s”)a?, ~ whence (te + tb +sa) (tc—tb—sa)=(t+8) (t—8s) xy’, if we put zy (either of which may be unit) for a. Decomposing the latter member into factors prime to each other, we may put tc+tb+sa =(t+s)a? é te—tb—sa =(t—s)y? which give C=2ie=(¢+ 90" +(—oy?; B=2tb=(t+s)a? —2sxy —(i—s)y?; A= 2a 2tay ; in which # and y may be any two numbers whatever ; it is edulis) however, to assume them with a common divisor. AX When the three sides BC, CA, AB, of a trigon, having the angle ACB equal 748 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. to the supplement of @, have been determined in integers, the angles BAC, CBA may be said to be muarvf of the system 0, and for the present we may call 6 the determining angle of the system. 71. Every rational sided obtuse-angled trigon is accompanied by two acute- angled trigons having their sides also rational and their areas commensurable. For let ABC be an obtuse angle, and let the three lines BC, CA, AB, be ex- E pressed by three integer numbers, a, 8, ¢. From A to the extension of BC, and from B to the extension of AC, inflect AK, BF, each equal to AB: then since C7 — 6" by the quotient , while CF is re- a c? —a? 6 presented by , both of which are rational. If EG be cut off equal to BO, and FE equal to AC, it is evident that the angles CAG, HBC, are each double of the complement of FCB or 6; wherefore the sides of ACE are a+ 20 cos 0, 6, c, while those of BCF are a, 6+ 2a cos @, C. The areas ACB, ACE, BCF, are proportional to the rectangles AC, CB, AC, CE, BC. CF, and must be commensurable since the containing sides are so. 72. If each of two angles be muarif of the same system 60, their sum and difference are also muarif of that system. Let (figure, page 747) CAB, yA, be two angles muarif of the system 6=180— ACB=180°—A7Yf, and let a, b, ¢; a,@,y, be the integer numbers which represent the sides of the two trigons; make AD equal to Cy units, and complete the con- struction as in article 48, only observing to draw EH making EHG equal to 6, and D’H’ making D’H’l’ equal to 6, then we easily obtain the values DE= D'H’= Ca, AE=CO6, EF=a8, AF=b8, EH=aa, DH=0a, D’H’=0a as before, while HI =2aa cos 6, H’I’=2b6a cos 6, whence . AD=cy AT ory AG=b6—aa AG’=b8 +aa+2ba cos 0 DG=a + ba +2aa cos 0 D’'G’ =a8—ba, which values are all rational when cos 6 is so, but are only integers when cos 6 =0, or when 2 cos 6 is integer. 73. If two angles of a trigon be both muarif of the system 6, its sides are commensurable, and its area is commensurable with that of a rhombus on the — linear unit, having an angle equal to 0. The truth of this theorem is obvious. . 74. If at the extremities of any line assumed as a base muarif angles of the system 6 be made, and the sides of these be indefinitely produced, all the inter- BA°’—AC?=BC.CE, CE is represented _ MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 749 cepted distances are commensurable with the base, and all the areas with the rhombus constructed on the base with the angle 0. 75. Ifat any of the intersections of the preceding article muarif angles of the same system be made, the segment and areas so intercepted are all commensurable. 76. If at the point of contact of a straight line with a circle any number of muarif angles of the system @ be made, all the lines joining the extremities of the chords so formed, and all the tangents there applied continued indefinitely, intercept segments and areas which are commensurable with each other. 77. If one muarif angle of the system @ be equal to an angle of the system ¢, the two systems are identic. Hence it follows that the determination of a system by the angle @ is not quite appropriate ; that is to say, the angle 0, no more than the angle ?, can be re- garded as the modulus or mastar of the system. 78. The numerical expressions for the sines of all muarif angles of the same system involve the same irreducible surd. Or, The numerical expressions for the areas of all muarif figures of the same system, when expressed in squares of the linear unit, involve the same irreducible surd. Let — and = be the expressions for the cosines of two angles @ and ©®, then have we ie Be a2) sin 0 = ves e ) sin © = a ee 2 ) and 68 y(@—s2).V (1? —S2)_ cos (0+ ©)= T~ T : now if the two angles 9 and © be both muarif of one system, their sum 6+ 0 must also be so; that is to say, the cosine of 6+ © must be rational, and for this it is necessary that the product of V(t?—s?) by W(T?—S?) be also rational, and this can only be when ¢’—s° and T’—S? involve the same unsquare factors. Since the area of any trigon expressed in squares of the linear unit is half the product of the two containing sides multiplied by the sine of the included angle, the same irreducible surd must enter into the expression for the area. 79. All muarif angles of which the sines involve the same irreducible surd, belong to the same system. Let 9 and ¢ be two muarif angles, of which the sines are respectively sin 0=‘“/m and sin patV m, m being a number which has no square divisor ; then, if the angles be muarif of any systems, their cosines must be rational. Now ‘ cos (0+ )=cos 0. cos P—sin O. sin p —cos @. cos o-am VOL. XXIII. PART III. 9P 750 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. which is rational, wherefore the sum of the two angles is muarif, and thus they must belong to the same system. 80. The irreducible surd which enters into the expression for the sines of the angles of one system, may be called the modulus or mastar of that system; we shall generally denote it by the symbol »/m. 81. Having given the modulus of a system, to find general expressions for the sines and cosines of all the angles belonging to it. Let Vv m be the sine of any angle ¢, then the expression for the cosine of that angle is,— cos, 0V eee if 3 and in order that 6 may be a muarif angle, it is necessary that its cosine be rational, or that /’—me’ be a square number. , We may then put /°—me’ =p’, or f’—p’=me’. Now, whether ¢ be prime or composite, we may always put e=ay, when we do not exclude unit from the values of # and y; and similarly we may put m=yy with the same generalisation ; our equation of condition then becomes, , (f+ p) F—p)=praty’, wherefore in general, ftp=pa", f—p=vy’, and =$ (ma? +yy?); p=} (ur? —vy?) so that arys/ py =sin 0; (acess eee 6 faa? + vy? 7 phar® + vy? ; and also, pan? + y? bya? +? 2oy/ PY _ gin Biz (Cert ge 6. are the expressions for the sines and cosines of all muarif angles of the system / uy, x and y being susceptible of all integer values including unit. It is obvious, that in assuming values for 2 and y, we may reject those — couples which have a common divisor. 82. The sines and cosines of the sum and difference of two muarif angles, determined by the above formule, belong to the same forms. Let { h cos saa rea cos ar ae sin ga 20 py si _? s yV py ba? + vy” px?+yy” ve cok (0+ ye ey me (pa x —vyy)? + py (ayt+y x) Sn ae YOY) hs Ey sin 0+ 0) Gr vy + wy yey xy MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 7o1 which can be brought into the preceding forms by multiplying each member of the fractions by F or by ». 83. The tetragonal system has for its modulus the symbol V/1. 84. The modulus of the trigonal system is /3. 85. If a trigon be constructed, having one angle muarif of one system, and another muarif of another system, its sides are incommensurable. For if ¢ and 6 be two muarif angles, the one involving the surd /y and the other the surd »/y, the sine of ¢+ 04 would involve the product Wy, but then the cosine would involve the two surds /p, »/y separately, wherefore the side inter- mediate between ¢ and 9 would be incommensurable with either of the other two. 86. Having given the three integers which represent the sides of a rational sided trigon, to find the modulus of the muarif system to which its angles belong. Let a, 6, c, be the three sides, then, the area of the trigon being s, we have, 4 S=J{(a+b+c) (—a+6b+0c) (a—b+c) (a+b—c)} wherefore, if we decompose each of the four numbers a+ b+¢, —a+b+¢,a—b+e, a+b — e, into its prime factors, and reject all those factors which occur twice, the square root of the product of the remaining factors is the required modulus.’ Thus we have the following cases :— a b c Modulus, a b c Modulus. 2 3 4 J15 9 Lowry dr so 3 4 5 J1 4 5 6 a 3 5 Ta) Wiel 5 6 7 J6 5 7 Ou tila 6 ih 8 J15 7 Oe alituay 195 7 8 9 Jb 9 11 Ie ies es, 87. If m be prime, for every pair of values of x and y, we have two angles, according as we combine m with «’ or with y’; but if m be composite, then for every way in which m canbe represented as a product py, we have two angles. SECTION 6.—Miscellaneous Propositions. 88. To construct a trigon, such that the three sides and the line bisecting one of the angles may be all commensurable. Let the angle BAC of the trigon BAC be bisected by the line AD; it is required to determine the dimensions, so that all the lines be represented by integer numbers. A From the principles of geometry we know ae that BA: AC:: BD: DC, while the square of | es D . AD is the difference between the two rectangles SAG ins tae Fe | BA.AC and BD.DC. If we denote the ratioof = \ BA to AC by p: g, p and g being prime to each A” other, we may put BA=ap, AC=aq; BD=yp, and DC=yq, whence BA.AC 752 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. =a’pqg and BD.DC=y’pq, so that AD’=(a#2*—y’) pq; thus it seems that the product (w+y) (e—y) pq must be a square; now p and g are prime to each other, wherefore they must be found as factors in the product (#+y) (e—y), the remaining factors being in couples. Hence the following cases are possible,— in all of which the effect of the c is only to augment the numbers. Ist. wt+y=arepy; x—y—b'e 2d. et+y=ae ; a—y=b'¢e 3d. w+y=a"pe ; Ae es ee 4th. e+y=a'qe ; x—y=b*pe | Hence the solutions,— 1. 22=a*pqt+b?; 2y=a*pq—v?; 2. 2a=a?+b?pq; 2y=a?—bpq; 3. 2a=a’p+b?q; 2y=a%p—b’q; 4. 2e=a7q+b*p; 2y=a*q—b*p: which give BC=(a’pq—6?) (p+q); CA=(apq + b’)q; =(a*pq + b’)p ; Fn —b*pq) (pt+q); CA=(@+b’pg)q ; =(a? + b*pg)p ; =(a*p—b’q)(p+q); CA=(ap+¢'qq; =(a*p + b?q)p ; =(a’q—0’p) (p+9); CA=(a?q+b?p)¢q ; ie (a?q+b?p)q: in which p, q, a, 6, may beassumed at will, subject only to the restriction, that the values of BC be not negative. These four solutions are complementary in pairs. A much more elegant solution of the problem is obtained from the properties of muarif angles. Since the trigons BAD, DAC have their sides commensurable, and their angles BAD, DAC alike, they must belong to the same muarif system. Wherefore, in any one system assume BAD= DAC=6@ and ADB=@, then we have sin ABD=sin (#+9), sin ACD=sin (¢—@) so that all the ratios are rational, since all the sines involve the same irreducible surd. 89. To construct a trigon, such that the three sides and the lines bisecting two of the angles may be all commensurable. To construct a trigon ABC, such that _ its three sides and the lines AD, CF bi- secting two of its angles may be all com- mensurable. In any system of muarif angles, as- sume two, 6 and @¢, of which the sum may be less than a right angle; then having © taken any base AC, make at A, CAD, DAB, each Pegi to 6, and at C, ACF, FCB, each equal to ¢, then all the lines andall the areas in the fig ure are commensurable. 90. To construct a trigon of which the three sides and the three lines biscoaiae ) the three angles may be all commensurable. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 375 The halves of the three angles of any trigon make together one right angle, wherefore they can only be all muarif in the system to which the right angle be- longs; and if two of them be muarif of that system, the third must also be so. Hence, if the two angles 6 and ¢ be taken from the tetragonal system, and j2 the trigon ABC be constructed, having BAC=20, ACB=2¢, ABE, the half of the third angle ABC, is also muarif, and therefore the segments intercepted on — and by the six lines AB, BC, CA, AD, BE, CF, are all commensurable. . Moreover, if we draw QAR, RBP, = \ PCQ, bisecting the supplemental angles, = / ~_ and then draw perpendiculars from O, P, Pat Q, R, to the three sides, all the distances % Q intercepted on those lines are also com- mensurable; hence, of such a trigon, the three sides, the three altitudes, the radius of the circumscribed circle, the radii of the four circles of contact, the distances of the centres of those four circles from each other, and from the corners of the trigon, as well as all the segments of the lines bisecting the angles inter- nally and externally, are commensurable, and may therefore be expressed in integer numbers. Example. If we take DAC=0=36° 52’, ACF=$=22° 37’, we have CBE=30° 3l’=4, and in 0=5, cos ie sin pa cos p= rae whence sin ~=cos (9+ ¢) =, cos ~=sin (P+0)= =" ; from which we obtain the sines of the whole angles, viz., 120 3696 sin A—7! oe sin C=j¢5> sin B= 5s. The three sides must be proportional to these sines, so that, when the common divisors are taken out, weobtain AC = 154, BA=125, CB=169. 91. To construct a trigon such that | the three sides and the two lines trisect- | ing one of the angles may be all com- mensurable. | Having assumed an angle ¢ muarif of i | any system and less than 60°, make ACB equal to 3, and then at A make any VOL. XXIII. PART III. 9Q 754 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. angle @ muarif of the same system, and less than the supplement of 3¢, and then the lines AC, CB, BA, CH, CI, are all commensurable. 92. To construct a trigon such that the three sides and the four lines tri- secting two of the angles may be all commensurable. Assume two angles 6 and ¢,the sum of which must be less than 60°, and make CAB equal to 30, ACB equal to 3¢, then all the lines AB, BC, CA, AD, AE, CH, CI, and all the segments of those lines, are commensurable. 93. To construct a trigon of which c the three sides and the six lines trisect- ing the three angles may be all commensurable. The third parts of the three angles A, B, C, make together 60°, wherefore if these third parts be muarif of any system, — 60° must belong to that system. Such a figure, then, can only belong to the trigonal system of which the modulus is /3. } Assume then from the trigonal sys- tem two angles, 6 and ¢, of which the ¢ sum is less than 60°, then the defect of their sum from 60° is also muarif of that system. Make BAC equal to 306, ACB equal to 3¢, and trisect the angles; these angles are all muarif, and consequently all the lines and all their segments are commensurable, while all the areas are commensurable with equilateral trigons constructed on any of the lines or parts. 94. It is impossible to construct a trigon such that its sides and also the lines dividing its angles into more than three equal parts may be all commensurable. If it were proposed to construct a trigon such that its sides and the lines” dividing each of two of its angles into m equal parts may be all commensurable, we should only have to assume 6 and @ muarif angles of any system, but such that (6+) may be less than 180°; and then to make the angles at A and © equal to 20 and to x respectively. But the n™ part of the remaining angle would not be muarif, unless, in the system »/1, ” were 2, or in the system »/3, m were 3; for no submultiple of 180°, excepting 90° and 60°, can be muarif of any system. Here it is worthy of remark that the tetragonal and trigonal systems are founded on the divisions of the whole revolution into 4 and into 6 equal parts; while 4 and 6 are the only two divisors which separate the prime numbers” greater than themselves into two groups; those groups being, for 4, of the two forms 4n+1 and 4n—1; while for 6 they are classed as of the forms 6n+1 and 6n—1. | MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 755 95. If a series of equal straight lines be drawn, making equal angles with each other, the angle being the supplement of the double of a muarif angle of any system, the distances of the extremities of the lines from each other are commensurable with the lines. Let the equal lines AB, BC, CD, DE, EF, &c., make equal angles ABC, BCD, BDE, DEF, &c., such that the supplement of ABC is double of a muarif angle of any system; then all the diagonals ie 2 AC, AD, AE, AF; BD, BE, BF, c D &e., are commensurable with AB. For the angle BAC being half the supplement of ABC is muarif; so is CDA its double, DEA its triple, and so on; wherefore, all the angles of the figure being muarif, all the sides of the trigons are commensurable. If the angles belong to the tetragonal system, the sides are also commensur- able with the radii of the circles described, one through the points A, B, C, D, E, F, and the other to touch the lines AB, BC, CD, &c.; and also the co-ordinates of the points referred to any system of rectangular axes making muarif angles with any of the lines may be obtained rational. 96. To construct a trigon such that its three sides and the line joining the middle of one side with the opposite corner may be all commensurable. Having bisected the side AB of the trigon ABC in F, and joined CF, we have AC?+CB?=2AF’+2FC?’, so that the problem becomes this: to find two square numbers whose sum is double of the sum of other two square numbers. Pit bC=—a, CA=b;: AF=s, FC=i, then A io A F a? + 0? =2k? 427? =(k+1)?+(k—1)? so that the sum of the squares of @ and 6 is also the sum of the squares of £+/ and k—/; now we have seen that every number which can be divided into two squares in more than one way is the product of two or more prime numbers of the form 4n+1. Hence we have only to take any two or more prime numbers a, 8, y, 0, of the form 4n+1, and decompose their product into two squares in two different ways, so as to obtain aByO=a?+b=p?+q’, and then we have k=3(p+q), /=i (p—q, or doubling all in order to avoid fractions, 756 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. BC=2A, CA=2b, AF=p+q; FC=p—g. It is evident that we may introduce powers of the primes @, @, y, and decom- pose such a product as a? @° y 6* into two squares in two different ways. For example, if we take ¢=5, @=13, we obtain 65=7? + 47=8"+ 1", whence BC—8, CA—14 AP—Pb—s7, FC 7, If CF were produced to an equal distance, and the extremity of the produced part joined with A and B, a rhomboid would be formed having its sides 8 and 14 with the diagonals 18 and 14 respectively; or, halving, the sides are 4 and 7, with the diagonals 7 and 9. As5 and 13 are the smallest primes of the class 4n+1, we may infer that the above are the smallest dimensions of a rhomboid having its sides and diagonals all integers. The subject may be viewed in another light thus: let the cosine of the angle at F be denoted by the fraction *, in which one or both of the factors of the numerator may be 1 or zero; while one of the factors of the denominator may be unit ; then denoting AF by & and FC by / as before, we have t =k? + = kl+ P=w?2? +2star+v7r2 bah —2= kl4+ P=u?a?—2star+vu7r? if we put k=ua, l=vnX. Hence a? —b?=(a+b) (a—b)=4star =4se . tr, which is satisfied on making a = 2sx+3 tN; b=2sx—3 tr, which gives a? =4s"4?+2star+4 72, so that we must have ura +7? = 48747 +4 72; or (4s?—u?) a? =(v?—4 2”) r2; that is (2s +u).(2s—u) a? =v?A?