ee ean Digitized by the Internet Archive in 2009 with funding from University of Toronto http://www. archive.org/details/proceedingscambr07camb PROCEEDINGS Cambridge Philosophical Society. VOLUME VII. — Cambringe: Riphieit “PRINTED. ‘BY C. J. CLAY, MAL AND sons, eee AT ‘THE UNIVERSITY PRESS. Ve PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. VOLUME VIL. OCTOBER 28, 1889—May 30, 1892. Cambridae : PRINTED AT THE UNIVERSITY PRESS, AND SOLD BY DEIGHTON, BELL AND CO. AND MACMILLAN AND CO. CAMBRIDGE BELL AND SONS, LONDON. 1892 eS 7 a PAT cilt eS WHY “WO »* ? 2 LADLHSTOCOITH iT CLES coy, Xt THLLIO® > & tp iG. \ Fy ie. a << | ; | = P | ae Pn oy: | ree) ERO | 7 » ? : Ci, ie Alf v7 oa Pee rigs dain Bana LTIREVIAY wT PA Gat ta hind ave eC » 09 A oe Auta avi a Una o > OUvaE 4x08 axh Tot, aray | CONTENTS. vor. Vit. October 28, 1889. The President’s Address . 3 F ‘ : On Newton’s Description of Orbits, By Dr C. Taylor . ; : On impulsive Stress in Shafting, and on Repeated Loading. By Pro- fessor Karl Pearson . ; : : : : : On Liquid Jets and the Vena Bart Gahan By H. J. Sharpe November 11, 1889. On the Varieties and Geographical Distribution of the common Dog- Whelk (Purpura lapillus L.). By A. H. Cooke : On the Increase in Thickness of the Stem of the Cucuricadee By M.C. Potter. : , : 3 On the Spinning Apparatus of G Gamat Sided By C. Warburton . On a new Result of the Injection of Ferments. By E. H. Hankin November 25, 1889. On the Relation between "iti and Conductivity of Electrolytes. By W. N. Shaw ; : : On the Finite Deformation on a Thin Elastic Plate. By A. E. H. Love On a Solution of the Equations for the Equilibrium of Elastic Solids having an Axis of Material Symmetry, and its application to Rotating Spheroids. By C. Chree : g F : On the Concomitants of Three Ternary Quadrics. By H. F. Baker PAGE vil Contents. January 27, 1890. On Non-Euclidian Geometry. By Professor Cayley On a Scheme of the Simultaneous Motions of a system of Risa con- nected Points, and the Curvatures of their Trajectories. By J. Larmor February 10, 1890. On the perceptions and modes of feeding of fishes. By W. Bateson Notes on Lomatophloios macrolepidotus (Goldq.). By A. C. Seward On the origin of the embryos in the ovicells of Cyclostomatous Polyzoa. By S. F. Harmer February 24, 1890. On vehicles used by the old Masters in Painting. Part I. A. P. Laurie On the Action of the Copper Zinc Couple on dilute solutions of Nitrates and Nitrites, NaHO and KHO being absent. By James Monckman On certain Points specially related to Families of Curves. By J. Brill . March 10, 1890. On the germination of Acacia sphaerocephala, By W. Gardiner Additional note on the thickening of the stem in the Cucurbitacee. By M. C. Potter : ‘ . ‘ Note on the action of Rennie Ae Fibrin- eement By A. S. Lea and W. L. Dickinson On some Skulls of Egyptian Marna Cats. By W. Bateaast April 28, 1890. On the series in which the exponents of the powers are the pentagonal numbers. By Dr Glaisher : On the Influence of Electrification on Feoplca By J. fone On Sir William Thomson’s estimate of the Ray of the Earth. By A. E. H. Love . 3 ; ‘ . PAGE 35 36 42 43 48 48 52 57 65 65 67 68 69 69 72 Contents. May 12, 1890. On the action of Nicotin upon the Fresh-water Crayfish. By J. N Langley ; : 5 : ; é : On a new species of Phy Te Arthur E, Shipley , : . On the action of the ERD y Muscles of the Heart. By J. George Adami ; On some living specimens of a ease Planar ian fund. in Gombe is By 8. F. Harmer May 26, 1890. On Solution and Crystallization. III. Rhombohedral and Hexagonal Crystals. By Professor Liveing On the Curvature of Prismatic Images, and on iltiet ce s PEG Rlencoit: By J. Larmor On some theorems connected aa Sein eine Quad. MBy R. PacHben October 27, 1890. On some Compound Vibrating Systems. By C. Chree . November 10, 1890. Note on the principle upon which Fahrenheit constructed his Thermo- metrical Scale. By Professor Arthur Gamgee . On: Variations in the Floral Symmetry of certain Flowers Peviae Irregular Corollas. By William Bateson and Miss Anna Bateson . On the nature of the relation between the size of certain animals and the size and number of their sense-organs. By H. H. Brindley On the Oviposition of Agelena labyrinthica. By C. Warburton 3 Supplementary list-of spiders taken in the neighbourhood of Cambridge. By C. Warburton , November 24, 1890. On the beats in the vibrations of a revolving cylinder or bell. By G. H. Bryan ‘ , On Liquid Jets. By H. J. Siar pe “ Note on the Application of Quaternions to as Bigion of Laplace's Equation. By J. Brill On a simple model to illustrate certain feta in dete cay with a view to Navigation. By A. Sheridan Lea Note on a paper relating to the Theory of F aeerans, By W. Burnside vil PAGE 94 98 vill Contents. January 26, 1891. On the Electric Discharge through rarefied gases without electrodes. By Professor J. J. Thomson ‘ : i On the Laws of the Diffraction at equate Sur nee By J. Larmor On the effect of Temperature on the Conductivity of Solutions of Sulphuric Acid. By Miss H. G. Klaassen February 9, 1891. On Rectipetality and on a modification of the Klinostat. By Miss Dorothea F. M. Pertz and Mr Francis Darwin On the Occurrence of Bipaliwm Kewense, Moseley, in a new ; Loca with a Note upon the Urticating Organs. By A. E. Shipley . On the Medusze of Afdlepora and their relations to the medusiform gonophores of the Hydromeduse. By 8. J. Hickson On the Development of the Oviduct in the Frog. By E. W. MacBr ee February 23, 1891. On Tidal Prediction—a general account of the theory and methods in use and the accuracy attained. By Professor G. H. Darwin On Quaternion Functions, with especial Reference to the Discussion of Laplace’s Equation, By J. Brill . March 9, 1891. On the disturbances of the body temperature of the fowl which follow total extirpation of the fore-brain. By J. George Adami ; On the nature of Supernumerary Appendages in Insects. By W. sateson E 5 : ; On the Orientation of Sees By Theo. 'T, Groom : On some experiments on blood-clotting. By Albert 8. Griinbaum. May 4, 1891. On the most general type of electrical waves in dielectric media that is consistent with ascertained laws. By J. Larmor 2 : On a mechanical representation of a vibrating electrical system, anit its radiation. By J. Larmor. On the Theory of Discontinuous Fluid Motibns: in ito dimansiall By A. E. H. Love : : é : On thin rotating isotropic disks. By C. Chree PAGE 131 131 137 141 142 147 148 151 151 164 165 175 201 = ae eS ae Contents. May 18, 1891. By A. H. Cooke Exhibition of models of double supernumerary oeedaee in Tiisetee also of a mechanical method of demonstrating the system upon which the Symmetry of such are is usually arranged. By W. Bateson : ‘ On the nature of the Birolos Yy processes in veaine Palgiod. By S. F. Harmer June 1, 1891. On the part of the parallactic class of inequalities in the moon’s motion, which is a function of the ratio of the mean motions of the sun and moon. By Ernest W. Brown é On Pascal's Hexagram. By H. W. Richmond On a Linkage for describing Lemniscates and other Tae of Conic Sections. By R.S. Cole . : On some experiments on liquid electr up in vacuum Penne By C. ath Note on a problem in the Linear Conduction of Heat. By G. H. Bryan October 26, 1891. On the Absorption of Energy by the Secondary of a Transformer. By Professor J. J. Thomson , : : : On an experiment of Sir Humphry Davy’ s. By G. F. C. Searle Some notes on Clark’s Cells. By R. T. Glazebrook and 8. Skinner Illustrations of a Method of Measuring Ionic Velocities. By W. C. D. Whetham . ; ; : On Gold-Tin Alloys. By A. P. Laurie November 9, 1891. Note on a Peripatus from Natal. By A. Sedgwick On Variations in the Colour of Cocoons (Saturnia carpini and Erio aie lanestris), with reference to recent theories of Protective Coloration. By W. Bateson . : d : Exhibition of Phylloxera ee iw. tee A. E. Shipley The Digestive Processes of Ammocetes. By Miss R. Alcock . : On the Reaction of certain Cell-Granules with Methylene-Blue. By W. B. Hardy : : ix PAGE 215 x Contents. November 23, 1891. The Self-Induction of Two Parallel Conductors. By H. M. Macdonald. The Effect of Flaws on the Strength of Materials. By J. Larmor The Contact Relations of certain Systems of Circles and Conics. By W. McF. Orr a . : ‘ On Liquid Jets under Grav oe By H. J. Sharpe . Theory of Contact- and Thermo-Electricity. By J. Parker February 8, 1892. On Long Rotating Circular Cylinders. By C. Chree February 22, 1892. Some preliminary notes on the anatomy and habits of Aleyonium digitatum. By Sydney J. Hickson . : b On the action of Lymph in producing ieee Clotting. By Dr Lewis Shore On the fever produced by the ecm of sailed ¥i ei Mesckntoa cultures into rabbits. By E. H. Hankin and A. A. Kanthack Note on the Method of Fertilisation in Jvora. By J. C. Willis March 7, 1892. Some Experiments on Electric Discharge. By Professor Thomson On the perturbation of a comet in the neighbourhood of a planet. By G. H. Darwin . ; : : : ; y On the change of zero of Thanet cies By C. T. Heycock On the Elasticity of Cubic Crystals. By A. E. H. Love Changes in the dimensions of Elastic Solids due to given sateen of forces. By C. Chree On the law of distribution of valoeities 5 ina ea oe moving snolgeniee By A. H. Leahy May 2, 1892. The application of the Spherometer to Surfaces which are not Spherical. By J. Larmor PAGE 259 262 262 264 269 283 305 308 311 313 314 314 319 319 319 322 .. 327 Contents. May 16, 1892. ecent advances in Astronomy with ao Illustrations. By i. F. Newall : Jn the pressure at which the Bene strehigtli of a gas is a minimum. By Professor Thomson Jn a compound magnetometer ee eae he miaweece apne af iron and steel. By G. F.C. Searle . ; ae ‘ , May 30, 1892. In the hypothesis of a liquid condition of the Earth’s interior con- _ sidered in connexion with Professor Darwin’s theory of the genesis of the Moon. By O. Fisher ; n Gy nodicecism in the Labiatae. By J. C. Willis ; n the Steady Motion and eas of — Systems By UA; B. Basset : : ; : xl PAGE 330 330 330 335 348 351 4 _ ~ in ee ahgesban'y ROPE DT woh lit nrApoadinth dl! iitovede: fe : wii ‘ i sone two ite ’ i un ow ete ae } toh) jaa \h lhc blag ea lol die earn i” R withers 43 vil = fl id at nthe oie (tl wiitntare” inte wertolt a Wg ead Page 344, Tie 14, for —— 773 read t 773mg a PROCEEDINGS OF THE Cambridge Philosophical Society. THE FOUNDATION AND EARLY YEARS OF THE SOCIETY: AN ADDRESS DELIVERED BY - JOHN WILLIS CLARK, M.A. Trin. Coll. President, ON RESIGNING OFFICE, 27 October, 1890. WHEN the President of a Society lays down his office, it is usual that he should take a more or less extended view of the past history of the body with which he has been connected, thank his officers, and anticipate a brilliant future from the efforts of his successor. I have no wish to depart from these excellent _ precedents. I am using no empty phrase when I say that I felt .< ~~ a it a distinguished, and not wholly deserved, honour to be chosen to succeed my dear friend Mr Coutts Trotter—one who by his intellectual attainments, by the breadth of his sympathies, and by his unwearied efforts to develop the scientific side of University training, was so distinctly marked out as the proper person to preside over a Philosophical Society. I, on the contrary, though the office which I have held for so many years in connection with the New Museums may have enabled me to be a promoter of a il Address of Mr J. W. Clark, President, science in others, have few claims to be called a man of science myself; and had I not been ably supported by the officers of the Society, the high reputation which we have so long maintained might have been somewhat tarnished by the appearance of a name so humble as mine in the list of Presidents. The Secretaries, however, have taken good care to provide our meetings with papers excellent in matter and varied in character; and the Treasurer has been most energetic and successful in improving our financial position. The Society has now been in existence for rather more than seventy years; and I may say, without fear of contradiction, that though our position is different from what it was in days which many persons can remember, we still hold our own in public estimation—still exercise a powerful influence in the University. The time has not yet come for the history of the Society to be written ; but it has occurred to me that it might be interesting to place on record a few notes respecting its origin, and the early years of its corporate life. In the Easter Vacation of 1819 Professor Sedgwick—who had been elected to the Woodwardian Chair in the May of the previous year—was taking a tour in the Isle of Wight, and collecting materials for his first course of lectures, which he delivered in the ensuing Easter Term. He was accompanied by Mr Henslow of St John’s College, and as the two friends walked and talked they deplored the want of some place in Cambridge to which those in- terested in science might resort, with the certainty of meeting per- sons of similar or kindred tastes, and where they might learn what was being done abroad. Their “first idea,” we are told, “was to establish a Corresponding Society, for the purpose of introducing subjects of natural history to the Cambridge students”; and on their return to the University they wrote “to their respective friends for their encouragement and support’.” Easter had fallen late that year (11 April), and therefore the Easter Term would be short. Sedgwick, moreover, was fully occupied with his lectures. The idea too, was novel, and in those days novelty, especially when it took the form of a combination for the prosecution of something foreign to the normal course of study in the place, was sure to encounter disapprobation, if not active opposition. Delay, therefore, was unavoidable; and it need excite no surprise that the Michaelmas Term was far advanced before the following notice was circulated, at the suggestion, it is said, of Dr E. D. Clarke, Professor of Mineralogy, who entered into the scheme with characteristic enthusiasm, and was always spoken of by Sedgwick as the founder of the Society. 1 Memoirs of the Rev. John Stevens Henslow, by the Rev, L. Jenyns. 8vo, Camb, 1862, p. 17. on resigning office, 27 October, 1890, ili CamBRIDGE, Oct. 30, 1819. The resident Members of the University, who have taken their first degree, are hereby invited to assemble at the Lecture-Room, under the Public Library, at twelve o'clock, on Turspay, Nov. 2, for the purpose of instituting a Society, as a point of concourse, for scientific communications. Hon. Geo. Neville’. Rey. A. Carrighan. [Joh.] Bishop of Bristol’. — T. Jephson. [Joh.] Dean of Carlisle’. a Baw: J. Holmes. [ Pet. | Dr Kaye’. — W. Mandell. [Qu.] Dr Davy’. *_ J. Hustler”. Dr Webb*. * —_ J. Brown. [Trin.] Dr E. Clarke’. G. Macfarlan. [Trin. } Dr Haviland’. *W, Hustler”. Dr Ingle’. *Rev. J. Lamb”. *Prof. Monk”. — T. Hughes”. Prof. Cumming". * — J. Evans. [Cla.] Prof. Sedgwick. * __ G. Peacock”. Prof. Lee”. — fF. Fallows”. R. Woodhouse”. — J. Whittaker”. Rey. T. Kerrich™. *__ RR. Crawiey. [Magd.] 1 Master of Magdalene 1813—53; Dean of Windsor 1845—53. 2 Will. Lort Mansel, D.D., Master of Trinity 1788—1820; Bp. of Bristol 1808—20. 3 Isaac Milner, D.D., President of Queens’ 1788—1820; Dean of Carlisle 1793 —1820. 4 John Kaye, D.D., Master of Christ’s 1814—30; Bp. of Bristol 1820—27; of Lincoln 1827—83. > Martin Davy, M.D., Master of Gonville and Caius 1803—39. 6 Will. Webb, D.D., Master of Clare 1815—56. 7 Edw. Dan. Clarke, LL.D., Professor of Mineralogy 1808—22. 8 Joh. Haviland, M.D., Regius Professor of Medicine 1817—3S1. 9 Tho. Ingle, M. 'D. Pet. 10 Ja. Hen. Monk, B.D. Trin., Regius Professor of Greek 1808—23; Bp. of Gloucester 1830—56. 1 Ja. Cumming, M.A. Trin., Professor of Chemistry 1815—61. 12 Sam. Lee, M.A. Queens’, Professor of Arabic 1819—31. 13 Rob. Woodhouse, M.A. Cai., Lucasian Professor 1820—22; Plumian Professor 1822—28. 14 Tho. Kerrich, M.A. Magd., Principal Librarian 1797—1828. 145 Ja. Devereux Hustler, B.D. Trin. 16 Will. Hustler, M.A. Jes., Registrary 1816—32. 17 Master of Corpus Christi 1822—50. 18 Tho. Smart Hughes, B.D. Emm., Christian Advocate, 1822. 19 Geo. Peacock, M.A. Trin., Lowndean Professor 1836—58, Dean of Ely 1839—58. 20 Fearon Fallows, M.A. Joh., Director of the Obsexyakary at the Cape of Good Hope 1820—31. 21 Joh. Will. Whittaker, M.A, Joh. a2 iv Address of Mr J. W. Clark, President, Rev. H. Robinson”. J. Henslow™. *W. Whewell*. It is interesting to remark that the thirty-three persons who signed the above notice differed widely in their pursuits and opinions, and were drawn from eleven Colleges. Among them are six Heads, six Professors, (of Mineralogy, Geology, Chemistry, Medicine, Greek and Arabic), and eleven tutors, or assistant- tutors”. It is clear, therefore, that from the first there was nothing sectarian about the Society; it represented no clique; its sup- porters were not distinguished by any singularity of dress, de- meanour, or speech; they merely recognised the need of extending the studies of the University in a scientific direction. No detailed report of the proceedings at this preliminary meeting was drawn up, but on the next day a brief memorandum was circulated in the University. It ran as follows: CamBripGE, Nov. 3, 1819. At a Meeting of the Members of this University, which took place on Tuesday, November 2, in the Lecture-Room under the Public Library, in consequence of a requisition to that effect, signed by a number of distinguished Individuals of the different Colleges, the following Resolutions were carried unanimously : 1,—That Dr Haviland be called to the chair. Proposed by Dr Clarke, and seconded by Mr Kerrich. 2.—That a Society be instituted as a point of concourse for scientific communication. Proposed by Prof. Sedgwick, and seconded by Mr Robinson. 3.—That a Committee be appointed, consisting of the following gentle- men, who shall report to all Members of the University desirous of belonging to the said Society, such regulations as shall appear to them to be proper for the proposed institution : Dr Kaye. Prof. Sedgwick. Dr Clarke. Mr Bridge. Dr Haviland. Mr Jephson. Prof. Farish. Mr Fallows. Prof. Cumming. Proposed by Prof. Monk, and seconded by Mr Hughes. *” Hastings Robinson, M.A. Joh. *3 Professor of Mineralogy 1828—32; of Moral Philosophy 1838—55 ; Master of Trinity 1841—66, *4 Joh. Stevens Henslow, M.A. Joh., Professor of Mineralogy 1822—-28; of Botany 1825—61. Mr Henslow did not formally resign the Professorship of Mineralogy on obtaining that of Botany until the mode of election had been settled by Sir J. Richardson’s award. Memoirs of Henslow, ut supra, p. 29. * To the names of these an asterisk has been prefixed in the above list, cla on resigning office, 27 October, 1890. V 4.—That the thanks of the Meeting be given to Dr Haviland, for his able conduct in the chair. Proposed by Prof. Farish, and seconded by Mr Hughes. N.B. It is requested that all those gentlemen who are desirous of adding their names to the Society previously to the next Meeting, will signify their intention to the Members of the Committee. The Committee to whom this important duty was entrusted must have set about their work without delay, for in less than a week the following “ Regulations ” had been drawn up. The paper containing them is endorsed: “ Report of the Committee appointed to form the regulations of a Society to be instituted in this Uni- versity for Philosophical Communication ; to be read at the first meeting of the Society, on Monday, November 15, at one o’clock, in the Lecture Room under the Public Library.” CaMBRIDGE, November 8, 1819. At a Meeting of the Committee appointed to form the regulations of a Society, to be instituted in this University, for Philosophical Communication, it was resolved : 1. That the Society bear the name of The Cambridge Philosophical Society. bo That this Society be instituted for the purpose of promoting Scientific Enquiries, and of facilitating the communication of facts connected with the advancement of Philosophy. 3. That this Society consist of a Patron, a President, a Vice-President, a Treasurer, two Secretaries, Ordinary and Honorary Members. 4. That a Council be appointed, consisting of the above-mentioned Officers, and five Ordinary Members; three of whom constitute a Quorum : and that no person under the standing of M.A. be of the Council. 5. That the Officers of the Society, with the exception of the Patron, be annually elected by Ballot. 6. That Ordinary Members be chosen from the Graduates of this University by ballot ; their Election being determined by a majo- rity of two thirds of the Electors present. 7. That any person desirous of becoming a Member, be proposed by three Ordinary Members; and his name hung up in the Society’s room, until the third meeting after the proposition has been made. 8. That Honorary Members be proposed by six Ordinary Members, and balloted for accordingly. al 9. 10. 16, We Address of Mr J. W. Clark, President, That the Meetings of the Society be held on a Monday, once in every fortnight during full term. The President to take the chair at seven o’clock, p.m. and to quit it at nine. That the business of each meeting be conducted in the following order : 1. The minutes of the preceding meeting read and approved. 2. Notices of new motions presented. . Members proposed. Members balloted for. Motions on the minutes brought forward and determined. Miscellaneous business. ag, eee ce ens ae Communications read and presents acknowledged. . That all communications be sent to one of the Secretaries. . That nothing be published by the Society which has not been previously approved by the Council. . That all questions involving a difference of opinion, be determined by a majority of Members at the next meeting. . That if the numbers of the votes be equal, the Chairman have a casting vote. . That the annual election of the Officers take place, and the accounts of the Treasurer be passed, at the last meeting of the Society for the year, in the Easter Term. That a Special General Meeting may at any time be called by the Secretary, in consequence either of instructions received from the President, or of a requisition signed by three Ordinary Members. The object must be stated to the Secretary, who shall give to each Member an intimation thereof, stating, three days previously, the time and place of meeting. That the annual Subscription for each member be One Guinea, to be paid in advance, or in lieu of it, a payment of Ten Guineas. . That all persons becoming Members, after the first meeting in 1820, pay an admission fee of Two Guineas. . That Members be at liberty to introduce each a Visitor; besides whom, the President, for the time being, may admit any person, with the limitation specified in the succeeding Resolution. . That no resident Member of the University be allowed to attend more than two meetings of the Society without becoming a Member. on resigning office, 27 October, 1890. vil At the meeting which took place on the 15th November, these draft Regulations were adopted, with some slight changes and additions, which are not without interest : In Rule 4 the number of ordinary members of the Council was increased to seven. To Rule 5, after the words “by ballot,” was added: “but that the President and Vice-President shall not be eligible for more than two years successively ; and that the three Senior Ordinary Members of the Council be changed every year.” To Rule 7 was added: “ But that all Noblemen, Heads of Houses, Doctors, and Professors, be ballotted for when they are proposed.” Rule 18 was omitted ; and a new Rule 20 was drawn up: “That the Chancellor of the University be requested to accept the office of Patron.” The Regulations, as altered, having been adopted by the meet- ing, the Council of the Society for the ensuing year was elected : PRESIDENT. The Rey. W. Farish, B.D. Magd. Coll., Jacksonian Professor. VicE-PRESIDENT. John Haviland, M.D. St John’s Coll., Regius Professor of Physic. SECRETARIES. The Rey. A. Sedgwick, M.A. Trin. Coll., Woodwardian Professor. The Rey. 8. Lee, M.A. Queens’ Coll., Professor of Arabic. TREASURER. The Rey. B, Bridge, B.D., Fellow of Pet. Coll. ORDINARY MEMBERS OF THE COUNCIL. The Rev. E. D. Clarke, LL.D. Jes. Coll., Professor of Mineralogy. J. Catton, B.D. Fellow of St John’s College. — TIT. Turton, B.D. Fellow of Catharine Hall. T. Kerrich, M.A. Magd. Coll., Principal Librarian. R. Woodhouse, M.A. Fellow of Caius College. The Rey. J. Cumming, M.A. Trin. Coll., Professor of Chemistry. R. Gwatkin, M.A. Fellow of St John’s College. We have seen that the meeting at which the above Regulations were adopted is called “the first meeting of the Society.” The Minute Book of the Society, however, takes a different view, and places the birthday of the Society a few weeks later. We there read : “Minutes of the first meeting of the Cambridge Philosophical Society held in the Museum of the Botanic Garden, Mon day, December 13, 1819, Professor Farish in the chair.” Vill Address of Mr J. W. Clark, President, At this meeting Professor Farish delivered an address, as also did Dr E. D. Clarke. His biographer says: ‘Of this scheme [of founding a Philosophical Society at Cambridge} whose direct object was the promotion of science, and its natural tendency to raise the credit of the University, Dr Clarke was of course one of the earliest and one of the most zealous promoters; and as it was thought advisable, that some address should be provided ex- planatory of the design and objects of the Institution, he was requested by a sort of temporary council to draw it up. Accordingly he under- took the task, and his address having been read at the first meeting, was afterwards printed by order of the Society, and circulated with the first volume of their Transactions; although for some reason it was not connected with the volume. Nor did his anxiety for the support and honour of the Society rest here ; he wrote letters to almost all the literary men of his acquaintance, to request their co-operation and support; combated with great spirit in several instances, the opposition that was made to it from others; and during the short remainder of his life, contributed three papers, which were printed in the first volume of their Transactions'.” Dr Clarke’s address is brief, and is chiefly occupied with pointing out the advantage of having a society to gather together scientific observations which, if scattered through journals, might escape notice altogether. It concludes with the following practical sug- gestions: “ Having thus set before the Society the main design and objects of its Institution, the Council beg to call the attention of this Meeting to considerations of a subordinate nature. It will be necessary to provide some place in which the future Meetings may be held, and where a repository may be found for the preservation not only of the archives and records of the Society, but also of such documents, books, and specimens of Natural History, as may hereafter be presented or purchased. The utmost economy will at present be requisite in the management of the Society’s funds; and therefore if the consent of the University could be obtained it would be highly desirable that the expenses of printing the Society’s Transactions should be defrayed by the University. His Royal Highness the Chancellor’ has accepted of the Office of Patron, and his Letter, containing the expression of his approbation, will be read by one of the Secretaries. The present Vice- Chancellor*; our High Steward*; both our Representatives in Parlia- ment’; and many other distinguished Members of the University, who are not resident, have also contributed towards the undertaking ; and there is therefore every reason to hope that the Graduates of this University, who associated for the Institution of the CAMBRIDGE 1 The Life and Remains of the Rev, E. D. Clarke, LL.D. By W. Otter. 