, Dr fi oes der ee 1 Y sh bet ry qt ‘ SR Aer A aa wre We Pare DOO CY 4 Wren Sr stete oearae ( oe (e 4% \! Mt X) oe =e ” Fahichy POO ' My ‘ ‘ Mea cy ea wi eu 4 as bd A rea" yoda heal gt ted Wy A tas CH = M4 hed a at rite ye bat ved 4 DCE UR ‘ aia ydasee fit shit tty ewe 4.4 at ot an " nh n at Aa ic ait eta Rei RSNA AOC a tea ed aay ae RENO gd irgk SERRA OWN ‘a te HWe ii pat tlstaley att ah ae vg y uit ee "yf : MACHER RON e Het PR 4 Ve Wag ey Te toe ann eH alg in Hinata te 4. yeee'h ite baa Aa te t eaten) jhe fay: i a ‘ MM ited alts ‘ ive i eee ae ata ¢ Lidia site Ay at x va Oe if He) woe Ae 1 ‘wy sae wi ilaralalyaiaete: 4 ahaa at Ae id ye Pie ihe M 42 v } Nh 34 a ( Aa ee aditine P44 bat ‘ an OOH RI Pen En Vaile Vy 4 ww HO A a ROL Lee f wed 4 ag hea 4 , “4 ies A itis cM yy it Vga “ Nes | a * pay : iti Nati avails Hs if 44 a Oe iFuer Ar vA rules Wit 4 tis tht ay 9 sas eae its A ni ry ‘fat aK « ae Has ee si an me iad: } Petey ww 4 uy ie veil a ei wld io 4 ‘ae My va ie dow * AUN REL HR AA sob a i a p v' ie noes “ TA a wa wet wh a BUNA Dy La A ¥ i ‘ Ba a a edt Hi ieee eG Ice eae ON “ dove cat Ne Aes iad Ae 4 md Nei ay it: DED) Coreen) Shek gia bn ae A a] Rati 4 aad PC EL Pn 4 calsteitata tie dd sae oi are ay A ae ’ ane & Ne ek Lae OAD our iit 4k lie vines eho Wat eayhe cs =a 8G Fk ‘ hs ‘ ioe NS Tec ts) eae crore tt ean: iin Bs " 4 wi an pra hal is isan Da) nig bo is } ane Phas ‘ie ican Nii wi ii = a } Re oe ee iad rads doit ah FANON ' y : Yeah hia) hy, Y ie f A ba y i va i s Rares cy ie sh fA mn cry Ce Aaa id 45 ' Uy BY x rye) Yat ie ‘i * he ig mo ie ae ; ¢ aa ‘at ty vee , ay {) ee a) Hi ne i it alt ae aN ny ta hf iin titty Hee 4 Ws aay oy it devi: * r whee nes sie no) ean i 4 ne sn ae tb ye Gak santas Etat re wh Wi We the ine i : Lid ae = a rn ve hoe : 3 ae ihe vi aie yh nt Ng PROCEEDINGS Cambridge Philosophical Society. VOLUME IX. Cambridge : PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. PROCHEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. VOLUME IX. OcTOBER 28, 1895—May 16, 1898. Cambridae : PRINTED AT THE UNIVERSITY PRESS, AND SOLD BY DEIGHTON, BELL AND CO. AND MACMILLAN AND CO. CAMBRIDGE. BELL AND SONS, LONDON. 1898 CONTENTS. VOL. IX. October 28, 1895. Annual General Meeting November 11, 1895. A method of measuring the loss of energy in Hysteresis. By G. F. C, Searle 3 , - : On the forms of cubic ee confainine 27 mal ay na fee (Plates I—Il). By W. H. Blythe ‘ Expansion produced by Electric Discharge. By Miss Tee November 25, 1895. Exhibition of a curious specimen of Travertine lining a wooden pipe: By Prof. T. McK. Hughes On Symmetry in the foliage of a Beauek of Mulberr 4 ath Pavdniietce in the individual leaves. By Prof. T. McK. Hughes The Origin of Vertebrates. By Dr W. H. Gaskell December 2, 1895. Discussion on Dr Gaskell’s Paper . < : . January 27, 1896. Longitudinal Electric Waves, and Réntgen’s X Rays. By Prof. J. J. Thomson The Equilibrium of feptropic ‘Blastic Solid Shells of nearly Spherical form. By Dr C. Chree Distribution of Solar Radiation, and i dégendencs on Wecionoriienl Elements. By R. Hargreaves PAGE 37 61 69 vi Contents. February 10, 1896. On an Osmometer. By Dr Lazarus Barlow . ° : : On the communication between peritoneal cavity And Sa veins through the nephrostomial tubules in the frog. By E. J. Bles On the effect of water currents on the assimilation of ae plants. By F. Darwin and Miss D. F. M. Pertz . : ‘ On a collection of plants from New Britain (Neu poner yy By lee Burkill February 24, 1896. Experiments on Liquid Air. By Prof. Dewar : On the Generalization of certain Properties of the Tisheiheiban. By J. Brill On the absolute Me neern i Optical Deretien "bap a Soren By a Larmor . : : : : . : : - : March 9, 1896. Notes on the Geological History of Monocotyledons. By A. C. Seward A description of the Crania found at Girton in 1881. By R. J. Horton- Smith : : On the Recurrence of ie Nese By Bron Ake McK. Hheties : On some Chipped Flints from the Plateau Gravel of Salisbury and elsewhere. By Prof. T. McK. Hughes On the Leakage of Electricity through Dielectrics sexowed by Rontgen Rays. By Prof. J. J. Thomson and J. A. M°Clelland April 27, 1896. On photographing the whole length of a Spectrum at once. By Prof. Liveing : F , : On dioxymaleic fea and fg edness By H. J. H. Fenton On the atomic weight of Oxygen. By A. Scott : On the combining volumes of Carbon Monoxide and Onan. By A. Scott : : The constituents of Tada hems resin. ey T. Jel, Hasterfield ol TB; Wood : : : Note on the Brirmeclonieall mecien of canines resin. By C. BR. Marshall . May 11, 1896. Note on the formation of the germinal layers in aug By EK. W. Mac Bride Note on the continuity of Mesenchynne one in “EEE tei ve. By E. W. Mac Bride Crania from Teneriffe. By F. C. Sherpa PAGE 111 114 120 126 141 142 143 144 144 149 150 153 154 Contents. May 25, 1896. On the spectroscope used in connexion with the 25-inch refractor. By H. F. Newall F : : : i On a suggestion for a form of SpoderolicliogneBh: By H. F. Newall On the Period of the Earth’s Free Eulerian Precession. By J. Larmor. Note on a point in theoretical dynamics. By Sir Robert Ball On the maximum deviation of a ray of light by a prism. By Prof. A. Anderson : : : . On a method of discussing the plane satus of satiabons “By A.C. Dixon October 26, 1896. Annual General Meeting ; : ; 4 On the casts of Zyuanodon bernissartensis, Pouloneee By 8S. F. Harmer On the proposed relationship of Birds and Dinosaurs. By H. Gadow On Cyclostomatous Polyzoa. By 8. F. Harmer November 9, 1896. On the Nature of the Réntgen Rays. By Prof. Sir G. G. Stokes On certain cases of Discharge in Vacuo and on the zigzag path of Lightning. By J. Monckman . November 23, 1896. On the Superficial Colour of a Silver-Zine Alloy. ne Cor ane and F. H. Neville On Thermometric “ Fixed Points.” “Re E. H. Griffiths - : January 25, 1897. On some results obtained by staining the Brain with the Chrome-silver method (télustrated by photo-micrographs). By Dr Hill . On a possible explanation of the quinqueloculine arrangement of the chambers in the young of the microspheric forms of Triloculina and Biloculina. By J. J. Lister : : On the theory of Osmotic Pressure. By J. Larmor February 8, 1897. On the Cathode Rays. By Prof. J. J. Thomson On Electricity in Gases and the formation of Clouds in Hinged eases By J. 8. Townsend Vili PAGE 179 179 183 193 222 224 Vill Contents. February 22, 1897. On the Diffraction Pattern near the Focus of a ae By R. H. D. Mayall On the marks made by stars on Theta mates eepowel near he focus of a telescope. By H. F. Newall : On Theorems on the contacts of spheres. By W. M°F. Om , On change of the independent variable in a coefficient. By E. G. Gallop March 8, 1897. On the injection of the intercellular spaces occurring in the leaves of Elodea during recovery from plasmolysis. By F. Darwin and Miss Pertz On the phenomena of (arbor [Droste reduction associated! wee reduced vitality in plants. By F. F. Blackman . On the leaves of Bennettites. By A. C. Seward April 26, 1897. On Lie’s Solution of a Partial Differential Equation of the First Order. By Dr Dixon On the Apparent Bileceiaeation in an istlestinte Field a ie Bounding Surface of Two Dielectrics. By A. Anderson . On Luminosity attending the compression of certain mameedt gases. By H. F. Newall May 10, 1897. Observations on Stomata by a new method. By F. Darwin Notes on hybrid Cinerarias produced a Mr Lynch and Miss Porte By W. Bateson : ; : ; : : May 24, 1897. The relationship of Amphiowus and Balanoglossus. By EK. W. MacBride On the degree of the Eliminant of Two Algebraic Equations. By Dr Lachlan 4 : F : Tides on the veces mieory: “Oe Dr Chree . Experiments on the Effect of Ultra-violet Light on the @onducheres of Iodine Vapour. By J. Henry. : 5 : : October 25, 1897. Annual General Meeting : : : : : Electrical Oscillations in Wires. By H. C. Pocklington On Circles, Spheres and Linear Complexes. By J. H. Grace Reduction of a certain Multiple Integral. By Arthur Black . On the Gamma Function. By H. F. Baker : On the lines of striction of a hyperboloid. By H. F. Baker On the Action of Uranium rays on the Condensation of Water Vapene By C. T. BR. Wilson . PAGE 259 269 271 272 272 273 273 279 292 295 303 308 309 313 318 319 323 324 332 332 302 333 333 Contents. November 8, 1897. Farmer’s method of demonstrating assimilation. By Francis Darwin . Artificial Cultures of Sterewm, a Tae eg Fungus. By Prof. Marshall Ward : : ; On Encephalartos Ghellinckir, iene a rare Cet By A. C. Seward November 22, 1897. Partial Differential Equations of the Second Order. By Prof. Forsyth . Electrical Properties of Newly Prepared Gases. By John 8. Townsend A chemical effect produced by the impact of kathode rays. By Prof. J. J. Thomson and 8. Skinner . : : : The effect of zinc and other metals on a Aire one pine By Prof. J.J. Thomson . December 6, 1897. Notes on some Hawaiian Insects. By R. C. L. Perkins Remarks on a journey to investigate the habits and dev ‘leprae of Lepidosiren paradoxa. By J. Graham Kerr January 24, 1898. A New Method in Combinatory Analysis with applications to Latin Squares and associated questions. By Major P. A. MacMahon Abelian Functions in connexion with two-dimensional fluid motions. By H. F. Baker On the production of a cloud by the action of lee violet fight on anv air. By C. T. R. Wilson On the use of logarithmic coordinates in Physics ne J a ie paneate On the Diffuse Reflection of Réntgen Rays. By Prof. J. J. Thomson February 7, 1898. Some Zoological Results of a Voyage to Melanesia during the years 1894—1897. By Arthur Willey February 21, 1898. On some differential equations in the theory of gies algebra. By Prof. Forsyth : : : : The Discharge of Electrification by Ultra- moles iaene By E. Ruther- ford . : : : Rontgen photoerape of. ertallic alow ey C. T. ercoce and F. H. Neville : : ‘ : : apouis : ‘ : 1x PAGE 338 340 340 345 345 371 372 373 380 381 381 392 393 363 398 x Contents. March 7, 1898. The Coral Reefs of Funafuti, Rotuma and Fiji together with some Notes on the Structure and Formation of Coral Reefs in general. By J. Stanley Gardiner Method for the Demonstration of “ Gonnecting Threads Zain ae Cell Wall. By Walter Gardiner May 2, 1898. On the theory of Order. By E. T. Dixon : On a certain system of differential equations donate pociedie fon cHone By H. F. Baker : : 5 , On the Total Eclipse of the oun 1898 fon 22, By H. F. Newall . May 16, 1898. On the figures produced on photographic plates by electric — By J. A. M°Clelland On a Method of facilitating the Tacasiverent of tempentine by means of Platinum Thermometry. By EK. B. H. Wade The development of Peripatus novae-britanniae. By Dr A. Willey On the possibility of deducing magneto-optic phenomena from a direct modification of an electro-dynamic energy function. By J. G. Leathem . On the solutions of the aruenion (Cue O in elliptic coordinates and their physical applications. By R. C. Maclaurin On the interpretation of divergent solutions of the hyper- ocomenee equation. By W. MCF. Orr The Harmonic Expression of the Daily Variation of Solar Radiation, and the Annual Variation of its coefficients. By R. Hargreaves INDEX PLATES. Tand II. To illustrate Mr Blythe’s paper . III. To illustrate Mr J. Stanley Gardiner’s paper IV and V. To illustrate Mr M®Clelland’s paper PAGE 417 551 531 532 PROCEEDINGS OF THE Cambridge Philosophical Society. ANNUAL GENERAL MEETING. Monday, 28 October 1895. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. The following officers and new members of Council were elected :-— President : Prof. J. J. Thomson. Vice-Presidents : Prof. T. McKenny Hughes, Mr F. Darwin, Prof. G. D. Liveing. Treasurer: Mr Glazebrook. Secretaries : Mr Larmor, Mr Newall, Mr Bateson. New Members of Council: Prof. Sir G. G. Stokes, Mr A. Sedgwick, Mr A. Scott. The names of the Benefactors were read. The President referred to the death of Prof. Babington and of Prof. Huxley. VOL, IX, PT. I. 1 2 Mr Searle, A method of measuring the [Noy. 11, The following resolutions were proposed by Prof. Liveing, seconded by Prof. Hughes, and carried unanimously. “That this meeting desires to place on record its sense of the loss the Society has sustained by the death of Prof. Babington and to convey to Mrs Babington the expression of their sympathy and condolence in her bereavement.” “That the President be requested to convey to Mrs Babington the foregoing resolution.” The following resolutions were proposed by Prof. Newton, seconded by Prof. G. H. Darwin, and carried unanimously. “That the Fellows of the Cambridge Philosophical Society at this their first meeting since the death of the Rt. Hon. Thomas Henry Huxley, LL.D., desire to express their sympathy with Mrs Huxley, and to record their sense of the depth of his influence on modern thought and on the progress of Biological Science.” “That the President be requested to convey to Mrs Huxley the foregoing resolution.” Monday, 11 November 1895. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. The following Communications were made to the Society : (1) A method of measuring the loss of energy in Hysteresis. By G. F. C. Seare, M.A., Peterhouse. The extensive employment of transformers in the distribution of energy by alternating electric currents has caused the measure- ment of hysteresis in iron to become a matter of such commercial importance as to stimulate efforts to find a means for readily testing iron as to its quality with respect to hysteresis. The subject is important not only commercially but also from the purely scientific point of view, for it can hardly be doubted that our knowledge of the molecular structure of iron would receive some extension if a means were provided by which the effects of various physical conditions—stress, temperature, the passage of electric currents &c.—upon the loss of energy in hysteresis could be investigated with a comparatively small expenditure of time. As is well known, the loss of energy occasioned by any cyclic change in the magnetization of iron is equal to f[HdJ in ergs per cubic cm. of iron per complete cycle, H denoting the magnetic force and J the intensity of magnetization, both im ©.G.s. units. The waste of energy, fHdJ, I shall denote by W. The value of fHdI may be obtained by plotting in a curve the simultaneous values of H and J from a numerous series of observations, and 1895.] loss of energy in Hysteresis. 3 then measuring the area of the curve. Or again, since, if B is the magnetic induction, we have B= H + 47TJ so that (for [HdH vanishes when applied to a cyclic change), it follows that the hysteresis loss may be determined by plotting and measuring the curve given by simultaneous values of B and H. To obtain any satisfactory curve at least a dozen simultaneous observations of H and B are needed. I have striven to design a method which should enable the hysteresis loss to be determined by a single observation of the “throw” of a spot of light along a scale. The method was far from being perfected when this communication was made to the Society on 11 Noy. 1895, but it has been represented to me that though at present imperfect it is of sufficient interest and promise to justify its finding a place in the Society’s pages. A bar of iron of cross section A is placed in a solenoid wound with WV turns of wire per cm. of its length. The current C which flows round the solenoid and magnetizes the iron, also passes round the fixed coils of a sensitive electrodynamometer. A se- condary coil of n turns is wound over the iron and is connected in series with the suspended coil of the electrodynamometer, the resistance of the secondary circuit being R. When the primary current C changes, the magnetic induction B changes and an E.M.F. AndB/dt is set up in the secondary circuit. If the time- constant of the secondary circuit is very small compared with the time of a complete cycle, the effects of self-induction may be neglected, and then there is a current y in the secondary circuit of amount y= fn ae Now the relation between C and H is R dt™ expressed by H=47NC, so that C=H/47N. Hence, if the couple experienced by the suspended coil when a current 7, flows in it and a current 7, flows in the fixed coil is qi, ergs, the couple experienced by the suspended coil at any instant due to ¢ and + 1s qcy ergs, supposing that the deflection is not so large that the value of q is appreciably different to its value in the equilibrium position. outs Now if the time of vibration of the moving coil is so great compared with the time occupied by the double-reversal of the current that this process may be regarded as completed before the coil has moved sensibly from its equilibrium position, the angular momentum acquired by the coil for a single double-reversal of the primary current is BOTTA a — dB _ gAn i 9 Ko =| q0yit = {rp HS dt= {oe [HaB ...2), 1—2 4, Mr Searle, A method of measuring the [Nov. 11, where K is the moment of inertia of the coil and @ its initial angular velocity. Thus since fHdB=47W we have NR Let T be the time of a complete vibration of the coil, @ its greatest angular displacement or “throw” and 7 the restoring couple exerted by the suspension per radian of displacement. We have, by the Conservation of Energy, Ko with (3). Initial kinetic energy = Potential energy at extremity of swing, so that bye A Sos 217) ch Ae AON ROR ER Rr hele 6-3. (4). Also JP = Bie ve SS eect ae ote Eee (5). From (4) and (5) we find Goss Ko = OF CT ajales el stetelelo\ ele lalalsterevecohoreletelatea=te (6) Thus from (3) we have NEnTP adn (7) The quantity 7/q 1s easily determined as follows :— Let currents 7,, 7. flow i the suspended and the fixed coils of the electrodynamometer respectively and let @ be the observed steady deflection, then Gist — COMPLE — Vn i iagese sete aoe (8), so that nlq = tite/¢. If there is any appreciable damping the expression must be multiplied by 1+ 4A, where » is the logarithmic decrement. We have finally _ NRT, ~ QrAnd Thus the “throw” of the coil is proportional to the energy lost in hysteresis. It is evident that this affords a very ready means of testing the hysteresis of iron under different physical conditions for a given maximum value of H, the magnetic force, for all that has to be done after the constant of the instrument has once been determined is to observe (by means of a mirror and lamp and scale) the throw produced by a single double-reversal of the magnetizing current. For instance, a steady electric current may be maintained through the iron and the value of W for each value of this current may be OCLEEEON) | al eee (9). 1895.] loss of energy in Hysteresis. 5 determined by simple observation of the “throw” in each case. If it is desired to investigate these effects for a given maximum value of B, the magnetic induction, the process is a little. more complicated, because the value of B has to be found by the bal- listic galvanometer method, and the strength of the magnetizing current so adjusted on each occasion that the value of B may be kept constant under the varying conditions imposed upon the iron. In the electrodynamometer which I have constructed for this experiment, the suspended coil is a long narrow coil of 120 turns, about 8 cm. long and 1°5 cm. wide, suspended by a silver wire woo Inch in diameter. The fixed coils have 500 turns and are designed so as to fit closely round the suspended coil. With 1285 turns in the secondary coil and with the resistance in the secondary circuit about 100 ohms, the instrument is sensitive enough to measure the hysteresis loss in the case of an iron wire ‘02 cm. in cross section. I have made the instrument sufficiently sensitive to measure W for so thin a wire with the view of investigating the effects of tensile and torsional stress upon the hysteresis. Up to the present (3 Dec. 1895) I have not been able to make any accurate determinations owing to the fact that I have so far used an ordinary rocking mercury key for reversing the primary current. With this key, on breaking contact, the primary current is stopped very quickly, and when contact is re-established the current very quickly rises to its full strength, and each of these changes takes place in a time not very large compared with the time-constant of the secondary circuit. On account of this the instrument has given results about 100 °/, too large, as judged by the value of W obtained by a B-H cycle. When, however, a coil with a large coefficient of Self-induction was inserted in the primary circuit so that in spite of the key the primary current could not vary rapidly, the discrepancy was reduced to about 5 °/,. But I have designed a key (somewhat after the fashion of Prof. Ewing’s “Sine Function” key) which will allow the current to be quite gradually reversed, and some preliminary observations have led me to expect that with this key the instrument may work quite satisfactorily. Nove added 18 Dec. 1895. The following method of deter- mining the constant of the instrument is much more convenient than that described in the paper. Let a constant current C’ flow in the primary circuit, and while this current is flowing suddenly produce a known change P in the number of lines of magnetic force passing through the secondary circuit. This is conveniently done by suddenly inverting an “earth inductor” which has been placed in the secondary circuit. The time-integral of the current 6 Mr Blythe, On the forms of [Nov. 11, thereby produced in the secondary circuit is P/R, and thus the initial angular momentum of the suspended coil is gC’'P where ’ is the initial angular velocity. But, if 0 is the “throw” produced, we have by (6) o/o’ = 0/@, so that by (3) and (10) Two determinations of C’PN/An@ on two different days agreed to within ‘5 °/,. The reversing key mentioned in the paper has been con- structed and measurements of the hysteresis for a specimen of steel wire have given results agreeing, within the limits of accu- racy of the observations, with the values obtained by B-H cycles. For very soft iron in which the maximum value of dB/dH is over 8000, and six times its average value, there is still a difficulty due to self-induction when a single wire about ‘01 cm.’ is tested. But I hope to overcome this difficulty shortly. G F.C. 8S. (2) On the forms of cubic surfaces containing 27 real straight lines. By W. H. Buytue, M.A., Jesus College, Cambridge. The following account of the transition between the various forms of these surfaces is a supplement to the paper in Proceed- ings, vol. VIIL., p. 241. A simple case of a cubic surface is that of a plane and a right cone shewn by one figure. Take a solid rectangular block, and let its upper surface represent the plane in question. Cut a right cone out of this block, axis vertical, having its vertex in the plane at a point A. Invert the solid cone, vertex at A. The surfaces of the solid and hollow cone, and that of the plane, represent a cubic surface. A straight line can be drawn to cut the surface in three points. Comparing this diagram (1) with (2) and (3), which are vertical sections of a cubic surface represented by the general equation, we see a similarity in form. In the case of (8) the upper hollow portion is connected with the lower. In passing from the form (2) to (3) and then from (3) to (2) it is evident that a “hole” is made, joining the upper to the lower hollow portion. In the case of a cubic surface having twenty-seven real straight lines there are three such “holes” or openings. Fia. I. Fia. II. Plate I TY Te Diagram (3). Diagram (2). Diagram (1), nr Phil. Soc. Proc. 1x. Pi 1. Geet Baty vy Plate TT Phil. Soc. Proc. 1x. Pt 1. 1895.] Cubic Surfaces containing 27 real straight lines. 7 Three drawings from photographs of a model shew these openings, the fourth being a view of the under part. [Plate I. Figs. I—Iv.] The lines on the solid upper portion which are the same as those on the lower hollow portion form a double six, these lines each pass through one opening. The lines through each opening form a double six. _ The lines between each opening and the next form a double SIX. Twelve lines pass through two openings namely 17, 23, 13, 19, fet; 20, 115, 16, 4, 22. Three lines 8, 18, 27 do not pass through any opening. One conic node. Take the lines 1,13; 14,6; 4,11; 22,16; 23,17; 10,2 and let them move up to one another namely 1 to 13, 14 to 6, &e. so as to form six lines only r,, r,, ..., 75. These lines will now all pass through a point, and the opening through which they go will close up to this point and become a conic node. We now have 15 mere lines and 6 rays of a conic node, Two conic nodes. If the two conic node rays 73, 7, now coincide, another opening closes up, namely that through which the double six 4, 22, 11, 16, 19, 9, 25, 5, 7, 26, 21, 12 passes. 73, 7, now coincide to form an axis A, joining the two conic nodes. The line 27 becomes a transversal meeting the axis. The lines 19,9; 25,5; 7, 26; 21, 12 coincide by pairs to form four rays of the second conic node T, Ts, 7, Mo. SIX more lines remain, each of which meets the transversal, namely 3, 8, 15, 18, 20, 24. Three conic nodes. Two rays from each conic node 7, 75; 77, 7 may be made to coincide. The third opening now becomes a point joined to the other nodes by axes A,, A;. 3, 20; 15, 24 unite to form ry, 7p rays of the third node. 8, 18, 27 are the transversals. Four conic nodes. The six conic node rays in this case may be made to coincide by pairs. We then get a fourth conic node caused by the closing up of the opening at the base of the model. 27, 8, 18 still remain transversals. Conic nodes may also have been found by considering the solid portions between two openings as diminishing in size, we then get a conical point formed by the meeting of two solid conical portions, instead of hollow ones. 8 Mr Blythe, On the forms of [Nov. 11, A case of great interest is that in which one of the tangent planes to the surface is at an infinite distance. The general equation in Cartesians is xyz = Aa? + By? + CP + 2Fx+ 2Gy + 2Hz+ K. The sections parallel to the coordinate planes are conics. Four of these sections in each case become pairs of straight lines and two are parabolas. It is clear that we get twenty-seven straight lines, namely three sets of four pairs together with three at infinity. ' Examining the meaning of this as regards the model we find that the three openings become infinitely elongated, we therefore get a central solid joined to four infinite solid conical shaped branches. These are so placed that a plane cannot cut both the central solid and the four branches at the same time. A correct idea of the shape of this model may be obtained by placing four cones with their vertices at the angular points of a tetrahedron, their axes being in the line joining these points to the centre of the tetrahedron. If this construction be made in wood or wire it can be covered over with wax or plaster of Paris to shew the surface exactly. If the equation is ayz= Ax + By+C2+4+K, we still get four sections parallel to the coordinate planes contain- ing straight lines, but in each case two pairs consist of parallel straight lines and the parabolic sections do not appear, for they have coincided with them. The symmetrical surface mentioned by Mr H. M. Taylor having four conical points, the equation to which is e+y+ 2+ 2eyz—-1=0, is here given. [Plate II.] A, B, C, D are the conical points and are angular points of a regular tetrahedron. a, b, ¢ are the middle points of BC, CA, AB. If we put 2, y, or z=0 we get circular sections, each bisecting four edges of ABCD. Portions of these are shewn passing through a, b; 6, ¢; ¢, a. Next the curve passing through A and a is a parabola which also goes through D, having its vertex at a. All sections at right angles to this parabola (that are also parallel to AD) are conics, and the extremities of their minor or major axes are upon it. There is another parabola passing through B, CU and the middle point of AD at right angles to this one, and is such that if the major axis of a section has its extremities on the first parabola, the extremities of its minor axis are on the second. —~ 1895.] Cubic Surfaces containing 27 real straight lines. 9 When looking at the diagram we see that a parabola (e.g. that through D, a, A) being visible on the face ABC passes through the point A, and being now on the further side of the solid branch at A passes out of sight. On each solid branch there are evidently three edges of the tetrahedron and three parabolas symmetrically placed, and if we cut any solid branch transversally by a plane at right angles to the line passing through its vertex and the centre of the tetrahedron we obtain a symmetrical cubic oval, a diagram of which is given, having its points of maximum and minimum curvature at M and m, where the edges and parabolas respectively meet it. There are also three infinite branches caused by the section of the plane and the three other solid portions. Kach edge of the tetrahedron coinciding with four straight lines on the surface and three being at infinity there are still of course twenty-seven straight lines on the surface. Some of the simpler cases of binodes yet remain to be con- sidered that have equations of the form aby = Képp. Construction of the surface. Take a8y= Kéuv as the equation of a cubic surface where a, B, y, 5, w, v are of the first degree and K constant. Nine of its twenty-seven straight lines may be at once obtained as the inter- sections of the planes a, 8, y with 6, uw, v respectively, and if we take them to be represented by the numbers 4, 2, 12, 13, 14, 15, 9, 8, 7 the planes and their intersections are shewn by the scheme ’ ey | a B 9/ eng heal ala w| 2, 14, 8, pr ee PS If we take the lines forming a diagonal of this table, e.g. 4, 14, 7, we can find three straight lines on the surface that meet all of these, and no more. By interchanging rows and columns we get in all six such diagonals. Therefore there are 18 beside the 9 at first found, making a total of 27. We can take it that 5, 16, 17 meet: 4, 14; 7. 6, 26, 27 meet 4, 8, 15. LO 1S. 19 (ot pp dse 8: 12. ea ena Bay ee PZ ZL) en, Oi 2G, LS. Wie 2a W105, Oy Ae 10 Mr Blythe, On the forms of [Nov. 11, Take areal coordinates, the tetrahedron of reference being that formed by the planes a, 8, y, 6; and let w=(Lat+m,8 —y)n + 6, vp = (la + mB —) n. + 4. Let the lines 4,9, 13 form an isosceles right-angled triangle, hypotenuse in 9. The planes 4, 12, 2 and 13, 14, 15 are per- pendicular to 4, 9, 13. 15 cuts the edge 18 in the ratio /, : 1, 14 ei 13 jeans 2s 5 4 Bs Ta 12 ‘ 4 ee Ws cask, If y=0 cut a=0, B=0 at a distance d, above 6=0, and 14, 2 and 12,15 meet a=0, 8=0 at distances d, and d; above 6 = 0, then % (d, iz d,) = d., Nz (ad; — d,) = ds. We see therefore that by taking arbitrary positions for nine of the straight lines we determine all the constants in the equation aBy = Kdouv, except K. Take a point 0, 8,, y,, 0 on the straight lme 4. Denote the ratio y, : 8, by p, we shall find that Nie — ON ANG ee Ny — will reduce to two independent equations both satisfied by 0, B,, Yi» 0 if Ay =m (m oa P), Ns P= Ta (Mg Ps ee ene eee (A). and Ay (Mg. — pp) = — Ny Ny (1, mz — 1, p) These two equations will represent a straight line on the surface if \,A,A;a8y = duv coincide with aBy= Kody, that is if rahe ke If K be known it is evident that using this equation with (A) we get a cubic equation for p. When p is determined we get but one value of Aj, As, A; for each value of p, and thus obtain three definite straight lines on the surface. If, however, we consider K as unknown, and take an arbitrary value for p, say p,, we find K from the equation Pi (Msy — 14,91) = — Kn?n.? (mM, — pr) (m2 — pr) (am — 1201), and the other values of p from the quadratic (Lm, — 1,p) (ms — p) (m1 — p) _ (argh, — Mp) p (2,m.—1,p1) (Mz — pr) (M,— pi) (MyN2— Nps) pr’ obtained after simplification and division by p — py. 1895.] Cubic Surfaces containing 27 real straight lines. ll In this case take as an arbitrary point that at which 16 meets 4, we get a quadratic which determines the points at which 5 and 17 meet 4. Similarly all the other lines may be found. When the position of all the lines is fixed, the form of the sur- face can be found by taking sections through any straight line on the surface. These sections are conics, the straight line forming part of the complete cubic section. Many points on these conics are known as being the intersection of the planes with lines already found. The rules for the geometrical construction given in Vol. VIIL., Pt. iv., page 241 may be deduced from the analytical method given above. For it has been shewn that the position of the lines 4, 12, 2, 13, 14, 15, 9, 7, 8, and the point at which 16 meets 4 may be placed in arbitrary positions, and that this construction determines all necessary constants. When this has been done the facts used to determine the remaining lines are (1) If three straight lines form a triangle this triangle is a section of the surface. (2) Any two triangular sections meet each other in three points in one straight line, e.g. 3,5, 7 and 13, 14, 15 are sections, 3 meets 15, 5 meets 14, 7 meets 15, and the three points of inter- section are in one straight line. (8) If we find four points on the surface in one straight line, this line lies wholly on the surface. (3). Hapansion produced by Electric Discharge. By Miss MARTIN. Acting under Professor J. J. Thomson’s directions, I have lately endeavoured to find some explanation of certain pheno- mena first mentioned, I believe, by Herr G. Meissner (ADA. d. Gesell. der Wissensch. zu Gott. 1871, Bd. xvi. p. 98). In the course of some experiments “iiber die elektrische Ozonerzeugung und iiber die Influenz-Elektricitiit auf Nicht-Leitern,’ Meissner ob- served that if a gas contained in a space between the plates of a condenser were subjected to a sudden rise or fall of potential the volume of the gas underwent a momentary increase. His apparatus consisted of two concentric glass tubes about 50 cm. long, both rounded off at the lower end and having no connection with each other in any way except that the inner tube was held in place at the upper end bya ring of wax. Between the two tubes was a space of 3—5 mm. The outer surface of the outer tube, and the inner surface of the inner were coated with tinfoil 12 Miss Martin, Expansion produced [Nov. 11, having an area of 264 sq. cm. and 136 sq. cm. respectively. Be- tween the two coatings there was—making allowance for the thickness of the tube walls—a space of 6—7 mm. Attached to the outer tube was a gauge to mark the variations of pressure in the gas under observation. Having tried various modifications of Meissner’s apparatus with no very satisfactory results, it seemed advisable to have his appa- ratus exactly copied—which was easily done as he gives very clear and careful measurements and descriptions. This was accordingly done, the only difference being that instead of the gauge used by Meissner a horizontal tube provided with a small quantity of sulphuric acid was used. Observations with this led to the belief that, very frequently at all events, the movement of the acid in the gauge was accom- panied by a luminous discharge through the tube due to induction, Before it could be ascertained if this was invariably the case the outer tube was accidentally broken and it seemed advisable to have the new one made of rather different dimensions. Accord- ingly a piece of tubing about 40 cm. long and having an outside diameter of 3°3 cm. was used for the outer tube whilst the same tube as before (57 cm. long, outside diameter 1:2 cm.) was again used for the inside. Instead of sealing up the lower end of the outer tube as before, this was now bent and drawn out to serve as a gauge and provided with a tap to cut off the acid from the 1895.] by Electric Discharge. 13 tube when the latter was being exhausted and refilled with what- ever gas might be under observation; for this purpose a short tube projected between the tap and the bend which communicated with a pump and with the source of gas employed. In this case the inner and outer tube, instead of being cemented together with wax, were provided with a rather loose ring of india-rubber be- tween which and the glass melted paraffin was poured and allowed to harden so that the joint was air-tight. For about 15 cm. below the india-rubber the space between the two tubes was completely filled with paraffin. Instead of lining the inside tube with tinfoil it was filled with mercury; the outer tube as before being coated with tinfoil in which spaces were cut to enable the observer to note what went on inside the tube. This outer tinfoil which extended from just below the lower end of the paraffin stopper to within 4 cm. of the bend was 28 cm. long and had an area of 290°3 sq. cm.—not allowing for the small spaces cut out —the effective mercury surface of the inner tube was 87-96 sq. cm. The two surfaces were distant from one another 1°15 cm. and the air space between the two tubes had a width of ‘9cm. The two latter measurements may not be perfectly correct as of course it is the smallest distance between the two tubes that is required and, though every care was taken, the two tubes may not be perfectly concentric; there may be an error of 1 or even of 1°5 mm. The condenser thus formed was mounted on a square of glass by means of a thick band of paraffin. The whole was then enclosed in a light-tight case so arranged that the lower part of the appa- ratus forming the gauge projected from an opening beneath, and provided with an opening in front fitted with a small blackened tube through which the interior could be observed. A mm. scale was affixed to the gauge tube. The mercury in the inner tube was connected to the inner coating of one Leyden jar, the tinfoil on the outer tube to another jar, the outsides of the two jars being connected to earth. The maximum charge upon the two tubes could be regulated by means of the distance between the ter- minals of the Wimshurst by which the apparatus was charged. With these arrangements it was easily seen that any move- ment of the acid in the gauge of not less than ‘25 mm. was accompanied by a luminous discharge through the space between the two tubes, but it appeared at first as though smaller move- ments than this were unaccompanied by any luminosity. Greater care however proved that this was not the case, but that every movement of the acid is accompanied by a corresponding lumi- nosity between the tubes. It requires great care and some practice however to see this when at its faintest; it is much easier to perceive the very slightest shake of the acid than the almost imperceptible luminous discharge which however un- 14 Miss Martin, Expansion produced [Nov. 11, doubtedly accompanies it. On the other hand no luminous dis- charge ever occurs without a corresponding movement of the gauge, and it is only when the sudden change of potential of the two tubes is sufficient to cause a visible discharge in the space between them that any alteration in volume of the gas therein contained is to be observed. Of course it might be urged that though a luminous discharge is always accompanied by an increase of volume in the gas the reverse may not be the case, but that sudden changes of potential too weak to give any luminous effect may produce a change in volume which the form of gauge used is not sufficiently sensitive to note. I do not think this is the case. In the first place the gauge is so sensitive that if two fingers be laid against the top of the outer tube the acid in the gauge below begins to move in from 1” to 1%5 and in 17” moves through a distance of 20 mm. There is however a much more conclusive proof that the gauge takes account of every change of volume and that every such change is accompanied by a luminous discharge through the gas. If the distance between the terminals of the Wimshurst be so arranged that the sudden fall of potential caused by the passing of the spark is sufficiently great to cause luminosity in the space be- tween the two tubes upon every discharge there 1s always a move- ment of the acid in the gauge; but when the fall of potential does not give rise to a luminous discharge there is never the slightest movement of the acid. When however the distance between the Wimshurst terminals is such that the sudden discharge causes sometimes a faint luminosity through the gas and sometimes none, the gauge some- times moves and sometimes does not. It would perhaps be more satisfactory to have a second observer in order to be perfectly certain that the two effects synchronize, but I do not think there can be any real doubt upon the matter. For it is possible so to arrange things that the majority of discharges of the condenser shall be accompanied by a luminous induction discharge, in which ‘case the acid generally but not always moves; if now the Wims- hurst terminals be caused to approach very slightly nearer to- gether so that the maximum charge possible upon the condenser plates is very slightly decreased, a smaller percentage of the discharge is accompanied by the luminous appearance in the tube, and the acid in the gauge moves a correspondingly fewer number of times. This is the result of several hundreds of observations. It is of course only within extremely narrow limits that this un- certainty as to whether the sudden discharge will or will not cause the effects under consideration is observable. It seems 1895.] by Electric Discharge. 15 fair to presume that the luminosity and the increase in volume are strictly simultaneous. If the charge upon the condenser plates be so increased that two or three luminous induction- discharges occur before the discharge of the condenser by the passing of the spark at the Wimshurst, two or three movements of the gauge are correspondingly observable. The minimum strength of charge capable of producing these effects varies slightly on different days according to temperature and pressure, but roughly speaking, at ordinary temperatures and pressures the distance between the Wimshurst terminals must be equal to the distance between the two tubes. That is to say, in my experience it has never required to be greater, nor have I been able to obtain any effect if the space between the terminals were more than 2°3 mm. less than the space between the tubes, Thus with the first tubes used, distant from each other about 4 mm., a spark 3:°4mm. was the smallest which produced any effect, whilst with the larger apparatus subsequently used having an air space = 9 mm. the minimum effective spark varied from 65 to 9 mm. but was generally about 8 mm. These observations were repeated with carbonic acid and coal gas but for a long time with no very satisfactory results, both these gases appearing to give very much the same effects as air— except of course that the colour of the induction-discharge was different. Meissner, however, is so very positive in his assertion that H gives distinctly smaller, and CO, distinctly greater, effects than air that I could not but think some essential point must have been overlooked. The cause for my failure in obtaining these differences at length became apparent. Meissner seems always to have first filled his vessels with the gas to be observed and then to have charged and discharged them. In my arrangements how- ever it was found more convenient to do the charging and dis- charging by mechanical means, and the Wimshurst which was worked by a small motor was turned on at the beginning of the observations and left to run undisturbed to the end; thus the gas, which was always admitted gradually into the vessel, was sub- jected to any chemical effects of the discharge before being put into communication with the gauge, the top of which had of course to be kept closed till the vessel was full of gas. Under these circumstances the three gases used, dried air, carbon dioxide and coal gas seem to behave practically identically. But if now the Wimshurst were disconnected whilst the tube was being exhausted and refilled, it was found that, on connecting it up again and discharging frequently as before, air underwent a con- siderable diminution of volume, and whilst this diminution was in progress sudden changes of potential would produce marked 16 Miss Martin, Expansion, etc. [Nov. 11, 1895. luminosity and movement of the gauge which after the air had assumed a steady volume were too weak to have any effect. Working with the same strength of charge it was found that coal-gas underwent practically no diminution—in comparison with air and CO,, that is to say, there was actually a small diminution most likely due to the presence of a small quantity of air in the tube—and the discharging of the condenser thus filled was at- tended with no greater effects than observed at the close of the observations with air. With CO, the first movements of the gauge were enormously greater than those obtained with coal gas and appreciably greater than those noticed with air; and the time taken by this gas to assume a steady volume was at least twice as long as that required by air. This steady volume how- ever having once been reached, the effects of any subsequent dis- charge were the same as with coal gas or air. It would therefore seem that any sudden and temporary splitting up of the molecules of the gas which may take place under the influence of the induction discharge is more easily and thoroughly accomplished while any definite chemical change is in progress. When nothing of this nature is taking place, all gases seem to behave more or less alike and to require equal forces to cause any disintegration. It is quite easy to understand how this may have escaped observation ; for if a vessel of the dimensions used has been filled with air whilst free from any electric dis- turbance, it requires about 600 discharges to reduce the air to its permanent volume when it gives the least movement for a given fall of potential; and to similarly reduce an equal volume of carbon dioxide at least 11000 discharges are necessary. It would seem that the chemical change which produces this diminution of volume takes place more easily and quickly at low pressures; for though, as was before remarked, the gas to be observed was let in slowly, the rate was not nearly so slow as the above figures would require ; nevertheless the volume was constant whenever the condenser had been exhausted and refilled whilst still connected to the Wimshurst. I should remark that the above phenomena were also ob- served whenever the apparatus was suddenly charged, but the great majority of observations were made on the sudden discharge through the spark at the Wimshurst as this method was found to be rather more convenient. 1895.] Prof. Hughes, Exhibition of specimen of Travertine. 