—4 PA’, whence (2s +u)+(2s—u) a? =2vA=21; Qua=2k (2s+u)—(2s—u)x?=tAr; so that ultimately, multiplying by 2 to remove fractions, 2a =A=4sa + (2s +u)— (2s —u) x 2b = B=4sa—(2s+u)+(2s—u) x? ) 2h 2 2) = (2s+w)+(2s—u) x? in which any values, positive or negative, may be assigned to s, uw, and z. MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. Right-angled Trigons. @aar| c Osa A. CG CD ft) 2 5| 4\| 8/36 52 11-64 989 | 240 aes 13°] 12 5 | 92 87 11°51 || 2 17 | 293 | 285 meen) 17 | 15 8|28 04 20:94 305 | 273 95 | 24 7/16 15 36-74 205 | 224 Gees) 29) 21) 20) 43° 36 10-15 | 12°13 | 313°) 312 fecal) 37-| 35) 12) 18° 55 98-71 | Iida | 317!|\'308 ges i) 41i| .40 9/12 40 49:38 325 | 323 peep 63 | 45.) 98 | 31 53 96-84 325 | 253 Guo) 61 | 60| 11/10 28 19:89 | 9 16 |°387 | 288 65| 63! 16|14 15 0012] 5 18 | 349 | 299 65 | 56 | 33|30 30 36-85 | 8 17 | 358 | 272 Bee 73 | 55 | 481 41--06 43-51 365 | 364 85 | 84| 13| 8 47 50-69 365 | 357 Son 7m) 36.) 25.08 27-49) op ees 7st) 276 5 8] 89| 80| 39|25 59 21-93 877 1) B02 fon 97) 72) 65% 42° 04° 80-11 377 | 345 1 10/101! 99] 20/11 25 16-27 |.10 17 | 389 | 340 3 10/109| 91| 60|33 23 54:57 || 6 19 | 397 | 325 meaietis (412) 15 | 7 387 41-34) 11-20) 401 | 399 125 | 117) 44120 36 34:89 || 3 20] 409} 391 4 11/137/105| 88| 39 57 5836] 14 15 | 421 | 420 145|144| 17] 6 48 58:52 425 | 416 145 | 143 | 24] 9 31 38-22 425 | 304 7 10|149/|140] 51/20 00 57-4612 17 | 483 | 408 6 11/157 |132| 85|32 46 44-69 445 | 437 169 | 120 | 119 | 44 45 937-00. 445 | 396 2 13/173|165| 52/17 29 32:38 || 7 20] 449 | 351 Odo |) 181 180 | 19| 6 O11 32-07 || 4:21 | 457)| 425 1185 |176| 57/17 56 42:92 | 10 19 | 461 | 380 185 | 158 | 104] 34 12 19°64 481 | 480 7 12/193|168| 95 | 29 29 1365 481 | 360 1 14|197/195!| 28] 8 10 16-44 485 | 483 205 | 187| 84] 24 11 22:25 485 | 476 205 | 156 | 133 | 40 27 58-98 493 | 475 | 221 | 220! 21] 5 27 09:44 493 | 468 921 | 171 | 140 | 39 18 27:54 505 | 456 2 15| 229/221] 60/15 11 21-44 505 | 377 8 13 | 233 | 208 | 105 | 26 47 0600} 5 22 | 509 | 459 4 15 | 241 | 209| 120/29 51 4619 | 11 20 | 521 | 440 1 16| 257! 255! 32] 7 09 09-60 533 | 525 265 | 264 | 293! 4 58 44-78 533 | 435 265 | 247 | 96|21 14 21:51 || 10 21 | 541 | 420 10 13 | 269 | 260! 69/14 51 4615 545 | 544 9 14| 277 | 2521115 | 24 31 46-36 545 | 613 5 16 | 281 | 231/160] 34 42 28-99] 14 19 | 557 | 532 VOMA exniS PART UL. 18-11 10-81 51°75 298-48 52-43 07:98 34°78 48:25 04:17 53°59 51:90 31:90 04:84 03°65 08°63 38°34 08:08 04:07 29°32 41:50 59°52 44°22 57°68 53°33 50°40 27°12 48-32 06:95 58°50 42°80 40-24 18°45 18°28 49-20 28-91 55°36 32°10 30°71 42:29 22°13 00°89 23°91 | 17:07 53°80 52°67 ~j 758 19 17 14 10 26 22 27 26 20 25 22 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. Right-angled Trigons—continued. 675 684 667 561 672 627 595 760 736 778 700 629 837 30°30 53-01 08-15 18°80 28-83 11°67 23°35 53°46 13°48 52°23 10°33 50:00 29°58 29°29 39°74 18°71 46°73 50:00 15°34 21:63 31:57 10°32 15°79 34:50 33°40 1311 22°05 14:19 50°91 13:14 15°37 04:76 41 47 26°94 03°66 51°63 31°40 08:88 57°63 08°45 46:60 39°70 25:34 18 22 11 a 6 23 29 29 25 33 29 ¢ 899 777 663 924 756 920 912 741 900 861 728 957 884 945 864 697 925 840 1012 779 1023 897 1015 988 812 999 861 780 975 952 1085 928 1104 1073 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. 759 Trigons of 120°. es) R wWreoHEy He or oo Co bo HD Por COwTan a oa bo © Ol © CO & OT — OmaT-T CG eH oO Or He ST Co FR Or ocowrenhls O~IO om bo “Ico r+ Or oD COWrF Oe _ 13 | 367 | 315 | 88 | 11 59 06:3 43 | 35 13 | 15 10 41:4 4 17 | 373 | 278 | 152 | 20 389 55°7 OG) 404) 82°) 24 25 1b 77 2 19 | 403 | 357 80 9 53 57:2 73 | 638 7A LT SEO OG?2 9 14] 408 | 388) 115 | 14 18 27-6 79 51 40 | 26 00 282 8 15 | 409 | 304/ 161) 19 55 55:2 91 80 19 | 10 25 02°8 1 20 | 421 | 399/| 41 4 650 17:0 91 85 11 6 00 32:3 3 19 | 427 | 352 | 123 | 14 26 44:9 97 57 55 | 29 24 33°5 6 17 | 427 | 253 | 240 | 29 07 400 103 | 77 | 40|19 389 10:3 11 138 | 483 | 407 | 48 Sn sO" ra2-9 109 95 24 | 10 59 383°8 5 18 | 4389 | 299 | 205 | 23 51 146 127 | 120 13 5 05 O91 TOU AW A0F | 5287)) 2405) 27) 08. 087 1335) 1204). 23 8 36 47°7 1 21 | 463 | 440] 43 4 36 478 133 88 65 | 25 02 22°8 3 20 | 469 | 391 | 129; 13 46 49:8 139 91 69 | 25 27 39°8 12 13 | 469 | 456 25) 2 38 45:3 151 | 115 56 | 18 44 02:4 5 19 | 481 | 386 | 215 | 22 46 272 157 | 143 25 7 55 36°3 9 16 | 481. | 369 | 175 | 18 21 56-7 163 | 112 | 75 | 23 28 59:0 2 21 | 487 | 487 | 88 9 00 114 169 | 161 15 4 24 30°4 7. 18 | 499 | 301 | 275.| 28 30 25:8 181 | 105 | 104 | 29 50 30-2 6 19>) S11 | 895'| 264) 26 34 41-4 193 | 175 5 8 15 20:2 11 15 | 511 | 451 | 104 | 10 O09 06-2 199 | 165 56 | 14 06 193 Ie | 528 | 387 | 208 | 20 08 47-7 48°8 Ta aA eS 1497 | 22.8260 59-9 93) a3 528 47 ae UBS Tey © — — — ie) On bo Ne} lo) Or oS i=) co or moo RH © i) ay Or poy — ee bo or _ ise) PN — ~J S =] 217 | 208 17 3 53 24:8 223 | 168 85 | 19 16 29:5 Wy UGeo9s)473)) 135 | 12 12 195 229 | 145 | 119 | 26 44 443 3 22 | 559 | 475 | 141 | 12 387 03:3 241 | 224 3l 6 23 45:2 10 17 | 559 | 440 | 189 | 17 O1 33:8 247 | 187 93; 19 O1 504 5 21 | 571 | 416 | 235 | 20 52 49:9 247 | 203 72 |14 387 20:0 Or U9) O77 17368;| 297 | 26 28 21-5 259 | 221 64|12 21 24-4 20 | 689 | 351 | 329 | 28 55 47°6 15 | 589 | 559 56 4 43 22:8 cf 3 271 | 261 19 3 28 51:6 1 24 | 6GOl | 575 49 4 02 560 : 3 9 23 | 607 | 520 | 147 | 12 06 23-4 19 | 613 | 423 | 280 | 23 18 06:5 283 | 192 | 183 | 24 00 59-8 301 | 209 | 186 | 23 02 061 5 22 | 619 | 459 | 245 | 20 02 45:2 301 | 279 40; 6 386 81:0 14 15 | 631 | 616 29 2) 16) 091-3 307 | 288 | 35 5 39 58:3 4 23 | 687 | 513 | 200 | 15 46 40:1 313 | 247 | 105 | 16 53 20-7 PA Ay Gar epao2nii4o | 11 22 09:7 331 | 320} 21 3 08 588 11 18 | 643 | 517 | 203 | 15 52 02:4 760 MR EDWARD SANG ON THE THEORY OF COMMENSURABLES. Trigons of 120°—continued. GCN 6. SO ie Jake. an BA ve OD ne BN 19 | 691 | 5389 | 240 | 17 30 18:3 16 S19 9°87) | 795") 136)" 7 46 ae 26 | 708 | 675 | 538] 38 44 36-7 16 | 721 | 705=| 3st 2 08 02:4 13 18 | 727 | 6387 | 156 | 10 38_ 24-7 1 ow orsT ~I CO or & w bo fon) ie} oO J fon) bo ~] a —t (vt) bo oo — oo b iio} ive} 1 OT Tat | 728) 08) Baedy 20 3 26 | 763 | 667 | 165 | 10 47 386 12 23 | 949 ! 656 | 385 | 20 34 909-0 9 22°) 763+) 477 14084) 27 e136 137 11 24 | 961 | 649 | 455 | 24 12 24:8 15 17 | 769 | 7385) 64) 4 OF 984 7 27 | 967 | 680 | 427 | 22 28 69-6 9°97 787 +| (2p) 112") 7 04 462 4 29 | 973 | 825 | 248|12 45 07:8 7 24) 793 | 527 | 385 | 24 51 476 17 19/973) 935 | 72] 3 40 27-4 11-21 | 798 | 583 | 320°] 20°.27 1772 || 9 (26 |:991'| 595 | 56494) 28° 40a 6 25] 811 | 589 | 3386] 21 O1 348 13 23 | 997 | 767 | 360 | 18 13 208 14 19] 8238 | 728 | 165; 9 59 53:3 ( 761 ) XLVI.— On the Relations, Structure, and Function, of the Valves of the Vascular System in Vertebrata. By James Bett Petticrew, M.D. Edin., Assistant in the Museum of the Royal College of Surgeons of England. Communicated by Witi1aM Turner, M.B. (Plates XXVIII., XXIX.) (Read 21st March 1864.) Introductory Remarks. The rapid advances made of late in the diagnosis of cardiac and other diseases affecting the organs of circulation, render the present inquiry into the normal or healthy condition of the valves of the vascular system, not more important anatomically, than medically. As the nature and composition of the parts in which valves are found in some instances materially influence their action, I have deemed it necessary to advert briefly to the properties and structure of the veins and arteries, when describing the venous and arterial or semilunar valves ; and to the arrangement of the muscular fibres in the ventricles, when point- ing out the peculiarities of the auriculo-ventricular ones. As, moreover, much information is to be obtained by comparing analogous structures, I have, in the present instance, not confined my observations to any particular form of valve, but have examined in succession the entire valvular arrangements of the fish, the reptile, the bird, and the mammal; my object being to arrive, if possible, at a correct knowledge of the more elaborate varieties as they exist in man, and in the higher mammalia. In order to simplify the numerous relations and complicated structure of the several valves met with, as well as to obviate the necessity for entering largely | into anatomical details, the present paper has been fully illustrated by photo- eraphs and drawings from dissections, and from casts representing the valves in _ action. The photographs, thirty-four in number, were taken for the most part _ from the specimens while in the fresh or recent state, by Mr Ayine and myself. | Of the drawings, twenty-three in number, that marked 33, Plate XXVIII. and | | the last six of Plate XXIX., are by my friend Dr Henry Season Witson. The remaining fourteen are by myself. For permission to examine and figure several of the specimens illustrating the peculiarities of the valvular arrangements of the | fish and reptile, 1am indebted to the kindness of the Council of the Royal College | of Surgeons of England. The dissections and casts, which are numerous, were | made with a special view to this inquiry, and are preserved in the Museum of the | Royal College of Surgeons of England, where they may be consulted. | VOL. XXIII. PART III. 9s 762 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, STRUCTURE OF THE VEINS AND VENOUS VALVES. Regarding the composition of the veins, there is, as the reader is aware, some difference of opinion, authorities not being agreed either as to the number or nature of the coats. This may in part be explained by the variation in the thickness of the coats themselves, these, according to Joun Hunter,* becoming thinner and thinner in proportion to the size of the vein, the nearer they ap- proach to the heart. In moderate-sized veins an external, a middle, and an internal coat are usually described; the first consisting of cellular, fibrous, and -elastic tissue, interlacing in all directions; the second, of waved filaments of areolar tissue, with a certain admixture of non-striped muscular fibres, which run circularly, obliquely, or even longitudinally ;+ the third, consisting of one or more strata of very fine elastic tissue, minutely reticulated in a longitudinal direction, the innermost stratum (when several are present) being lined by epithelium. Of these layers, the second and third, from the fact of their contri- buting to the formation of the venous valves, are the most important. The coats of the veins, as has been long known, are tough, elastic, and possessed of con- siderable vital contractility. Of these qualities, the toughness prevents undue dilatation of the vessel when distended with blood; the elasticity and vital con- tractility assisting the onward flow of that fluid, and tending to approximate the segments of the valves, by contracting in the direction of the axis of the vessel. As the valves of the veins are very ample and very flexible, they readily accom- modate themselves to the varying conditions in which they are placed by the elasticity and contractility of the vessel, and by the reflux of the blood. The valves of the veins vary as regards the number of the segments com- posing them, and also slightly as regards structure. In the smallest veins, and where small veins enter larger ones (Plate XXVIII. fig. 9 6), one segment only is present. In middle-sized veins, as they occur in the extremities, two segments (Plate XXVIII. figs. 3, 4, and 7 ab), are usually met with;{ while in the larger veins, as in the internal jugular of the horse, three, and even four segments (Plate XXVIII. figs. 1 and 2, abc, fgh), are by no means uncommon.§ The segments, whatever their number, are semilunar in shape || (Plate XX VIII. * Hunter on the Blood, pp. 180, 181. + Dr Cuevers says, that in the deep as well as in some of the superficial veins of the trunk and neck, the middle coat is composed of several layers of circular fibres, with only here and there a few which take a longitudinal course; while the middle coat of the superficial and deep veins of the limbs consists of a circular layer, and immediately within this of a strong layer of longitudinal fibres—Med. Gazette, 1845, p. 638. + In the heart of the frog-fish, sun-fish, sturgeon, American devil-fish, python, and crocodile, — a semilunar valve, consisting of two segments, guards the orifice of communication between the — sinus venosus and the right auricle. ; y § When four segments are present, two are usually more or less rudimentary (Plate XXVIL fie. 2 fg). R || Joun Hunrer in speaking of the form of the venous valves, says, their free edges are cut of ; straight, and are not curved as in the arteries, This, however, is not the case; as may be seen by ~ OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 763 figs. 3 and 4 ab); the convex border being attached to the wall of the vessel obliquely (Plate XXVIII. fig. 5 ab), the crescentic or concave margin, which is free (Plate XXVIII. fig. 4 ¢), and directed towards the heart, projecting into the vessel. When one segment constitutes the valve, and it occurs in the course of a vein, it is placed obliquely in the vessel (Plate XXVIII. fig. 9), its attached convex border (@) occupying rather more than a half of the interior. When the segment occurs at the junction of a smaller with a larger vein, its convex border is attached to a half or more of the orifice of the smaller one where it joins the larger, its free margin running transversely to the larger trunk. In such cases the segment acts as a moveable partition or septum, common alike to both vessels, but its position and relations are such, that while it readily permits the blood from the smaller vein to enter the larger one, it effectually prevents its return. When the valve consists of two segments, they are semilunar in shape, and very ample, the vertical measurement of each, being not unfrequently nearly twice that of the diameter of the vessel itself (Plate XXVIII. figs.3 and4q@6). In such cases both segments are usually of the same size, so that they divide the vessel into two equal parts (¢). They are placed obliquely with regard to each other (Plate XXVIII. fig. 5 ab), their convex borders, which are attached to the interior of the vessel, starting from a common point above (Plate XXVIII. fig. 2 2), and gradually diverging (¢) to curve round and reunite on the opposite side of the vessel (d); their concave and free margins inclining towards each other (Plate XXVIII. fig. 12 ¢), and being directed, as in the more simple valve, towards the heart. The free margins of the two segments, like the attached ones, start from a common point (Plate XXVIII. fig. 4 7°), but such is the shape of the segments, and such the angle at which they are placed with regard to each other, that they do not diverge to the same extent, but run more or less parallel.* This relation of the segments to each other above, is in part accounted for by the presence of a fibrous structure (Plate XXVIII. fig. 4 7), which extends from the wall of the vessel into the interior, and supports them at a certain distance from the sides of the vessel. The fibrous structure referred to is well seen in the semilunar valves of the pulmonary artery and aorta (Plate XXVIII. fig. 36 27’), and seems to have escaped observation. In a line corresponding to the attached border of each of the segments (Plate XXVIII. fig. 4 ab), the middle and internal coats of the vein are thickened, as may be ascertained by a vertical section, or by reference to photographs 1, 2, 3, and 4, Plate XXVIII. The edges referred to are least curved when the valve is distended or in action (Plate XXVIII. fig. 13 ¢), but the curve is never altogether absent.—Treatise on the Blood, pp. 181, 182. * I was much struck, on injecting the external saphenous vein of the human subject from the dorsum of the foot, to find, on dissection, that the free margins of some of the segments were in contact throughout; clearly showing, that when the segments are allowed to float in a fluid, they are so projected against each other, that even the slightest reflux will instantly close them. 764 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, introducing coloured plaster of Paris* into the vessel. I particularly direct attention to this circumstance, as the thickenings referred to form jibrous zones (Plate XXVIII. fig 6h), which extend for a short distance into the substance of the segments, and afford them a considerable degree of support. They further assist in preserving the shape of the segments, and in enabling them to maintain the proper angle of inclination—the said angle inclining the segments towards each other in ° the mesial plane of the vessel (Plate XXVIII. figs. 3 and 4). When a valve, consisting of two segments, is situated at the junction of a smaller with a larger vein, one of the segments is usually placed between the two vessels at the point of juncture (Plate XXVIII. fig. 11 4), the other on the wall of the smaller vein (a). The position of the segments in such instances varies, their long diameter some- times running parallel with the larger vessel, sometimes obliquely, but more commonly transversely. When the valve consists of three segments (Plate XXVIII. figs. 1 and 8, abc, 7 st), the segments, as a rule, are unequal in size, one of them being generally a little larger (¢) than either of the other two (7's). They are semi- lunar in shape, as in the smaller and middle-sized veins, and differ from the latter in being less capacious. ‘The tri-semilunar valves in the veins, may therefore be regarded as intermediate between the fully developed bi-semilunar valves found in the veins of the extremities, and the fully developed tri-semilunar valves which occur at the origin of the pulmonary artery and aorta. The existence of valves in the veins is indicated externally by a dilatation or enlargement of the vessel ; the dilatation consisting of one, two (Plate XXVIII. figs. 3, 5, and 12 44g), or three (Plate XXVIII. fig. 8 gab) swellings, according as the valve is composed of one two, or three segments. These dilatations or swellings are analogous to the > sinuses of VausaLva in the arteries (Plate XXVIII. figs. 17 and 18 d), their direction in the veins of the extremities being from below upwards and from — within outwards. They form, with the segment to which they belong, open sinuses or pouches which look towards the heart, and as they extend nearly as far in an outward direction as the segments project inwardly, they give a very good idea of the size and shape of the segments themselves. The only point regarding the dilatations deserving of special attention, is the gradual thinning in a direction from above downwards, of those portions of the coats of the vessel which enter into their formation. The thinning referred to, is well seen when vertical sections of the vessel are made, or when the vein is distended with coloured plaster of Paris, as recommended. The swellings present a deeper colour the nearer we approach to the attached border of the segments, the attached borders, on account of their greater thickness, appearing as dense fibrous _ zones (Plate XXVIIL. fig. 5 a6, fig. 6 h). The object of the swellings is evidently — * I have derived much information from the employment of this material; its use having — enabled me to determine with something like accuracy, the relation of the segments of the valves to — each other when in action, and other points connected with the physiology of the heart. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 765 twofold,—jirsily, to cause the blood to act on the segments of the valve from above downwards, and from without inwards, in the direction of the mesial plane, or of the axis of the vessel, according as there are two or three segments present; and, secondly, to increase the area over which the pressure exerted by the reflux of the blood extends. When the vein is opened between the segments, when two are present, each of the segments is seen to form two curves,—one curve giving its concave or free margin (Plate XXVIII. fig. 4 ¢), the other its convex or attached one (a); but when the section is carried through the wall of the vein, and through the centre of one of the segments, one curve only is obtained (Plate XXVIII. fig. 3 g) ; and itis useful to remember this, as it shows with what facility the structures entering into the formation of the segments, viz., the lining mem- brane of the vessel and certain parts of the middle and internal coats, are given off. It also shows how the lower portion of the dilatation (g), while it supports a certain quantity of the refluent blood, guides by far the greater quantity on to the valves (0), rendering their closure not a matter of accident, but of necessity. The segments of the venous valves are exceedingly flexible, and so delicate as to be semi-transparent. ‘They possess great strength and a considerable degree of elasticity.* Usually they are described as consisting of a reduplication of the fine membrane lining the vessel, strengthened by some included fibro-cellular tissue, the whole being covered with epithelium. This description, however, is much too general to convey any very accurate impression of their real structure, and the following, drawn up from the examination of a large number of specimens taken from man, the horse, ox, sheep, and other animals, may prove useful. When one of the segments of a well-formed bi-semilunar valve removed from the human femoral vein, is stained with carmine, fixed between two glasses, and examined with the microscope or pocket lens, the subjoined phenomena are wit- nessed :— 1st, The lining membrane of the vessel covered with epithelium is seen to form the investing sheath of the segment, no breaeh of continuity being any- where perceptible. 2d, Large quantities of white fibrous tissue, mixed up with areolar and yellow elastic tissue, from the middle and internal coats of the vessel, are observed to extend into the segment. The fibres composing these tissues pursue a definite arrangement. Thus running along the concave or free margin of the segment (Plate XXVIII. fig. 14 a), as likewise on the body, especially where the segments join each other (0), are a series of very delicate fibres, consisting principally of yellow elastic tissue. These fibres proceed in the direction of the long diameter * Hunter denies the elasticity of the segments, on the ground that the valvular membrane is not formed of a reduplication of the lining membrane of the vessel, an opinion at variance with recent investigation.—Treatise on the Blood, pp. 181, 182. VOL. XXIII. PART IIT. 9T 766 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, of the seoment, but transversely to the course of the vessel, and may be denomi- nated the horizontal jibres. : . Running in a precisely opposite direction, and confining themselves principally to the body of the segment, are a series of equally delicate fibres (c), having a like composition, and which, for the sake of distinction, may be described as the vertical series. These two sets of fibres are superficial, and to be seen properly, a power magnifying from 200 to 250 diameters is required. hadiating from the centre of the segment (Plate XXVIII. fig. 15 e) towards its attached border (iv), and seen through the more delicate horizontal and vertical ones, is a series of stronger and deeper jibres, composed of white fibrous and yellow elastic tissue, the former predominating. Still stronger and deeper than either of the fibres yet described, and proceeding from the attached border of the segment (Plate XXVIII. fig. 16 s 4), is a series of oblique fibres, continuous in very many instances with corresponding fibres in the middle coat of the vessel. These © fibres cross each other with great regularity, and form the principal portion of the segments. They are most strongly marked at the margin of the convex border of the segment, where they form a fibrous zone or ring, which, as has been explained, supports the segment, and carries it away from the sides of the vessel into the interior. I have also detected, in the vicinity of the attached border of the segment, some non-striped muscular fibres. The segment of a venous valve is therefore a highly symmetrical and complex structure, the fibrous tissues com- posing it, being arranged in at least three well-marked directions ; viz., horizontally, vertically, and obliquely. The great strength which such an arrangement is cal- culated to impart to the segment is readily understood. In conclusion, the segment is thinnest at its free margin, and thickest towards its attached border; the body being a little thicker than the free margins, and where the extremities or narrow portions of the segments join each other, but not so thick as the attached border. The Venous Valves in Action. The manner in which the venous valves act, is well seen when the vein is sus- pended perpendicularly overhead, and water, oil, glycerine, or liquid plaster of Paris, poured into it by an assistant from above; the vein beneath the valve being cut away, the better to expose the segments to the view of the spectator. When the valve consists of one segment only, the fluid is observed to force it obliquely across the vessel, and to apply its free crescentic margin to the interior or convex | surface with such accuracy as to prevent even the slightest reflux. When two segments occur in the course of a vein, they are forced by the fluid simultaneously towards each other in the mesial plane of the vessel (Plate XXVIII. figs. 3 and 12), the sinuses (gh) behind the segments becoming distended, and directing the OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 767 current and regulating to a certain extent the amount of pressure. The closure in this instance is almost instantaneous, and so perfect that not a single drop escapes. It is effected by the free margins of the segments, and a large proportion of the sides, coming into accurate contact, the amount of contact increasing in the inverse of the pressure applied. If liquid plaster of Paris be used for distending the vein, and the specimen is examined after the plaster has set, one is struck - with the great precision with which the segments act (Plate XXVIII. figs. 6 and 11 ad), these coming together so symmetrically, that they form by their union a perpendicular wall or septum (Plate XXVIIL figs. 6, 11, and 12, e) of a beauti- fully crescentic shape* (Plate XXVIII. fig. 13 ¢). This fact is significant, as it clearly proves that the concave or free margins of the segments, and a consider- able proportion of the sides, run parallel to each other when the valve is in action, a circumstance difficult of comprehension, when it is remembered that the convex borders of the segments are attached obliquely to the walls of the vessel, and that the segments, when not in action, incline towards each other at a considerable angle. The very accurate apposition of the segments, when the valve is closed, is to be traced :— lst, To the direction and shape of the venous sinuses, which conduct the fluid employed, on to the segments in almost equal quantities. 2d, To the disposition of the free margins of the segments, which, as was explained, run side by side, and are supported by fibrous structures which carry them away from the sides of the vessel for some distance; and, 3d, To the amplitude of the segments themselves, which allows them to come together without difficulty, and when the pressure is applied, to flatten them- selves against each other to form the perpendicular crescentic wall adverted to. In the event of two segments occurring at the entrance of a smaller into a larger vein, one of them being situated at the junction of the smaller vessel with the main trunk (Plate XXVIII. fig. 11 0), the other on the wall of the tributary branch (a); the former, 7.¢., the common or septal segment, is forced by the fluid in a slightly outward direction, the latter in an opposite or inward direction, the free margins and sides of the segments being by this arrangement accurately applied to each other to form an impervious wall or septum (@) as already described. When the entrance of a smaller into a larger vessel is guarded by two segments situated on the tributary branch at its orifice, their action is precisely the same as when they are placed in the course of a vein. When three segments are present, as happens in the larger trunks, the closure is effected in a manner greatly re- sembling that by which the semilunar valves of the pulmonary artery and aorta * In order to see the perpendicular wall formed by the flattening of the sides of the segments against each other when the valve is in action, the vein and the plaster should be cut across im- mediately above the valve, and the segments forcibly separated by introducing a thin knife between them. In fig. 13, Plate XXVIII, one of the segments has been quite removed. 768 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, are closed; the fluid employed, in virtue of the direction given to it by the venous sinuses, causing each of the segments (Plate XXVIII. fig. 8 rst) to bend or double upon itself at an angle (2) of something like 60° ;* the three lines formed by the doubling and union of the three segments dividing the circle corresponding to the wall of the vessel, into three nearly equal parts. In the doubling of the segments upon themselves, each segment regulates the amount of bending which takes place in that next to it, and as the free margins of the segments so bent advance synchronously towards the axis of the vessel, they mutually act wpon and support each other. As the three segments are attached obliquely to the wall of the vessel, while the free margins, after the folding has taken place, are inclined towards and run parallel to each other (a0), they form an inverted dome consisting of three nearly equal parts, the margins of the segments, and a certain portion of the sides, when the pressure is applied, flattening themselves against each other to form three crescentic partitions or septa} which run from the axis of the vessel towards the circumference. The tri-semilunar valve, as will be seen from the foregoing explanation, is closed in a very different manner from the bi-semilunar one. The occlusion of the vessel, however, is not the less complete; the segments, when three are present, being wedged into each other in a direction from above downwards, and from without invards ; the first of these movements, by tending to flatten the segments, pressing their margins and sides together: the second, by urging the segments towards the axis of the vessel, impacting them more and more tightly, especially towards their apices or points. As the apices or points formed by the doubling of the segments whilst in action, are composed principally of the flexible and free crescentic margins, and are at liberty to move until the wedging process is com- pleted, a careful examination has satisfied me, that they rotate to a greater or less extent before the valve is finally closed. This spiral movement, which is simply indicated in the venous valves, is more strongly marked in the semilunar ones of the pulmonary artery and aorta (Plate XXVIII. figs. 26, 27, and 28, v, w, x,) and attains, as will be shown subsequently, a maximum in the auriculo-ventricular valves of the mammal (Plate XXIX. figs. 53 and 54, min,s7). By whatever power the blood in the veins advances—whether impelled by the heart alone, or by muscular contractions occurring in different parts of the body, or by rythmic movements which take place in the vessels themselves, or by efforts of inspiration, or by all or combinations of these; there can, I think, be little doubt that this fluid, in its backward or retrograde movement, acts to a great extent mechanically on the valves as described. It ought, however, to be borne in mind that the veins and the valves are vital structures, and that * The angle is never precisely 60°, from the fact of the segments varying slightly as regards size. + The crescentic partitions, as they occur in the semilunar valves of the pulmonary artery and aorta, are shown at 6 0’, of fig. 25, Plate XXVIII. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 769 although a perfect closure may be effected by purely mechanical means in the dead vein, it is more than probable that in the living one, the contraction of the coats of the vessel exercises a regulating influence. STRUCTURE OF THE ARTERIES AND ARTERIAL VALVES. The coats of the arteries, as is well known, are thicker than those of the veins, while the layers composing them are more numerous. The external coat, accord- ing to HENLE, consists of an outer layer of areolar tissue in which the fibres run obliquely or diagonally round the vessel, and an internal stratum of elastic tissue ; the middle coat in the largest arteries, according to RAUSCHEL, being divisible into upwards of forty layers. The layers of the middle coat consist of; pale, soft, flattened fibres, with an admixture of elastic tissue, the fibres and elastic tissue being disposed circularly round the vessel. The internal coat is composed of one or more layers of fibres, so delicate that they constitute a transparent film, the film being perforated at intervals, and lined with epithelium. The arteries, as might be ¢xpected from their structure, and as was proved by the admirable ex- periments of Joun Hunter, whose beautiful preparations I have had an oppor- tunity of examining, possess a high degree of elasticity and vital contractility, and are extensible and retractile both in their length and breadth; the power of recovery, according to that author, being greater in proportion as the vessel is nearer the heart. From this it follows that the pulmonary artery and aorta are most liable to change in dimensions. As, however, any material alteration in the size of the pulmonary artery and aorta might interfere with the proper function of the semilunar valves situated at their orifices, it is curious to note that the great vessels arise from strong and comparatively unyielding fibrous rings. These rings (particularly the aortic one) are so dense as to be almost cartilaginous in consistence, and Professor DonpErs* has lately discovered, that they contain stellate corpuscles similar in many respects to those stellate and spicate corpuscles, found in many forms of cartilaginous tumours. They have been more or less minutely described by Vatsatva,t Gerpy,{ Dr Joun ReErp,§ and Mr W. S$. Savory, || and merit attention because of their important relations to the segments of the semilunar valves. The following description of the aortic and pulmonic fibrous rings, has been drawn up chiefly from the examination of a large number of human hearts. Each ring, as will be seen by a reference to * « Onderzockingen betrekkeligh den bouw van het menchclijke hart,” in ‘“ Nederlandsch Lancet” for March and April 1852. t+ Opera Varsatv#, tom. i, p 129, + Journal Complimentaire, tom. x. § Cyc. Anat, and Phy. article «« Heart,” pp. 588, 589. London, 18389. || Paper read before the Royal Society in December 1851. VOL. XXIII. PART III. 9uU 770 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION Plate XXVIII. figure 30, taken from a photograph of a boiled heart, consists, as was shown by Rem, of three convex portions (7s¢). Each convex portion is directed from above downwards, and from without inwards, and as it unites above with that next to it, the two when taken together form a conical-shaped prominence (z), which is adapted to one of the three triangular-shaped inter- spaces occurring between the segments of the valve (Plate XXVIII. fig. 17 h). The arterial rings are therefore placed obliquely, the under surface, which gives attachment to many of the fibres of the ventricles anteriorly (Plate XXVIII. fig. 30 dd’), resting on the rounded oblique border of the ventricular walls (Plate XXVIII. fig. 17 ¢). The ring surrounding the pulmonary artery, as was pointed out by Rerp, is broader, but not quite so thick as that surrounding the aorta, and both are admirably adapted for the reception of the large vessels which, as was shown by that author, originate in three festooned borders. These borders, I am inclined to think, consist of two parts,—an outer (Plate XXVIII. fig. 17 77’), composed of the outer, and a small portion of the central layer of either the aorta or pulmonary artery; and an inner (t), composed principally of the central and inner layers. The outer border (Plate XXVIII. fig. 18 7), which is the thinner of the two, is attached to the superior and outer margin of one or other of the fibrous rings (g), chiefly by the serous membranes; the inner (Plate XXVIII. fig. 17 ¢), which projects further in a direction from above downwards, and corresponds to the thickened convex border of the seg- ments (s), to the formation of which it contributes, being attached to the inferior and inner margin (g’). These points are well seen, when a vertical section is made of the aorta or pulmonary artery between the segments com- posing the semilunar valves. In such a section (Plate XXVIII. fig. 17), the vessels are observed to be thickened in a direction from above downwards, — the thickening beginning at the point where the segments meet above (6d), and gradually increasing until the vessels bifurcate (27). The reverse of this holds true of those portions of the vessels which enter into the formation of the sinuses of VausaLva (Plate XXVIII. fig. 18 2), these being unusually thin, particularly where attached (7).