4to, Lond, 1824, p. 650. * H. R. H. the Duke of Gloucester, 3 Mr Serjeant Frere, Master of Downing College. 4 Lord Hardwicke. 5 Viscount Palmerston, M.A, St. John’s Coll., and J. H. Smyth, M.A. Trin. Coll. on resigning office, 27 October, 1890. ix PuitosopuicaL Society, by their assiduity and diligence in its support, and by their conspicuous zeal for the honour and well-being of the University, will prove to other times that their Lives, and their Studies, have not been in vain.” At this meeting the designation of the Society was altered, The third Minute runs : “That the words ‘and Natural History’ be added to the second regulation, which will then stand as follows, viz. ‘That this Society be instituted for the purpose of promoting scientific enquiries and of facilitating the communication of facts connected with the advancement of Philosophy and Natural History.’” The change is slight, but not unimportant, for it determined, for many years, the direction of the Society’s labours. Before long, thanks to the enthusiasm and industry of Professor Henslow and Mr Leonard Jenyns, it commenced the formation of a Museum, long the only Zoological Museum in Cambridge ; and the legitimate parent of those collections which I may venture to describe as among the most valued possessions of the University. The Society was now fairly launched; the Syndics of the University Press undertook to publish the Z'vansactions free of charge ; the number of members increased so rapidly that before the end of 1820 it had reached 171; the finances were in so flourishing a condition that £300 was invested in the funds’; and opposition gradually died away. “Among the senior members of the University,” wrote Sedgwick to Herschel, 26 February, 1820, “some laugh at us; others shrug up their shoulders and think our whole proceedings subversive of good discipline; a much larger number look on us, as they do on every other external object, with philosophic indifference ; and a small number are among our warm friends *.” It was further agreed at the first meeting of the Society: “that the High Steward of the University, and the Vice-Chancellor for the time being be Vice-Patrons of the Society” ; and at the second meeting: “that the members of the Cambridge Philosophical Society be designated by the name Fellows of the Cambridge Philosophical Society.” Early in the following year Dr Clarke proposed: “ that the Society be hereafter styled The Cambridge Philosophical and Literary Society.” This proposal was not adopted, as I have always thought, most unfortunately. The name would have cemented a connexion between science and literature from which both would have reaped considerable advantage. As time went on the Transactions of the Society would probably have had a literary division, as is not uncommon on the continent ; and the first object 1 Minutes of the Society, 21 February, 1820. 2 Life of Rev. A. Sedgwick, Vol. 1. p. 209. x Address of Mr J. W. Clark, President, of the Society’s formation—the gathering together of observations and researches that would otherwise be scattered and lost, would have been promoted. For a few months the Society met in the lecture-room of the building on the east side of what was then the Botanie Garden, built in 1784 for the use of the Professor of Botany and the Jack- sonian Professor, and now used by the Professor of Pathology. The selection of Professor Farish as the first President doubtless deter- mined this place of meeting. It was, however, obvious, as Dr Clarke had pointed out, that the Society must have a home of its own as soon as possible. In April, 1820', arrangements were made for securing the use of a house in Sidney Street, opposite to Jesus Lane. The Society entered into occupation without delay, and at once commenced the formation of a Museum and a Library; for among the Minutes of the first meeting “held in the new rooms,” 1 May, 1820, we find : “The thanks of the Society voted to Mr Henslow for his liberal donation of a valuable collection in some departments of Natural History ; and cabinets ordered to be procured for the reception of the specimens.” And at the next meeting (15 May): “‘The thanks of the Society voted to Dr Clarke, Dr Haviland, and Mr Bridge for books presented by them to the Society.” Again, 13 November, 1820: “The thanks of the Society voted to Mr Henslow for a valuable collection of British Insects and Shells systematically arranged in the new cabinet.” The enthusiasm of those days of youth and hope is amusingly illustrated by a notice of motion handed in by Dr Clarke: “that communications announcing discoveries take the precedence of all others.” This was agreed to, in a slightly different form, 13 November, 1820. The Society was barely two years old when a project was started for giving it a social as well as a scientific side, by establish- ing a reading-room, amply stocked with newspapers, reviews, and magazines, both English and foreign, as well as with scientific journals, A meeting to carry out this scheme was held 22 May, 1821; and so warmly was it taken up that before the end of the year it was agreed that: “the establishment and funds of the Reading-room shall be considered as under the control of the Society.” A committee consisting of the Treasurer (Mr Bridge), 1 Minutes of the Society, 17 April, 1820. on resigning office, 27 October, 1890. x1 Mr Carrighan (Joh.), Mr Griffith (Emm.), Mr Peacock (Trin.), Mr Crawley (Magd.), Mr Whewell (Trin.), Mr Henslow (Joh.), was appointed to draw up the following regulations for the manage- ment of it, which the Society adopted, 25 March, 1822. rw) 10. 44; RuLEs AND REGULATIONS OF THE READING Room. Any Fellow of the Society elected before the Ist of January, 1822, may become a member of the Reading-room by writing his name in the book for that purpose and paying the subscription of the current year. Every Fellow of the Society elected after the Ist January, 1822, is a member of the Reading-room during residence. Every Fellow of the Society after becoming a member of the Reading-room continues so during residence. Every member of the Reading-room shall pay an annual subscrip- tion of one guinea to the Society, the subscription to be due on the Ist January for the current year, or he may become a member for life by paying ten guineas for the use of the Reading-room in any one year. The following publications shall be taken in’. Every alteration proposed in the list of publications taken in, shall be signed by at least three members of the Reading-room, read at a meeting of the Society, and suspended in the Room for a fortnight during full Term, for any member to signify his assent or dissent. If the majority in its favour amount to one-third of the signatures and the Council determine that the funds will permit, the alteration shall take place. No Newspaper shall be taken out of the room, and no periodical publication shall be removed, before a succeeding number has appeared. Any member, upon taking out a book, shall give to the servant of the house, a paper, with the title of the book, signed and dated by himself. Any member violating this rule shall pay a fine of 10s. Every publication taken out to be returned in a fortnight under a penalty of 2s. 6d. Any member having lost or damaged a book or paper shall replace it by a fresh copy of the same. 1 A space of nearly a full page is left in the Minute Book for the list of publications, but it has never been written in. X1l Address of Mr J. W. Clark, President, 12. The Reading-room shall be open every day from 8 o’clock in the morning to 10 at night. 15. Strangers may be introduced by a member, but no person resident in Cambridge can be introduced to the room, 14. Non-resident Fellows of the Society when visiting Cambridge shall be entitled to the use of the Reading-room. 15, A Steward’ shall be appointed at the Annual Meeting of the Society and considered as a member of the Council. 16, The office of the Steward shall be: to procure and take care of the books, to see that the papers are filed, and the room properly prepared for the reception of the members: to collect the bills and to sign them before they are paid by the Treasurer. It should be remembered that in those days Combination Rooms were ill-supplied with newspapers, and the few that were taken in were generally im the hands of the Senior Fellows. Moreover, in some colleges at least, the juniors were not allowed to use the Combination Room at all, except on Feast Days. The opportunity therefore, of having access at all times to a well- stocked reading-room was eagerly embraced, and formed, with many persons, one of the principal inducements to join the Philo- sophical Society. At the beginning of 1832 it became known that the Society would be deprived of the occupation of their house at Midsummer, 1833 ; nor could another, equally suitable, be either hired or pur- chased. Under these circumstances it was decided (7 April, 1832), mainly through the influence of Mr Peacock, to apply to St John’s College for the lease of a site at the corner of All Saints’ Passage, on which the Society might erect “a house of their own, built expressly to suit the objects of the institution.” As a preliminary to what the Minutes rightly call “this considerable undertaking,” it was decided to obtain a Charter of Incorporation. The Fellows of the Society were evidently warmly in favour of these proposals. A sum of three hundred pounds was subscribed in less than a month to defray the cost of the Charter; and at a special general meeting held 5 May, 1832, the Council was directed (1) to pre- pare a petition for a charter ; (2) to apply to St John’s College for a building-lease ; (3) “to apply to Mr Humfrey’ for working-plans, and complete estimates for the New House for the Society, the 1 The Rey. W. Whewell was Steward of the Reading-room from 1822 to 1826, when he was succeeded by the Rev. Joh. Lodge, University Librarian. He held the office till 1832, when it was discontinued, and a third Secretary was appointed, with the understanding that he should have charge of the Reading-room. * A local builder, who obtained the confidence of the University at this period. He erected the buildings for Human Anatomy. Architectural History, Willis and Clark, Vol. 11. p. 156. | on resigning office, 27 October, 1890. xiii same to be submitted hereafter to a general meeting of the Society for its approval.” Lastly, it was resolved: “that the money re- quisite for building the Society’s house be raised among the members of the Society by shares of £50 each, bearing interest at the rate of four per cent. per annum.” So eager was the Society to begin, that it was decided not to wait for the Charter; the plans were approved somewhat hastily, and at a special meeting held 16 May, 1832, the architect was directed to invite tenders. Early in the Michaelmas Term of 1832 the Charter arrived. Professor Sedgwick happened to be President, and, in order to avoid additional expense in fees’, it had been agreed that his name alone should appear upon the document. It therefore begins: “ Whereas Adam Sedgwick, Clerk, Master of Arts [etc], has by his petition humbly represented unto Us, That he, together with others of our loyal subjects, Graduates of the said University, did in the year One thousand, eight hundred, and nineteen, form themselves into a Society,” and so forth. No man had a better right to occupy so prominent a position; and it will be readily understood what pleasure he himself derived from seeing it there. He was never tired of telling the story of the Charter, when, as he put it, “I was the Society.” A special meeting was summoned, 6 November, 1832, to accept the Charter. Sedgwick read it, together with an abstract of it—and it is almost needless to record that it was accepted unanimously. The Council was then directed to prepare a body of Bye Laws—the code by which, with only a few slight alterations, we are still governed. It was on the occasion of the reception of the Charter that the first of those dinners was held which have now become an annual institution. It seems to me that Sedgwick and the Council of that year wished that November 6, 1832, should be kept as the birth- day of the Society—to commemorate the fact that on that day it had assumed a corporate existence. I need not remind you that such a decision involves a sacrifice of twelve years of the Society’s life ; but, on the other hand, it commemorates an important event in its history—-for I believe I am right in saying that it was the first Society out of London to which a Royal Charter was conceded. The new house was ready for the occupation of the Society in the autumn of 1833. The situation was convenient, and it was itself spacious and well-arranged, with a large meeting-room, museum, and reading-room. The change inaugurated an era of prosperity which lasted for several years. The meetings were well-attended—indeed the Monday evenings on which the Society met were held, by common consent, to be pre-occupied, and no rival attractions were allowed to interfere with them ;—The 1 The fees amounted to £271. Minutes, 6 November, 1832, X1V Address of Mr J. W. Clark, President, museum grew apace, under the fostering care of Professor Henslow and his friends : and the reading-room. became more popular than ever—a sort of club in fact—where many members of the Uni- versity passed several hours of each day, reading and writing or conversing with their friends. I will next quote an excellent account of the Society’s Museum, contributed by Mr Leonard Jenyns, in 1838, to The Cambridge Portfolio. The Cambridge Philosophical Society has been employed from the period of its first establishment in 1819, in gradually forming a Museum of Natural History. With a view to this end, it has from time to time effected several purchases, as well as received the con- tributions of various donors. The Museum however is not large; partly owing to the limited funds which can be appropriated to its support, and partly to the necessarily restricted space allotted for its reception in the Society’s house. It is principally, though not exclu- sively, devoted to the illustration of the British Fauna. The foundation of the Museum may be attributed to Professor Henslow, who presented to the Society at its first institution his entire collection of British Insects and Shells, arranged respectively in two cabinets. Several smaller donations quickly followed, leading the Society to take an increased interest in this part of its establishment. In 1828, a spirited subscription was commenced amongst its members to assist In pur- chasing a most valuable collection of British Birds, for obtaining which an opportunity then offered itself. This collection had belonged formerly to Mr John Morgan of London. It was extremely rich, especially in the rarer species. Many additions however have been since made to it; and the whole forms now a range of thirty large cases, which are placed round the principal room in the Museum. The birds are beautifully preserved; and the cases of sufficient size to admit, in many instances, of containing entire families. One of the cases contains British Quadrupeds. In 1829, the Society purchased a small collection of British Insects which was incorporated with that pre- viously presented by Professor Henslow. This collection, which con- sisted of about 2000 species, was valuable from the specimens having been arranged and named by Mr Stephens, the celebrated Entomologist of London. Various additions in the same department have been since made from time to time by different contributors. In 1833, the Society purchased Mr Stephen’s entire collection of British Shells, contained in two cabinets and comprising a most extensive series of species as well as of individuals of each. The Museum has been further enriched, in the department of the British Fauna, by a collec- tion of Birds’ Eves, presented in part by Mr Yarrell and in part by Mr Leadbeater ;—also by a collection of Fish, obtained principally on the southern shores of the island by Professor Henslow and the Rey. L. Jenyns;—and by a small collection of marine Invertebrata, obtained at Weymouth by the former of the two gentlemen last mentioned, on resigning office, 27 October, 1890. XV The foreign department of the Museum is not extensive, consisting for the most part of single specimens which have been presented at different times by different individuals. It contains, however, a small collection of reptiles presented by Mr Thomas Bell. It is also rich in Ichthyological specimens ; having been presented some years back with a collection of fish made at Madeira by the Rev. R. T. Lowe; subse- quently, with another collection made in China by the Rev. G. Vachell; and yet more recently, with the entire collection of Fish brought home from South America and some other portions of the globe by C. Darwin, Esq., of Christ’s College, and accompanying Naturalist in the late voyage of the Beagle, under the command of Captain Fitzroy. The whole of the fish above alluded to, as well as those belonging to the British collection, are preserved in spirits. They amount to several hundred species ; and many of those comprised in the Darwin collection are entirely new. Altogether, they constitute a highly valuable as well as interesting portion of the Society’s Museum. Independently of the collections above enumerated, the Philosophical Society has made it an object to establish a separate collection of the principal animals found in Cambridgeshire. This is a step of the utility of which there can be no doubt. Local collections of this nature tend to illustrate the Faunas of particular districts; and local Faunas offer the best materials for completing our knowledge of the Zoology of the whole kingdom. They also throw light upon the geographical distribu- tion of animals. In proportion to the number of places in which such collections are established, they assist in determining the extreme range of the different species, as well as the districts to which they are ordi- narily confined. In this department, however, the Birds of Cambridge- shire and a few of its Mammalia are alone as yet fitted up for public inspection ; but considerable collections have been made in the other classes, which are destined one day to take their place in the Museum also. The Museum of the Society, and that part of it in particular which has been just alluded to, has been probably instrumental in exciting much interest in the University in the science of Zoology, and diffusing amongst its members a taste for such pursuits. Nor is the surrounding neighbourhood at all unfavourable for the researches of the naturalist. On the contrary, Cambridgeshire may be considered as rich in animal productions. From combining within itself a considerable variety of soil and situation, it adapts itself to the habits of very different species. The fens in particular are inhabited by many rare aquatic birds and insects ; and some of these, previous to the introduction of the present system of drainage, were in considerable abundance. It may perhaps be interesting to mention, that the entire number of vertebrate animals found in Cambridgeshire amount to 281. Of these 38 belong to the class Mammalia; 204 to that of Birds; 9 to that of Reptiles; and 32 to that of Fish. The invertebrate animals require further investigation ; but they probably exceed 9,000, of which the greater portion belong to the division of Annulosa. The Society has a small collection of minerals and fossils ; but there XVi Address of Mr J. W. Clark, President, being other Museums in the University devoted to these departments, they have received less of its attention than the Zoological part of the Museum above noticed. There are also a few antiquities, some of which were obtained in the county. The Society’s house had been built, to a great extent, with borrowed money, as I have related, and it had cost a far larger sum than had been anticipated. It was possible to pay the interest on the loans, but the Society found itself unable to establish a sinking- fund for the repayment of the capital. Moreover, the number of Fellows gradually decreased. At one time it was usual for nearly every Fellow of a College to become a Fellow of the Philosophical Society ; but, when the novelty of the existence of such a body in Cambridge had worn off, and when the reading-room had several rivals, not to mention the reduction of the price of news- papers, which enabled them to be taken in at home—there seemed to be no special reason for joining a Society where the papers read were chiefly mathematical, and which offered no other attractions not to be found elsewhere. The officers of the Society did their best in these adverse days; and some of those who had lent money cancelled their bonds—as for instance Professor Peacock, Professor Sedgwick, Professor Adams, and Professor Babington; but the financial difficulty could not be overcome. Finally, in 1865, the Museum was offered to, and accepted by, the University’; the house was sold; and the Society found a home at the New Museums’. In this brief review I have of necessity omitted much that I should have been glad to record, had I not determined to write a sketch and not a history. I cannot, however, conclude without drawing attention to our publications. No one, I think, can look through the volumes of Transactions and Proceedings without admitting that the papers therein printed or abstracted will hold their own in originality and value against those of almost any society. The Proceedings, as you are aware, do not begin before 1843. I have therefore appended to this paper brief notices of the communications made before that date, as recorded in the Minute Book. These will, I feel sure, be found interesting. They show what some of the best men in the place were working at; and they testify to the genuine interest taken by them in the Society. Whatever they did, they hastened to communicate it, though, to our great loss, they too often neglected to prepare their work for our Transactions. I have also prepared a list of the Presidents, Secretaries, and Treasurers, from the beginning to the present time. 1 Grace, 24 May, 1865. 2 Grace, 8 June, 1865. Date of Election. 1819. 15 Noy. 22 May, 13 May, 17 May, 22 May, 19 May, 17 May, 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 6 Nov. 7 Nov. 6 Nov. 26 Oct. 31 Oct. 28 Oct. 26 Oct. 30 Oct. — 28 Oct. 25 Oct. — 30 Oct. | 27 Oct. 25 Oct. 1821. 1823. 1825. 1827. 1829. 1831. 1833. 1835. 1837. 1839. 1841. 1843. 1845. 1847. 1849. 1851. 1853. 1855. 1857. 1859. 1861. 1863. 1865. 1867. 1869. 1871. 1873. 1875. on resigning office, 27 October, 1890. Xvil OFFICERS OF THE SOCIETY. PRESIDENTS. Rey. Will. Farish, M.A. Magd., Jacksonian Professor. Rey. Ja. Wood, D.D., Master of S. John’s College. John Haviland, M.D. Joh., Regius Professor of Physic. Rey. Ja. Cumming, M.A. Trin., Professor of Chemistry. Rey. Joh. Kaye, D.D., Master of Christ's Coll. and Bp. of Lincoln. Rev. Tho. Turton, D.D. Cath., Regius Professor of Dwinity. Rev. Adam Sedgwick, M.A. Trin., Woodwardian Pro- Jessor. Rey. Joshua King, M.A. Qu., President of Queens’ College. Rey. Will. Clark, M.D. Trin., Professor of Anatomy. Rev. Joh. Graham, D.D. Chr., Master of Christ's College. ; Rey. Will. Hodgson, D.D. Pet., Waster of Peterhouse. Rey. Geo. Peacock, D.D. Trin., Lowndean Professor. Rev. Will. Whewell, D.D. Trin., Master of Trinity College. Rev. Ja. Challis, M.A. Trin., Plumian Professor. Rev. Hen. Philpott, D.D.Cath., Master of S. Catharine’s Coll. Rev. Rob. Willis, M.A. Gony. and Cai. Coll., Jack- sonian Professor. Will. Hopkins, M.A. Pet. Rev. Adam Sedgwick, M.A. Trin., Woodwardian Pro- Jessor. Geo. Edw. Paget, M.D. Gonv. and Cai. Coll. Will. Hallows Miller, M.D. Joh., Professor of Mine- ralogy. Geo. Gabriel Stokes, M.A. Pemb., Zucasian Professor. Joh. Couch Adams, M.A. Pemb., Lowndean Professor. Will. Hepworth Thompson, M.A. Trin., Regius Pro- JSessor of Greek. Rev. Hen. Wilkinson Cookson, D.D. Pet., Master of Peterhouse. Rev. Will. Selwyn, D.D. Joh., Lady Margaret's Pro- JSessor. Art. Cayley, M.A. Trin., Sadlerian Professor. Geo. Murray Humphry, M.D. Down., Professor of Anatomy. Ch. Cardale Babington, Botany. Ja. Clerk Maxwell, M.A. Trin., Professor of Experi- mental Physics. M.A. Joh., Professor of b XVlll 27 Oct. 1879. 31 Oct. 1881. 30 Oct. 1882. 27 Oct. 1884. 26 Oct. 1886. 30 Jan. 1888. 15 Nov. 1819. 22 May, 1821. 9 May, 1826. 6 Nov. 1833. 7 Nov. 1836. 6 Noy. 1839. 7 Nov. 1842. 6 Nov. 1851. 6 Noy. 1854. 6 Nov. 1855. 25 Oct. 1858. Address of Mr J. W. Clark, President, Date of Election. 