17 Monday, 25 November, 1895. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. L. A. BoRRADAILE, B.A., Selwyn College, was elected a Fellow of the Society. The following communications were made to the Society : (1) Lwhibition of a curious specimen of Travertine lining a wooden pipe. By Professor T. McK. Huaues, M.A., F.R.S. The interesting specimen exhibited was presented to the Woodwardian Museum by Mr Benjamin Holgate, of Headingley, near Leeds, who has furnished me with the following information respecting it. It is a deposit of travertine formed inside a rectangular wooden pipe, used for conveying water from near the surface to the bottom of a mine under Magnesian Limestone. The wood decayed away and was entirely removed, leaving on the surface of the travertine the impression of every detail of the woody structure, so that it looks more like wood replaced than a cast of the interior surface of the pipe. Where a rusty nail projected into the travertine some of the iron scaled off, and the rust stained the deposit for a considerable distance round it so as to increase the deceptive resemblance to sawn timber. Another curious point in this specimen is the manner in which there is always a tendency to break along what may be called the miter joints. The deposit is built up in layers parallel to the inside surfaces of the pipe, and when crystallization is set up, the crystals are formed at right angles to those surfaces. The faces of the parallel prisms readily coalesce to form one crystalline mass, but the faces of the pyramids do not so easily unite, espe- cially under conditions in which, owing to the continuously reduced extent of surface, the marginal terminations are imperfectly de- veloped. The same phenomenon occurs in iron casting. If the metal cools against an irregular surface, which would tend to cause crys- tallization to start from surfaces arranged at various angles to one another, where the iron crystallized from one surface meets the iron whose fibres of crystallization have originated from another differently inclined surface, these two masses will not coalesce, but a plane of separation will extend some distance into the body, and be a source of weakness though the exterior may have been planed down so that the cause is not obvious. VOL. IX. PT. I. 2 18 Prof. Hughes, On symmetry in Mulberry foliage. [Nov. 25, In seeking the explanation two facts have to be borne in mind. First, that where the two masses meet at the miter their direction of increment does not coincide. And secondly, that the growth of the crystals is arrested along the margin by the ever-diminishing surface upon which they are built up. (2) On symmetry in the foliage of a branch of Mulberry with asymmetry in the individual leaves. By Professor T. McK. HucuHes, M.A., F.R.S. The question of the forms of leaves has often been treated of, but I do not know whether the particular point to which I now call attention has been noticed. Looking at the mulberry trees in the Fellows’ Garden at Christ’s College, I observed that young branches thrown out from near the base of the trunk are apt to bear scalloped leaves something like those of a vine. When in the progress of the growth and development of the branch these scalloped leaves are replaced by the normal forms, the change does not take place by the gradual withdrawal of the lobes equally all along the margin of the leaves, but the inside of the leaf, that is the side next the branch, first returns to the undivided condi- tion, while on the outside of the leaf the lobes are still conspicuous. On one flat twig all the leaves were shaped like gloves, which had a separate place for the thumb only, the other fingers being inclosed together in a sort of bag. In this case the thumbs were all turned outward, and the undivided margin was next the twig. Some apparent exceptions were found in which a leaf lobed on the right was found projecting from the left side of a twig, or vice- versd, but in all these cases, as far as I have been able to observe, the leaf which appears not to conform to the rule is growing from a small offshoot of the twig, so that a leaf which is left-handed in form with reference to the principal twig to which it at first seems to be attached, is right-handed with reference to the subordinate twig from which it really grows. It would thus appear that the symmetry which has been lost in the individual leaves still exists in the branches, so that the twig with all its leaves may be regarded from this point of view as one large leaf lobed on its margin, and therefore only the outside margin of each individual leaf partakes of this scalloping, that is, the left side of those on the left of the twig, and the right side of those on the right of the twig. 1895.] Dr Gaskell, The Origin of Vertebrates. 19 (3) The Origin of Vertebrates. By W. H. Gasket, M.D., LL.D., F.R.S., Fellow of Trinity Hall. The problem of the ancestry of the Vertebrates can be attacked from the side of the Invertebrates or from that of the Vertebrates. To my mind the best chance of a successful solution is to be found in the study of the Vertebrates themselves, and especially of the variation which has occurred in each organ or group of organs within the Vertebrate phylum. The principles upon which I have investigated the problem are based upon the continuity of the evolutionary process and- may be stated as follows— 1. Whenever it is possible to state that the variation of an organ or set of organs within the vertebrate phylum has taken place in a well-defined direction, then, by tracing that same curve of variation a step further, we must arrive at the condition of the organ or set of organs in the immediate ancestor of the Ver- tebrate. 2. The same principle holds good whether the curve of variation is an ascending or descending one, i.e. whether the organ in question is becoming more important and more con- spicuous as we ascend the vertebrate phylum, e.g. the cerebellum, or becoming less important and degenerate, e.g. the pineal eye and ganglion habenule. In this preliminary paper I propose to give a short sketch of the history of all the most important organs and tissues which I have investigated up to the present time and to shew that in the case of all of them the phylogenetic signpost points directly to the same group of animals, viz. the Limulus and its congeners, as the ancestor of the Vertebrates. When once the clue has been found then embryology confirms it and illustrates it; of itself it is a bad guide but affords an excellent illustration of what phylogeny teaches. To illustrate my meaning I will rapidly sketch the downward path of the central nervous system and point out the conclusions to which such a study directly leads. The history of the Vertebrate central nervous system. The highest vertebrate nervous system possesses large cerebral hemispheres, a large cerebellum, a small pineal gland, choroid plexuses which are pushed into the ventricles and a small mem- branous roof to the IVth ventricle. As we descend the dorsal part of the brain becomes more and more membranous, the cerebral hemispheres are more and more confined to the ventral 2—2 20 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, side and the pallium becomes membranous; the cerebellar hemi- spheres are seen in Elasmobranchs to be formed by the invasion of nervous matter over the membranous folds on each side of the median lobe or worm, and in the Amphibians the whole cerebellum is reduced to a small band of nervous matter accompanying the IVth nerve across the dorsal part of the membranous tube ; finally in Ammoccetes the whole of the dorsal part of the mid and hind- brain is formed by large membranous folds with the nervous system lying ventral to this membranous tube; at one place only is there any crossing of nervous matter to the dorsal side, viz. at the IVth nerve and commencing cerebellum. We see then that the phylogeny of the vertebrate central nervous system shows a distinct tendency towards the separation of the nervous system into two parts, viz. a non-nervous epithelial tube and a purely “nervous part; follow that tendency one step further than the stage reached in Ammoccetes, separate the two entirely and we find immediately a nervous system placed in the same position with respect to this epithelial tube as the nervous system of an Arthropod with respect to the epithelial tube of its alimentary canal; we see moreover that in the lowest Vertebrate, the Ammoccetes, the old mouth and esophagus, the old cephalic stomach and straight intestine are most easily seen and recognised. Further, in absolute accordance with this gradual and perfect evolution, is the history of the nervous system apart from its tube, for just as parts like cerebellum and cerebral hemispheres diminish in size as we descend, so other parts which are insignificant in the highest Vertebrates come out more and more conspicuously as we descend. This is especially true of the ganglia habenule and pineal eye, and we see that in Ammoccetes the pineal eye is most conspicuous, is arthropod in type and that the large right ganglion habenule is its optic ganglion. In fact, as already shown in previous papers, the central nervous system of Ammoccetes fits in both topo- graphically, histologically and physiologically with the central nervous system of an invertebrate such as Limulus or Scorpio. Embryologically the phylogenetic history of the old alimentary tube is represented by the formation of the medullary canal with its external anal opening by means of the neurenteric canal; while the history of the formation and growth of the nervous system round this canal is illustrated by the formation of the cerebral vesicles, the formation of the posterior fissure, and of the substantia gelatinosa Roland: and of the raphé. Again, trace downward the formation of the cavity of the cranium and spinal cord. In the highest Vertebrate a cranium so filled with nervous matter as to leave its impress on the confining walls and a spinal cord surrounded by membranes containing the cerebro-spinal fluid. As we descend, more and more room in the 1895.] Dr Gaskell, The Origin of Vertebrates. 21 cranium, until at last in Ammoccetes a large cranial and spinal cavity containing a small brain and spinal cord surrounded by a large mass of peculiar glandular tissue. One step further, enlarge the extent of this glandular tissue and make it functional and we find immediately that in position and relative distribution we are face to face with the old cephalic liver and generative organs of the Limulus and Scorpio, and that the same gradual evolution which has explained the nervous system itself gives the same ex- planation of the peculiar tissue which originally fills up the greater part of the cranium and is gradually squeezed out of existence as the brain grows. This characteristic glandular tissue, the remains of the old generative glands and liver of the Limulus, is found nowhere else in the Ammoccetes except in the auditory capsule, where its presence will be explained later. The history of the Vertebrate skeletal system. Passing from the nervous system let us now consider the | skeletal system. In the highest Vertebrates a bony skeleton enclosing the nervous system to which is attached a facial skeleton, a thoracic skeleton and bones for the extremities. This bony skeleton can be traced step by step into the bony skeleton of the fishes and thence into the cartilaginous skeleton, where it is then found to form a cartilaginous cranium and vertebre from which spring ventrally a series of cartilaginous bars associated with the branchize and viscera. Further downwards we can trace the whole system to its simplest beginning in the Ammoccetes, where we find the cranial cartilaginous skeleton consists of the basal trabecule, in front of which are the nasal cartilages, the parachordals with the auditory capsules and the branchial bars with a cartilaginous continuation of the parachordals along each side of the notochord. We may then conclude that the immediate ancestor of the Vertebrates possessed a simple cartilaginous skeleton consisting of a cartila- ginous bar on each side of the axis which was in connection with an auditory capsule, extra-branchial bars and a nasal cartilage. We can go further than this, for the cartilages in Ammoccetes are of two kinds, hard and soft, the matrix of the first stains yellow with picro-carmine, and of the second red, and we find that the cartilages of the branchial basket-work and of the two disjointed rods along the notochord are of the soft variety, while the auditory capsules and trabecule are of the hard variety. Further, when transformation takes place the new cartilages are all of the hard variety so that the evidence points to the soft cartilage being older phylogenetically, a conclusion which is in accordance with Shipley’s a Dr Gaskell, The Origin of Vertebrates. —[Nov. 25, observation that the branchial cartilages are the first to be formed in the Ammoccetes. We may then argue that in the direct ancestor of the Vertebrate two axial lines of cartilage ought to be found and from them a series of branchial bars should issue, which bars should lie external to the branchie. We ought in fact to find a cartilaginous skeleton exactly of the kind which exists in Limulus; where the two axial cartilaginous bars are found in the two entapophysial cartilagimous ligaments of Ray Lankester and the cartilaginous branchial bars are found in the cartilaginous rods which spring from each entapophysis into each branchial appendage as described by Gegenbauer. This is the only true cartilaginous skeleton of Limulus, for the ento-chondrite is not cartilaginous but is made up of tendon and muscle like the central tendon of the diaphragm (as shown by Schimkewitsch); it stains also like tendon and not like cartilage. Again, tracing back the histology of the skeletal tissues we see how bone is formed from cartilage, and that cartilage is by no means always quite the same in structure. Among the different kinds we find that the branchial cartilages of Ammoccetes are quite distinct and different to any found in the higher Ver- tebrates. Further i Ammoccetes there is in addition to these cartilages a peculiar fibro-massive tissue, from which according to Schneider the cartilages arise, called by him muco-cartilage (Schleim-knorpel or Vor-Knorpel). This tissue-like cartilage gives a characteristic deep purple stam with thionin. It shows its ancestral importance by disappearing entirely at transformation, being either converted into cartilage or invaded by blood and con- verted into an areolar fat tissue. . I conclude then that the immediate ancestor of the Vertebrate possessed branchial cartilages of the structure of those of Ammo- coetes, which themselves arose from muco-cartilage. In other words we are again led directly to the branchial cartilages and enta- pophysial ligaments of Limulus, for their structure is word for word the same as that of the branchial cartilages of Ammoccetes, they stain in the same way with thionin, and the cartilage arises from a fibro-massive tissue which resembles absolutely both histologically and in its staining deep purple with thionin the muco-cartilage of Ammoceetes. This muco-cartilage of Limulus is formed from cells of the chitinogenous layer belonging to the entapophyses, so that we see not only how the direct agreement of the cartilaginous skeleton of Limulus with that of Ammoccetes both topographically and histologically points to the identity of these two skeletal systems, but also how we thereby obtain striking evidence of the manner in which the chitinous skeleton of the Invertebrate gave origin to the cartilaginous skeleton of the Vertebrate. 1895.] Dr Gaskell, The Origin of Vertebrates. 23 The history of the Vertebrate muscular system. It would take too long to trace out the changes which have taken place in the arrangement of the voluntary muscles as we ascend from the fish to man; it is sufficient to say that such a comparative myology has been largely worked out, with the result that the voluntary muscular system of Vertebrates falls into two well-marked groups, viz. the body or somatic muscles and the muscles connected with the branchize and viscera. This division is so marked and so characteristic in the cranial region that the segmentation of the body is looked upon as double, viz. Branchio- merie and Mesomerie, and the researches of v. Wijhe have shown that in the head region of Elasmobranchs segmental sets of well-defined ventral and dorsal plates of mesoblast give rise to the muscles of the splanchnic or branchial segments and to those of the somatic segments respectively. Passing to the Ammoccetes we see these two sets of muscles still more separated from each other, so that we may conclude that such double seg- mentation, being more and more conspicuous as we descend, is a marked characteristic of the immediate ancestor of the Vertebrate. The importance of this division of the voluntary muscles of the body into a splanchnic and somatic group is still further increased by the fact that the nerve supply for these two sets of muscles is also well defined and separate in the cranial region. Thus we see that the splanchnic voluntary muscles are innervated by a seg- mental set of nerves having well-defined cell origins in the central nervous system, apart from the groups of cells giving origin to the somatic muscles. These nerves are V,,, VII, IX, X. Thus we come to the conclusion that the double segmentation of the body was brought about because the immediate ancestor of the Vertebrates possessed a double muscular segmentation of which the ventral segments were connected with the movement of a branchial and allied apparatus, and that the cells of origin of this more perfectly segmented part of the body were grouped in well-defined groups, separate from the cells of origin of the less perfectly segmented somatic muscles. Again, we see that the conditions which exist among the Crus- taceans and Arthropods, as described by Hardy, exactly fulfil the requirements just mentioned, for he has shown that the well- marked segmented muscles of the appendages, whether branchiz bearing or not, are innervated by nerves arising from well-defined cell groups in the ganglia, quite distinct from the more diffused cell groups which give origin to the less completely segmented somatic muscles. We see, in fact, that just as the consideration of the skeletal tissues led directly to the conclusion that the branchial bars were 24 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, derived from the branchial bars of Limulus, so also does the con- sideration of the muscular system lead to the same conclusion, viz. that the branchial muscles are derived from the muscles of the branchial appendages of Limulus, and therefore to the further conclusion that the Branchiomerie is due to the segmentation of appendages: in other words, that V,,, VII, IX and X were all originally appendage nerves; the proof of this will be given later. Again, we find that histological considerations point in a most striking way to the same conclusion: for we find in Verte- brates that these splanchnic muscles are not of the same struc- ture as the somatic, and this difference of structure is most striking, as shown by Schneider, when we reach the lowest Vertebrate—the Ammoccetes. Here indeed we see the evidence of its ancestry in that its branchial muscles are to a large extent composed of tubular fibres such as are found in Invertebrates, very similar to many found in scorpions, and not found in Verte- brates. These muscles are as significant a finger-post as the pineal eye, and show their phylogenetic meaning by disappearing entirely at transformation. The history of the respiratory system and of the I[Xth and Xth nerves. Perhaps the best known phylogenetic development of any system in the Vertebrates is that of the respiratory system, for we can trace the lungs back to the swim bladder and pass from the air breathing to the gill breathing Vertebrate, and from thence to the Elasmobranchs with indications of extra-branchial carti- laginous bars in addition to the mternal cartilaginous bars, until we reach the oldest known vertebrate respiratory system, that of Ammoceetes with its extra-branchial cartilaginous basket-work, and its segmental branchiz dependent from the basket-work into the large open respiratory chamber. Throughout the water breathing Vertebrates the innervation is the same, the VIIth nerve supplying the Ist or hyo-branchial segment, the IXth the second or lst branchial segment, the Xth the remaining segments and throughout, even in the highest lung-breathing animals, the respiratory centre still keeps its primitive position in connection with the origin of the [Xth and Xth nerves. In Ammoccetes we find in strict accordance with the arrange- ment and nature of the branchial cartilages and muscles that the separate branchize may be considered as paired branchial ap- pendages hanging suspended into a chamber so as to leave a narrow slit between opposite pairs for the passage of water and food. Further, we find that the blood circulates in these branchize 1895.] Dr Gaskell, The Origin of Vertebrates. 25 not by means of capillaries as in the higher Vertebrate, but by narrow channels caused by the subdivision of a large blood space, just as in the branchie of Limulus or Scorpio. The conclusion then is that the ancestor of Vertebrates breathed by means of lamellar branchial appendages which had united together so as to form a scorpion-like body surface, and that the nerves to these appendages were the VIIth, IXth and Xth. In fact, the method of formation of the scorpion from Limulus as given by Macleod precisely illustrates the manner in which a respiratory chamber like that of Ammoccetes may be compared in the first place with that of Eurypterus, and so with that of Limulus. To this point I will revert later on. The history of the thyroid and of the VIIth nerve. If we compare the ventral surface of Eurypterus with that of Ammoccetes, we see that the comparison of the branchial seg- ments with each other does not complete the ventral surface in either animal, for in each case a triangular projection passes down in the middle line and separates the Ist three branchial segments from each other. This projection in the case of Eurypterus is the middle projection of the operculum, and in the case of Ammoccetes is a middle plate of muco-cartilage underneath which lies the thyroid gland. In all scorpion-like animals the respiratory segments of the body are terminated anteriorly by the operculum, just as the operculum is the first of the lamellar appendages of Limulus, and in all cases the operculum carries the terminations of the gene- rative organs, while in a great number of cases, as in Eurypterus, Thelyphonus, Phrynus, the operculum is double, the posterior part being gill bearing, while the anterior part carries the organs in connection with the external orifice of the generative organs. In Ammoccetes we find that the first of the branchial segments (the hyo-branchial) is not like the rest of the branchial segments, the gill surface being confined to the posterior part of the segment while the anterior part of the segment carries on its inner surface the ciliated groove called by Dohrn the pseudo-branchial groove ; this groove as is well known passes from the dorsal to the ventral side and there joins with its fellow of the other side to form the so-called duct of the thyroid gland; this bilateral gland lying under the ventral median tongue of muco-cartilage which separates in so remarkable a manner the cartilaginous basket-work of either side. In position, then, the segment composed posteriorly of the hyo-branchial, anteriorly of the ciliated groove and the median thyroid corresponds exactly to the operculum of Thelyphonus or of 26 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, Phrynus or of Eurypterus with its anterior genital part and its posterior branchial part. Further, the nerve which innervates the hyo-branchial portion of this segment is the VIIth nerve, and Miss Alcock’ has shown that a branch of the VIIth passes along near the ciliated groove to extend ventrally tailwards as far as the thyroid itself extends ; so that looking upon the whole of this segment as the opercular segment we see that the VIIth nerve was originally the opercular nerve just as the [Xth was the nerve of the first branchial appen- dage and the Xth of the remaining branchial appendages. The comparison of the thyroid segment of Ammoccetes with the anterior genital half of the operculum in Eurypterus and Thelyphonus means, that the thyroid gland must resemble closely the median part of the genital apparatus lying under the oper- culum of these latter animals; and indeed the resemblance both in position and in structure is extraordinarily close. The thyroid of Ammoceetes consists of a long tube curled up at its posterior end, that tube containing along the whole of its length a very peculiar glandular structure which is confined to a small portion of its wall. This glandular structure has no alveoli, no ducts, but consists simply of a column of elongated cells arranged in a wedge-shaped manner, the apex of the wedge being in the lumen of the tube; each cell contains a spherical nucleus situated at the very extreme end of the cell furthest away from the lumen of the tube. Such a structure is different to any other vertebrate gland, its secretion is not in any way evident, it certainly does not secrete mucus or take part in digestion, and it seemed impossible to compare it with any other known glandular structure. Looking however at the pictures given by Blanchard of the genital apparatus of Thelyphonus and Phrynus it is striking to see how closely in appearance the median part of the genital mechanism resembles the thyroid gland of Ammoccetes, and upon cutting sections of the Scorpion (the only material available) I found under the operculum in the middle line a tube, the walls of which in one part were thickened by the formation of a gland with long cells of the same kind as those of the thyroid, the nucleus being spherical and situated at the very further end of the cell, and the cells being arranged in wedges so that the extremities of each group of cells came to a point on the surface of the inner lining of the tube. This point is marked by a small round opening in the internal chitinous lining of the tube; these cells form a column along the whole length of the tube just as in the thyroid gland, so that the chitinous lining along that column is perforated by numbers of small round holes. 1 Miss Alcock’s paper ‘‘On the cranial nerves of Ammoccetes”’ is not yet pub- lished but will appear shortly, 1895.] Dr Gaskell, The Origin of Vertebrates. 27 So characteristic is the structure, so different to anything else, that I have no hesitation in saying that the thyroid of Ammoccetes is the same structurally as the thyroid of Scorpio, and therefore in all probability of Thelyphonus and of Eurypterus. It follows consequently that the respiratory chamber in Ammoccetes just as in Scorpio, Eurypterus, Limulus &c. is formed by a series of branchial lamellar appendages, the most anterior of which is known as the operculum and was connected with the genital apparatus as well as with branchie. Whatever the function of the thyroid may be in Scorpio, in Thelyphonus &c., it is of so great importance to the Ammoccetes that it persists until transformation takes place, i.e. until the time of puberty; then when the animal becomes sexually ripe, it disappears, being eaten up by phagocytes, the branchial segments come to- gether in the middle line and nothing remains of the opercular segment, except the remnants of the thyroid, the hyo-branchial part of the segment and the embryonic puzzle whether the VIIth nerve supplies two segments or one. Still throughout the Verte- brate kingdom the modified thyroid remains to show by the serious effects following its removal what an important part in the economy of the body is played by this modified genital gland. The history of the motor part of the Vth nerve. This nerve through the whole of the vertebrate class belongs to the same series as the VIIth, [Xth and Xth, and as we pass downwards to the fishes, we find that just as the facial nerve was the nerve belonging to the hyoid segment, so the motor part of the Vth supplies the muscles of the mandibular segment, and even as low down as Petromyzon it is still possible to speak of a man- dibular segment. When however we pass still lower to the Ammoceetes we find that great changes have taken place at trans- formation in the muscles supplied by the Vth nerve, and that now the Vth nerve supplies a series of structures which are directly comparable with the appendages of Limulus and Eurypterus. These structures are the velar and tentacular appendages of Ammoceetes, and they correspond strictly with the locomotor and tentacular appendages of Eurypterus and so with the locomotor appendages of Limulus. The large velar appendage is the least modified, possessing as it does the arthropod tubular muscles, a blood system of lacunar blood spaces, a surface covered with a regular scale-like pattern formed by cuticular nodosities just as in Eurypterus and in Scorpio, and at its base a serrated gnathite edge guarding on each side the place where the old mouth came to the surface, and still acting as a grinder according to Langerhans, or more probably a 28 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, strainer for the mixed food and mud which the Ammoceetes takes in to its pharyngeal chamber. The velar appendages have been further utilized in line with the respiratory appendages to assist in respiration, their movements being synchronous with the respi- ratory movements. The separate part of the Vth nerve which supplies the velum passes within it from the dorsal to the ventral surface of the animal, and then, as shown by Miss Alcock, turns abruptly forwards to supply the large median tentacle, so that this extraordinary course leads to the direct conclusion that this median tentacle which is really double constitutes with the velum of each side the true velar appendages, and that that separate part of the Vth nerve corre- sponds to the nerve of the large oar appendage of Eurypterus. Again on each side of the middle line there are in Ammoccetes four large tentacles each of which possesses a system of muscles, muco- cartilage and blood spaces precisely similar to the median ventral tentacle already mentioned. Each of these is supplied, as Miss Alcock has shown, by a separate branch of the motor part of the Vth, and each branch is comparable to the branch supplying the large velar appendage with its median ventral tentacular part. As might be supposed from what has already been said, all these tentacles and the velar appendages vanish upon transforma- tion, and in their place is found the remarkable tongue and suction apparatus of the Petromyzon. The very process of transformation of the locomotor appendages of the Limulus into the tactile and velar appendages of Ammo- ccetes 1s shown to us by the condition of affairs in Eurypterus, where these appendages are no longer chelate, but have been changed into short tactile appendages with the exception of the last one which acted as an oar appendage. We see how their basal parts are all hidden by the lower lip or metastoma which is strictly comparable to the lower lip of Ammocceetes, and how all the foremost ones are capable of being retracted into the large hood which is strictly comparable with the large hood or upper lip of Ammoccetes; let the lower lip grow larger and let the last appendage follow the example of the others, and we have imme- diately no longer Eurypterus but Ammoccetes, with the separate branches of the motor part of the Vth nerve representing the nerves of the locomotor appendages of Limulus, and so bringing this nerve into its true position as an appendage nerve with the VIlth, [Xth and Xth. 1895.] Dr Gaskell, The Origin of Vertebrates. 29 The history of the VIIIth nerve. Throughout the vertebrate kingdom the auditory apparatus remains constant in position, varying in structure to the extent that the cochlea becomes more developed as we pass upwards, yet throughout a gradual development can be traced from the simple auditory capsule of the Cyclostomi to the complicated bony and membranous labyrinths of man; the changes which took place owing to the passage from water breathing to air breathing animals, the formation of a membrana tympani with the remarkable history of the ossicles does not concern the history of the VIIIth nerve. We see then that the auditory apparatus and the VIIIth nerve arises in connection with a simple auditory capsule and a special sense nerve which is situated between the trigeminal and vagus group of nerves. Going one step further this means that an auditory apparatus and nerve similar to that of Ammoccetes existed be- tween the locomotor or thoracic appendages and the branchial or abdominal appendages of the Eurypterus-like animal from which the Ammoccetes arose, and when we turn to Limulus we find exactly in the same position an organ which is the counterpart of the auditory organ of Ammoccetes. For, situated at the base of the last large digging appendage—between therefore the locomotor appendages and the operculum—is found a large hemispherical organ to which a moveable spatula-like process is attached, known as the flabellum and called by Ray Lankester an “ epipodite.” This organ is confined to the base of this limb; it is undoubtedly a sense organ, being composed mainly of nerves, and an elaborate arrangement of nerve cells in connection with innumerable fine hairs, which are thickly embedded in the chitin of the upper surface of the spatula. By the varying thickness of the chitin these sense hairs vary with considerable regularity in length, and when the animal is at rest this sensory surface projects upwards and backwards into the crack between the thoracic and abdominal carapaces, so that while the eyes only permit a look out forwards and sidewards, and the whole animal is lying half buried in the sand, any vibrations in the water around can still pass through this open crevice and so reach the sensory surface of this organ. The structure of this sense organ is of a somewhat similar cha- racter to that of the lyriform organs described by Gaubert and supposed to be auditory. Further, the most striking and complete proof that this sense organ of Limulus is the same as the auditory capsule of Ammo- coetes is found in the fact that in each case the nerve is accom- 30 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, panied into the capsule by a diverticulum of the liver and generative organ. In the Limulus the liver and generative organ, which surround the central nervous system from one end of the body to the other, do not penetrate into any of the appendages, whether thoracic or abdominal, with the single exception of the flabellwm. In the Ammoceetes the peculiar glandular and pigmented tissue which we have already recognised as the remains of the liver and generative organ, which surrounds the brain and spinal cord, does not penetrate into the velar or other appendages with the single exception of the auditory capsule where it enters with and sur- rounds the auditory nerve just as in Limulus. Although this organ is not apparent in Eurypterus, yet we can see how the VIIIth nerve came into closer relations with the VIlIth or opercular nerve than with the Vth as in Limulus, when the scorpions arose from a Limulus-like form; for im the scorpion we see that a large organ similar in structure to the lyriform organs, evidently a special sense organ with a nerve of its own, viz. the pecten, 1s situated in closer relationship to the operculum than to the thoracic appendages ; so that looking at it superficially Ray Lankester considers it as the second abdominal appendage. In reality its nerve leaves the nervous system anteriorly to the nerve of the operculum, and the pecten therefore belongs to a segment immediately anterior to the operculum, and is in all probability simply the -flabellum of Limulus enlarged and pushed downwards to gain room, its proper metameric position being shown by the origin of its nerve from the central nervous system between the opercular and last locomotor appendage nerves. « In Limulus the auditory apparatus is enclosed in a chitinous envelope, not yet become cartilaginous, and as already mentioned the cartilaginous auditory capsule and the trabeculee of Ammoccetes are more recent formations than the branchial cartilages, which latter are already found in Limulus. The history of the cranial segments and nerves. From what has been said it follows that the mystery of the vertebrate cranium and cranial nerves is now solved, for we see that the question of the bony segments can be traced back to Petromyzon and so to Ammoceetes, with its direct genetic relation- ship to Eurypterus, and that the cranial nerves are in their origin the nerves of the prosomatic and mesosomatic appendages of Eurypterus, and so of Limulus. We may tabulate them as follows: 1895.] Dr Gaskell, The Origin of Vertebrates. 31 Cranial nerves Ammoceetes Limulus I olfactory organ olfactory organ (well Supra seen in Thelypho- cesophageal ‘i Pea ee ganglia op aa , lateral lateral eyes Il’ pineal eyes median eyes oa ss t yet ked out ee ys someon Vina | tentacles locomotor appendages m3 m4 Vins velar appendage last locomotor ap- Infra pendage cesophageal | V, corresponding epimeral sensory nerves and VIII auditory organ flabellum abdominal | VII, thyroid genital operculum (foundin Thelyphonus, gangha | VII, hyo-branchial branchial operculum | &c., not in Limulus) IX 1st branchial Ist branchial ae 2nd 7 2nd ” X, | 3rd » 3rd ” Pe th, Sth The comparison of the sensory part of the Vth with the epi- meral nerves of Limulus, the meaning of the II[Ird and IVth nerves, of the sensory branches of the vagus group &c., must be left until the completion of Miss Alcock’s investigation of the course and distribution of all the branches of the cranial nerves in Ammoceetes, and their comparison with the homologous nerves of Limulus and Scorpio. Two points of interest may be mentioned here, viz. the genesis of the medulla oblongata and the reason for the invariable position of the glossopharyngeal as the separate nerve of the first true branchial segment. The comparison between the medulla oblongata of Ammoccetes and of Limulus shows that in the latter, the only nerve belonging to the lamellar appendages which arises from the medulla ob- longata is the nerve of the operculum, ie. the VIIth nerve of Ammoceetes, the [Xth and Xth nerves arising from the separate abdominal ganglia; in other words, only one ganglion and nerve belonging to the abdominal or mesosomatic appendages has 32 Dr Gaskell, The Origin of Vertebrates. [Noy. 25, travelled up into the thoracic or prosomatic fused mass of ganglia. In the Scorpions Lankester has shown a further amalgama- tion in the Scorpionini where the 1st branchial appendage as well as the genital operculum is innervated from the medulla oblongata; and yet again a still further amalgamation in the Androctonini where the two foremost branchial appendages are innervated from the medulla oblongata. In fact, we see in the passage of the Crustacean into Limulus, and Limulus into Scorpio and Androctonus, the same law of gradual fusion of more and more of the ganglia of the ventral chain to form the medulla oblongata, until at last all the nerves of the branchial appendages arise from these fused ganglia, and the vagus nerves of Ammoceetes result. The same process has con- tinued onwards into the Vertebrates higher than Ammoccetes with the result of the inclusion of vertebra and spinal nerves into the occipital region of the skull as seen in various Elasmobranchs and Ganoids. Further, the solitary position of the glossopharyngeal, separated as it always is from the vagus, is suggestive when we find that in all the scorpions the nerve to the 2nd gill appendage is taken up and no more, and that in Thelyphonus and the Pedipalpi generally there exists only one gill-bearing appendage im addition to the gill- bearing part of the operculum. In other words, the nerves which correspond to the glossopharyngeal and facial nerves are in- variably found in connection with the operculum and a gill- bearing appendage even when the appendages homologous to those supplied by the vagus nerve did not carry gills. The history of the heart and ventral aorte. Without tracing the modifications of the vascular system throughout the vertebrate kingdom, it will be sufficient to say that the simplification which takes place as we pass down to the Elasmobranchs shows that the heart and conus arteriosus arose from the subintestinal vein which by dividing into two formed the two ventral aorte, the main function of which was to send the blood into the gills for purposes of aeration. Further, Paul Mayer in his paper on the origin of the heart and blood vessels in Elasmobranchs, has shown that this appa- rently single subintestinal vein is in its origin double, and that therefore in all Vertebrates the heart and ventral aorta arises from two long veins which are originally situated on each side of the middle line; by the formation of the head-fold these come together ventrally, coalesce into a single tube which forms the subintestinal vein and heart, still remaining double as the two ventral aortz with their branchial branches into each gill, as is well shown in 1895.] Dr Gaskell, The Origin of Vertebrates. 33 the case of Ammoccetes. The heart, then, of all Vertebrates, unlike the invertebrate heart, is formed from the coalescence of two main venous trunks or sinuses situated ventrally, its original purpose being to send blood into the gills for the purpose of aeration. One step further leads to the conclusion that these two longitudinal venous sinuses are the two longitudinal venous collecting sinuses of Limulus and Scorpio. In both cases they form two large ven- trally situated blood vessels from which the blood passes to the gills, and, further, in both cases the walls of these two sinuses are connected with the pericardium bya system of transparent muscles described by Milne Edwards and named by Lankester veno-peri- cardiac muscles. These muscles are hollow, both near the vein and near the pericardium, so that the blood in each case fills the cavity, and as they contract with the heart, that part of them in connection with the venous collecting sinus already functions, as pomted out by Milne Edwards and Blanchard, as a branchial heart. The ventral aorte of Ammoccetes correspond exactly in position and in function with these two venous collecting sinuses in Scor- pion, and therefore in Limulus; and we see in Ammoccetes the position of the original dorsal heart represented by that extra- ordinary column of peculiar tissue containing fat which is situated in the middle line between the spinal canal and the surface. The further relation between the vascular and lymphatic sys- tems of Ammoccetes and the vascular system of Scorpio to- gether with the consideration of the pronephros, will be considered later. The history of the Alimentary Canal. The history of the vertebrate alimentary canal is the history of nature’s great mistake and how she rectified it; for at the time when Vertebrates were formed, the lines upon which evolution was working led straight to an increasing antagonism between the increase of brain power and the sufficient feeding of the organism ; for the increase of brain power meant the increase of connections between the supra-cesophageal ganglia and the lower nerve centres, meant therefore an increase of nervous matter around the csophagus with the result of diminishing the size of the cesophagus to such a degree that at first only liquid nourish- ment could be taken in, and finally the choice lay between starvation and cessation of growth of brain. In Limulus we already see the commencement of the struggle, and in the forma- tion of the Scorpions and Arachnids we see not only how narrow the cesophagus has become so that the whole class are able only to take in liquid food—, and indeed in certain Arachnids a special suction pump arrangement has been devised in their stomachs VOL. IX. PT. I. 3 34 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, to get through even liquid food—, but also how with the increasing brain development the great mass of liver and generative organ was shifted from the cephalic to the abdominal region, thus bulging out the ventral surface of the body until it came into contact with and fused with the lamellar branchial appendages on each side. In this way the great class of Arachnids was formed, but in vain as far as further evolution went, for no amount of room around the brain could prevent the constricting action of the enlarged cesophageal commissures on the cesophagus. Still among those Limulus and Scorpion-like forms which were in those days lords of creation and amongst whom the struggle for existence was very keen, there were some in which the ventral surface did not reach up to and fuse with the lamellar appendages, although by the coming together of these latter a body surface like that of Hurypterus was formed. In these cases then a respiratory chamber was formed with gills and gill slits between the fused appendages, then came the piercing of the operculum so as to put this chamber into communication with the oral cavity. Such opening of communi- cation is preserved for us embryologically as the breaking through of the septum of the stomatodzum, for this septum is in the exact position of the operculum and has nothing to do with the velar appendages. In this way then these animals took in water of respiration through the mouth or gill slits into a chamber formed by the branchial appendages and with this respiratory water food of various kinds was naturally taken. Such food could be digested because as shewn by Miss Alcock the skin of Ammoceetes pours out a secretion for the purpose of keeping its skin clean, which is easily capable of digesting fibrin. It appears from Hardy’s researches that a similar secretion is poured out on the carapace of Daphnia and other Crustaceans. With the growth of the lower lip or metastoma and the modification of the basal portion of the last locomotor appendage, which basal part was inside the lower lip, into a valvular arrangement like the velum, the animal was able to close the opening into the respiratory chamber and feed as blood sucker in the way of the rest of its kind, or when food of the kind was scarce, keep itself alive by the organic material taken us respiratory chamber with the muddy water in which it ived. In this way then we see how little by little a chamber was formed by the lamellar branchial appendages which functioned also as a digestive chamber. Such I imagine to have been the origin of the respiratory part of the vertebrate alimentary canal, and the manner of forma- tion of the rest of the tube is shown to us by the evidence of phylogeny, embryology and paleontology. Tracing back the alimentary canal along the Vertebrates we 1895.] Dr Gaskell, The Origin of Vertebrates. 