* As the thickened portions of the vessels — correspond to the fixed margins of the segments (Plate XXVIII. figs. 17 and 35 btm), and extend between them in an arched direction above (c), they — give the precise boundaries of the sinuses of Vausatva (Plate XXVIII. figs. 1 17 and 18 d), and furnish the segments with three fibrous frameworks analogous, in some respects, to the thickenings which occur in similar situations in the — veins. These frameworks extend for a short distance into the segments (Plate XXVIII. fig. 17 6, and fig. 36 2), and assist not only in affording the segments . * The several points adverted to are seen to advantage in the whale (Physalus antiquorum, Gray), the aorta of which I had an opportunity of dissecting for the Museum of the Royal College of Surgeons of England. . OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA, qi the requisite degree of support, but in carrying them away from the sides of the vessel, and in inclining them towards each other at such an angle as insures that their free margins, especially where they unite above (Plate XXVIII. fig. 36 0 c), shall be more or less parallel when the valve is in action. That the frame- works afford the support here indicated, is proved by the fact, that when liquid plaster of Paris is introduced into the ventricles, and forced through the pul- monary artery and aorta, in the direction of the circulation, the attached borders of the segments do not fall back into the sinuses of Vatsatva (Plate XXIX. figs. 50 and 51 vw) to the same extent as the sides and free margins, but project so as to furnish the casts thus obtained, with corresponding depressions (7's). The sinuses of VausaLva are formed above by the dilatations or expansions of the great vessels, and the one occupies a higher position than either of the other two. They are further unequal in size (Plate XXVIII. fig. 26 wav), the highest and smallest occurring anteriorly, that which is intermediate in size being placed posteriorly, while the lowest and largest is directed towards the septum. They correspond in situation and dimensions to the segments behind which they are found, and differ from the venous sinuses in being more capacious, a section of the sinus and its segment (which is likewise very ample) giving a sweep of nearly half a circle (Plate XXVIII. fig. 18 62s). Asaresult of this amplitude, those portions of the segments which project into the vessel are, during the action of the valve, closely applied to each other throughout a considerable part of their extent (Plate XXVIII. fig. 26 abc); the great size of the sinuses furnishing an increased quantity of blood for pressing the segments from above downwards, and from without inwards, or in the direction of the axis of the vessel. The sinuses of VALSALVA curve towards each other in a spiral direction ; and this ought to be attended to in speaking of the action of the semilunar valves, as the sinuses direct the blood spirally on to the mesial line of each segment (Plate XXVIII. fig. 26 v w x), and cause the segments to twist and wedge into each other, as re- presented at v w 2 of figs. 26, 27, and 28, Plate XXVIII. In order to determine this point, I procured a fresh pulmonary artery and aorta, and after putting the valves into position with water, caused an assistant to drop liquid plaster of Paris into the vessels. The greater density of the plaster gradually displaced the water, and I was in this way furnished with accurate casts of the sinuses and of the valves. The segments of the semilunar valves, unlike the venous ones, are almost invariably three in number.* They differ in size and in position, and in this respect resemble the sinuses of Vausatva, to the inside of which they are found. Thus the segment which is smallest is situated anteriorly, and occupies a higher position than either of the others; that which is second in * Dr Jonn Hucues Bennett speaks of a case in which four were present, but whether the addi- tional segment was congenital, or the result of disease, is not easy to determine. ‘“ Principles and Practice of Medicine,” 1858, p. 550. 772 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, size being placed posteriorly, and a little lower than the anterior segment. The remaining segment, which is the lowest, is directed towards the septum. They are flexible, more or less opaque, very strong, and somewhat crescentic in shape (Plate XXVIII. figs. 19 and 20). In structure, the semilunar valves are intermediate between the venous and auriculo-ventricular ones. ‘They consist of a reduplication of the fine membrane lining the vessel, strengthened by certain tendinous bands, and, as was first satisfactorily demonstrated by Mr W. S. Savory, of a considerable quantity of yellow elastic tissue.* Some of the older anatomists, among whom may be mentioned Lancisci,t S—nac,{ MorGaent§ Winstow,|| and Coorer,{ believed that they had detected the presence of car- neous or muscular fibres; but HALLER,** and many since his time, have gravely doubted the accuracy of their observations. Very recently, Mr Moore}} has figured two sets of muscular fibres, which he has termed according to their supposed action, dilators and retractors; and Dr Monnerer{{ has described two similar sets, which, for like reasons, he has named elevators and de- pressors. I have sought in vain for the muscular fibres in question, and am inclined to think that when found, they have been mistaken for the tendi- nous bands accidentally stained with blood. The tendinous bands have hitherto been regarded as following three principal directions,—one band being said to occupy the free margin, and to be divided into two equal parts by the nodulus or Corpus Arantii, otherwise called Corpusculum Morgagni, and Corpus sesamoideum; a second band, proceeding from points a little above the middle of the segment, and curving in an upward direction towards the Corpus Arantii; the third band, which is the thickest, surrounding the attached border of the segment. A careful examination of a large number of mammalian hearts, particularly those of man, has induced me to assign to the semilunar valves a more intricate structure. In a healthy human semilunar valveS§ taken from the pulmonary artery, the follow- ing seems to be the arrangement. Proceeding from the attached extremities of the segment above (Plate XXVIII. fig. 19 6, fig. 20 z, and fig. 29 a), and running along its free margin, is a delicate tendinous band, which gives off still more delicate * PurxkincE and RarvuscuEt had detected elastic tissue in the Corpora Arantii, but knew nothing of its existence throughout the other portions of the valves. Of its presence I have frequently satis- fied myself. t De motu Cordis. t Traité de la Structure de Coeur, livre i. § Adversaria Anatomica Omnia. || Exposition Anat. de la Structure du Corps Humain, p. 592 { Myotomia Reformata. ** Elementa Physiologie. Liber iv. sect. 10. tt Med. Gazette, March 8, 1850. tt Lancet, Dec. 29, 1850. §§ It is very difficult to get a perfectly healthy human semilunar valve, especially if the patient is at all advanced in years. Out of twenty adult hearts examined by me, nearly a half of that num- ber had the valves abnormally thickened. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 773 slips (Plate XXVIII. figs. 20 and 29 7), to radiate in a downward and inward direction, i.¢. in the direction of the mesial line (Plate XXVIII. fig. 20 c) and body of the segment. These fine slips interdigitate in the mesial line, and are attached below to the uppermost of a series of very strong fibrous bands which occupy the body of the segment (Plate XXVIII. figs. 20 and 29 s). In the interspaces between the slips, the valve is so thin as to be almost transparent. Those portions of the segments included within the delicate fibrous band, running along the free margin and the uppermost of the stronger bands occupying the body, and which are situated to the right and left of the mesial line, are somewhat crescentic in shape (Plate XXVIII. fig. 20 7), and have, from this circumstance, been termed lunule. They do not form the perfect crescents usually represented in books, the horns of the crescents directed towards the mesial line of the segment (Plate XXVIII. fig. 20 ¢), being much broader than those directed towards the extremi- ties, or where the segments unite above (Plate XXVIII. fig. 200). The object of this arrangement is obvious. The crescentic portions referred to, are those which, when the segment is folded upon itself during the action of the valve, are accu- rately applied to corresponding and similar portions of the two remaining seg- ments (Plate XXVIII. fig. 25 60’). If, however, the lunulee had been symme- trical, in other words, if they had terminated in well-defined horns towards the mesial line, or where the segments fold upon themselves, then the union between the segments in the axis of the vessel (Plate XXVIII. fig. 25 2x), where great strength is required, would have been very partial, and conseqiently very imperfect. Proceeding from the attached extremities of the segments at points a little below the origins of the marginal band, and curving in a downward and inward di- rection, is the first of the stronger bands (Plate XXVIII. fig. 20 6). The band referred to essentially consists of two portions, these splitting up into brush-like expansions as they approach the mesial line (c), where they interdigitate and become strongly embraced. Other and similar bands, to the extent of three (s) or four, usually the latter number, are met with (Plate XXVIII. fig. 29 v), and as they all curve in a downward and inward direction, and have finer bands running between them in a nearly vertical direction, they suspend the body of the segment; so that when water is poured upon it, the various parts of which it is composed, radiate from the attached or convex border like a fan; each band dragging upon that above it ; the whole deriving support from the thickened convex border. The bands, which are thus six in number, are best seen on that aspect of the segments which is directed towards the sinuses of Vatsatva.* They are thickest at their attached extremities, where they interlace slightly, and are mixed up to a greater or less ‘extent with the pale, soft, flattened fibres, and elastic tissue of the central layer * The surfaces of the segments directed towards the axis are perfectly smooth, and so facilitate the onward flow of the blood, VOL. XXIII. PART III. 9x 774 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, of the vessel itself. They in this manner form a fibrous zone (Plate XXVIII. fig. 17 bn), which corresponds to the attached convex border of the segment, and may be regarded as an expansion of the inner of the two divisions (Plate XX VII. fig. 17 tr) into which, as I formerly pointed out, the pulmonary artery and aorta resolve themselves. As the bands under consideration are exceedingly strong when compared with those occurring in other portions of the segment; and project in an inward direc- tion, or towards the axis of the vessel, when the preparation is sunk in water; their function, as ascertained from numerous experiments on the semilunar ~ valves of a whale (Physalus antiquorum, Gray), seems to be the following :— Ist, They carry the body of the segment aay from the sides of the vessel, and incline the free margins towards each other, at such an angle, as necessitates the free margins of neighbouring segments, being always more or less-in apposition. Tn this they are assisted by the thickened portion of the pulmonary artery (Plate XXVIII. figs. 17 and 36 6 n) which projects between the segments (Plate XXVIII. fig. 36 nn’) where they unite above, and by the fibrous zones which correspond to the convex border of each segment. 2d, The stronger jibres suspend the body of the segment from above, and permit the reflux of blood to act more immediately upon the mesial line of each segment where thinnest (Plate XXVIII. fig. 20 c), and where least supported ; to occasion that characteristic folding of the segment upon itself, when the valve is in action. Other bands, intermediate in thickness between those occupying the free margin and the body of the segment, are found towards its lower portion (Plate XXVIII. figs. 20 and 29 0). These bands cross and interdigitate to a greater or less extent, and as their prevailing direction is from below upwards, are instru- mental in keeping the lower portions of the segment, away from the sides of the — vessel. Each segment may therefore be described as consisting of three por- — tions—a superior and thinner portion, an inferior and thicker one, and a central portion, which is the thickest of all. It ought also to be remarked that the three portions of the segment corresponding to its mesial line, where the folding occurs when it is in action, are comparatively thinner than the parts to either side of the line in question. The varying thickness of the segments is well seen in the semilunar valve of the whale (Plate XXVIII. fig. 29 avn). ; While the foregoing may be considered a literal description of a healthy human semilunar valve, there are modifications to which it is necessary to direct — attention. Thus, in some instances, the band occupying the margin of the segment _ splits up near its origin, as represented at Plate XXVIII. fig. 19 b, and maps out a triangular portion (¢). This portion is very thin, and contains delicate tendinous ~ fibres, which terminate in brush-shaped expansions towards the mesial line. — The remaining and stronger bands are similar to those already described, but the difference in the thickness of the several portions of the valve, is not so marked. OF THE VALVES OF THE VASCULAR SYSTEM IN. VERTEBRATA. 775 In other cases (Plate XXVIII. fig. 21), the marginal band not only splits up and contains a fully developed Corpus Arantii (d), but gives off two or more well- marked tendinous slips (a) which connect the free margin with the stronger or central portion of the segment (7). Radiating from the Corpus Arantii as a centre (Plate XXVIII. fig. 24 d), and proceeding along the free margin, I have sometimes detected a series of hair-like fibres (¢), which are apparently of use in strengthening this the weakest portion of the segment. This is the more probable, since other and similarly delicate fibres proceed from the attached extremities in the direction of the Corpus Arantii. On other occasions, the . tendinous bands proceeding from the marginal one (Plate XXVIII. fig. 22 s) are abnormally thickened (¢), and terminate in brush-shaped expansions in the body of the segment (v) ; the body under such circumstances, projecting in an upward direction towards the Corpus Arantii (d). In such cases, those portions of the valve (77) which occur between the thickened bands proceeding from the mar- ginal one, are exceedingly thin, and in some diseased conditions altogether awant- ing, so that the segment very much resembles one of the segments of the mitral or tricuspid valve, with its chorde tendineze. That there is an analogy between the semilunar and the mitral and tricuspid valves, and that the chordze tendineze is a further development, seems probable from the fact, that in the bulbus arteriosus of certain fishes, as in the grey and basking sharks (Plate XXIX. figs. 41 and 48), Lepidosteus, &c. (Plate XXIX. fig. 40 0), the semilunar valves are furnished with what may be regarded as rudimentary chorde tendinee, (Plate XXIX., fig. 48. a), while in the auriculo-ventricular valves of fishes, which have hitherto been regarded as semilunar, but which exhibit some of the pecu- liarities of the mitral valve of the mammal, chord tendineze in various stages of development occur. A scheme of the arrangement of the tendinous bands in the semilunar valves has been given at Plate XXVIII. fig. 23, and shows the segments to be not only bilaterally symmetrical, but to be constructed on a plan which secures the greatest amount of strength with the least possible material; the bands mutually acting upon and supporting each other. Thus the bands marked a and d, which re- present the central portion of the segment, split up into brush-shaped expansions, one portion of each curving in an upward direction (be), and representing the tendinous slips proceeding from the marginal one (7); the remaining portions curving in a downward direction (fc), and giving the inferior set of fibres which curve from below, towards the body of the segment (ad). The Corpus Arantii is rarely present in a perfectly healthy semilunar segment; nor will its absence occasion surprise, when it is remembered that its presence materially interferes with the folding of the segments upon themselves, when the valve is in action. That its existence is not necessary to the perfect closure of the valve, is proved by its complete absence in a great number of cases. In the semilunar valve of the 776 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, whale, where one would have naturally expected it in perfection, I could not detect even a trace of it. What has been said of the semilunar valves of the pulmonary artery, may with equal propriety be said of those of the aorta; the only difference being that the segments are stronger and more opaque, to harmonise with the greater strength of the left ventricle. The Arterial or Semilunar Valves in Action. As the manner in which the semilunar valves are closed, does not seem to be well understood, the following experiments conducted with various fluids and liquid plaster of Paris, may prove interesting :— When the aorta is cut across two inches or so above the aortic semilunar valve, and water introduced, the segments, if watched from beneath, are seen to act with great alacrity, the smallest segment (Plate XXVIII. figs. 26, 27, and 28, w), Which is situated highest, descending with a spiral swoop, and first falling into position ; the middle-sized segment (x), which is placed a little lower, descending in like manner, and fixing the first segment by one of its lunule or crescentic surfaces (Plate XXVIII. fig. 26 a); the third and largest segment (v), which occupies a lower position than either of the others, descending spirally upon the crescentic margins (bc) of the other two, and wedging and screwing them more and more tightly into each other. The spiral movement, as has been already explained, is occasioned by the direction of the sinuses of VaLsaLva, which curve towards each other, and direct the blood in spiral waves upon the mesial line of each segment (Ww 2 0). It is well seen when liquid plaster of Paris is used, as the plaster, on setting, enables the experimenter to examine the relations of the segments to each other at leisure. Figures 27 and 28, Plate XXVIIL, have been taken from specimens so prepared. On removing one of the segments in such specimens, it is found to be folded upon itself (Plate XX VIII., fig. 27 1), and to present two semilunar surfaces, each of which is accurately applied to a corresponding and similar surface of that segment of the valve which is next to it (Plate XXVIII. fig. 25 60’). The union, therefore, between any two of the segments of a semilunar valve, is analogous in many respects, to that occurring in a venous valve consisting of two segments. There is, however, this difference ; in a venous valve, the segments, simply flatten themselves against each other in the mesial plane of the vessel, to form a perpendicular crescentic wall (Plate XXVIII. figs. 11 and 13 ¢); whereas in thes emilunar valves, the segments in addition curve into each other, and so form three perpendicular crescentic walls, each of which radiates from the axis of the vessel (Plate XXVIII. fig. 26 rso). In the venous valve, moreover, those portions of the segments which come into apposition form systemetrical crescents (Plate XXVIII. fig. 13 e); OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 