29 Oct. 1877. Geo. Downing Liveing, M.A. Joh., Professor of Che- mistry. Alf. Newton, M.A. Magd., Professor of Zoology and Comparative Anatomy. Fra. Maitland Balfour, M.A. Trin. Ja. Whitbread Lee Glaisher, M.A. Trin. Mich. Foster, M.A. Trin., Professor of Physiology. Rey. Coutts Trotter, M.A. Trin, Joh. Willis Clark, M.A. Trin. SECRETARIES. Rev. Adam Sedgwick, M.A. Trin., Professor of Geology. Rev. Sam. Lee, M A. Qu., Professor of Arabic. Rey. Geo. Peacock, M.A. Trin. Joh. Stevens Henslow, M.A. Joh. Rev. Joh. Stevens Henslow, M.A. Joh., Professor of Mineralogy and Botany. Rey. Will. Whewell, M.A. Trin. Rey. Joh. Stevens Henslow, M.A. Joh., Professor of Botany. Rey. Will. Whewell, M.A. Trin. Rev. Joh. Lodge, M.A. Magd., University Librarian. Rev. Joh. Stevens Henslow, M.A. Joh., Professor of Botany. Rey. Will. Whewell, M.A. Trin. Rev. R. Willis, M.A. Gonv. and Cai. Rev. Will. Whewell, M.A. Trin. Rev. R. Willis, M.A. Gonv. and Cai., Jacksonian Professor. Will. Hopkins, M.A. Pet. Rev. R. Willis, M.A. Gonv. and Cai., Jacksonian Professor. Will. Hopkins, M.A. Pet. Will. Hallows Miller, M.D. Joh., Professor of Mine- ralogy. Will. Hallows Miller, M.D. Joh., Professor of Mine- ralogy. Ch. Cardale Babington, M.A. Joh. Geo. Gabriel Stokes, M.A. Pemb., Lucasian Professor. Ch. Cardale Babington, M.A. Joh. Joh. Couch Adams, M.A. Pemb. Rey. Ch. Fre. Mackenzie, M.A. Gonv. and Cai, Ch. Cardale Babington, M.A. Joh. Joh. Couch Adams, M.A. Pemb. Geo. Downing Liveing, M.A. Joh. Ch. Cardale Babington, M.A. Joh. Geo. Downing Liveing, M.A. Joh. Norman Macleod Ferrers, M.A. Gony. and Cai. on resigning office, 27 October, 1890. xix Date of Election. 29 Oct. 1866. Ch. Cardale Babington, M.A. Joh., Professor of Botany. Geo. Downing Liveing, M.A. Joh., Professor of Che- mistry. Rey. T. G. Bonney, M.A. Joh. 31 Oct. 1870. Rev. T. G. Bonney, M.A. Joh. Joh. Willis Clark, M.A. Trin. Rev. Coutts Trotter, M.A. Trin. 27 Oct. 1873. Joh. Willis Clark, M.A. Trin. Rev. Coutts Trotter, M.A. Trin. Rev. Joh. Batteridge Pearson, B.D. Emm. 28 Oct. 1878. Joh. Willis Clark, M.A. Trin. Rey. Coutts Trotter, M.A. Trin. Ja. Whitbread Lee Glaisher, M.A. Trin, 30 Nov. 1882. Joh. Willis Clark, M.A. Trin. Rey. Coutts Trotter, M.A. Trin. Will. Mitchinson Hicks, M.A. Joh. 29 Oct. 1883. Rev. Coutts Trotter, M.A. Trin. Ri. Tetley Glazebrook, M.A. Trin. . Sydney Howard Vines, M.A. Chr. 26 Oct. 1886. Ri. Tetley Glazebrook, M.A. Trin. Sydney Howard Vines, M.A. Chr. Jos. Larmor, M.A. Joh. 31 Oct. 1887. Sydney Howard Vines, M.A. Chr. Jos. Larmor, M.A. Joh. Matth. Moncrieff Pattison-Muir, M.A. Gony. and Cai. 29 Oct. 1888. Jos. Larmor, M.A. Joh. Matth. Moncrieff Pattison-Muir, M.A. Gony. and Cai. Sidney Fre. Harmer, M.A. King’s. 28 Oct. 1889. Jos. Larmor, M.A, Joh. Sidney Fre. Harmer, M.A. King’s. Andr. Russell Forsyth, M.A. Trin. TREASURERS. 15 Nov. 1819. Rev. Bewick Bridge, B.D. Pet. 17 May, 1825. Fre. Thackeray, M.D. Emm. 6 Nov. 1834. Rev. Geo. Peacock, M.A. Trin. 6 Nov. 1839. Geo. Edw. Paget, M.D. Gonv. and Cai. 7 Nov. 1853. Rev. Tho. Hedley, M.A. Trin. 26 Oct. 1857. Rev. Will. Magan Campion, M.A. Qu. 23 Oct. 1876. Ja. Whitbread Lee Glaisher, M.A. Trin. 28 Oct. 1878. Rev. Joh. Batteridge Pearson, D.D. Emm. 29 Oct. 1883. Joh. Willis Clark, M.A. Trin. 31 Oct. 1887. Ri. Tetley Glazebrook, M.A. Trin. XX Address of Mr J. W. Clark, President, COMMUNICATIONS MADE TO THE SOCIETY. February 20, 18201. By Professor Farish (President): On Isometrical Perspective. By Prof. E. D. Clarke: On the discovery of Cadmium in some of the English ores of zinc; with some directions respecting the mode of operating. By Captain Fairfax (presented by Mr Okes): On Soundings at Sea. March 6, 1820. By Joh. Hailstone, M.A. (Trin.): On the probable origin of a fossil body found on the coast of Scarborough. By Professor Farish (President): On Isometrical Perspective (concluded). Trans. 1. 1—19. By Joh. Fre. Will. Herschel, M.A. (Joh.): On functional equations. Zvrans. I. 77—87. By Mr Okes: On some fossil remains of the Beaver, found near Chatteris. Trans. 1. 175—177. March 20, 1820. By Professor Sedgwick: On the Geology of Cornwall, ete. By Mr Thompson (Joh.): A translation from Gemmellaro’s account of the last great eruption of Etna, in 1819. (Presented by Dr E. D. Clarke.) April 17, 1820. A letter from the Rev. J. Davis to the Rev. Dr Wood, detailing certain optical phenomena observed at Hilkhampton in Cornwall on Wednesday, April 5th, 1820, was read to the Society. By Joh. Fre. Will. Herschel, M.A. (Joh.): On the rotation impressed by plates of rock crystal on the planes of polarization of the rays of light as connected with certain peculiarities in its crystallization. Trans, 1. 483— 52. By Will. Whewell, M.A. (Trin.): On the position of the apsides of orbits of great eccentricity. TZrans. 1. 179—191. May 1, 1820. By Professor Farish (President): On the mode of conducting Polar navigation. By Joh. Fre. Will. Herschel, M.A. (Joh.): On certain remarkable instances of deviation from Newton’s scale in the tints developed by crystals with an axis of double refraction on exposure to polarized light. Zrans. 1. 21— 41. By Ch. Babbage, M.A. (Trin): On the Calculus of Functions. Trans. 1. 63-— 76. May 15, 1820. 3y Mr Emmett: Researches into the mathematical principles of chemical philosophy. sy Prof. E. D, Clarke: On the chemical constituents of the purple precipitate of Cassius. Trans. 1. 53—61. 3y Professor Sedgwick: On the physical structure of Cornwall, etc. (con- tinued from 23 March). Trans. 1. 89—146. 1 The Minute Book says: ‘‘ Monday, February 21, 1820”; but in 1820 February 21 fell on a Tuesday. on resigning office, 27 October, 1890. xxi By Sam. Hunter Christie, M.A. (Trin.): On the laws according to which masses of iron influence magnetic needles. 7Zvrans. 1. 147—173. A letter from the Rev. J. Davis to the Rev. Dr Wood, containing some further details respecting certain optical phenomena mentioned in the Minutes of the Society’s Meeting on the 17th of April. November 13, 1820. By Prof. E. D. Clarke: On a method of giving to common Paris Plaster casts the appearance of polished Rosso Antico. By Professor Lee: On certain astronomical tables by Mohammed al Farsi, a MS. copy of which exists in the University Library. Trans. 1. 249—265. November 27, 1820. By Prof. E. D. Clarke: On the discovery of native natron in Devonshire. Trans. 1. 193—201. By the same: Notice respecting the sarcophagus brought from Egypt by Mr Belzoni. By Will. Cecil, M.A. (Magd.): On the application of hydrogen gas to produce a moving force in machinery, with the description of an engine where the moving force is produced on that principle. Trans, 1, 217—239. December 11, 1820. A communication from Dr Wavell (Hon. Member), with some observations by Dr E. D. Clarke on the decomposition of a quartzose rock, and on the formation of natron. By Professor Haviland, Vice-President: On some unusual appearances pre- sented by the stomach of a man who died of a fever. Trans. 1. 287— 290. By Professor Lee: A demonstration of the properties of parallel lines, by ‘Nasir el Din, translated from the Arabic. March 5, 1821. . —. from Professor Leslie and Dr Wavell read by Dr E. D. arke.” By Fra. Lunn, B.A. (Joh.): On the analysis of a native phosphate of copper. Trans. 1. 203—207. By Prof. E. D. Clarke: On the crystallization of water. Trans. I. 209—215. March 19, 1821. A communication (read by Professor Sedgwick) from Mr Ross respecting some minerals found at Buralston. By Prof. E. D. Clarke: On Arragonite. April 2, 1821. By Joh. Leslie, Professor of Mathematics in the University of Edinburgh (Hon. Member): On the effect of hydrogen gas on the propagation of sound. (Read by Professor Lee.) Zvans. 1. 267. By Professor Cumming: Exhibition of experiments and communication read on the effects of the galvanic fluid on the magnetic needle. Trans. I. 269— 279. By Professor Sedgwick : On the geology of the Lizard district. XXxil Address of Mr J. W. Clark, President, May 7, 1821. By Joh. Fre. Will. Herschel, M.A. (Joh.): On the refraction of Apophyllite. Trans. 1. 241—247. By Professor Sedgwick: On the geology of the Lizard (concluded). Trans. I. 291—330. May 21, 1821. By Professor Cumming: On the connexion between galvanism and magnetism. Trans. I. 281—286. By Will. Cecil, M.A. (Magd.): On the application of regulators to machinery. November 12, 1821. The following communication from Dr Brewster was read by Prof. E. D. Clarke : “T have examined with great care a specimen of Leelite, and I find it to be an irregularly crystallized body, like Hornstone, Flint, and having a sort of quaquaversus structure, or one in which the axes of the elementary particles are in every possible direction, instead of being parallel, as they must be in all regular crystals. The alumina which Leelite contains gives it quite a different action upon light from any of the analogous siliceous sub- stances ; and I have thus obtained an unerring optical character by which Leelite may be distinguished from them with the greatest facility. In examining the different kinds of topazes, I have found that the colour- less topazes, and the blue topazes of Aberdeenshire, differ not merely from the yellow Brazil topazes, but also from one another.” Signed, D. Brewster. By Mr Okes: On a peculiar case of an enlargement of the ureters in a boy of eleven years of age. Trans. 1. 351—358. November 26, 1821. By Fre. Thackeray, M.D. (Emm.): On a remarkable instance of organic remains found on the turnpike road between Streatham and Wilburton in the Isle of Ely. Trans. 1. 459. By Will. Mandell, B.D. (Qu.): On an improvement in the common mode of procuring potassium. Trans. 1. 343—345. By Will. Whewell, M.A. (Trin.): On the crystallization of fluor spar. Trans. I. 331—342. By Joh. Stevens Henslow, M.A. (Joh.): On the geology of the Isle of Anglesea. December 10, 1821. By Professor Cumming: On a remarkable human calculus in the possession of the Society of Trinity College. Trans. 1. 347—349. By Joh. Stevens Henslow, M.A. (Joh.): On the geology of the Isle of Anglesea (continued). By Ch. Babbage, M.A. (Pet.): On the use of signs in mathematical reasoning. (Read by Mr Peacock.) Trans. 11. 325—377. February 25, 1822. By Joh. Hailstone, M.A., late Fellow of Trin. Coll., and Woodwardian Pro- fessor: Some observations on the weather, accompanied by an extra- ordinary depression of the barometer, during the month of December, 1821. (Read by the Secretary.) Trans. 1. 453—458. ah on resigning office, 27 October, 1890. XXlil By Joh. Stevens Henslow, M.A. (Joh.): On the geology of the Isle of Anglesea (concluded). TZrans, 1. 359—452. March 11, 1822. The President proposed that, in consequence of the death of the Vice- President of the Society, Prof. E. D. Clarke, the meeting should be adjourned without proceeding to the regular business of the evening. This proposition was agreed to unanimously, and the Society adjourned immediately. March 25, 1822. By Will. Mandell, B.D. (Qu.): A description of a new self-regulating lamp. By Mr H. B. Leeson: A description of a safety apparatus to the hydrostatic blowpipe of Tofts, by which it may be converted into an oxyhydrogen blowpipe without danger to the operator. (Read by Mr Peacock.) A model of the safety apparatus, and of the blowpipe, was exhibited to the Society and explained by Mr Leeson. By Geo. Biddell Airy, student of Trinity College: On the alteration of the focal length of a telescope by a variation of the velocity of light and of the observations to which the change may give rise. (Read by Mr Peacock.) April 22, 1822. By David Brewster, LL.D., Honorary Member of this Society: On the differ- ence of optical structure between’ the Brazilian topazes and those of Scotland and New Holland. Trans. 11. 1—9. May 6, 1822. By Will. Whewell, M.A. (Trin.): On the rotation of bodies. Trans. 11. 11— 20. By Dav. Brewster (Hon. Member): On the distribution of the colouring matter, and on certain peculiarities in the structure and optical properties of the Brazilian topaz. Trans. 1. 1—9. May 21, 1822. By Professor Sedgwick: On the basaltic dykes in the county of Durham, and the great basaltic formation in Teesdale. Zvrans. 1. 21—44. November 11, 1822. By Will. Whewell, M.A. (Trin.): On the oscillations of a chain suspended vertically, and on the oscillations of a weight drawn up uniformly by a string. By Fra. Gybbon Spilsbury: On a peculiar relation existing between gravity and the production of magnetism in galvanic combinations. (Read by Mr Henslow.) TZrans. u. 77—83. November 25, 1822. By Geo. Biddell Airy, Scholar of Trin. Coll.: On the construction of achro- matic reflecting telescopes with silvered lenses in the place of metallic mirrors. Read by Mr Peacock. Zvrans. 11. 105—118. December 9, 1822, By Will. Cecil, M.A. (Magd.): On an apparatus for grinding telescopic mirrors and object-lenses. 7Zrans, 11. 85—103. XX1V Address of Mr J. W. Clark, President, February 17, 1823. No papers recorded. March 3, 1823. No papers recorded. March 17, 1823. No papers recorded. April 14, 1823. By Will. Whewell, M.A. (Trin.): On the different methods which have been proposed to grind lenses and mirrors by machinery to a parabolic form. By Joshua King, M.A. (Qu.): A new demonstration of the parallelogram of forces. Trans. 11. 45—46. By Geo. Peacock, M.A. (Trin.): On the analytical discoveries of Newton and his contemporaries. April 28, 1823. By Professor Cumming: On the development of electro-magnetism by heat. Trans. 1. 47—76. May 12, 1823. By Geo. Peacock, M.A. (Trin.): On the irregular indications of the thermo- meter. November 10, 1823. By Professor Cumming: On rotation produced by electro-magnetism as developed by heat. A letter was read by Mr Peacock from Will. Joh. Bankes, M.P., on the subject of the manuscript on papyrus of the lost book of the Iliad, recently discovered by one of his agents in the island of Elephantina in Upper Egypt, accompanied by a facsimile made by Mr Salt of the ten first lines of the manuscript. By Geo. Biddell Airy, B.A. (Trin.): Explanation of an instrument exhibited to the Society, for the purpose of proving by experiment the constancy of the ratio of the sines of incidence and refraction in liquids. (Read by Mr Peacock.) By Joh. Murray, F.S.A.: Some remarks on the temperature of the egg, as connected with its physiology. (Read by Mr Peacock.) By the same: Experiments and observations on the temperature developed in voltaic action, and its unequal distribution. (Read by Mr Peacock.) November 24, 1823. By Will. Whewell, M.A. (Trin.): On the expressions for the cosine of the angle between two lines and two planes when referred to oblique co- ordinates. Trans. 11. 197—202. By Olinthus Gregory, LL.D.: An account of some experiments made in order to ascertain the velocity with which sound is transmitted in the atmosphere, (Read by Mr Peacock.) Trans. 1. 119—137. December 8, 1823. By Professor Cumming: Exhibition of Dobereiser’s experiments of the con- tortion of platina wire by a stream of hydrogen gas. 3y Will. Cecil, M.A. (Magd.): Exhibition of a model of an improved ear- trumpet. — _ ll ak | = on resigning office, 27 October, 1890. XXV By Geo. Peacock, M.A. (Trin.): On the analytical discoveries of Sir I. Newton. (Concluded.) Mr Peacock read three unedited letters of Newton to Dr Keill on the subject of the controversy on the discovery of the method of fluxions. March 1, 1824. By Mr Okes: Notice of a magnificent collection of fossil bones, found near Barnwell, of the Elephant, Rhinoceros, Buffalo, Deer, Horse. By Will. Mandell, M.A. (Qu.): A letter of Sir Isaac Newton to Mr Acland of Geneva was read. The following is a copy of the letter. Vir celeberrime, Gratias tibi debeo quam maximas quod schema experimenti quo lux in colores primitivos et immutabiles separatur, emendasti, et longe elegantius reddidisti quam prius. Sed et me plurimum obligasti quod schema in Caminé ene& incisum et inter imprimendum obtritum refici curasti, ut impressio libri elegantior redderetur. Gratias igitur reddo tibi quam amplissimos. Quod inventa mea de natura lucis et colorum viris summis Domino Cardinali Polignac et Domino Abbati Bignon non displiceant, valde gaudeo. Utinam hec vestratibus non minus placerent, quam elegantissime vestre et perfectissime delineate picturz nostratibus placuerunt. Ut Deus te liberet a doloribus capitis et salvum conservet ardentissime precatur Servus tuus humillimus et obsequentissimus Dabam Londini Isaacus NEwTon. 22 Oct. 1722. Celeberrimo viro D™. Acland. By Professor Sedgwick : On the geology of Teesdale. March 15, 1824. By Will. Mandell, M.A. (Qu.): Description of a self-regulating lamp. By Geo. Biddell Airy, B.A. (Trin.): On the figure of the planet Saturn. ' Trans, 11. 203—216. By Professor Sedgwick: On the geology of Teesdale (continued). March 29, 1824. By Will. Mandell, M.A. (Qu.): On a means of protecting locks from the insertion of skeleton keys. By G. Harvey, F.R.S.E., M.G.S.V.: On the fogs of the Polar seas. By Professor Sedgwick: On the geology of Teesdale (concluded). Trans. 11. 139—195. May 3, 1824. By Cha. Babbage, M.A. (Pet.): On the determination of the general terms of a new class of infinite series. (Read by Mr Peacock.) Trans. 11. 217— 225. By Geo. Biddell Airy, B.A. (Trin.): On the construction of a new achromatic telescope. May 17, 1824. By Joh. Hogg, B.A. (Pet.): On two petrifying springs in the neighbourhood of Norton in the County of Durham. (Read by Professor Henslow.) By Geo. Biddell Airy, B.A. (Trin.): On the principle and construction of the achromatic eyepieces of telescopes, and on the achromatism of micro- scopes. Trans. 11. 227—252. XXV1 Address of Mr J. W. Clark, President, May 24, 1824. By Professor Haviland, President: On the cases of secondary smallpox, and of smallpox after vaccination, which have occurred in Cambridge during the last year. By Professor Farish: On a method of obviating the inconveniences arising from the expansion and contraction of the iron in iron bridges. November 15, 1824. By Professor Cumming: On the use of gold leaf in the detection of galvanism. By Will. Whewell, M.A. (Trin.): On the principles of dynamics. November 29, 1824. By Professor Cumming: On the history of electro-magnetism. December 13, 1824. By Professor Farish: On the construction of the cogs of wheels. Professor Farish likewise exhibited to the Society the action of wheels in the form of involutes of circles upon each other as an illustration of the subject of his paper. February 21, 1825. By Professor Cumming: On the conversion of iron into plumbago by the action of sea-water. Trans. 11. 441—443. By Geo. Biddell Airy, B.A. (Trin.): On a peculiar defect of his eyes producing distortion of images, and on the means of correcting it. Trans. 11. 267— 271. By Professor Sedgwick: On the essential distinction between alluvial and diluvial deposits. Annals of Philosophy, x. 1825, pp. 18—387. March 7, 1825. By Will. Whewell, M.A. (Trin.): On a general method of converting rectilineal figures into others which are equivalent, such as squares, etc. By Professor Sedgwick: On alluvial and diluvial deposits (continued). March 21, 1825. By Jos. Power, M.A. (Cla.): A general demonstration of the principle of virtual velocities. Trans. U1. 273—276. April 18, 1825. By Professor Farish: On the construction of the cogs of wheels (concluded). May 2, 1825. By Geo. Biddell Airy, B.A. (Trin.): On the generation of curves by the rolling of one curve upon another, and on the formation of the curves of the teeth of wheels which may work in each other with perfect uniformity of action. Trans. 11. 277—286. By Professor Sedgwick: A portion of a paper on the geology of the Yorkshire coast, a section of which was exhibited to the Society. By Will. Whewell, M.A. (Trin.): Exhibition of drawings of the appearances Sha ge by the spokes of wheels in motion when seen through parallel ars, and which consist of a series of quadratures. + ‘ee mr ——— on resigning office, 27 October, 1890. XXVil May 16, 1825. By Ja. Alderson, B.A. (Pemb.): An account, with measurements, of an enormous whale cast upon the coast of Holderness. (Read by Professor Cumming.) Trans. 1. 253—266. By Professor Sedgwick: On the geology of the Yorkshire coast (concluded). By Will. Whewell, M.A. (Trin.): On the classification of crystalline forms, particularly with reference to the systems of Weiss of Berlin and Mohs of Freyberg. November 14, 1825. By Ri. Wellesley Rothman, B.A. (Trin.): On the discrepancies between the magnetic intensities at different places on the earth’s surface, as deter- mined by observation, and by a formula partly empirical and partly theoretical of Horsteen and Barlow. Tras. 11. 445. By Geo. Biddell Airy, B.A. (Trin.): On the connection of impact and pressure, and the explanation of their effects on the same principles. By Leonard Jenyns, M.A. (Joh.): On the ornithology of Cambridgeshire (read by Professor Henslow). November 28, 1825. By Leonard Jenyns, M.A. (Joh.): On the ornithology of Cambridgeshire (con- cluded). Trans. 1. 287—324. December 12, 1825. By Ch. Babbage, M.A. (Pet.): On the principles of mathematical notation (read by Mr Peacock). February 13, 1826. By Will. Whewell, M.A. (Trin.): On the notation of crystallography. Trans. 0. 427-439. By Professor Farish: Explanation of a method of correcting the errors from the near position of a meridian mark. February 27, 1826. By Will. Woodall, M.A. (Pemb.): On a method of finding the meridian line. By Professor Farish : Supplement to a paper read at the last meeting. By Geo. Peacock, M.A. (Trin.): On Greek arithmetical notation. March 13, 1826. By Will. Hen. Wayne, M.A. (Pet.): On beds containing fossil bones inter- mixed with clay and gravel. A letter read, with observations, by Profes- sor Sedgwick. By Geo. Peacock, M.A. (Trin.): On Greek arithmetic (concluded). April 10, 1826. . By Geo. Peacock, M.A. (Trin.): On the origin of Arabic Numerals, and the date of their introduction into Europe. April 24, 1826. By Will. Whewell, M.A. (Trin.): On a new method of Perspective ; particularly for objects comprehending a large vertical and a small horizontal space. By Geo. Peacock, M.A. (Trin.): On the origin of Arabic Numerals, etc. (con- cluded). XXVili Address of Mr J. W. Clark, President, May 8, 1826. By Geo. Biddell Airy, M.A. (Trin.): Observations on the Mécanique Celeste of Laplace, Book III., with some remarks on the objections of Mr Ivory. Trans. U1. 379—390. By Professor Sedgwick: On the Geology of the Isle of Wight. November 13, 1826. By Professor Sedgwick: Exhibition of a pair of large fossil horns, of some species of the genus Bos, found near Walton in Essex. By Will. Whewell, M.A. (Trin.): On the classification of crystalline combina- tions, and the canons of derivation by which their laws may be investi- gated. Trans. 11. 391—425. November 27, 1826. By Geo. Biddell Airy, M.A. (Trin.): On the motion of a pendulum disturbed by any small force, and on the application of this method to the theory of escapements. TZ'rans. 11. 105—128. December 11, 1826. By Geo. Peacock, M.A. (Trin.): On the numerals of the South American lan- guages. After the meeting Professor Airy gave an account of the construction and application of the steam-engine in the mines of Cornwall. February 26, 1827. By Professor Airy: On the mathematical theory of the Rainbow. After the meeting Professor Henslow gave an account of the structure of the capsules of mosses, illustrated by coloured drawings. March 12, 1827. By Geo. Peacock, M.A. (Trin.): On the discoveries recently made on the subject of the Egyptian Hieroglyphics. March 26, 1827. By Professor Henslow: On the specific identity of the Cowslip, Oxlip, and Primrose. By Will. Whewell, M.A. (Trin.): Note on the perspective projection of objects on a horizontal plane. After the meeting Professor Cumming gave an account of the different forms of the Galvanometer, and of the discoveries recently made in Electro- dynamics. April 30, 1827. By Will. Sutcliffe, M.A. (Trin.): On the application of mathematics to Politi- cal Economy, and the effects of a partial Tithe. By Will. Whewell, M.A. (Trin.): On the Perspective of Panoramas. After the meeting Professor Sedgwick exhibited a large pair of horns of [some species of the genus Bos] found near Walton in Essex; and an Jchthyo- saurus, found at Lyme; on which he offered some observations, May 14, 1827. By Will. Sutcliffe, M.A. (Trin.): On the application of mathematics to Politi- cal Economy, etc. (concluded). a | on resigning office, 27 October, 1890. XX1X By Professor Airy: On the defects of the eye-pieces of telescopes. After the meeting Professor Sedgwick gave an account of the peculiarities of the Coal Strata in the neighbourhood of Whitehaven: and George Noakes (zt. 7), a boy remarkable for his powers of calculation, was ex- amined by several members of the Society. May 21, 1827. By R. M. Fawcett: On the use of Iodine in cases of Paralysis. By Professor Airy: On the observation of eye-glasses depending upon their spherical figure, and on the periscopic Panorama. Trans. 111. 1—63. After the meeting Mr Peacock gave an account of the discoveries recently made in Hieroglyphics. November 12, 1827. By Tho. Jarrett, B.A. (Cath.): On Algebraical Notation. Trans. 111. 65—103. By Will. Whewell, M.A. (Trin.): On the History and Principles of Chemical Nomenclature and Notation, with suggestions of some alterations in the Notation hitherto in use. By Will. Mandell, B.D. (Qu.): Exhibition of a piece of breccia, supposed to be a fragment of a Roman quern or hand-mill, found on the Hills Road. November 26, 1827. Professor Sedgwick read a letter from Mr Ri. Tho. Lowe, concerning certain petrifactions, apparently of vegetable origin, which are found in the Island of Madeira. By Professor Henslow: An account of the application of the chloraret of lime to the purpose of disinfecting and neutralizing putrid and noxious sub- stances. December 10, 1827. Dr Fre. Thackeray presented a sword of the sword-fish, and read some obser- vations on the bones of the head, and especially those which seem to belong to its olfactory system. By Leonard Jenyns, M.A. (Joh.): On the monstrous prolongations of teeth, etc., which have been observed in different animals, particularly the teeth of a rabbit and the bill of a rook which exist in the Collection of the Society; and on the circumstances by which such deformities have been observed to be accompanied. February 17, 1828. By Alex. Ch. Louis D’Arblay, M.A. (Chr.): Remarks on a pamphlet by Messrs Swinburne and Tylecot of St John’s College, concerning the proofs of the Binomial Theorem, and especially that of Euler. After the meeting Mr Peacock gave an account of the representations occurring in Egyptian monuments of the deities of that country, and of the funeral rituals. March 3, 1828. By Alex. Thomson (Joh.): On a mode of obtaining exact measures of the cranium. By Will. Whewell, M.A. (Trin.): On the different systems of mineralogical classification. After the meeting Professor Sedgwick gave an account of the geological struc- ture of Scotland, as collected from the observations made by himself and Mr Murchison during the preceding summer. XXX Address of Mr J. W. Clark, President, March 17, 1828. By Tho. Jarrett, M.A. (Cath.): On the development of Polynomials. By Will. Whewell, M.A. (Trin.): On the different systems of mineralogical classification (concluded). After the meeting Hen. Coddington, M.A. (Trin.) gave an account of the ex- periments on vibrations and nodal lines of Chladni, Savart, on the con- struction of organ-pipes, etc. April 21, 1828. By Will. Whewell, M.A. (Trin.): On mineralogical nomenclature, By Temple Chevallier, M.A. (Pem.): On certain properties of numbers. By Rob. Willis, B.A. (Cai.): On the pressure of the air between two discs when affected by a stream of air passing through a tube perforating one of the dises. Trans. 