35 find in the highest forms a great length of intestine innervated by the vagus nerve, between the hind-gut with its innervation from the sacral region and the fore-gut innervated by the glosso- pharyngeal and facial as well as by the vagus. Passing downwards we see the fore-gut becoming branchial still connected with the hind-gut by a long intestine innervated by the vagus nerve, but the length of this latter in proportion to the length of the whole is much less. In fishes the length becomes smaller and smaller, the tube is straight instead of thrown into innumerable folds and at last in the Ammoccetes we find a small intestine innervated by the vagus between the large branchial fore-gut and smaller hind-gut. In other words, the phylogenetic history of the vertebrate gut shows that the line of tendency as we descend the phylum is steadily towards an approximation of the cranial and sacral portions of the gut: pass one step further and we should find as in Limulus the end of the branchial chamber close to the cloacal termination of the gut, i.e. close to the cloacal termination of the old gut. In other words, the branchial chamber was continued on as a short tube which broke through into the old existing cloaca and the elongation of that tube is the striking fact in the phylogeny of the vertebrate gut. The formation of this tube from the respiratory region by the coming together of the ciliated hyper- and hypo-pharyngeal ridges is well seen in Ammoccetes, and embryologically the travelling down of the vagus and the fact of this part of the gut being always supplied by the great branchial nerve, the vagus, is strong confirmatory evidence that the middle part of the intestine has arisen in the vertebrate phylum as the gradual elongation of an originally small junction between the respiratory chamber and the cloacal region. The evidence of this junction taking place is preserved for us embryologically by the breaking through of the septum of the proctodeum just as the passage from the mouth region to the respiratory chamber through the operculum is represented by the breaking through of the septum of the stomatodzum. Again, the embryological development of the Vertebrate illus- trates this history in the most striking way, for not only does it show that the embryo grows in length by additions made between the head end and the tail end, but also that at a time when the fore-gut and hind-gut are well formed the mid-gut is still a mass of yolk ; this is especially well shown in Shipley’s specimens and is a clear indication that the formation of the mid-gut takes place em- bryologically and therefore took place phylogenetically much later than the formation of the fore-gut or hind-gut, for the argument often used, that yolk retards development and for that reason the mid-gut is formed latest, is to my mind evasive rather than real, 3—2 — 36 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, and it seems to me much more probable that the yolk is there because that part is last formed, than that it is last formed because the yolk is there. The paleontological evidence. It is clear from what has been said that the evidence of paleontology ought to show, firstly, that the Vertebrates appeared when the waters of the ocean were peopled with the forefathers of the Crustacea and Arachnida, and secondly, the earliest fish-like forms ought to be characterised by the presence of a large cephalic part to which is attached an insignificant body and tail. Such was clearly the case, for the earliest fish-hke forms appear in the midst of and succeeding to the great era of strange proto- crustacean animals, when the sea swarmed with ‘rilobites, Eurypterus, Slimonia, Limulus, Pterygotus, Ceratioceras and a number of other semi-Crustacean and semi-Arachnid creatures ; and when we examine these ancient fishes we find such forms as Pteraspis, Ptericthys, Astrolepis, Bothriolepis, Cephalaspis, all characterised by the enormous disproportion between the extent of the head region and that of the body. Such forms would have but small power of locomotion, and further evolution consisted in gaining greater rapidity and freedom of movement by the elonga- tion of the abdominal and tail regions, with the result that the head region became less and less prominent, until finally the ordinary fish-like form was evolved, in which the head and gills represent the original head and branchial chamber, and the flexible body with its lateral line nerve and intestine innervated by the vagus represent the original smal] tail-like body of such a form as Ptericthys. Nay more, the very form of Ptericthys and the nature of its two large oar-like appendages, which according to Traquair are hollow like the legs of insects, irresistibly remind one of a form like Eurypterus in which the remaining appendages had shrunk to tentacles as in Ammoccetes, but the large oar-like appendage still remained, coming out between the lower and upper lips and assisting locomotion. The Ammoceetes-like forms which existed between the time of Eurypterus and the time of Ptericthys not having developed bony plates have not yet been found, although the recent find of Traquair of Paleeospondylus Gunni is exceedingly interesting in this respect. The evidence of paleontology as far as it goes confirms absolutely the evidence of anatomy, physiology, phylogeny and embryology and assists in forming a perfectly consis- tent and harmonious account of the origin of Vertebrates, the whole evidence showing how nature made a great mistake, how excellently she rectified it, and thereby formed the new and mighty kingdom of the Vertebrata. 1895.] Dr Gaskell, The Origin of Vertebrates. 37 In the discussion which followed, Mr A. SEDGWICK said that: The arguments used by Dr Gaskell to prove that Vertebrates are descended from Arthropods might with equal cogency be used to prove the reverse, viz. that Arthropods are descended from Vertebrates; Arthropods being quite as highly specialised as Vertebrates. Further the facts alleged in support of the conten- tion are of a superficial and unimportant character, and not of a kind to be brought forward or considered until the more important and deep-reaching anatomical differences between the two groups have been reconciled. For instance such important anatomical matters as the condition of the ccelom, of the nephridia, of the relation of the blastopore to the neural surface are not even referred to. Nor is a single embryological fact brought forward in support of the astounding contention that the alimentary canal of the Arthropod has been changed into the central nerve-tube of the Vertebrate. It was further pointed out that Dr Gaskell’s paper was wanting in that precision and accuracy of statement required in a specu- lative investigation of this kind; that it showed internal evidence suggesting that he did not fully appreciate the relative importance of anatomical facts, and finally by the use of certain words and expressions in an erroneous and inaccurate sense it seemed to show that. Dr Gaskell was ignorant of some of the most important principles which must underlie all sound and useful phylogenetic speculation. Mr MacBripke said that Dr Gaskell had brought forward some interesting points in the anatomy of Ammoccetes but that no step in advance had been made in the direction of solving the ques- tion of Vertebrate ancestry. The objections to be urged against Dr Gaskell’s theory on this subject were mainly two. 1. The Vertebrates in the fundamental constitution of some of their most important organs—viz. ccelom excretory organs— belonged to a much more primitive grade of evolution than the Arthropods, masmuch as the same general arrangement was found in the less differentiated members of many quite distinct phyla, viz. Mollusca, Brachiopoda, Polyzoa, Annelida, &., whereas the arrangement found in Arthropods was highly specialized. 2. The reasoning Dr Gaskell employed to prove the descent of Vertebrates from Arthropods was illegitimate. In postulating changes which they suppose to have occurred in the history of the race, zoologists confined themselves to those which could be inferred by comparing together animals of undoubted affinity with each other. There was no evidence that fundamentally important organs such as the alimentary canal could be lost and redeveloped in another place. 38 Dr Gaskell, The Origin of Vertebrates. [Nov. 25, If such assumptions were allowed the descent of any animal from any other could be proved. Mr 8. F. Harmer pointed out that Dr Gaskell had based his conclusions on two main lines of argument; the first being the assumption that the comparative study of any particular organ within the limits of a single group will not only enable us to retrace the steps which evolution has taken, but will give some clue to the conditions which existed prior to the evolution of that organ as such; and the second being derived from a detailed comparison of Limulus with Vertebrates. Instances were given to show that the first assumption is fallacious. The evolution of the lung may have been retraced to the simplest form in which that organ exists in Vertebrates, but it does not follow that the line can be produced backwards so as to give any indication of the conditions antecedent to the evolu- tion of the air-bladder. Nor does the retracing of the lime of evolution of the Perissodactyle hand or foot give any information with regard to what preceded the pentadactyle condition. It was admitted that the resemblances between Limulus and Vertebrates were, on Dr Gaskell’s showing, of a remarkable nature; but many of the details could be satisfactorily criticized only by one who has made a special study of both Limulus and the Ammoccet. It was, however, suggested that since the resem- blances extended to such minute points of detail, 1t would be remarkable, if Dr Gaskell’s theory were true, that differences should exist in what would appear to be fundamental points; as, for instance, the numerical difference between the branchial appendages of Lamulus and the branchial bars of Petromyzon. Dr Gaskell concludes that the fact that the intestine is elon- gated in the higher Vertebrata and straight in the Ammoccet points to an original “approximation of the cranial and sacral portions of the gut”; and that therefore the branchial chamber formerly terminated close to the cloaca. It would equally well follow from this line of argument that other groups of animals in which the intestine of the higher members is convoluted and of the lower forms straight were also descended from ancestors in which a secondary alimentary canal had been evolved. The argument from the position of the yolk in Vertebrate embryos has no real weight. Dr Gaskell, in dealing with the Vertebrata, has put a special interpretation on a very general embryological phenomenon. He has entirely ignored other groups of animals, in this respect; and he is no more justified in his conclusion that the embryological evidence indicates a late evolution of the mid-gut in Vertebrates than he would have been in drawing a similar inference from the developmental history of Mollusca. On the motion of Mr H. Gapow the discussion was adjourned. 1895.] Dr Gaskell, The Origin of Vertebrates. 39 Monpbay, December 2, 1895. PRoFeEssor J. J. THOMSON, PRESIDENT, IN THE CHAIR. The discussion of Dr GASKELL’sS paper “On the Origin of Vertebrates” was resumed. Mr H. Gapow said that Dr Gaskell combines the study of physiology with that of morphology, the latter not being restricted to the small branch of ontogenetic research which can be guided only by the method of comparative anatomy. Much of the ordnance store of embryologists consists of weapons which are not those of precision, because at present our knowledge of their nature and meaning is far from satisfactory; for instance notochord, neurenteric canal, nervous system, ccelom, metamerism. Objections to Dr Gaskell’s hypothesis, which are based upon such features, are very precarious. The incredulity, which Dr Gaskell’s hypothesis has met with, is referable to two reasons. First, we were ignorant of the astonishing number of important anatomical and _ physiological features to which Dr Gaskell has drawn our attention n Ammo- ceetes and in Limulus, especially the larval Ammoccetes being full of revelations. Secondly, we are prejudiced in favour of one or other hypothetical pedigree of vertebrate descent, although it is not obvious which are at present the favourites, namely Worms, Sea Squirts, Sea Anemones or even Sea Urchins. Anyhow, be Dr Gaskell’s hypothesis right or wrong, he has stirred up so many morphological questions, which can no longer be neglected, that work has been cut out for us for many years to come. Mr BaTEsoN said that it was difficult to make any criticism which should adequately express to the minds of those who were not acquainted with the leading facts of the structure and develop- ment of animals how impossible it was to entertain Dr Gaskell’s hypothesis of Vertebrate descent. Several difficulties had already been spoken of, regarding Amphioxus, the Vertebrate Ccelom, the Notochord, &c., any of which seemed sufficient disproof. ‘Two points might perhaps be taken which would make the objections clearer to those who were not professed zoologists. It was natural however that these difficulties should appeal most to those whose zoological studies had taken a wider range. First regarding the relation of the nervous systems of Arthro- pods and Vertebrates. Setting apart all phylogenetic speculation it is known by observation that the central nervous system of a Vertebrate separates from ectoderm in the middle line of the dorsal side [of a Vertebrate], that is to say that that nervous system 40 Dr Gaskell, The Origin of Vertebrates. [Dec. 2, is a piece of the dorsal ectoderm. In the Arthropod it is equally certain that the nervous system separates from the ectoderm in the ventral middle line [of the Arthropod], and is therefore a piece of the ventral ectoderm. Nevertheless Dr Gaskell held both that the nervous system of the Vertebrate was homologous with that of the Arthropod, and that it was the dorsal surface of the Arthropod which corresponded with the dorsal surface of the Vertebrate. Dr Gaskell had made no attempt to reconcile the different modes of development in the two cases. Extraordinary changes of structure and function were postu- lated by Dr Gaskell. These were supposed to have occurred in evolution, in the course of lineal descent, by the process of varia- tion. If anyone would try to conceive these variations taking place before his eyes, he would realize the difficulties imvolved. For example if it was alleged that a specimen of Limulus had been found which had developed a mouth in its operculum, or a perforation from the space occupied by the branchize leading into the intestine, or feeding or digesting by means of that space, or with its nervous system enveloping its alimentary canal, no one would credit the observation without overwhelming testimony. But Dr Gaskell assumed that all these things and many others no less astonishing had occurred as variations. No evidence had been offered that any such variations or any approach to them had ever occurred, or even that they were possible. In the absence of such evidence there was no reason why Dr Gaskell’s suggestion should be seriously considered at all. Dr Gaskell had mentioned Pterichthys, Coccosteus, and other fossil Fishes, hinting that he regarded them as possible links between Arthropods and Vertebrates: had Dr Gaskell any reason for supposing that these animals were anything but Fishes in the strictest sense ? Mr SHIPLEY said he thought that in attempting to derive one group of animals from another, certain principles were usually observed, (1) one of these was that in assuming variations to arise in an ancestor the amount of change assumed and its direction should be checked by the kind of variation which is already known to exist in the various members of the group to which the ancestor belongs, but although no one could deny that the members of the Arthropoda varied in almost every possible direction, none of them varied along the lines laid down by Dr Gaskell; (11) the amount of variation assumed should be limited: there was no fact known amongst animals which led us to believe that they ever lost and redeveloped such funda- mental organs as the entire alimentary canal, the renal organs and the reproductive organs, yet this was assumed in Dr Gaskell’s hypothesis; (111) changes of function can arise when the new 1895.] Dr Gaskell, The Origin of Vertebrates. 41 function coexists, perhaps subordinately, with the primary func- tion, or coexists in another member of the same group or in one of its larval forms: the remarkable changes of function assumed by Dr Gaskell had no such origin; (iv) in any attempt at Phylo- geny we must observe the “embryological unities”: Dr Gaskell derives the epiblastic lining of the nervous system from the—in the main—endodermic lining of the alimentary canal and the mesoblastic “packing” cells around the vertebrate nerve-tube —in part—from the endodermic “liver” of the Arthropod: (v) in Phylogeny we must look at the most elementary of the animals whose ancestor we seek, yet Dr Gaskell started some way up the Vertebrate scale and omitted from his consideration the Amphioxus and the larval Ascidian possibly because he regarded them as degenerate but the same reasoning which led to a belief in the degeneracy of these groups has been applied to shew that the Lamprey is itself degenerate. The Arthropod characters of which we should expect to find some trace in a Vertebrate descended from a Limulus-like ancestor are (1) the cwlom, which in the Arthropod is rudimentary and replaced by a body cavity of a highly specialized character and yet the ccelom reappears in the Vertebrate in the most primitive form, just as it exists in the ancestor of the Arthropods them- selves; (i1) the chitinous skeleton which dominates the structure of the Arthropods from one end of the group to the other, is un- represented in their supposed descendants: in connection with this it may be pointed out that cilia which with the exception of the Nematodes, are universally present in all animals but the Arthropods, have re-appeared in the Vertebrata; (111) the pazred, segmented limbs of Limulus, which are only represented by sensory papillz round the mouth or by the branchiz. The result of the whole hypothesis is that we are asked to believe (i) that the functional alimentary canal of the Limulus, with its—in the main—endodermic lining, has become the lining of the Vertebrate nervous system which is epiblastic in origin ; (ii) that the endodermic “liver” and the testes of the Arachnoid ancestor have become the mesoblastic tissue surrounding the nerve-cord of the Ammoccete; (i11) that the Arachnoid ancestor has developed an entirely new alimentary canal along its ventral median line, and that this chitinous-lined tube is completed ventrally by the fusion of the limbs; (iv) that such of the seg- mented limbs as are not required for this purpose become minute sensory papille surrounding the mouth; (v) that the renal organs of the Arachnoid ancestor degenerate into an appendage of the brain, the pituitary body; (v1) that part of the tissue representing the testis of the ancestor is to be found inside the internal ear ; (vil) that the hemoccel of the Arthropod is again replaced by — 42 Dr Gaskell, The Origin of Vertebrates. [Dec. 2, the primitive ccelom which is reduced almost to extinction in the adult ancestor; (viii) that cilia which are primitive have been lost in the ancestor and re-acquired in the descendant, whilst the chitinous coating of the former leaves no trace; (ix) that the heart has disappeared; (x) that with the exception of a part of the branchial skeleton, the entire skeleton including the notochord is a new formation, and so are the kidneys and the generative organs; the paper before us throws no light upon the question as to their origin. Mr E. J. Bres said that the gap between an Arthropod ancestor and the vertebrates is as great as the gap between the vertebrates and any other ancestral form hitherto put forward. In considering Dr Gaskell’s theory it is therefore necessary to make sure that besides deriving support from resemblances in anatomy and histology, the theory takes into account the main distinctions between the hypothetical ancestor and the verte- brates. Using a table from the most recent authority (Haeckel, Systematische Phylogenie der Wurbelthiere, p. 12), it appears that all the valid distinctions drawn between Articulata and Vertebrata have been dealt with in Dr Gaskell’s paper. As for the remaining points: (1) the presence of a cuticular layer in vertebrates has been recognised by Leydig, F. E. Schultze, etc., and demonstrated to be chitmous by G. Wolff; (2) the structure and mode of deve- lopment of the notochord throughout the chordates is so uniform that no distinct clue is given to its origin from any pre-existing organ in an ancestral form. Dr GASKELL said in reply—I have listened most carefully to the arguments brought forward against my theory, and it seems to me that the most important of them may be summed up as follows. “The resemblances and coincidences between the structure of Ammoceetes on the one hand and of Limulus and Scorpions on the other which I have brought forward are mere trivialities in com- parison with the true criteria of what constitutes a Vertebrate, viz. the presence of a ccelom of a more primitive type than that of an Arthropod, and the existence of a notochord. These are the two most important points, and as I have given no explanation of them, the coincidences which I have pointed out, although inter- esting, are of no real importance.” I quite understand that these close resemblances between similar parts in Limulus and Scorpions and in Ammoccetes are very unorthodox, but they are certainly not trivial. The argument reminds me of the commotion made in the orthodox world when it was first suggested that man and the ape were closely akin ; 1895.] Dr Gaskell, The Origin of Vertebrates. 43 how it was then said by an eminent comparative anatomist—These coincidences and resemblances between the structure of man and the ape are merely trivial and have no weight in comparison to the great fact that man has a hippocampus minor in his brain and the ape has none—to which was afterwards added—man has an opponens pollicis and the ape has none. I venture to compare the argument about the ccelom with that of the hippocampus minor in the earlier controversy, and just as in the latter it was shown that the ape did possess a hippocampus munor so I propose to show, not only that there is no vital differ- ence between the ccelom of the Vertebrate and that of Limulus or Scorpio, but also that no stronger evidence could be adduced of the correctness of my theory than is afforded by this very appeal to the ccelom. It is clear that the ccelomic cavities which must be compared in order to test the truth of my theory are in the case of the Vertebrate the head cavities of Balfour and in the case of Limulus the prosomatic and mesosomatic ccelomic cavities, for the whole strength of my argument is based upon the comparison of the prosomatic and mesosomatic segments of Limulus with the cranial segments of Ammoccetes. Fortunately a recent paper by Kishinouyi on the development of Limulus allows such a comparison to be made; he not only shows that the ccelomic cavities in each segment of Limulus are formed by the splitting of the splanchnopleur and somatopleur in the same way as in Vertebrates, but also that although each one of the mesosomatic segments possesses a coelomic cavity, this is not the case for the prosomatic segments. In these latter the Ist ccelomic cavity is a large preoral one, common to the segment of the Ist appendage and all the segments in front of it; the segments belonging to the 2nd, 3rd and 4th appendages have no ecelomic cavities formed in them; the 2nd ccelomic cavity belongs to the segment of the 5th appendage and then each subsequent segment possesses a ccelomic cavity. Clearly on my theory the Ist large preoral ccelomic cavity common to the most anterior segments of Limulus corresponds to the Ist large preoral head cavity of Balfour and of v. Wijhe. Balfour’s 2nd head cavity is the mandibular associated especially with the Vth nerve. According to my view the motor part of the Vth represents the five locomotor appendages of Limulus, and we see already in Limulus that the segments corresponding to the three foremost of these appendages do not form ccelomic cavities. Posteriorly to the segments belong- ing to the Vth nerve a head cavity is found in each segment in Elasmobranchs and Ammocetes just as in Limulus, the main difference between v. Wijhe and Balfour being that according to the former Balfour's hyoid segment is in reality double. +4 Dr Gaskell, The Origin of Vertebrates. [Dec. 2, It is clear that the study of the ccelomic cavities in the head not only gives no support to the opponents of my theory but like the corresponding argument of the hippocampus minor affords yet another extraordinary coincidence, so that I presume that the resemblances between the head cavities of the Vertebrate and of Limulus must now be included among the rest of the trivial coincidences. Before leaving the consideration of the ccelom, I must say that I heard to my utter astonishment the statement of both Mr Macbride and Mr Shipley that my theory was preposterous, because I made the generative and excretory organs of the Vertebrate arise de novo. Seeing that I have not said a word about the origin of the excretory and generative organs of Verte- brates and have never even dreamt of making them arise de novo, I cannot understand how such an argument can be used against me. It is true that I believe that the pituitary gland is simply the coxal glands of Limulus and Scorpions, but that does not imply, as Mr Shipley asserts, that the renal organs of the Arachnoid ancestor degenerate into the pituitary body; for undoubtedly Scorpions and other Arachnids possess a well-defined renal system known by the name of the Malpighian tubes. Then I am told that the Arthropod does not possess a noto- chord, while the notochord is the great characteristic of the Vertebrate; and I am asked, Where is the notochord in Limulus ? Similarly in the old controversy it was asked, Where is the opponens pollicis in the ape? Just as in the latter case the opponens pollicis is an attribute of man because he has discarded the quadripedal method of progression and become a biped, so the notochord is an attribute of the Vertebrate because it has dis- carded the old alimentary canal and formed a new one. I had not intended to discuss the origin of the notochord at present, but as stress has been laid upon its presence and I have been challenged, I will simply ask the following questions:—“Do embryologists consider that the notochord arose as a simple tube of hypoblast which terminated in the region of the infundibulum and extended the whole length of the body?” If so, “Is it possible to conceive of more than one interpretation of the original purpose of an un- segmented hypoblastic tube in a segmented animal which extends the length of the body from mouth to anus?” I will also point out that just as the notochord is formed by the proliferation of cells in the median line ventral to the nervous system, so later on in the history of the animal a similar proliferation of cells takes place in the same region to form the sub-notochordal rod ; and again when the Ammoccetes transforms into the Petromyzon, yet another similar proliferation takes place in exactly the same region, but now confined to the ancient part of the animal, viz. the head 1895.] Dr Gaskell, The Origin of Vertebrates. 45 region; a proliferation which forms a solid rod of cells entirely occluding the opening from the branchial chamber to the anterior intestine, and then, by a hollowing out process beginning at the posterior end, forms ultimately the new gut of the Petromyzon. Mr Bateson objected that the neural plate of the Arthropod is derived from the ventral epiblast and the gut is dorsal to it; on the contrary, in the Vertebrate the central nervous system is derived from the dorsal epiblast,—including in the term central nervous system both the nervous layers and the layer of the central eanal,—and ventral to it is the notochord and vertebrate gut. This difficulty seems to me more apparent than real; the nerve layer in the Vertebrate as soon as it can be distinguished is always found to le ventrally to the layer of epiblast which forms the central canal. In the middle line of the body, owing to the absence of the mesoblast layer, the cells which will ultimately form the notochord and those which form the central nervous system form a mass of cells which cannot be separated in the earlier stages. The nerve layer in the Arthropod hes between the ventral epiblast and the gut, the nerve layer in the Vertebrate lies between the so-called hypoblast (i.e. the ventral epiblast of the Arthropod) and the neural canal (i.e. the old gut of the Arthropod). The new ventral surface of the Vertebrate in the head region is not formed until the head fold is completed ; before this time when we watch the vertebrate embryo lying on the yolk, with its nervous system and central canal formed and its lateral plates of mesoblast, we are watching the embryonic representation of the original Limulus-like animal; then when the lateral plates of mesoblast have grown round and met in the middle line to form the new ventral surface and the head fold is completed, we are watching the embryonic representation of the transformation of the Limulus-like animal into the Scorpion-like ancestor of the Vertebrates. Mr Bateson and Mr Shipley object that my theory necessitates enormous jumps, both in conformation and function ; I feel sure upon further consideration they will see that this is not so, and that in fact the main jump is not, as Mr Bateson humorously put it, the sudden transformation of a Limulus into an Ammoccetes, but rather the transformation of a Limulus into a Scorpion-like animal by the meeting of the branchial appendages in the middle ventral line. My whole argument and the whole of my work show that Ammocetes is closely allied to a Scorpion-like animal such as Thelyphonus and Eurypterus, the Limulus-like animal being the more remote ancestor of all three. Messrs Bateson and Shipley’s objections therefore are not directed against my theory of the origin of Vertebrates, but against the current view of the manner in which Scorpions arose from Limulus-like forms ; a view which 46 Dr Gaskell, The Origin of Vertebrates. [Dec. 2, is based on Macleod’s observations, and is considered reasonable and indeed highly probable by all comparative anatomists who know anything about the subject. There is on my theory no need to assume any sudden change of function or of anatomical arrangement; I do not presuppose any transformation anything like as sudden or as marvellous as that which takes place under our eyes at the time of transfor- _ mation, when the Ammoccetes becomes a Petromyzon. Mr Shipley’s difficulties about the absence of cilia and the presence of chitin in Arthropods do not appear serious, seeing that the alimentary canal of Daphnia appears to be ciliated according to Hardy’s paper and also the laminated layer of the skin of Ammoccetes is histologically exactly the same as an internal chitinous layer. Finally, in answer to the argument of Mr Sedgwick and Mr Shipley that Ammoccetes is not the lowest Vertebrate, that therefore I ought to have compared the Limulus and Scorpion forms with Amphioxus and the Tunicates, to which Mr Shipley was careful to add that, if I answered that these were degenerate vertebrate forms, then he had as good right to call the lamprey degenerate too, I wish to point out that the whole trans- formation of the Ammoccetes to the Petromyzon is characterised by the discarding and throwing away of invertebrate character- istics and the putting on of a more distinctly vertebrate appear- ance. We see how by a process of histolysis, the tubular muscles, the muco-cartilage, the thyroid gland, the velar, tentacular and branchial appendages are all destroyed, or utterly changed and new tissues are formed, the net result of which is not degeneration but the formation of an animal of a distinctly higher grade, distinctly more comparable with other vertebrates, as instanced by the possibility of a direct comparison between the skull of Petromyzon and that of a tadpole, by the growth of the brain and the appearance of new nerves such as the hypoglossal, the coming out of the eyes, and the free swimming fish-hke form. In fact just as the comparison between the Scorpion-like ancestor and the Vertebrate is shown in the organs of the larval stage, viz. in Ammoccetes, so the comparison between the higher Vertebrates and Ammoccetes is shown by the organs of the adult stage, viz. Petromyzon. I utterly fail to see any reason for considering the lamprey as degenerate, and suppose that Mr Shipley is referring to Dohrn’s overstrained and untenable hypothesis that the lamprey is a degenerate Elasmobranch. | On the other hand the nearest allies to the Amphioxus and the Tunicates are the very Ammoccetes themselves, but how transformed! in the case of the former, no eyes, no cerebral hemispheres, no special organs of sense; while in the latter, with 1895.] Dr Gaskell, The Origin of Vertebrates. 4.7 the degeneration of the central nervous system, the adult animal -has degenerated into an alimentary bag with almost all its vertebrate characteristics gone. It would almost seem as though in the minds of my opponents the ego of each individual is to be looked for in his alimentary canal and not in his brain, whereas the one certain rule in Nature’s law of Evolution may be summed up as follows—If you want to rise in this world you must get more brains. Bitte ann, "Rye ot ae oto ene aera ie ine ante 1 hi Be ee ae cee 4 Hitt efit eet ae barat ae ey ar Ape he es PROCEEDINGS OF THE Cambridge Philosophical Society. Monday, 27 January 1896. ProFEessor G. D. LIVEING, VICE-PRESIDENT, IN THE CHAIR. The following communications were made to the Society : (1) Longitudinal Electric Waves, and Réntgen’s X Rays. By J.J. THOMSON, M.A., F.R.S. In the theory of Electric Waves given by Maxwell the only currents considered are (1) displacement or dielectric currents, and (2) conduction currents; the first of these is proportional to the differential coefficient of the electric intensity with respect to the time, while the second is directly proportional to the electric intensity itself, When we confine our attention to these currents Maxwell’s investigation shows that both the electric intensity and the magnetic force are in the wave front. There is thus no longitudinal wave, and X, Y, Z the components of the electric intensity satisfy the condition d ne dY dZ — 1 + +} =0; dt (dx dy dz this, which expresses that the volume density of the electrification remains constant, is the condition that there should be no longi- tudinal wave. Now though the dielectric and conduction currents leave the volume density of the electrification unaltered, there is a third class of currents, not considered by Maxwell, which may alter the volume density of the electrification; these are convec- tion currents, i.e. currents due to the motion of electrified bodies through the ether or of the ether past electrified bodies. When these currents exist the condition for the vanishing of the longi- tudinal wave is not satisfied, and in fact in this case we may evidently have longitudinal waves. Thus we know that in a vacuum tube the electrification has a finite value in certain parts VOL. IX. PT. IL. 4 50 Professor Thomson, Longitudinal Electric Waves, [Jan. 27, of the tube, and that the charges producing this electrification can move about, and by so doing produce a convection current. Let us suppose, for example, that we have a vacuum tube, and that in this tube all the atoms of the gas which are charged at all are charged with electricity of the same sign and move with a velocity p parallel to the axis of the tube, let the electric intensity be parallel to this axis and equal to X, let K be the specific induc- tive capacity of the medium in the tube, p the volume density of the electrification. Thus in this tube there is a dielectric current equal to and a convection current equal to 1d pp =P 4 Gg, (KX); the total current parallel to the tube is thus d (K ie ad Fi lig Ett? ie ag EX and this must be the same at all parts of the tube. For if wu, v, w are components of the total current du dv. dw and in this case V—0, 0 — 0. Hence we have ¢ (KX) +p © (KX) =f, where / (¢) represents a function of the time. The solution of this is Kee i f(t) dt + F (w — pb), where F’ denotes an arbitrary function of «—pt. This represents a longitudinal wave of electric intensity, travelling with the velocity p: the velocity of translation of the electrified atoms. When, as in the case of a vacuum tube, we have free charged atoms present the existence of convection currents is quite obvious. The following considerations show that such currents may, how- ever, occur in a solid dielectric, with all its molecules intact, pro- vided each molecule consists of a positively electrified atom paired with a negatively electrified one. For though in this case p will vanish if we take its value over a space enclosing a large number of molecules, yet if we are dealing with phenomena a 1896.] and Réntgen’s X Rays. 51 involving lengths comparable with the size of a molecule, if we are, for example, considering waves whose wave lengths are comparable with molecular distances, it is evident that we cannot assume that pis zero; we must regard p as having at each point of space a finite value which will be given by the equation d d d Suppose now that the ether is moving past the molecules with a velocity whose components are p, qg, 7; or more generally let ~p, 7, r be the components of the ether relative to the molecule, then this will produce convection currents whose components are pp, gp, rp; these convection currents will give rise to longitudinal waves. ‘Thus in this case the conditions for the production of such waves are (1) that we should have some means of producing waves whose length is comparable with molecular distances, (2) that we should be able to set the ether in motion. Now it follows from the laws of electrodynamics that if we regard the ether as a perfect fluid the pressure due to which is equal in all directions, then it must in general be set in motion when changes are occurring in an electric field. For each unit volume in the electric field possesses a momentum whose com- ponents are K K K = {Zb — Yc}, ig Xe 4a}, ae {Yb— Xa}, where K is the specific inductive capacity, X, Y, Z the components of the electric intensity, a, b, c the components of the magnetic induction. Let U, V, W denote the differential coefficients of these three quantities with respect to the time. Then a force having the components U, V, W must act on each unit volume of the field. This force will set the ether in motion unless it can be balanced by the pressure due to- the ether, the conditions for this are, if p is the pressure of the ether, apis -) dpe iden. BEng oul viggg a or —- = - 6d 0:08:42): unless conditions (a) are satisfied the ether will be set in motion. These conditions are not, however, satisfied in general when the electric field is changing; they are not, for example, satisfied in the field produced by the ordinary dumb-bell vibrator. Thus a vary- ing electric field will in general set the ether in motion, and thus fulfil requirement (2) for the production of longitudinal electric 4—2 52 Professor Thomson, Longitudinal Electric Waves, [Jan. pari waves; thus if there were any centre of disturbance to generate waves whose length is comparable with molecular dimensions longitudinal waves will spread through the dielectrics in the variable field. Before proceeding to discuss mathematically the laws of pro- pagation of these waves it may be of advantage to state some of their peculiarities. We shall call the longitudinal waves due to the motion of the charged atoms in a vacuum tube convective waves, those due to the motion of the ether through a dielectric, longitudinal dielectric waves; these second waves might exist m a vacuum tube along with the convective waves. In the first place we notice that each of these classes of waves requires for its propagation the presence of matter carrying electric charges as well as ether ; longitudinal waves could not on Maxwell’s theory be propagated through pure ether. The wave length of the convec- tive waves is not limited, while longitudinal dielectric waves can only be transmitted when their wave lengths are comparable with molecular dimension, and therefore are exceedingly small com- pared with the lengths of the visible and ultra violet rays; the finer the structure of the dielectric the more limited the range of waves that can get through. The velocity of propagation of the convective waves is equal to the velocity of translation of the charged atoms, while that of the longitudinal dielectric waves is equal to the velocity of the ether through the dielectric, this velocity will depend upon the strength of the varying electric field being larger in strong fields than in weak. If the ether moves freely through the dielectric then its velocity will not change abruptly in passing from one medium to another. Neither of these waves produce any magnetic effects if they travel in the one case in the direction of the moving atoms, in the second case in that of the moving ether. We shall now proceed to find the equations which hold when convective currents are present in the medium. We shall begin with the case of convective waves where the convective currents are carried by moving charged atoms, and we shall begin with the case when all the charged atoms, whatever the sign of their charges, are moving with the same velocity: let p,q, 7 denote the components of this velocity, X, Y, Z the com- ponents of the electric intensity, a, 8, y the components of the magnetic force; uw, v, w the components of the total current, K the specific inductive capacity of the medium, and yp its magnetic permeability. Then p, the volume density of the electrification, is given by the equation d d , d Amp =F {KX } a {KY} Rae {KZ}. 1896.] and Réntgen’s X Rays. 53 The convection current has for components Pp, YP, Tp. Hence d /(K d/(K fie u=4,(—-X)+pp, v= 5(7-¥) +0, w= 9, (q, 4) +7 _dy dB But ea are fe.’ as dy dZ ay. dB _adX dz Gey ada de de Hence we have d(d/K 1 . d/jdX adY dZ ila) + pe} =p l\WX-a(Z ie eh with similar equations for Y and Z. By differentiating the equation for X with respect to a, that for Y with respect to y, that for Z with respect to z and adding, we get d (dp _ dp dp _ dp) _ di ete tage + 7} =9. This equation merely represents that the changes in the volume of electrification at any point is due to the motion of the charged atoms into or away from the small volume surrounding the point. To consider the case of a plane wave put X =A sin = (wt — (lz + my +nz)), Y=Bsin i (wt — (lv + my + nz)), Z = C sin = (at — (la + my + n2)). And substitute in equations 1, we get A (o* Zz) = (1A + mB + nC) (wp 2 -z): B G ia) =(1A + mB + nC) (og == a eh a speek C (© = =z) =(1A +mB+ nC) (wr a 54 Professor Thomson, Longitudinal Electric Waves, [Jan. Ts Eliminating A, B, C we find two values for o, the first is given by the equation »?