770 whereas in the semilunar one, the surfaces referred to, are non-symmetrical ; in other words, the horns of the crescents forming the lunule, are broader towards the mesial line of the segments (Plate X XVIII. fig. 20 c) than where they meet above (6). As aresult of this want of symmetry in the lunule or opposing surfaces of the semilunar valves, the apices or central portions of the segments come together in the axis of the vessel throughout a considerable space (Plate XX VIIL. fig. 25 x), and form a union of the most perfect description. The extent of the union increases in the inverse of the pressure applied (compare dotted lines, Plate XXVIII. fig. 25 mm’ with plain ones 60’), and is rendered very secure from the segments being wedged into each other in a direction from above downwards and from with- out inwards (Plate XXVIII. fig. 26 vwwx). Retzius,* who figures the manner of closure of the semilunar valves, does not seem to have been aware of this fact, for he represents the segments as coming together in the axis of the vessel at three points, an arrangement which could scarcely fail to occasion a certain amount of regurgitation. Ifthe closure of the semilunar valves be watched from above, other phenomena are observed. When, for example, the aorta and semi- lunar valve of the whale were sunk in water and permitted to remain un- disturbed, the thicker portions of each segment were seen to project in an upward and inward direction, the free margins being by this arrangement brought more or less closely into contact, and supported on a level corresponding to the top of the sinuses of Vatsatva. When, however, the preparation was raised in the vessel, so that the water acted from above on the central and more unsupported portions of the segments; the free margins, together with the more moveable parts of the bodies, descended to the extent of fully an inch and a half. In so doing, the free margins of the segments were projected against and accurately applied to each other, clearly showing that the fluid, because of its weight and the spiral downward and inward direction communicated to it by the sinuses of VaLsALva, is sufficient to effect the closure. When the closure was taking place, the seg- ments fell into position in rotation, but at so nearly the same interval of time, that they mutually regulated the amount of downward and inward movement ; and so prevented each other from protruding too far into the interior of the vessel. When the hand was introduced into the aorta, which the great size of the speci- ment} readily permitted, and one of the segments was pushed in an outward direction, it was found to apply itself to the sinus of Vausatva behind it, with more or less accuracy; the extremities of the segments, where they unite above, projecting to form three ridges, which are spirally inclined with reference to each other, and are no doubt useful in directing the blood into the aorta proper. From the foregoing description of the venous and arterial semilunar valves in mam- * Om Mekanismen af Semilunar Valvlernes tillolutning. + In this case, the aorta had a girt of 27 inches; the average size of the segments being 9 inches by 7. VOL. XXIII. PART III. 9Y 778 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, malia, it will be evident that there is nothing, either in their structure or rela- tions, to betoken any great degree of activity on their part. That these structures are, on the contrary, principally passive, seems certain from the fact, that a stream of water or other fluid directed upon them from above as recommended, at once closes the orifices which they guard. STRUCTURE OF THE BULBUS ARTERIOSUS OF THE FISH, AND OF THE VENTRICLE OF THE FISH AND REPTILE SEMILUNAR AND OTHER VALVES FOUND THEREIN. The semilunar valves in the bulbus arteriosus of the fish, and the auriculo-ven- tricular valves in the fish and reptile, differ from the venous and arterial ones, in being, for the most part, connected either directly or indirectly, or exposed in some way to the influence of muscular contractions. In order the better to understand the position which these valves occupy in the gradually ascending scale of valvular arrangements, a brief description of the bulbus arteriosus, of the fish, and of the ventricle of the fish and reptile, is necessary. In the ventricle a of the fish, the fibres, as I have pointed out elsewhere,* consist of three layers ;— an external layer, in which they proceed from base to apex, and occasionally _ interdigitate and become strongly embraced ; an internal layer, in which they are aggregated into fascicular bundles, and have a more or less vertical reticu- lated arrangement; and a central layer, in which they run transversely, or at right angles to the fibres of the external and internal layers. These layers are connected to each other by certain fibrous bands, which run in a direction from without inwards. Rising from the base of the ventricle anteriorly is a muscu- lar structure of a more or less bulbous form, the so-called bulbus arteriosus (Plate XXIX. figs. 38, 39, 40, 41, and 48), the arrangement of the fibres in which, resembles that in the ventricle itself. The ventricle of the fish, and the bulbus arteriosus contract in every direction, and in this respect they are analogous to the veins and arteries, which, as Joan HunTER showed, are exten- sible and retractile, both in their length and breadth. One point to be noted in the ventricle of the fish, is the absence of musculi papillares ; the auriculo-ventri- cular valves being so placed, that certain of the fasciculi constituting the internal layer, run parallel to them, and extend, in not a few instances, into their sub- stance. The effect of this arrangement is to modify the action of the valves in question; and I direct attention to the circumstance, because of the purely mechanical views entertained by some with regard to them; views which to me appear inconsistent with the nature of the textures involved. The arrangement of the fibres in the ventricle of the reptile is nearly the same as that in the fish. There is, however, this difference, and it is worthy of mention as bearing — directly upon the structure and function of the auriculo-ventricular valves in this ; * On the Arrangement of the Muscular Fibres, in the Ventricles of the Vertebrate Heart, ie Physiological Remarks. —Phil. Trans,, vol. 154, pp. 445-47. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 779 class of animals. The fibres of the external and internal layers pursue a slightly spiral course. The spiral direction of the fibres here indicated is so marked in the ventricles of the bird and mammal, as to influence not only the position of the musculi papillares and carneze columnee, but also the shape of the ventricular cavities, and the closure of the mitral and tricuspid valves. In the bulbus arteriosus of the fish, the valves as a rule, may be said to be fairly within the range of muscular influence, and it is interesting to note that in this struc- ture, the segments vary both as regards number, size, and shape. Thus, in the frog-fish (Lophius piscatorius), the origin of the bulbus arteriosus is guarded by a semilunar valve, consisting of two ample and very delicate segments (Plate X XIX. fig. 47 a), resembling those found in the middle-sized veins (Plate XXVIII. fig. 3; compare with ab); while in the sun-fish (Orthago- riscus mola, Schneider), the same aperture is guarded by a semilunar valve, con- sisting of three segments (Plate XXIX. fig. 48 abc); the segments being analo- gous in every respect to those found in the largest veins (Plate XXVIII. fig. 1; compare withabc). As the valve in these cases is situated between the bulbus arteriosus and the ventricle, and surrounded by a fibrous ring similar to that occur- ring at the origin of the pulmonary artery and aorta, it is not affected by the struc- tures between which it is situated to any great extent. The semilunar valves in the frog-fish and sun-fish, may therefore be regarded as connecting links between the venous and arterial ones in the bird and mammal; and that more complex system of analogous valves, which is found in the bulbus arteriosus of the fish generally. In the bulbus arteriosus of the skate (fava batis), the segments occupy the whole of the interior of the bulb, and are arranged in three pyramidal rows of five each (Plate XXIX, fig. 38 abc). As the segments in this instance are very small, and altogether inadequate to the obliteration of the bulbus cavity, they must be looked upon as being useful only in supporting the column of blood in its onward progress; it being reserved for the segments at the termination of the bulb, which are larger and more fully developed, to effect the closure. The action of the segments in the bulbus arteriosus of theskate, is rendered more perfect by the pressure from without, caused by the contraction of the bulb itself (d). In the bulbus arteriosus of the sturgeon (Accipenser sturio), the segments are arranged in three rows of eight each (Plate X XIX. fig. 39 a). They are more delicate, and less perfectly formed than in the skate. In the bulbus arteriosus of the American devil-fish (Cephalopterus giorna), they increase to thirty-six, are more imperfect than in any of the others, and are supported by three longitudinal angular mus- cular columns. As these segment-bearing columns, from their shape, project into the cavity, so as almost to obliterate it during the contraction of the bulb, they in this way bring the free margins of the segments together. The orifices of the bulbus arteriosus, however, are not closed by the imperfect segments referred to; these being guarded by two well-formed and fully developed tri-semilunar 780 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, valves, the one of which is situated at the beginning, the other at the ter- mination of the bulb. In the bulbus arteriosus of the grey shark (Galeus communis’, we have a slightly different arrangement, the two rows of segments . of which the valve is composed being connected to each other by means of tendinous bands, resembling chorde tendinez (Plate XXIX. fig. 48 a). In the bulbus arteriosus of the Lepidosteus (Plate X XIX. fig. 40 6), and that of the basking shark (Selachi maxima, Cuv.), (Plate XXIX. fig. 41 6), the same arrange- ment prevails; the segments being stronger and less mobile, and the tendinous bands which bind the one segment to the other, more strongly marked than in the grey shark. As the tendinous bands referred to are not in contact with the wall of the bulbus arteriosus, but simply run between the segments, and are in some instances, as in the basking shark, very powerful (Plate XXIX. fig. 41 0), they must be regarded in the light of sustaining or supporting structures; their function being probably to prevent eversion of the segments. Other examples might be cited, but sufficient have been adduced to show, that the nature, as well as the number and arrangement of the segments, is adapted to the peculiar wants of the structure in which they are situated; and it ought not to be over- looked, that when a multiplicity of segments are met with in an actively con- tracting organ, the two act together or in unison. If we now direct our attention to the auriculo-ventricular valves of the fish and reptile, similar modifications as regards the number of the segments, and the presence or absence of chordz tendineze and analogous structures, pre- sent themselves. Thus in the heart of the serpent (Python tigris), the two crescentic apertures by which the blood enters the posterior or aortic division of the ventricle, are each provided with a single semilunar valve. The same may be said of the aperture of communication, between the left auricle and ventricle of the crocodile (Crocodilus acutus) and of the sturgeon (Accipenser sturto, Linn.) In the heart of the Indian tortoise (Testudo Indica, Vosmaer), the left auriculo-ventricular orifice is guarded by a single membranous fold, the right orifice having in addition a slightly projecting semilunar ridge, which ex- tends from the right ventricular wall, and may be regarded as the rudiment of the fleshy valve which guards the same aperture in birds (Plate XXIX. fig, 45 gh). In the heart of the bulinus, frog-fish, American devil-fish, grey shark, and crocodile, the auriculo-ventricular orifice is guarded by a semilunar valve consisting of tivo cusps or segments ; while in the sturgeon, sun-fish, and others, it is guarded by four, two larger and tivo smaller. So much for the number of the segments constituting the auriculo-ventricular valves in fishes and reptiles ; but there are other modifications which are not less interesting physiologically. In the bulinus, frog-fish, and crocodile, the segments of the valves are attached to the auriculo-ventricular tendinous ring, and to the sides of the ventricle, and have no chorde tendinee. In the sun-fish OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA, 781 (Plate XXIX. fig. 43 /), the valve is destitute of chordze tendinese likewise; but in this instance the muscular fibres are arranged in the direction of the freemargino f the segments of the valve, and no doubt exercise an influence upon them. In the grey shark the membranous folds forming the segments, are elongated at the parts where they are attached to the ventricular walls, these elongated attach- ments being more or less split up, so as to resemble chordee tendinee. In the American deyil-fish the semilunar valve consists of two strong well- developed membranous folds, which, like the preceding, are attached by elongated processes to the interior of the ventricular wall; these processes consisting of dis- tinct tendinous slips, which are attached to rudimentary musculi papillares. In the sturgeon (Plate XXIX. fig. 37), three tendinous chords (b) from rudimentary muscult papillares, are seen to extend into the half of each of the segments; while in the left ventricle of the dugong, siw chords, proceeding from tolerably well-formed musculi papillares, are distributed to the back, and six to the margins of each of the segments. It is, however, in the bird and mammal, particularly the latter, that the musculi papillares are most fully de- veloped, and the chord tendinee most numerous—the number of tendinous chords, inserted into each of the segments, amounting to eighteen or more (Plate XXVIIL fig. 33 77’, ss’). As the auriculo-ventricular valves are attached either to the interior of the ventricle, or to the musculi papillares or carneze columne, it is plain that the contraction of the ventricle must influence them to a greater or less extent. That, however, the presence of muscular substance in no way interferes with the efficiency of the valves, is proved by the fact, that some valves are partly muscular and partly tendinous, a few being altogether muscular. Thus, in the heart of the cassowary, the right auriculo-ventricular orifice is occluded by a valve, which is partly muscular and partly tendinous; the muscular part, which is a continuation of two tolerably well-formed musculi papillares, extending into the tendinous substance of the valve, where it gradually loses itself. In the right ventricle of the crocodile (Plate XXIX. fig. 42 7), a muscular valve, resem- bling that found in the right ventricle of birds, exists. In birds the muscular valve (Plate XXIX. figs. 45 and 46 g h 7) is usually described as consisting of two parts, from the fact of its dependent or free margin (g) being divided into two portions by a spindle-shaped muscular band (h), which connects it with the right ventricular wall (j). As, however, the wall consists of one continuous fold towards the base (7), and the two portions of the margin are applied during the systole not to each other but to the septum (¢ é' e”), itismore correct to say that the valve is single; the spindle-shaped mus- cular band representing the musculus papillaris of the right wall of the ventricle with its attached chorde tendineze.* In the serpent, the opening between the right * For the relations, structure, and function, of the muscular valve in birds, see paper already referred to, Phil. Trans, vol. 154, pp. 470—1-2. VOR, XXII, PART TI: . 9Z 782 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, and left ventricle, occurs as a spiral slit in the septum (Plate X XIX. fig. 44 7), and is guarded by two projecting muscular surfaces, which are rounded off for this purpose. The opening into the left ventricle also occurs as a muscular slit (s) ; and the orifices of many of the venous sinuses are closed by purely muscular adap- tations ; the fibres in such instances running parallel to the slit-like opening (Plate XXVIII. fig. 10), and being continuous with two or more bundles of fibres (6 ¢), which supply the place of musculi papillares. From the great variety in the shape and structure of the auriculo-ventricular valves, and from the existence in almost all of tendinous chords, which connect them with actively contracting textures, there can, I think, be little doubt, that they possess an adaptive power peculiar in a great measure to themselves; this power being traceable to the contractile properties residing in muscle. As it would greatly exceed the limits of the present paper, to give a detailed account of the structure of the numerous auriculo-ventricular valves, to which allusion has been made, I have selected for description the auriculo-ventricular valves of the mammal, and those of man more particularly. Before, however, entering upon this the most difficult part of the present investigation, a brief account of the arrangement of the muscular fibres in the ventricles seems indis- pensable; these, as has been explained, modifying the action of the valves to a very considerable extent. ARRANGEMENT OF THE MuscuLar FisrEs IN THE VENTRICLES OF THE MAMMAL—SHAPE OF THE VENTRICULAR CAVITIES, &c. The fibres of the ventricles in the mammal, as I have ascertained from numerous dissections,* are arranged in seven layers; three external, a fourth or central, and three internal. The fibres constituting these layers in the left ven- tricle, to which these remarks more particularly apply, pursue a spiral direction ; the external fibres becoming more and more oblique, in a direction from left to right downwards, as the central layer is approached—the internal fibres becoming more and more vertical, in a direction from right to left upwards, as it is receded from. ‘The fibres, therefore, of corresponding external and internal layers, cross each other. ‘The fibres of the several layers are further arranged in two sets; the two sets, forming each of the external layers, being continuous at the apex and at the base, with two similar sets belonging to a corresponding internal layer. — This arrangement of the fibres renders the ventricles bilaterally symmetrical, and in part accounts for the great precision with which the heart acts, and for its roll- ing movements. Its bearing on the action of the organ is obvious, for as muscular fibres contract in the direction of their length, the more vertical external and internal fibres, diminish the ventricular cavities from above downwards, and from — * Of these upwards of an hundred are preserved in the University of Edinburgh Anatomical ‘ Museum, where they may be examined. For a detailed description of the specimens, and for accurate representations thereof, see Phil. Trans, vol. 154, pp. 445-500, Plates 12 to 16. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 783 below upwards; the downward movement preceding the upward by an almost inappreciable interval of time. In that brief space, however, which elapses between the downward.and upward movements, the ventricles, owing to the contraction of the more circular fibres, are visibly diminished from without in- wards; and it is important to note this circumstance, as the auriculo-ventricular orifices are, at this instant, reduced in size, and the mitral and tricuspid valves, consequently liable to a certain amount of displacement. The ventricular wall of the left ventricle, as was known to Grerpy and other investigators, is thickest at the upper part of its middle third (Plate XXVIII. fig. 35 7), and tapers towards the apex (wv) and base (v’) respectively ; and it is interesting to observe that the thickest part of the ventricular wall, corresponds with the widest portion of the ventricular cavity, whence the blood is projected into the aorta; a fact of some significance, since the contractions at this point are necessarily more intense than at any other. As the two sets of fibres composing the first external layer are continuous at the left apex with the two sets of fibres forming the carneze columnz and musculi papillares, and these structures, especially the latter, bear an important relation to the segments of the bicuspid valve, with which they are connected by the chordze tendineze, a more minute description than that given of the other layers, is requisite for clearness. On looking at the left auriculo-ventricular opening (Plate XXVIII. fig. 30 0), the fibres of the first layer are seen to arise from the fibrous ring surrounding the aorta (@), and from the auriculo-ventricular tendi- nous ring (7) in two divisions; the one division (d) proceeding from the anterior portions of the rings, and winding in a spiral nearly vertical direction, from before backwards, to converge and enter the apex posteriorly ; the other set (Plate XXVIII. fig 30 f) proceeding from the posterior portions of the rings, and winding in a spiral direction from behind forwards, to converge and enter the apex anteriorly. Having entered the apex, the two sets of external fibres are collected together, and form. the musculi papillares and carneze columnee; the one set, viz., that which proceeded from the auriculo-ventricular orifice anteriorly and entered the apex posteriorly, curving round in aspiral direction from right to left upwards, and forming the anterior musculus papillaris (Plate XXIX. fig. 50 y), and the carnece columne next to it; the other set, which proceeded from the auriculo-ventricular orifice posteriorly, and entered the apex anteriorly, curving round in a correspond- ing spiral direction, and forming the posterior musculus papillaris (Plate XXIX. figs. 50 and 51 x), and adjoining carne columne. As the external fibres con- verged on nearing the apex, so the internal continuations of these fibres radiate towards the base; and hence the conical shape of the musculi papillares. I am particular in directing attention to the course and position of the musculi papil- lares, as they have hitherto, though erroneously, been regarded as simply vertical columns, instead of more or less vertical spiral columns.* The necessity for in- * Plate XXIX. fig. 49, 2 y, gives the spiral track of the musculi papillares, 784 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, sisting upon this distinction will appear more evident when I come to speak of the influence exerted by these structures on the segments of the bicuspid valve. It is worthy of remark, that while the left apex is closed by two sets of fibres, the left auriculo-ventricular orifice is occluded during the systole by the two flaps or seg- ments constituting the bicuspid valve (Plates XX VIII. and XXIX. figs. 28 and 51 mn). The bilateral arrangement, therefore, which obtains in all parts of the ven- tricle and in the musculi papillares, extends also to the segments of the valve in question. What has been said of the arrangement of the fibres in the left ventricle, applies with slight modifications to the fibres of the right one; and many are of opinion (and I also incline to the belief) that the tricuspid valve, is in reality bicus- pid in its nature (Plate XXVIII. fig. 34 m m; and Plate XXIX. fig. 51 gh). The shape of the ventricular cavities of the heart of the mammal greatly influences the movements of the mitral and tricuspid valves, by moulding the blood into certain forms, and causing it to act in certain directions. Itis seen to advantage when the ventricles are filled with wax or plaster of Paris, and the ventricular parietes re- moved to expose the casts or moulds thus obtained (Plate XXIX. figs. 50 and 51). The form of the left ventricular cavity, which I regard as typical, is that of a cone twisted upon itself (Plate XXIX. fig. 49); the twist or spiral running from left to right of the spectator, and being especially well marked towards the apex.* The cone tapers slightly towards its base (b), and the direction of its spiral corre- sponds with the direction of the fibres of the carneze columne and musculi papillares (Plate XXIX. fig. 50 wy). As the two spiral musculi papillares project — into the ventricular cavity, it follows that between them, two conical-shaped spiral depressions or grooves, are found (Plate XXIX. fig. 49 g7). These grooves, which are especially distinct, are unequal in size; the smaller one (Plate XXIX. figs. 49 and 507) beginning at the right side of the apex, and winding in an up- ward spiral direction, to terminate at the base of the external or left and smaller segment of the bicuspid valve (Plate XXIX. figs. 50 and 51 ); the larger groove (Plate XXIX. fig. 49 g) beginning at the left side of the apex, and pursuing a similar direction, to terminate at the base of the internal or right and larger seg- ment (Plate XXIX. fig. 51 m). Running between the grooves in question, and corresponding to the septal aspect of the ventricular cavity, is yet another groove, larger than either of the others (Plate X XIX. fig. 51 q). The third or remaining groove winds from the interior of the apex posteriorly, and conducts to the aorta (a), which, as the reader is aware, is situated anteriorly. The importance of these grooves physiologically _ cannot be over-estimated, for I find that in them the blood is arranged or moulded into three spiral columns, and that towards the end of the diastole and the beginning of the systole, the blood in the two lesser ones is forced in two spiral streams upon the segments of the bicuspid valve, which are in this * In this description the heart is supposed to be placed on its apex. OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 78d way progressively elevated towards the base, and twisted and wedged into each other, until regurgitation is rendered impossible (Plate X XIX. fig. 51 mn). When the bicuspid valve is fairly closed, the blood is directed towards the third and largest groove, which, as has been stated, communicates with the aorta. The spiral action of the mitral valve, and the spiral motion communicated to the blood when projected from the heart, is due to the spiral arrangement of the musculi papillares and fibres composing the ventricle, as well as to the spiral shape of the left ventricular cavity. These points are determined in the following manner :— When a cast of the interior of the left ventricle is made, by introducing liquid plaster of Paris into the left ventricular cavity, by means of a tube inserted into the aorta and reaching to the left apex, it is found, on cutting away the parietes of the ventricle, that the segments of the mitral valve are borne up on the plaster,* and wedged into each other on a level with the ventricular orifice. It is further found, that the two spiral streams of plaster (now spiral columns) which closed the segments of the mitral valve, merge towards the base, into the third column, communicating with the aorta. That portion, therefore, of the left ventricular cavity (Plate X XIX. figs. 50 and 51 0), which corresponds to the conus arteriosus or infundibulum of the right one (Plate XXIX. fig. 50 2), is conical in form. It is moreover furnished with three conical-shaped spiral depressions, which in the cast appear as conical-shaped spiral prominences (po), and are continuous with the three spiral columns of plaster proceeding from the apex of the ventricle. As the apices of the three conical-shaped infundibuliform prominences referred to are directed between the three segments of the aortic semilunar valve, the blood from this arrangement must on its onward progress throw the semilunar segments hastily apart, by causing them to fall back upon the spirally disposed sinuses of VatsaLva (4iwv). The spiral channel, which is thus provided for the blood, is not confined to the heart, but extends for a short distance into the great vessels. As the semilunar valves are closed by a reverse move- ment to that by which they are opened, it is not difficult to perceive how the spiral action of the segments constituting them is induced. What has been said of the left ventricular cavity and aorta, applies, with slight alterations, to the right ventricular one and the pulmonary artery (Plate XXIX. figs. 50 and 51 cz), the cone formed by the right cavity being flattened out and applied to or round the left. Intricate Structurk oF THE MiTraL AND TRICUSPID VALVES IN MamMauia; RELATIONS OF THE CORDH TENDINEE TO THE SEGMENTS AND TO THE MUSCULI PAPILLARES. The auriculo-ventricular valves are composed of segments, which differ in ' size, and are more or less triangular in shape. They are much stronger than * In order to see the spiral movement of the segments to advantage, the plaster ought to be , made very thin. Should any difficulty occur, the experimenter is recommended to use water until he is familiar with the phenomena to be observed. ViOn, 767.) ’ Fig. 4. External Jugular Vein of Horse opened, To show the relations of the segments (a b) above (re). (See p. 763.) Fig. 5, Portion of Femoral Vein distended with plaster of Paris, Shows dilatations (hg) in the course of the vessel corresponding to the position of the valve. (See p. 765.) Fig. 6. Shows Venous Valve, consisting of two segments (ab), in action, (See p. 767.) Fig. 7. The same, not in action, (See p. 763.) 8. Venous Valve from External Jugular of Horse, consisting of three segments. (See p. 764.) 9. Venous Valve, consisting of one segment, situated at the entrance of a smaller into a larger vein. (See p. 763.) Fig. 10. Venous Sinus from Auricle of Heart of Sturgeon. (See p. 782.) Fig. 11. Femoral Vein distended with plaster of Paris. Shows venous valves in action, where a smaller vessel enters the larger one (a 6), and in the main trunk (a’b’). (See pp. 767, 768.) Fig. 12. Vertical Section of Vein distended with plaster of Paris. Shows the nature of the union between the segments (e). (See p. 767.) Fig. 13. The same, the section being carried between (e) instead of across or through the segments. (See p. 767.) Figs. 14, 15, and 16. Show the Structure of the Venous Valves. (See p. 766.) Fig. 17. Section carried through Pulmonary Artery and Right Ventricle of Human Heart, between the segments of the semilunar valves (s). Shows the variation in the thickness of the vessel (ab), and how it bifurcates (r7’) at its origin. (See p. 770.) Fig. 18. A similar section, carried through the middle of one of the segments (s). Shows how the Pulmonary Artery (ab) behind the segments diminishes in thickness in a direction from above downwards (7). See p. 770.) 804 DR PETTIGREW ON THE RELATIONS, STRUCTURE, AND FUNCTION, Figs. 19, 20, 21, 22, 23, and 24, Show the Structure of the Semilunar Valves in the Human Pul- monary Artery. (See pp. 772, 773, 774, 775.) Fig. 25. Human Semilunar Valve distended with plaster of Paris, and one of the segments (g) re- moved, to show the precise shape of the lunulz, or opposing surfaces (6 b’), between which union takes place when the valve is in action. (See pp. 776, 777.) Fig. 26. Shows the spiral relation of the Sinuses of Varsaztva to the segments (v w a) of the semi- lunar valve in the Human Pulmonary Artery, and how the segments are spirally wedged into each other, and fixed by six non-symmetrical semilunar surfaces, to form three per- pendicular crescentic walls (rs0). Seen from beneath. (See pp. 776, 777.) Fig. 27. Shows the Semilunar Valves in the Heart of the Sheep (vu w x) distended with plaster of Paris, or as they appear in action, together with the spiral nature of that action. (See pp. 776, Fig. 28. Shows the same in the Aorta (vw x) of the Human Heart, and in addition, the bifid nature of the musculi papillares (ab, ed), and the distribution of the chord tendinez to both segments of the mitral valve (mn). (See pp. 776, 777, 787, 788, 789.) Fig, 29. Vertical Section carried through the Aorta and through the middle of one of the segments of the Semilunar Valve of the Whale. Shows the variation in the thickness of the vessel (ce), and the structure of the semilunar valve (a7 s’0). (See pp. 770, 773, 774.) Fig. 80. Shows Arterial and Auriculo-ventricular Orifices, with their fibrous rings (wu nn’). (See pp. 769, 770.) z Fig. 31. Human Mitral Valve, Chorde tendinexz, and Musculi papillares inverted. Shows the bifid nature of the musculi papillares (a 6), and the threefold distribution of the chorde ten- dine (s). (See pp. 786, 787, 788, 788.) Fig. 32. Shows Structure of the Mitral Valve in the Sheep. (See pp. 786, 787, 788, 789.) 5 Fig. 83, Anterior Segment of Human Mitral Valve. Shows the threefold distribution of the chord tendinez, from above downwards, and from the mesial line towards the margin of the segments, (See pp. 786, 787, 788, 789.) Fig. 34. Example of Mitral Valve in the Right Ventricle of the Human Heart. (See pp. 789, 790, 791.) Fig. 35. Vertical Section, carried through the aorta (aa’) semilunar valve (ss’s”), left auricle (dd’,yy’), the segments of the mitral valve (mm’,nm’), and the left ventricle (vv), of the Human Heart. Shows the greater thickness of the aorta, where the segments of the semi- lunar valve unite above (b b’, cc’), and its greater tenuity behind the centre of each seg- ment (0) ; also how a portion of the aorta (p) is continued into the larger or anterior seg- ment of the mitral valve (mm’). It also shows the relation of the left auricle (y y’, dd’) to the aorta (a @), mitral valve (mm’, nn’), and left ventricle (v 0’). rr’, Openings of coronary arteries. _ nn’, Segments of semilunar valve uniting above. wa’,ee’, Auricle terminating by wedge-shaped process in mitral valve. z2', Left coronary artery. t tt’, Convex, or attached borders of segments of semilunar valve. g, Septal wall of left ventricle. hi’, Chordee tendinee. iv’, Musculi papillares, w’, Apex of left ventricle. (See pp. 770, 771). Fig. 36. Left Ventricle of Human Heart laid open to show the semilunar (ss’) and mitral (m) valves in situ. (See pp. 770, 771.) Pratt XXIX. Fig. 37. Portion of Heart of Sturgeon. Shows auriculo-ventricular valve (a) with three chorde tendinez (6) proceeding from it. (See p. 781.) Fig. 38. Ventricle and Bulbus Arteriosus of Skate laid open. Shows several rows of semilunar valves (abc) increasing in size in a direction from below upwards. (See p. 779.) OF THE VALVES OF THE VASCULAR SYSTEM IN VERTEBRATA. 805 Fig. 39. Bulbus Arteriosus and Ventricle of Sturgeon,—the former displaying five rows of semi- lunar valves (a), the latter an auriculo-ventricular valve (6), with numerous tendinous bands running into it. (See p. 779.) Fig. 40. Bulbus Arteriosus and Portion of Ventricle of Lepidosteus. Shows the great thickness of the bulb (a), and of the valves (b) contained within it, and between which tendinous bands run. (See p. 780.) Fig. 41. Portion of Bulbus Arteriosus of Basking Shark. Shows the great thickness of the bulb (a) and of the valves (), and how the latter support each other. (See p. 780.) Fig: 42. Heart of Crocodile. Shows spiral semi-muscular, semi-tendinous valve (7), situated between right auricle (a) and ventricle (a), (See p. 781.) Fig. 43. Bulbus Arteriosus and Ventricle of Sun-fish. Shows three semilunar valves (a 6 c) at orifice of bulb, and an auriculo-ventricular valve (f), consisting of two segments. (See pp. 779, 781.) Fig. 44. Heart of Serpent (Python tigris). Shows muscular semilunar valve at orifice of left superior cava (s); also spiral muscular slit (r), occurring between the ventricles. (See pp. 781, 782). Fig. 45. Heart of Emu, showing spiral muscular valve (g A), occurring in right auriculo-ventricular orifice. (See p. 781.) Fig. 46. Heart of Swan, with right and left ventricles laid open. Shows spiral muscular valve of right ventricle (7), and mitral valve (v) of left, and how one portion of the former (j) corresponds in position to the anterior musculus papillaris (y) of the latter. (See p. 781.) Fig. 47. Heart of Frog-fish. Shows three sets-of semilunar valves ; one occurring where the large veins join the auricle (c) ; a second, where the auricle opens into the ventricle (b) ; the third being situated at the orifice of the bulbus arteriosus (a). (See p. 779.) Fig. 48. Bulbus arteriosus and portion of Ventricle of Grey Shark. Shows semilunar valves, with ; tendinous chords running between them (a) ; also, auriculo-ventricular valve (9). (See pp. 779, 780.) Fig. 49. Wax cast of Left Ventricle (b) and portion of Right Ventricle (a) of Deer. Shows spiral nature of the left ventricular cavity,—the spiral course or tracks of the musculi papillares (xy), and how between these, two spiral grooves (j q) occur, which direct the blood on to the segments of the mitral valve in spiral waves. (See pp. 784, 785.) Fig. 50. Plaster of Paris cast of Right and Left Ventricles of Zebra. Shows infundibulum or conus arteriosus (¢) of right ventricle, and analogous portion of left ventricle (po); also three prominences on each (d e kr v), corresponding to the sinuses of Vatsatva. It also shows the double cone formed by the left ventricular cavity, the one apex pointing towards the apex of the heart (7), the other towards the aorta (h). (See pp. 784, 785.) Fig. 51. Same cast seen posteriorly. Shows the mitral (mn) and tricuspid (gh) valves in action, and how the blood, when these are closed, assumes a conical form (0) for pushing aside the segments of the semilunar valves, and causing them to fall back upon the sinuses of Vausatva (vw). It also shows how the right ventricular cavity (c) curves round the left one (#), and how the pulmonary artery (6) and aorta (h) pursue different directions. (See pp. 784, 785.) Figs. 52, 53, and 54. Show the Mitral (rs) and Tricuspid (min) Valves of the Sheep in action, How the segments, acted upon by the spiral columns of blood, roll up from beneath towards the end of the diastole (fig. 52); how, at the beginning of the systole, they are wedged and twisted into each other, on a level with the auriculo-ventricular orifices (fig. 53); and how, if the pressure exerted be great, they project into the auricular cavities (fig. 54). (See pp. 796, 797, 798, 799, 800, 801.) Figs. 55, 56, and 57. Show the same in the Human Heart, with this difference, that in the right ventricle, a true mitral valve (mn), as not unfrequently happens, has taken the place of the tricuspid. (See pp. 796, 797, 798, 799, 800, 801.) Note.