10. 129—140. After the meeting Mr Willis exhibited various experiments illustrative of the laws of pressure described in his memoir. May 5, 1828. By Tho. Jarrett, M.A. (Cath.): On the arithmetic of lines. By Professor Whewell: On mineralogical classification (concluded). After the meeting Professor Haviland gave an account of the nature and use of the stethoscope. May 19, 1828. By Thos. Jarrett, M.A. (Cath.): On two theorems useful in the integration of certain functions. By Joh. Will. Lubbock, M.A. (Trin.): On the calculation of Annuities, and some theorems in the doctrine of chances. Trans, 1. 141—154. November 10, 1828. By Ja. Challis, M.A. (Trin.): On the Law of Distances applied to the Satel- lites. After the meeting Professor Whewell gave a lecture on the granite veins of Cornwall. November 24, 1828. By Professor Airy: On the Longitude of Cambridge. Trans. 111. 155—170. By Rob. Willis, M.A., Gony, and Cai. Coll.: On the vowel sounds. After the meeting Mr Willis exhibited experiments illustrative of his doctrines. December 8, 1828. By Joh. Warren, M.A. (Jes.): On the doctrine of impossible quantities, and their geometrical representation, and on the proof that every equation of m dimensions has 7 roots. By Fre. Thackeray, M.D. (Emm.): On the case of Ann Carter, a young woman at Stapleford, said to be a trance. By Ja. Challis, M.A. (Trin.): On the Law of Distances, etc. (concluded). Trans. 11. 171—183. After the meeting Mr Leonard Jenyns gave an account, illustrated by draw- ings, of the comparative anatomy of Birds and Mammals, and of several particulars respecting the former Class. March 2, 1829. By Pierce Morton, B.A. (Trin.): On the focus of a conic section. Trans. IM. 185—190. on resigning office, 27 October, 1890. XXXi By Professor Whewell: On the application of mathematical reasoning to cer- tain theories of Political Economy. After the meeting Professor Whewell gave an account of various contrivances employed in dipping needles, and of some suggested improvements. March 16, 1829. By Professor Whewell: On the application of mathematical reasoning, etc. (concluded). Trans. 111. 191—230. By Rob. Willis, M.A. (Gonv. & Cai.): On the theory of the sounds of pipes as relating to their vowel quality (concluded from 24 Nov. 1828). Z'rans, U1. 231 —268. After the meeting Mr Willis exhibited experiments illustrative of the influence of the length of the pipe on the vibrations of the reed, and of the different ways in which the vowel sounds may be produced. March 30, 1829. By Ja. Challis, M.A. (Trin.): Abstract of a memoir on the vibrations of elastic fluids. Trans. 111. 269—320. By Joh. Will. Lubbock, M.A. (Trin.): On the tables of the chances of life, and on the value of annuities. Tvans, 111. 321—341. After the meeting Professor Henslow gave an account of the organization and classification of ferns, illustrated by drawings. May 4, 1829. By Professor Whewell: On the mineralogical systems proposed by Nordenski- old, Bernsdorff, Kefersheim, and Naumann. After the meeting Mr Leonard Jenyns gave an account of the construction, properties, and mode of growth, of feathers. May 18, 1829. By Will. Hallows Miller, M.A. (Joh.): On caustics formed by successive re- flexions at a spherical surface. By Rob. Willis, M.A. (Gony. & Cai.): On the mechanism of the human voice. Trans. IV. 323—352. After the meeting Mr Willis exhibited various experiments and models, and explained the action of the organs of voice. November 16, 1829. By Professor Airy: On a correction of the length of a pendulum consisting of a wire and ball. Zvrans. 111. 355—360. By Professor Whewell: On the causes and characters of Pointed Architecture. After the meeting Professor Whewell described the kinds of vaulting employed oo churches, with their history; illustrating his account with models. November 30, 1829. By Ri. Wellesley Rothman, M.A. (Trin.): On an observation of a solstice at Alexandria recorded by Strabo. Trans. 111. 361—363. By Professor Whewell: On Pointed Architecture (concluded). By Will. Hallows Miller, M.A. (Joh.): On the forms and angles of certain erystals. Trans. 111. 365—367. After the meeting Professor Sedgwick gave an account of the geology and structure of the Alps, illustrated by a section from the plains of Bavaria to those of Trieste. XXXil Address of Mr J. W. Clark, President, December 14, 1829. By Professor Airy: On the mathematical conditions of continued motion, Trans. 111. 369—372. By Ch. Pleydell Neale Wilton, M.A. (Joh.): On the geology of the shore of the Severn in the Parish of Awre in Gloucestershire. After the meeting Mr Leonard Jenyns gave an account of the circumstances connected with the migration of Birds. February 22, 1830. By Ja. Challis, M.A. (Trin.): On the integration of the equations of motion of fluids; and on the application of this to the solution of various problems. Trans, 11. 383—416. By Leonard Jenyns, M.A. (Joh.): On the Natter-Jack of Pennant, with a list of Reptiles found in Cambridgeshire. Trans. 111. 373—381. After the meeting Professor Henslow explained the discoveries of M. Dutro- chet on Endosmose and Exosmose. March 8, 1830. By Ch. Pleydell Neale Wilton, M.A. (Joh.): Account of a visit to Mount Wingen, the burning mountain of Australia. By Hen. Coddington, M.A. (Trin.): On the construction of a microscope invented by him, which he exhibited to the Society. After the meeting Professor Airy gave an account, illustrated by models, of the instruments which have been used to measure altitudes: viz. the Zenith Sector, the Quadrant, the Refracting Circle, the large Declination Circles of Troughton, and the Circles of Reichenbach. March 22, 1830. By Will. Hallows Miller, M.A. (Joh.): On the measurement of the angles of certain crystals which occur in the slags of furnaces. J'rans, 111. 417—420, By Hen. Coddington, M.A. (Trin.): On the advantages of a microscope of a new construction. Z’rans. 111. 421—428. By Hugh Ker Cantrien, B.A. (Trin.): On the Calculus of Variations. Mr Willis gave an account, illustrated by models and drawings, of the con- struction and muscles of the tongue, palate, and pharynx, and of the mode in which these operate in the production of vowel and modulated sounds. April 26, 1830. By Leon. Jenyns, M.A. (Joh.): On the late severe winter. 3y Hen. Coddington, M.A. (Trin.): On his new-invented microscope. 3y Professor Whewell: On the proof of the first law of motion. After the meeting Professor Whewell gave an account of Géthe’s objections to the Newtonian theory of Optics, and of the doctrine proposed by that author. May 10, 1830. 3y Tho. Chevallier, M.D.: On the anatomy and physiology of the ear. After the meeting Professor Cumming explained the construction and use of the areometer of Professor Leslie, and its resemblance to the stereometer of Captain Say ; and the construction of an instrument for measuring the whole quantity of sunshine which operates during any given time. on resigning office, 27 October, 1890. XXXill May 24, 1830. By Professor Airy: On the peculiar form of the rings produced by a ray circu- larly polarized, and on the calculation of the intensity of light belonging to this and other cases. By Will. Webster Fisher (Down.): On the appendages to organs as provi- sionary to the modifications of the functions. By Rob. Murphy, B.A. (Gonv. and Cai.): On the general properties of definite integrals, and on the equation of Riccati. Trans. 111. 429—443. By Hen. Coddington, M.A. (Trin.): A further explanation of his microscope. After the meeting Mr Willis exhibited and explained an instrument for making orthographical projections of objects. November 15, 1830. By Aug. De Morgan, B.A. (Trin.), Professor of Mathematics in London University : On the Equation of Curves of the second degree. Trans. Iv. 71—78. By Will. Okes, M.A. (Gonv. and Cai.): On the Wourali poison used by the Maconshi Indians; a blow-pipe, quiver, and arrows were exhibited. By Professor Cumming: A communication from Mr Edwards on a substance resembling cannel coal, found in digging a canal near Norwich. By Ri. Tho. Lowe, B.A. (Chr.): On the Natural History of Madeira. After the meeting Professor Whewell gave an account of a method of con- structing cross vaults without boarded centering, revived and described by M. de Lassaulx of Coblentz. November 29, 1830. By Ri. Tho. Lowe, B.A. (Chr.): On the Natural History of Madeira (con- cluded). Trans. tv. 1—70. By Professor Whewell: Rules for the selection and employment of symbols of mathematical quantity. After the meeting Mr Leonard Jenyns gave an account, illustrated by draw- ings, of the quinary system of Natural History proposed by Mr M*Leay. December 13, 1830. By Professor Whewell : Rules for the selection, etc. (concluded). By Professor Henslow: On the mode of reproduction of the Chara. After the meeting Professor Henslow made some observations on tall ferns, exhibiting a specimen of a stalk. A machine was exhibited invented by Professor Airy for the purpose of ex- hibiting the mode of propagation of undulations along a line of particles. February 21, 1831. By Professor Airy: On the nature of the two rays formed by the double refraction of quartz. Trans. tv. 79—123. After the meeting Professor Airy exhibited a machine for illustrating the nature of the undulations supposed in circular polarization; an instru- ment for exhibiting the rings, spirals, etc. produced by double refraction ; and an instrument for exhibiting the same phenomena by means of the light produced by the combustion of lime in oxygen. March 7, 1831. By Rob. Murphy, B.A. (Gonv. and Cai.): On the general solution of equa- tions. Trans. tv. 125—153. Wer Vil. PT. LV. c XXXIV Address of Mr J. W. Clark, President, After the meeting Mr Willis exhibited a series of experiments on the trans- verse and longitudinal vibrations of strings, membranes, and solids, illus- trative of the researches of M. Savart. March 21, 18381. By Will. Hallows Miller, M.A. (Joh.): On the elimination of the time from the differential equations of the motion of a point, whether affected by a resisting medium, or by any disturbing forces. By the same: On measurements of the angles of certain artificial crystals. After the meeting Mr Willis exhibited and explained a machine constructed for the purpose of illustrating the motion of the particles of any medium in which undulations are propagated. April 18, 1831. By Professor Whewell : On the mathematical exposition of some of the leading doctrines of Mr Ricardo’s Principles of Political Economy and Taxation. By Professor Airy: Notice of an apparatus constructed under his direction by Mr Dollond, and of the phenomena of elliptically polarized light exhibited by means of the apparatus. Trans. Iv. 199—208. After the meeting Professor Henslow exhibited a series of appearances pro- duced by two wheels revolving one behind the other. May 9, 1831. By Ch. Pritchard, B.A. (Joh.): A method of simplifying the demonstration of the two principal theorems respecting the figure of the earth considered as heterogeneous. By Professor Whewell: On the mathematical exposition, etc. (concluded). Trans. IV. 155—198. After the meeting Mr Willis exhibited apparatus illustrating the nature of sound, and the vibrations which produce it, especially an instrument which he calls a Lyophone. May 16, 1831. By Ja. Francis Stephens: Description of Chiasognathus grantii, a new Luca- nideous insect forming the type of an undescribed genus, together with some brief remarks upon its structure and affinities. Trans. Iv. 209—216. By Professor Clark: On a monster of the kind called semidouble. Trans, Iv. 219—255. After the meeting Mr Willis exhibited Mr Trevelyan’s experiment on the rocking of a bar of hot brass placed upon a plate of cold lead. Mr Leonard Jenyns gave an account of the application of the quinary system of Mr M‘Leay to the classification of Birds. November 14, 1831. By Professor Airy: On some new circumstances in the phenomena of Newton’s rings. Trans, Iv. 279—288. By Professor Henslow: On a hybrid plant between Digitalis purpurea and D. lutea. After the meeting Professor Sedgwick gave an account, illustrated by sections, of the geological structure of Caernarvonshire. November 28, 1831. By Leonard Jenyns, M.A. (Joh.): A monograph of the British species of bivalve mollusca belonging to the genera Cyclas and Pisidium, Trans. 1v, 289— 312, on resigning office, 27 October, 1890. XXXV By Sam. Earnshaw, B.A. (Joh.): On the integration of the general linear differential equation of the xth order, and the general equation of differences with constant coefficients. After the meeting Professor Whewell gave an account of the theories of evaporation, the use of Daniel’s hygrometer, and the forrnation of clouds. December 12, 1831. By Professor Cumming: Exhibition of a calculus found in the intestines of a horse, with remarks. By Professor Henslow: On a hybrid Digitalis (concluded). Trans. tv. 257-- 278. After the meeting Mr C. Jenyns gave an account, illustrated by drawings, of the rules of the perspective of shadows, and explained the use of the cen- trolinead. March 5, 1832. By Professor Airy: On a new analyser of light polarized in a peculiar manner. Trans. Iv. 313--322. By Rob. Murphy, B.A. (Gony. and Cai.): On an inverse calculus of definite integrals. (Zrans. Iv. 353—408.) After the meeting Professor Airy exhibited an apparatus illustrative of some of the phenomena referred to in his paper. Professor Henslow gave a lecture, illustrated by specimens and drawings, on the age of trees. March 19, 1832. By Professor Airy: On the phenomena of Newton’s rings when formed between two transparent substances of different refractive powers. Trans. Iv. 409--424. By Will. Brett, M.A. (Corp.): On the phenomena of double stars. After the meeting Mr Whewell gave an account, illustrated by diagrams, of the forms and course of the cotidal lines according to the causes which - influence them, and according to the observations made in different places. ~ April 2, 1832. By J[ohn] Pfrentice] Henslow: On the habits of two hybrid pheasants pre- sented by him to the Society. By B. Bushell: On the anatomy of the same birds. By Will. Brett, M.A. (Corp.): On the theory of stars of variable brightness. May 7, 1832. By Sir Joh. Fre. Will. Herschel, M.A. (Joh.): Description of a machine for : solving equations. Tans. Iv. 425—440. By Will. Holt Yates, M.B. (Joh.): Account of the magnetic mountain of : Sipylus near Magnesia. ; After the meeting Professor Sedgwick gave an account, illustrated by maps and sections, of the Physical Geography and History of the Fens of Cambridgeshire. May 21, 1832. By Sir Joh. Fre. Will. Herschel, M.A. (Joh.): Description of a machine, ete. (concluded). By Rob. Willis, M.A. (Gonv. and Cai.) : On the ventricles of the larynx. By Professor Henslow : On a monstrosity of Reseda. Trans. v. 95—100. After the meeting Mr Willis gave a lecture, illustrated by experiments, on various phenomena of sound, c2 XXXV1 Address of Mr J. W. Clark, President, June 4, 1832. By Joh. Hogg, M.A. (Pet.): On the classical plants of Sicily. By Professor Henslow : Exhibition of a drawing representing the construction of Reseda, in illustration of his former paper. By Professor Clark: Exhibition of a semi-double fetus of a pig, with explanation. By Professor Cumming: On Mr Faraday’s recent discoveries in magneto- electricity, with illustrative experiments. November 12, 1832. By Geo. Green: Mathematical investigations concerning the laws of the equilibrium of fluids analogous to the electric fluid ; with other similar researches. Trans. v. 1—63. By Aug. De Morgan, B.A. (Trin.): On the general equation of surfaces of the second degree. Trans. v. 77—94. After the meeting Professor Henslow gave an account, illustrated by various drawings and diagrams, of various observations of Geology and Natural History made by him during a residence at Weymouth during a portion of the summer. November 26, 1832. By Rob. Murphy, M.A. (Gony. and Cai.): On an elimination between an in- definite number of unknown quantities. Trans. v. 65—75. By Will. Whewell, M.A. (Trin.) : On the architecture of Normandy. After the meeting Mr Ch. Brooke (Joh.) gave an account of the history and recent improvements in Lithotripsy, illustrated by the exhibition of the instruments used, and by several drawings. December 10, 1832. By Will. Whewell, M.A. (Trin.): On the architecture of Normandy (continued). After the meeting Mr Sims gave an account of the various methods of engine- dividing, and of original dividing practised with regard to graduated instruments; and explained particularly the method of original divid- ing invented by Mr Troughton, and recently applied by Mr Sims to the division of the mural circle of the Observatory. This explanation was illustrated by models and apparatus. February 25, 1833. By Will. Whewell, M.A. (Trin.): On the architecture of Normandy (continued) After the meeting Professor Airy gave an account, illustrated by models and diagrams, of his researches concerning the mass of Jupiter by means of observations of the Fourth Satellite. March 11, 1833. By the Marchese Spineto: An examination of the grounds of Sir Isaac Newton’s system of chronology. After the meeting Professor Sedgwick gave an account, illustrated by repre- sentations of sections, of the Geology of North Wales. March 25, 1833. By Jos. Power, M.A. (Trin. Hall): On the effect of wind on the barometer. By Professor Clark: On an unusual situation of the origin of the internal mammary artery, with a drawing and explanation. After the meeting Professor Henslow gave an account, illustrated by dia- grams, of a method of classifying and designating colours, particularly with reference to their use in natural-historical descriptions, on resigning office, 27 October, 1890. XXXVI April 22, 1833. By Professor Miller: On lines produced in the spectrum by the vapour of Bromine, Iodine, and Euchlorine. Phil. Mag. 1833, i. 381. By Will. Whewell, M.A. (Trin.): On the architecture of Normandy (concluded). After the meeting Mr Whewell explained some of the difficulties which had attended his researches concerning co-tidal lines. May 6, 1833. By Mr Millsom: A description of the anatomy of a hybrid animal—a lion- tiger (communicated by Dr Haviland). By Geo. Green: A memoir on the exterior and interior attractions of ellip- soids (communicated by Sir Edw. Tho. French Bromhead, Bart., M.A. Gony. and Cai.). Trans. v. 395—429. By the Marchese Spineto: On an insect which appears in the Egyptian Hieroglyphics. By Professor Airy : On diffraction. Trans. v. 101—111. May 20, 1833. By Will. Hopkins, M.A. (Pet.): On the position of the nodes of the vibration of the air in tubes. Trans. v. 231—270. Mr Hopkins also exhibited experiments illustrating the interference of the vibrations of the air. November 11, 1833. By Rob. Murphy, M.A. (Gony. and Cai.): A second memoir on the inverse method of definite integrals. Trans. v. 113-148. By Professor Airy: An account of various observations made on the Aurora Borealis of September 17 and October 12. Phil. Mag. 1833, ii. 461. November 25, 1833. By Professor Henslow : Observations on a beetle found in a block of maho- . gany presented to the Society. By Ri. Tho. Lowe, M.A. (Chr.) : Description of a molluscous animal of the genus Umbrella, with a drawing and remarks. By Will. Hopkins, M.A. (Pet.) : On the geology of Derbyshire, illustrated by maps and sections. Phil. Mag. 1834, i. 66. December 9, 1833. __ By Hen. Moseley, B.A. (Joh.), Professor of Natural Philosophy in King’s Coll. Lond.: On the general conditions of the equilibrium of a system of variable form; and on the theory of equilibrium, fall, and settlement, of the arch. Trans. v. 293—313. By Professor Farish : On the appearance of a meteor, or falling star, of great splendour, observed by him at a quarter before seven o’clock, on 5 September 26 (he being near Magdalene College). By Professor Sedgwick : On the geology of Charnwood Forest, illustrated by maps and sections. Phil. Mag. 1834, i. 68. February 17, 1834. By Fra. Lunn, M.A. (Joh.): On a specimen of Proteus anguinus, presented by him to the Society. : By Professor Miller: Some optical observations on lines in the vapour of Iodine, Bromine, and Perchloride of Chrome. Phil. Mag. 1834, i. 312. By Will. Whewell, M.A. (Trin.): On the nature of the truth of the Laws of Motion. Trans. v. 149—172. XXXV1ll Address of Mr J. W. Clark, President, March 3, 1834. By Ja. Challis, M.A. (Trin.): On the motion of fluids. Trans. v. 173—203. By Temple Chevallier, B.D. (Cath. H.): On the polarisation of the light of the atmosphere. Pil. Mag. 1834, i. 312. By Professor Miller : Notice of experiments on the Perchloride of Chrome. March 17, 1834. By Jos. Power, M.A. (Trin. Hall): On the theory of Exosmose and Endosmose. Trans. V. 205—229. By Professor Henslow: On Braun’s speculations concerning the arrangement of the scales on fir-cones, with additional remarks. By Professor Airy: On the polarisation of light by the sky, and by rough bodies. Phil. Mag. 1834, i. 313. April 14, 1834. By Professor Airy: On the latitude of the Cambridge Observatory, as deter- mined by means of the mural circle. Trans, v. 271—281. By Will. Whewell, M.A. (Trin.): On Sir J. Herschel’s hypothesis concerning the absorption of light by coloured media. Phil. Mag. 1834, i. 463. April 28, 1834. By Professor Miller: On the axes of crystals. Phil. Mag. 1834, i. 463. By Sam. Earnshaw, B.A. (Joh.): On the laws of motion. — Ibid. After the meeting Mr Willis explained a machine of his construction for jointing together the bones of skeletons. May 12, 1834. By Aug. De Morgan, B.A. (Trin.): An attempt to shew that the principles of the Differential Calculus may be established without assuming the forms of any expansion (in a letter to Mr Peacock). After the meeting Professor Miller exhibited and explained an instrument for taking the specific gravities of bodies. [By Rob. Willis, M.A. (Gony. and Cai.): Exhibition and explanation of an instrument constructed by himself, which he proposes to call an Ortho- graph. By Will. Webster Fisher, M.B. (Down.): On the origin of Tubercular diseases. ] November 10, 1834. By Ri. Tho. Lowe, M.A. (Chr.): Descriptions of six new or rare species of fish from Madeira, with drawings. Tans. vI. 195—201. By Will. Whewell, M.A. (Trin.): Observations of the tides made from June 7 to June 22, 1834, at the coastguard stations; with some observations on the mode of discussing them. November 24, 1834. By Professor Airy: On the rings produced by viewing the image of a star through an object-glass of circular aperture. Trans. v. 283—291. By the same: On the longitude of the Cambridge Observatory, as compared with the result of the Trigonometrical Survey. By Ri. Stevenson, B.A. (Trin.): On the establishment of propositions by the infinitesimal method combined with the doctrine of projections. By Professor Sedgwick: On the geology of Cambridge. Phil. Mag. 1835, i. 74. on resigning office, 27 October, 1890. XXXI1X December 8, 1834. By Professor Miller: On the position of the optical axes of crystals. Trans. v. 431-438. By Professor Henslow: On the Green Sand at Haslingfield, Barton, etc. By the same: On the age of trees, as determined by their size. By Professor Airy : On the echo from the open end of a tall chimney. [By Professor Cumming: A statement of Melloni’s discoveries on the trans- mission of heat by radiation. ] March 2, 1835. By Rob. Murphy, M.A. (Gony. and Cai.): On the inverse method of Definite Integrals. Trans. v. 315—393. By Ri. Stevenson, B.A. (Trin.): On the solution of some problems connected with the theory of straight lines and planes by a new symmetrical method of coordinates. By Will. Hopkins, M.A. (Pet.): On Physical Geology. Trans. vi. 1--84. March 16, 1835. By Will. Webster Fisher, M.B. (Down.): On the nature, structure, and changes, of tubercles, illustrated by coloured drawings. Phil. Mag. 1835, i. 395. After the meeting Mr Willis gave an account, illustrated by drawings and models, of the progress of Gothic Architecture, and especially of the formation of tracery. Ibid. March 30, 1835. By Aug. de Morgan, B.A. (Trin.): On the theorem of M. Abel relative to the algebraical expression of the roots of equations which are connected by the law of periodic functions. By Will. Whewell, M.A. (Trin.): Exhibition and explanation of an Anemome- ter of a new construction; with a statement of the use which might be made of observations made by means of it. May 4, 1835. By Professor Airy: An account of results recently obtained at the Observatory with respect to: (1) the obliquity of the ecliptic ; (2) the mass of Jupiter ; (3) Jupiter’s time of rotation. By Will. Whewell, M.A. (Trin.): On the results of the Tidal Observations of the Coast Guard of June, 1834; and on those intended to be made in June, 1835. May 18, 1835. By Archib, Smith (Trin.): A communication containing the eliminations by which the equation of the wave surface in Fresnel’s theory of undulations is determined in a manner more simple than in previous investigations of other authors on the same subject (read by Professor Airy). Trans. vI. 85—89. By Will. Whewell, M.A. (Trin.): An extract of a letter from Professor Schu- macher, stating that Messrs Beer and Médler had found the time of Jupiter’s rotation to be 9° 55™ 26°, 5; and that M. Bessul had made a long series of observations which give the mass of Jupiter nearly identical with those of Professor Airy. By Will. Webster Fisher, M.B. (Down.): On tubercles (continued). June 1, 1835. By Rob. Willis, M.A. (Gonv. and Cai.): An account, illustrated by models, of the progress of decorative construction in vaults. Phil. Mag. 1835, i. 71. xl Address of Mr J. W. Clark, President, November 16, 1835. By Rob. Murphy, M.A. (Gony. and Cai.): On the resolution of equations of finite differences. Trans. v1. 