=1/uK which corresponds to the transverse waves as in this case 1A + mB+4+nC=0; the second by the equa- tion w= pl+qm+rn. This represents a longitudinal wave propagated with the velocity pl+qm+rn. We see that x Y Z so that unless DG ae Ai ae ie. unless the direction of propagation of the wave is parallel to the direction in which the particles are moving the electric intensity is not at right angles to the wave front. We see from these equations that a longitudinal wave of electric intensity parallel to a fixed direction, say x, can be propa- gated by a medium containing moving charged atoms even though the velocity of these atoms is not parallel to «. Thus suppose the wave of electric intensity parallel to « is being propagated by the atoms moving with a velocity whose components parallel to a, y, z are p, qg, 0, then since Y=0, Z=0 we have n=0, m= = , where V is the velocity of the transverse electrical waves through the ether. Thus the wave front is not at right angles either to the direction of motion of the charged atoms or to that of the electric intensity. If the velocity of the charged atoms is small compared with the velocity of light m will be small, 7 nearly unity, hence m = approximately. Now m is the angle which the normal to wave front when q is finite makes with the direction of the electric intensity. Hence this angle varies as the square of the ratio of the velocity of the atoms to the velocity of light. The angular deflection of the front of the waves produced by a transverse velocity imparted to the atoms would be almost infinitesimal compared with the deflection of the atoms themselves. When the charged atoms move in a magnetic field they are deflected from their rectilinear course, so that as the preceding investigation shows a wave in which the electric intensity is parallel to a fixed direction would be deflected, but the deflection would be infinitesimal compared with those produced by the magnetic field on the cathode rays. 1896.] and Roéntgen’s X Rays. 55 We see from equation (2) that if we neglect the square of the ratio of the velocity of the atoms to that of light we have ee ae EL Sines on > so that to this approximation the direction of propagation of the wave coincides with the direction of the electric intensity ; in this case there is no magnetic force propagated with the wave. An interesting case of these convective waves 1s afforded by the problem of a column of air moving like a wind and carrying along with it both positively and negatively electrified atoms. Some experiments by Hertz (Wied. Ann. 19, p. 78, 1883) seem to indicate that something of this nature exists in the neighbourhood of the positive electrode. Let us consider the simple case when the velocity (uw) of the column of gas as well as the electric intensity X is parallel to the axis of a. In this case the dielectric current is equal to K dx Aare dt © The convection current is equal to up where p is the density of the electrification ; we have however 4p — © (KX)=0. So that the total current, ie. the sum of the dielectric and convection currents is equal to K (dX Ley dX Ac | at da)’ if K is constant. The total current however in this case vanishes, so that Now let us consider the case when w depends to some extent on the intensity of the electric field, let for example Uspt+ax, where p is independent of X. Then equation (1) becomes dX wee? Stagg mle Ober rate 56 Professor Thomson, Longitudinal Electric Waves, [J an. 27, The solution of which is X= fie — (p+ OX) theses coscanneeeeee (2), where f(#) denotes an arbitrary function of X. Let us take a case where initially the volume density of the electrification is represented by a harmonic function of « so that so that when ¢= 0, and hence by (2) X=0+5 cos m(e—(p + aX) t), aX __Asinm {w—(p+aX)t} dz 1—Aatsinm{x—(p+aXx )t}’ We see from this equation that the denominator of this ex- pression can vanish and thus p become infinite. The earliest time at which this takes place is given by thus 1 t= Fa? _ darcy ane ghee +(2n+4)—. The value of dX/dz, which is proportional to the volume density of the electrification, at the time t = 1/Aa is given by the equation dX 2 A sin|m(a—? a) an ae ; p+aXx\)’ 1 —sin}m(«— ae )t comparing this with the initial value — A sin mX, we see that the effect of the motion of the air in the neighbourhood of the positive electrode has been to enormously increase the maximum value of the density of the negative electrification, while it has diminished the maximum value of the positive electrification. It has thus accentuated the difference in the initial state of electrification in the tube, for all the negative electrification is practically con- centrated in a series of equidistant spots on the tube, while the positive electricity is more evenly distributed than it was initially. This effect, which is represented by equations similar to those 1896.] and Réntgen’s X Rays. bi which represent the breaking of a sea wave as it rushes into shallow water, would tend, if there were any inequalities in the distribution of electrification in the tube to begin with, to accen- tuate these inequalities, and may possibly show itself in the sharply defined striations in the positive column. Normal Waves in a Moving Ether. We have seen that the ether in a varying electromagnetic field must in general be moving. Let us consider the differences between this case and the ether at rest. In the case of insu- lators with a quiescent ether the dielectric current is proportional to the rate of increase of the polarization with the time, in this case there is no ambiguity,—but when the ether is in motion the rate of increase to which the current is proportional may either be estimated at a point fixed in space or at a point moving along with the ether. The phenomena connected with the effect of the motion of a refracting substance on the velocity of light passing through it seem on the whole to be in favour of the latter view. But if this is the case then the motion of the ether through an electric field im which the electric intensity varies from point must produce forces which tend to keep the intensity constant at a point moving with the ether; for example, when the ether is moving through an electrified plate, forces must be generated tending to make the electricity leave the plate and travel along with the ether. When the ether is at rest the variation of the electric in- tensity at any point is opposed by all the inertia of the electro- magnetic field, while when the ether is moving all the influence of the inertia is on the side of making the electric intensity at a fixed point vary, the variation being such that the intensity remains constant in a given portion of the moving ether. Let us take the simple case when the electric intensity, X, and the velocity of the ether, p, are each parallel to the axis of X. Then the dielectric current parallel to x is tee =| dt '? da}’ Thus if the ether were moving in a field in which the electric intensity was constant with respect to the time, but which varied from place to place, i.e. a field in which dX /dt vanishes, but where dX /dzx is finite, the motion of the ether would produce a system of 58 Professor Thomson, Longitudinal Electric Waves, [Jan. 27, currents, and a magnetic field; the establishment of this field would have to contend against all the inertia of the system. If we have a part of field where initially dX/dz is finite but varies rapidly from point to point, regarding dX/dx for simplicity as a harmonic function of «, let us suppose that the wave length is comparable with molecular distances: then if the molecule of a substance consists of a positively and a negatively electrified atom, the molecules could arrange themselves so as to produce a distri- bution of dX/dx of the kind considered. Now if the molecules group themselves so that X keeps con- stant at a pomt moving along with the ether, there will be no current, no magnetic field, and no electrokinetic energy. There consequently will be a tendency for the molecules in the tract of the moving ether to arrange themselves so as to produce this result. This alteration in the disposition of the molecules implies a longitudinal wave of the electric intensity. If the wave length of the original distribution of # exceeded molecular distances the molecules would have to split up into atoms to reproduce this distribution of X, and there will, in consequence of the inertia of the system, be a tendency for them to do so. The equations representing the transmission of wave in the moving ether are as follows: Using the same notation as on page 52, p, g, r now denoting the velocity of the moving ether, we have d d d d\ K with similar equations for v and w, we have also _dy dB A ay > tr ie Mas aa az ia ae Pax 1 dy rE) a dz’ d d d d dX dZ wget Pag tag tae) mae ody: Hence when p, g, r are independent of 2, y, z we have d d d d )? Ge 6 Ce a? dé pK atPastia teal =| erate age (1) where yes h eMnydZ WT Gnidia fide with similar equations for Y and Z. 1896.] and Réntgen’s X Rays. 59 Take the case of a plane wave, when we may put saintly og = (o — (le + my + nz)), Y=Bsin =z (@ — (la + my +nz)), Z=Csin _ (w — (lx + my + nz)), substituting these values in equation (1) we get BK {fo —(pl+qm+rn)PA=A-— 1 {lA +mB+4 nC}, LK {ow —(pl+qm+rn)}P? B= B-m{lA+mB + nC}, BK {wo —(pl+qmt+rn)P C=C — n {lA +mB+4+ nC}. Eliminating A, B, C we find that either Vuk (@ — (pl +qm+rn)=1, or wo —(pl+qm+rn)=0. If we take the first solution, we have 1A+mB+nC=0, Le. the wave is a transverse wave; while if we take the second solution, we have Se 2B e it ¢_m_n Dns) Gone Ae This represents a normal wave, the direction of propagation coinciding with the direction of the electric intensity, the velocity of wave propagation is equal to the component of the velocity of the ether in the direction of the electric intensity. If there is only the normal wave, then since av_dX dz_d¥ aX_az dai dy incdy edz70\ dat ida the magnetic force will vanish. Since, however, dX he d Y. dZ dz dy dz is not zero throughout the wave, the volume density of the electrification is not zero; thus the wave could not be propa- gated through space devoid of matter, nor could the wave be propagated without dissociation through an insulator unless the wave length were comparable with molecular distances. 60 Professor Thomson, Longitudinal Electric Waves, (Jan. 27, We thus see that on the electromagnetic theory normal waves of very short wave lengths can be propagated if the ether is moving. A normal wave in passing from one medium to another would be deflected if the lines of electric intensity were bent in passing from one medium to another. At the junction of two media of different specific inductive capacity the lines of electric intensity are refracted, being bent away from the normal as they pass from a medium of small specific inductive capacity to one of large. In the case of these very short waves there seems, however, no reason to suppose that the specific inductive capacity of a medium would differ from unity. For if we regard a molecule as made up of a positively electrified atom joined to a negatively elec- trified one, then, just as the magnetic permeability may be re- garded as due to the setting of molecular magnets under the influence of the magnetic force the specific inductive capacity will be due to the setting of these molecules under the influence of the electric intensity. If now the wave length of the electric intensity is comparable with the size of a molecule, a molecule at one part of its length will be acted on by a force tending to make it set in one way, and at another part of its length by a force tending to make it set in the opposite way; the resultant effect therefore will be little or nothing, and the specific inductive capacity will practically be the same as that of a vacuum. Quite recently Professor Rontgen has discovered some remark- able effects which he is inclined to attribute to normal waves. We do not know enough about the laws governing those new rays to be able to say whether they could or could not belong to the type of normal waves we are investigating; we do not even know at present that they are normal waves at all. A series of photographs taken by Professor Réntgen’s method was shown, and a photograph was taken during the meeting of the Society. A very noticeable feature in the bulb producing these Réntgen rays 1s the phosphorescence of the glass of the bulb. I thought it therefore of interest to try if these rays were generated when the phosphorescence of the glass was produced by other means than the discharge from a negative electrode. To do this, I produced a ring discharge in an electrodeless bulb; this when the pressure of the gas is very low is accompanied by intense phosphorescence of the glass. I exposed a photographic plate protected by thick cardboard for an hour to such a bulb, but without the slightest effect. I next tried filling the bulb with oxygen, a gas which is itself made phosphorescent so as to have both the glass and the gas phosphorescent, but again a photographic plate was not affected after an hour's exposure. 1896.] and Réntgen’s X Rays. 61 I also tried without success to photograph in this way by the phosphorescence excited in a screen powdered over with luminous paint, by the sparks passing between the terminals of a Ruhmkorff coil placed close to the screen. It would thus appear that we can have vivid phosphorescence without any production of these rays. I next tried whether the negative electrode could excite these rays without the aid of the walls of the tube. To test this, I cut a piece off a photographic plate and enclosed it in a small ebonite box in the tube in such a way that it came between the negative electrode and the glass; in this case the plate was not affected. The next experiment I tried was designed to try if any evidence as to the transverse or longitudinal nature of these rays could be obtained by comparing the depth of the shadows cast by two plates of tourmaline, (1) when the axes were crossed, (2) when the axes were parallel. Two pairs of plates A and B were used and a series of photographs were taken; in some the axes of A crossed, and those of B parallel, while in others the axes of A were parallel and those of B were crossed. A very considerable number of photographs were taken, but there was no evidence of any effect being produced by the relative position of the AXES. A series of experiments (which were not completed until Jan. 29, the day after the paper was read) were made to test whether a charged electrified plate would retain its charge of electricity when exposed to these rays: it was found that the inci- dence of these rays produced a rapid discharge of the electricity from the plate, whether this was charged with positive or negative electricity ; the rate of leak was independent of the sign of the charge. The potential difference used in these experiments was about 200 volts. An uncharged metallic plate when exposed to these rays was not sensibly electrified. I have much pleasure in thanking Mr Everett and Mr Hayles for the assistance they have given me in these experiments. (2) The Equilibrium of Isotropic Elastic Solid Shells of nearly Spherical form. By C. CHREE, Sc.D. The equations of equilibrium for isotropic elasticity can be solved approximately in cases where the surface is not exactly but only nearly spherical by a method which I have applied in the American Journal of Mathematics, Vol. 16, pp. 299 et seg. In all the problems solved in the paper referred to, the material was bounded by a single surface, but it was indicated J. ¢. p. 382, how the method could be applied to a shell. The present paper deals 62 Dr Chree, The Equilibrium of Isotropic [Jan. 27, in detail only with a simple case of the shell problem, viz. that in which the forces consist exclusively of uniform normal pressures, different over the two surfaces. The equations to be solved prove to be ultimately identical with those treated by me in the Society’s Transactions, Vol. Xv., p. 351. Attention is mainly directed to the case of a thin shell whose surfaces are concentric, similar and similarly situated, as being that of most physical interest. Let p, p’ denote the uniform pressures, and let the equations to the two surfaces be PSO, Ai AEG} Wa hod eee tecece ese (1); p=b Gere Gt) Sea ee (2) where ¢ and ¢’ are small quantities whose squares are neglected, and o; is a surface harmonic of degree 7. For simplicity there is supposed to be only one harmonic term, but the method obviously applies, however numerous these terms may be, supposing the sum of their numerical values small compared to unity. Referred to the fundamental polar directions r, 0, @ at any point on the surface (1), the direction cosines of the normal, since e is neglected, are do. 4 1 do; ie “d0’ ~ “snd do’ similar results with e’ written for e apply over (2). If the shell were truly spherical the complete solution would consist in the radial displacement oe (PP ae ea Di: (3)*, 3m — Nn 7p An 1, where m and n are the elastic constants in the notation of Thomson and Tait’s Natural Philosophy. Answering to (3), the dilatation A and the stresses, in the notation of Todhunter and Pearson’s History, are given by A = (b%p' — ap) + (m -) (a* — v} ; os ool ~ op +(> ios PO}, (4. 00 = $6 = =e oP — ap +3() ('-)}, rd =rb = 66 =0 * Cf. Transactions, Vol. xv., p. 343. 1896.] Hlastic Solid Shells of nearly Spherical form. 63 When the surfaces are no longer spherical, but are given by (1) and (2), the solution (3) is obviously incomplete, and we require the addition of some terms from the general solution contained in my paper above referred to in Vol. xv. of the 7rans- actions. For brevity I shall simply refer by number to the equations of that paper, distinguishing them by the letter A. The terms required are the “mixed radial and transverse” of: degree 7 containing the harmonic o;. For these from (30,), (31,), (32,,) we have ea ame Ans, u a | r (2 43)n > ef _.(@+1)m+ 2n y I—-1 7, mt c a—t—2 2 +r Z,—1 3@i—1)n | ee Tp ac (5), v= a | ign (4+8) m + 2n meade 2(2i+3)("+1)n * ae ae (1— 2)m—2n ated a5 A 7 Z;+ ue 9 (i A 1) in ——s rae 1 r Zips 5)! ae) dd [same expression as inside square bracket in (6)] Here it should be noticed Y;, Z;, Y_;,, Zi+ are simply arbitrary constant multipliers of the harmonic o;, and not them- selves surface harmonics as in the paper from which the results are quoted. They are determined presently from the surface condi- tions. These constants are all of the order ¢ of small quantities ; the terms containing them will thus be called “subsidiary terms” when it is desired to distinguish them from the “ principal terms ” as given by (3). The contributions of the subsidiary terms to the stresses rr, r@, rd are given in (33,), (84,), (35,); their contributions to the other stresses are not required for our present purpose. As terms of order é are neglected, the surface conditions over (1) take the form ~ das Bde i 2 eg tamOdee ov Di Perak Boccapes (8), > do; de dagen ee cag > sn dda) ese siaisieleleivislele'sie Co) doiz 1 da; 1 do; ee sin Odie aed 64 Dr Chree, The Equilibrium of Isotropic [Jan. 27, The surface equations over (2) are obtained from these by writing ¢’ for e and p’ for p. The two equations (9) and (10) lead to such results as af (O, $) _ 1d 2 cee ae? Ce a and are really tantamount to but a single equation a (Gacp)i— 0: To obtain the values of principal terms over the surface (1) we must write a (1 + eo;) for r and retain terms containing the first power of ¢; for instance the contribution to rr of the principal terms is easily found from (4) to be ou ee stacey ce (p' — p). In the subsidiary terms proceeding from (5), (6) a (7) it suffices to write a for r. In such an expression as set m7 e776 the contribution of the subsidiary terms would be of order e and so is negligible. Bearing these points in mind, and noticing that the terms independent of « cut out, it is easy to verify that the surface conditions take the form : ah doh 5 Ee ONE eo AM pr 21+3 ahtarah 5 Ee ees (ou yae 2(4¢ —i-3 7 30° y —2 (4+ 2) na i =73 pat PP) se otertes (11), a(a+2)m—n —- il) ee a Y; na’ Z, ERIS) 8 ran =I) =D 3 =) eee a4+2) 3 & 2 nae. =— 5 (PP) ---- (12), (?—1—3)m+n,, a sn 2+ 3¢i—-1)m+n,_, fe oF poe 9 (1 ee 30, ; —2 (0+ 2)nb—*>3 Z_,, = —— ¢ (p—p) ......... (13), a? — b3 1896.] Elastic Solid Shells of nearly Spherical form. 65 _t@+2)m—n 7, 2-1) ,., iG, «ers (1) m= 1s ry Ces baal 1 a) Ge ' 42 Oa Zin =— 35 pe (p—p’) pocac (14). These equations are identical with (38,) to (41,) if in the latter we put V; = Viiv — 0, R, = — 27; = 30° e(p — p’)/(e — b’), fh’, = — 271"; = 30 & (p—p’)/(a’ — b°) The values of Y;, Z;, Y_;., Z-; in the present problem are thus given by (68,) to (71,) when the substitutions (15) are made. To obtain the subsidiary terms in the displacements for the present problem, all we have to do is to take the results (92,), (93,) and the corresponding expression for w, and in them replace R; by 30° ec; (p — p’)/(a’ — 8°), Ri, , 8a? éo;(p—p')/(a? —b), (16) 7; 3) aarh : BF €0; (p — p)/(a _ 6°), a eens Ps, — Sato: (p— pa —B) A similar substitution in (94,) and (95,) gives the subsidiary terms in the expressions for the stresses rr, 76. This substitution is perfectly straightforward, but the results of it in general a little cumbrous; I propose giving them explicitly only for the case when ce“ €) and h/a = (a —b)/a is very small. In this case we make the substitutions (16) in (96,), (97,) and the corresponding expression for w, putting e’=e. After effecting the substitutions I have written h for a—b in the terms depending on o;. Combining the subsidiary terms with the principal term (3), it will be found that VOL. IX. PT. II. 5 66 Dr Chree, The Equilibrium of Isotropic [Jan. 27, ee ae U= Wa = Sma Amr? a » (20? + 21-3) m+n Wy Ce es) seresy oper aa eeccee (17). pi coeae i= a) _ el p=p dé / \sin 6 do h 4n The subsidiary terms vanish when p’=p. It is obvious in fact from (11) to (14) that they must do so in any case, irrespective of the magnitude of (a—b)/a. Along the same radius vector they are constant, to the present degree of approximation. The varia- tion of the principal term in wu along a radius vector was considered in my previous paper (see (13,) &c. writing —p for R, — p’ for FR’). This variation is important only when (p ~ p’)/p is small, and in this case the subsidiary terms in e tend to vanish. As our present object is to examine the significance of these terms it will be supposed that (p ~ p’)/p is not small. Omitting the small part of the principal term in w which varies throughout the thickness, we may write (17) in the form eae a (p—p’) aloe ih eo; {(20? + 24-3) m+n} = h 4n FE 4n (3m — 2) d | ) mae) 4 | C25 oy (sy = _ et (p— Pp’) | a | sin 6 ddb/ 4nh where # is Young’s Modulus, 7 Poisson’s ratio. Remembering the values of the direction cosines of the normal, we see that (18) is equivalent to the following three displacements: a displacement — a?(p—p’)/4nh along the normal, e i ne (p—p)/Eh _,, » radius vector, eo," (p — p’) {(20? + 20 — 3) m+n} if i 4n (8m — n)h along the normal or radius vector. Thus to the present degree of approximation the displacement is along the normal, that is in the line of action of the applied force, when G— 0: The nature of the change produced by the pressures in the shape of the thin shell is easily found as follows. It will suffice to treat the outer surface (1), as the results for the inner are of the same character. Denote the radius vector by prmewlen ea; = (p —a)/a. 1896.] Elastic Solid Shells of nearly Spherical form. 67 Then we easily find ulp=C+1@+1)(p—a)(p ogee pee Le ey, Seen (19), 0/ Baw /(gr 99h) - ote p’)|(Anh) = 1 (pa—po b?(p—p’)) - where C=- a | am —n ae ie , A displacement u= Cp, be it noticed, would simply change the surface into one similar and similarly situated to itself, and so leave the shape unaltered. If pressure be applied over the outer surface only, we have u/p=—C,+¢(¢+1)(p—a@) p/(2hE)............ (20), where C, is positive and numerically large compared to the other term on the right. The radius vector is thus everywhere reduced, and the proportional reduction is above or below the average according as p is less or greater than a. Under the same conditions ase AT TEED skid o anh dd?” ~ 4nh sin O Gide eas The resultant tangential displacement is thus along the direction in which p increases most rapidly; e.g. in a spheroid the tangential displacement is along the meridian, being directed away from the axis of symmetry or towards it according as the spheroid is oblate or prolate. (21). It is thus obvious that pressure on the outer surface tends to exaggerate the departure of the surface from the truly spherical form. If, on the other hand, pressure be applied over the inner surface only, we have nif AE d (4-D) (p= Bp hI x iczecwneas (22), 2 SLU i a Lael ° =~ anh db? ~~ nh sin 0 didics > Je ey ee) where (C, is positive. Here every radius vector tends to lengthen, but the lengthen- ing is proportionally least where the radius vector is initially greatest ; also the tangential displacement is along the direction in which the radius vector shortens most rapidly. Pressure on the inner surface thus tends to make the shape more nearly spherical. 5—2 68 Dr Chree, The Equilibrium of certain Shells. [Jan. 27, In all cases it will be noticed that for a given magnitude in the maxima values of eo; the importance of the subsidiary term in uw increases rapidly with 2 It has been tacitly assumed that the subsidiary terms are relatively small, so that the solution should not, without further investigation, be applied to cases in which ei?o; is anywhere comparable to unity. The effect of the departure from sphericity on the change of density produced by the pressure is deducible at once from the value of the dilatation A. For the thin shell we have from (10,) and (101,), putting in the latter P,= fh, — R%, where R;, R; are given by (16), Say san! é weasel Kx a®p — b8p Sedo; (p — p’) (24), 7) @=aQG2D i Crenwe > Thus if p as before be the surface radius vector, pes: (a*p ie bp’) i 3 (p = a) (p =p) (25) (m — n/3) (a3 — 6°) (8m—n)h 7 j Thence in the case either of internal or external pressure, A is numerically largest—i.e. the change of density of the material is greatest—in the neighbourhood of the longest radi vectors. In the case of nearly spherical shells exposed to bodily forces depending on solid harmonics, or surface forces depending on surface harmonics, the equations determining the values of the constant multipliers in the subsidiary terms required are of the types (36,), (87,) or (88,) to (41,)—the latter including the case 1=0. The quantities on the right-hand sides of these equations, answering to f,;, T; etc., are deduced in the same way as the corresponding quantities for nearly spherical solids were deduced in my paper in the American Journal. The only mathematical difficulty consists in representing products of spherical harmonics, and products of their differential coefficients &., as simple spherical harmonics or differential coefficients of simple spherical harmonics. The necessary results of this kind for the shell problems analogous to the single surface problems I treated in the American Journal already exist there. When the quantities answering to &,, T; &c. in (36,) to (41,) are known, nothing remains but to substitute them for R,, T;, &c. in the general formule, such as (91,). 1896.] Mr Hargreaves, Distribution of Solar Radiation, etc. 69 (3) Distribution of Solar Radiation, and its dependence on Astronomical Elements. By R. Harcreaves, M.A, formerly Fellow of St John’s College. (Printed in full in Zransactions, Vol. xvt.) (A bstract.) This investigation was undertaken with the object of providing exact data for the discussion of the influence of changes in certain astronomical elements on the distribution of solar radiation on the surface of the earth. It is well known that secular changes of climate, of such extent as to give rise to the terms Glacial and Genial epochs, have been attributed by some authors to this cause. In view therefore of the interest which this question has for geologists and others, who might be repelled by the mathematical analysis, this is preceded by a somewhat full outline, and numerical results are given in connection with each point. The paper begins with the expression of the amount of heat due to the earth in any latitude, on the assumption of a dia- thermanous atmosphere, by means of a harmonic series which is carried numerically as far as the term with one quarter of a year for period. Denoting by H/r? the amount of radiation on unit-surface in unit-time exposed perpendicularly to the sun’s rays at distance 7, the element of heat-supply is @ being the orbital angle of the sun measured from the spring equinox. If the orbit of the earth (or any other planet) was circular @ would be proportional to mean time. The actual conversion to mean time is given later, but various conclusions can be drawn from the present form. The constant hf is introduced by the relation r°d0/dt =h; when a year is unit of time, its value is 27rab. As the minor axis is dependent on eccentricity, but only varies within very narrow limits, the effect of this general divisor is very slight. The coefficients Z,, L,, L, ... are functions of latitude, and obliquity of the ecliptic, the same for both hemi- spheres, expressed in finite terms by complete elliptic integrals of the three kinds, and also in series of zonal harmonics. The coefficient of the annual variation L, has the simple form T. : —~ sin JA SIN €, . 2 with opposite signs in the two hemispheres. 70 ‘Mr Hargreaves, Distribution of Solar Radiation, [Jan. 27, On ZL, depends the total annual supply ; with no obliquity its value is cosd, vanishing at the pole; as the obliquity is m- creased the value in low latitudes slowly diminishes, that in high latitudes rapidly increases. The character of the resulting change in distribution is first considered generally, and then with special reference to the limits within which the obliquity is supposed to vary, Stockwell’s limits 21° 58’ 36” and 24°36’ being used. Within these limits the total range of Z, amounts at the equator to 93 per cent. of its present value, diminishes to zero in lat. 43° 20°; here the sign of the change is reversed and the total range of L, in- creases up to 104 per cent. at the pole. This alteration affects both hemispheres alike. For the normal annual amplitude ZL, the total range is in every latitude 104 per cent. of its value, but this effect blends with changes due to eccentricity, the influence of which appears on transferring to mean time. This transformation is made for the present position, numerical results being tabulated; and also for those positions in which eccentricity has its most pronounced influence in modifying the annual term, viz. when the line of equinoxes is at right angles to the major axis of the orbit, making the inequality in duration of summer and winter greatest. If these epochs be described as genial and glacial, the first has for element of heat-supply in north latitude expressed in mean time = Q’dt, where Q =L, —(L, — 2eL,) cos 27... , while for the second Q’=L,4+ (L, + 2eL,) cos 2at ... ; only the more important terms of the coefficient of annual term cos27t being here written. Attending only to these terms, in high latitudes Z, is large, and a high value of eccentricity is required to produce any considerable modification. But L, vanishes on the equator and is small in low latitudes, while Z, has its greatest value there, so that a moderate value of e makes the difference between the two epochs quite considerable. One of these formule is derivable from the other by changing the sign of L, which is precisely the change made in passing from north to south latitude. Hence in so far as change of eccentricity is a vera causa for glacial epochs it acts in opposite senses in the two hemispheres, making a genial epoch in the one contemporaneous with a glacial epoch in the other. Also apart from the minute effect mentioned at the outset, the action of eccentricity is through the periodic terms, whereas the alterations due to obliquity affect also the non-periodic term. The effects of changes in obliquity of the 1896.] and tts dependence on Astronomical Elements. 71 ecliptic are small in low latitudes, and well marked in high latitudes ; those of eccentricity, with appropriate position of peri- helion, are conspicuous in low latitudes, while producing a fair modification in high latitudes, In each case the effects are so different in high and in low latitudes that an average taken over so large a range as a hemi- sphere quite obscures their special character. The question of drawing inferences as to temperature is rendered extremely complex by a variety of modifying conditions, of which the principal is the action of the ocean and atmosphere as carriers and reservoirs of heat. Apart from these, a solution for temperature may be easily obtained, but it is important to observe that it is necessary to take non-periodic and the various periodic terms separately, these being affected with different multipliers in the integration, and the latter subject each to a different modification of phase. This may render the comparison of terms such as midsummer and midwinter heat with the corresponding temperatures seriously fallacious. It appears to be important in every case to compare non-periodic only with non-periodic under other conditions, amplitude of annual term with amplitude of annual, and so on. In order to estimate the effect of absorption, the transmitted part is assumed to be equal to @&+e,cos[+e,coPrl+..., where J is angle between the rays and the normal to the surface. This seems suited to express an absorption increasing as the sun’s altitude diminishes, with considerable generality, and has the advantage that each term is exactly integrable in the manner of the diathermanous case. This integration is effected, and some results tabulated, from which it appears that in low latitudes the periodic terms are exaggerated in comparison with non-periodic, the effect tailing off as the pole is approached; the amount of the absorption being of course much less for low than for high latitudes. This relative alteration ought to be taken into account in drawing conclusions as to temperature. 02 Dr Lazarus Barlow, On an Osmometer. [Feb. 10, Monday, February 10, 1896. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. Professor H. Marshall Ward, Sc. D., Christ’s College, and W. H. Duckworth, B.A., Fellow of Jesus College, were elected Fellows of the Society. The following communications were made: (1) By Dr Lazarus Bartow. The author exhibited an osmometer designed for the estimation of the initial rate of osmosis and a modification of the same suitable for the examination of small quantities of fluids. The principle of both is the same, viz. that the stem of the osmometer is kept horizontal, and the level of the fluid inside the osmometer is the same as the level of the fluid outside the osmometer. The larger instrument is fully described in the Journal of Physiology, vol. XIX. 1896, p. 140 and foll.; the smaller instrument differs from it in that it is immersed in water until the stem of the osmometer just shows above the surface. By these instruments the author found that the initial rates of osmosis are not indicated by their final osmotic pressures, or in other words by their freezing points ; thus, to give an example, with a copper-ferrocyanide membrane the initial rate of osmosis of a decinormal solution of urea was half as great again as the rate of osmosis of a decinormal solu- tion of glucose, whereas urea and glucose being indifferent sub- stances, decinormal solutions of each have the same freezing point and the same final osmotic pressure. The object for which the research was performed was to see whether it is justifiable to apply deductions from the freezing point of fluids existing in the animal body to the question of lymph formation. Since the freezing point determinations give no indications as to the relative amounts of osmosis of two solutions of different composition at pressures possible within the animal body, 2.e. approximately at atmospheric pressure, application of the laws of osmosis which are true at final osmotic pressures are not justifiable in the case of the animal body where such pressures can at best but rarely occur. 1896.] Mr Bles, Nephrostomial Tubules. 73 (2) On the communication between peritoneal cavity and renal veins through the nephrostomial tubules in the frog (R. temporaria). By Epwarp J. BLEs, B.Sc. The discovery of nephrostomes in the kidneys of adult Am- phibia was announced by Spengel in his fine paper: Das Uro- genitalsystem der Amphibien, published in 18761 In this he showed clearly that the nephrostomial tubules in Urodeles and in Ceecilia have a lumen persistent throughout life and always con- tinuous with the perivisceral space at one end and with the lumen of the neck of the Malpighian body at the other end. Semper? and Balfour? had both described in 1874 a similar state of things in the Wolffian bodies of Elasmobranch embryos, and Semper‘ gave a list of Elasmobranchs in which the nephrostomes remain open in the adult. Thus it was shown that in this respect there is a close resemblance between adults of many species of Elasmobranchs, Urodeles and Ceecilia. When Spengel, however, examined the adult kidney of Anura, although the nephrostomes were clearly visible, he could not trace a single tubule from them into the neck of a Malpighian body. F. Meyer of Leipzig, who discovered the “stomata,” as he called them, independently of Spengel, was equally unable to find the inner opening into a tubule of the kidney® The subject was next investigated by M. Nussbaum who published in 1880 a short paper’, without illustrations, containing the statement that the nephrostomial tubules in adults of the genera Rana, Bufo and Bombinator communicate at their inner ends with veins which he identified with renal portal veins. This result was accepted by Wiedersheim both in his Lehrbuch’ and his Grundriss* der ver- gleichenden Anatomie der Wirbelthiere and in his portion of Ecker’s Anatomie des Frosches*. Still the observations seem to have been met with incredulity and Nussbaum with his pupil Wichmann 1 Arb. a. d. zool. zoot. Inst. d. Univ. Wiirzburg. Bd. ur. (1876), p.1. The development of the kidneys and fat-bodies in the Frog. Studies Biol. Lab. Owens Coll. Vol. 11. 1890. p. 183. 1896.] Mr Bles, Nephrostomial Tubules. 75 it worth while to exhibit before this Society specimens to demon- strate the point. A kidney of a common frog (not one year old) was hardened in Hermann’s fluid, imbedded in paraffin after gradual impregnation in xylol and paraffin, cut in a series of sections and stained on the slides either with aniline blue-black or by the Biondi-Heidenhain (acid) method. The latter gives plasma well stained with fuchsin and blood corpuscles differentiated with methyl green. A bunch of flagella can be seen protruding through the imner opening of the tubule into a space lined with squamous endothelial cells, and either containing blood corpuscles or standing in open communi- cation with similar spaces on the adjoining sections which do contain blood corpuscles. These vascular spaces can easily be traced into the renal veins. On all four sections shown the peri- toneal opening of the tubule could also be seen. On one section a nephrostomial tubule could be traced from the peritoneum and running towards the flagellate neck of a Malpighian body, but just short of reaching this opening into a narrow space lined with endothelium and containing a blood corpuscle, the space being continuous with venous spaces on neighbouring sections. These facts do not stand alone as isolated instances of a channel of communication between ccelom and vascular system. Mr Shipley read a paper before this Society in 1888 (Proc. Phil. Soc. vol. vi. p. 218) in which he cites, with the exception of M. Nussbaum’s, the cases occurring in the animal kingdom of such a communication. Some of these cases still hold good and amongst them cer- tainly the communication through the peritoneal stomata of the diaphragm in mammals from the great abdominal serous cavity through the lymphatic spaces and ducts into the great veins. Physiologically these lymph channels can be compared with what exists in the above-mentioned five forms of Anura. The perivisceral cavity is a lymph space continuous with the cisterna | magna lymphatica and passing lymph into it, and there are reasons for thinking that the peritoneal lymph can also pass into the renal veins through the nephrostomes. Anatomically considered, the adult Rana fusca can be easily brought into line with the other Amphibia with respect to its nephrostomial tubules when it is borne in mind that the larva in its ontogeny passes through stages in which the tubules have successively relations corresponding (1) to the tubules in adult Urodela, (2) to an indifferent condition still persisting in part in other adult Anura, viz. ending blindly, (3) to a condition which occurs in at least four other forms of Anura and easily derived from the indifferent condition. 76 Mr Darwin and Miss Pertz, On the effect of [Feb. 10, (3) On the effect of water currents on the assimilation of aquatic plants. By Francis Darwin, M.A., F.R.S., and D. F. M. PERTZ. The principal fact established by our research is the notable increase in the gas given off by certain aquatic plants in the process of assimilation, when the water in which they are culti- vated is disturbed by stirring. The fact is of interest as bearing on our general knowledge of the gaseous interchange in aquatic plants. It also bears on the nutrition of these plants in still and running water. Moreover it is of interest on the question of method, 2.e. on the question of how far the yield of gas represents assimilative activity. This last point is illustrated by the history of our research which began with a chance observation made a few years ago. If a small quantity (about 5 p.c.) of alcohol is added to the water in which a sprig of Hlodea canadensis is bubbling under the influence of light, the rate of bubbling at once shows a con- siderable temporary increase. It becomes about twice as quick, and returns to its normal pace in four or five minutes. It seemed possible that the plant was stimulated by the alcohol, but it appeared more probable that the result was physical rather than physiological. We therefore fitted up a simple apparatus by means of which air was forced by the pressure of a column of water to escape through a capillary tube (0:2 to 03 mm.) into a beaker of water. The air ceased to escape from the tube while the column of water showed a pressure of about 20 cm. When alcohol was added in such a way as to mix with the water in the beaker close to the opening of the tube, air at once escaped from the capillary and the water column fell several cm. This result obviously depends on the fact that the surface-tension of a mixture of alcohol and water is less than that of water. To discover whether the effect of alcohol on water-plants also depended on diminished surface-tension at the pomt of escape of the bubbles, it was necessary to eliminate the possible stimulative effect of alcohol on the leaves. This was done by Devaux’s method’. The tube of a funnel was cut short below the conical part, and in this opening the stalk of a Hottonia was held by a plug of cotton-wool, so that the cut end projected mto the expanded part of the funnel. Melted gelatine was then poured in from above, which became solid rapidly and thus closed the funnel below with a water-tight plug through which the stalk passed. The main body of the plant could now be immersed in a beaker of water, while the bubbles from the cut end of the stalk escaped into water contained in the funnel. When alcohol (5 p.c.) was 1 Annales des Sciences Naturelles, 1x. 1889. p. 67. In our experiments the plant is in a reversed position to that figured by Devaux. 1896.] water currents on the assimilation of aquatic plants. Cie added to the water in the funnel the rate of bubbling became about eight times as quick, returning after two minutes to about its previous rate. p-m. Rate 2.21 14 2.23 14 5 pc. spirit added 2.25 111 2.27 18 A similar striking effect was obtained by adding 10 p.c. after a few minutes. Later in the day the effect was not so marked, the rate of bubbling was doubled when alcohol was added to the water in the funnel. The result is what might have been ex- pected since the escape of gas varies with the pressure at the cut end of the stalk. This well-known fact may be simply demon- strated by cementing the cut stalk with gelatine into the lower end of a vertical tube which is filled with water to various heights by means of a side opening and rubber tube, and thus exposes the cut end of the stalk to varying pressures. The following table shows a diminution in, and final cessation of, the bubbling as the pressure rises, and a rise as it is allowed to fall again. 27th June, 1895. LHlodea canadensis. Time Pressure Rate Temperature ce | 15 em. 66 me \ 24 cm. Al 21-40 - } 30 cm. 50 91-4 x 51 em. 33 21°4 a } 64 cm. 14 21-4 ee | 80 cm. 0 91:3 Ba 64 em. 15 21.3 fe 51 cm. 30 a } 30 cm. 71 21:2 s k 15 cm. 166 21-2 78 Mr Darwin and Miss Pertz, On the effect of [¥Feb. 10, Having shown that alcohol added to the water in the funnel increases the rate of bubbling by diminishing the surface-tension, we expected to find that alcohol, added to the beaker in which the leaves were, would produce either no effect or less than the normal effect. It turned out however that the addition of alcohol to the beaker produced nearly the usual effect. This proved that the accelerating effect produced by alcohol when the cut stalk and the leaves are in the same vessel of water is not simply due to diminished surface-tension, although this cause undoubtedly has some effect. At this pomt Mr Blackman made the useful suggestion that water should be added instead of alcohol. It was found that this treatment greatly increased the rate of bubbling, and it at once became clear that this result and the chief part of the alcohol effect were due to the currents set up in the water by the act of pouring in the fluid, water or alcohol as the case may be. This was confirmed by gently stirring the surface-water with a rod, until, by the movement of small particles floatmg im the water, it could be seen that the lower strata were in rotation. Under this treatment the rate of bubbling at once became nearly doubled. It should be noted that the plant was not visibly shaken or moved, so that the effect was not due to the bubbles being helped to escape by mechanical shock. This point is worth mention, because a blow on the table was found to cause a slight escape of gas from the glass capillary of the above described apparatus at a pressure which had ceased to produce a flow of bubbles. Method. -The experiments were made in a dark room illuminated by one of the Incandescent Gas Company’s burners, in which a white-hot mantle, surrounding an argand flame, gives a brilliant steady light. Between the gas and the vessel in which was the bubbling plant we placed a glass trough through which a current of water flowed. In this way the plants could be kept at a tempe- rature sufficiently constant. The plant to be experimented on was tied to a glass rod sup- ported vertically in a beaker of water. In all the earlier ex- periments the yield of gas was estimated by taking with a stop-watch the time which elapses during the evolution of a given number of bubbles. The reciprocals of these times will be pro- portional to the rate of bubbling. The “rates” given in our experiments are simply derived from the reciprocals by moving the decimal place. The “rates” are comparable throughout any given experiment, but the rate in one experiment is not neces- sarily comparable with that in any other. 1896.] water currents on the assimilation of aquatic plants. 79 In our later experiments the gas yielded during half-an-hour was collected and measured in the modification of Timiriazeff’s Eudiometer described and figured in Darwin and Acton’s Prac- tical Physiology}. As the times involved were short, and the temperature re- mained fairly steady during the experiments, we dispensed with barometric and thermometric corrections, and we believe that the readings of the eudiometer are fairly comparable inter se during any given experiment: although they certainly do not give absolute amounts with accuracy. It will be seen that the variations in the yield of gas as given by the eudiometer do not always agree with the rates obtained by timing the bubbles given off. When this is the case, we are inclined to trust the eudiometer readings rather than those of the stop-watch. To stir the water uniformly, we hung a microscopic slide to an ordinary bottle-jack, such as is used for roasting meat. The glass slide makes five turns in about four seconds, and then reverses and rotates in the opposite direction. Experiments with Elodea. In the following experiments we have given the average rate of bubbling during periods in which the water was alter- nately left quiet and disturbed. Where the amount of gas yielded during the same period was measured the rate of yield per minute is given in terms of a graduation of the eudiometer : each graduation is equal to 0:01 c.c., and is of such a length that the quantity of gas can be roughly read to 0:002 c.c. A single experiment is given in full, in order that it may be seen that the effect of stirring is fairly well kept up for a period of half-an-hour. 1 Edition 1. p. 45. 