—The spiral downward movement of the mitral and tricuspid valves has only been partially represented (figs. 52 and 55) owing to the great difficulty experienced in representing spiral cavities. VOL. XXIII. PART III. 10 . Roy. Soc Edin® Vol. XXIIl Plate XXVIII. by W.S.Aylimg and the Author Drawings by the Author WH M‘Farlane, Lith? Bdirt Roy. Soc. Bdin® Vol. XXII Hy Ws Ayling and the Author. Drawings by H.S.W ERRATA. 21, line 4 from bottom, for value v read value of v. 23, line 7 from top, for (cos t+sin #) read (sin t —cos ft). — line 4 from bottom, for e~* read e—*. — line 8 from bottom, the first minus sign in the line should be plus. 26, line 2 from bottom, for 23° 23° read 66° 37’. ' Fat piste 633, line 23 from top, for treatise read charge. 644, line 2 from bottom, for 1778 read 1781. 714, line 5 from bottom, for two primary affinities read two secondary affinities. PROCEEDINGS OF THE STATUTORY GENERAL MEETINGS, LIST OF MEMBERS ELECTED AT THE ORDINARY MEETINGS, Since JANuARY 6, 1862 ; WITH LIST OF DONATIONS TO THE LIBRARY, : From Noy. 25, 1861, tint Nov. 23, 1864. VOL. XXIII. PART III. 10e PROCEEDINGS, &c. M onday, November 25, 1861. At a Statutory General Meeting, Dr Curistison, V.P., in the Chair, the io Wt of the General Meeting of 26th November 1860 were read and confirmed. 7 The following Office-Bearers were duly elected :— | a His Grace the Duke or Arey Lt, K.T., President. . a 0 Sir Davin Brewster, K.H., Dr Curistison, | _ } Professor KELLAND é : a: Hon. Lord eee ' Vice-Presidents. ne The Very Rev. Dean Ramsay, | Principal Forszzs, Dr Joun Hutron Batrour, General Secretary. Dr Lyon Prayrair, C.B., ‘ : ‘ Drs@von ua thewiMtnae } Secretaries to the Ordinary Meetings. J. T, Grsson-Craic, Esq., Treasurer. ,e Dr Dovetas Mactacan, Curator of Library and Museum. COUNCILLORS. Dr Lowe. Dr Scumirz. Professor W. J. M. Rankine. Dr Seer. James Datmanoy, Esq. E. W. Dattas, Esq. Dr Joun Brown. : Rev. L. S. OrpE. ! Professor Fraser. Professor Tat. James Lesuiz, Esq., C.E. Joun Muir, D.C.L. The following Gentlemen were, on the motion of Dr Burr, appointed to audit the — Treasurer's Accounts :— f Dr SELLER. A. Bryson, Esq. W. T. Tuomson, Esq. The Meeting then adjourned. | (Signed) R. Curistison, VP. Wi 4 PROCEEDINGS OF STATUTORY GENERAL MEETINGS. 809 a Monday, January 6, 1862. At a meeting of the Society, held on Monday 6th January 1862, the Hon. Lord NEAvVEs in the Chair, the following Address to Her Majesty, expressing the sorrow of the Society on the death of H.R.H. the Prince Consort, was read and adopted :— To THE QUEEN. May rt please your Majesty, We, the President and Fellows of the Royal Society of Edinburgh, beg leave most humbly to offer to your Majesty the sincere expression of our condolence for the great bereavement which your Majesty has sustained, and of our grief for the great loss which has befallen the nation by the death of His Royal Highness the Prince Consort, who, by his exemplary discharge of every duty, by his sympathy with the feelings, and his solicitude for the welfare, of his adopted country, and by his unwearied efforts to promote the progress of Learning, Science, Industry, and Art, had won for himself the just admiration, esteem, and gratitude of the whole community. That in this heavy affliction, your Majesty may be supported by the consolations of religion, by the honoured memory of the departed, by the reverence and affection of your Majesty’s children, and by the devotion of a loyal and united people, who recognise in your Majesty's government the great source and security, under Providence, of the high degree of prosperity and happiness which they enjoy, is the prayer of your Majesty’s most dutiful subjects and servants. Signed in name and by authority of this Society, by his Grace the Duke of Areyun, President. (Signed) R. Curistison, V.P. Monday, January 20, 1862. At a meeting of the Society, held on Monday 20th January 1862, James T. Grpson- Craic, Esq., Treasurer, in the Chair, the following reply to the Address to Her Majesty was read :— WuiTEHALL, 13th January 1862. My Lorp Dux, I have the honour to acknowledge the receipt of the loyal and dutiful Address of the President and Fellows of the Royal Society of Edinburgh, on the occasion of the death 810_ PROCEEDINGS OF STATUTORY GENERAL MEETINGS. of His Royal Highness the Prince Consort, and to inform your Grace, that I shall take an early opportunity of laying the Address before Her Majesty. I have the honour to be, My Lord Duke, Your Grace’s obedient Servant, (Signed) 3 G. GREY. His Grace the Duke of Arcyut, &c, &e. (Signed) R. Caristison, VP. Monday, November 25, 1862. At a Statutory General Meeting, Dr Curistison, V.P., in the Chair, the Minutes of the General Meeting of 25th November 1861, and those of Ae 6th and 20th January 1862, were read and confirmed. The following Office-Bearers were duly elected :— His Grace the Duxz or Arcytt, K.T., President. Sir Davip Brewster, K.H., Dr Curistison, Professor KELLAND, Hon. Lord Neaves, Principal Forsgs, Vice-Presidents, Professor Cosmo Innzs, Dr Joun Hutton Batrovur, General Secretary. Dr Lyon Prayrarr, C.B. ; Secretaries to the Ordinary Mectings. Dr Grorcre James ALLMAN, y e J. T. Gizson-Craic, Esq., Treasurer. Dr Doveias Macracan, Curator of Library and Museum. COUNCILLORS. Professor FRASER. Professor Tair. James Lesuig, Hsq., C.E. Joun Murr, D.C.L. Dr Scamitz. A, CampsBett Swinton, Esq. Dr SELLER. Dr Wititam Rosertson. E. W. Datuas, Esq. Dr E. Ronaxps. Rev. L. S. Orpe. T, C. Arcner, Esq. PROCEEDINGS OF STATUTORY GENERAL MEETINGS. 811 The following Gentlemen were, on the motion of Dr Burr, seconded by Professor KELLAND, appointed to audit the Treasurer’s Accounts :— James CuNNINGHAM, Esq. Dr Witiiam SELLER. Sheriff CLecHory. The Meeting then adjourned. (Signed) R. Curistison, V.P. Monday, April 20, 1863. At a meeting of the Society, held on Monday the 20th April 1863, Principal Forzes in the Chair, the following Address to His Royal Highness the Privcz or Wates was read and adopted :— To His Royat HIGgHNESS THE PRINCE or WALES. May it please your Royal Highness, We, the President and Fellows of the Royal Society of Hdinburgh, desire humbly to approach your Royal Highness, with the expression of our dutiful and heartfelt congratula- tion on your Royal Highness’s marriage. Ever ready to rejoice at whatever affords a prospect of increased happiness to your Royal Highness, and a further security for the continued sway of a Royal House which has conferred on this realm so many benefits and blessings, we hail with especial interest and gratification the union of your Royal Highness with the Daughter of an ancient uation, dis- tinguished at all times for noble and generous qualities, and which holds a high place among the countries of Europe in literature and science ; and, above all, we regard it as an unspeakable boon, that the Royal Lady whom we now welcome to our shores is endowed with all the virtues and attractions which are best calculated to bless and adorn domestic life, to assist in cheering the widowed solitude of our beloved Sovereign, and to sustain in unsullied lustre the honour and dignity of the British Court. We earnestly hope and pray, that this auspicious alliance may be productive of all the happiness with which we wish to see it attended. . (Signed) R. Curistison, V.P. VOL. XXIII. PART III. 10H 812 PROCEEDINGS OF STATUTORY GENERAL MEETINGS. Monday, November 23, 1863. At a Statutory General Meeting, Professor Curistison, V.P., in the Chair; the Minutes of the last General Statutory Meeting, and those of 20th April 1863, were read and con- firmed. The following Office-Bearers were then elected for 1863-64 :— His Grace the Duke or Arey.t, K.T., President. Sir Davip Brewster, K.H., Dr Curistison, Professor Ke.ianp, Hon. Lord Neaves, Principal Forzzs, Vice-Presidents. Professor Cosmo Innzs, Dr Joun Hurron Barrour, General Secretary. Dr Lyon Prayrair, Secretaries to Ordinary Meetings. Dr Gzorce James ALLMAN, } es het ake . Davin Smiru, Esq., Treasurer. Dr Dovetas Mactacan, Curator of Library and Museum. COUNCILLORS. E. W. Daxtas, Esq. _ 7. C. Arcusr, Esq. Rev. L. 8S. Orpz. W. F. Sxenz, Esq. Professor Tair. A. Keitu Jounston, Esq. A. CampBeLt Swinton, Esq. Rey. Dr STEVENSON. Dr Witt1am RosBertson. Dr Stevenson Macapam. Dr E. Ronatps. Hon. Lord Jerviswoove. ’ The Chairman read the following intimation from the Council :— “The Council consider it expedient that one Vice-President should’ annually be — removed from the list of Vice-Presidents, and that he should be ineligible for election for twelve months. On submitting future lists to the Society, the Council propose to omit the — name of the senior Vice-President in the list for each year, and to submit another name in substitution.” On the motion of Dr Burt, seconded by Dr Srtiter, Mr W. T. Toomson, Mr James 7 CunnincHam, and Dr Witiiam Rosertson were appointed a Committee to examine the Treasurer’s accounts. j The following letters from His Royal Highness the Prince or WaLEs were read :— PROCEEDINGS OF STATUTORY GENERAL MEETINGS. 813 Marxegoroven House, July 16, 1863. - Lieut.-General Knoniys has been desired by His Royal Highness the Prince or Watss, to thank the President and Fellows of the Royal Society of Edinburgh for their Address on the occasion of His Royal Highness’s marriage,—for their congratulations,— and for the gratifying sentiments they have expressed towards the Princess. To His Grace the Duke or ARGYLL, President. ABERGELDIE, BALLATER, ABERDEENSHIRE. My Lorp Dugg, I have the honour to acknowledge, by command of the Prince or WALES, the receipt of the diploma constituting His Royal Highness an Honorary Fellow of the Royal Society of Edinburgh ; and am further commanded to convey to you His Royal Highness’s extreme gratification at having received the same. I have the honour to be, My Lord Duke, Your very obedient Servant, W. Kwyottys, Lieut.-Gen. The meeting then adjourned, To His Grace the DuKE oF ARGYLL. 814 LIST OF MEMBERS ELECTED. LIST OF MEMBERS ELECTED. January 6, 1862. Rev. Witiiam G. Briaixte. Henry Cueyne, Esq., W.S. January 20, 1862. Avex. Mackenzie Epwarps, Esq. February 3, 1862. Dr Watter Borp M‘Kintay. Dr Joun P. Macartney. Dr Epmunp Ronatps. February 17, 1862. Tuomas C, Arcuer, Esq. Rev. V. GrantHam FaItTHFULL. ) Dr James Hector. March 17, 1862. Nicnozas ALex. Daze, Esq. April 7, 1862. Hon. Lord Barcapre. Rev. Rozpert Boog Watson. December 1, 1862. Rovert CamMPBELL, Esq. Dr H. F. C. Crecuorn. Professor BLacktE. January 5, 18638. Epwarp Metprvum, Esq. Cuar.es Lawson, Esq. James Hannay, Esq. Dr ALEXANDER PeEpDIE. January 19, 1863. The Right Hon. Lord DunrerMiine, Witi1aM Jameson, Esq. W itiiam Brann, Esq. Dr Murray Tuomson. February 2, 1863. Dr Joun Youne. Davin Pace, Esq. February 16, 1863. Dr J. G. Witson, Dr J. Martuews Duncan. GeorceE R, Maitianp, Esq. W. Ditrmar, Esq. March 2, 1863. Rev. Dr NisBet. March 16, 18638. Hon. Lord Ormipatez. Professor J. D. Everett. LIST OF MEMBERS ELECTED. 815 April 6, 1863. Hon. G@. Waxprcrave Lestiiz. Hon. Cuartes Batiire (Lord Jerviswoops). James SANDERSON, Esq. April 20, 1863. Cuares Cowan, Esq. Dr Joun ALeEx, SMITH. December 7, 1863. Dr AtEex. Crum Brown. Dr Arex. Woop. December 21, 1863. Dr Anprew Woop. Ropert Witttam Tuomson, Esq., C.E. January 4, 1864. James Davin Marwick, Esq. January 18, 1864. Rev. D. F. SanpForp. Rosert 8. Wyxp, Esq. February 1, 1864. Peter M‘Lacan, Esq. Wii1aM Linpsay, Esq. Professor W. Y. SELLar. Rosert Hurtcutson, Esq. Rey. Joun Hannan, D.D., re-elected. February 15, 1864. Winuiam Wattace, Ph.D. March 7, 1864. Professor Rozert Dyce, M.D. May 2, 1864. ArtHur ABNEY WALKER, Esq. Dr Joun Fouterton. VOL. XXIII. PART III. 101 (OB PSINY LIST OF THE PRESENT ORDINARY MEMBERS, Corrected up to November 1, 1864 IN THE ORDER OF THEIR ELECTION, His Grave tHE DUKE OF ARGYLL, K.T., PRESIDENT. Date of Election. 1808 James Wardrop, Esq., London. Sir David Brewster, K.H., LL.D., F.R.S. Lond., Principal of the University of Edinburgh. 1812 Sir George Clerk, Bart., F.R.S. Lond. 1815 Henry Home Drummond, Esq., of Blair-Drummond. William Thomas Brande, F.R.S. Lond., Professor of Chemistry in the Royal Institution. 1818 Patrick Miller, M.D., Exeter. 1820 Charles Babbage, F.R.S. Lond. Sir John F. W. Herschel, Bart., F.R.S. Lond. Dr William Macdonald, Professor of Natural History, St Andrews. 1821 John Cay, Esq., Adwocate. Robert Kaye Greville, LL.D. Robert Hamilton, M.D. 1822 James Smith, Esq., of Jordanhill, F.R.S, Lond. William Bonar, Esq. George A. Walker-Arnott, LL.D., Professor of Botany, Glasgow. Sir James South, F.R.S. Lond. Sir W. C. Trevelyan, Bart., Wallington, Northumberland. 1823 Captain Thomas David Stuart, of the Hon. East India Company's Service. Warren Hastings Anderson, Esq. Alexander Thomson, Esq., of Banchory. Liscombe John Curtis, Esq., Ingsdon House, Devonshire. Robert Christison, M.D., Professor of Materia Medica. LIST OF ORDINARY MEMBERS. 817 Date of Election. 1824 Robert E. Grant, M.D., Professor of Comparative Anatomy, University College, London. Rey. Dr William Muir, one of the Ministers of Edinburgh. 1827 John Gardiner Kinnear, Esq. Very Rev. Edward Bannerman Ramsay, A.M. Camb., LL.D. 1828 David Maclagan, M.D. Sir William A. Maxwell, of Calderwood, Bart. John Forster, Esq., Architect, Liverpool. Thomas Graham, M.A., D.C.L., Master of the Mint, London. David Milne-Home, Esq., Advocate, of Milne-Graden and Wedderburn. Dr Manson, Nottingham. 1829 A. Colyar, Esq. Sir William Gibson-Craig, Bart., of Riccarton. Right Honourable Duncan M‘Neill, Lord Justice- General. Venerable Archdeacon Sinclair, Kensington. James Walker, Esq., W.S. 1830 J. T. Gibson-Craig, Esq., W.S. Sir Archibald Alison, Bart., Sherif’ of Lanarkshire, James Syme, Hsq., Professor of Clinical Surgery. Thomas Barnes, M.D., Carlisle. 1831 James D., Forbes, D.C.L., F.R.S. Lond. Principal of the United College, St Andrews. 1832 Montgomery Robertson, M.D. 1833 Rear-Admiral Sir Alexander Milne, R.N. His Grace the Duke of Buccleuch, K.G., Dalkeith Palace. David Craigie, M.D. Sir John Stuart Forbes, Bart., of Pitsligo. Alexander Hamilton, LL.B., W.S. 1834 Mungo Ponton, Esq., W.S., Clifton, Bristol. Isaac Wilson, M.D., F.R.S. Lond. Patrick Boyle Mure Macredie, Esq., Advocate, of Perceton. William Sharpey, M.D., Professor of Anatomy, University College, London. 1835 John Hutton Balfour, A.M., M.D., F.R.S. Lond., Professor of Botany. William Brown, Esq., F.R.C.S. R. Mayne, Esq. 1836 David Rhind, Esq., Architect. 1837 John Archibald Campbell, Esq., W.S. John Scott Russell, Hsq., A.M., London. Charles Maclaren, Esq. Archibald Smith, Esq., M.A., Camb. Lincoln’s Inn, London. Richard Parnell, M.D. Peter D. Handyside, M.D., F.R.C.S. 1838 Thomas Mansfield, Esq., Accountant. Alan Stevenson, Esq., Civil Engineer. 1839 David Smith, Esq., W.S. Adam Hunter, M.D. 818 LIST OF ORDINARY MEMBERS. Date of Election. 1839 Rev. Philip Kelland, A.M., Professor of Mathematics. F. Brown Douglas, Esq., Advocate. 1840 Alan A. Maconochie Welwood, Esq., of Meadowbank and Pitliver. Martyn J. Roberts, Esq., Fort-William. 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. John Mackenzie, Esq. James Anstruther, Esq., W.S. 1841 John Millar, Esq., Civil Engineer, Millfield House, Polmont. James Dalmahoy, Esq. 1842 James Thomson, Esq., Civil Engineer, London. John Davy, M.D., Inspector-General of Army Hospitals. Robert Nasmyth, Esq., F.R.C.S. John Goodsir, Esq., Professor of Anatomy. 1843 A. D. Maclagan, M.D., Professor of Medical Jurisprudence. John Rose Cormack, M.D., F.R.C.P., Putney. Allen Thomson, M.D., Professor of Anatomy, Glasgow. Joseph Mitchell, Esq., Civil Engineer, Inverness. Andrew Coventry, Esq., Advocate. John Hughes Bennett, M.D., Professor of Physiology. D. Balfour, Esq., of Trenaby. Henry Stephens, Esq. 1844 Archibald Campbell Swinton, Esq., Advocate. James Begbie, M.D., F.R.C,P.E. James Y. Simpson, M.D., Professor of Midwifery. David Stevenson, Hsq., Civil Engineer, Thomas R. Colledge, M.D., F.R.C.P.E. 1845 John G. M. Burt, M.D. Thomas Anderson, M.D., Professor of Chemistry, Glasgow. 1846 A. Taylor, M.D., Pau. S. A. Pagan, M.D. Alexander J. Adie, Esq., Ciwil Engineer. L. D. B. Gordon, Esq., C.E. L. Schmitz, LL.D., Ph.D., Rector of High School. Charles Piazzi Smyth, Esq., Professor of Practical Astronomy. 1847 William Thomson, Esq., M.A. Camb., Professor of Natural Philosophy, Glasgow. J. H. Burton, Esq., LU.D., Advocate. James Nicol, Esq., Professor of Natural History, Aberdeen. William Macdonald Macdonald, Esq., of St Martins. Alexander Christie, Esq. John Wilson, Esq., Professor of Agriculture. Date of Election. 1847 1848 1849 1850 1851 1852 1853 1854 LIST OF ORDINARY MEMBERS. 819 Moses Steven, Esq., of Bellahouston. 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. William Stirling, Esq., of Keir, M.P. John Thomson Gordon, Esq., Sherif’ of Mid-Lothian. William Thomas Thomson, Esq. Honourable Lord Ivory. William E. Aytoun, D.C.L., Professor of Rhetoric and Belles Lettres. W. H. Lowe, M.D., Balgreen. Honourable B. F. Primrose. David Anderson, Esq., of Moredun. W. R. Pirrie, M.D., Professor of Surgery, Aberdeen. His Grace the Duke of Argyll, Inverary Castle. The Most Noble the Marquis of Tweeddale, K.T. Edward Sang, Esq. William John Macquorn Rankine, Esq., C.E., Professor of Civil Engineering, Glasgow University. Alexander Keith Johnston, Esq. Sheridan Muspratt, M.D., Liverpool. James Stark, M.D, (Re-admitted.) Lieutenant-Colonel W. Driscoll Gossett, R.E. William Seller, M.D., F.R.C.P.E. Hugh Blackburn, Esq., Professor of Mathematics, Glasgow. J. S. Combe, M.D. Sir David Dundas, Bart., of Dunira. John Stewart, Esq., of Nateby Hall. E. W. Dallas, Esq. Rev. James Grant, D.C.L., D.D., one of the Ministers of Edinburgh. Eyre B. Powell, Esq., Madras. Thomas Miller, A.M., LL.D., Rector, Perth Academy. Allen Dalzell, M.D. James Cunningham, Esq., W.S. Alexander James Russell, Esq., C.S. Andrew Fleming, M.D., Bengal. James Watson, M.D., Bath. Lieutenant-Colonel Robert Maclagan, Bengal Engineers. Rey. Dr Robert Lee, Professor of Biblical Criticism and Biblical Antiquities. Rev. John Cumming, D.D., London. Hugh Scott, Esq., of Gala. Greme Reid Mercer, Esq. Sir John Maxwell, Bart., of Polloc. VOL. XXIII. PART IIl. 10K 820 LIST OF ORDINARY MEMBERS. Date of Election. 