91—106. Extracts of letters written by Sir J. F. W. Herschel, M.A. (Joh.) from the Cape of Good Hope, on meteorological observations made by him there. Extracts of letters from Ch. Rob. Darwin, B.A. (Chr.) containing accounts of the geology of certain parts of the Andes and 8. America. November 30, 1835. By Will. Wallace, F.R.S., Prof. of Mathematics, Edinburgh (Hon. Member) : On a geodetical problem. TZvans. v1. 107—140. By Professor Airy: On a supposed analysis of the spectrum by Sir D. Brewster. December 14, 1835. By Ri. Potter (Qu.): On the explanation of the phenomena of the rainbow by the doctrine of interferences. Trans. vI. 141—152. By Ch. Rob. Darwin, B.A. (Chr.): On viviparous lizards, and on red snow. February 21, 1836. By Phil. Kelland, B.A. (Qu.): On the dispersion of Light on the Undulatory Theory. Trans. v1. 153—-184. By Will. Whewell, M.A. (Trin.): On the Tides. Phil. Mag. 1836, i. 430. March 7, 1836. By Will. Whewell, M.A. (Trin.): On the recent discoveries of Professor Forbes and others respecting the polarisation of heat. Phdl. Mag. 1836, i. 430. After the meeting Mr Willis gave a lecture on the composition and resolution of the entablature in Egyptian and Grecian architecture. Ibid. March 21, 1836. By Sam. Earnshaw, M.A. (Joh.): On the solution of the equation of con- tinuants of fluids in motion. Trans. VI. 203—233. By Professor Miller: On the position of the axes of optical elasticity of certain crystals. Trans. VII. 209—215. By Tho. Webster, M.A. (Trin.): On the connection of the periodical [motions] of the barometer with the changes of temperature; and on the relation of the accidental changes with the occasional changes. Apri 18, 1836. By Professor Sedgwick: An account of the system of formations inferior to the Carboniferous Series, as illustrated by his own researches in Wales, and those of Mr Murchison in the same country. May 2, 1836. By Geo. Biddell Airy, M.A. (Trin.), Astronomer Royal: On the intensity of light in the neighbourhood of the caustic. Trans. vi. 379—402. By Will. Hopkins, M.A. (Pet.): On the agreement between his theoretical views of the elevatory geological forces, and the phenomena of faults, as observed by him in the strata of Derbyshire. May 16, 18386. By Aug. De Morgan, B.A. (Trin.): Sketch of a method of introducing discon- tinuous constants into the arithmetical expressions for infinite series. (In a letter to Mr Peacock.) Trans. v1. 185—193. ; § € on resigning office, 27 October, 1890. xli By Phil. Kelland, B.A. (Qu.): On the constitution of the atmosphere and the connexion of light and heat. Zvrans. v1. 235—288. By Will. Hopkins, M.A. (Pet.): Observations on the temperature of mines, and the doctrine of central heat. By Geo. Biddell Airy, M.A. (Trin.): Observations of temperature during the great Solar Eclipse of 15 May. November 14, 1836. No papers recorded. November 28, 1836. By Joh. Thompson Exley (Joh.): On the leading features of a new system of Physics. By Professor Henslow: On various kinds of pebbles and agates, with conjec- tures respecting the origin of the bands of colour with which they are marked. December 12, 1836. By Sam. Earnshaw, M.A. (Joh.): On the appearance of light received on a screen after passing through an equilateral triangle placed behind the object-glass of a telescope. Trans. v1. 431—442. By Ja. Jos. Sylvester (Joh.): On elimination, and the use of indeterminate constants. By Will. Hopkins, M.A. (Pet.): On the formation of veins in Derbyshire. February 13, 1837. By Professor Challis: On the temperature of the higher regions of the atmo- sphere. rans. vi. 443—455. By Steph. Pet. Rigaud, Savilian Professor of Astronomy, Oxford: On the rela- tive proportions of Land and Water. Trans. v1. 289—3800. By Phil. Kelland, B.A. (Qu.): On the transmission of light through crystal- lised media. Zvrans. VI. 323—352. February 27, 1837. By Joh. Warren, M.A. (Jes.): On the algebraical sign of the perpendicular from a given point upon a given line. By Ch, Rob. Darwin, B.A. (Chr.): An account of fused sand-tubes found near the Rio Plata—which were exhibited, along with several other specimens of rocks, By Will. Webster Fisher, M.B. (Down.): On a case of Spina bifida. Phil. Mag. 1837, i. 316. March 13, 1837. By Phil. Kelland, B.A. (Qu.): Supplement to his paper read 13 February. By Sam. Earnshaw, M.A. (Joh.): On the laws of fluid motion. By Hen. Joh. Hales Bond, M.D. (Corp.): A medical-statistical Report of Addenbrooke’s Hospital for 1836. Trans. v1. 361—377. By Will. Whewell, M.A. (Trin.): An account of the recent results of his researches respecting the Tides. April 17, 1837. By Leonard Jenyns, M.A. (Joh.): On the temperature of the month of March last past. Phil. Mag. 1837, i. 485. By Rob. Willis, M.A. (Gony. and Cai.): Exhibition and explanation of a Tabuloscriptive Engine. Ibid. xl Address of Mr J. W. Clark, President, May 1, 1837. By Art. Aug. Moore (Trin.): Solution of a difficulty in the analysis of Lagrange noticed by Sir W. Hamilton (read by Mr Peacock). TZrans. v1. 3L7—322. By Will. Whewell, M.A. (Trin.): On the results of his Anemometer for the first three months of 1837. Trans. vi. 301—315. By Phil. Kelland, B.A. (Qu.): On the elasticity of the aether in crystals. Trans. Vi. 353—360. May 15, 1837. By Geo. Green (Gony. and Cai.): On the propagation of an undulation in heavy fluids in a canal of small depth and width. Trans. v1. 457—462. By Will. Hopkins, M.A. (Pet.) : On the refrigeration of the earth, and on the doctrine of internal fluidity of the earth. By Hen. Moseley, M.A. (Joh.): On the theory of the equilibrium of bodies in contact. Zrans. v1. 463—491. [By Will. Webster Fisher, M.B. (Down.): On Spina bifida. Phil. Mag. 1837, i. 486.] November 13, 1837. By Car. Jeffreys, M.A. (Joh.): Exhibition and explanation of the Respirator invented by his brother. By Professor Sedgwick : On the geology of Charnwood Forest and the neigh- bouring coaltields. November 27, 1837. By Geo. Green (Gony. and Cai.): On the vibration of air. Trans, v1. 403— 413. By Will. Hopkins, M.A. (Pet.): On certain elementary principles of geological theory ; and on Professor Babbage’s speculations. December 11, 1837. By Geo. Green (Gonv. and Cai.) : On the reflexion and refraction of light in non-crystallised media. Trans. vil. 1—24. By Ri. Wellesley Rothman, M.A. (Trin.): On the observation of Halley’s comet in 1836. Trans. V1. 493—506. By Will. Hopkins, M.A. (Pet.): On Precession and Nutation, assuming the interior fluidity of the earth. February 26, 1838. By Dav. Tho. Ansted, B.A. (Jes.): On a new genus of fossil shells. Trans. VI. 415—422, By Aug. De Morgan, B.A. (Trin.): Ona question in the theory of probabilities. Trans. V1. 423—430. By Dan. Cresswell, D.D. (Trin.): On the squaring of the circle. March 12, 1838, By Phil. Kelland, M.A. (Qu.) : On molecular attraction. Trans. Vil. 25—59. By Professor Henslow: On plants brought by Mr Darwin from Keeling Island. March 26, 1838. By Geo. Biddell Airy, M.A. (Trin.): On the intensity of light in the neighbour- hood of a caustic. Trans. VI. 379—402. By Professor Challis : On the proper motions of the stars. on resigning office, 27 October, 1890. xl April 30, 1838. By Ri. Potter, B.A. (Qu.): On a new correction in the construction of the double achromatic object-glass. Trans. vi. 553—564, By Will. Hen. Trentham, M.A. (Joh.): On the expansion of a polynomial. By Hen. Joh. Hayles Bond, M.D. (Corp.): Statistical report on Addenbrooke’s Hospital for 1837. Trans. v1. 565—575. By Pet. Bellinger Brodie, B.A. (Trin.): On the occurrence of recent land and fresh-water shells with bones of some extinct animals in the gravel near Cambridge ; communicated by Professor Sedgwick. Trans. vit. 138— 140. May 14, 1838. By Joh. Tozer, B.A. (Gony. and Cai.) : On the application of mathematics to calculate the effects of the use of machinery on the wealth of a com- munity. Trans. vi. 507—522. By Duncan Farquharson Gregory, B.A. (Trin.): On the real nature of symbolical algebra. By Professor Miller: On measures of spurious rainbows. May 28, 1838. By Professor Miller: An account of experiments illustrating the unequal expansion of crystals by heat. By Ri. Tho. Lowe, M.A. (Chr.). On the Botany of Madeirat. Trans. vi. 523 —d5l1. November 12, 1838. By Professor Whewell : On certain rude kinds of architecture. November 26, 1838. By Duncan Farquharson Gregory, B.A. (Trin.): On the logarithms of negative quantities. By Professor Henslow : On the formation of mineral veins, illustrated by a specimen. December 10, 1838. By Hamnett Holditch, M.A. (Gony. and Cai.): On rolling curves (com- municated by Professor Willis). Zvans. vu. 61—86. By Ri. Wellesley Rothman, M.A. (Trin.): On the climate of Italy. By Ri. Tho. Lowe, M.A. (Chr.): An additional note on the Flora of Madeira. By Professor Henslow: On the structure of wasps’ nests, illustrated by specimens. February 18, 1839. By Ri. Wellesley Rothman, M.A. (Trin.) : On the climate of Italy (concluded). By Ri. Potter, B.A. (Qu.): On the determination of the value of (A), the length of an undulation of light. By Geo. Green, B.A. (Gonv. and Cai.): Appendix to a former paper on waves, read 15 May, 1837. Trans. vu. 87—9°. March 4, 1839. By Will. Hopkins, M.A. (Pet.): On the geology of England and France in the neighbourhood of the Channel. 1 This paper is not mentioned in the Minutes. The date assigned to it is derived from the Transactions. xliv Address of Mr J. W. Clark, President, March 18, 1839. By Sam. Earnshaw, M.A. (Joh.): On the equilibrium of a system of particles. Trans. Vu. 97—112. By Geo. Biddell Airy, M.A. (Trin.): On the diurnal changes of the variation of the magnetic needle. April 22, 1839. By Duncan Farquharson Gregory, B.A. (Trin.): On photogenic drawings. By Professor Sedgwick: On the geology of Cornwall and Devon. May 6, 1839. By Professor Miller: On the calculation of halos, according to Fraunhofer’s theory. By Geo. Green : Note on reflection and refraction. Trans. vi. 113—120. By Duncan Farquharson Gregory, B.A. (Trin.): On chemical classification. May 20, 1839. By Geo. Green, B.A. (Gony. and Cai.): On the motion of light through crys- tallised media. Trans. vu. 121—140. By Dav. Tho. Ansted, B.A. (Jes.): On the tertiary formations of Switzerland. Trans. Vu. 141—152. By Professor Whewell: An account of observations made with his Anemo- meter since May, 1837. November 11, 1839. By Professor Whewell: On a new theory of the Tides. PAil. Mag. 1839, li. 476. November 25, 1839. By Professor Sedgwick: On the geology of northern Germany, east and west of the Rhine. December 9, 1839. By Aug. De Morgan, B.A. (Trin.): On the foundations of Algebra. Trans. vil. 173—187. By Dav. Tho. Ansted, B.A. (Jes.) : On the geology of the Transition Rocks in the north-east of Bavaria and the Principality of Reuss. By Will. Webster Fisher, M.B. (Down.): On the malformation of certain parts of the nervous system. March 2, 1840. By Geo. Biddell Airy, M.A. (Trin.): On a new construction of the Going Fusee, applied in the Northumberland telescope. Trans. vu. 217— 277. By Ch. Pritchard, M.A. (Joh.): On the achromatism of the telescope. March 16, 1840. By Aug. De Morgan, B.A. (Trin.): On the foundation of algebra. By Joh. Tozer, M.A. (Gony. and Cai.): On some doctrines of Political Economy. Trans. vil. 189—196. March 30, 1840. By Phil. Kelland, M.A. (Qu.): On the quantity of light intercepted by a grating placed before a lens. Trans. vu. 153—171. on resigning office, 27 October, 1890. xlv May 4, 1840. By Phil. Kelland, M.A. (Qu.): On the Law of molecular attraction. May 18, 1840. By Day. Tho. Ansted, M.A. (Jes.): On the Green Sandstone formation of Blackdown, Devon. By Professor Miller: On the structure of the Heliotropes of Gauss, Steinheil, and Schumacher. June 1, 1840. By Will. Hopkins, M.A. (Pet.): On certain geological phenomena of elevation, and their connection with the formation of volcanoes. Phil. Mag. 1840, ii. 154. November 16, 1840. By Roderick Impey Murchison: On the geology of Russia. By Geo. Biddell Airy, M.A. (Trin.): On an optical fact, and its explanation on the undulatory theory. November 30, 1840, By Professor Henslow : On the diseases of wheat. December 14, 1840. By Aug. De Morgan, B.A. (Trin.): On the composition of forces. By Professor Whewell: On the equilibrium of oblique arches. February 22, 1841. By Professor Whewell : Additional remarks on oblique arches. By the same: Is all matter heavy? Trans. vit. 197—207. March 8, 1841. By Joh. Tozer, M.A. (Gonv. and Cai.): On some mathematical formule for determining the permanent effects of emigration and immigration on numbers. Phil. Mag. 1841, i. 318. March 22, 1841. By Professor Miller: On supernumerary rainbows. Trans. vit. 277—286. April 26, 1841. By Professor Challis : On the resistance of air to a pendulum with a spherical bob. Trans. VII. 333—353. May 10, 1841. By Professor Willis: On the arrangement of the joints of crustaceous animals. By the same: On the original nomenclature of Gothic mouldings. May 24, 1841. By Professor Challis : On a new kind of interference of light. November 15, 1841. By Professor Sedgwick : An account of the comparative classification of the older strata in the British Isles, xlvi Address of Mr J. W. Clark, President, November 29, 1841. By Aug. De Morgan, M.A. (Trin.): On the foundation of algebra. Trans. vil. 287—300. By Jos. Power, M.A. (Trin. Hall): On the late accident on the Brighton railway. TZrans. v1. 301—317. By Joh. Fre. Stanford, B.A. (Chr.): On a newly invented locomotive. December 13, 1841. By Will. Hopkins, M.A. (Pet.): On the forms of the isothermal surfaces within the earth ; and on the thickness of the earth’s solid crust, supposing the central portion to be fluid. By Aug. De Morgan, B.A. (Trin.): On the foundation of algebra (continued). February 14, 1842. By Rob. Leslie Ellis, M.A. (Trin.): On the foundations of the doctrine of chances. Trans. vit. 1—6. February 28, 1842. By Rob. Leslie Ellis, M.A. (Trin.): On the doctrine of chances (concluded). Trans. Vit. 1—6. March 14, 1842. By Mr Taplin: On the solution of a cubic equation. By Professor Whewell (Master of Trinity College): Are cause and effect simultaneous or successive? Trans. vu. 319—331. April 11, 1842. By Professor Challis: On the differential equations of fluid motion. Trans. vil. 371—396. By Professor Owen: On the fossil remains of a new genus of Saurians called Rhynchosaurus, discovered in the New Red Sandstone of Warwickshire. Trans. Vil. 355—369. April 25, 1842. By Matth. O’Brien, M.A. (Gonv. and Cai.): On the propagation of luminous waves in the interior of transparent bodies. 7rans. vil. 897—437. By Geo. Gabriel Stokes, B.A. (Pemb.) : On the steady motion of incompressible fluids. Trans, vit. 439—453. May 9, 1842. By Professor Kelland: On the motion of glaciers. 3y the same: On the laws of fluid motion. : By Jos. Power, M.A. (Trin. Hall): On fluid motion. 7’rans. vit. 455—464, 3y Professor Miller : An account of the Dioptrische Untersuchungen of Gauss, November 14, 1842. By Professor Fisher: On the development of the spinal ganglia in animals, and on the malformation of various portions of the nervous system in Man. Phil. Mag. 1842, ii. 485. November 28, 1842. By Matth. O’Brien, M.A. (Gonv. and Cai.): On the intensity of reflected and refracted light, the absorption of light, and the stability of the luminous ether. Trans, vil. 7—26, on resigning office, 27 October, 1890. xlvii December 12, 1842. By Will Hopkins, M.A. (Pet.): On the glaciers of the Bernese Alps. February 20, 1843. By Art. Cayley, B.A. (Trin.): On some properties of determinants. Trans. vill. 75—88. By Matth. O’Brien, M.A. (Gony. and Cai.): On the absorption of light by transparent media. Trans. VIII. 27—30. March 6, 1843. By Professor Challis: On a new general equation in Hydro-dynamics. Trans. Vut. 31—43. By Geo. Kemp, M.B. (Pet.) : On the nature of the biliary secretion : to shew that the bile is essentially composed of an electro-negative body, in chemical combination with one or more inorganic bases. Trans. VIII. 44—49, March 20, 1843. By Professor Sedgwick : On Professor Owen’s memoir on the skeleton of the Mylodon ; and on the structure and habits of certain extinct genera of gigantic Sloths. May 1, 1843. By Professor Challis : On the comet of 1843. By Will. Williamson, M.A. (Cla.): Two letters on the same subject. By Will. Hopkins, M.A. (Pet.): On the motion of glaciers. Trans, VIII. 50—74. May 15, 1843. By Hamnett Holditch, M.A. (Gonv. and Cai.): On small finite oscillations. Trans. Vi. 89—104. By Professor Willis: On the vaults of the Middle Ages. May 29, 1843. By Geo. Kemp, M-:B. (Pet.): On the relation between organic and organized bodies ; with some remarks on the theory of organic combinations as proposed by Laurent. By Geo. Gabriel Stokes, B.A. (Pemb.): On some cases of fluid motion. Trans, Vit. 105—137. October 30, 1843. By Will. Hopkins, M.A. (Pet.): An account of the large reflecting telescope which the Earl of Rosse is now constructing; with an account of the manner in which its 6 feet speculum has been prepared. November 13, 1843. By Professor Sedgwick: An account of the structure and relations of the slate rocks of North Wales. Between 1831 and 1843 the Proceedings of the Society were reported— somewhat irregularly—in the Philosophical Magazine. The notices, as a general rule, are extremely brief ; but I have thought it worth while to add references to those papers that are not printed in the Society’s Transactions xlvi Address of Mr J. W. Clark, President. whenever the abstracts give details. Moreover, this Journal preserves the titles, and brief abstracts, of four papers not noticed in the Minutes of the Society. These I have included between square brackets. They belong to the meetings held May 12, December 8, 1834; May 15, 1837. P.S. Since writing the above sketch, I have discovered that a somewhat similar scheme for the establishment of a Philosophical Society had been projected in 1782. “The death of some persons interested in the plan, and several accidents, occasioned the scheme to be postponed till February 18th, 1784,” when Professor Milner, Mr Farish, and some others “associated them- selves under certain laws and regulations.” They were presently joined by several of the most distinguished men in the University, among whom occurs the illustrious name of Porson, and a volume of “Tracts, Philosophical and Literary, by a society of gentlemen of the University of Cambridge” was projected, but never published, though two of the contributions were printed. “This little society of learned men, not being adequately supported, was dissolved about the close of the year 17861.” One promoter at least of this noble, though unsuccessful, attempt, Mr Farish, Jacksonian Professor from 1813 to 1837, became a member of the Philosophical Society. 1 This information is derived from: Memoirs of John Martyn, F.R.S., and of Thomas Martyn, B.D., F.RS., F.L.S., Professors of Botany in the University of Cambridge. By G.C. Gorham. 8yo. Lond, and Camb. 1830, p. 165. INDEX OF CONTRIBUTORS. AY. Airy, Geo. Biddell, xxiii, xxiv, xxv, xxvi, RRVMXXVI, XKIK, XXX, XXX1, XXXIi, Ree XKXIV, XXXV, XKXVi, XXXvVii, XXXVili, xxxix, xl, xli, xlii, xliv, xlv Alderson, Ja., xxvii Ansted, Day. Tho., xlii, xliv, xlv B. Babbage, Ch., xx, xxii, xxv, xxvii Bankes, Will. Joh., xxiv Bond, Hen. Joh. Hales, xli, xliii Brett, Will., xxxv Brewster, Dav., xxii, xxiii Brodie, Pet. Bellinger, xhii Brooke, Ch., xxxvi Bushell, B., xxxv C. Cantrien, Hugh Ker, xxxii Cayley, Art., xlvii Cecil, Will., xxi, xxli, xxiii, xxiv Challis, Ja., xxx, xxxi, xxxli, xxxviii, xli, xlii, xlv, xlvi, xlvii Chevallier, Temple, xxx, xxxviii a9 Tho., xxxii Christie, Sam. Hunter, xxi Clark, Prof., xxxiv, xxxvi Clarke, Prof., xx, xxi, xxii, xxiii Coddington, Hen., xxx, xxxii, xxxiii Cresswell, Dan., xlii Cumming, Prof., xxi, xxii, xxiv, xxvi, XXVIil, XXXii, XXXili, XXXV, XXxXVi, xxxix D. D’Arblay, Alex. Ch. Louis, xxix Darwin, Ch. Rob., xl, xli Davis, J., xX, Xxi De Morgan, Aug., xxxiil, xxxvi, xxxviil, xxxix, xl, xlii, xliv, xlv, xlvi KE. Earnshaw, Sam., xxxy, xxxviii, xl, xli, xliv Ellis, Rob, Leslie, xlvi Emmett, Mr, xx Exley, Joh. Thompson, xli F. Fairfax, Capt., xx Farish, Prof., xx, xxvi, xxvii, xxxvii Fawcett, R. M., xxix. Higher Wee Wey) SEX KXXOEX, XL xii xliv, xlvi G. Green, Geo., xxxvi, xxxvii, xlii, xliii, xliv Gregory, Duncan Farquharson, xiii, xliv i Olinthus, xxiv H. Hailstone, Joh., xx, xxii Harvey, G., xxv Haviland, Prof., xxi, xxvi, xxx Henslow, Joh. Stevens, xxii, xxiii, XXVili, XXIX, XXXi, XXXIi, XXXIil, Xxxiv, XXXV, XXXVi, XXXVii, XXXVili, xxxix, xli, xlii, xliii, xlv Joh, Prentice, xxxv Herschel, Joh. Fre. Will., xx, xxii, xxxv, xl Hogg, Joh., xxv, xxxvi Holditch, Hamnett, xliii, xlvii Hopkins, Will., xxxvii, xxxix, xl, xl, xlii, xliii, xlv, xlvi, xlvii J. Jarrett, Tho., xxix, xxx Jeffreys, Ch., xlii. Jenyns, C., xxxv - iheon.,, SXvils xxix (XXX, XXXI; XXXli, Xxxlii, xxxiv, xli d l Index of Contributors. K. Kelland, Phil., xl, xli, xlii, xliv, xlv, xlvi Kemp, Geo., xlvii King, Josh., xxiv L. Lee, Prof., xxi Leeson, H. B., xxiii Leslie, Prof., xxi Lowe, Ri. Tho., xxix, xxxiii, xxxvli, XXxvlil, xlili Lubbock, Joh. Will., xxx, xxxi Lunn, Fra., xxi, xxxi, XxxVii M. Mandell, Will., xxii, xxiii, xxv, xxix Miller, Will. Hallows, xxxi, xxxii, XXXIV, XXXVil, XXXViil, xxxix, xl, xliii, xliv, xlv, xlvi Millsom, Mr, xxxvli Moore, Art. Aug., xlii Morton, Pierce, xxx Moseley, Hen., xxxvii, xlii Murchison, Roderick Impey, xlv Murphy, Rob., xxxill, xXXxV, XxxvVi, XXXVii, XXxix, xl Murray, Joh., xxiv N. Newton, Sir L., xxv O. O’Brien, Matth., xlvi, xlvii Okes, Will., xx, xxii, xxv, xxxiii Owen, Ric., xlvi ize Peacock, Geo., xxiv, XXv, XXvii, xXvili, Xxix Potter, Ri., xl, xliii Power, Jos., xXvi, xxxvi, xxxviii, xlvi Pritchard, Ch., xxxiv, xliv R. Rigaud, Steph. Pet., xli Ross, Mr, xxi Rothman, Ri. Wellesley, xxvii, xxxi, xlii, xliii 8 Schumacher, Prof., xxxix Sedgwick, Prof., xx, xxi, Xxii, xxiii, EXV, XXVi,; XXVil,. KXVIli| Xxixyme XXXIV, XXXV, XXXVi, XXXVIJ, XXXViil, xl, xlii, xliv, xly, xlvii Sims, Mr, xxxyvi Smith, Archib., xxxix Spilsbury, Fra. Gybbon, xxiii Spineto, Marchese, xxxvi, xxxvii Stanford, Joh. Fre., xlvi Stephens, Ja. Fra., xxxiv Stevenson, Ri., xxxviii, xxxix Stokes, Geo. Gabr., xlvi, xlvii Sutcliffe, Will., xxviii Sylvester, Ja. Jos., xli ie Taplin, Mr, xlvi Thackeray, Fre., xxii, xxix, xxx Thompson, Mr, xx Thomson, Alex., xxix Tozer, Joh., xlili, xliv, xlv Trentham, Will. Hen., xliii W. Wallace, Will., xl Warren, Joh., xxx, xli Wavell, Dr, xxi Wayne, Will. Hen., xxvii Webster, Tho., xl Whewell, Will., xx, xxii, xxiii, xxiv, xxvi, XXVI, XXVlll, XXIX, XXX, XKxI, oer, XXXili, XXXIV, XXXV, XXXVI) xoamvils XXXvill, xxxix, xl, xli, xlii, xliii, xliv, xlv, xlvi Williamson, Will., xlvii Willis, Rob., xxx, Xxxi, Xxx, xxx XXXIV, XXXV, XXXVill, xxxix, xl, xli, xlv, xlvii Wilton, Ch. Pleydell Neale, xxxii Woodall, Will., xxvii ¥. . Yates, Will. Holt, xxxv CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AND SONS, AT THE UNIVERSITY PRESS, PROCEEDINGS OF THE Cambridge Philosophical Society. October 28, 1889. ANNUAL GENERAL MEETING. Mr J. W. CLARK, PRESIDENT, IN THE CHAIR. THE following Fellows were elected Officers and new Members of Council for the ensuing year: President: Mr J. W. Clark. Vice-Presidents: Dr Routh, Prof. Babington, Prof. Liveing. Treasurer: Mr Glazebrook. Secretaries: Mr Larmor, Mr Harmer, Mr Forsyth. New Members of Council: Prof. Cayley, Prof. Darwin, Prof. Lewis, Dr Gaskell. VOL, VII. PT. I. 1 2. President's Address. [Oct. 28, The names of the benefactors of the Society were recited by the Secretary. On the motion of the PRESIDENT, seconded by the TREASURER, it was resolved :—That during the ensuing session the meeting of the Council of the Society be fixed for 4 o’clock in the afternoon; that the meeting of the Society be fixed for 4.30, when tea will be provided, and that the formal business of the meeting be taken at 5 o'clock. The President delivered the following address : I rise, according to custom, to say a few words at what would, under ordinary circumstances, be the close of my first year of office as your President. It happened, however, that in con- sequence of the lamented death of Mr Coutts Trotter I was elected on Monday, 30 January, 1888, instead of at the usual time in November. I have therefore had the honour of holding the office for a year and nine months. During that period the Society has pursued the even tenour of its way, undisturbed by revolutions or dissensions, but at the same time giving signs of vigorous and healthy life. It is evident that we can no longer expect that a majority of those elected to College Fellowships in this University will seek the further dis- tinction of our Fellowship, almost as a matter of course, as they used to do; but it may still be a subject of congratulation that our annual recruits make up in quality for defects in quantity; and, if I am not too sanguine, I think that the ancient popularity of our Society may, at any rate to some extent, be revived. Our meetings have been well attended; but it seems to me that it might be possible to render them still more attractive, and so to make them fortnightly gatherings of those who, being in- terested in scientific pursuits, are anxious to meet persons of tastes similar to their own. With this object in view a proposal will be submitted to you for changing the hour of meeting. You remember that in 1881-82 the hour was changed from eight in the evening to three in the afternoon. That change was received with approbation; but since then it has been represented to the Council that a further change to a somewhat later hour in the afternoon would now be more convenient. It is now, therefore, proposed to meet at half-past four; and further, to offer, before the meeting, that refreshment which, in all circles, whether rich or poor—scientitic, literary, or social—offers a resting-place be- tween lunch and dinner—or between dinner and supper—namely, tea. It was remarked long ago that “great events from little causes spring;” so let us hope that this innocent beverage, which has not, as yet, fallen under the ban of any school of reformers, 1889.] President's Address. 