80 Mr Darwin and Miss Pertz, On the effect of [Feb. 10, Experiment 1: 5th June, 1895. Llodea. a.m. Rate! Temp. 10.37 100 15-4 100 47 76 47-5 76 56 62 Still 11 66 if 5D 8 76 74 10 62 15-4 12 Started jack 12°5 166 166 200 13 200 15-7 200 14 200 15 200 16 166 18 166 166 Stirred 20 166 21 142 23 142 25:5 166 27 166 29 153 30 41) | (Sudden change in rate of 32 a bubbling for 3 minutes.) 33 125 43 35°5 181 181 Stopped jack 16 37 153 Gp 38 111 | 40 90 |} 43 83 46 86 S45 50 80 Still 53 76 76 55 76 12.3 tel 16-4 1 rate means rate of bubbling calculated from the readings of the stop watch. 1896.] water currents on the assimilation of aquatic plants. p.m. Rate yt 125 142 142 5 166 166 142 6 142 9 166 153 ll 153 15 142 15°5 153" 16 142 18 142 142 19 133 Dil 1325 23 125 ee vy elas 26 100 27 100 29 100 30 105 IEF 30 105 Temp. Started jack 166 Stirred 16°8 WOT Ex. Pl. iT: 81 82 Mr Darwin and Miss Pertz, On the effect of [Feb. 10, Experiment 2: Ist June, 1895. Elodea in Tap-water. a.m. Time Rate Temp. Hoey 16m. | Still 45 19-4C. 9 7 ae 25 m. Stirred 7A = : 11.57 20 ion Vim | SH 27 ae ., isan, | SHimed | oy 20-2 Experiment 3: 4th June, 1895. Elodea in Tap-water. a.m. | Time | | os | be uy re 40 m. Still 40 i Ts, 26 m. Stirred 50 167 i Oa. Stirred 30 a A 20m. | Still | 13 | 17-2 C nat 12m Stirred 29 | i 1896.] water currents on the assimilation of aquatic plants. 83 Experiment 4: 5th June, 1895. Elodea in Tap-water. a.m. Time | | Rate | Temp. 10.37 ; eis \ 33m. | Still | 76 | 15-4C. ise } 17m. | Stirred | 166 | 15-4 a ies } | Pe | . | 40 | 158 11.33 9 35-5} seas és | ee | po as } | 26 m | Still 90 16-2 12.4 16-6 , BT } 33m. Stirred 142 16:8 12.38 , BB | 17m Me 34 17 t | | cele | ean | Still | 29 | 17-1 Experiment 5: 6th June, 1895. Elodea in Tap-water. | Time | Rate | Temp. 9.33 13-6 C 103} 53m. | Still | 76 We 10.29 14:5 ish | 44m Stirred 111 14:8 84 Mr Darwin and Miss Pertz, On the effect of [Feb. 10, Experiment 6: 10th October, 1895. Elodea. Fresh Tap-water. a.m. | Time Rate Quantity ? Temp. 10.35 . nie \ 30 m. Still 18 13 18 C. eth Aan | eee | Ae 27 18 a0 30 m. | Still | 15 Ag 18 Experiment 7: 12th October, 1895. Elodea, Fresh Tap-water. a.m. | Time | Rate Quantity | Temp. Sil Slim: Still 14 17 18 C. Soe Anam | Siteeal | - a0 35 18 tea Bllim, || Seni 6 25 18 1 rate means rate of bubbling. 2 quantity means amount of gas collected, expressed in eudiometer-graduations per minute, 1896.] water currents on the assimilation of aquatic plants. 85 Experiment 8: 21st November, 1895. Elodea. Old Tap-water. Aan Time | | Eafe’ | Oaaray |e Temp: niet 35m. | Still 52 10 15C. mcr Bin, 1) Seiecedhl| 9 45 ‘Id | 185 1236 30m, Stil 30 | 08 16 aait 30 m. | Strredsl)) 28 | AI Experiment 9: 9th October, 1895. Elodea in Fresh Tap-water. unde Rate | Quantity | Temp. 16m., 4 »,Still 19 31 16-5 0. 15m. Stirred 25 D8 16:5 teams Pe Sei 12 - 36 16-5 15 m. Stirred a ‘48 15m. | Still 45 31 | 165 Lam: Stirred | 22 | Z510) 16°5 86 Mr Darwin and Miss Pertz, On the effect of (Feb. 10, Experiment 10: 20th November, 1895. Elodea in Tap-water which had stood 24 hours. a.m, Time Rate Quantity Temp. 10.23 ; i115 BOn ese 16 08 150. | NOsrwerl) Kittel | 9% 10 fs = apf 39 m. Still 17 06 16 ei Wem | Sheed | 22 12 16°5 Altogether eleven experiments were made with Elodea. The results are fairly uniform, that is to say, the rate of bubbling - as taken by the stop-watch is nearly always markedly increased. Exceptions occur, however: for instance, in the “stirred” periods of Experiment 8 stirring did not increase the rate of bubbling, but in both cases the amount of gas actually yielded was greater. The same thing is true of the final “stirred” period of Experi- ment 9. Indeed there were no exceptions to the statement that the actual yield of gas per minute was greater when the water was stirred. We are inclined to believe that the results obtamed by measuring the gas are trustworthy because the amount of effect due to change of condition does not vary greatly. The following figures give, in round numbers, the effect of change from the “stirred” to the “ still” condition. 180 : 100 1 75: ery 16k fi ea wee M65. 1, 1896.] water currents on the assimilation of aquatic plants. 87 Experiments with Hottonia palustris. Only two experiments were made with this species: the results agree with those obtained for EHlodea. Experiment 11: 10th June, 1895. Hottonia. a.m. Time Rate Temp. he 35m. | Still 43 165 C ” 35 ; ; et Sse Saaremaa He ; teh | 4m. | Still 37 Experiment 12: 15th August, 1895. Hottonia. Old Tap-water. | p.m. |; Pime Rate Quantity Temp. 12 : ; 29 29 m. Still 21 22 24C 12.3) | aim. | Stirred | 35 32 Experiments with Potamogeton bilupsii. This plant, which is said to be a cross between P. coriaceus and P. plantagineus, happened to occur in convenient quantities in the Botanic Garden and was therefore used. The results were of a conflicting character: in two experiments in which freshly-drawn tap-water was used, the stirring un- doubtedly produced an increase in the yield of gas. But in the other ten experiments for which water was used which had stood in an open vessel for twenty-four hours, the stirring produced either increase or decrease or else was without effect on the yield of gas. 88 Mr Darwin and Miss Pertz, On the effect of [Feb. 10, Cause of the phenomenon in Elodea. There can be no doubt that the increased yield of gas when the water is stirred is simply due to the movement of the water bringing the leaves rapidly in contact with fresh layers of water and thus hastening the process of diffusion. It illustrates in fact the same phenomenon as the well-known experiment in which a strong solution of a coloured salt (e.g. potassium bichromate) is covered by a layer of water in order to demonstrate the extreme slowness with which the yellow colour spreads to the upper layers if the jar is undisturbed. It is clear that the effect of stirrmg on water-plants is a physical phenomenon in the sense that it is not necessarily con- nected with the act of assimilation. This is proved by taking advantage of the fact that aquatic plants placed in water highly charged with gas give off bubbles in the dark}. We observed this form of bubbling by using a feeble illu- mination just enough to enable us to count the bubbles, but quite insufficient for assimilation. When the water was stirred the rate of bubbling was clearly increased. In other cases where the dark- bubbling had ceased, 1t was started again by means of stirring. Assimilation. The question whether the increase in the yield of free gas produced by stirring necessarily implies increased assimilation is one to which we cannot give a complete answer. The solution involves a more complete control of the physical conditions than obtained in our experiments, as well as analytical data which we cannot at present supply. The gaseous exchange of an aquatic plant does not necessarily involve any yield of free gas, it depends primarily on diffusion of dissolved gases both into and out of the plant. The escape of bubbles is, as Devaux and others have pointed out, an accidental occurrence depending on the existence of fortuitous openings into the intercellular spaces. It is clear therefore that the yield of free gas cannot, without further inquiry, be assumed to represent assimilation. There is, moreover, as already pointed out, an evolution of gas quite independent of the action of light, depending on the gas- pressure in the water. Devaux has explained how it is that, in spite of the above considerations, the rate at which gas is given off does fairly well represent the activity of assimilation. 1 See Devaux, dnnales des Sc. Nat., 1889, p. 38, where the literature of the subject is given. 1896.] water currents on the assimilation of aquatic plants. 89 The oxygen which arises as a bye-product of assimilation is less diffusible than the CO, absorbed, and this necessarily leads to a rise of gas-pressure in the intercellular spaces, and to an escape of the internal atmosphere at any openings which may exist. It therefore follows that the more vigorous the assimilation becomes the more rapid is the escape. We have shown that in some cases at least stirring the water produces an increased yield of gas, there is therefore prima facie evidence that assimilation is actually increased. But unless we can ascertain in what way the amount of oxygen yielded as free gas and by diffusion is affected by stirring, we cannot be sure of the point. We have made a few analyses of the gas collected over water from Hlodea, using water which had stood for twenty-four hours as well as freshly-drawn water, so as to avoid errors from bubbling due to gas-pressure. Elodea. Feb. 13, 1896. Fresh Tap-water. O per cent. 9.58 to 11.34 am. | still 22 11.38 a.m. to 12.43 p.m. | stirred | 20 Feb. 17, 1896. Fresh Tap-water. 9.55 to 11.10 a.m. stirred | 19 11.13 a.m. to 1.10 p.m. | still 22 Feb. 12, 1896. Old Tap-water. 9.55 to 11.32ta.m..|) still 22 11.38 a.m. to 12.44 p.m. | stirred | 19 Feb. 18, 1896. 10 to 11.23 a.m. | stirred | 19 11.26 a.m. to 12.45 p.m. | _ still 20 The percentage of oxygen is remarkably low in these cases. Devaux found the percentage of oxygen yielded by Hlodea in the light to be about 25 p.c., and we have, in earlier experiments, found a similar proportion. On the other hand we have also found Elodea yielding no more than 20 p.c. when the evolution of gas was certainly nearly all due to assimilation since it was diminished to a quarter of its former amount by darkening the plant. Moreover, Devaux has shown that in darkness Hlodea may give off gas containing only 16 p.c. of oxygen, and we have found that Hottonia may only give off 14 p.c. of oxygen. It seems possible therefore that a yield of 19 p.c. of oxygen may be an index of assimilative activity. 90 Mr Burkill, On a collection of Plants [Feb. 10, With Hottonia the few experiments we made were more satis- factory. Aug. 1. Old Tap-water. still 23 p.c. oxygen stirred 22 ,, si Aug. 2. Old Tap-water. still 9923 stirred 23 In the case of Potamogeton the results were conflicting, but on striking an average it was clear that no marked effect on the percentage of oxygen was produced by stirring. It is worth noting that the percentage of oxygen yielded by Potamogeton is always much higher than that given by Hlodea or Hottonia, being occasionally as high as 58 per cent. We are unable to suggest a reason for this difference. For Elodea and Hottonia the case stands thus: stirrmg does not seem markedly to affect the percentage of oxygen, while it increases the yield of gas. If so, the total amount of free oxygen yielded must be increased, and this probably implies increased assimilation. Although the evidence from gas analysis is not conclusive, we have shown by a direct evidence that assimilation is increased by movement of the water. This was proved to be the case by cultivating water-plants in still and running water, and observing, by means of Sachs’ iodine-test, the relative amounts of starch produced. The plants were de-starched by darkness before being used for the experi- ment, and care was taken to ensure identity of temperature and illumination. Two trials were made with Hlodea and one with Potamogeton, with identical results; namely, that all the specimens from the running water contained distinctly more starch than those from the still water. : (4) On a collection of plants from New Britain (New Pommern). By I. H. BurkI1u, M.A., Gonville and Caius College. In 1875 Baron A. von Hiigel visited several islands in the Pacific, and brought back collections of plants from Ovalau in the Fiji group, Upolu in the Samoa group, from the Duke of York’s Island (New Lauenburg), and from New Britain. The last-named island he was unable to visit in person, and had, therefore, to entrust the collecting entirely to his collector. Unfortunately a number of accidents caused the loss of a large part of the collections, and the remaining material only represents a portion of what had been obtained. These collections were subsequently presented to the University Herbarium. 1896.] from New Britain (New Pommern). 91 The specimens from Ovalau proved to be all known Fijian forms ; so also those from Upolu were, with one exception—a new orchid!,—known Samoan forms. Our knowledge of the botany of New Britain is very incomplete, and consequently the following enumeration will be found to contain the names of many plants hitherto unknown from this island. At the end of this paper is a bibliographical list to which reference will be made by means of roman numerals. One early botanist, Commergon, who accompanied Bougainville in his voyage round the world, came very near to landing on New Britain; but the island, called New Britain in the narrative of the voyage, is in reality New Ireland. The part of New Ireland visited by him is in the south, or New Britain end of the island—a district, Bougainville says, ‘not very rich for the botanist’. Commergon’s collections, including more than 3000 species from all parts of the world, which he never lived to bring to Europe, lie in the Paris Museum ; but it must be remembered that it is erroneous to refer to any of them as from New Britain. The north end of New Britain, constituting the Gazelle Penin- sula, though not yet completely explored, is known to be a very rugged region with steep volcanic mountains, rising to considerable heights in Mts Fitzgerald and Beautemps Beaupré. On the north coast of this peninsula les Blanche Bay, in the neighbourhood of which these plants were collected. The bay les under a range of hills rising to 2000 feet and containing an active volcano. Our knowledge of the botany of the island is practically confined to its vicinity. The interior, as indeed the greater part of the coast, remains a terra incognita. New Britain is by no means isolated. The channel between it and New Ireland (New Mecklenburg) is only 30 miles wide, and in it lies the Duke of York’s Island (New Lauenburg) with its attendant islets: through this long island of New Ireland we have a land-link to the island of New Hannover, and so to the Admiralty Isles. To the South-east at no very great distance le the Solomon Isles; but unfortunately the island of Bougainville, which is the nearest, is the least known. The western extremity of New Britain approaches very near the coast of New Guinea, and the gap between the two islands is bridged over by a number of islets. From its geographical position, we should then expect New Britain to possess a flora of a Papuan type, and such indeed the fauna seems to be’*. 1 Rolfe, New Orchids. Decade 17. Kew Bulletin of Miscellaneous Information, 96. 2 A Voyage round the World. English edit., London, 1772, p. 330. 3 Wallace, Australasia. London, 1888, p. 469. 92 Mr Burkill, On a collection of Plants [Feb. 10, ENUMERATION OF SPECIES obtained in the vicinity of Blanche Bay. PTERIDOPHYTA. Asplenium Nidus L. Aspleniwm falcatum L. Nephrodium latifolium Baker. Nephrolepis acuta Presl. Polypodium adnascens Sw. Polypodiwm sinuosum Wall. Polypodium [inne Bory. Lycopodium carinatum Desv. Selaginella canaliculata Baker. ANGIOSPERMH. Monocotyledones. Panicum jgavanicum Poiret. Centotheca lappacea Desv. (recorded XVIIL). Mariscus Sieberianus Nees. Calamus sp. Cordyline terminalis Kth. var 71 Baker. Alpinia (Hellenia) oceanica mihi (A. nutans K. Schum. non Rose.) (recorded xvi.). Professor Schumann has described this species, although not yet found in New Guinea, in the flora of Kaiser Wilhelms Land?, and, supposing it to be a form described by Rumphius, on which Linnezus founded his species Globba nutans, named it Alpima nutans. I cannot agree with him in this complicating of the synonymy. The matter may be sifted somewhat as follows. In the Herbariwm Ambot- nense? Rumphius describes five species of Globba, of which the last Globba sylvestris was found in two forms; these he distinguishes as Globba sylvestris major and Globba sylvestris minor sive florida’. Linneus did not see even varietal ditference between them, and called Globba sylvestris of Rumphius Globba nutans’. Subsequently Roscoe® thought his Alpinia nutans to be Globba nutans L., the two being in size and habit somewhat similar, but probably erred. Miquel® saw in Alpinia gigantea Bl. one element of Linnzeus’ species, 1 Schumann u. Hollrung, Flora von Kaiser Wilhelms Land. Berlin 1889, 28 p. 28. 2 Amsterdam 1750. Lib. x1. Cap. xx1x. 3 loc. cit. Cap. XXXII. 4 Mantissa, ii. Stockholm 1767, p. 170. 5 Roscoe in Smith, Ezotic Botany, 1. London 1805, p. 93, and Monandrian plants of the order Scitamineae. Liverpool, 1828, t. 73. 6 Flora Indiae batavae, 11. Amsterdam 1855, p. 605. 1896.] from New Britain (Neu Pommern). 93 namely Rumphius’ form major; and there are many reasons which make one regard this as correct. Now Schumann sees in his Alpinia nutans the other element, namely Globba sylvestris minor, —a decision the correctness of which is questionable. The follow- ing statements give the reasons for and against Schumann’s iden- tification. Alpinia nutans K. Schum. agrees with Globba sylvestris minor in its nodding inflorescence, persistent bracts, leaves less than two palms’ breadths broad, and narrow petals. In other points, however, it differs, thus :—leaves oblanceolate instead of lanceolate and not undulate (cf. Rumphius’ figure LXIII.), tapering very rapidly above to a shortly acuminate point, flower not conspicuously red, yellow and white. The reader, remembering the difficulties which beset the identification of species of Alpinia, will form his own opinion upon the necessity of caution in this case. The probabilities seem to be in favour of the following decisions being correct. Alpinia nutans Roscoe (1805), not known till described by Wendland! as Zerumbet speciosum in 1798. Alpinia gigantea Blume (1830), apparently the plant figured by Rumphius as Globba sylvestris major, and therefore is Globba nutans L. Alpinia nutans K. Schumann (1889) may possibly be, but probably is not, Globba sylvestris minor, but if so is also Globba nutans L. For this last species I propose the name A. oceantca. Hollrung collected A. oceanica on the two islets of Mioko and Kerawara belonging to the New Lauenburg group’; Warburg has obtained it from Kerawara and the north of New Britain (XVII). In the Kew Herbarium are specimens from the following sources: Quadalcanar, Solomon Isles, Milne, 1855,—Admiralty Isles, Moseley, ‘Challenger’ Expedition,—and New Ireland, Barclay*. All these localities lie fairly close together, the most westerly being more than 1200 miles from Amboyna. A. oceanica lies very near A. scabra Benth. from British India, and is easily distinguished from other species of the section Hellenia with a nodding inflorescence such as A. decurva Ridley. Baron von Hiigel’s specimens lead one to suppose that the curvature of the inflorescence becomes more marked as it grows older, being very slight when the buds first begin to open, In cases where the flowers are much crowded the axis of the inflor- escence becomes twisted so as to obscure the 4 divergence which is present. Such might account for the want of it in Rumphius’ figure. 1 Schrader et Wendland, Sertum Hannoverianum, tv. Gottingen, 1798, 3, t. 19. 2 Flora v. Kaiser Wilhelms Land. loc. cit. 3 Bentham recognised it as a new species. Enumeration of plants collected in the Feejee Islands, Tanna, New Ireland and New Guinea. Hooker’s Lond. Journ. of Bot. 11. (1843), p. 235, 94, Mr Burkill, On a collection of Plants [Feb. 10, Dicotyledones. Piper caninum Dietz. Pouzolzia indica Gaudich. (recorded XVIII). Ficus tinctoria Forst. Amarantus melancholicus L. var. tricolor Lam. (recorded from Blanche Bay 111.), and also an intermediate form approaching the type. Celosia cristata L. Muehlenbeckia platyclados Meissn. (recorded VIII). Clematis aristata R. Br. var Pickering O. Kze. Indigofera Anil L. Desmodium wmbellatum D.C. (recorded XvIt1.). Uraria lagopoides D.C. Phaseolus Mungo UL. (recorded 1x. and Xv.). Vigna retusa Walp. (recorded XVIII). Cassia glauca Lam. Soulamea amara L. (recorded vViil.). Mallotus ricinoides Mill. Arg. Macaranga sp. near WM. tanarius Mill. Ar ge. ff only. | The pith has been bored, probably by an ant; the leaves, which are very similar to those of I. tanarius, bear on the upper surface near the base 5—7 nectaries. Doubtless it is myrmecophilous. | Cordieum variegatum Bl. both the variegated form and that with green leaves. Phyllanthus Finschti K. Schum. (recorded xvut). To the known distribution of this plant,—viz. New Guinea (XvV.) up to 1800 metres!, Gazelle peninsula and Mioko (xvut.),—I can add New Ireland, from whence a specimen collected by Barclay is pre- served in the Kew Herbarium. The proportion of ¥ flowers to ¢ must be very high if the trees are equally divided between the two sexes. Schmidelia littoralis Bl. Colubrina asiatica Brongn. Calophyllum imophyltlum L. Triumfetta suffruticosa Bl. (2) Thespesia populnea Soland. Abutilon graveolens W. and A. Urena lobata L. (recorded vu.) var. scabriuscula Mast. Hibiscus rosa-sinensis L. flore pleno. Hibiscus tiliaceus L. Sida rhombifolia L. Melochia indica Wall. Dischidia Collyris Wall. (recorded XV1I1.). u Warbares Bergpflanzen aus Kaiser Wilhelms Land. Engler’s Bot. Jahrb. xvi, (1893), p. 14. 1896.] from New Britain (Neu Pommern). 95 L[pomea Turpethum R. Br. Physalis minima Don. (recorded 111.). Solanum tetrandum R. Br. Hemigraphis reptans Eng). Eranthemum Huegelii mihi n. sp. Caulis fulvide scaber. Folia lanceolata, in petiolos sensim contracta, supra minute sca- brida, subtus nervis exceptis glabra, nervis lateralibus utrinque 10—12 arcuatim ascendentibus. Inflorescentia foliis longior, floribus in cymulis, infimis 2—3-floris, supernis 1-floris, dispositis, pedicellis quam bracteis subulatis longioribus, calyci eequilongis. Calyx, apicibus glabrescentibus exceptis, glaber, laciniis anguste linearilanceolatis quam tubo 3—4-plo longioribus. Corolle tubus longus, lobis oblongis 3—4-plo longior. Antherz ultra fauces exserte. The leaves have the lamina about 15 cm. in length by 4 cm. in breadth, and resemble considerably those of Hranthemum malac- cense Clarke; the petiole is less than 2 cm. long: the flower is most conspicuous, having a tube 3°5 to 4 cm. long and lobes up- wards of 15 mm. long: the ovary is about 2 cm. long when ripe, and carries 4 seeds: the anthers are exserted to the distance of 3 mm. Of two inflorescences, in one the lower part carries no deve- loped flowers, and in the other the lowermost flowers appear to be cleistogamic, while the upper ones are chasmogamic. Cleisto- gamy is known in the Indian members of the genus from the re- searches of Kurz? and Scott”. E. affine Warbg. (Xvul.) connects #. Huegelii with EF. paci- ficwm Engl. (111.), but is quite distinct. H. Huegelit is a more robust plant than H. malaccense. E. affine and E. pacificum are known from the neighbourhood of New Britain, and £. malaccense only from the Western Malayan region. LH. Huegeli belongs, like all these species here mentioned, to Lindau’s genus Pseuderan- themum’. Eranthemum sp. near E. laxiflorum A. Gray. Tournefortia argentea Forst. Leucas flaccida R. Br. Orthosiphon stamineus Benth. Callicarpa pedunculata R. Br. Callicarpa eriochlona Schauer. This plant, first described from the Philippine Isles and since found in New Guinea, is by no means identical with C. cana L. to which it has been united. 1 Dimorphism in Eranthemum. Journ. of Bot. x. (1872), p. 46. 2 Dimorphism in Eranthemum. Journ, of Bot. x. (1872), p. 161. 3 Xantheranthemum und Pseuderanthemum, zwei neue Gattungsnamen d. Acan- thaceen. Gartenflora, 1893, p. 612. 96 Mr Burkill, On a collection of Plants [Feb. 10, C. cana has a hoary appearance due to stellate hairs which branch once or rarely a second time; while C. eriochlona is very densely covered on the stems and below the leaves with a dense wool of tawny shaggy hairs branching 4—8 times or even more. Morinda citrifolia L. Benincasa cerifera Savi. Scevola Kenigit Vahl. Wedelia strigulosa D.C. In concluding it may be well to gather together the shreds of information which we possess on New Britain botany, and see what can be constructed out of them. In the various papers hitherto published we find mention of just over 160 species,—a fact which testifies to our ignorance of its flora. Of these species a considerable portion consists of wide-spread plants common on the Pacific and Malayan coasts, and some such as Touwrnefortia argentea and Bea Commersoni R. Br.* which are confined to a coral formation. About two-thirds of the whole number are known from German New Guinea, one-seventh from the little- known Admiralty Isles, a fair percentage from the Solomon Isles, and barely one-half from Fiji. A small number of new species, described from specimens from New Britain, have not yet been discovered elsewhere; but it is very improbable that most of these are endemic forms. An island which helps to connect three regions such as Australia, Malaya and Polynesia, may be expected to yield in- teresting results in botanical geography; but at present many years must pass before this is brought about. A few of the specimens in Baron v. Hiigel’s collection could not be determined: among them were three species of Ficus which were too imperfect, a Macaranga (?) probably new, and some others. Finally, I wish to tender my sincere thanks to the members of the staff of the Kew Herbarium, to Mr C. B. Clarke and to Baron Sir Ferdinand von Mueller for the considerable assistance which they have given me, and most especially to Baron A. von Hiigel for the many kindnesses which I have received from him. BIBLIOGRAPHY OF NEW BRITAIN BOTANY. 1. Baxer, J.G. A Summary of New Ferns, 1874-91. Anns. of Bot. v. (1891), p. 480. 11. Bockener, O. Die auf d. Expedition S.M.S. ‘Gazelle’ gesam- melten Cyperaceen. Engler’s Bot. Jahrb. v. (1884), p. 89. 11. Eneurer, A. Die auf d. Expedition 8.M.S. ‘Gazelle’ gesam- melten Siphogamen. Engler’s Bot. Jahrb. vir. (1886), p. 444. 1 Clarke, ‘“‘ Cyrtandree”’ in De Candolle’s Monographie Phanerogamarum, v. 1883, p. 145. 1896.] from New Britain (Neu Pommern). 97 Iv. Hackent, E. Die auf d. Expedition 8.M.S, ‘Gazelle’ gesam- melten Gramineen. LEngler’s Bot. Jahrb. vi. (1885), p. 233. v. Hennines, P. Fungi novo-guineenses. 11, Engler’s Bot. Jahrb. xvull. (1894), Beibl. 44, p. 22. vi. Linpau, G. Acanthacee papuane. Engler’s Bot. Jahrb. x1x. (1894), Beibl. 48, p. 3. vi. MueEwuer, F. v. Description of a species of Eucalyptus from New Britain. Australian Journ. of Pharm. 1886. July. VIII Two new species of Sterculia discovered by R. Parkinson in New Britain. Australian Journ. of Pharm. 1887. Feb. Ix. -———- Descriptive notes on Papuan plants. v. Melbourne, 1878. x, Mutter, J. Die auf d. Expedition d. Gazelle gesammelten Flechten. Engler’s Bot. Jahrb. 1v. (1883), p. 53. x1. Naumann, W. O. Vegetationscharakter d. Inseln d. Neu- Britannischen Archipel u. d. Insel Bougainville. Engler’s Bot. Jahrb. vi. (1885), p. 422. xu. Parkinson, R. Im Bismarck Archipel. Leipzig, 1887. xin, Preit,G. J. Land u. Volk in d. Bismarck Archipel. Verhandl. d. Ges. fiir Erdkunde zu Berlin, xvii. (1890), p. 144. xiv. Powerit, W. Wanderings in a wild country. London, 1884. xv. Scuumann, K. Die Flora d. deutschen ost-asiatischen Schutz- gebietes. Engler’s Bot. Jahrb. 1x. (1888), p. 189. xvi. Stuper, T. Ein Besuch auf d. Papua-Inseln nordlich von Neu-Guinea. Deutsch. geogr. Blatter, 1. Bremen (1877) p. 182. xvi. WarsurG, O. Die Flora d. asiatischen Monsungebietes. Ges. fiir deutsch. Naturf. u. Aerzte. Leipzig, 1890. Beitrage zur Kenntniss d, papuanischen Flora. Engler’s Bot, Jahrb. x11. (1891), p. 230. xix. Askenasy, E., THtmen, F. v., Kunn, F., Encaurer, A., and others in Forschungsreise 8.M.S. ‘Gazelle’ in den Jahren 1874-76. iv. Berlin, 1889. Monday, 24 February, 1896. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. J. Reynolds Green, Se.D., Trinity College; Charles Cave, B.A., Trinity College; J. Parkin, B.A., Trinity College, were elected Fellows of the Society. The following Communications were made to the Society : (1) Kaxperiments on Liquid Avr. By Professor DEWAR. VOL, IX, PART II, 7 98 Mr Brill, On the Generalization of [Feb. 24, (2) On the Generalization of certain Properties of the Tetra- hedron. By J. Britt, M.A., St John’s College. 1. Ina paper? published in the Messenger of Mathematics for last August, I obtained a generalization of some of the properties of the plane triangle with the aid of ordinary algebra. I now propose to utilize the theory of binary matrices to obtain a generalization of the corresponding properties of the Tetrahedron. The methods used will be found to bear a close analogy to those used in a paper printed in the sixth volume of the Proceedings of the Society®. 2. In order to facilitate the working out of the subject, we will adapt the notation used by Hamilton in his theory of quater- nions to the theory of binary matrices, which is really the theory of quaternions in a somewhat different form’®. Let m be a binary matrix whose characteristic equation is We will define the operators U and W with the aid of the equations Um=x, (WmP=p, where, for the sake of definiteness, we suppose that Wm represents the positive value of Vu. The operator K will be defined by the equation Km = 2X —m, so that we have TO Aes = VAUD apecasebasosesedbecsos: (2). We also have m.Km=Km. m= 2\m —m?=p=(Wm)?......-.. (3). In addition to the above operators, we will introduce an operator V defined by the equation m= Um+ Vm, so that we have 1 «Note on the Application of Analysis to Geometry.” Messenger, xxv. 49—59. 2 « A New Geometrical Interpretation of the Quaternion Analysis.” Proc. Camb. Phil. Soc., vi. 156—169. 3 It will be seen that K and V correspond to Hamilton’s K and V, while U coaepene to his S, and W to his T. Hamilton has no symbol corresponding to L, 1896.] certain Properties of the Tetrahedron. 99 and therefore (Wm) =m. Km =(Um + Vn) (Um — Vm) = (Um) - (Vm). Thus we obtain, for the characteristic equation of the matrix Vm, the equation (Vmy +(Wmy — (Umy = 0, from which it follows that UVm=0, WVm= {(Wmy —(Um)}3........004. (5). We also have (Kmy =(Umy — 2UmVm + (Vimy = 2 (Umy— 2UmVm— (Wm) = 2UmKm —( Wm), or (Kmy —2UmKm + (Wm) =0, from which it follows that Ran Oni Wk = Witte 2 to area es (6). Now suppose that we have a second matrix mm’, whose character- istic equation 1s DUS —— Pe cole flO acon 5 o'tain tem spe (7). Then, in addition to equations (1) and (7), we have an equation involving both m and m’, of the form mov’ + m'm — 2r’m — 2m’ + 2v=0 1... eee (8). The equations (1), (7), (8) are said to constitute the catena of relations satisfied by m and m’. We will introduce one more symbol L, defined by the equations dsp, = Li 90S Wises bi4 Werveytaee> Abd. (9). We have mKm' +m’ Km = m(2Um' — m') + m' (2Um — m) = 2mUm’ + 2m’ Um — (mn + m'm) SS OMAR RS Pie cll acicta de cake anda acnane (10), by means of equation (8). In the sequel we shall sometimes be concerned with the matrix unity. When it is necessary to bring this matrix in evidence we shall denote it by the symbol w, otherwise we shall treat it in th customary manner. ‘The said matrix has both its latent root: equal to unity, and thus we shall have Uw=1, Ww=1, Ko=o, Vo=0, Imo = Lom = Um. ~I | bo 100 Mr Brill, On the Generalization of [Feb. 24, The catena of relations satisfied by m and m’ may be written in the form m —2mUm +(Wm) = 0, m?— 2m’ Um’ + (Wm'P= 0, mm + mm — 2mUm' — 2m’ Um + 2Lmm’ = 0. From these we may readily deduce the characteristic equation of a matrix of the form wm+ ym’, where w and y are scalars. We have (am + ym’) = am? + vy (mm' + m'm) + ym? = 2 (am + ym’) (ca@Um + yUm’) — {a (Wmy + 2eyLmm' + y? (Wm'y}. Thus we obtain U (am + ym’) = 2Um + yUm’............... (11), and, as a special case, Uaem = «Um. Thus the operator U is commutative with scalars, and is also distributive in its operation. It follows from equations (2) and (4) that the operators K and V possess the same properties. Further, the formula (11) is capable of generalization by suc- cessive application, so that we obtain UxSam=ZaUm, KYam = X«2Km, Viren Sa Vii ee eee (12). We also have {W (am+ ym’)}? = 2 (Wm) + 2ayLmm' + y? (Wim'y. This equation also may be generalized by means of a property of the symbol L, which we proceed to develope. We have 20 (2am .m)=(Lam) Km’ +m’ Kam = La (mKm’ +m’ Km) = Opals 10), Been ee een (18). Also, if in (8) we write m’=™m, it reduces to (1), so that we have Im? = (Wm). Thus we obtain . (Wiamy = L (Samy = alm? + QSaa' Lm’ = 2a? (Wm) + 22ae' Lmim’...(14). 1896.] certain Properties of the Tetrahedron. 101 The characteristic equations of mm’ and m’m may readily be deduced from the catena of relations satisfied by m and m’. They will be found to be (mm) — 2mm’ {2Um Um! — Imm’} + (Wm. Wm')?= 0, (m'm)? — 2m'm {2UmUm' — Imm’} + (Wm. Wm') = 0. Hence we have Umm = Um'm = 2UmUm’ — Imm’ ...........4... (15), and Ward = Weare = Win WI esac ssxvaneinx Sargon (16). We must here take notice of a peculiarity of the symbol Z, which does not belong to the other operative symbols we have made use of, viz. that L (mm’.m’) is not equivalent to L(m.m'm’), nor may we replace L(mm’.w) by Imm’. This is evident from the definition of Z, and may also be brought out with the aid of equation (15), which may be made to furnish us with ex- pressions for the two quantities to be compared. Finally, we have Km. Km =(2Um’ — m’)(2Um—m) =4Um Um’ — 2mUm' —2m'Um+ m'm = 4UmUm' — 2Lmm' — mm’ =2Umm — mn’ = Kmnv. 3. The matrices that we shall make use of in this paper will, for the most part, be expressed in a special form. We will suppose p and q to be two constant matrices satisfying the catena of relations ap? — 2hp + b=0, aq? — 29q+c¢=0, a (pq + gp) — 29p — 2hg + 2f=0, where a, b,c, f, g, h are scalar constants; and the matrices with which we shall be chiefly concerned will be of the form m=x+ py + QZ, where w, y, 2 are scalars. Now we have aUp=h, aUq=g, a(Wp)=b, a(WaqyP=c, aLwp =alpwo=aUp=h, aLwg = algo =aUq=4Q, alpq = aLqp =f. 102 Mr Brill, On the Generalization of [Feb. 24, Hence, by means of the first of equations (12), we have aUm= ax + hy + gz. From equation (14) we obtain a (Wm) = aa? + by? + cz + 2fyz + 2gza + 2hey. If we introduce a second matrix of the given form, viz. m’ = x + py’ + gz’; then, with the aid of equation (13), we readily deduce aLmm' = axa’ + byy’ + ze +f (yz +y'2) +9 (za +20) +h(ay' +2'y). 4, We now come to the establishment of a connection of our analysis with geometry. We will suppose in the first place that our axes of coordinates constitute a right-handed screw system. Next, we will suppose that we have a set of three points whose coordinates are (4, Y:, 21), (@2, Yo 22), (Xs, Ys, Zs), and also a second set whose coordinates are (a, Y1, 21), (25 Yos 2), (#3, Ys, 23). We will consider these two triads of points as determining two planes ; and will suppose the origin to be so placed that the cyclical order of the subscripts given above corresponds, in each instance, to a right-handed rotation about that normal to the plane of the triad which is drawn away from the origin. Further, we will write 2X = My “A; 1 ? 2Y= 4, %, 1 ? Uhp Gp ak LEU Peta | ho, Cap. Ley dee dl WAS iy Oho loll, Fis Op. Gis Ding Ab and will suppose that X’, Y’, Z’ denote quantities formed in a similar manner from the coordinates of the points constituting the second triad. We will now write m=X+pY +qZ, m'= X'+pY'+qZ; and, then, by means of the results obtained in the last article, we have a(Wm) = aX?+ bY? + 0Z?4+ 2fYZ+2gZX + 2hXY, a( Wm’)? =aX"+bY 2+ cZ24+ 2fY'Z! + 2gZ'X’ + 2hX'Y’, aLmm =aXX'+ bYY'+¢ZZ'+f(YZ' + YZ) +9 (ZX'+ ZX) +h(XV'+ X’Y). 1896.] certain Properties of the Tetrahedron. 103 We will suppose (a, Y, 2) to be the coordinates of some point lying on the line of intersection of the two planes defined by our two triads of points. Then the equation of any plane passing through the said line of intersection may be written in the form (# —ao) (X + kX") +(y — yo) V+hY’) +(2—%4)(Z+k2Z’)=0............. (17). Now consider the cone A (@— mY + Bly — yy +O (2-— al + 2F (Cy — yo) (2 — 2) + 2G (2—%) (¢ —%) + 2H (a — x) (y—y) =0.....(18), where A=be-f?, B=ca-g*, C=ab—h?, F=gh—af, G=hf—bg, H= fg —ch. To find the values of k corresponding to the two tangent _ planes to (18) passing through the line of intersection of the planes defined by our two triads, we have to express the con- dition that the normal through (a, y, %) to (17) lies on the normal cone of (18). This gives us a(X +khx’Py+b(V+kY'P+e(Z+kZ’y + 2f(V+kY’)(Z+kZ’) + 29g (Z+hZ') (X +kX’) + 2h(X +kX')\(VY+kY’)=0. If this be expanded, it will be seen that it can be written in the form (Wm) + 2kLimm’ + kh? (War'y? = 0....... 0.00008 (19). If k, and k, be the roots of (19), we have 2Imm’ pete V Gay: aS (Wm'y?’ and therefore 1 ((la\* a) Dam _ 2 (2) + ~~ Wm. Wm’ Now k,/k, is one of the anharmonic ratios of the set of four planes constituted by the two planes defined by our two triads and the two tangent planes to (18) through the edge in which they meet. If we replace this ratio by the symbol e8, we have Linn’ = — Wm Wim’ cos @. 104 Mr Brill, On the Generalization of [Feb. 24, 5. Suppose that (i; Y1> 2), (a, Yr, 2), (5, Ys 23), (Gans Ys; Z,) denote the coordinates of four points, so situated that the origin of coordinates lies within the tetrahedron formed by them. We will write 2X,=| Yo, 2, 1), 2X.=| ys, 4%, 1 Thy iy | Wig) Cio ok Oh Gy il | Ope Vang P= Oy Big Il |, 2h =| ty Ao 1! ; Wey ig 1s Ops Wie. to by 25 Il (opie Ak | We will also write Y’s with the same subscripts to denote what these expressions become when for the 7’s are substituted the corresponding z’s, and for the z’s the corresponding 2's. Also we will use Z’s with the same subscripts for the expressions obtained when for the y’s are substituted the corresponding 2’s, and for the 2’s the corresponding ys. In the above it is to be understood, as before, that our axes of coordinates constitute a right-handed screw system. Also the corners of the tetrahedron are understood to be so placed that the cyclical order of the subscripts in the expression for any X is sup- posed to be that given by a right-handed rotation about the outward drawn normal to the corresponding face of the tetra- hedron. We have X,4+ X%,4+ X,+ X,=0, Y,+ Y.4+ Y,+ Y,=0, 1,+ 4,4+ 4,4 Z,=0. Therefore, if we write m, =X,+pY,+q4, m,=X,+pY,+ qh, m;= X;+pY;4+ qZ;, m= X,+pV¥,4+94,, we have My +s “EN s 1, —\O Pawn caisaeeen aeeecee ee (20). 1896. ] certain Properties of the Tetrahedron. 105 From this we immediately deduce the equation Km, + Km, + Kim; + Kimg=0 oo. ec eee eee ee (21). From (20) we have mKm, + mkm, +mKhm, + m,km, = 0, and from (21) we deduce mKm, +m,Km, + mK; + mK, = 0. Adding these two equations, and making use of equations (3) and (10), we obtain (Wm, + Lmym, + Lmyms; + Lnym, = 0... cece (22). For simplicity we will denote the edges of the tetrahedron by the symbols (12), (13), (14), (84), (42), (23), the numbers denoting the subscripts of the coordinates of the points joined by these edges. We shall also denote the angles of the anharmonic ratios corresponding to the edges (12), (13), (14), (34), (42), (23) by the respective symbols a, 8, y, 8, ¢, y. Further, we shall write aX2+bY2+cZ2+ 2fY,2, +e 297,X + 2hX,Y,= P?, and shall denote by the symbols Q, R, S the quantities corre- sponding to P when the subscripts 2, 3, 4 are substituted for the subscript 1. This being premised, we immediately obtain for the interpre- tation of equation (22), the relation P=Qcos6+ Roos $+ Scos wp. Similarly we should obtain Q=Rcosy +8 cosB+P cos @, R=S cosa + Pcos$+Q cosy, S=Pcosp+Qcos8 +f cosa. Eliminating P, = R, S from these four equations, we obtain lee cos @, cos, cos | =0. | cos j —1, cosy, cos B | cos, cosy, —1, cosa | cosy, ‘cos 8, cosa, —1 Thus the six angles a, 8, y, 8, , w are connected by a relation exactly similar to Cayley’s relation connecting the dihedral angles of a tetrahedron. 106 Mr Brill, On the Generalization of [Feb. 24, If m; be the matrix corresponding to any fifth plane, we readily obtain from equations (20) and (21) the result Imm, + Lmm; + Lmym; + Imm; = 0. Hence if x1, x2, Xs, Xs denote the angles of the anharmonic ratios corresponding to the respective sets of four planes consti- tuted by the given plane, one of the faces of the tetrahedron, and the two tangent planes to (18) through the line in which they meet, we have P cos x, + Q cos x. + L cos x, +S cos x, = 0. 6. From equations (20) and (21) we have mK = (m, + ms + ms) (Km, + Km; + Km,). Expanding this we obtain (Wm)? = ( Wm.) + (Wins)? + (Win)? + 2Lmyin, + 22mm, + 2Lm,ms, that is P= Q?+ B+ 8 — 2RS cos a — 28Q cos B — 2QRK cos x. Similarly we should obtain Q = e+ 8? + P?—28P cos vw —2PR cos d — 2RS cos a, R2= 8 + P?+Q?—2PQ cos 6 — 2QS8 cos B —2SP cos wp, S= P?+ + R?-—2QR cos y —2RP cos 6 — 2PQ cos 0. By adding these four relations we obtain a symmetrical rela- tion, which may be obtained direct from equations (20) and (21) as follows. We have (m, + M+ m3 + m,) (Km, + Km, + Km;,+ Km,) = 0, which on expansion becomes (Wm)? + (Wm) + (Wms)? + (Wm)? + 2Lmsm, + 2Lmn, + 2Imym,; + 2Lm ym, + 2Lnym; + 2Lm,m, = 0. Interpreting this we have P24+Q04+ +8 =2RS cosa+28Q cos 8 + 20K cos y + 2PQ cos 0+2PR cos d + 2PS cos wp. We also have a set of equations of the form (m, + m.) (Kinny + Km) = (ms + ms) (Kim; + Ky). On expansion this gives P?+@— 2PQ cos 0= R?+ 8S? — 2RS cosa. 1896.] certain Properties of the Tetrahedron. 107 The other relations of this set are P?+ R-2PReoos $= 8+ Q? — 28Q cos B, P? +S — 2PS cosw= Y@ + R?—2QR cos x. 7. If we write down the first three results of Art. 5 in their symbolical form, we have (Wm, + Liym, + Lim; + Lm, = 0, Imm, + (Wm.) + Imm; + Imm, = 0, Imm; + ILmym; +(Wms;)?+ Lmym, = 0. From these three equations we readily deduce (Wmy, Imm, Imym, |+| Lim, Lmm,, Lmygm, | =0. Imm,, (Wm,), LImyms Imam,, (Wm.?, Lmn, Imm, Imm, (Wms)? Imm,;, Imm, (Wms)? Thus, taking account of equation (20), we obtain | (Wm, Lmm,, Imm, Imym,, (Wm), Lmzms Imyn,, Im,m;, (Wms) =| L(m,+ms+ ms) my, L(m,+m;,+m,)m,, Lm, + ms + m4) ms; ILmm,, (Win.), Imm, Imym,, Lmms, (Wms)? =| (Wm), Lmm, Lmym, Imym,, (Wm), LIm,ms Imm, LImm;, (Wms)? =|(Wm.,), Lmm;, LImyn, Im.m;, (Wm;,)?, Lmgsm, Imyn,, Lmgm,, (Wim) This result may be written in the form P?| —1, cos @, cosd |=S?| —1, cosy, cos cos@, —1, cosy cosy, —1, cosa cos, cosy, —1 cos, cosa, —1 108 Mr Larmor, On the absolute Minimum _ [Feb. 24, We may also obtain similar relations connecting Q and R with S. Thus we have JOE OA A Jao SF 3 | ib eesinn, GOS/S: cosy, —1, cosa cos 8, cosa, —1 —1, cosa, cosh cosa, —1, cos w cos , cosy, — 1 —1, cosy, cos8|:| —1, cos, cosh cos, —1, cosé cos @, —1, cosy cos8, cos@, —1 cos ¢, cosy, —1 (83) On the absolute Minimum of Optical deviation by a Prism. By J. Larmor, M.A., St John’s College. When a ray of light crosses a prism in a principal plane, it is of course well known, and easy to verify graphically, that the deviation suffered by the ray is least when it crosses the prism symmetrically. It seems also to be recognized that no deviation smaller than this can be obtained when the ray does not pass in a principal plane; though I have not met with any valid demonstration’ of this result. The following proof may therefore be worth recording. The inclinations y and 7’ of an incident and refracted ray to any plane normal to the refracting surface, for example their inclinations to the principal plane of the prism, obey the law of sines sin» =p Sin 7’. Hence, after passing across a prism, the emergent ray is in- clined to the refracting edge at the same angle $a — 7 as was the incident ray. When directions are projected on to a spherical surface, let & represent the direction of the edge of the prism, and P, Q those of the incident and emergent rays. Then #P and HQ are each 4a7—7; and if the arcs EPp and HQq are each a quadrant, p and q will represent the projections of these rays on the principal plane of the prism. 1 The proof quoted by Czapski, Treatise, p. 156, from Heath, Treatise, p. 31, does not seem to be valid. 1896.] of Optical deviation by a Prism. 109 These projected rays are refracted across the prism in accord- ance with the law of sines, the index being not yw but pcos 7’/cos yn, where sin 7 =p sin 7’. If D denote the actual deviation PQ, and d the projected de- viation pq, then, from the isosceles spherical triangle, sin 4D =sin 3d cos 7. Thus, of all incident rays which have the same inclination 4a —~7n to the edge of the prism, that one has its projected devia- tion d, and therefore also its true deviation D, least, whose pro- jection passes across the prism symmetrically. This least value is given by the equation 1 ob _p cosy’. sin 5 (d+ A)= ae sin 5A, where A is the angle of the prism. As yw cos7’/cos n is greater than p, it follows that d is greater than D,, the minimum deviation for an actual ray passing in the principal plane: but as it is also greater than D, no inference can be drawn in this way as to the relative magnitudes of D and D,. We may however find the absolute minimum of D by com- paring with one another the rays, corresponding to different values of », whose projections cross the prism symmetrically. In the annexed spherical diagram £# represents the edge, N, N’ E N 0 N’ the normals to the faces, J, J’ the incident and emergent rays, and #& the ray inside the prism. The pole of VN’ is #, and EI, EI’ are equal; the symmetry of the projection of the rays on the plane NN’ requires that ON, ON’ shall be also equal, 110 Mr Seward, Notes on the [Mar. 9, so that HRO is the plane bisecting the external angle between the faces. Thus as JJ’ =D, NN’= 4, we have sn¢D_ sin(@#—7) sn4A sinr where 7, r are the angles of incidence and refraction JN, RN. It is easy to see by geometrical construction that the right- hand side of this formula increases with vr. It then follows that D is least when 7 is least, that is, when R is at O: thus the absolute minimum of deviation belongs to the ray passing in the principal plane of the prism. Monday, March 9, 1896. PROFESSOR J. J. THOMSON, PRESIDENT, IN THE CHAIR. Mr R. Hargreaves, late Fellow of St John’s College, was elected Fellow of the Society. The following Communications were made to the Society: (1) Notes on the Geological History of Monocotyledons. By A. C. SEWARD, M.A. In discussing the relative antiquity of the two great divisions of Angiospermous plants, the statement is commonly made that Monocotyledons occur in older rocks than those containing the earliest traces of Dicotyledons. The evolution of the Angiosperms and the lines of develop- ment of Monocotyledons and Dicotyledons, are among the most — interesting botanical problems; and it is of the utmost importance to critically examine the evidence afforded by paleobotany as to the order of appearance of these two classes of plants. Fragments of parallel-vemed leaves and pieces of stem struc- tures have frequently been described as species of Monocoty- ledonous genera; such determinations, however, as are based on mere external and superficial resemblance, cannot as a rule be accepted as trustworthy. The cone-like fossils from Jurassic and Lower Cretaceous rocks described under the generic name Kaidacarpon, and referred to the Pandanacee on the grounds of a similarity of form and structure to the inflorescence of recent genera of that family, are most probably Araucarian cones, and should be placed in the genus Araucarites. 