1854 Dr John Addington Symonds, Clifton, Bristol. Dr William Bird Herapath, Bristol. Robert Harkness, Esq., Professor of Mineralogy and Geology, Queen’s College, Cork. Sir James Coxe, M.D. Ernest Bonar, Esq. 1855 Stevenson Macadam, Ph.D. Robert Etheridge, Esq., Clifton, Bristol. Right Honourable John Inglis, Lord Justice-Clerk. Rev. James S. Hodson, D.D. Oxon., Rector of the Edinburgh Academy. Wyville T. C. Thomson, LL.D., Professor of Geology, Belfast. Dr Wright, Cheltenham. James Hay, Esq. R. M. Smith, Esq. 1856 David Bryce, Esq. William Mitchell Ellis, Esq. George J. Allman, M.D., Professor of Natural History. Honourable Lord Neaves. Dr Frederick Penny. Thomas Laycock, M.D., Professor of the Practice of Medicine. Thomas Cleghorn, Esq. James Clerk Maxwell, Esq., Professor of Natural Philosophy, King’s College, London. 1857 James Black, M.D. John Ivor Murray, M.D. John Blackwood, Esq. Reverend Dr James Macfarlane, Duddingston. W. M. Buchanan, M.D. Thomas Login, Esq., C.E., Pegu. Edmund C. Batten, M.A., Lincoln’s Inn, London, 1858 Thomas Williamson, M.D., Leith. Robert B. Malcolm, M.D. James Duncan, M.D. Alexander Bryson, Esq. Frederick Field, Esq., Chali. James Leslie, Esq., C.E. Cosmo Innes, Esq., Professor of History. Rev. Alexander C. Fraser, Professor of Logic. Rev. William Stevenson, D.D., Professor of Ecclesiastical History. 1859 William F. Skene, Esq., W.S. G. W. Hay, Esq. © Robert Russell, Esq. — Joseph Fayrer, M.D. George Robertson, Esq., C.E. Lyon Playfair, C.B., Professor of Chemistry. John Brown, M.D. Date of Election. 1859 1860 1861 1862 1863 LIST OF ORDINARY MEMBERS. 821 Professor Richardson, Durham. Rev. John Duns, D.D. Lieut. John Hills, Bombay Engineers. Captain Gordon Forlong. William Robertson, M.D. Frederick Guthrie, M.D., Professor of Chemistry, Mauritius. J. Alfred Wanklyn, Esq. Patrick C. MacDougall, Esq., Professor of Moral Philosophy. George A. Jameson, Esq. Rev. Leonard Shafto Orde. Patrick Dudgeon, Esq., of Cargen. William Chambers, Esq., of Glenormiston. W. A. F. Browne, Esq., one of H. M. Commissioners in Lunacy for Scotland, Rev. Thomas Brown. Robert EKdmund Scoresby-Jackson, M.D. James M‘Bain, M.D., R.N. Peter Guthrie Tait, Esq., Professor of Natural Philosophy. John Muir, D.C.L., LL.D. William Turner, M.B. William Lauder Lindsay, M.D. James Lorimer, A.M., Professor of Public Law. Archibald Geikie, Esq. William Handyside, Esq. George Berry, Esq. Thomas Herbert Barker, M.D. James Young, Esq. Alexander Eugene Mackay, M.D., R.N. Rev. William G. Blaikie, D.D. Henry Cheyne, Esq., W.S. Alex. Mackenzie Edwards, Esq., F.R.C.S.E. Walter Boyd M‘Kinlay, M.D. John P. Macartney, M.D. Edmund Ronalds, Ph.D. Thomas C. Archer, Esq. James Hector, M.D. Nicholas Alex. Dalzell, Esq. Hon. Lord Barcaple, LL.D. Rey. Robert Boog Watson. Robert Campbell, Esq., Advocate. ° H. F. C. Cleghorn, M.D. John Stuart Blackie, Esq., Professor of Greek. Edward Meldrum, Esq. Charles Lawson, Esq. James Hannay, Esq. 822 LIST OF ORDINARY MEMBERS. Date of Election. 1863 Alex, Peddie, M.D. Right Hon. Lord Dunfermline, Colinton House. William Jameson, Esq. William Brand, Esq., W.S. Murray Thomson, M.D. John Young, M.D. David Page, Esq. J. G. Wilson, M.D. J. Matthews Duncan, M.D. George R. Maitland, Esq., W.S. W. Dittmar, Esq. Rev. Dr Robert Nisbet, one of the Ministers of Edinburgh. Honourable Lord Ormidale. J.D. Everett, Professor of King’s College, Windsor, Nova Scotia. Honourable G. Waldegrave Leslie. Honourable Charles Baillie, Lord Jerviswoode. James Sanderson, Esq. Charles Cowan, Esq. John Alex, Smith, M.D. 1864 Alex. Crum Brown, M.D., D.Sc. Alex. Wood, M.D. Andrew Wood, M.D. Robert William Thomson, Esq., C.E. James David Marwick, Esq. Rev. Daniel F. Sandford. Robert S. Wyld, Esq., W.S. Peter M‘Lagan, Hsq., of Pumpherston. William Lindsay, Esq. W. Y. Sellar, M.A., Professor of Humanity. Robert Hutchison, Esq., Carlowrie Castle. Rev, John Hannah, D.D., Glenalmond. William Wallace, Ph.D. Robert Dyce, M.D., Professor of Midwifery, Aberdeen. Arthur Abney Walker, Esq. John Foulerton, M.D. ( 823°) NON-RESIDENT MEMBER, “ELECTED UNDER THE OLD LAWS, Sir Richard Griffiths, Bart., Dublin. LIST OF HONORARY FELLOWS. His Majesty the King of the Belgians. His Royal Highness the Prince of Wales. FOREIGNERS (LIMITED TO THIRTY-SIX). Louis Agassiz, Cambridge, Massachusetts. Alexander Dallas Bache, Washington. J.B. A. L. L. Elie de Beaumont, Paris. Victor Cousin, Do. Jean Baptiste Dumas, Do. Charles Dupin, Do. Christien Gottfried Ehrenberg, Berlin. Johann Franz Encke, Do. Pierre Marie Jean Flourens, Paris. Frangois Pierre Guillaume Guizot, Do. Wilhelm Karl Haidinger, Vienna. Christopher Hansteen, Christiania. Johann Friedrich Ludwig Hausmann, Gottingen. J. Lamont, Munich. Urbain Jean Joseph Leverrier, Paris. Baron Justus von Liebig, Munich. Carl Friedrich Philip von Martius, Do. Henry Milne- Edwards, Paris. Lambert Adolphe Jacques Quetelet, Brussels. Henri Victor Regnault, Paris. Prof. Henry D. Rogers, Glasgow. Gustav Rose, Berlin. B. Studer, Berne. Friedrich George Wilhelm Struve, Pulkowa. VOL. XXIII. PART III. 10 L LIST OF HONORARY FELLOWS. BRITISH SUBJECTS (LIMITED TO TWENTY, BY LAW se John Couch Adams, Esq., George Biddell Airy, Esq., Michael Faraday, Esq., Thomas Graham, Esq., Sir William R. Hamilton, Sir John Frederick William Herschel, Bart., Sir William Jackson Hooker, William Lassell, Esq., Rey. Dr Humphrey Lloyd, Sir William E. Logan, Sir Charles Lyell, Bart., Sir Roderick Impey Murchison, Richard Owen, Esq., Sir John Richardson, M.D., Earl of Rosse, William Henry Fox Talbot, Esq.., Rev. Dr William Whewell, Cambridge. Greenwich. London. Do, - Dublin. Collingwood. Kew. Liverpool. Dublin. London. Do. Do. Do. Lancrig, Westmoreland. Parsonstown. Lacock Abbey, Wiltshire. Cambridge. ( 825 ) LIST OF FELLOWS DECEASED AND RESIGNED, FROM NOVEMBER 1861 TO NOVEMBER 1864. HONORARY FELLOWS DECEASED. His Imperial Highness the Archduke John of Austria, His Royal Highness the Prince Consort. Jean-Baptiste Biot, Paris. Hilert Mitscherlich, Berlin. Baron Giovanni Plana, Turin. ORDINARY FELLOWS DECHASED. James Pillans, Esq., Professor of Humanity. William Somerville, M.D., F.R.S. Leonard Horner, Esq. Alexander Maconochie Welwood, Hsq., 0f Meadowbank. Robert Bald, Esq., Civil Engineer. Thomas Stewart Traill, M.D., Professor of Medical Jurisprudence. James Keith, M.D., F.R.C.S.E. John Russell, Esq., P.C.S. Andrew Fyfe, M.D., Professor of Medicine and Chemistry, King’s College, Aberdeen, Admiral Norwich Duff. James Pillans, Esq. James Walker, Esq., Civil Engineer. Honourable Lord Wood. James Russell, M.D. Arthur Connell, Esq., Professor of Chemistry, St Andrews, David Boswell Reid, M.D. Robert Allan, Esq., Advocate. Robert Morrieson, Esq. Archibald Robertson, M.D., F.R.S. Major-General Swinburne, of Marcus. James Forsyth, Esq., of Dunach. John Cockburn, Esq. George Smyttan, M.D. James Miller, Esq., Professor of Surgery. J. Burn Murdoch, Esq., Advocate, of Gartincaber. Patrick Newbigging, M.D. Robert Dundas Thomson, M.D. Beriah Botfield, Esy., Norton Hall, Northamptonshire. James P. Fraser, Esq. RESIGNATIONS. Rev. V. Grantham Faithfull. D. R. Hay, Esq. Robert Maclachlan, Esq. ( 826 ) 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. 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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. Stockholm, Royal Academy of Sciences. St Petersburgh, Imperial Academy of Sciences. M. Kupffer. Pulkowa Observatory. Turin, Royal Academy ot Sciences. Turin, M. Michelotti. Venice, Royal Institute. Vienna, Imperial Academy of Sciences. Geological Society. UNITED STATES OF AMERICA. Boston, the Bowditch Library. Academy of Arts and Sciences. New York State Library. Philadelphia, American Philosophical Society. ‘Academy of Natural Sciences. Yale College, Professor Silliman. Washington, the Smithsonian Institution. (All the Honorary and Ordinary Fellows of the Society are entitled to the Transactions and Proceedings.) 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Abstracts of Principal Lines of Spirit-levelling in England. With plates. Col. Sir Henry James. 1861. 4to. Przefationes et Epistole Editionibus Principibus Auctorum Veterum Preposite, curante Beriah Botfield. 1861. 4to. Von J. Overbeck. By Smithsonian Contributions to Knowledge, Vol. xii. 1860. 4to. Alloys of Copper and Zinc. By Frank H. Storer. 1860. 4to. Translation of Gauss’s “ Theoria Matus,” with an Appendix. By Charles Henry Davies. 1857. Ato. 829 DONORS. The Greenwich Observatory. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. The Society. Ditto. Ditto. Ditto. The Institute. Ditto, The Society. The Institute, Ditto. The Observatory. The Academy. Ditto. Roy. Saxon Acad. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. Ditto. The Society, The Ord. Survey. The Author. The Institution. The Author. Ditto. 830 LIST OF DONATIONS. - DONATIONS. Absorption and Radiation of Heat by Gases and Vapours. By John Tyndall, F.R.S. 1861. 4to. 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Report of the Topographical and Geographical Exploration of the Western Dis- tricts of the Nelson Province, New Zealand. 1861. 8vo. Proceedings of the Academy of Natural Sciences, Philadelphia. Quarterly Journal of the Geological Society. No. 68. 8vo. Abstracts of the Geological Society of London. No. 72. 8vo. Monthly Notice of the Royal Astronomical Society. November 1861. Monthly Returns of Births, Deaths, and Marriages. November 1861. On the Concrete used in the late Extension of the London Docks. Robertson, C.E. 8vo. An Investigation into the Theory and Practice of Hydraulic Mortar. Robertson, C.E. 8vo. 8vo. 8vo. 8vo. By George By George 833 DONORS. The Royal Univ. of Christiania. Ditto, Ditto. Ditto. Ditto. Ditto. © Ditto. Ditto. Ditto. Ditto. Ditto. The Academy. The Society. The Author, The Society. The Academy. Ditto. The Society, Ditto. Ditto. The Institute. The Ro. Acad. of Sci., St Petersb. Ditto. Ditto. The Academy. Ditto. Ditto. Ditto. The Observ. of St Petersburg. 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Voli wiz Nok: February 17, 1862. Manual of Civil Engineermg. By William John Macquorn Rankine. 1862. 8vo. Proceedings of the Royal Horticultural Society. Vol. ii. No. 2. 8vo. List of the Fellows of the Royal Horticultural Society, corrected to January 1862. 8vo. Proceedings of the Royal Society of London. Journal of the Chemical Society. Vol. xv. No.1. 8vo. Journal of the Royal Dublin Society. Nos. xx.-xxili, 8vo, Monthly Notices of the Royal Astronomical Society. Vol. xxii. No.3. 8vo. Abstracts of the Proceedings of the Geological Society of London, No, 75. 8vo. Ofversight af Kongl. Vetenskaps-Akademiens férhandlingar. 1860. 4to. Voliexa i eNom yim 18ivo: Kongliga Svenska Vetenskaps-Akademiens handlingar. 1859. 4to. Kongliga Svenska Fregatten Eugenies Resta omkring Jorden under befal af C. A. Virgin ’aren 1851-53. Botanik Haft ii, Part 2. Zoologi Haft x., Part 5. Fysik Haft viii., Part 2. 4to. DONORS. The Highland and Agri. Society. The Society. Ditto. Ditto. Ditto. Ditto. Ditto. 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The Journal of Agriculture and the Transactions of the Highland and noe cultural Society of Scotland, No. 76. 8vo. Quarterly Return of the Births, Deaths, and Marriages registered in the Divisions, Counties, and Districts of Scotland. No, xxvii. 8vo. Supplement to the above. Supplement to the Monthly Returns of the Births, Deaths, and Marriages registered in the eight principal towns of Scotland. Year 1861. 8vo, Monthly Return of the Births, Deaths, and Marriages registered in the eight principal towns of Scotland. January 1862. 8vo. Illustrations of the genus Carex. By Francis Boott, M.D. Part ii. Tab. 311-411. Folio. March 17, 1862. History of the University of Edinburgh from the Foundation. By Andrew Dalzel, Professor of Greek, With Memoir of the Author. Cosmo Innes, Two vols. 1862. Reise der dsterreichischen Fregatte Novara um die Erde in den Jahren 1857-1859, unter den Befehlen des Commodor B. von Wiillerstorf Urbair. Zwei Bander, Wien, 1861. 8vo. 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A Acari, existence of, between the Laminz of Mica in optical contact, 95. Aeriforms, the Law of the Volumes of, 581, Agrarian Laws of Lycurgus, 425. AtiMan (Professor). On a Pre-brachial stage in the Development of Comatula, and its importance in relation to certain aberrant forms of extinct Crinoids, 241. Arran, great Drift Beds, with shells, in the south of, 523. Atmosphere, Polarisation of, 211. Auriculo- Ventricular Valves, on the structure and action of, 761. B Beryl, Pressure Cavities in, 39. Buacxie (Professor), On the Agrarian Laws of Lycureus, and one of Mr Grors’s Canons of His- torical Criticism, 425. Brewster (Sir Davip), K.H. On the pressure cavities in Topaz, Beryl, and Diamond, and their bearing on Geological Theories, 39, On the existence of Acari between the Laminz of Mica in optical contact, 95. On certain Vegetable and Mineral formations in Calcareous Spar, 97. On the Structure and Optical Phenomena of ancient Decomposed Glass, 193. On the Polarisation of Light by rough and white surfaces, 2085. Observations on the Polarisation of the Atmosphere, made at St Andrews in 1841, 1842, 1843, 1844, and 1845, 211. Description of the Lithoscope, an instrument for distinguishing Precious Stones and other bodies, 419. Brown (A. Crum), M.D. On the Theory of Isomeric Compounds, 707. C Calcareous Spar, certain Vegetable and Mineral formations in, 97. Chondracanthus Lophu, on the Structure of, 67. Cho caudata, Zoological Characters of, 185. Coelenterata and Molluscoida, Morphological Relationships of, 515. Comatula, Pre-brachial stage in the Development of, 241. Commensurables, on the Theory of, 721. Cooling of the Earth, 157. D Datmanoy (James). On a difficulty in the Theory of Rain, 29. Davy (Joun), M.D., F.R.SS.L. & E. On the Rain-fall in the Lake District in 1861, with some observations on the composition of Rain-water, 53. On the freezing of the Egg of the Common Fowl, 508. vol, XXII. PART "I. 10 u 858 INDEX. Diamond, Pressure Cavities in, 39. Drift Beds in the South of Arran, 523. Duncan (J. Mattuews), M.D. On the variations of the Fertility and Fecundity of Women, according to age, 475. 10} Earth, Secular Cooling of, 157. Egg, on the Freezing of the, 505. Everett (Professor Josepu D.), M.A. Investigation of an expression for the Mean Temperature of a Stratum of Soil, in terms of the time of year, 21. F Fagnani’s Theorem, 285. Frreuson (Professor Apam), Biographical Sketch of, 599. Fertility and Fecundity of Women, according to age, 475. Firola, Anatomy of the Genus, 189. Forzes (James D.), LL.D., D.C.L. Experimental inquiry into the Laws of the Conduction of Heat in bars, and into the Conducting Power of Wrought Iron, 133. Freezing of the Egg of the Common Fowl, 505. G Glass, Decomposed, Structure and Optical Phenomena of ancient, 193 H Heat, Laws of the Conduction of, in Iron, 133. Heteropoda, Anatomy and Classification of, 1. Hot-Springs in the Pyrenees, Temperature of, 451. I Iron, conducting Power of Wrought, 133. Isomeric Compounds, on the Theory of, 707. J Jackson (R. E. Scoreszy), M.D. On the Influence of Weather upon Disease and Mortality, 299. On the Temperature of Certain Hot-Springs in the Pyrenees, 451. K KeEtianp (Professor). On the Limits of our Knowledge respecting the Theory of Parallels, 433. ———— On Superposition, 471. L Lerneopoda Dalmanni, on the Structure of, 77. Light, Polarisation of, by rough and white surfaces, 205. Lithoscope, Description of, 419. Lycurevus, Agrarian Laws of, 425. M Macponatp (Joun Denis), R.N., F.R.S., Surgeon of H.M.S. “ Icarus.” On the Anatomy and Classification of the Heteropoda, 1. On the Representative Relationships of the Fixed and Free Tunicata, regarded as two Sub-classes of Equivalent Value, with some General Remarks on their Morphology, 171. Notes on the Anatomy of the Genus Firola, 189. INDEX. S09 Macponap (Joun Denis), R.N., F.R.S., Surgeon of H.M.S. “Icarus.” On the Zoological Characters of the Living Clio caudata, as compared with those of Clio borealis given in Systematic Works, 185. On the Morphological Relationships of the Molluscoida and Ceelenterata, and of their Leading Members, inter se, 515. Macvicar (Rev. J. G.), D.D. The Law of the Volumes of Aeriforms extended to Dense Bodies, 581. Magnetic Calms, Karth Currents during, 355. Molluscoida and Celenterata, on the Morphological Relationships of, 515. Murr (Jouy), D.C.L., LL.D. Some Account of the Recent Progress of Sanskrit Studies, 253. On the Principal Deities of the Rigveda, 547. N Numbers, Theory of, 4 5. FP Parallels, Theory of, 433. - Petroleum (American), Volatile Constituents of, 491. Perricrew (James B.), M.D. On the Structure and Action of the Auriculo-Ventricular Valves, 761. Placenta and Umbilical Cord, Structure of, 349. Plummet, Deflection of, due to Solar and Lunar Attraction, 89s Polarisation of the Atmosphere, 211. of Light by rough and white surfaces, 205. Pyramid (Great), On the Reputed Metrological System of the, 667. R Rain, Difficulty in the Theory of, 29. Rain-Fall in the Lake District in 1861, 53. Rankine (W. J. Macauvorn), LL.D. On the Density of Steam, 147. Rigveda, on the Principal Deities of the, 547. Ronatps (Epmunp), Ph.D. On the most Volatile Constituents of American Petroleum, 491. S Sane (Epwarp). On the Deflection of the Plummet due to Solar and Lunar Attraction, 89. On the Theory of Commensurables, 721. Sanskrit, Recent Progress of, 253. SELLER (Witt1aM), M.D. Memoir of the Life and Writings of Rozert Wuytt, M.D., Professor of Medicine in the University of Edinburgh, from 1747 to 1766, 99. Simpson (Professor J. Y.), M.D. On the Anatomical Type of Structure of the Human Umbilical Cord and Placenta, 349. Smart (Joun), M.A. Biographical Sketch of Apam Frreuson, LL.D., F.R.S.E., Professor of Moral Philosophy in the University of Edinburgh, 599. Smyru (Professor C. Pazzi). On the Great Refracting Telescope at Elchies, in Morayshire, and its Powers in Sidereal Observation, 371. On the Reputed Metrological System of the Great Pyramid, 667. Soil, Expression for the Mean Temperature of a Stratum of, 21. Steam, Density of, 147. Stewart (Batrour), M.A., F.R.S. On Earth-Currents during Magnetic Calms, and their Connec- tion with Magnetic Changes, 355. On Sun-Spots and their Connection with Planetary Configurations, 499. Sun-Spots, in connection with Planetary Configurations, 499. Superposition, 471. 860 INDEX. ale Tatsor (H. F.) On the Theory of Numbers, 45. ————— On Fagnani’s Theorem, 285. Telescope, Great Refracting, at Elchies, 371. Temperature of a Stratum of Soil, in terms of the time of year, 21. Temperature of Hot-Springs, 451. Tuomson (Professor Wirtiam), LL.D. On the Secrlan Cooling of the Earth, 157. Topaz, Pressure Cavities in, 39. | Tunicata, Representative Relationships of the Fixed and Free, 171. Turner (Wm.) M.B. Lond., and H. 8S. Wirson, M.D. On the Structure of the Chondracanthus Lophii, with Observations on its Larval Form, 67. On the Structure of Lerneopoda Dalmanni, with Observations on its Larval Form, 77. U Umbilical Cord, Anatomical Type of the Structure of, 349. W Watson (Rev, Rozert Booa), B.A. On the Great Drift Beds with Shells, in the South of Arran, 523. Weather, Influence of, upon Disease and Mortality, 299. Wuyrt (Professor Rozert), M.D., Memoir of Life and Writings of, 99. Women, Fertility and Fecundity of, according to Age, 475. END OF VOLUME TWENTY-THIRD. 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