3 may operate as a charm to bring our members together, and pro- mote the ends we have in view. There is another matter to which I would briefly allude—our Library. The importance of having a central scientific Library in these buildings, in addition to departmental libraries, has long been recognised in principle; and I cannot but think that when the practical usefulness of it becomes more widely known, members of the University will gladly support it by becoming Fellows of the Society. At present the number of students who use it steadily increases; but I am sorry to say that the power of the Society to support it is diminishing. In this year it became necessary to ask the Museums and Lecture Rooms Syndicate to defray the cost of certain periodicals which had heretofore been borne by the Society. This the Syndicate agreed to do; but I would remark that, while they fully recognise the value of the Library, and are willing to spend money liberally upon it, the funds at their disposal are by no means large, having regard to what they have to do with them. Meanwhile the Library is deficient in numerous works which are being continually asked for, and which neither the Society nor the Syndicate are rich enough to purchase. The smallness of our funds operates to our disadvantage in another way—we are unable to illustrate our publications as fully as is desirable. You will, I am sure, give credit to those in charge of our Proceedings for the pains they bestow upon them, and for the praiseworthy rapidity with which they are circulated. A number of the Proceedings completing Vol. vi. is now on the table; and a part of the Transactions, completing Vol. XIv. is now ready. I beg to return my most cordial thanks to the Council and the officers of the Society for the assistance they have rendered to me personally; and I am sure that you will recognise the admirable zeal with which they have discharged their duties to the Society. The Treasurer, Mr Glazebrook, should be specially congratulated on the success which has attended his efforts to obtain payment of arrears of subscriptions due to the Society. Lastly, it is my duty to record the names of those Fellows of the Society whom we have lost by death during the past year. I will take them in the order of seniority. The Rey. Richard Okes, D.D., Provost of King’s College. The Rey. Benjamin Hall Kennedy, D.D., Regius Professor of Greek. William Henry Drosier, M.D., Fellow of Gonville and Caius College. _ The Rev. Churchill Babington, D.D., formerly Fellow of St John’s College. . is + Dr C. Taylor, On Newton's description of Orbits. [Oct. 28, John Reynolds Vaizey, M.A., Peterhouse. Besides these, we have lost one honorary member: James Prescott Joule, F.R.S. It had been my intention to attempt a short biography of each of these; but I found that I had neither time nor materials to perform such a task efficiently. Moreover, they are for the most part too well known, and too intimately connected with this University, to need such commendation. It would, however, be a personal satisfaction to myself to remind you that in Mr Vaizey—who died from the results of an accident at the beginning of this year—the Biological School has lost an energetic worker, whose usefulness as a teacher had been already recognised, and who, had he lived, would probably have risen to eminence in his own special science, Botany. The following Communications were made to the Society: (1) On Newton’s description of orbits. By CHARLES TAYLOR, D.D., Master of St John’s College. The Master drew attention to the fact that the problem of constructing a Conic Section to satisfy given conditions has been treated incidentally with great power and considerable complete- ness in the Principia. A comparison was made between the methods of Newton and the more modern methods: and some improvements were suggested. The way in which Newton passes from cases of real intersection of lines with conics to cases in which real points of intersection do not exist, strongly suggests the question whether he had possession of the idea of imaginary points, which is usually ascribed to a much later period. (2) On impulsive stress in shafting, and on repeated loading. By Prof. Kart Pearson, University College, London. (3) On Inquid Jets and the Vena Contracta. By H.J. SHARPE, M.A., St John’s College. 1. When liquid flows out of a vessel through an orifice, a liquid particle in coutact with the vessel describes an ordinary stream-line as long as the particle is within the vessel, but the moment it escapes through the orifice, this stream-line suddenly becomes also a line of constant velocity, if no force acts on the liquid. In the solutions presently to be given, which are capable of infinite variety, the coincidence between the outer stream-line of the jet and a line of constant velocity is not (as in Kirchhoff’s solutions) mathematically perfect, but (even near the orifice, where it is most imperfect) can be made, as will be seen from examples, very close, and as we pass along the jet. becomes very 1889.] Mr H. J. Sharpe, On Liquid Jets, &e. 5 rapidly nearly perfect. If the position of the orifice (subject however to the limitation that the coefficient of contractoin must be >4) be arbitrarily chosen, it will be seen that it can be so chosen as to make the coincidence as close as may be desired. If however, which seems the more correct course, it be chosen from a consideration presently to be given (Art. 5) it is not easy, I think, to say for certain whether the above-named coincidence can be made as close as may be desired. It is an interesting ques- tion which remains for solution. The motion is in two dimensions and everywhere finite. The species of vessel for which solutions are obtained may be described generally as a canal, whose sides up to a certain point are straight and then turn off abruptly at right angles into a curve towards an orifice, at the axis of the canal, on each side of which the fluid motions are symmetrical *. The jet ultimately approaches an asymptote parallel to its axis. The ratio of the breadth of the vessel to the ultimate breadth of the jet can be made anything we like, but we shall always suppose it an even integer. 2. Liquid is supposed to be flowing from right to left, roughly speaking parallel to the axis of 2, which is taken as the axis of the vessel and jet. The stream-line AF BH is taken for the boundary of the vessel. Fig. 1 may be taken as the type of the Fic. 1. ‘general case. OE is always 7, and OB, OD submultiples of 7. In figures of which fig. 2 is a type B and D coincide. At present * Tt will be seen, however (Art. 6), by an obvious extension of the method, that it is not confined to canals having this peculiarity, but is applicable also to canals having flowing curvilinear boundaries. 6 Mr H. J. Sharpe, On Liquid Jets [Oct. 28, the only limitation we shall put upon the position of the orifice H is that its ordinate must not exceed twice OD. Pras 2: uf ee O Zz 3. Different analytical expressions, containing an arbitrary © number of arbitrary constants, will be assumed for the velocities on either side of Oy, but it will be shewn that they can be so chosen as to make the velocities on either side of Oy continuous, and leave any required number of arbitrary constants to satisfy conditions now to be given. It will be shewn that in all cases the equation to BHC can be expressed in the form (putting, for brevity, z for e’), y=a—czsiny—t1¢,2’ sin 2y — &..........00: ; and the velocities on the left of Oy in the form -F =1+¢zcosy+c,z’ cos 2y+ &e., Zz =¢,zsiny+c,2 sin 2y + &c., where of course @ is the ultimate value of Cz’. We are concerned only with the velocities at all points along HC, so that # and y in (1) are the same as w and y in (2). As z is less than 1 we can solve (1) so as to express y in a series of ascending powers of 2. We shall have therefore at every point of HC to the second order of approximation y= a—c,28In @4- We. .....ccedsesnneces (3), = (u' 4a) = 1 + 2¢,2cosa+ &e.. .. 2.0... (4). 1889. ] and the Vena Contracta. 7 Ifa=7/2 the coefficient of z vanishes, and it will be shewn that the remaining disposable constants can be so chosen as to make the coefficients of 2’, 2°, &c. (any desired number of them) also vanish. Next suppose that c,=0, then to the third order of approxi- mation ae re (u’ + v*) =1 + 2¢,2° cos 2a + Xe. If a=7/4 the coefficient of z* vanishes, and if there are con- stants enough, the coefficients of 2°, z*, &e. could be made to vanish. And generally if c,,c,...c,,_, vanish, then to the (m+ 1)th order of approximation 1 ve (ut £ vy?) = 1 + 2,2" COS MZ secrsoaeceee (5), and if a=7/2m the coefficient of z” vanishes, and the coefficients of z"** &c. could be made to vanish. We have supposed at first, for simplicity, all the powers of z in (1) to exist, but in every case we shall find that many are wanting. For instance, after the first few terms, only even mul- tiples of y may occur—or again multiples of 6y. Again, even if (1) is complete, yet it will be found that if a=7/2, (3) will consist only of odd, and (4) of even powers of z. This considera- tion not only simplifies the work, but also enables us with greater ease to make (w’+v") constant to a higher degree of approxi- mation. 4. We shall now shew how to make the velocities on either side of Oy continuous. We shall take the case to which fig. 2 refers, where OB is 7/2 and where the ultimate value of Cz’ is OB. I give this case, not only because it is one of the first I solved, but because I believe it exhibits the method under the greatest disadvantages, and yet it will be found that the approxi- mation obtained is very close. We will take for the stream function 1, and the velocities on the left of Oy, ae =—u=a,e" cos y + a,e” cos 3y + Za,,€"" cos 2ny + A a (6), - ie =v=a,esiny+a,e" sin 3y + La,,e"" sin 2ny J > indicates summation for all integral powers of m from 1 to #. Only two odd multiples of y appear in the above, but it must be distinctly understood (in fact it is the characteristic feature of the present method) that any number of any odd multiples of y could 8 Mr H. J. Sharpe, On Liquid Jets [Oct. 28, be similarly used, and each assumption would give a distinct case. The same also must be understood for the stream function and velocities presently to be assumed on the right of Oy. Then the equation to BHC is a ; ae” sin y + La,e" sin 8y + = =e" sin 2ny 2n a,: Aw + Ay=a,- 3 pas te Since the ultimate breadth of the jet is supposed to be 7/2, we must have @, — 44, =0......cs0rdecnss weve (8). It will be convenient to replace a,, a, each by two new quan- tities, such that “,=G,+A,, 6,24, + Ayiic.sccceeeee (9). Then when «=0, we have at every point of OB, on the left of Oy —u=(a,+ A,)cosy+ (a,+A,) cos 3y + Xa,, cos 2ny+A (10). v=(a,+A,)sin y + (a,+-A,) sin 3y + Sa,, sin 2ny On the right of Oy assume for the velocities d Z , ue = =—u=b." cos y-+b,e cos 3y + =b,,€°"” cos 2ny + B : (11). = = =v=—be*sny—b,e sin 3y — Xb, e°” sin 2ny It will be convenient to replace b,, 6, each by two new quan- tities, such that b,=a,—A 2 ee a | 1? 6, = GA Tess eee (12). Then when «=0, we have at every point of OB, on the right of Oy, —u=(a,—A,) cosy + (4,—A,) cos 3y + XD,, cos 2ny + B) v=—(a,—A,)sin y—(a,—A,)sin3y—b,, sin2Qny Jf oS By Fourier’s theorem, suppose we have, from y= 0 to 7/2, 2A, cosy+2A,cos3y=p+ =p,, cos 2ny ......... (14). This will be true at both limits. Then the first equation of (10) will be identical with the first equation of (13) if Hh Me BL Oe ancy ekaees bs atone (15), 1889.] and the Vena Contracta. 9 Again, by Fourier’s theorem, suppose we have from y=0 to m/2 2a, sin y + 2a, sin 3y = Xq,, sin 2ny.........4.. (17). This will be true at both limits if see Oc iui Mane Re. (18) Then the second equation of (10) will be identical with the second equation of (13) if GeO) Boodle go acsecacas (19). Then if the constants satisfy equations (15), (16), (18), (19) the motions on the left and right of OB will be continuous. From (11) the equation to AFB is : oe Ge. Wet be*siny +b, sin 3y+ > an € "? sin Qny b, Br 5. We will now suppose that 0, Bar b- De (21). When (21) is fulfilled, the stream-line AFB will consist of an infinite straight line AF’, whose ordinate is 7, and a curved portion FB. The peculiarity at # will be presently explained. It must be carefully observed that AF’ is not an asymptote. It will be found that we get the following relations 8 g—¢ +A, Mh, = —F7n= (17a, + 16A,), 8 a, => 32,+ 3A, a, = 1057 (61a, 4 64.4), Men oa 2 é tn = cos ne. 1a, ( An 4n +1 )+4,(,8 PET Ne )f. b,, | 2\4n*—1 4n?—9 ie as b=4,-4, —0,= 4, (+164), b=-2,-84, b=, = (292, + 644,), An, B= = Says Ta (22), Tt will be noticed that for moderately large values of 1, a,, and b,, ultimately vary as 1/n’, so that all the series employed 10 Mr H. J. Sharpe, On Liquid Jets [Oct. 28, are convergent even for points very near Oy. I believe this property is common to all the solutions obtained by the present method. It is interesting to notice that unless we assumed the equation (18) to hold, we could not establish the obvious relation a 2B. 6. We will now make the curve HC as far as_ possible identical with a line of constant velocity. It will be convenient to put for shortness €* =z, aj/A=c. aie See 40,/4=c,, ce. Then (7) can be written 7 . a y=5—G2siny — $c,2" sin 2y — &e. ...... (23), and from (6), —G=l+ezcosy + ¢,2" cos 2y + ke. seaelaanes (24). Vv = : aoe NG) & 4 = or siny + ¢,2° sin 2y + We. In (23) expressing y in terms of z, we have T y=5 —¢2+ Ge, —¢0, + £¢,) a” + Gee, eae (25). It will be found that this series consists only of odd powers of z, the simplification arising from our having taken 7/2 for the ulti- mate breadth of the jet. If we now substitute the above value of y in (24) and form the value of wu’ + v*, we shall get = (u? + v*) = 1+ (8¢,"? — 2¢,) 2° + (— 4c, + 8c,%c, + ¢,’ — f¢,c, + 2c,) 2* + &e....(26), the series consisting only of even powers of 2. If we want to carry the approximation to the fourth order, we shall have to cause the coefficient of z* here to vanish. This will give us for determining the ratio of A, to a, the equation BS (a, +A)? + a (17a, + 164,)=0. Solving this equation we get A,/2,=— 10635 or — 40127 nearly......... (27). Either of these gives a solution. If we take the first, we see from the equations (22) at the end of Art. 4, that all the quan- tities G,, d,, U,, 4, are small, therefore the curve BHC clings all along very closely to its asymptote. 1889. ] and the Vena Contracta. 11 From equations (6) or (11) we shall get for the direction of the fluid motion at B, u 10 For the first solution this becomes — ‘06, and for the second — 2'84. If we wished to carry the approximation to the sixth order, we should have to introduce terms with the sine and cosine of 5y in (6) and (11) and make the coefficient of z2* in (26) vanish. This solution would involve two arbitrary constants. By making in addition the coefficient of z* in (26) vanish we could carry the approximation to the 8th order, and the solution would involve one arbitrary constant. 7. We proceed now to discuss the solutions obtained. And first for the point F’, where there is a peculiarity which was pointed out to me by Sir George Stokes. From (20) the equation to A#'B can be written (putting for shortness 2 for €~*), B(y— 7) =b,zsin (y—7) + 4),2 sin 3 (y — 7) Ogi —> "sin 2n (y—7)...4:. 2 9, Sih 21 (y —77) (28). Dividing out by (y—7) and then putting y =7, we get for deter- mining the abscissa of F, eA ssa ci osin« nase Gob BEA (29). For the first solution in (27) this gives us z =‘58, from which we get # = 23/43 nearly. Further it will be seen from (28) that for points near F, z does not vary, for on account of the values of z and b,, (see end of Art. 4) the series converges pretty rapidly. Therefore the stream-line turns sharply at right angles at F. This curious result may be further corroborated simply by comparing the first equation of (11) and (29) from which we at once get w=0 at F. It may be noticed that we are not compelled to make the ultimate ordinate of the stream-line on the right of Oy equal to 7. For instance, in the present case, we arbitrarily assumed (21) to hold. If we did not assume this, the outer stream-line on the right of Oy would have no sharp corner. The ultimate ordinate however, whatever it is, must not exceed mr, otherwise the motion would be discontinuous. 8. Kirchhoff has shewn (Lamb’s Motion of Fluids, Art. 96) that at such a point as H (where the motion of the fluid having 12 Mr H. J. Sharpe, On Liquid Jets, &c. [Oct. 28, been restricted suddenly becomes free) the radius of curvature should be zero in the true solution. In the present approximate solutions we cannot of course expect this to hold. But I am inclined to believe that in all solutions obtained by the present method there will be found on the line BHC (near where we might expect the orifice to be) a point where the radius of curva- ture is a minimum, and here I propose to place the point H. At any rate there is such a point in the case of the first solution in (27), as we proceed to shew. From (25) putting in it c,= $c,’ and from (8) c, = 3a,, the equation to BHU is y= — Cette etc) e+ ae (30). From (27), &c. eae Cyst ayaa: OTE + ~ a A = 16 0635: It is evident therefore that c, is small and that (80) may be ap- proximately written y= — 0, (2-2) + &e. As dy/da is always small all along BHC, we may get sufficiently near the point required by finding the point where d*y/da* is a maximum. We see at once that this is got from the equation z* is equal to 1/27 which gives « =— 71/43 nearly for the abscissa of H. We can readily see that at H the curve is conver to the axis and that a maaimum value of d*y/dx* has been obtained, also that the coefficient of contraction is ‘99545. 9. It will now be interesting to calculate the limits of error in the velocity at the point H. From (26) it can be shewn that the coefficient of z* reduces to 155¢ 4 —26c," + 2e,. This is equal to 1654 nearly. Therefore at the point H only ‘000011 of the velocity is variable. Of course as we pass to the left of H this small proportion rapidly diminishes. 10. If we examine equation (20) we shall find that the curve FGB cuts the line y=7/2 in a point @ whose abscissa is about 3/43. Also if we imagine twa points on the same curve whose ordinates are 47/6 and 57/6 we shall find that their respective abscissae are about 16/43 and 36/43. 1889.] Mr A. H. Cooke, On the common Dog- Whelk. 13 November 11, 1889. Dr GASKELL IN THE CHAIR. The following Communications were made: (1) On the Varieties and Geographical Distribution of the com- mon Dog-Whelk (Purpura lapillus L.). By A. H. Cooke, M.A, King’s College. THE author, while unable to advance any satisfactory theory to account for colour variation, held that variations of form largely depended upon the station occupied by the animal. Shells occur- ring in exposed situations (e.g. Land’s End, Scilly Islands, coasts of N. Devon and Cornwall) were stunted, with a short spire and large mouth, the latter being developed in order to increase the power of adherence to the rock, and of resistance to wave force. Shells occurring in sheltered situations, estuaries, narrow straits, &c. where there was no severe wave force to encounter, were of great size, spire well developed, mouth small in proportion to area of shell. This view was illustrated by series of specimens collected at various points on the British coasts. With regard to the question of geographical distribution it was shewn that Purpura lapillus (a “north temperate” species) occurred on the East Asiatic coasts from Behring’s Straits to Hakodadi (41°), on West European coasts from North Cape to Mogador (32°), not entering the Mediterranean, on East American coasts from Greenland to Newhaven (42°), and on West American coasts (assuming the identity of the West American Purpuras with lapillus) from Alaska to Margarita Bay (24°). Thus on the two western coasts it had a far more southern range than on the two eastern. The author regarded this fact as due to the direct influence of the surface temperature of the ocean. The mean annual temperature (taken from the Meteorological Society’s charts) of the surface water at Hakodadi was 52°, with an extreme range of 25°; that of Mogador was 66°, extreme range only 8°; that of Newhaven was 52°, extreme range 30°; that of Margarita Bay 73°, extreme range only 5°. Violent changes of temperature were fatal to life, zones where such changes occurred acted as barriers to distribution; it was possible on the other hand for an organism to bear a gradual change from cold to extreme heat. On the western coasts of Europe and America the change from cold to heat was very gradual, hence the Purpura had been able to creep as far south as 32° in the one case and 24° in the other; while on the opposite eastern coasts, where the Atlantic and Pacific Gulf-streams caused a sudden change in the temperature of the surface-water, the species was barred back at a point many degrees further north. 14. Mr M. C. Potter, On the increase of the thickness [Nov. 11, (2) On the increase in thickness of the stem of the Cucurbitacee. By M. C. Porter, M.A., St Peter’s College. THE Order Cucurbitacew consists for the most part of her- baceous plants climbing by means of tendrils; like many other climbing plants, the members of this order have an anomalous distribution of the fibro-vascular bundles in the stem; the bundles being arranged in two concentric rings, and each individual bundle being bicollateral, with phloem both on its external and internal sides. (Fig. 1.) The structure of these stems was first described by Hartig* and then by von Mohl+ and has been the subject of investigation by various botanists, most of whom have confined their attention to the structure and contents of the sieve tubes. Bertrand? how- ever has described the manner in which a cambium between the xylem and both inner and outer phloem adds respectively both xylem and phloem to the bundle, whilst Petersen, in his article on Bicollateral Bundles, gives a short account of the increase of the stem of Zehneria swavis; stating that there is no interfascicular cambium, but that while the bundles increase the cells of the medullary rays increase passively in a radial direction and finally divide. With this statement de Bary || agrees. Fischer{ also says that there is no interfascicular cambium present whereby these stems can increase in thickness. The fact that all the investigated species of Cucurbitacew have been herbaceous ex- plains why the interfascicular cambium has hitherto not been described. Lately I have had an opportunity of investigating the woody stems of Vephalandra indica (Naud.), Trichosanthes villosa (Bl.) and T. anamalayana (Bedd.), and find that they increase by a well- marked interfascicular cambium. ‘The stems of these plants agree with those of. the other members of the order in possessing the two rings of bicollateral bundles (fig. 1), but differ in having no ring of sclerenchymatous tissue between the epidermis and vas- cular bundles. The structure of these species being similar in all respects it will only be necessary to describe the stem of Cepha- landra indica. Cephalandra indica, a climbing woody plant, reaches to a considerable height and its stem, which is perennial, attains to several inches in diameter. In its young stage the stem contains * Bot. Zeit. 1854. + Bot. Zeit, 1855. + ‘Theorie du faisceau,” Bull. Sci. du département du Nord, 1880..: § Engler Bot. Jahrb. vu. p. 374. || Comparative Anatomy, English edition, p. 456. “| Untersuchungen tiber das Siebrohren-system der Cucurbitaceen, p. 6. 1889. ] of the stem of the Cucurbitacee. 15 ten fibro-vascular bundles in two concentric rings, the five inner bundles being larger than the five outer ones (fig. 1), The stem increases slowly for some time, because the cambium on the outside as well as on the inside of each bundle adds xylem and phloem to the bundle; the cells of the medullary rays increase radially and divide. Thus far Cephalandra is similar to the herbaceous members of the order. The latter, being annuals or at least not requiring a continual enlargement of the stem, have no provision for such increase, whilst Cephalandra being woody and perennial requires means whereby its stem can continue to grow, and there- fore by division of the cells of the medullary rays adjacent to the bundles and contiguous to the outer cambium cells there is formed an interfascicular cambium (fig. 2a). This interfascicular cambium soon stretches from bundle to bundle across the medullary rays (see dotted line fig. 1), and its development agrees with that of normal Dicotyledons. After the completion of the ring of inter- fascicular cambium, xylem is formed on the exterior of the existing xylem, and phloem on the interior of the outer phloem and secondary medullary rays are formed in the xylem in the normal manner (Plate mu. fig. 4 mr,). The stem therefore grows in the same manner as a normal Dicotyledon. The cambium which is placed on the inner side of the xylem ceases to produce new elements about the time the interfascicular cambium is formed, and finally disappears; so that the internal phloems are left at the centre of the stem and do not undergo further increase. The above description shews that the mode of increase of the stem of Cephalandra indica corresponds exactly with that of a normal Dicotyledon in which no intermediate bundles are formed, inasmuch as each possesses a cambium which forms on its inside xylem and medullary rays, and on its outside phloem and paren- chyma. But the stem of the former differs in the primary ar- rangement of the bundles in two rings and in having some phloem on the central side of the xylem. It would seem therefore that de Bary’s* view that the two concentric rings of bundles in the stem behave as a single ring curving alternately outwards and inwards is correct. EXPLANATION OF PLATES I AND II. Fig. 1. Diagram shewing position and relative size of the fibro- vascular-bundles of the stem of Cephalandra indica. “Ph=Phloem, Xy= Xylem, the wavy line indicating where the interfascicular cambium will be formed. * Comparative Anatomy, English edition, p. 456. 