1896.] Geological History of Monocotyledons. 111 A case in point is the species Kaidacarpon minus Carr. from the Lower Greensand of Potton; this it is proposed to transfer to Araucarites. In the Geological department of the British Museum there are several specimens of fossil stems discovered many years ago in the Iguanodon quarry at Maidstone, and named by Konig Dracena Benstedtir. The reasons for making use of the recent generic name are quite inadequate, and it is much more probable that the stems are Cycadean and not Monocotyledonous. In some species of Zamia, e.g. Z. Skinneri, Warsz, Z. Loddigesii, Miq. and others the stem is without the characteristic armour of leaf-bases, and presents an appearance very similar to that of the Cretaceous fossils from Maidstone. The pre-Cretaceous, and some of the Lower Cretaceous fossils described as Monocotyledons, cannot be quoted as trustworthy evidence bearing on the question of Angio- spermous development. As yet we are without any definite proof of the existence of either Monocotyledons or Dicotyledons before Cretaceous times, and the statement that the former preceded the latter does not seem to be supported by the facts of palzeo- botany. (2) A description of the Crania found at Girton in 1881. By R. J. Horton-Smitu, B.A., St John’s College. The following Crania of which a short description is here given were excavated from the Anglo-Saxon cemetery discovered at Girton in 1881. The work of excavation was undertaken by Mr F. J. H. Jenkin- son, and a description of the results is to be found in the Journal of the Cambridge Antiquarian Society of that year. In the cemetery many crania were found, together with a large amount of pottery of early Anglo-Saxon date. It would seem that before the Anglo-Saxons made use of this piece of ground as a cemetery it had been devoted by the Romans for a similar purpose. This one might have expected, inasmuch as it lies alongside the old Roman road, and this supposition is supported by the fact that some Roman cinerary urns were discovered at a lower level than those of the Anglo-Saxons; and with these urns were also found a carved lion’s head and a military torso, both of Roman workmanship. All the human remains, however, were found with the Anglo- Saxon urns and other relics, and as no Roman coins were to be seen with the skeletons, we may fairly presume that the skeletons 112 Mr Horton-Smith, A description of the [ Mar. 9, belong, not to the Romans, but to the Anglo-Saxon race. This fixes the earliest possible date of the cemetery at about 410 4.D., the year in which the Roman legion were recalled from Britain. The latest date possible is not so easy to determine, but inasmuch as no Christian emblems or relics of any description exist in these graves, we shall not in all probability be wrong in assuming that the Anglo-Saxons buried here had not been converted to Chris- tianity. ‘Their conversion took place about 650 A.D.; and hence the date of this cemetery may be said to lie between the years 410 and 650 A.D. The importance of these skulls lies in the fact that they help us to draw the boundary line between the East Anglians and East Saxons, for we can see by a study of them whether Girton was in the East Anglian or East Saxon territory. As far as one can judge from such a limited number of crania as eight—for these are all that have reached us—I think Girton must be considered as an Kast Anglian possession. In a paper to be published shortly in the Journal of the Anthropological Institute I have given what I consider to be the typical indices of both the East Anglian and Saxon skulls. As the paper has not been published yet, 1 may perhaps be allowed to reproduce them here. By “East Anglian” skulls, I mean skulls which were found, some at Hauxton, some in Cam- bridge itself. re wad iu cs is 3 RODS | acs Ss 3 q 24/8 |e2lsxeleelax SUES iE ES ale S = ae €Q/4S/SS/S 0180) So (ae Slag 2\oH Soe o| So Sole |Sslseulsa| 2s o|sAalaisg|ahics oS Bela lsall@a/Sa| Sa Se slEossesisaag| og 84) = 6364/54/25 |e Fags e eslea4) ge & Et Ss ES Ibs a MS Se 195 | eee East I) 50 * Anglians| 74 | 71 | 155°) 85 | 96 Eee 56") | 19-78" oe aines I I) II Mean of Girton | 74°4 |72°7| 1410| 81°8 | 95°5 | 48:9 | 56°7*| 90°3*| 77°6* | 124°7*| 108°4 Skulls (?) * Mean of Male Indices only. By glancing at the comparative table given above, it will be seen that the East Anglian skull differs from the Saxon in being broader, rather more lofty, and of greater capacity. Its orbital index is higher and, above all, the face of the East Anglians is distinctly longer than that of the Saxons. 1896.] Crana found at Girton in 1881. 113 In most of these points the skulls found at Girton show a greater resemblance to the Anglian than to the Saxon type. The two main exceptions are the cranial capacity and the orbital index, where they approach the Saxon type: with regard to the capacity, I would say that the mean index given for these Girton skulls is very doubtful. I have been able to take the capacities of no more than four out of these eight skulls, and of these four one is a female skull. The index given is the mean of the three male crania, two of which differ widely from the third, while No. 272, considering it is a female skull, has in reality a very high capacity. It is therefore quite possible, that if there had been more of these skulls at my disposal I should have found the mean index to be, not 1410, but somewhere about 1550. And unsatisfactory also is the orbital index given. Im all cases I examined both orbits where it was possible, and the total number examined was ten. Now considering how widely different the indices are, varying from 73°7 to 92:1, it is obvious that not much stress can be laid on the mean index, which comes to 81°8. Taking all in all, then, I think it may be said that these crania belong to the East Anglian and not the Saxon race. Before giving the measurements of the various skulls, I may perhaps make a few remarks on the peculiarities of each. No. 267. On the right side the Temporal Bone meets the Frontal. The supraorbital notches are extremely large, measuring 3 mm. from above downwards and 6 mm. transversely. No. 268. Most of the Sagittal Suture is synostosed, and the skull has been posthumously deformed: I have therefore omitted the indices of this skull, when taking the mean indices of the series. No. 269. In this female skull the Metopic Suture persists. No. 271. This skull belonged to an adult or rather old male: an epactal bone is present. On the top of the cranium in the - middle line is to be found an instance of “ prehistoric trephining.” The hole is just by the bregma. It is of course hard to say with absolute certainty whether this hole owes its origin to primitive surgical skill, or not, but there is no doubt that the hole was made either on purpose or by accident during life, and judging from the edges it seems probable that the individual survived the operation some little time. No. 272. Female skull, contaiming a very large number of Wormian bones. These are to be found in the squamous and lambdoidal sutures of both sides and in the coronal suture on the left side. Epipteric bones exist on either side and the Metopic Suture persists. \ VOL, IX. PART II. 5 114 Prof. Hughes, [Mar. 9, x a re = re * 3. w 3 4 g re 3 x g S 3 gfe (ge ts | SS (eS sa eae par (S| fs| par rm page) |) ears S ‘S| | a m Sa) Sales iss QU | ee = Ge lies 2 2 |g |ae|ss3l2s| 33 |S C oa 80 a) = re} B Sx | Sa z mol ieyaes Sz ° 2, i) S 2 cs Ss ga Sa 5.8 | O98 =| qq ® an S 5 & 42 ioe a S|) ae | Ae 2 Ss 2 tS) pai | Sn | eal aS —$—$<$<< | | | ee ee a penne ne ee Right) Left 267 $ || 75°7 | 73°8 | 1335 | 77°1 | 79 | 95°9 | 48°5 | 56°7 | 90°3 | 82-2 | 130°8 | 107°6 271 $ || 74°3 | 70°4|1525| 779 | 76'2|99 |50 | — | — | 71 __ | 11375 | 106°9 273 i SN 27°9)| 74.9 |) il ee 7397 |. 90° | 4859 | — | —— | 7 556 ie ae 274 d | 73:1 | 737 | 1375) — | 85295-4494 | — | — S19 iza ror are 269 @ || 72°6| 72°9) — | 92°1 | 88°6 | 92°38 | 4776} — | — | 79°5| — | rII't 270 2M 73 Oo) = Se il Papas lpaeny. lhe bac cet) arm e ne = 272 | 2 |] 73°9| 70°4 | 1480 82°4 | 85°3}99 | 49°1)54 | — |73'2| — | 1052 268+ | 3s || 67°7 | — — |771|— |— |42:2)/— | — | 87-2) — — Mean indices . 72°7 | 1410 81:8 a 8: 6°7*| 90°2* 7 -6*| 124°7*| r08- of all except 74°4 4 9555) | 429) SO SOS aa 4°7 4 No. 268 + Posthumously deformed. * Mean of Male Indices only. (3) On the Recurrence of Ice Ages. By Prof. T. McKenny HuaGuHeEs, M.A., F.R.S. Part IV. ON SOME SCRATCHED STONES FROM THE PERMO-CAR- BONIFEROUS ROCKS OF SOUTH-EASTERN AUSTRALIA AND THEIR MODE OF OCCURRENCE. I have on a former occasion? laid before the Society a large number of sections and specimens bearing upon the question of the recurrence of ice ages and discussed the inferences which it appeared to me might be drawn from the evidence. I then laboured under two difficulties; one was that I had no specimens to exhibit im illustration of the glaciation of the basin of the Indian Ocean, and no trustworthy information as to the exact manner of occurrence of the glaciated rocks in it. The other was that a plausible and attractive theory referrmg the phenomena to extra terrestrial causes was in favour and the conclusions I urged were proportionately depreciated. Now, however, through the kindness of Professor Edgeworth David of the University of Sydney I am able to exhibit specimens of the striated rocks which he obtained from the boulder beds of South-eastern Australia and photographs of sections in the deposits in which they were found. 1 Proceedings Camb. Phil. Soc., 1894, Vol. viii., pp. 98 and 219. 1896.] On the Recurrence of Ice Ages. 115 Moreover the chief arguments formerly urged in favour of the popular astronomical theory have been found to have been based upon error, and, though some of its supporters still cling to it for auld lang syne, they are waiting till some new facts may turn up in support of it. It seems therefore opportune to urge the terres- trial theory again. There seems to be an attempt to retreat behind the well-known fact that ice makes ice, or the cumulative effect of refrigeration, especially beyond a certain point. But it seems to be forgotten that this applies equally to terrestrial causes, and that if a moun- tain range were upheaved, say, a thousand feet above what would be the estimated snow line for that locality, the existence of that snow and ice would so lower the temperature that practically the snow line would creep down far below the altitude estimated from considerations of latitude, longitude and level only. Further, I must point out in passing that the demonstration offered by Professor David does not provide a bill of indemnity for those who have been claiming credit for the discovery of glacial beds and have offered in proof only slickensided pebbles and similar unsatisfactory evidence. At the Geological Society when Professor David exhibited, among others, these specimens which he has kindly presented to the Woodwardian Museum, a stone was exhibited from the Indian boulder beds. This I had no hesitation in pronouncing to be merely a slickensided pebble, a view in which Professor David entirely concurred. Dr Heim has written to me in answer to enquiries I had addressed to him in regard to the stone I had noticed in the Museum at Zurich and said to have been found 7n situ in the “ crystalline boulder beds,” or “palzeozoic glacial bed” in the Salt range of Sandschal in India. “The striations,” he says, “are different on different distinctly cornered sides. That is a phenomenon of quite another order than glacial striation.” As I have before explained, the character which is most common in pebbles which have been subjected to crushing action in a conglomerate, and most clearly distinguishes them from glacially striated rocks is the manner in which they often appear to be pinched out and scored in the same direction on both sides up to the edge; so that, whereas the same set of glacial striz seldom run far over the margin on the surfaces of any glacial boulder, and flat sides are the rule, in crushed conglomerates, on the other hand, the grooves follow the curvature of the stone, and the edge is sometimes crushed up as if the pebble had been nipped out. One of these Australian specimens shows furrows due to the weathering of the rock along weaker divisional planes, but these cannot be confounded with the true glacial striz. We may, I S—2 116 Prof. Hughes, [Mar. 9, think, reject the possibility of the scratched stones collected by Professor David being due to earth-movements in a conglomerate. In order however that we may avoid all possible sources of error we must consider the curious cases of polished floors and striated fragments due to landslips. Of these I exhibited examples! from Wales and the south of England on the former occasion. The condition of the surfaces would be in many of these identical with that produced by glacial action. In both cases in order to produce it the stones must be in contact. The striations on fragments from landslhps have however a greater tendency to be parallel, whereas in all glacial boulder clays it is seen that the direction of the striz has been frequently changed, owing to the shifting position of the stones as they have been carried forward in the frozen mass and scrunched against one another on a far longer journey and over a much more irregular surface than in the case of landslips. Heim and Baltzer attach considerable importance to the difference in character and effect produced by slips of superficial debris (Schuttstiirze) and falls of solid rock (Felsstiirze), and Mr Wickham King recalls examples from the Dumberg landslip near Elm in which the fallen rock produced a bruise from the force of impact and a groove beyond it where the mass was forced forward. Heim points out that when the soil is of a clayey nature the slickensided surface is as smooth as a mirror, with fine parallel striations in the direction of the movement. A still more conspicuous polishing of the surface is always produced upon the solid rock under the slipped mass: and sometimes it is only the solid rock at the base that is polished. The polished surfaces in the slipped mass generally occur in the lowest layers, and some- times, instead of there being one uniform surface so polished, _ there are several such planes succeeding one another at various angles. These polished surfaces often extend with remarkable constancy over very wide areas. In the channels cut to carry off the water under the landslip at Villnockenn on the Bozberg railway, which was of small vertical descent but of great breadth, it was possible to trace a perfectly smooth surface polished lke glass and extending for several hectares (a hectare is something under 24 acres). Dr Baltzer mentions that, after the fall and slip of débris at Bilten, clearly defined striations, caused by the stones in the sliding mass, were observed on the upper slopes, some of them running in sinuous curves. He also states that ruts, like those made by the wheels of a cart, have been observed after a landslip in the Suabian Alps; and that, after the landslip of Bottstein, the 1 Nos, 32, 33, 41, op. cit. pp. 120, 121. 1896. ] On the Recurrence of Ice Ages. 117 inclined beds of Opalinthusthone, wherever laid bare, were found to have a perfectly smooth and polished surface’. If a mass of slipped earth with scratched stones were found resting on a rounded, smoothed, and striated surface and were consolidated into a compact rock it might be difficult in sections of limited extent to feel sure whether we had not before us an ancient consolidated boulder clay—and, if such a mass were by any peculiar combination of circumstances transported piecemeal and the stones scratched by landslips were dropped in clay, so as to appear as isolated boulders, it would be difficult to pronounce very positively as to its origin. But the account given of the mode of occurrence of these ancient Australian boulder clays makes it extremely improbable that they can have been produced directly or indirectly by land- slips. In no case do they appear to have been formed on or near the flanks of any steep slopes, but when they rest on a rounded and polished and grooved surface of Archzan or Ordovician rock, the direction of the striz on the solid floor is always from the south, showing that the phenomena are not produced by any merely local agency. Some of the boulder clays are interstratified in a vast series of sandstones and conglomerates of marine origin, which attain a thickness in places of 5000 feet. This also points to some remote origin and a mode of transport other than currents of water. The marine deposits in which they occur are identified with the Glossopteris and Gangamopteris beds of Tasmania, South Central Africa, India, and Central America. This gives us no data for an exact correlation with any known horizon in Europe. They may have been laid down at any time in the vast interval between the deposit of our newest Carboniferous beds and the first conglo- merates of the Poikilitic series—a period so vast that it may be looked upon as comparable with the time that has elapsed from the age of the New Red to the present day. Those who adopt the very unsatisfactory name Permo-Carboniferous seem to favour this view. There are those however who think that some of them may belong to the same age as part of the Poikilitic or even Jurassic series. It is clear therefore that in the present state of our knowledge the occurrence of glacial deposits in these beds lends us no aid in settling the question of alternate or contemporaneous glaciation of either hemisphere. But they do afford very strong evidence in favour of the view that somehow or another the incoming and disappearance of glacial conditions is always connected with great earth movements. Here we have a depth of 5000 feet at least getting silted up 1 « Ueber Bergstiirze in den Alpen.” Neuen Jahrbuch fiir Mineralogie &c, 1875 and footnote. 118 Prof. Hughes, [Mar. 9, by material carried from adjoining lands where glaciers crept down valleys to the sea. That cannot have been a country totally covered with ice and snow, for the glaciers must have passed through regions where rocks were exposed and broken up into fragments which fell upon the ice. They must have been long glaciers, for there are no scratched stones in short glaciers, in which there is not sufficient time for the fragments to get into the crevasses and work their way down to the stony mass where alone striz could be produced. Besides this there must have been land on which ferns and other such plants grew. It is clearly therefore incorrect to speak of the glaciation of South-eastern Australia. All that has been proved is that some- where to the south of Australia there was land with glaciers from the end of which icebergs carrying clay and scratched stones drifted north. When the water was too shallow to float them they touched the bottom and grooved the rocks on which they grounded. Afterwards when the subsidence of the area had gone on and the water was deeper they melted and dropped their loads over a sea bottom covered with the débris carried down by torrents from lands which had not so severe a climate. Far from bemg a district of ice and snow, South Australia was then deep down beneath the waters of the sea, with probably a compensating elevation of the land in the adjoining regions. Sir John Lubbock? has pointed out that an examination of the form of continents suggests a great and comparatively recent submergence of the Southern hemisphere. The long pear-shaped promontories pointing south, whether continuous as in the case of Africa or interrupted as in the case of Australia, are according to this view only the backbones of continents plunged deeper and deeper under the water as we follow them to the south. This implies some great earth movement affecting nearly the whole southern hemisphere. But local conditions must have determined what exact effect should follow in each area. For instance if there were an upheaval of 25,000 feet along some transverse fold, would it make no difference whether that affected a portion of the earth’s surface which was 20,000 feet deep under water, or already 20,000 feet above the sea level? These are far within observed heights and depths. Again, supposing any pull upon earth’s crust, of such a kind as men have had in their minds when speculating upon the dragging of the waters of the ocean from one hemisphere to another, were to tend to pull a portion of the surface out of place would it make no difference that the trough in which there had been a sea 20,000 feet 1 Nature, 1887. Geographical Journal, Dec. 1896. 1896.] On the Recurrence of Ice Ages. 119 deep was now filled with solid minerals 24 times the specific gravity of water—all of which had been transferred from an adjoining continent 20,000 feet high ? In this connection how suggestive is the fact that “all the extreme depths in the ocean are near land or shallow water, and apparently follow the trend of such upheaved parts of the earth’s crust’.” It is also worth noting that the deepest depressions yet found in the ocean, namely, between 30,132 feet and 30,930 feet, were those proved by Captain Balfour about 500 miles N.E. of New Zealand along approximately the same belt of latitude as that of the depression containing glacial deposits in South-eastern Australia. If regional movements depend upon terrestrial causes such as denudation and deposition, and if shrinkage of the nucleus and astronomical causes determine only the time when the necessary readjustments shall take effect, it 1s clear that the general con- tinuity and never the permanence of oceanic and continental areas must follow as a matter of course. Migration along the growing land leaves at the end of a long period a record of similar fauna and flora, continuous, but not contemporaneous. Hence the difficulty of assigning an exact date to the deposits containing the wide-spread Glossopteris and Gangamopteris. Here we have at last exact observations on an ancient glacial deposit occurring in a region where the conditions are now such that no glaciation is possible, and we find that no glaciation took place in that area on the former occasion either, but only that glaciated stones were carried there. We have evidence of great earth movements such as would account for all the phenomena over the whole of that region, even down to recent times. It would be well if astronomers and physicists would cease to consider only the view that the different amount of heat received from the sun alternately in either hemisphere is sufficient to account for the variations of climate which have been experienced by different regions. They are not asked to account for any deformation of the whole mass of the earth, nor for any violent dragging of the topographical poles from the ends of the axis of rotation. What they are now asked to consider is, whether there are no forces which have a tendency to distort and dislocate portions of the surface of the crust; forces which shall be always tending towards a readjustment of equilibrium over those regions where transference of vast masses of material from one area to another has deranged it; which shall have some tendency to 1 Wharton, W. 1. L. Nature, Vol. 53, Feb. 27, 1896, p. 393. 120 Prof. Hughes, On some Chipped Flints from [Mar. 9, produce results upon the great table-lands and protuberant masses analogous to what are called “marginal effects” in earthquakes ; which might explain what are called overthrusts, that is, nearly horizontal slides of masses of rock; it may be where the friction has been reduced by the liquefication of deep-seated strata when the pressure is relieved by the pull, or it may be where there already existed molten lakes below, or where fractured and lubricated divisional planes occur in the solid rock. It is a matter of observation that such movements have taken place. Can they be explained by any well-supported theory of earth movements which shall be consistent with all the other operations which we know have been going on ? If astronomers and physicists would account for the observed periodicity of earth movements by allowing the sun and moon to pull the trigger when denudation and deposition with secondary iternal changes have loaded the gun they would be speculating along lines suggested by observation from many different points of view. (4) On some Chipped Flints from the Plateau Gravel of Salisbury and elsewhere. By Prof. T. McKenny Huaues, M.A., F.RS. It has long been an accepted fact that flints showing traces of man’s handiwork are found in river gravels which from their relation to the physical geography of the district and by the shells and bones found in them are referred to a very remote antiquity. These implements are connected by similarity of form and by the associated remains with others which have been found in caves, where a much larger and more varied assortment of remains of human art and appliances have led to the inference that the man of that period was not at all low down in the scale of civilization but might be compared rather to the Esquimaux of to-day. Seeing therefore that the earliest men of whom we know any- thing for certain do not exhibit characters pointing to a low stage of development, we are always looking out for traces of some still earlier race. Many a time has the discovery been announced and primeval man been referred further and further back until some have even assigned a place in this hierarchy to “man’s pre- cursors.” I would invite the attention of the Society this evening to the evidence which has been recently brought forward in support of the view that among the flints and in the patches of gravel which occur scattered, both over the beds which rise from below the chalk, and over Tertiary beds which rest on the chalk, as well as over the chalk hills themselves, we have evidence of man’s 1896.] the Plateau Gravel of Salisbury and elsewhere. | work of a much earlier date than that of the river gravels in which flint implements have long been recognized. It has been proposed to group these “most ancient stone” implements under a new name, palzotatoliths, or for shortness, palzotoliths. The subject falls into two parts, (1) the age and origin of the beds in which the flints in question are found, and (2) the character of the flints themselves. The upper chalk is mostly covered with a thick layer of what is known as “Clay-with-Flints.” This consists of the insoluble residue left when, by the action of the surface water charged with carbonic and other acids, the carbonate of lime has been removed. But it is generally the lowest part only of this deposit which is obviously derived directly from the chalk. In it the flints are not worn nor broken, or, if they have been broken, the several parts have not been separated, but all the upper part of the Clay-with-Flints consists of broken and apparently weathered flints in a matrix of red clay. This can only be ex- plained on the supposition that there has been a kind of soil- creep going on for ages. Had it been due to the agency of floods the stones and clay would have been sorted and the deposit would have been more or less stratified. The subsidence neces- sarily accompanying such enormous subterranean denudation would initiate and keep up the movement of the superficial mass. A rough measure of the amount of such subterranean denudation may be obtained by an inspection of the nearest sections of upper chalk where it will be seen at a glance what an immense thickness of the chalk with flints would have to be removed to furnish, say, 10 feet of the insoluble residuum. Every here and _ there, especially on its margin, the clay has been all washed out of the “ Clay-with-Flints” and carried away, and a universal covering of white-weathered fragments of flint is distributed all over the surface. These flints are also on the move. They creep down the slopes and accumulate on every ledge and terrace. They more obviously travel down the “dry chalk valleys,” where also the motion is largely due to subterranean denudation, the water which runs through the porous gravel removing the soft and soluble chalk below it and only appearing at the surface in very wet seasons when there is more water than can pass even through this very open gravel. If there happen to have been any remnants of older superficial deposits left on the hill side, they too start as the underlying chalk gets destroyed, and travel down by all the processes of soil-creep, finally becoming worked into the general superficial mass. When these various deposits come within the action of either occasional or perennial streams they are handed on more rapidly and are dropped as ordinary river gravels or silts. 122 Prof. Hughes, On some Chipped Flints from [Mar. 9, Professor Prestwich’ has given an instance of a sudden out- wash due to heavy rain. In this way such superficial deposits have often been carried down and deposited in stratified masses hanging on the hill side. The relative levels of these gravels may be complicated by contemporaneous or subsequent earth movements, but it will be long before they lose the character they acquired from their mode of origin, as they consist chiefly of surface-weathered flints. | These are all operations going on still, and the recent causes and effects being obvious, we reason back by analogy to the ex- planation of the more ancient results. Take such a district as that between Six Mile Bottom and Linton. The higher ground, but not the highest only, is covered with boulder clay. ‘The chalk is rapidly perishing by subterranean chemical and mechanical erosion. The upper chalk furnished the flints which creep down hill by various processes, a large proportion of them being at one time or another exposed on the surface. Finally on the Six Mile Bottom side they creep down the long “dry chalk valley” by Lark’s Hall to the railway station, carrying with them from above fragments out of the Boulder Clay, and lower down incorporating the remnants of terraces of river gravel of the age of the Mammoth and Tichorine Rhinoceros. | Over the undulating plateau on top, the stony patches creep outwards and downwards as the inequalities admit of movement. Down the steep slope by Linton the débris slips fast, overlying the patches of boulder clay and still older superficial deposits on the brow of the hill and creeping out over the lower beds of the chalk. If the outcrop of chalk is beimg eaten back, these stony masses will by and by lie on isolated hills and old terraces far out in front of the new chalk escarpment. In the country round Salisbury we find very similar conditions prevailing and similar results followmg. There is an extensive plateau, or rather “plain of marine denudation” over which there are patches of Tertiary loams We. resting, along the margin of the Hampshire basin, on the upper or flint-bearing Chalk. On lower ground along the valleys there are terraces of Mam- moth gravel. The “trail,” consisting of the sweepings of ancient and modern surface soils, has in one place crept off the chalk on to the Tertiary beds, in another has travelled down and got mixed up with the gravel of the old river terraces, which were themselves largely made up of still more ancient surface débris, with a few sarsen stones, black flint pebbles from the lower ' Quart. Journ. Geol. Soc., Vol. xlv. 1889, pp. 278, 279. 1896.] the Plateau Gravel of Salisbury and elsewhere. 123 Tertiary beds, and boulders of various far-travelled rock which had got distributed over the surface by earlier operations, not always easy to explain after so many changes have taken place. It is from one of these patches of gravel, resting on a bed of sandy loam of Tertiary age, at Alderbury, three miles south of Salisbury, that most of the flints I now lay before the Society in illustration of my paper were procured. Some of them were collected and given to me by Dr Blackmore, who kindly drove us to the locality and gave us much information about the district. I exhibit also some of the Kentish paleotoliths of Prof. Prest- wich and Mr Harrison, kindly lent by Mr Fisher, and some collected by myself, near Cambridge. The flints and fragments show evidence of having been long exposed on the surface. The sandstones are often fretted and eaten away rather than rolled. Some of the flints have a good coating of soft white silica, from which the more soluble colloidal portion has been removed, and they exhibit traces of the innumerable accidental chippings and crushings and breaking up under the influence of frost and sun to which surface-flints are liable; while some were deeply stained by dark red oxide of iron when buried in the gravel into which they had found their way after they had been long knocked about and chipped and weathered on the surface of the ground. It was clear that the particular beds we were examining were not merely a surface soil formed in place, but a violently trans- ported drift from a chalk surface covered with weathered flints, such a deposit in fact as would be carried down a slope of chalk in storms when the rainfall was greater than the soil could absorb, and ran off in torrents, tearing up the rubbly disintegrated chalk and hurrying along the surface soil and flints. In such a case a chalky gravel is formed with irregular beds of fine marl, the matrix bemg almost entirely made up of chalk. When this is afterwards exposed to the slow decomposing action of percolating waters and the carbonate of lime is carried away, only the in- soluble flints and sand and iron oxides remain. Of this we see distinct proofs in the Alderbury beds. The flints did not all lie as they would in an ordinary river-gravel with their longer axes horizontal or so inclined as to enable the mass to offer best resistance to the current, but they were fre- quently arranged vertically in loops and hollows into which they had sunk owing to the gradual but irregular removal of the in- ‘cluded masses of chalky material. In one place I observed that a part of the chalky matrix had been banded by infiltered iron oxides, so that the iron ran in wavy lines conforming to the outline of the included fragments. When the calcareous portion was dissolved away, those stood out in separate septarian bands of iron oxides. 124 Prof. Hughes, On some Chipped Flints from [Mar. 9, Mutatis mutandis we may offer the same explanation of the origin of the superficial deposits along the North Downs of Kent and of the mode of occurrence of gravels largely derived from surface flints and from the destruction of the top of the chalk which occur in that area, not only over the surface of the chalk itself but over beds which crop out from below the chalk in front of the great escarpment that overlooks the weald and over the Tertiary beds which cling to the dip slope of the chalk on the north as described in the works quoted above. The reason why it is of the greatest importance to clear up this question is that, if the views now put forward are correct, these deposits may be of any age and that they are even being formed still. Some of the gravels on ledges and terraces, and the outlying knolls which represent old ledges and terraces, may be patches of trail or be due to rain-wash and soil-creep which have used up remnants of older river gravels, while some of them may be ancient river gravels which have largely if not wholly derived their material from the surface. Sometimes it may be possible to refer a given bed to one or other of these two gravels so different in mode of transport, if not in the origin of the material. If many, perhaps most, of the patches in question have been formed by the local rainwash and soil-creep, the height of the deposit above the sea or above the existing rivers goes for nothing, but, if we must suppose that an escarpment has receded far since it fed the now outlying hills with its débris, we must admit that as an argument in favour of an enormous lapse of time since the objects found in the gravel were deposited where now found, or we must believe in a much more rapid destruction of the chalk than has been until recently advocated’. To consider now the character of the flints found on such surfaces and in such deposits as those just described. A blow or crush takes off pieces of flint with a bulb of per- cussion and a conchoidal fracture. Changes of temperature make it crack and often remove large lenticular flakes which show no bulb. This is what so commonly spoils flint implements which have been lying long exposed on the surface of the ground. None of these operations necessitate the presence of man. Any movement which would force one flint against the other would be likely to produce fractures. The stampede of a herd of oxen or deer must make many a flake and chip the edge of many a flint. The whole of the surface from Balsham to Six Mile Bottom is covered with flints showing every variety of fracture. Most 1-See Howorth, Geol. Mag. Feb. 1896, pp. 58 et seq. 1896.] the Plateau Gravel of Salisbury and elsewhere. 20 of these are broken-up tuberous flints, some few are pieces of tabular flint, that is, flint which has replaced the chalk along lines of joint oblique to the bedding and across the bands of tuberous flints. Of course the parts of each flint which are most likely to get chipped are the more exposed points and thinner edges or the curved margins which would hold a round stone when pressed into the hollow. Thus we can easily make a selection of forms which look as if they had got bruised at the point or edge by being used. We can find many tabular flints which have got chipped along an exposed corner or edge, many tuberous flints which fit comfortably into the hand at one end, and have at the other or on one side a point or edge which has got chipped. If over such a land surface we have here and there some unfinished implements and misfits, both paleeolithic and neolithic as well as recent strike-a-lights, and now and then all get washed together, or creep down the hill into the same bed of gravel, it might have been and it has been suggested, that a large number of the natural pieces of flint owe their chips to their having been picked up and used by primeval man. The paleotoliths, says Mr Montgomerie Bell’, “are not shaped into particular forms by the will and skill of the workman as palzeolithic flints are. They are chipped flints rather than shaped flints, used tools, not made tools.” There is now in Jermyn Street a collection of flints, which I made to illustrate the view that almost all the artificial forms of implement, certainly all the common ones, were suggested by the forms into which flint naturally breaks. If there be anything in this, we might expect to find rude transitional forms among surface-weathered flints. The points therefore which I would accentuate are that, unless the mode of origin by rainwash and soil-creep above described be borne in mind, these high-level gravels and flints may be referred by some to a period the remoteness of which is measured by the time it has taken to cut the valley down or the escarpment back to the level of the existing rivers or the base of the present slopes ; that all the specimens I exhibit are natural forms chipped by the accidents common to all surface-soils; that they are identical with and represent every type of the paleotoliths upon the character and mode of occurrence of which the theory of the existence of man in Britain before the paleolithic age has been founded. We are all aware that the genuineness of the first found paleeo- lithic implements was questioned by many who now believe in them, especially when @ prior? reasons made them doubtful as to the possibility of such a discovery. 1 Brit. Assoc. Rep., Edinburgh, 1892, Trans. Sects., p. 900. 126 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9, But the difficulty of convincing the public or even the scientific world of the authenticity and genuineness of any of the specimens was greatly increased by the enormous mass of false or incon- clusive evidence that was then adduced in favour of the discovery. Those therefore who believe most firmly that traces of man earlier than those now known as paleolithic will be found, should be the most careful in their examination of the evidence adduced while the enquiry is in progress. (5) On the Leakage of Electricity through Dielectrics tra- versed by Réntgen Rays. By Prof. J. J. THomson, M.A., F.RS., and J. A. McCLeLLanp, Fellow of the Royal University of Ireland, Trinity College, Cambridge. Experiments proving that dielectrics when traversed by Réntgen rays conduct electricity were described by one of us in papers read before the Philosophical Society on Jan. 28, 1896, and before the Royal Society on Feb. 13, 1896. The following paper contains an account of further experiments made to in- vestigate the laws governing the passage of electricity through dielectrics exposed to Réntgen’s rays. Method of making the Experiments. The induction coil and the bulb for producing the rays were inclosed in a large iron tank, fitted with a metallic lid. A small hole was bored in the lid and the bulb placed underneath this hole. The radiation from the bulb passed through the hole and fell upon the dielectric whose conductivity was to be investigated. In the experiments with gases two different methods were employed; in the first of these, which we shall call method (A), the lower end of a piece of glass tubing about 4 cm. in diameter was closed by a piece of thin sheet aluminium, a paraffin stopper was placed in the upper end of the tube, a stout metallic rod passed through the paraffin and supported a metallic disc with its plane parallel to the plate of aluminium. The rod and disc were connected with one pair of quadrants of a quadrant electrometer. The plate of aluminium rested on the iron tank, which was connected with the earth. To determine the rate of leak through the dielectric the two pairs of quadrants of the electrometer were connected together and with one terminal of a battery of small storage cells, the other terminal of which was connected with the earth. The quadrants of the electrometer were then disconnected from each other and from the battery. Before the Réntgen rays were turned on the insulation was so good that there was no movement of the spot of light 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 127 reflected from the mirror of the quadrant electrometer, as soon however as the rays passed through the dielectric there was leakage through the dielectric, the potential of the disc approached that of the aluminium plate and the spot of light moved across the scale. The rate of leak was determined by measuring with a stop-watch the time taken by the spot of light to pass across 50 scale divisions. The wire attached to the middle of the electro- meter carried a vane which make the deflections of the electro- meter dead beat. In the other method, which we shall call method (B), a mica window was inserted in the side of a glass vessel shaped like a lamp-glass, the window was placed opposite to the hole in the tank containing the coil and bulb. The open ends of the glass vessel were fitted with paraffin plugs, through each of these plugs a metal rod passed carrying a metal disc, the two discs were parallel and opposite the window. As long as the gas between the discs insulated no electricity could pass from one disc to the other. One of the discs was kept permanently connected with one terminal of a battery of small storage cells, the other terminal of which was connected with the earth, while the other disc was connected to one pair of quadrants of the electrometer. The other pair of quadrants were connected to earth. If the two pairs of quadrants were connected together and then disconnected the spot of light reflected from the mirror would remain at rest if the gas between the discs (which are at different potentials) remained an insulator, when however electricity can leak through the gas the potentials of the two discs will tend towards equality and the spot of light will move across the scale. The spot of light remained at rest when the gas between the plate was not traversed by the Réntgen rays; as soon however as these passed through it the spot of light began to move, and the conductivity of the gas was determined by measuring the time taken for the spot of light to pass over 50 scale divisions. Conductivity of different gases when traversed by the Rontgen rays. The following results were determined by the method A. The vessel was filled with air at atmospheric pressure and tem- perature and the rate of leak when the rays were passing through the air determined. The air was then pumped out and the vessel filled with the gas to be examined and the rate of leak again determined; after this the gas was again pumped out and the vessel refilled with air and another determination of the rate of leak made; this process was repeated several times. For these determinations it is necessary to use a bulb whose rate of emission of the Réntgen rays remains steady. There is sometimes a little difficulty in getting the bulb into this state, many bulbs which will produce satisfactory photographs are so 128 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mavr. 9, variable that they are useless for these measurements. We generally found that a bulb got steadier after bemg used, indeed we never found a bulb that was steady enough for our purpose when first taken off the pump. The following table contains the rate of leak of different gases at atmospheric pressure, and unless when otherwise stated at a temperature of about 15° C., the rate of leak through air at this temperature and at atmospheric pressure being taken as unity. Name of Gas. Molecular Weight. Relative rate of Leak. Hydrogen 2 5 Coal gas 8 Ammonia gas Ih ‘9 Sulphuretted Hydrogen 34 35 Carbonic acid gas 44 12 Sulphur dioxide 64 3 Nitrogen peroxide (N.O,) 92 3 Chlorine 71 12 Bromine (at the temperature of boiling bromine) 160 9 Iodine (at the temperature of boiling iodine) 230 7 Hydriodic acid gas 126 + Mercury vapour (at the tempera- ture of boiling mercury) 200 10 It will be seen from the preceding table that the electrical conductivity of the heavier gases when exposed to the Réntgen rays is greater than that of the lighter gases, the order for electrical conductivity does not however exactly correspond with the order of the molecular weight. A very marked feature of the table is the high conductivity of the halogens, in fact the leakage of electricity from a charged disc through a tube filled with chlorine is a very sensitive and convenient measure of the inten- sity of the Réntgen rays, and was used by us in many of the experiments described in the later part of this paper. The high conductivity of mercury vapour is very remarkable, for this gas only allows the ordinary electric discharge to pass through with great difficulty, whereas under the influence of the Roéntgen rays it is one of the best conductors among the gases we investigated. In the case of most of the preceding gases the rate of leak was determined when the charged disc was electrified positively as well as when it was electrified negatively, but no difference was ever detected between the rate of leak in the two cases. 