16 Mr E. H. Hankin, On a new result [Nov. 11, Fig. 2. Portion of stem of Cephalandra indica shewing two interior and one exterior fibro-vascular-bundle. a cells dividing to form the cambium. C centre of stem. Sz sieve-tubes. P the periphery. Fig. 3. Portion of an older stem of Cephalandra indica. cc centre of stem. Sz sieve-tubes, cam cambium, ph position of interior phloem of two other fibro-vascular-bundles, mr, primary medullary ray, mr, secondary medullary ray. (8) On the Spinning Apparatus of Geometric Spiders. By C. WARBURTON, B.A., Christ’s College. THE structure of the external and internal spinning organs of the Epeiride was described, and the special functions of the several distinct kinds of spinning glands investigated. The Ampullaceal glands were shewn to be the sources of the framework and radial lines of the geometric web. The Acinate. and Piriform glands are those mainly used in binding up captured insects. A Spider’s line is not composed of many strands interwoven or coalescent, as has been hitherto believed. It usually consists of two or four non-adherent threads, and when more are present they do not fuse, but remain distinct, although contiguous. The foundation line of the spiral consists of two strands only, not adhering on account of their own viscidity, but enveloped in a common viscid sheath which subsequently breaks up into bead- like globules, and which is probably furnished by the aggregate glands. (4) A new result of the injection of ferments. By EK. H. Han- KIN, B.A., St John’s College (Junior George Henry Lewes Student). THE following experiments were performed in Professor Koch’s laboratory at the Hygienisches Institut, Berlin. Although the theoretical considerations that led me to perform these experi- ments are by no means proved by them, the results appear to be sufficiently interesting to publish in detail. Experiment 1. Three rabbits, Nos. 11,12, and 13, were inocu- lated with virulent anthrax*. No. 13 served as control and died in 36 hours of typical anthrax. Nineteen hours after inoculation rabbits 11 and 12 were subjected to a further treatment. No. 11 had two cubic centimetres of a ‘1 per cent. solution of trypsin injected into the lateral vein of its ear, and No. 12 had two ce. of a one per cent. solution of pepsin similarly injected. * These rabbits were of medium size, No. 11 weighed 855 grammes. + The pepsin and trypsin employed were both obtained from Schering’s Griine Apotheke, Chaussée Strass, Berlin. In my later experiments I employed some very pure pepsin which I owe to the great kindness of Dr Theodor Weyl. 1889.] of the Injection of Ferments. 17 Rabbit 12 died 66 hours after its inoculation with anthrax. The anthrax bacilli in the lung, spleen, and lymph gland near seat of inoculation, instead of appearing in the form of short rods characteristic of virulent anthrax, were arranged for the most part in long chains as is usual with attenuated virus. The chains consisted of as many as 12 and sometimes even more jomts. Two mice were inoculated from the heart-blood of this rabbit, and died of anthrax after the rather unusually long period of 60 hours. No. 11 died only 13 days after its inoculation. It had slight diarrhcea for some days before its death. Its spleen contained but few bacilli arranged in chains generally of six or seven but sometimes of as many as fifteen joints. Three days after the inoculation of these rabbits another rabbit, 22, was inoculated from the same culture. The next day three cc. of one per cent. pepsin was injected intravenously. The rabbit died six days afterwards and its spleen shewed very few bacilli all arranged in chains. Experiment 2. Three rabbits were inoculated with virulent anthrax. Two days afterwards only one was still alive. It was treated with four cc. of one per cent. trypsin injected into its ear vein. It died four days after its anthrax inoculation. The spleen contained numerous bacilli, which were for the most part arranged in chains, one of which contained as many as 24 joints. These chains shewed signs of degeneration, in that they stained very irregularly. In the same chain some joints were colourless while others were deeply tinted. The spleen of this rabbit was par- ticularly large, and a great many of the cells contained more than one nucleus, while other nuclei had a dotted aspect. Ap- parently these appearances indicate an increased rate of nuclear division *. Experiment 3. Professor Koch kindly inoculated for me five rabbits, Nos. 26 to 30, each with a large quantity of anthrax spores suspended in a normal salt solution. No. 29 served as control and died in 36 hours. I injected three to four cc. of one per cent. trypsin into the ear vein of Nos. 26, 27 and 28 directly afterwards. No. 26 died in the same time as the control. None of the bacilli were in very long chains, none of more than six joints were seen, while most of the bacilli were exceptionally short. This fact and also the way in which they were arranged on the slide suggested to me that the bacilli had at first grown in longer chains, but that at a later period (perhaps when the effect of the trypsin had passed away) they had broken up into separate segments. * My observations were all made on fresh preparations of the spleen pulp, to which some dilute aqueous solution of methyl blue was generally added. WOH. Vil, PT. I. : a 18 Mr E. H. Hankin, On a new result [Nov. 11, No. 27 died in about 50 hours. The bacilli in the spleen were rather longer than usual. No. 28 died in 21} hours. Unfortunately I have mislaid my notes of its post mortem appearances. No. 30 had four cc. of one per cent. trypsin injected intra- venously the day after it was inoculated with anthrax. It died in 36 hours and the spleen shewed the bacilli arranged in long chains. Experiment 4. Five rabbits, Nos. 34 to 38, were as before in- oculated by Professor Koch with anthrax spores. Dhirectly after- wards I administered intravenously from one to 34 cc. of ‘05 per cent. solution of trypsin. No. 38 was control and died between 50 and 60 hours after inoculation, No. 34 weighed 1500 grammes and had one cc. of the above solution of trypsin. It died 51 hours after inoculation. Some of the bacilli were isolated, but many were in chains of more than 12 members. No. 35 weighed 1507 grammes and had 34 ce. of the ‘05 per cent. trypsin solution. It died in 60 hours, and the bacilli were arranged in chains. No. 36 died after 36 hours*. The spleen contained very few bacilli and of these some were arranged in chains. No. 37 weighed 1865 grammes. It had 24 cc. of the above solution of trypsin. It was very ill for some days, but at last recovered and is now alive and well nearly three months after the operation. The temperature record of this unfortunately unique case is very interesting. The day after inoculation the temperature was 37°°4 Centigrade, ie. 2-4 degrees below the normal tempera- ture of a rabbit. It remained at approximately this low figure for some days, shewing a very gradual rise, and only on the sixth day after inoculation had it reached 38°. From this point it rapidly rose till on the 11th day after inoculation it was 40%1. On the 12th day it stood at 40°05, when observation of its tem- perature was discontinued. Another interesting point about the case was the appearance of pus at the seat of inoculation. On the 8th day after the experiment began, a small hard tumour about half-an-inch in diameter was found at the seat of imocu- lation. On the 13th day a second larger tumour appeared in front of the former. This gradually increased in size and was found to contain caseating pus. About a week later, no further increase in size could be noted. The animal appeared to be ema- * I noticed while this rabbit was being inoculated that it had a cough. This point is worth noting, as I have usually observed that a lung disorder increases susceptibility to anthrax. 1889. ] of the Injection of Ferments. 19 ciated. At the present time it appears to be strong and fat, and only a trace of the swellings can be seen. Experiment 5. Three rabbits, Nos. 40, 41 and 42, were in- oculated with virulent anthrax spores. No. 42 served as control and died within 60 hours. Its spleen contained very few bacilli which were never arranged in chains of more than six joints, No. 40 received five cc. of one per cent. pepsin solution the day after inoculation with anthrax. It died after about 60 hours. The bacilli in the spleen were mostly in chains of 10 to 20 joints. Generally they were arranged in clusters which often surrounded a phagocyte. A few phagocytes containing bacilli were seen. No, 41 weighed a little over two kilos. It had three cc. of the pepsin solution the day after inoculation, another three ce. were injected after a few hours, and again six cc. on the following day. It died 71 hours after its anthrax inoculation. The spleen was full of bacilli arranged in rows so long as to be difficult to count, reminding one of a gelatine culture. Chains of over 30 segments were noted. The above experiments appear to be interesting from several points of view, though it must be confessed that they raise more questions than they settle. In the first place, so far as I know, this is the first time that a substance prepared independently of the pathogenic microbe, and administered after its advent, has been found to exert an influence on the development of the microbe within the body of the animal and so on the course of the disease. Since the ferments that I experimented with have no special known relation to the anthrax bacillus it is to be expected that the same ferments will exert an analogous influence on the course of other diseases, which are similarly produced by pathogenic micro-organisms. Further I have worked with virulent anthrax, a virus which kills 100 per cent. of the rabbits inoculated with it. That is to say, the rabbit shews practically no power of resisting the onset of the malady. May it not be expected that these ferments will shew a still greater power of antagonising the microbe in those diseases and with those animals in which the mortality is only 10 or 20 per cent. ? Secondly, the above results are interesting from the point of view of the phagocyte theory. The upholders of this theory assert that natural or acquired immunity against a disease is due to the greater activity of phagocytes. But by the injection of ferments 1 have in some cases at any rate endowed the animal with an increased power of resisting anthrax virus. The ferments were injected into the blood plasma, and in this liquid the bacilli lived and were apparently affected independently of any increased phagocyte activity. One of these ferments, the pepsin, is at any 2-2 = a 20 Mr E. H. Hankin, On the Injection of Ferments. [Nov. 11, rate a post mortem constituent of most of the animal tissues, and I think these experiments seem to uphold a theory first sug- gested to me by Dr Lauder Brunton, that the “germicidal power” that the animal body seems to possess is connected with the power it had of producing ferments. This suggestion that I have either increased or closely imitated the natural germicidal power by ferment injection is supported by the symptons exhibited by rabbit No. 37 which finally recovered. As mentioned above, a quantity of pus was found at the seat of inoculation. This is rendered interesting by the fact that a similar effect is produced by inoculating with anthrax an adult rat, an animal which is natu- rally refractory to this disease. In the case of rabbit No. 37 and of a rat inoculated with anthrax we find a large pus formation at the seat of inoculation ; that is to say, not increased activity on the part of the leucocytes but an increased degeneration of these cells. Does it not seem probable that these cells give out certain substances (possibly ferments) which hinder or prevent the growth of the bacilli till at length they can be devoured like any other inert granules by the active phagocytes ? Lastly, these experiments suggest another possibility; namely, that by injecting ferments, other microbes which cannot easily be cultivated outside the body of the animal may be attenuated within it. Possibly in this way attenuated tubercule bacilli could be obtained which might be used as a means of vaccinating against consumption. Note. Since communicating the above results to the Society, I have succeeded in obtaining similar results by injection of Halliburton’s cell globulin after inoculation with anthrax. This cell globulin is a proteid, obtained from cells of the lymphatic glands, which is either identical with fibrin-ferment or very closely connected with it. In my experiments with this substance, the elongation of the spleen bacilli was not always so marked as with pepsin and trypsin, but longer chains could always be found in the lymphatic glands near the seat of moculation. Perhaps more of the individual joints were degenerated than in my former experiments, and in cases where the chains did not consist of many members, the individual joints were often unusually long. I have not yet finished this course of experiments, but the results, as far as they go, support the view I have enunciated in my paper con- cerning the mechanism of the germicidal power; and the fact that two out of three substances which I have employed are probably constituents of leucocytes appears to me to be particularly sug- gestive. December 7, 1889. 1889. ] Mr W, N. Shaw, On Electrolytes. 21 November 25, 1889. Mr J. W. CLARK, PRESIDENT, IN THE CHAIR. The following were elected Fellows of the Society : Arthur Berry, M.A., Fellow of King’s College. H. F. Baker, B.A., Fellow of St John’s College. E. W. Brown, B.A., Fellow of Christ’s College. C. Warburton, B.A., Christ’s College. The PRESIDENT announced that the adjudicators of the Hopkins Prize for the period 1880-82 have awarded the Prize to Mr R. T. GLAZEBROOK, F.R.S., for his researches in Physical Optics. The following Communications were made to the Society : (1) On the relation between Viscosity and Conductivity of Electrolytes. By W. N. Suaw, M.A., Emmanuel College. It has long been suspected that the resistance offered by an electrolyte to the passage of electricity through it, depends in some way upon the viscosity of the liquid. The mere fact that the conduction of electricity is in reality convection by moving ions suggests of itself that resistance may be the opposition offered by the fluid to the motion of the ions. It is not however in any way obvious that the resistance which moving ions would meet with would be identical with the ordinary viscosity that has to be overcome when a fluid is driven through a capillary tube ; so that when G. Wiedemann, in 1856, found that there was an analogy between the relative magnitudes of the numbers express- ing the conductivity of certain solutions and those expressing the fluidity (the reciprocal of the viscosity), the implied relation between electric conductivity and fluidity was not at once accepted as proved. And indeed, in its crudest form, the hypothesis that conductivity is identical with fluidity, as we measure it by Cou- lomb’s method or Poiseuille’s method, or that the two are propor- tional, evidently cannot be maintained. For clearly a salt solution becoming gradually more and more dilute approaches a finite limit of viscosity, namely the viscosity of pure water, whereas the conductivity apparently diminishes without limit. Moreover there are numerous mobile liquids which do not conduct at all. Nor is the mobility which is characteristic of fluids really necessary to electrolytic conduction. Professor W. Kohlrausch has examined the conductivity of fused salts of silver through a wide range of temperature, and he finds that in the case of iodide of silver there is no discontinuous change in the conductivity at the melting- point, on the contrary the resistance only increases very gradually after solidification takes place, remaining less than the minimum 22 Mr W. N. Shaw, On -the relation between —[Nov. 25, resistance of H,SO,, until the mass becomes crystalline and then a sudden increase of resistance occurs. The curve representing the variation of resistance with temperature for the mixed chloride and iodide shews similar properties. Moreover Arrhenius has measured the resistance of electrolytes which contain gelatine, and these solidify without producing any sudden change of resistance. Hence clearly resistance and ordinary viscosity are not the same thing. Furthermore, in comparing the numerical values of conductivity and fluidity we are met with an obvious contradiction of any such » I! =) ol tivity “tity | of Hg x vw 2x1071 Equivalents per litre. generalisation; for on the addition of an acid or a salt to water the viscosity may be increased, whereas the conductivity of the solution depends entirely on the presence of the salt or acid. If the curves shewing the variation of conductivity with concen- tration be compared with those for fluidity and concentration no similarity is conspicuous although there are some striking in- stances, particularly that of sulphuric acid, of concurrence of pecu- | Gramme zy ae 1889. ] Viscosity and Conductivity of Electrolytes. 23 larities which arrest attention. As an example of very normal type, I have in fig. 1 reproduced the curve (k) of conductivity and concentration in gramme equivalents per litre of NH,Cl from Wiedemann’s Llectricitdt, vol. 1. p. 610. And to compare with it I have plotted a curve, from observations (f) of Grotian*, of the fluidity of solutions of NH,Cl for the same range of concentration. There is no striking resemblance but rather the reverse. In fact, the curves for conductivity and concentration are generally roughly parabolic in shape with a vertex of maximum conductivity, the equations of a series of the curves are given by Wiedemann*, and the curves for fluidity are according to Reyhert and Arrhenius§ very exactly represented by the equation »= A’, where 7 is the viscosity relative to water, z the number of gramme equivalents per litre, and A a constant not differimg much from unity. Such curves are of course quite different from the conductivity curves, and yet, when tables of conductivities and fluidities of different solutions are compared, the connexion is very striking; and the obvious suggestion is that both fluidity and conductivity are very complex phenomena, but that for a given solution they are both dependent ultimately in some way upon temperature and con- centration, and are so related that, other things being unaltered, if the fluidity be increased the conductivity is consequently im- proved. It therefore seems more hopeful to compare, as Grotian has done, fractional rates of variation of the two quantities rather than the quantities themselves. Grotian has chosen the rate of variation with temperature, and in parallel columns on pp. 949—952 of vol. 11. of Wiedemann’s Electricitdt are values of 10*¢ and 10%, where d= (3) a and «= (=) , for different con- : : dt 2J 18 dt oe centrations of solutions of a large number of salts. The suffixes indicate temperatures, f is fluidity relative to pure water at 10°C., k conductivity referred to mercury, and t temperature. A further advantage of this method of comparison is that the units in which the conductivity and fluidity are measured do not affect the result. In order to get a better general view of the comparison of the two magnitudes ¢@ and x, I have examined the curves plotted from all the results recorded in Wiedemann, and the general parallelism of corresponding curves is very striking. The set of lines representing either one of the properties for the solu- tions of the different substances traverse the paper at a very great variety of inclination to the axes; some of them are nearly * Pogg. Ann., vol. cLx., p. 259, 1877. + Electricitét, vol. 1., p. 600. + Zeitschrift fiir Phys. Chem., vol. u., p. 744, 1888. Ib., vol. 1., p. 285, 1887. 24 Mr W..N. Shaw, On the relation between [Nov. 25, parallel to the axis of abscissae, others are inclined positively to it, others again negatively; but in all cases, with the possible exception of acetic acid, which exhibits irregularity, the corre- sponding curve for the other property is a curve which though not coincident is very nearly parallel, and generally speaking when there is a change in the inclination of the curve for one property there is a corresponding change of inclination in the curve for the other property. When we add to the general appearance of parallelism for the lines which present no special peculiarity the remarkable parallelism in the exceptional cases of NaHO, the curves for which are both very steeply but equally inclined to the axis, and of H,SO,, which furnishes two irregular but still parallel curves each shewing a maximum for the same degree of concen- tration, the evidence is convincing that there is a real relation not of identity, but of parallelism between these temperature co- efficients of the two quantities for different concentrations. Another means of altering the viscosity without altering the other properties of a solution might be found in adding an imert non-conducting liquid to the solution and thereby altering the solvent. Experiments have been made in this direction by C. Stephan*, who has measured the viscosity and its temperature coefficient for some mixtures of alcohol and water, and the con- ductivity and its temperature coefficient for dilute solutions of NaCl, KCl, LiCl, NaI, KI in these mixtures. The investigation differs from Grotian’s inasmuch as the temperature coefficients of fluidity are not determined for the solutions but only for the solvents, so that while the fluidity temperature coefficient seems, for the alcoholic solvents, again to be of the same order of magnitude and to exceed the conductivity temperature coefficients of the solutions, no precise comparison can be made. Stephan’s comparisons of results are mainly concerned with an enquiry as to the constancy of the products of conductivity of the solution and viscosity of the solvent for the different solvents; the con- stancy is not established though a limiting value is indicated for very dilute solutions. E. Wiedemann+ has moreover compared the conductivities of corresponding solutions of NaSO, in water and glycerine, but again no numerical relation between conductivity and resistance is exhibited. The relation between resistance and viscosity seems therefore not to be a simple one, though the relation between the tempera- ture coefficients does seem from Grotian’s observations to be comparatively simple. With the view of exhibiting this aspect * Wied. Ann., vol. xvi1., p. 673, 1882. + Ib., vol. xx., p. 537, 1883. 1889. ] Viscosity and Conductivity of Electrolytes. 25 of the question we may consider some of Grotian’s observations a little more closely. . I have reproduced in fig. 1 the curves of temperature co- efficients for NH,Cl plotted from his tables (reducing the abscissae to gramme equivalents per litre) and placed them on the diagram with the curves for fluidity and conductivity already alluded to. The curves for KCl, KBr and KI are strictly analogous, so that the diagram may be taken as exhibiting the comparison for a group of salts which seem to form a special class of solutions with respect to conductivity and fluidity. Strict parallelism of the plotted curves would correspond of course to a constant difference between the corresponding values of ,ldf ,idk a ae and 10 iE ak: interpolation, for the four salts, These differences are tabulated below, by Tase I, Concentration, | HCl. KCl. KBr. KI. per cent. 5 34 10 29 30°6 35°0 WS 29 | 30-0 28°4 31:0 20 2 30-4 30°0 29-0 25 23°8 28-4 28°4 30 24-0 28°4 35 22-6 28:0 40 27:0 45. 23°4 50 20-0 The differences are very nearly the same for all the salts for concentrations between 10 and 20p.c., but the two values ap- proach one another slightly when the concentration is large. As a simple assumption we may take however that the relation between the temperature coefficients of fluidity and conductivity is one of a constant difference o, independent of the concentration and of the nature of the salt for this particular group of salts. It may vary with the temperature and with the nature of the solvent, but we will assume for the moment that it is a constant. We then get bedf »l-dk ra pcnmiast. Auniciedaeds gvih siak (1), where co is a small quantity (about 30 x 10%) independent of 26 Mr W. N. Shaw, On the relation between [Nov. 25, concentration but depending on the solvent and possibly also on temperature. The physical interpretation of this equation would be that the effect of temperature upon the conductivity of the solution is of a two-fold nature, (1) the conductivity is indirectly increased by the increasing fluidity of the liquid and (2) it is diminished by some alteration of the properties of the solvent which does not affect the fluidity. In electrolytes at ordinary temperatures the first effect is predominant, but on very great rise of tempera- ture (without secondary alterations of condition) the second effect might become very great compared with the first. Thus if the solution (with the salt) were volatilized, the conductivity of the gaseous mixture might be only a small fraction of the conductivity of the solution though the viscosity might have become much less. Integrating equation (1) with regard to temperature (as- suming o to be constant) we get fr hy or k,= My aid coal) MER (2). to ki ° expresses the relation between conductivity St = ky er (tt), In equation (2) 0 and fluidity at a standard temperature*. If this relation be a complicated function of the concentration, as it appears to be, there is no reason to infer a general simplicity of relation between k and f from the fact of their having temperature coefficients which are connected by a simple relation. If we were possessed of experimental data that would enable us to refer the properties of one class of electrolytes to concentration and temperature as variables, in a manner somewhat similar to that in which the properties of gases are referred to pressure and volume, further insight into the nature of the relation might be obtained. The evident relation between viscosity and resistance has not yet been satisfactorily accounted for. The hypothesis that the motion of the ions, if these be atoms, is opposed by frictional resistance which can be measured as viscosity for ordinary motion of the liquid seems to be regarded as dubious, although Kobl- rausch+ has shewn “that the supposition of mechanical and electro- * Since this paper was read I have seen a paper of Arrhenius (Zeitschr. fiir Phys. Chem. Band. tv. Heft. 1, July 1889), in which an equation practically identical with (2) is deduced directly from the theory of dissociation. On that hypothesis ¢ would be the fractional temperature coefficient of dissociation, and being negative would imply, as Arrhenius points out, a temperature of maximum conductivity beyond which the temperature coefticient of conductivity would be negative. + B. A. Report, 1886, p. 343; Wied. Ann. vol. vi., p. 207, 1879. 