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 129 Influence of pressure on the rate of leak. A series of experi- ments, using the method A, were made to determine the rates of leak through air at different pressures. As the following numbers show, the rate of leak diminishes as the pressure diminishes though the rate of diminution in the rate of leak is not so rapid as that of the pressure. Rate of leak through air at different pressures. Time in seconds taken for the Pressure. spot of light to pass over 50 {Pressure}? scale divisions. x time. By gy 39 752 Hee 57 655 55 81 600 15 109 422 Second set of experiments. 750 34:5 931 470 41 902 320 51 918 170 74, 962 45 97 650 Rate of leak through sulphuretted hydrogen at different pressures. 771 15 417 551 18°5 454 341 23°5 454 101 48 480 31 97 533 ile 140 462 Rate of leak through sulphur dioxide at different pressures. Tol 22 611 501 28 616 291 42 714 150 60 730 | 160 528 VOL, IX. PART II. 9 130 Prof. Thomson & Mr M°Clelland, On the Leakage of (Mar. 9, Rate of leak through coal-gas at different pressures. 769 58 1606 579 70 1680 374 81 1563 Rate of leak through hydriodic acid gas at different pressures. 769 7 194 489 8'5 189 289 10°5 178 89 20°5 193 These numbers show that over a considerable range of pressures the rate of leakage through the gas, 2. the electrical conductivity of the gas, is approximately proportional to the square root of the pressure. Now we know from the theory of the dissociation of gases that in cases where the dissociation is small, z.e. where the number of ions is small compared with the number of the un- dissociated molecules, the number of ions is proportional to the square root of the pressure. Hence the results of our experiments indicate that the electrical conductivity of gases traversed by the Réntgen rays is proportional to the number of ions, and as long as the gas and the number of ions is the same is independent of the number of undissociated molecules, or in other words, the electrical conductivity is a function of the number of ions and not of their mean free path. Effect of temperature upon the conductivity of a gas at con- stant pressure. A few experiments were made to determine the effect of temperature upon the conductivity of air at constant pressure. It was found that the conductivity at high tem- peratures was slightly less than that at the temperature of the room. Further experiments showed that as the gas was heated up the conductivity attained a maximum value, after which it began to diminish. As an instrument for measuring high temperatures was not available at the time of making these experiments, further consideration of these effects must be reserved for a future aper. Effect of Variation in the Potential Difference on the rate of leak under the influence of the Réntgen rays. A very remarkable and characteristic property of the conductivity produced by these rays in a gas, is that the rate of leak as the potential difference increases soon reaches a maximum value and becomes almost independent of the potential difference. Many experiments were made to investigate this point, using both methods A, B. The 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 131 following may serve as specimens of such experiments; the method used was B, and the gas in the tube was air. Potential difference in volts between Time required to leak through the discs in the tube. 50 scale divisions. 2 58 + 44 6 30 8 25 10 25 12 28 16 26 35 26 73 25 108 25 138 24 278 23 Another set of measurements gave, when the gas in the tube was chlorine, 35 8 75 8 132 7 A third set with a chlorine tube with two sheets of tinfoil between the exhausted bulb and the discs, 3d 18 75 17 132 15 These numbers show that the rate of leak and the current through the gas is almost independent of the electromotive force. If we regard the conduction as electrolytic the gas being ionised by the Réntgen rays, the fact that the current is independent of the electromotive force indicates that the velocity of the ions is independent of this force. This result is consistent with the law connecting the conductivity with pressure for we saw that this implied that the conductivity was propor- tional to the number of ions but independent of their mean free path. Now if the conductivity depended upon the velocity ac- quired by the ions under the action of the electromotive force it would depend upon the coefficient of viscosity between the ions and the molecules, and hence upon their mean free path. The current increases with the potential difference when this is small, but soon attains a maximum value. This effect would result if the passage of the Réntgen rays through the gas produced chains 132 Prof. Thomson & Mr MClelland, On the Leakage of [Mav. 9, of molecules or aggregations of some kind in which the component atoms with their electrical charges could rearrange themselves with facility; the time 7 required for this rearrangement being independent of the intensity of the electric field. The effect of such a rearrangement would be that in a time 7’ a definite quantity of electricity passed from one end to the other of the chain of molecules. If these chains of molecules were distributed in an unpolarized way through the gas their breaking down would not lead to a current, as as much electricity would pass in one direction as in the opposite. As soon however as the chains are polarized there will be a current. Suppose now that these chains get polarized under the influence of an external electro- motive force and that the polarization is analogous to that of the molecular magnets in a piece of soft iron under an external magnetic field. Then until all the chains get pulled so as to set in one direction the current will increase with the potential difference, but as soon as all the chains get pulled into one direction the current will reach a maximum value and be in- dependent of the electromotive force. Rate of leak through solid dielectrics traversed by the Rontgen rays. Solid dielectrics when traversed by these rays become con- ductors of electricity, but the conduction through these substances, inasmuch as it approximately obeys Ohm’s law, differs in one very important respect from that through gases. The conduction through solid dielectrics is also remarkable for the extent to which polarization is developed. If the two discs im method AB are imbedded in paraffin, and the paraffin when exposed to the Rontgen rays has a current sent through it, then if the discs are removed from the battery and connected together, and the paraffin kept exposed to the rays a current in the opposite direction flows through the paraffin. If the Réntgen rays are shut off from the paraffin, the polarization can be kept locked up in this substance almost indefinitely, and can after any lapse of time be liberated by again exposing the paraffin to the influence of these rays. Solid sulphur showed exactly similar polarization effects to those shown by paraffin. The amount of this polarization may be realized from the fact that the times taken to leak through 50 divisions under a constant electromotive force, were in four consecutive experiments taken quickly one after another 20, 47,68 and 80 seconds respectively. In comparing the rates of leak under different electromotive forces, it is therefore essential to get rid of polarization between each ex- periment. In the following experiments this condition was care- fully attended to. 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 133 Leakage of electricity through paraffin under different electro- motive forces. Voltage. Time required to leak through Product of voltage 50 divisions. and time, 278 14 3892 208 21 4368 138 29°5 4071 fs 56°5 4124 35 140 4900 Thus the conduction approximately obeys Ohm’s law. Leakage through sulphur. 278 10 2780 208 13°5 2808 138 21 2898 73 37 2701 35 67 2345 And again the conductivity approximately obeys Ohm’s laws. On the law connecting the rate of leak through a dielectric with the distance of the dielectric from the vacuum tube. In the experi- ments made to investigate this law, the vacuum tube was placed immediately behind a small hole in the metal tank enclosing the coil and tube. Method B was used to measure the rate of leak, the vessel in which the discs were placed being filled with paraffin, as the leak through this gas is very rapid. The bulb used in the experiments (1), (2), (3) below was of the shape shown in Fig. 1. The distance of the tip of the negative negative electrode positive electrode section of wall of tank 134 Prof. Thomson & Mr M°Clelland, On the Leakage of (Mar. 9, electrode from A was about 5 centimetres, and the length of the electrode about 4°5 centimetres. The bulb was placed so that the negative electrode was perpendicular to the plane of the hole in the side of the tank, and its prolongation passed through the centre of the hole. The discs in the chlorine tube were placed opposite the hole with their planes parallel to the normal to the plane of the hole. EXPERIMENT 1. Distance between the middle of the discs Time in seconds required to leak and the point A of the bulb. 50 scale divisions. 6-7 3 13°4 6'°5 201 13 26°8 18 40:2 36 53'6 48°5 67 80 The results of these experiments are plotted in the curve in Fig.2. The abscisse are proportional to the distance of the middle -—10 0 10 20 30 40 50 60 ieee Le | ae Fic. 2. point of the discs from the point A of the bulb. The ordinates on the dotted curve are proportional to the time required to leak 50 divisions, those on the continuous curve are proportional to the square roots of these times. The continuous curve is a straight line, passing through a point on the axis which corresponds to a point C, 7 cm. behind A. Hence this experiment shows that the times required for a given leak are proportional to the squares of the distance of the discs from C, or that the rate of leak is inversely proportional to the square of the distance from C. This suggests that the Réntgen rays originate chiefly in the neighbour- hood of C. There is no evidence of any coming from the glass in the neighbourhood of A, though this is brightly phosphorescent. 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 135 EXPERIMENT 2. (Made on a different day with the same bulb arranged in the same way as in Experiment 1.) Distance from centre of the discs to A. Time required to leak 50 divisions. 55 2°5 ue 5 16°5 fi 22 13°25 oN 15a 33 25 38°5 35 The curves plotted in Fig. 3 show the results of these measure- ments, the ordinates are proportional to the square roots of the Ere. 3. times of leak and the abscissee to the distances from O. We see again that a straight line passing through approximately the same point as before represents fairly well the relation between the distance and the square root of the time required to leak 50 divisions. Thus the results obtained by experiments (1), are confirmed by (2). EXPERIMENT 3. Same arrangement as before. Distance of discs from A. Time required to leak 50 divisions. 6°5 less than 2 a5 13 32°5 32 52 61 The results are plotted in Fig. 4, and confirm the conclusion already drawn. In the next (3) experiments, a tube of another pattern was used. This is represented in Fig. 5, A is a flat aluminium plate, B and C aluminium wires fused in the tube. The dimensions of the tube are marked on the figure. The bulb was placed so that D was close to the hole. In Experiment 4, 136 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9, when the plate A was the positive electrode and the wire B the negative, the followimg results were obtained. Fie. 5. EXPERIMENT 4. Distance of the centre of the discs from D. Time required to leak 50 divisions. Ard 6 9 10 13°5 15°5 18 25 22°5 30 27 40 31°5 60 -10 0 10 20 30 40 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 137 The results are plotted in the curve shown in Fig. 6, where the ordinates are the square roots of the times and the abscisse the distance of the centre of the discs from D. We see that the measurements are represented by a straight line cutting the hori- zontal axis at a point corresponding to a point in the tube about 6cm. behind D. Thus the rate of leak varies inversely as the square of the distance from a point distinctly behind the flat aluminium plate, which in this experiment is used as the positive electrode. EXPERIMENT 5. In this experiment the same tube was used as in Experiment 4, but in this case C was the positive electrode, while B was again the negative electrode. The following results were obtained. Distance of centre of discs from D. Time required to leak 50 scale divisions. 4°5 675 9 15) 13°5 29°5 18 545 22°5 $5 Ere. 7. These results are plotted in the curve shown in Fig. 7, where the ordinates are proportional to the square roots of the time of leak and the abscissse proportional to the distances of the centre of the discs from the point D. The observations are well represented by a straight line cutting the horizontal axis at a point correspond- ing to the point in the tube about 35 centimetres behind D. This poit is very nearly on the flat plate A, so that in this case the rate of leak varies inversely as the square of the distance from the plate. EXPERIMENT 6. In this experiment C’ was the negative and B the positive electrode. The following results were obtained. . Distance of centre of discs from D. Time required to leak 50 divisions. 6 45 12 ua 18 22 24 33 30 60 VOL. IX. PART I. 10 a 138 Prof. Thomson & Mr M°Clelland, On the Leakage of [Mar. 9, These results are plotted in the curve shown in Fig. 8, where the ordinates are proportional to the square roots, times of leak —10 0 10 20 30 Fic. 8. and the abscissze proportional to the distances of the centre of the discs from D. The observations are represented by a straight line cutting the horizontal axis at a pot corresponding to a point in the tube about 4 centimetres behind D, and this point is approxi- mately on the flat plate A and thus in this case as in the preced- ing, the rate of leak varies inversely as the square of the distance from the flat plate. Thus reversing the electrodes has produced no change of the place of origin of the Rontgen rays. The origin of these rays in these tubes seems to be the flat plate, though when this is made the positive electrode the origin seems slightly displaced. To test this point a set of experiments were made with a tube whose shape and dimensions are shown in Fig. 9. In the experiments made with this tube the plate was the Fie. 9. positive and the wire the negative electrode. The following results were obtained. Distance of centre of discs from A. Time required to leak 50 scale divisions. 5 5 10 145 15 23 20 34 25 44-5 1896.] Electricity thro’ Dielectrics traversed by Réntgen Rays. 139 These results are plotted in the curve shown in Fig. 10. The ordinates are again proportional to the square roots of the time and the abscissve to the distances of the centre of the disc from A. The results are represented by a straight line which cuts the horizontal axis at a point corresponding to a point in the tube about 7 centimetres behind A, ze. the rate of leak varies oy as the square of the distance from a point behind the plate. Absorption of the Réntgen rays by sheets of tinfoil. A number of experiments were made on the effect produced by inserting between the vacuum tube and the gas exposed to the Réntgen rays sheets of tinfoil in gradually increasing numbers. The result of these experiments would seem to indicate that the rays are not all of one kind, for it was found that the effect produced by the insertion of a given number of leaves of tinfoil was greater when the number of leaves already placed between the vacuum tube and the gas was small than when it was large. This effect would occur if some of the rays were readily absorbed by the tinfoil, while others passed through with greater facility. 'Thus when the rays had already passed through a number of layers of tinfoil most of the more absorbable rays would be already absorbed, and any more leaves of tinfoil would only have the less absorbable ones to deal with. The effect is very marked with some bulbs, though it is hardly noticeable in others. We shall first give a specimen of the results obtained with a bulb showing this effect. Number of leaves of tinfoil between the Time required to leak through bulb and the gas. 50 divisions. 0 8 1 10 2 bal 3 11 4, 12 6 16 8 19 10 22, 12 25 16 29 20 36 24 44 28 48 36 60 44 61 Thus to take a few examples, the effect of increasing the number of leaves from 2 to 10 is to diminish the rate of leak 140 Prof. Thomson & Mr M°Clelland, On Electricity. [Mar. 9, 1896. “in the proportion of 2 to 1, increasing the number from 12 to 20 decreases it in the proportion of 1°44 to 1, from 20 to 28 m the -—10 0 10 20 - 30 | Ere. 10: a proportion of 1:33 to 1, from 28 to 36 in the proportion of 1°25 to 1, and from 36 to 48 only in the proportion of 1:01 to 1. With this bulb the effect is clearly marked. But im the following experiments made with another bulb it is much less noticeable. Number of leaves of tinfoil between the Time required to leak through bulb and the gas. 50 divisions. 0 3 2 5 4 8 6 10 8 15 10 20 14 32 18 51 In this case increasing the leaves from 2 to 6 increases the time of leak in the proportion of 2 to 1, from 6 to 10 in the same pro- portion, from 10 to 14 in the proportion of 1:6 to 1, and from 18 to 14 again in the same proportion. Thus, though there are traces of the effect, it 1s not nearly so marked as in the preceding bulbs ; we therefore conclude that the different rays are emitted by different bulbs in different proportions. We have always found this effect most marked in the most efficient bulbs, z.e. the bulbs which produced the greatest leakage. We have in conclusion much pleasure in thanking Mr E. Everett for the assistance he has given us in the preceding ex- periments. . PROCEEDINGS OF THE Cambridge Philosophical Society, Monday, 27 April, 1896. Proressor J. J. THOMSON, PRESIDENT, IN THE CHAIR. At a meeting held in the University Chemical Laboratory, the following were elected Fellows of the Society: Professor J. B. Bradbury, M.D., Downing College. A. J. Wallis, M.A., Corpus Christi College. C. T. R. Wilson, M.A., Sidney Sussex College. The following Communications were made: (1) On photographing the whole length of a Spectrum at once. By Pror. LIvEIna. Professor Liveing exhibited photographs of a variety of spectra in which the whole length of the spectrum between the wave- lengths 550 and 214 was depicted on a celluloid film at one operation. A concave grating of 104 feet radius was used, with the slit in the centre of curvature, and the slide which held the sensitive film formed part of a cylinder with a radius of 54 feet, so that, when the axis of this cylinder was midway between the slit and grating, every part of the spectrum was perfectly focussed on the film. The length of the photograph between the limits of wave-length above-mentioned was 65 centimeters. To obviate the confusion caused by the overlapping of the spectra of different orders, he projected on to the slit the image of the source of light by means of a combination of two quartz lenses with a quartz prism of 30° between them. The slit being vertical the edge of the prism was made horizontal, with the result that the more VOL, UX, PT. LIT, il 142 Prof. Liveing, On photographing a Spectrum. [April 27, refrangible rays were somewhat diverted downwards, and the image of the slit produced by them fell on the film at a different level from that produced by less refrangible rays. Consequently the spectrum of the second order in the photograph was about half the length of the lines lower than the part of the spectrum of the first order at the same place, and the two orders were at once distinguished. It is not at all difficult with a table of sines to set out a scale of wave-lengths for a spectrum formed in this way, and such a scale once made would of course apply to all photographs taken with the same instrument, provided there were no inequalities in the shrinking of the films when drying after development. Un- fortunately Professor Liveing had found that the films, imelastic as they seem even when wet, did not shrink uniformly, and he was therefore turning his attention to glass plates. Glass plates will not bend to cylinders of so short a radius as 5} feet without danger of fracture, but thin sheet glass can easily be bent to a cylinder of double that radius. He was therefore fittimg up a suitable camera for use with a large grating of 21 feet radius, and hoped to obtain photographs with it which should not only be useful for reference, but from which wave-lengths could be read off to a close approximation. At present he could only read off wave-lengths from the films by photographing a known spec- trum, such as that of iron, at the same time and on the same film as the other spectrum, and measuring the distance of the unknown line from the nearest lines of known wave-length, a much more troublesome process than the simple application of a scale. (2) On diozymaleic acid and its derwatives. By H. J. H. FENTON, M.A., Christ’s College. By oxidation of tartaric acid, in presence of a ferrous salt, a substance results which has powerful reducing properties, and which gives a beautiful violet colour with ferric chloride. This substance has been isolated and proves to be an acid having the formula C,H,0,. It crystallizes with 2H.,O in flat diamond-shaped plates, having a pearly lustre. The isolation of the acid was a matter of extreme difficulty owing to the unstable nature of its aqueous solution, which decomposes slowly at ordinary tempera- tures, and very rapidly when heated, giving glycollic aldehyde and carbon dioxide. Glycollic aldehyde has, in this way, been isolated as a syrupy liquid; when heated to 100° in a vacuum it undergoes polymerization, a sweet-tasting solid gum being pro- duced which has the formula C,H,,0,. 1896.] Mr Fenton, On Dioxymaleic acid and tts derivatives. 143 By oxidation with bromine the original acid is converted quantitatively into dioxytartaric acid. It is easy to prepare considerable quantities of free dioxytartaric acid in this way, and the author suggests the use of this acid as a delicate reagent for sodium. The constitution of the original acid has been established by determination of its molecular weight (in various ways), its basicity, the behaviour of acetyl chloride, benzoyl chloride, aniline and other reagents, and by its relation to succinic tartaric and dioxytartaric acids. It is shewn to be a tetrahydroxylic, dibasic, unsaturated acid belonging to the maleic series. Its formula is therefore OH. C.. COOH | OH. x1COOH. By action of hydrogen bromide, an isomeric modification has been obtained having a distinct crystalline form and yielding a more stable aniline salt. It is suggested that this may be the corresponding dioxyfumaric acid. (3) On the atomic weight of Oxygen. By A. Scott, M.A., Trinity College. Mr Scott gave a short account of the present state of our knowledge as to the atomic weight of oxygen, and said that it might be regarded as conclusively proved that if H=1, O=15°87 to 15°88. Morley determined the densities of hydrogen, and oxygen, the ratios by volume in which the gases combine (by a somewhat indirect method) and finally combined known weights of hydrogen and weighed the water produced. Thomsen made similar determinations but with far less pretension to the highest accuracy attainable. The results were Morley. Thomsen. Weight of a litre of paren at 0°C. and 760mm. at 1:42900 1°42906 sea level, lat. 45°. ditto for hydrogen............ ‘089873 089947 Ratio of densities ............ 15°9002 158878 Ratio of combining volumes 1: 200269 1: 2:00237 Atomic weight of oxygen... 15°879 15°869 m0) The ratios by volume in which the gases combine agree well w that published by the author directly three years ago, viz. 1 : 2:00245 at about 15°, on and 1 : 2:00285 at 0°C. 11—2 144 Mr Scott, On Carbon Monoxide and Oxygen. [April 27, (4) On the combining volumes of Carbon Monoaide and Oxygen. By A. Scott, M.A., Trinity College. Mr Scott described some preliminary experiments made to determine the ratio by volume in which carbon monoxide and oxygen unite to form carbon dioxide and to determine at the same time the volume of the latter gas in terms of the others. Experi- ments so far shewed that the ratio was very nearly 2:1 for the combining gases, but that satisfactory determinations of the volume of carbon dioxide produced had not been obtained as yet. (5) The constituents of Indian hemp resin. By T. H. HASTER- FIELD, M.A., Clare College, and T. B. Woop, M.A., Caius College. Cannabis Sativa (syn. indica) is made use of by nearly all the nations of Southern Asia and Northern Africa on account of the toxic constituents which it contains. It is stated that the plant when grown in Europe has no narcotic action, but this statement requires confirmation. The most common use to which the plant is put is as a substitute for opium or tobacco amongst smokers, but sweetmeats, drinks, and pills are also prepared, and all possess narcotic effects to a greater or less degree. The word Haschish is generic and applies to any preparation from the hemp plant ready for immediate use. Many investigators have already endeavoured to isolate from the hemp plant the substance to which the characteristic physio- logical action is due. Amongst the earliest workers in this direction T. and H. Smith of Edinburgh (1847) should be specially men- tioned. They prepared a resin from the alcoholic extract of the plant which produced the effects obtainable from Haschish. At a later date Personne attributed the effects of Cannabis to volatile oils; other observers again have stated that alkaloids are present in the plant but they have not succeeded in shewing that the alkaloidal substances can produce the same effects as are usually produced by Haschish. The experiments of the authors have shewn that the resin of T. and H. Smith contains a large per- centage of the narcotic constituent, but that the resin itself is pot a pure chemical compound. m. That the narcotic constituent is most certainly to be found in aq? plant resin is emphatically shewn by the fact that the prepa- tuion which is universally regarded by the natives of India as and cast powerful and dangerous drug which the plant can yield isolajning more nor less than the natural resin exuded in large quantity by the ripe plant but more particularly by the full grown, unfertilised female plants. To this resin the name “Charas” is 1896.] Messrs Kasterfield and Wood, On Indian hemp resin. 145 given; it is collected by the natives of India, who are said to walk through the ripe hemp fields dressed in leather jackets to which the resin adheres. This substance is sold in the bazaars at about 10 rupees per seer, but only small quantities may be bought at one time without a special license. The substance is mixed with tobacco and smoked; it produces almost instant intoxication fol- lowed by no unpleasant symptoms. One of the most remarkable points about Cannabis intoxication is the sensation of complete lack of responsibility which accompanies it, and there is little doubt that the great popularity of Haschish is due to this fact. No chemical investigation of Charas has been recorded, and since the narcotic constituent is so highly concentrated in this substance it appeared desirable to make a complete examination of the substance ; the authors would here express their indebted- ness to Mr C. A. Silberrad of Peterhouse, who has procured for them a considerable quantity of Charas, and has supplied them with much information regarding the use of the substance in India where he is now resident. Chenucal examination of Charas. The crude Charas is a substance with a greenish-brown earthy appearance; held between the fingers 1t becomes intensely sticky; its smell is highly characteristic. In order to isolate the con- stituents the Charas was extracted with alcohol, ether, or other organic solvent, whereby a large quantity of insoluble matter was separated. The alcoholic solution was concentrated and eventually submitted to fractional distillation, at first under atmospheric pressure, and finally in a partial vacuum. By this treatment the following substances were obtained :— (a) Insoluble residue. This substance has only been super- ficially examined; it consists to a very large extent of the hairs of the hemp plant; it contains upwards of fifty per cent. of ash and about three per cent. of nitrogen. Systematic examination for alkaloids gave negative results. (b) The distillate from the aleoholic extract coming over below 300° C. at atmospheric pressure. (c) The portion distilling between 270° and 290° at 15 to 60 mm. pressure. (d) A small quantity of pitch which was not submitted to further examination. Constituents of fraction (b). Terpene, C,,H,,. By re-fractionation (b) was separated into two- constituents: one of these boiled between 160° and 180° and came over for the most part at 165° to 175°; the substance is a terpene. 146 Messrs Easterfield & Wood, On Indian hemp resin. [April 27, Analysis. Calculated for 10Ha6 Found CESS 2 ye 2 ee 87:8 Gale SHEE. AY. 5 eae 12:0 Vapour density. Calculated Found 68 65 The specific gravity at 17° = 0819. The substance is laevo-rotary, it forms a mono-hydro-chloride. Sesqui-terpene, C,;H.,. / The second substance isolated from fraction (b) boiled at 258° —259° Analysis. Calculated for Crl tbe Found Cig 1S Sis Gas teeta ae 87:9 SSeS et eon casas ee ape a 116 Vapour density. Calculated for C,;H., Found 102 99°8 and 101°'8 The specific gravity = °898 at 18°. This compound has been isolated by other observers as a con- stituent of Personne’s “ Cannabene.” Constituents of fraction (c). When fraction (c) was allowed to stand crystals separated ; these were found to be sparingly soluble in alcohol, and were thus readily separated. Analysis shewed the substance to be a higher paraffin, and since the melting and boiling points of the substance agree with those which can with considerable certainty be pre- dicted for normal-nona-kosane there is some probability that the compound is this hydrocarbon. Analysis. Calculated for C,5H 60 Found Cb Saree tee eee 84:9 1896.] Messrs Easterfield and Wood, On Indian hemp resin. 147 Physical constants. Calculated for Oral s Py Found Melting point = 63—64 ............ 63°5—64 Boiling point) _ 85286 I85—290 at 15 5 mm. ok ee a Narcotic Red Oil, “Cannabinol,” C,,H.,O,. This forms more than 96 per cent. of fraction (c); it distilled constantly at 265°C. (20mm.). Analysis agreed with the formula © ..u,,0). Analysis. Calculated for C,,H.,0,5 Found ORE (Ue Seen a 791 |S VESw Cc hemh sss 55 ae 9-0 The figures are the mean of four concordant analyses made upon different preparations. The molecular weight by Raoult’s freezing-point method was found to be 273, the formula C,,H.,O, = 272. The substance is liquid above 60°C., below that temperature it is a cherry-red, semi-solid resin. It is insoluble in water, but dissolves easily in most organic solvents. The compound yields mon-acetyl and mono-benzoy] derivatives, both of which can be distilled under diminished pressure ; it is hence to be regarded as a hydroxy] compound; it yields nitro and apparently sulphonic derivatives and must therefore be a closed chain derivative. Further experiments upon the constitution of this remarkable substance are in progress. The authors propose the name Cannabinol for the compound. Cannabinol has been isolated by the authors from all the usual pharmaceutical preparations of Cannabis Indica. The experiments of Mr C. R. Marshall, Assistant to the Downing Professor of Medicine, shew conclusively that the narcotic action of the hemp plant is to be ascribed to the presence of this compound. The main results arrived at in the present investigation are summarised in the subjoined table : suoqivo-orpAFT 21q 878.1} 1U- TOU d pus TH WAN [fozueq-ouo;T pue [Aqooe-top, = {e) a /,$1g="SwuIs YEg “UU 0% 4% OLZ—oG9% oka = are) jourqvuueg ILO pert aa “] o8= ‘smIsQgT “Ayo ONPISEl o[IV[OA-UON ‘dd ON}IN-IC | (.€8%) .066—oE8% "THU GT 38 “g"g 5, (F9) oF 908-89 “dM /,GT.="sumis ¢ 4% Ho unyered SUITEISAX() “SUIS (G9 “ssord “UU Q9—0Z 1B 0066018 48 eo °/.% = "SULIs OF 06 S6— 0896 “dL euedi94-mnbsag —- 990171981 P2TYSIp wresey9 °/o OT ="SU13 00% ‘7 0008 AO SUI[IOg */[oG-T = SUuI3 0g o08T— 0ST “d'£ euediay, —————| SloS: GIN °/o Lp = 10948 SULeIBEAO *fo8g= *lo88 =‘sur13 eG), 10q}0 UL Tea: anpisery qsy SOI] G—SeIVyO 1896.] Mr Marshall, Pharmacological action of cannabis resin. 149 (6) Note on the pharmacological action of cannabis resin. By C. R. Marsuatt, M.B, (Vict.), Assistant to the Downing Professor of Medicine. The pure products: isolated by Messrs Easterfield and Wood were passed on to me for pharmacological investigation. They included the resin cannabinol, the terpenes, and a small quantity of the residue. As it was probable that the active principle lay in the resin, my attention was first turned to this body: a few experiments were made on animals and afterwards I took some myself. The effects produced were similar to those described by other observers as resulting from the crude drug. These did not occur after the use of the other substances, and it therefore seems probable that the effects of the hemp plant are due to the canna- binol which it contains. This is further supported by the fact that Messrs Easterfield and Wood have shewn that cannabinol exists in charas (the most potent of cannabis compounds) to the extent of 33 per cent., and that it can be obtained, in amounts varying with the activity, from all the cannabis preparations they have examined. In this communication I merely wish to establish the activity of cannabinol, and I shall therefore confine myself to a description of its effects without commenting upon it further. I was under the impression that I had taken a small dose of impure cannabinol sometime previously without any result, so, about 2°30 on the afternoon of Feb. 19 last, whilst engaged in putting up an apparatus for the distillation of zine ethyl, I took ‘l g— 15 g. of the pure substance from the end of a glass rod. The substance very gradually dissolved in my mouth, it possessed a peculiar pungent aromatic and slightly bitter taste, and seemed after some time to produce slight anesthesia of the mucous membrane covering the tongue and fauces. I forgot all about it and went on with my work; but soon after the zinc ethyl had commenced to distil—about 3:15—I suddenly felt a peculiar dryness in the mouth, apparently due to an increased viscidity of the saliva. This was quickly followed by paresthesia and weak- ness in the legs. Gradually my mental power diminished—I was no longer able to control the steps of the operation and com- menced to wander aimlessly about the room. I had the most irresistible tendency to laugh; everything seemed ridiculously funny. At times I felt more rational; but these lucid intervals gradually grew shorter and I fell under the full influence of the drug. i was now in a condition of acute intoxication : my speech was slurring; my gait ataxic. I was free from all sense of care and worry and consequently felt extremely happy. Fits of laughter 150 Mr Marshall, Note on cannabis resin. [April 27, occurred, especially at first, and sometimes the muscles of my face were drawn to an almost painful degree. The most peculiar effect was a complete loss of time relation: time seemed to have no existence. I was constantly taking out my watch thinking that hours must have passed, whereas only a few minutes had elapsed. This I believe was due to a complete loss of memory for recent events. The occurrence of lucid intervals was also peculiar in many ways. They seemed to come on suddenly, sometimes, but not always, as if the result of an effort of the will; they lasted a variable time, being shortest when the symptoms of intoxication were most marked; and in them I could converse in a rational manner and even direct the work of the laboratory to a certain extent. Except in a few instances I do not remember falling under the full influence of the drug again. About 6 o’clock I had two cups of coffee and afterwards feeling somewhat better walked home. The fresh air and exertion revived me. I ate a good dinner, afterwards read a little, and retired to bed at 11 o'clock without having experienced any symptoms of sleepiness. During the action of the cannabinol my pulse rose from 60 to 96 per minute; sensibility as determined by pinching was blunted; and my appearance was described as “ashy pale.” The pupils were dilated somewhat, but throughout reacted well to hight and accommodation. At no time do I remember having had any hallu- cinations ; no unpleasant after-effects were experienced ; and the substance seems to possess no constipating action. Smaller doses produced similar though less marked effects; with doses of less than ‘01 g. no distinct action was obtained. Monday, 11 May, 1896. PRoFEssoR J. J. THOMSON, PRESIDENT, IN THE CHAIR. The following communications were made to the Society : (1) Note on the formation of the germinal layers in Amphioxus. By E. W. Mac Bripg, M.A., Fellow of St John’s College. The account of the early development of Amphioxus incor- porated in text-books is due to Hatschek (“Studien iiber die Entwicklung des Amphioxus,” Arb. Zool. Inst. Wien, 1881). Briefly summarized it is as follows: the segmentation of the egg results in the formation of a regular blastula, which becomes converted into a gastrula by regular embolic invagination. The mesoblast 1896.) Mr Mac Bride, Germinal Layers in Amphiouvus. 151 y yp arises aS successive pairs of hollow diverticula of the gut, each of which gives rise to an adult myomere. When about half-a-dozen pairs of somites have been formed the most anterior part of the gut buds off two forwardly directed diverticula, which are at first symmetrically placed and equal to one another, but of which later the left becomes a small thick-walled pouch, which acquires an opening to the exterior. The right on the other hand is converted into a thin-walled vesicle, which extends forward and constitutes the cavity of the snout. When rather more than a dozen somites have been formed the remainder no longer arise as outgrowths of the gut, since a dorso- lateral fold of the alimentary canal (by the division of which the first somites were formed) becomes now completely separated from the rest of the alimentary tract and constitutes a kind of primitive streak, out of which the remaining somites are formed. Quite recently Basilius Lwoff (“Die Bildung der primiren Keimblatter und die Entstehung der Chorda und des Mesoderms ber den Wirbelthieren,” Bull. de Moscou, 1894) has given a divergent account of the early development of Amphioxus. Ac- cording to him the mesoblast is a dorso-lateral solid outgrowth of the gut, in which the ceelomic spaces (cavities of the myomeres) appear later as secondary splits: it is true that the pressure of the notochord on the mid-dorsal wall of the gut depresses it and raises up the sides as two folds, but these have nothing to do with the formation of the ccelom. The development of Amphioxus is exceedingly important from a theoretical point of view, since in it we meet with the only instance of a Vertebrate egg (outside the secondarily modified eggs of the Mammalia), where the yolk is small in quantity and evenly distributed, and where consequently the early developmental processes are not impeded by its presence. Hence it is necessary to interpret the development of other Vertebrates in terms of the development of Amphioxus, and not vice versé: and in view of this consideration, and also of the doubt in which Lwoff’s paper had enveloped our ideas on the subject of the formation of the layers, I undertook a reinvestigation of the whole subject, and hope to be able to publish my completed results this autumn. I am greatly indebted to Mr Sedgwick for placing at my disposal a large amount of valuable material collected in Sicily by himself in 1889 and by Mr Willey in 1890. If we examine a section of a just completed gastrula we ob- serve that it is roughly triangular in shape with the apex directed ventrally, and that each of the lateral angles is produced into a hollow ridge. In a slightly later stage we find that the cavity of this ridge is shut off from the enteric space in front, whereas behind it still opens into it. In a still later stage we find the 172 Mr Mac Bride, Note on the formation of [May 11, same appearance as before posteriorly and also in the most anterior sections: but between there is a place where the lumen has become obliterated, so that the front part of the cavity has now no connec- tion with the hinder part, and thus from a forwardly-directed hollow diverticulum of the gut a mesoblastic somite has been cut off. As the larva grows in length this hollow diverticulum grows also, and from its anterior end a succession of somites are segmented off. In the meantime however, owing to the consumption of the yolk, the larva has diminished very much in diameter, and the cavity of the groove which we may term the ccelomic groove has disappeared owing to the apposition of its opposite walls; conse- quently it appears as a solid outgrowth of the gut-wall, with which however it does not, so far as I have seen, lose its con- nection. The mesoblast of Amphioxus may thus be said to originate as one pair of pouches, opening into the gut behind, which gradually become divided into somites; and it 1s of great interest to notice that according to recent investigations this is true also of the lower Reptilia. (Will, ‘‘Zusammenfassende Uebersicht,’ Zool. Centralblatt, April 15, 1894.) The vesicles, however, which later become the first pair of myomeres have a different origin. They arise as an independent pair of gut pouches situated anterior to the pouches we have just been considering, and placed also nearer the middle line; that on the left side retains for some time its connection with the gut; and although later the continuity of the two lumina ceases to be observable, owing no doubt to the same cause as that which obliterates the lumen of the ccelomic groove, the continuity of the gut and somite walls is traceable in all the stages I have as yet examined. As Hatschek’s “nephridium” is found in precisely the same position in the later larva as this neck of communication between the left anterior somite and the gut, I have no doubt that the two structures are identical. The tube known as Hatschek’s nephridium is placed in front of the mouth in a horizontal position, and Van Wijhe (“Ueber Am- phioxus,” Anat. Anz., 1893) has found that it communicates with the gut; this observation I can confirm, and can add that at its anterior end it opens into the left anterior somite. Van Wijhe imagined that it was derived from the connection between the gut and the left of those anterior outgrowths from the gut, described by Hatschek, which we may term head-cavities; but these latter soon lose all trace of their primitive communication with the gut. On reviewing the facts now related we see first that the ecelom of Amphioxus is an indubitable enteroccele, and secondly that the formation of the mesoblast in this animal is easily refer- able to the type which Bateson has described in the case of 1896.] the germinal layers in Amphioxus. 153 Balanoglossus (Q. J. M. S., 1884). The head cavities represent the proboscis cavity, the first myomeres the collar cavities, and the great posterior mesoblastic pouch which becomes segmented into somites the trunk cavity. ZoonocicaL LABORATORY, May 15, 1896. (2) Note on the continuity of Mesenchyme cells in Echinid larve. By E. W. Mac Brive, M.A., Fellow of St John’s College. About a year and a half ago Mr Sedgwick read a paper before this Society (“On the Inadequacy of the Cell-theory and on the Development of Nerves,’ A. Sedgwick, Proc. Camb. Phil. Soc., Vol. virt., Part rv.) in which he strongly insisted on the view that free stellate mesoblast cells such as are commonly figured are not to be found in the Elasmobranch embryo, but that the appearances thus interpreted were really only the thickened nodes of a protoplasmic network. Last vacation I had the opportunity of examining numerous larve of Echinus esculentus, and my observations support those of Mr Sedgwick in a very striking manner. The larvee specially referred to were in the gastrula stage and possessed a comparatively narrow alimentary tract, outside which was a wide blastoceele or primary body cavity; and in this latter were numerous mesenchyme cells. These mesenchyme cells were of two main kinds: (1) aggre- gated masses of rounded cells, which formed the matrix of the future larval skeleton, (2) wandering cells or amcebocytes. Of these latter again there were two varieties, of which the first were obviously stellate in form and connected with each other and the walls of the blastoccele by long processes. This kind of cell has been seen and figured by Théel (“The Development of Echino- cyamus pusillus,” Hjalmar Théel, Royal Soc. Upsala, 1892), who however regarded the union of the processes of these stellate cells as a secondary phenomenon. The second kind of wandering cell is rounded in form, and is in fact precisely similar to the Amoebocyte familiar to all who have studied Echinoderm anatomy. It has always been described and figured as if it were perfectly free: yet 1f one examines a slightly compressed living gastrula of Kchinus esculentus one observes that these rounded cells, which at first sight look as if they were completely free, are in every case connected either with neighbouring cells or with the walls of the blastoccele by exces- sively fine threads along which they apparently travel. 