1839. ] Viscosity and Conductivity of Electrolytes. 27 lytic frictional resistance of about equal amount allows the finding of an absolute size of molecules which approaches the sizes found by other methods.” But is it necessary to suppose that the individual atoms are moved through the liquid? May the ions not be parts of complex molecules of salt and solvent which have to be dragged through the liquid? Wiedemann* mentions that such a suggestion has already been made but that it is very risky, yet the doctrine of electrolysis of molecular aggregates as oppcsed to that of disso- ciated atomic ions has some adherents, and expressions might be quoted from the writings of well-known supporters of the dis- sociation-theory to shew that they acknowledge the necessity for regarding the electrolytic molecule as complex in some special cases. I think it may be well to recall that certain phenomena may naturally lead to the same view, although I am well aware that these phenomena have been otherwise explained in a manner that is accepted as satisfactory. The view that electrolysis consists in the convection of elec- tricity by single atoms only, or their chemical representatives, is based upon the resolution of the processes taking place in an electrolytic cell into independent phenomena. Electric endos- mose, the unequal dilution of solution at the electrodes and the deposition of ions are all treated separately. Electric endosmose is regarded as the result of the electrification by contact of the boundary layer of the solution in the porous partitions which divide the cell, and the explanation has been regarded as com- plete since von Helmholtz shewed that the difference of potential of the boundary layer necessary to explain the effect was not more than a few volts. The unequal dilution at the electrodes is explained by the theory of migration of the atomic ions with unequal velocities, and this explanation has received strong con- firmation from Kohlrausch’s calculation of resistance, based on these atomic ionic velocities and Lodge’s experimental veritication of the calculation in the case of hydrogen. But, apart from these reasons, we have no direct evidence that the ions are simply atoms, or their chemical representatives. One of the greatest desiderata in electrolysis is the determination of the actual ions in any case of electrolysis, but it does not seem practicable to identify them. Hitherto the tendency has been to assume atomic ions if possible, and yet complex ions cannot be excluded. I have taken the following cases of electrolysis from Wiedemann+, who is himself a strong opponent of the idea of complex molecular decomposition in general. * See Electricitat, vol. 11., pp. 953, 962. + Ib., vol. 1m. 28 Mr W. N. Shaw, On the relation between [Nov, 25, We see therefore that in spite of the present tendency to reduce the electrolytic action to convection by atomic ions if possible, there are many cases in which the ions are aggregations of atoms, if not strictly molecular, and in some cases molecules are associated with a moving atom in electrolysis. It seems therefore not altogether unreasonable to assume that the decom- position of a complex molecule may not be exceptional but the general rule. Let us therefore take the venturesome step of considering that the whole result of electrolysis consists in the separation of complex molecular aggregates of salt and water each into two parts, each part containing one dissociated atom or its Taste II, +Ion. Electrolyte. — Ion. K KHO HO H, NH, NHCl Cl 2 K,Cr,0, 2CrO,, O Na, Na,HPO, 1 (H,O, P,O,, O,) UO, UO,Cl, Cl, K, K,Fe (ON), Fe (CN),, (GN), Ag Ag,ON, AgCN, CN Cd K K ifs CdI,, I Cd 2 (CalI,) Cdl, I (in alcohol) Ca 3CdI, Cdl, I (in alcohol) chemical representative, and suppose that the complete result of electrolysis, including the transference of liquid known as endos- mose, the migrations of ions, and the deposition on the electrodes may be accounted for by this splitting up of the complex molecule into two parts and the transference of the separated parts in opposite directions, so that each separated atom would be loaded with a number of water molecules or salt molecules or both. If this be assumed, the effect of a porous diaphragm in a solution would be not to cause the transference of liquid but to prevent it slipping back again, and the friction against the plug which would prevent the slip back would be very similar in its mathe- matical expression to the force supposed by von Helmholtz to cause the transference. The reasoning by which Wiedemann, on p. 592 of vol. IL of his Electricitét, shews that electric endosmose is independent of migration seems to me to be as follows. The total gain of cation 1889. } Viscosity and Conductivity of Electrolytes. 29 in the cathode vessels is not the same for different degrees of dilution when there is a porous diaphragm, but if you subtract the amount due to the increase of volume of solution, the amounts are approximately the same; hence if the increase of volume be regarded as an entirely independent phenomenon the cations may be assumed to be the same; viz. atoms of copper, for all the dif- ferent degrees of dilution. But the same result would be arrived at if we assumed that in the more dilute solutions a greater number of molecules were associated with the atoms. Assuming that of the salt which is decomposed half is taken from the anode vessel and half from the cathode vessel, I have calculated the molecules that must be decomposed to give the required total gain at the cathode which is tabulated for CuSO, by Wiedemann for solutions of different strengths. They are as follows TasxeE III, Concentration Beatonper Molecule decomposed. per 100 cc. 33793 | Cu, (OuSO,, 5H,0)/(SO,), 3118 Cu, (CuSO,, 6H,O)/(SO,), 2-263 Cu, (CuSO,, 8H,O)/(SO,), The molecules which are actually decomposed may be more complex than those given, by combination with molecules of solu- tion, but the association of such molecules with the ions would not affect the ultimate relative distribution of the electrolyte. More- over all the ions in a specific solution need not be of the same order of complexity. It would be a natural consequence of this view to suppose that when the solutions became very dilute, the number of mole- cules of water associated with the moving atoms would be very large, ultimately being proportional to dilution ; in that case the electrolysis would depend mainly on the motion of these large molecular aggregates past each other and the resistance would be of the nature of ordimary viscosity. Under these circumstances the number of molecules associated might depend on the number and be independent of the nature of the atoms and the ionic velocities, and the resistance of all electrolytes would tend to the same value as they are known to do in solutions of extreme dilution*. * F. Kolrausch, Gegenwiirtige Anschauung, éc., p. 28. 30 Mr W. N. Shaw, On Electrolytes. [Nov. 25, I have not hitherto dealt with the difficulty raised by the remarkably accurate calculations of resistance of electrolytes from ionic velocities based on the assumption of atomic ions and verified experimentally by Lodge in the case of hydrogen. In the first place however I find it difficult to realise the conception of an ex- tremely large number of small bodies (atoms) moving in opposite directions through an aggregation of other small bodies (the solu- tion). There is also an objection to Kohlrausch’s theory on the ground that it assumes all the atoms of the dissolved salt to be moving. It seems to me that the conception is easier if we regard the whole of the solution as divided between the dissociated atoms; the effect of the electromotive force would then be to pull the whole of one set of atoms with their associated molecules in one direction and the whole of the other set with their associated molecules in the opposite direction, and we thus get a stress shearing the one set of molecules past the other set; the result will be a relative motion of the atoms carrying their loads and the mean velocity will depend on the electromotive force and the viscosity ; but the motion is relative; as to the absolute velocity of each set the velocities in the two directions may be regarded as equal. A particular atom may at one time be a dissociated one moving to meet a partner with this velocity, at another time it may belong to an associated molecule and be travelling with another dissociated atom in the same direction as before or in the opposite; to deter- mine the mean velocity of all the cation atoms for instance, in one cross-section, we must deduct the number of backward steps it takes in the unit of time as part of a molecule associated with an anion atom from the number of forward ones it takes either as a dissociated atom or part of a molecule associated with a cation; this mean velocity will be equivalent to a transference of the atom through the solution. It is this mean rate of trans- ference which must be always the same for the same atom in very dilute solutions, no matter with what other atom it was associated as a salt, and it is this mean velocity which Lodge has measured. I think, therefore, that it may be possible to frame a general theory of electrolytic action on the basis of a hypothesis of com- plex molecular aggregates, dissociated in a solution, or separated by the current, into ions consisting of atoms with attached mole- cules; and such a theory might explain all the various electrolytic phenomena, including migration, endosmose, and the relation between viscosity and resistance. I am well aware that the brief sketch contained in the foregoing paper cannot be regarded in any way as a complete statement of such a theory, and that further application m detail is necessary before the theory can claim to be satisfactory. All that I venture to say is that there 1889.] Mr C. Chree, On Elastic Solids. 31 are no crucial experiments, that I am acquainted with, which definitely and finally contradict it, and until such experiments are made it may be well to bear in mind the possibility of such explanations as the theory affords. (2) The finite deformation of a thin elastic plate. By A. E. H. Love, M.A., St John’s College. _ _ (3) A solution of the equations for the equilibrium of elastic solids having an axis of material symmetry, and its application to rotating spheroids. By C. CHREE, M.A., King’s College. [A bstract.] A solution is obtained of that type of the elastic solid equations which contains five elastic constants, answering to those bodies in which the structure is symmetrical round an axis. The solution proceeds in ascending powers of the variables x, y, z. In the expressions for the displacements terms containing powers of the variables below the fourth are retained. Thus the solution, while complete so far as it goes, can solve exactly only certain classes of problems. One of the problems which it can completely solve is that of a spheroid of any eccentricity rotating uniformly about the axis of revolution, this axis being in the direction of the axis of symmetry of the material; and it is to this problem that atten- tion is mainly directed. The solution obtained for the general case of a rotating sphe- roid being somewhat complicated, certain special cases are first considered. The first of these cases, that of a very flat oblate spheroid, applies approximately to a thin plate rotating about the normal to its plane through the centre. The second case, that of a very elongated prolate spheroid, applies even more satis- factorily to the non-terminal portions of a rotating cylinder of length great compared to its diameter. In these two cases the material is of the 5-constant type. The third special case is that of uniconstant isotropy in spheroids of every form. From the light thrown on the question by the results obtained in the third special case it becomes possible to dissolve out of the complicated mathematical expressions for the general case a very considerable amount of information as to the state both of stress and strain throughout the spheroid. The key to this information is supplied by the recognition in every material whether of the 5-constant or of the isotropic type of a “critical” spheroid. The ratio of the “polar” to the “ equatorial” diameter of this spheroid depends only on the elastic constants of the material, and is given by a simple expression. The following, which are only a few of 32 Mr H. F. Baker, On the Concomitants [Nov. 25, the results obtained, will show the importance of the critical spheroid :— In any 5-constant or isotropic rotating spheroid one of the principal stresses is everywhere perpendicular to the “ meridian” plane, and of the two in the meridian plane the greater makes an obtuse or an acute angle with the perpendicular on the “ polar” axis produced outwards according as the spheroid is more or less oblate than the critical spheroid. In particular the surface is under a tangential tension in the meridian plane in the former case, but under a compression in the latter. In the critical spheroid one of the principal stresses is everywhere zero, and on the surface there is no stress at all in the meridian plane. In any species of bi- constant isotropic material, for a given value of the equatorial diameter, the critical spheroid is the form in which the “ tendency to rupture” on Saint-Venant’s theory is the greatest. In the case of uniconstant isotropy the character of the strain throughout rotating spheroids of all shapes is completely investi- gated, and is shewn in a table. In the general case of 5-constant material a similar, though not so exhaustive, analysis is given. Tables supply the values of the changes in the lengths of the equatorial and polar diameters, and the strains at the centres for various kinds of biconstant isotropic materials in spheroids of various forms. The variations of some of the more important quantities are also shewn graphically. (4) On the concomitants of three ternary quadrics. By H. F. Baker, B.A., St John’s College. [A bstract.] The author applies a modification of the symbolical method suggested by Clebsch and Gordan (Math. Annal. 1. 90 and 1. 359) to obtain the set of concomitants in terms of which all the system are expressible as rational integral algebraic functions. The result is given by the following table. The forms are taken respectively to be 66, = 8. Sant bP bet SbF ise Cr Se Sef 2d Also (aa'u) is abbreviated into wu.” =U,” = Ug” = -.-5 and (aa’a’”’)’ into a,” etc.; and so for the other two forms. Such a symbol as (523) preceding a form indicates that the form is of the fifth degree, second class, and third order. bo 1889. ] of three Ternary Quadrics. 33 Only one form of a given type is written down; the others may be obtained by interchanging the letters—the number of forms so obtainable is given by the number in brackets which follows. The forms are arranged i in sets, as obtained, according to their degrees. . (011) =u, (1) 3. (300), =a, (3) IE (300), = 6." (6) al °) (800), = (abe} (1) . (212) =(beu) b,c, (3) (311), = w.b.b, (6) (220), = ua" (3) (311), = (abe) (bev) a, ( (220), = (beu)? (3) [303] = (abc) a,b,¢, ( (410) =(beu) bec. 3) (330) = (bew) (cau) (abu) (402), = b.cab,c, (3) 5. [501], = (abc) a,b.¢a (3 (402), = (By) (3) (501), = (By) aga, (3 (421), = (bew) bac,Ue (6) (520) = ugu aga, (3 (421), = (beu) b,c,uy (6) (512), = (Bryx) aga,u, (6 [421], = (a’bc) (uca) (wab) a,’ (3) [512], = (abc)agugb,c, (6 (421), = (Byx) ugu, (3) (512), = (Bra) c,cgu, (6 (600) = (aBy)° (1) 7. [710], = (aB raga (3 (611), = (a8) (By2) Ua (3) [710], = (bew) aga,b,cg (3 [611], = ap2,b,b,ug (6) [721] = (aBry) b.b,uerty (6 630 By) Uatlaly el a oe oat 3 8. [801], = (By2) 6 jes (3 [630], = (bow) ugu,b (3) [801], = (a’bc) aga,b,cga, (8 (603); = (ya) (yar) (a2) (1) (S12) = (#8) ae) (aBeyus (2 [603], = (Byx) a,b,a—b, (6) 9, [911] = aga,b,bocaC,Ug (6 [603], = (Aya) b,c,b,¢2 (3) wh oe ( [1010] = (a’By) bycgbaCatla’ The degree—class—order symbols of eighteen of the types are placed in square brackets. This indicates that they are reducible after multiplication by Uy Some of them are further reducible on multiplication by w,”: namely these are (501),; (710),; (801),; (911); (1010). Allowing these reductions the system is expressible by 13 kinds of forms, viz. by : me anmeas"'(bcu) bc, (bew)* Uabab, (abc) (beu) a, (a8ry)° We (Bry) Uptty (Byx)’ (28y) (Bryz) Ue ie (cau) (abu) (Beu)beCa DaCabd,c, (bow) bala (bew)b,c,u, (Bye) (aBx) (yar) (Bya)apd, Uptyapa, (Bye) apa.tty (Arya) cacadlp VOL. VII. PT. I. 3 pa + > — SS “ Se SY Oe 34 Mr H. F. Baker, On Ternary Quadrics. [Nov. 25, 1889. where a form and its 1eciprocal, as well as forms of the same type, are counted as being of the same kind. Notr. There are often identical integral relations among forms of the same type. These are not here set down. Further, if we allow algebraic functions of any rational kind, all the simul- taneous concomitants can be expressed in terms of fifteen con- comitants (Forsyth, American Journal of Mathematics, X11. p. 54). COUNCIL FOR 1889—90. President. JOHN WILLIS CiaRK, M.A., F.S.A., Trinity College. Vice-Presidents. J. Routu, Sc.D., F.R.S., Peterhouse. C. Baxrneton, M.A., F.R.S., Professor of Botany. D. Livernc, M.A., F.R.S., Professor of Chemistry. Treasurer. R. T. GuazeBrook, M.A., F.R.S., Trinity College. QO PH Secretaries. Larmor, M.A., St John’s College. F. Harmer, M.A., King’s College. . R. Forsytu, M.A., F.R.S., Trinity College. > RS Ordinary Members of the Council. J. E. Marr, M.A., St John’s College. J. C. Apams, Sc.D., F.R.S., Lowndean Professor. A. S. Lga, Se.D., Gonville and Caius College. T. McK. Huaues, M.A., F.R.S., Woodwardian Professor. J. W. L. GuatsHER, Se.D., F.R.S., Trinity College. W. N. SnHaw, M.A., Emmanuel College. W. Garviner, M.A., Clare College. W. Bareson, M.A., St John’s College. A. Carey, Se.D., F.R.S., Sadlerian Professor. G. H. Darwin, M.A., F.R.S., Plumian Professor. W. J. Lewis, M.A., Professor of Mineralogy. W. H. GaskeELL, M.D., F.R.S., Trinity Hall. { Phil. Soc. Proc. Vol. V7. Pt. Ae, ’ ‘ > t i ? ; 4 - - 7 * ' aes at - f i 2 a7 Phil. Soc. Proc. Vol. VI. PLI x aH . Lith.& Imp. Camb. Sci. Inst Co. PROCEEDINGS OF THE Cambridge Philosophical Society. January 27, 1890. Mr J. W. CLARK, PRESIDENT, IN THE CHAIR. The following were elected Fellows of the Society : J. G. Adami, M.A., M.B., Christ’s College. T. Roberts, M.A., St John’s College. R. H. Solly, M.A., Downing College. E. H. Hankin, B.A., St John’s College. The PRESIDENT called attention to the proposed International Memorial to Dr Joule, late Honorary Fellow of the Society, and announced that subscriptions might be sent to the Honorary Secretary, Joule Memorial, Royal Society of London, or that they would be received by Mr R. T. Glazebrook, Treasurer of the Cam- bridge Philosophical Society. The following Communications were made to the Society : (1) Non-Euclidian Geometry. By Prof. CAYLEY. (A bstract.) The chief object of the Memoir is the development of the analytical theory: and as the form assumed for the equation of the Absolute is 27+ y? + 2° + w*® =0, the formule obtained may be regarded as belonging to Elliptic Space. But this is not the point of view of the Memoir; the space considered is ordinary space, it is only the notion of distance (linear, angular, and dihedral) which is modified. Thus for instance, lines perpendicular to each other, Wok, Vil, PT, IT. 4 36 Mr Larmor, On Rigidly connected Points, »[Jan. 27, in the ordinary sense, exist, but there is no occasion to consider them: in place thereof we consider lines which are in the new sense perpendicular to each other, and the theory is an entirely distinct one; given any two lines, we have perpendicular to each of them (not a single line, but) two lines, or say there are two perpendicular distances: the theory of these distances is con- sidered in some detail. (2) A Scheme of the Simultaneous Motions of a system of Rigidly connected Points, and the Curvatures of their Trajectories. By J. Larmor, M.A., St John’s College. The following analysis is suggested by the theorems of De la Hire and Savary, whereby the determination of the cur- vatures of the trajectories of the different points of a solid moving in one plane is reduced to geometrical construction. In this theory the construction is based on the circle which at the instant in question is the locus of points for which the curvature is zero, the well-known circle of inflexions. See Williamson’s Differential Calculus, Chapter X1x.* In the generalized theory, when the motion of the solid is not confined to be uniplanar, the first problem is to determine the nature of the locus of inflexions. This is easily effected by kinematical considerations; for the criterion of a point a, y, 2 being on the locus is that its acceleration is in the same direction as its velocity, viz. that Now we may specify the motion of the solid by w, v, w the components of the velocity of the origin, and @,, @,, , the component angular velocities of the body round the axes of coordinates. Then, as usual, B= b— YO, + 2M, Soa ee Ae (2), &=t— yo,+ 20, — @, (Vv — 20, + ro,) + w, (W — £0, + YO,)..0eecereees (3), with two pairs of other similar formulae. The equations of the curve of inflexions are now obtained by substitution in (1). * I find that questions similar to the ones here discussed are analyzed by the method of vectors from a fixed origin in the Comptes Rendus, 1888, pp. 162—5, by Gilbert, who also gives references to other writers on this subject. His investiga- tions relate chiefly to the case when a point of the system is fixed. The principal results obtained in this note have been stated in the Cambridge Mathematical Tripos, Part II., June 1, 1889. (Camb. Exam. Papers, 1888-9, p. 569.) — 1890. ] and the Curvatures of their Trajectories. 37 The result will be simplified if we take the central axis of the motion for the axis of z, so that w=V, w,=, while the other components vanish, though their fluxions remain finite. We thus obtain the equations L M-Oy N-QOz 2 aE et ee cil w eRe (4), O z =e! ’ wherein L=% —yo,+ 20, fe ee 2 er eee eee (5), N =w—-«2o,+ yo, and a is written for V/, the pitch of the given screw-motion. The equations (4) thus obtained may readily be verified by intuition; for Z, M, N represent the component accelerations due to the motion of the origin and the change of values of the angular velocities, while 0, — Q*y, — Q*z are the components of the centrifugal force round the central axis, and it is clear that these together make up the total acceleration. These equations (4) represent the curve of intersection of two paraboloids. To reduce them to the simplest possible form, first turn the axes of y, z round that of z, so as to make @, zero. Then move the origin along the central axis a distance h, so that the equation referred to this new origin is obtained by writing +h in place of w, and take h=w/o,. We thus have finally u+2o, 0—20,—-O*%y —4#0,+ yo,— O*x a) Z | -y where we notice by the way that the numerators give the simplest form to which the rectangular component accelerations for a moving solid can be reduced. The equations (6) represent the curve of intersection of a parabolic cylinder having its generators parallel to the axis of « with a rectangular-hyperbolic paraboloid having its axis in the same direction. These surfaces intersect on the plane infinity along the line where any plane z=constant meets it. The finite part of their curve of intersection, which is the proper inflexional curve, is therefore a twisted cubic. Its equations (6) may be put in the form ae ose, |) a=y(a+ Bz) which are unicursal in the parameter z. We remark that a wire of this form is the most general solid that can be moved with rotation so that all its points are in- stantaneously describing straight paths; also that any wire whose 4—2 38 Mr Larmor, On Rigidly connected Points, [Jan. 27, form is given by (7) possesses this property, the movement being a screw of pitch — 87% (1+ 5B") round the axis of a, eased off in a way that retains one degree of indeterminateness. We proceed to investigate the trajectory of any point of the solid by the aid of this cubic. Through any point, as is well known, one and only.one chord of the cubic can be drawn. We may regard this chord as a line of constant length moving with its extremities on two fixed lines, which may be considered straight so far as the determi- nation of accelerations and curvatures is concerned. Consider two consecutive positions of it," bC and BC’; let BP=B'P' =p, and CP=C’P'=p', and let p+p’'=a. Complete Fig. 1. the parallelogram C'CBA, and draw P'M, P'N parallel to AB, AC’,as in Fig. 1. The circumstances of the motion are given by the velocities of the extremities of BC; let then BB =bt+ 1b OC’ = ct +40? so that b, c are the velocities, and b, éthe accelerations of Band C along their straight trajectories. The point @ moves in a fixed plane which is parallel to both BB and CC’, being parallel to the plane ABB’. The coordinates of Q referred to axes of « and y parallel to BB’ and CC’ are the same as the coordinates of V referred to axes BB’ and BA. They are therefore given by BB =" x2=dt4 bt | P | O0' =e y=ct+ her @ J oa eres TS 1890. ] and the Curvatures of their Trajectories. 39 These are the equations of the path of P, correct as far as the second order, and referred to the parameter t. The determination of the radius of curvature / at the origin may now be made by the usual methods, bearing in mind that the angle between the axes is w, the angle between BB' and CC’. It is sufficient to give the result bip'* + cip" + 2bepp’ cos w) k= ( : asin w (bé — be) pp’ for its interpretation suggests a purely geometrical method of arriving at it, as follows. The velocity V of P’ is the same as that of V, and is therefore the resultant of velocities ' b and fe parallel to BB’ and BA; thus aS a b’p’* + c’p® + 2bepp' cos @) .....4.... Gil): In the same way, the acceleration f of P’ is the resultant of accelerations Fb and Fé parallel to BB’ and BA ; its value may therefore be written down. Also, if @ denote the angle between V and f we have Vf sin @ equal to the area of the parallelogram contained by the vectors representing V and /; therefore Vsin a = (0 bP g_Pe aed sin @ a a a a =" (BG