154 Mr Mac Bride, Mesenchyme cells in Echinid larve. [May 11, Whilst not wishing to go so far as Mr Sedgwick in denying reality to the conception of the cell, I am inclined to hold that the cell structure of the Metazoa is largely due to secondary differentiation, and that a multinucleate Protozoon like Actino- spherium is to be compared to the Metazoon body, and not to a single unit of the same. (83) Crania from Tenerife. By F. C. SHRUBSALL, B.A., Clare College. When engaged in a course of study at the Vesalianum at Basel, Professor Kollmann poimted out the importance of the Guanches and advised a detailed examination of that race if ever an occasion should offer. This spring, having to spend a short time in Teneriffe, I gladly availed myself of the opportunity to measure and describe all the Guanche skulls of whose existence I could learn in the island. I first examined those in the pos- session of the British Vice-consul, and afterwards worked at various private collections, both im Santa Cruz and Orotava, besides which I have measured the crania in the Vesalianum at Basel, those in the Anatomical museum at Cambridge, and those in the museum of the Royal College of Surgeons, London. To the owners and curators of these collections I must return my sincere thanks for the great kindness and courtesy with which they gave me every facility in their power for my study. Altogether I have examined 54 male and 39 female skulls, and some 200 long bones, while in the seriations at the end of the paper I have included the various indices of the skulls in the collection from the Canary archipelago at Las Palmas, a printed copy of the measurements of which was lent me by Don Ramon Gomez of Puerto-Orotava. The following are the details of the examination : Cranium. On taking the cranial capacity of skulls from Teneriffe it is at once apparent that while they can roughly be divided into two series, the large and the small, the classification thus established does not extend to other features, all the variations of face and cranium hereinafter to be described being found in either series. The average capacity of the large male skulls is 1550 cc. (maximum 1600 cc., minimum 1425 cc.), while that of the series of small male skulls is 1180 ce. (maximum 1250 cc., minimum 1155 cc.). The total mean of the male skulls is 1451 ce., and the average capacity of the females is 1875 cc., a mean sexual difference of 75 ce. or 75 of capacity. This at first sight anomalous result being doubtless 1896.] Mr Shrubsall, Crania from Teneriffe. 155 due to the fact that all the female crania available for the purpose of this measurement belonged to the type of large skulls. On seriating the table of capacities maxima appear on the curve at - 1525 and 1160, shewing the existence of the two series. The mean capacity of male skulls from Teneriffe is given by Verneau as 1672 cc. and by Flower as 1426. Comparing the capacity of these crania with that of other representatives of the Mediterranean race we have Cromagnon, No. 1, 1590, Solutré, No. 5, 1500, Caverne de L’Homme Mort, 1606, Grotte Baye, 1534, Basques, 1564, Teneriffan (excluding small skulls), 1550. Crania from Teneriffe are on the average long and fairly broad, the greatest transverse diameter being usually bitemporal and the length being due to development of the occipital region. The average length of male skulls is 181 mm., and the average breadth 139 mm., giving a mean cephalic breadth imdex of 76°8, while in females the average length 178 mm. and the average breadth 139 mm., giving an index of 78:1; the mean index for males and females combined being 77°3. Comparing this with the mean indices of crania from the different islands of the Canary archipelago as represented in the museum at Las Palmas and with other races, we have Teneriffe, 78 aa are i os mean for the whole archipelago, 76°3, Hierro, 73:2 Caverne de L’Homme Mort, 73:2, Grotte de Baye, 78, Spanish Basques, 77°6. These figures shew a general relationship between the Cro- magnon race and the former inhabitants of Teneriffe, which is further brought out by a comparative seriation of the cephalic indices of adult skulls. [May 11, Mr Shrubsall, Crania from Teneriffe. 156 So[BUla,T BIOULOL) SO[BULIT Areweg purty OS OS OS BP ee | maa Sa[vUle T aye J, Lael OO 4 6 OH OO b= C/E iS SOTVUA,T ® SOTRIAT ‘osejediyory Oo Hon last of os] AeUBQ = *UOT}D2T Sse = of Se Sec ee -[OD svueg sary se) = OIE BHODAAHANA ysruedg ie we \IOJ[ OULULO FT ap ou1eAeD mam NOOO MS AN Osvedrqo1y d CO ANDROHNAMMODAHH AN 1¥40.L ANAANAN BLIULOY) | 4 OHH OMDOMHMANH A Areue @) + HANIARMMOMOANA purty ayiaauey, | Teeter eit Nee Seat eC. Sh Se Xopuy DRHOFAMHIDOnRDAROHANOH OOM rerererererrnnnno classifying the indices Comparisons are also furthered by according to Brocas divisions. Table of Percentages of Cephalic Index. osvjedipor1y > SMHS an 10 GD k= 0 oO = ANE | AAA 3 xy 5 6 6 O> ~ H BOUL Ornron LOS OPS | osejediyo1y SHO O19 69 e410 aDaOOs n TOL oD oO g ES a D010 RSOBEN G OA 619 Sug AN NvIu.1d A > OH ‘setoueny) I~ ODD n oo SH ro o ee — 3s = paelery ‘eavyo19 qe ATVNSSQ WOT ST[MYS Uropojy QO OH 1d Nr oO Of} (2) es ee ae a eicl ee 3 lS Oe eo 85 aos sig @ iS} ISI 4 OS era FF S985 (SB) © i (Ss aa gals Begcs as Qe & Hnane 1896.] Mr Shrubsall, Crania from Teneriffe. 157 The wide range covered by the indices, viz. 13 units both in male and female skulls is sufficient to indicate a mixture of races, while the foregoing table shews that comparative uniformity must have existed at the time of the Spanish conquest of the Canaries. With regard to height, the skulls in the main are low rather than high, the mean altitudinal index for males from Teneriffe being 70°5, and for females 72°2, as against male 72°5, and female 71:9 for the whole archipelago. Contrasting with other series, we have for males, Guanches, 705, Cromagnon, No. 1, 65'3, Solutré, No. 5, (pre Caverne de L’Homme Mort, 68°8, Spanish Basques, 70°7, Modern Teneriffan, (aoe and for females, Guanches, G22, Grenelle, No. 2, 72, Solutré, No. 2, 74°6, again shewing the close resemblance to the Cromagnon race of the former inhabitants of the archipelago. The division into classes by the altitudinal index is as follows: Males Females Total | | Total Teneriffe Archi- || Teneriffe Archi- pelago pelago Chameecephalic 24:1 18:9 30°8 27°4 Orthocephalic 569 BOs i. 90 58-9 Hypsicephalic 19 21:3 19:2 13:7 1 esos Sete aot ee DL Contrasting breadth and height, the mean index for male Teneriffan skulls is 92°9, and for females 92:1. Compare Cromagnon, 88°6, Solutré, No. 5, 93°7, Caverne de L’Homme Mort, 96°4, Spanish Basques, 92°4., VOL. IX. PT, III. 1 158 Mr Shrubsall, Crania from Teneriffe. [May 11, Classifying by this index according to Brocas divisions, we obtain the following table: Males Females Teneriffe | anes | Teneriffe anes Akrocephalic 40 28-1 44-4 37°5 Metriocephalic 45°5 45°5 48:1 45°8 Tapeinocephalic 14:5 26-4 7:4 16°7 In the great majority of crania from Teneriffe the frontal region is well developed, the forehead being full, rounded and decidedly broad, although in some which constitute a distinct type by themselves it is low and receding. The glabella is only moderately prominent, but the superciliary ridges are well developed even in the female, the subcerebral curve contributing on the average in the male 23:9 per cent. and in the female 17-2 per cent. of the total frontal curve. The frontal eminences are usually prominent but do not reach to the level of the mid-sagittal line. The sagittal curve in most typical cases runs uniformly back to the lambda, but in some crania the annular post coronal depression of the middle third of the parietal bone described by M. Vernau is to be seen. This depression, which somewhat resembles that produced by a bandage tied tightly round the head during early youth, is, according to that author, not an artificial deformity but a natural variation in the sagittal curve. After passing the lambda this curve often shews a distinct flatten- ing over the upper part of the occipital bone, and when this is present there is a decided fulness of the whole occipital region, the projection backwards taking place immediately at the parieto- occipital suture. From the mion the curve passes sharply down- wards and forwards to the opisthion, the bone in this region being flattened and strongly marked by muscular impressions. In many cases the conceptaculz cerebelli are so far developed that the skull rests posteriorly upon them rather than upon the mastoid processes or the occipital condyles. The inferior portion of the occipital bone is horizontal. The relationships in point of size of the various portions of the curve are shewn in the following table, in which they are compared with the length of the total sagittal curve (= 100): 1896.] Mr Shrubsall, Crania from Teneriffe. 159 Frontal | Parietal | Occipital Males 30°D 34:4 3 Females 33°7 32°6 3 Making similar comparisons for other curves. The relation of the supra-auricular to the total transverse curve (= 100) is in males 65°6 and in females 66°8, while that of the preauricular to the total horizontal (=100) is for males 47-7 and for females 45:4 as compared with 45°3 in skulls from Caverne de L’ Homme Mort, and 46°1 in Basques. However on seriating the results of this last relation, we find that very few crania present this actual mean relationship but group themselves round the numbers 41 and 52, indicating a greater frontal and occipital development respectively. Viewed in norma occipitalis the skulls are somewhat penta- gonal in form, but the parietal eminences are not very prominent, and the greatest transverse diameter in about 80 per cent. of crania lies between the temporal bones. In the better class of mummies, presumably those of chieftains of some importance, there is in several instances, more frequently so than in the less cared for bodies, a prominent median sagittal ridge along a groove in which the interparietal suture runs for the posterior half of its course. The temporal crest is always well marked both in male and female crania, the double nature of the ridge being very distinct. The zygomatic processes are stout, strongly arched outwards and with a supramastoid ridge usually extending up on to the posterior inferior angle of the parietal bone. The pterion is of the ordinary H shape and anomalies are rare in this situation. In many cases the sphenoid and frontal bones close behind the external orbital process are markedly bulged outwards, and in the average among males the transverse diameter from one pterion to the other is greater than the bistephanic breadth. Viewed in norma verticalis the crania are plainly pheenozygous, and appear either pentagonal or, as in a smaller number of cases, oval ; a slight projection of the face is also noticeable. The mean dimensions appear in the following table: 12—2 160 Mr Shrubsall, Crania from Teneriffe. [May 11, “i Males Females S| | rs} = efi | 22 | ose | a= 255 Sy || 255 a S28) 8S | > eagier ao ee | Minimum Frontal Breadth 95 | 68°3 94 | 67:6 Interpterion Breadth 112). | (80:6) |) (Osea Bi-stephanic Breadth 111 REY LL 80:6 Bi-asteric Breadth 114 82 1077 em Maximum Transverse Breadth 139 LOO) || TSoe ue | The fronto-zygomatic dex of skulls from Teneriffe is for males 83°3 and for females 89. Cf. Caverne de L’Homme Mort, 89:9, Basques, 91°8, Grotte de Baye, 83°5. This series of crania may readily be classified into two groups according to the complication of their sutures. In the first and smaller division the sutures are simple and wormian bones the exception ; while in the second series the sutures, more especially the lambdoid and coronal, are excessively complicated, while it is rare to find even the sagittal suture simple and wormian bones are very common. A persistent metopic suture is to be found in about 8 per cent. of crania of the second series; it may be com- plete, or persistent near either the bregma or the glabella, the latter arrangement being the more frequent. Synostosis usually commences in the sagittal and lower part of the coronal sutures; contrary to the usual custom the lambdoid suture is quite the last to close. M. Verneau indeed describes a case in which the squamous suture had closed up while the lamb- doid was still open. Wormian bones are the rule in the lambdoid suture, the com- monest arrangement being a series with their long axes nearly vertical and their short axes arranged along the line of the suture, the two sides being frequently asymmetrical. There may be a single ‘os-epactal’ or an ‘os-epactal’ with a small median wormian bone in front of it. - Passing on from the study of the cranium to that of the face we find a considerably greater range of variation, Faces from 1896.] Mr Shrubsall, Crania from Teneriffe. 161 Teneriffe are for the more part orthognathous, broad above, nar- rowing down in the maxillary and mandibular regions, with low, broad very rectangular orbits, superciliary ridges well marked and frontal sinuses capacious and extensive; but one also meets with skulls presenting the features of long, uniformly narrow, slightly prognathous faces with high and rounded orbits. The nose is as a rule straight, prominent and leptorhine, but in other cases it is platyrhine, and the lower border instead of being sharply cut, as is typical, may be rounded off or even present simian grooves. The nasal spine is not prominent. The palate is of almost all forms and sizes, the most typical being the ellipse, although the parabolic form is also well represented, the alveolar border projects forwards and accounts for the slight alveolar sub- nasal prognathism frequently found in skulls from the Canary archipelago. The lower jaw is strong, broad at the condyles and angle, but narrow at the chin. The angle is frequently very markedly everted, shewing the strength of the muscles, thus correlating well with the strength of the zygomatic arch and the great wearing down of the teeth, all bemg doubtless due to the grinding efforts necessary to masticate the but partially cooked cereals which constituted then, as now, the staple diet of Teneriffe, and which also accounts for the frequent traces of alveolar abscess in Guanche skulls. The various facial indices are tabulated in order below. Superior facial index of Broca. Mean male, 63; female, 65. In the seriation table of this index the range is from 58—87 (29 units) exhibiting maxima at 62 and 66 for males and at 68 for females. Cf. males, Cromagnon, No. 1, 63°4, Grenelle, 667, Grotte de Baye, 66°4, Homme Mort, 67:6, Basques, 67°8. females, Grenelle, No. 2, 66°5, Solutré, No. 2, 66°4. Upper facial index of Kollmann. Mean for males, 50°2; mean for females, 47°7. The skulls therefore lie on the border line of lepto and chame- prosopy, the percentages in either division being as follows: 162 Mr Shrubsall, Crania from Teneriffe. [May 11, Males | Females Teneriffe | }000 | Teneriffe | 310, Chamezeprosope 499 47:1 82°3 85:7 Leptoprosope 57-1 52°9 16-7 14°3 This shews that while the males tend towards leptoprosopy the females are almost entirely chameprosopic, and if these indices are viewed together with the orbital and nasal indices the very disharmonic nature of the face, more especially in the female skulls, is at once brought to notice. The distribution of skulls from Teneriffe among the types of Prof. Kollmann is shewn by the following table : | Males | Females Chameeprosope Dolichocephals 30 15°4 Chameprosope Mesocephals 36°4 38:5 Chameprosope Brachycephals 6:1 23°1 Leptoprosope Dolichocephals iki Leptoprosope Mesocephals 42-4 15-4 Leptoprosope Brachycephals | lh | The mean orbital index is for males 83°6 and for females 87:2. Seriation of this index shews a range from 68—97 (29 units) with maxima at 80, 83, and 89. Cf. Solutré, No.1, 74:3, Homme Mort, 80, Grotte de Baye, 81:4, Spanish Basques, 82°6. The orbits are frequently asymmetrical, the difference in index between the right and left sometimes amounting to 3 or 4 units. The nasal index shews a range from 41—60 with maxima at 45—48 and 52. Mean indices being male 47-6; female 41°5. Cf. Cromagnon, No. 1, 45:1, Grenelle, No. 1, 49-2, Solutré, No. 5, 52°4, Homme Mort, 454, Spanish Basques, 43°S. 1896.] The nasal index of the ancient can be compared with that of the modern inhabitants of Teneriffe, in whom there is a considerable admixture of Guanche blood, by means of this table of percentages, Mr Shrubsall, Crania from Teneriffe. | PS ilivilse ~ i= | b= | [32 Ss eee Be s3s <4 SS nes RS: | np jo) Leptorhine 27 44 |_Mesorhine —_ 7 35-4 Platyrhine | 8 20°6 shewing the convergence to a mean type in the modern skull. The general features of the face can easily be traced in a combined table of facial, orbital and nasal indices, in which I compare the results of my measurements in Teneriffe and else- where with those of the collection of skulls from the whole archipelago at Las Palmas and with those of M. Verneau in Teneriffe itself. Males. Teneriffe. M. Verneau Teneriffe Archipelago Wesel culeciiesete | a | 8 |S Microseme | 25:9 | 55°6 | 74:1 || 38:5 | 48-5 | 50 44-2 | 46°3 | 50°4 Mesoseme af | d0°8 | 18:5 || 34°6 | 31°8 | 32°8 || 22:1 | 33°6 | 38-2 Megaseme | 37 | Vil | 7-4 || 26-9 | 19-7.) 17-2 || 33-7 | 20-1 | 11-4 Females. Teneriffe. M. Verneau | Teneriffe Archipelago ell eo) ie ba fc ae Pace |e Sew Nil Slee vei alae Microseme) 30 | 42-9 61:5 || 25 | 29 , 39-4 Bee 38 | Mesoseme | 40 | 28°6 | 30°8 || 33°3 | 25:8 | 30°3 | 27°6 | 30°8 | 38 Megs 30 | 28-6 | 7:7 |] 41-7 | 45-2 | 30:3 || 36-2 39-7| 24 | 164 Mr Shrubsall, Crana from Teneriffe. [May 11, The palatal index has a range of 61—94 with maxima at 78 and 89, mean index for the series male, 79°3; female, 78°9. Cf. L’Homme Mort, 72°7, Spanish Basques, 75-2, Grotte de Baye, 75°5, French Basques, 79°6. Classifying these indices according to Virchow’s divisions we find among males well represented lepto- and brachystaphylinic groups with somewhat smaller numbers intermediately. Males. | Females. Teneriffe | Archipelago || Teneriffe | Archipelago | Leptostaphylin 56°5 59°5 | 98°6 66:2 Mesostaphylin 16:1 Iie I Bir 23:9 Brachystaphylin 27-4 21:4 13°8 9°9 The mandible is characterised by the narrowness of the chin, the strength of the muscular impressions and alveolar border ; the eversion of the angle and the prominence of the genial tubercles. The mean goniozygomatic index is in the male 77:6, and in the female, 72:5, ef. Mediterraneans, 77, Mean European, 77°6, Arabs, 74:2, Summing up the results of the foregoing measurements it appears that four types of skull existed in Teneriffe at a period anterior to the Spanish invasion. I. The first and most important type in respect of numbers presents the features of a capacious skull with moderately pro- minent glabella and superciliary ridges, a well-developed frontal region and full rounded forehead. It has a sagittal curve pre- senting a post coronal depression, a lambdoid flattening and a great fillmg out and projection of the occipital region of the cranium, while the greatest breadth is bitemporal. The sutures are very complicated, metopism is not infrequent and wormian bones are very prevalent in the lambdoid suture. The face is short, broad above, narrowed below, orthognathous, with low broad very rectangular orbits, a leptorhine sharply cut nose, slightly sunken at the root, an elliptical palate and greatly worn teeth. 1896.] Mr Shrubsall, Crana from Teneriffe. 165 This type, which from its superior numbers and greater prevalence in Teneriffe than in the other islands of the group is to be regarded as that of the Guanches, may be shortly described as mesaticephalic, orthocephalic, orthognathous, microseme, lepto- rhine and leptostaphylin. All the succeeding types of skull differ from the above in the absence of the Jambdoid flattening of the sagittal suture and in the absence of the fulness and projection of the occipital region. II. The second type, distinguished by a smaller capacity, a retreating forehead, greater height of skull and lower cephalic index combined with simpler sutures, comparative absence of wormian bones, much stronger muscular impressions, larger mas- toids, and more prominent inion, is somewhat wedge-shaped when viewed in norma verticalis. It differs but little from the pre- ceding in facial features, but has a narrower mandible and a parabolic palate. This type, which is well represented in Teneriffe and Hierro, may be described as dolichocephalic, orthocephalic, mesoseme, leptorhine and brachystaphylin. III. The third type presents the features of an ovoid skull of small capacity with glabella, superciliary ridges and parietal eminences not very prominent, although the greatest transverse diameter is interparietal. It is dolichocephalic and hypsisteno- cephalic with a sagittal curve rising directly and uniformly from the nasion, a face prominent and slightly prognathous, a nose straight, sharply cut at lower border but not depressed at the root, orbits high and rounded and a palate decidedly long with the ends of its dental arcade seldom or never incurved. This type of skull, found more frequently in Grand Canary than in Teneriffe, is apparently that described by M. Verneau as Semitic. IV. The fourth type is a short broad skull of fair capacity, with a nose not sharply cut but rounded off at its lower border and often platyrhine or high mesorhine, with high and rounded orbits and a palate in some cases long and parabolic, but in a few, elliptical. This type appears to occur in the N. and E. of Teneriffe and in Gomera more freely than in the rest of the archipelago. Long Bones. As these were only studied in the actual burial caves and their Vicinity, situations somewhat difficult of access, but a few slight observations were possible. Taking the bones in order: The humerus as a rule was strong and well-marked, the deltoid impression and musculo-spiral groove being especially prominent, 166 Mr Shrubsall, Crania from Teneriffe. [May 11, the olecranon fossa was frequently perforated (in 23 per cent. of the bones examined). The average maximum length was in the male 323 mm. and in the female 304 mm. The radius and ulna were in most cases strongly marked, but presented no special features of interest. Average length, radius male 247 mm., female 232 mm., but, however, very few examples were measured of the forearm bones of the latter sex. Ulna. Male 265 mm., female 243 mm. The femora were large and strong, deeply marked by muscular impressions and often pilastered. The average length in the oblique position with both condyles touching the lower end of the measuring apparatus was for males 424mm. and for females 414mm. The tebiae were strong and in some instances platycnemic, the average length being for males 365 mm. and for females 335 mm. The jfibulae, which were deeply channelled, were of the mean length of 352mm. in the case of the male and 331 mm. in that of the female bones. Calculating the height of the former living inhabitants from these measurements by means of M. Manouvrier’s sliding scale it is found to have been 1642 mm. for the males and 1552 mm. for the females. The results from each series of bones is sShewn in the subjoined table. Calculated height of living individual in millimetres: Bone | Male Female Humerus | 1637 1560 Radius 1666 == Ulna | 1668 1578 Femur | 1610 IES SKS | Tibia 1644 1542 Fibula 1626 1542 | | Mean height | 1642 1552 giving a mean sexual difference of 90 mm. Comparing the mean obtained for Teneriffe with the heights arrived at by Manouvrier’s scale for the races with which the crania were compared, we have Teneriffe, 1642, Cromagnon, 1750, L’Homme Mort, 1620, Grotte de Laugerie, 1650. 1896.] Mr Shrubsall, Crania from Teneriffe. 167 A seriation of the heights computed from bones in Teneriffe shews a range in the case of males of 1550—1710 (160 units) and in the case of females of 1460—1660 (200 units) with maxima at 1640 and 1550 respectively: this range is sufficient to indicate a probable original mixture of tall and short races, although it is clear from historical evidence that the height was fairly even throughout the island at the time of the Spanish invasion and that the Guanches were tall. In an attempt to reconstruct the features of the former in- habitants we draw our evidence from three sources, the present population, the chronicles of the Spanish invasion and such ancient records of the history of the island as we possess. Turning to the first, we find congregated in and near the towns on the north and east people with olive skins, dark eyes and black or dark brown hair, obviously of Spanish descent; lying further out and distributed in the country districts throughout the island is a fairer complexioned, brown eyed, chestnut haired race mixed among whom are isolated families of the former type, while in the rugged and less easily accessible southern side where the Guanches last held out and where their descendants are still supposed to remain in the greatest purity, there are many of fair complexion, blue eyes and fair or flaxen hair and golden haired children are quite common. From the second source we learn that many of the inhabitants of the north of the island at the time of the invasion were fairer than the Spaniards, although some of those in the South were dark, while the native records tell the ad- ventures of a golden haired blue-eyed princess. When added to this we find in many mummies a profusion of short yellow hair, although this latter evidence is not strictly admissible owing to post mortem changes, there is some reason for concluding that at any rate one race in the island presented the features of a fair complexion, blue eyes and light coloured hair, and belonged essen- tially to the blonde type of Eurafrican peoples. It is also very probable that there were also in the island from early times people of darker complexion and hair. In the eastern islands of the Canary archipelago early voyagers describe a race with dark skins, dark hair and thick lips; some of these people doubtless of African origin might have spread into Teneriffe and account for some of the peculiar features of that country. ' In conclusion there appear to have been in Teneriffe, (1) A dominant race, the Guanches, tall, blonde, blue-eyed, muscular, with a skull of the first type. (2) A race with a skull of type two, also tall and, as far as evidence from their mummies go, probably blonde. 168 Mr Shrubsall, Crania from Teneriffe. [May 11, (3) A Semitic race, with a skull of the third type, probably dark and of medium height. (4) A brachycephalic race (type IV) probably short and dark. The records in European history anterior to the X Vth century relating to the Canary islands are very scanty, but from them we learn that the only races known to have been aware of the exist- ence of that archipelago and thus to have come in contact with and possibly had some influence on its population are the Greeks and Phoenicians possibly, the Carthaginians certainly; the Mauri- tanians who invaded the islands but were repulsed except at Lanzarote and Furteventura; the Irish, whose missionaries under St Brondan appear to have reached the ‘Fortunate Islands,’ and finally the modern Europeans of whom one nationality, the Span- iards, conquered the Archipelago. At the time of the conquest the islands were certainly inhabited by mutually hostile tribes differing however only slightly in physical features and speaking similar languages, although on these last points there is a conflict of evidence between the various chroniclers of the invasion, and as the earliest accounts of these people agree in most respects with those of the ‘conquistadores’ and also with later descriptions, there can be no doubt that the islanders must have been left undisturbed for a great number of years, perhaps of centuries, uninfluenced by the great migrations which have shaken Europe and rendered racial differentiation therein so difficult. Possibly then the Guanches, or typical race of Teneriffe, may represent an early race of mankind existing down to the present day in com- parative purity under conditions similar to those which have preserved the characteristic fauna of Australasia. Their physical features lend support to such an hypothesis; for, on the one hand, the Guanches resemble the Cromagnon race, more especially those relics of it discovered at Solutré, and also the Basques of North- western Spain, while, on the other hand, they have many features in common with the Kabyles, Berbers, and Hamitic tribes gener- ally of North Africa. The other and less dominant types in the island have very probably been introduced at the time of the various discoveries of the archipelago by the Mediterranean races. 1896.] Mr Shrubsall, Crania from Teneriffe. 169 TABLE OF SERIATIONS. Length, Height, Index. ae Teneriffe Gomera | heonanae 3 | 2 8 s Aisle) ea/e& |/aje] 3) 4 63 1 ae 64 1 a 65 Oe || 1 3 66 a) 1 Oe ed 67 | | 4 4 1 68 )-23)| 4 2 3 1 AAT 5 2) eae | ime EY | 10 5 Re eeun eda. ee AO OP Sod! yall we rise a |, We Ba iS. 199) 18 Bo hon |S) il) Bl Sse lees | 20m) 12 ie 3) | 3 "i Gale l4 | a7) 14 MA Uh | ce || 3) 4/3] 18 | 12 75 | 6 Ho 4 | i 94 7) 3) | 3 dene oe i gm) 14 os aeteet $e | 7 ay alas er aber | i ete 02 1 hese | 80 ae | 1 | 170 Mr Shrubsall, Crania from Teneriffe. [May 11, TABLE OF SERIATIONS. Breadth, Height, Index. Grand : Total Canary Teneriffe Gomera. Archipelago = 3 5 3 I = I 3 =I 5 = ey = = cy = cs 78 1 I 9 80 1 1 81 2 2 82 1 1 83 84 if 1 85 86 1 2 | 1 D, 3 87 1 1 4 ie 4 88 1 4 4 2 i | 6 6 89 1 6 2 1 1 | 8 4 90 il 1 3 3 2 ie Ale NZ 9 91 5 6 1 5 8 | 92 1 1 6 1 2 Wap ae, Ties 93 4 3 a 3 2 2 14 8 94 2 2 9 8 2 13 12 95 1 5 3 4 3 q 11 96 9 1 4 3 By 2 V5) 6 97 1 3 1 4 oy 98 2 2 5 1 1 1 8 4 99 3 4 2 1 1 8 3 100 3 1 1 4 2 101 6 1 2 8 2, 102 2 1 2 1 103 Hi 1 2, 104 1 y 3 105 1 1 106 1 1 107 1 1 108 1 1 Ne ee Mr Shrubsall, Crania from Teneriffe. 171 1896.] TABLE OF SERIATIONS. Upper Facial Index of Broca. a oe ° ey SO[VULI FT 4+ Ae ANE OMMErNOS OHO AN 4 il o = = = = — = — — 3 5 SolTBIL BAAN MD DOO O D 119 19 HO 69 OD 09 aa _ < a s So[BULO eS Sqn NAAN o g = —— = S) S sr AAA AMANNG AA 2 SO[VUlI TT a UN SH MOAR ANAST AN cl a : ——_ oe cB) —— — = 5 al Sole SH SAIN OHAG AON AA - il OA a ANAM = Sb SOT BUI, aes ga os S sole AH OHONAT NAAN aa ORORDOHNAGHODORDROAAMDHNOrRDHOAVAGDHGAOMrA DIDDMOODSDSHSOSSOOOREREEEEEEErDDDDHDDHHDD xopuy 172 Mr Shrubsall, Crania from Teneriffe. TABLE OF SERIATIONS. Orbital Index. [May 11, | Gane | Teneriffe | Gomera Archipelago & 3S @ S % 3 2 es cue cer ch Pe eGo secs |S 1 i 1 1 1 1 1 2 3 3 2 2 1 4 iT 1 3 # 3 1 a 1 1 11 D) 1 1 3 4 1 1 1 3 1 1 5 9 AN) 2 7 1 2 ees 3 4 3 2 6 7 1 1 4 3 4 9 9 G 6 6 5 Di 8 7 6 4 5 l 1 11 6 2 1 2 2 2 1 6 4 2 11 3 5 7 15 13 1 1 2 1 3 3 5 8 12 4 3 16 22 tS} 1 1 i 1 2 1 D) 5 1 3 1 4 1 ee ad 2 | 6 2 1 3 1 1 1 3 1 3 1 1 Mr Shrubsall, Crania from Teneriffe. 173 1896.] TABLE OF SERIATIONS. Nasal Index. So a SoTBULAT OO AA AMDIDOOIDHNODOMOONAHAGN — a3 g = SO[RTL AGH OPM tHMDMORANHINMN NA Fe < SS — J So[ Bula, fo] Aes aH Neo — —_— Sy g = S SORIA NAMA HOAN HON _ P| So[BUl9 TT ARAN HHO KN He OS OD NN — 5 [| a 8 iS SOR] nN ol MID NO DHOOM OM He AAO H _ a] a So[VUla,T ANS AN Noo] ey ee ee q4 a2 - —— aS o STB — NA SoH es HN HNO es] = FDHOTANDHOOPrARDTOHNAMAMONRDADON xopuy OD Of GO SH SH SH SH SH OH OSH SH OH SH 19 19 19 1091 19 191919 19 SO 13 WOOL, Lx. PT: Tit. 174 Mr Shrubsall, Crania from Teneriffe. [May 11, TABLE OF SERIATIONS. Facial Angle. | j a Total ee ane Cal SORoe Archipelago ca 2 ra % = 3 a R e Sl a) 8 ley Ue Ba eae & = es = es = ey = | & 68 1 Heed. 2 | 69 | 70 1 2. hla 2 2 ale eee | ilies teal On eal eo Tat bia Mee et on la Ce ed onl ee 5 | (elo Pa Be) Bolle fo Bio. | 8 75 7 2 5 CAN 3 16 12 Go| Se Be Gi 2 cll wile lee lee UG 3 3 4 MW 7 6 a al? 78 3 2 4 i 2 3 9 5 ao 1 2 2 1 4 80 2 3 rhe | 7 81 2 i | 3 82 Ibe il 83 1 2 | 1 2 2 84 1 | 1 85 1 1 1896.] Mr Shrubsall, Crania from Teneriffe. 175 TABLE OF SERIATIONS. Height (by Manouvrier’s method). Teneriffe. | | Teneriffe. Bimcode A Sy : cid Sails Weds ue Salted eee Sindr fliers a chee _ = Bie i a a || | 1460 1 |} 1620 |°13 | 1470 | || 1630 | 18 | 1480 WL WeaiG40 | |.23) 1490 1 | 1650 |.16 | _ 1500 2 | 1660 | 19 1 | 1510 3 1670 | 9 1520 3 1680 4 1530 | 7 || 1690 3 1540 | 15 ee 10) | 1550 2 LO” fehl 2 1560 | 8 1720 | 1570 | 9 1730 1580 | 8 3 | 1740 1590 | 5 | 1750 1600 | 7 | 2 || 1760 | 1610 ke | | | | | 138—2 LENGTH OF LonG BONES AND HEIGHT CALCULATED THEREFROM. | Sex | Length | Height] Sex| Length | Height | Mf. 425 | 1613 || M. d 1599 | M. 429 GO eee 315 1491 Sgrigs I. | M. 445 1648 || F. 329 1529 | M. 453 1660 || F. 342 1557 Sex Length Height | M. 437 1633 M. 360 1634 Femora 413-5 | 1584 || M. 373 1661 413 1583 Series LV. F. 339 1550 439 1636 M. 375 1664 417°5 | 1614 413 1536 || M. 381 1677 F. 412 1580 || m 440 1638 | M. 361 1636 422 1608 || F. 419 1546 || M. 363 1640 397 1496 | M. 414 1585 || M. 358 1630 4105 | 1576 | 425 1613 || ™. 372 1659 408 1527 || F. 400 1505 | M. 355 1624 406°5 | 1524 | F. 411 1532 || F. 343 1560 419-5 | 1604 | M. 437 1633 || M. 365 1644 425 1612 || ™. 441 1640 || M. 363 1640 BS EE BPP REFER BER SE 439 1636 429 1566 || M. 376 1666 447 1607 455 1662 || M. 369 1653 454 1661 | 462 1672 || M. 382 1679 | 434 1575 || M. 377 1668 Series II. 44] 1640 || F. 333 1538 453 1660 || M. 395 1624 459 1668 || M. 358 1630 427 1616 || M. 367 1648 412 1530 || M. 373 1661 44() 1638 || M. 366 1646 455 1663 || M. 374 1662 445 1648 || M. 369 1653 437 1633 || M. 363 1640 F. 413 1536 | M. 42] 1606 | M. 435 1629 | M. 419 1602 F. 385 1462 M. AAAS) |) IL XSsI M. 427 1615 Bei io Slee eS el elie is is ela is ler ba el ba ia & M. 440 1638 431 1569 || M. 341 1595 M. 471-5 | 1693 418 1546 || M. 357°5 | 1629 F. 410 1530 443 1644 M. 416°5 | 1593 429 1566 Fibula M. 418 1599 481 3 M. 429 1608 A Sea la 3 F, 413 1536 417 1582 || . 343 M. 426 1614 432 1624 M. 356 F. 409 1529 428 1617 || F. 339 F. 407 525 416 1593 || M. 352 M. 423 1609 496 | 1614 || m. 361 M. 490 1606 [hore 341 M. 436 1627 Tibia | M. 344°5 M. 417 1595 M. 345 | F. 499 1552 M. 357 | | M. 359 1632 || M. 359 Series ITI. | M. 368 1651 || m. 361 | F. 342 1557 || F. S28 M. 440 1638 || M. 375 1661 F. 327 F. 418 | 1544 | M. 360 1634 | M. 345 | | May 11, 1896.] Mr Shrubsall, Crania from Teneriffe. a LENGTH oF Lona BoNnES AND HEIGHT OF LIVING CALCULATED THEREFROM. | Sex | Length Height| Sex | Length | Height pas lw. | 328 | 1652 || v.| 307 | 1566 : M. 316 1619 || F 297 1542 Sex | Length | Height |) M. a2at 4/4637" | ¥. 302 1555 M. 322 =| 1634 | . 325 1644 || M. Hill 1605 1b | F F mm | 331 1659 | mw. | 329 | 1655 997-5 | 1546 m | 327 1648) |u| 33 1659 282 1513 m. | 310 | 1600 || w. | 340 1675 ; 298 1547 mee 299 «=| «1546 || uw. | 332 @«6| 1662 || w. | 329 1666 F. 288 1512 | a | 328 1652 F. | 298 1548 || x. 305 1564 mM. | 325 1643 | F. 319 | 1600 Radius m. | 316 LOLS wa ele oon GED = F, 319 1601 || M. 333 1664 Wares, | esd | Je sar | roan || | O22) | ee m. | 324 | 1640 | w | 299 |-1546 || | gas | 1660 r. | 306 | 1564 | w.| 319 | 1626 a nee er RReed me s09 8 11570 |r. | 323 | 1612 |)" 7 F. | 281 1480 || m. | 329 1655 || Meet Polo 1616 || M. 331 1659 Ulna F. 298 1511 || Mm. 338 1677 || F. 303 1556 || M. 326 = |_:1646 || M. 315 1616 | . 317 1621 || M. 274 1710 M. 306 1584 || F. 314 1583 || M. 268 1677 M 322 1634 || M. 330 1657 || M. 270°5 | 1694 F 307 1567 || F. 306 1564 | M. 265 1669 M 331 1659 | F. 309 1570 | M. 267 1674 F. 296 1538 | M. 318 | 1624 || M. 256 1638 F. M M 302. | 1554 | Mm. 324 | 1640 || F. 231 1542 307 =| 1585 | Mm. 315 1616 || F. 243 1583 314 1614 | F. 298 1541 || F. 255 | 1645 Recent literature on the physical anthropology of Teneriffe. Verneau. Rapport sur une mission scientifique dans l’archipel Canarien. Archives des Missions Scientifiques et Littéraires, Vol. x1. Paris, 1889. Verneau. Pluralité des races dans l Archipel Canarien. i> Bull. See. d Anth. 1. 3. 1878. 2. Bull. Soc. dAnth. 1881. Lajard. La Race Ibére. Bull. Soc. d’Anth. 1892. Lobau, Die Insel Tenerifa. 1896. With complete bibliography. Chil, Estudios historicos, climatologicos y. patologicos de las Islas Canarias. Por Dr Gregorio Chil y Naranjo. Sabin Berthelot. Antiquités Canariennes. Paris. Sabin Berthelot. Mémoire sur les Guanches. Mém. Soc. Ethno- logique, 1. 1841, p. 129; 11. 1845, p. 77. 1.0L ¥.€9 — 14 — 6.69 18 18 2z.69 £.89 Atk” ss vonuT oumUwobhz-or1m0y AB. GiOkinm i = LG OLE SL = ~ (ammoy) xopuy [BloVy [eo], Zr gel — 611 — IE€I OI OLI Ozt ozi Pettis in lg oyvwobhz-1¢7 SOl col S01 — — SIE 06 SiON terra BIOR [CIOVd 18101, ogt £91 ot ogr I4t o12 — — oO9gr get ogi" “" QAIND [BIUOH-1q Os a HS 66 LG WS Oe Org Gls Ya yg fg. BOPRbeS cingn es “aU BIaFT IVTOT Vel Oem OCHNE GCs aL Oe Ol eZ Ol IGT Otc Osea aac aue ““Uypeerg snurery Cv LY 9f gt 1S es ob zs ov 09 c¢ Deemer twee ee tet eee ene oe yysuerTy snurery fe BG — A SI AS IB RS PPPOTPRODAL “oo aasrep peiskydursg SA Ate SOAS RUE ANAS Ao sled = ee PAA LON Ze mehehiegh PUPDAERROGeI028E0 Ypvatg [eyuey-1q Cit Q) CO ee 9 nC Ole On LOnmne LOM COl OOM NON mmr ice mata DOLE Teno CyEnch SOI ZOI ZOL QOl €11 — 111 SII’ ZI OI OBI Ypverg projApuop-1q —_ ~+---——— —_—~—_—— —<${!___~.,—__—————" biS €1S gos suoesang jo BABIOIO ZNIQ VAUBG “ vaquny anbopninp puv unasnyr asa][0H [BAO It OT 6 8 L 9 ig v § G T roquinN “SHIVAAA S.1o1 6.2£ S.zg 9.$9 L.¥9 2S9 — — — — — £.16 1.9 £.16 2.49 — g.2Q ¥.Lg°* (wumuppoxy) vapuy ynrong 10107, b.SL S.zl v.ZL 6.0L £.0f g.€Z Ke? it lA/h xV Al, TiS) = Ke Ce /Z2eQ00ReRIO AA0 Xepuy oreuosA7 -o1u0y wfr ifr LZE1 mbr m1 cer — — — — — oz £1 ozir 61 — Er here Ypvatgq owuobh7-1q7 eee O Dame cri liens Tene Mee © Temetci Tes OTe ee ee ITS TAN Ces CL Tem ZU Tews cil eri DoD ie DT Te octane nian “qu SIex] [VlOey [BIO], v6r 961 Ive g61 blr “li S61 Sgr g61 Loz vor — — — = —- — gor eo SBI Ie “* @AINO [RIMOH-1g Ws GIS SSeS SI Of aS Sp gS SS AS IAS grip, COSeaBODHEROADOEPOPODNA TAT UCIENKS FALE oo) TS 7 WG Gr wip YS GIS ge) OG oh? 00020, 2ornonpmonpoo| Ie. (i pbehaeI [tates p ET Ot Ve Ws SOE Ce bE we Ge C8 OY G46 Se Site Ge Sus i Ke lig cprnrnnrcacepscneqcoocomeitn real cll Os Ge ge if} Ss Ce os ims G4 Ce Gs we iis oe (tS tS (4 (GA CPQPPEDRAPROHODOS ANG Phe ey | entsy NO fo boots, 7b 61%) «6b CEE CCE COOLS he GHEE PE rt Ga peerg [eyUeTT-1g BLOOM ONO ODmECOL sc ONm OOM VONNN Ou CQ ROOI ELC) SICOle LOL sGo) OO) mECONenS DT macO) source aA BOLT eILOm Te, ber or ZII — 611 HII oOzt II or Oz E11 vir zr — Sz oir S.vII OU meet cel plopApuop-tq i OSS — — ss ZY SS ~———uvu Ss, sc s- y69S 69S go0S LoS 99S o1S$ go0S SoS SuUOddsING Jo asa][00 [vAory MWOTJO9T[ON BAVIOIO Zin vyueg ossprliquivg’* waqunyy anbo)nynp puv wnasnyy STAB prvureg SM Ae Ok SR ih OL GO GB TE eiheeaahag — PSietagyan SHULANITIIN NI WIGIGNVW HO SINGWAYOSVAIN 1 142 Barnard Davis Collection 494 503 505 508 510 a TN — 43 195 146 44 QI 136 129 g2 100 114°5 26 128 III 81 135 374 305 419 45 46 47 182 138 140 48 49 50 51 52 53 Royal College of Surgeons 566 567 568 aa aa 569 | 5694 570 571 MEASUREMENTS IN MILLIMETRES OF MALE SKULLS. Number... 1 2 3 4 5 6 7 8 9 10 at ay TB} GS aS Wak) SG) EN) EPR) OBS et F arab . Cambridge University Museum Private Collections, * ae Vantin ya Basel Bie tee oe Se e grog ey Ce Belo ee 460 47 «48 49 useum. Catalogue Number = $0 FG PS GOR ups Sant Cx Hemeretite M15 mIS m20 M21 m22 m23” m25 m26 m27 m29 m3z0 rivato Colleotion at Orotava | Barnard Davis Collection Royal Cotte oreo ae i 20 re . ¢ ~ e » s Maximum Length. — 174 189 188 177°5 191 181 173°5 179 182 1176 188 178 180 174 189°5 183 180 179 180 189 184 187 182 195 — 476 189 181 190 186 ~ - pa 593 $05 S08 510 566 567 568 569 560, 570 571 573 Maximum Breadth . — 135 137 139 138 — 140 148 135 142 138 144 134 139 135 144 142 137 132 140'5 143 140 145 143 146 — 136 143 137° = ee ete 182 — 169'5 179 183 182 177 179 185] 183 195 191 181 18 182 7 - ‘i Basi-Bregmatie Heigh — 120 — 1395 128 — 137 130 126 128 28 135 124 127 121 132 134 133 127 136 134 138 132 128 — — far tar a ae ey oa 144 — 129 140 138 134 138 132 136} 139 146 136 140 193 138 193 T94 187 192 187 18r 182 Minimum Frontal Breadth 94 89 94 95 925 96 100 96 95 99 |95 89 96 94 97 98 96 92 92 955 96 93 99 98 97:5 — 96 101 a 35 128 136 128 130 12I'5 130 134 130 127 138] 127 130 129 137 137 14 143 140139 145 146 140. 137 Bi-Stephanic Breadth . 10§ 110 105 113 121 125 99 is = 95 875 98 88 81r 90 86 94 96 88 o4 92 98 103 92 98 37 140 I4O 140 133 128 134 131 130 Pterion Breadth ... — TOF SUG TOY OeHy Tots FO Tere) — = Sa = = 121 114 100 a 93 To2 105 104 98 99 99 91 Oy Asterion Breadth .... = jo = WG ie WE HO We _ = = 113 120 — aS ae a 123 124 108 127 106 111 108 Sub-Cerebral Zin 129) 27) 31) 18) 116) 21) 20 = =i = 108 106 114°5 07 ee ao 1o7 12 107 113 107 110 108 Total Frontal — 116 125 124 117 131 130 129 130 112 I2 115 — — — 122 121 118 121 130 =

= 435 418 ro) oe 33 312 320 302 323 305 303 302 Total Horizontal — 493 515 512 501 — 509 498 516 524 510 530 — — — 515 516 507 468 == 253 245 SS 246 455 AOI 27 451 449 430 428 Foramen Magnum Length ... 35 38 (O Bo Gs O23 (ho “A By BS sy? YO aa aa oS7 = = = =: 507 516 503 515 468 530] 598 — — sto 4g9 516 oe ae Bae 241 221 226 220 Foramen Magnum Breadth 31 30 34.32 «32 «30 |28 27 28 33 31 33:5 31 34 27 a = sae SUi3) TAOS 53359 932)) 37/0092 bas) mons STONES MEG TT ah 2 33 ses a “ 503 Basi-Nasal Length . — 95 — 105 101 — 96 96 100 95 102 105 102 95 93 1015 100 104 92 95'5 9 iyo, es a i go 32° 31 29) 427 30} 30, 34 32° gn i290) |a] bam an Role S37 3737 Basi-Alveolar Length — 90 — 100 99 — 92 89 92 89 |95 100 98 91 89 94 92 985 83 ae w % 875 a = of 35 ca aa x06) a 2 9r 91 95 98 98 96 92 103 101'5 Tor Tor 160, an a oh 5 88 30 313031 External Bi-Orbital Brea Tor 98 104 115 105 102 109 108 = & 94 go 87 895 101 95 — 83 95] 99 or 90 of 94 03 08 o7 < D 102 99 102 104 Internal Bi-Orbital Breadth 92 93 97 105 97°5 96 100 101 1 = = = = 10S 105 103 107 102 11t II rie 108 ot or MELO Bi-Jugal Breadth ......... 108 106 116 123'5 117 105 115 121 125 — 120 122 123 121 126 i. = — — =] 101 97 98 99 oyunoaetos 18 ae oH aa 33 a Bi-Zygomatic Breadth — 125 127 134 134 — — 143 135 — 130 130 136 132 129 139 126 131 126 1 129 I 3 6) = 2 2 = —} 11355 — — 113 108 8 ar ab Bi-Maxillary Breadth 99 91 93 Il0 Yor — 102 08 = E 110. OI a7 gr 38 36 36 fe iD B 95 aes za 233 om “ ae rH = 20 117'5 1330 — — 126 134 a _ aS 122 ar a rc a ng mw peat Bi-Malar Breadth ...... 112 107 116 124 119 112 2 yj 9 4 94 95 95 99 85 — oF 102] 1043 — — 94 91 99 G0 Ios Tor a 37 29. 129 Ophryo-Alyeolar Height 80 90 95 101 82 80 84 80 —}| 116 — — wo 107 119 11a Wi8 113 118 ae ae oh Naso-Alveolar Height ... 59 65 68 72 66 62 64 59 62 71 67 68 64 67 66 65 B om OF CH Oo «6 65 Go. EF. " = go 86 84 92 S88 8 6 8s 8 S: Spino-Alveolar Height 15 22 20 21 15 142 17 I5 17 24 16 21 15 13 20 14°5 15 20 13 21 ie % 3 ee 7 we a S7 64 88 87 35 8 38 fo 58 68 65 — 61 70} 69 65 62 68 58 65 nH 7 64 “ a e a Orbital Breadth... 38 37 37 41 40 39 39 40 35 35 9 41 37 36 35 41 40° 37 40 40. 38 gs 35 41 ay MAGMMASINMO 36) gi qa 8 4 99) 40) 4s) ae) Ghee ace cel) LS SOs Ran ao ao ats s eo ea ae Orbital Height . BL 29) 32) 30: 33 29 33-30) (27) BO) 33° 30) 20 28 31 432 32) 32° 35) 34) 28) 30) 34m s5peesdmmen m0 33) 358261 32 3 oe aS Ag 30 40 38 39 37 40° 37 37 37 40' 4a 39 “do 4g) 38) a8 Nasal Height. 44 49 52 50 49 47 45 46 48 52 48 50 55 47 51 50 Sr 52 46 49 53 45 53 555 SI'S a7 51 48 48 49 43 46 SES 2 030) 130 ay 1920092 ]/ 132) 134 p32) 32) 3015 gah cc cOmed Sa Nasal Breadth . 23) (24. 22) 23-26 «23, «24° (23) 25) 125) 2015) 26) 28) 22) 23:5\ 21 “2275) 23) (25) (25:5) 23! 25) 22) 27 enmeezme2S) 22) 20'5) 122) 26/8 21 Be ah a7 pox st = 2 2 50 48 49 41 47 55 52 45 56 St 47 B Bi-Dacrye Breadth ... 22, 24 23'5 23 20 23 23 24 26 (25 25) 22 25 23, 25 21 24 23 24 23/ 22 24 25 245) 24N2AccN 27, 26 (25) 22 2 2 25 1 23 2 5 ce - Pky EINE PXY ey FY - 2 a2 2 25 2 2 2 2, ar Pxternal Palatine Length 2 58 55 54 — 53 48 G) G3 Gy 76 Go Ge 7h Ga Ho Sis 2e 123 7 ee 20 A 3° Fs 20 20 — 25 27'5 25 21 a5 320 92° 30 a0 Internal Palatine Length 46 55 47 — — 48 44 St 52 47 50 52 45 SO 52 46 54 40 42 2 nal & f f \ 52) 55 49 52) 49 Sr 51 50 45 56 ‘0 External Palatine Breadth .. 57 G6 665 62 — 04 56 ms Sano nee th es ae eS SF SoS) 9 AP ich a han erRmr Ss ask Maen cnt: ee ee 68 oo i AM i Internal Palatine Breadth .. w wy p= = F a Gi (2 2 20 Mm gH eB gy) sh co 2 8 to) 6 2 2 — a ee 2 59 56:5 Or s4 O61 60 68 60 68 65 — 4 3 3 Bs 4! 4 4 35 36 40) 42, “41, 935) 35) <4 37) 140) 40) 932) — 2 46 35 32 31 EE SEN RYO Co ky cK} 38 30 9 INDICES. Length-Breadth we — 776 72'4 74-7777 ~ — ~—«'77°3 85°3.-75°9 78 76'4 766 75°3 772 776 76 77°3 761 73°7 78 75°6 76" a VAS 6 — I : 6 75" : ‘ . . . D 3 , . ? 2 Length-Height = TES 74 TA TET TRS akg Jo8 703 127 719 097 Jo6 60's 698 752 139 709 756 709 78 Joe Jon ~ — fog fet © deo yg Be Fee — Foy ope Sat 36 7m om Tae Gon GOS cae Fue 2a 188 an 1s3 Tes Tas Ta 77a) 183 Brendes ae — 88'9 — 103'6 92°38 — 97°9 87°8 93°3 901 92°8 93°7 92°5 91°4 89°6 91°7 94°4 97°1 96'2 96'8 93°7 98°6 91 89'5 — — 96:3 986 — 938 of fb Le = RS 88 an qa es hee a hi Re aie tee a ais rae api my a ns Upper Facial (Kollmann) — 52 538 53°7 493 — — 413 459 — 51°5 52°3 471 S0°8 S12 4677 50 514 '2 51°9 50°7 53°1 582 47°8 — 52:4 41'6 48:1 52°3 52'S 40'S 414 — on een Se ere an te 9 103, 1014 97'9 95'0 9517. 88:4 O1'8! 93/0 949 ao aaeiill (Brood) je = WAG eh Ge a6 SOReS: 53 49°2 $§1°9 50°7 53°1 58°2 47 52°4 416 481 52°3 52°8 49'S 41-4 50 49"4 52°33 — — 484 52'2 _ — ars 49/6 Fes ae Ae 59°8 sor fort ct Orbital 85°7 83°8 78'4 78 75 84°6 74°4 82'5 85°7 771 83'3 80°5 81:1 806 80 75°6 77°5 86°5 80 87°5 89°5 80 85°7 82°9 83°7 79 842 77'5 79°5 80'5 83:3 684 78 74°4 77° We 8a) Ll ROB ad Ba. Gig) |Boy BER GRE REC ree URE GRICa Ee ean Ste Nasal ..... SII 523 49 42°3 46 5311 48:9 53°3 SO S21 481 55:2 52 50°9 46°8 46°7 42 441 44°2 54°3 52°1 43°4 55°60 41°5 48% 44°6 408 54°9 158 552 48-9 60°4 467 ar He a0 gon 4a = 142 14 12 ta sat ue oe ion He He Lae LE LER US Eh Palatal (Vitchow) S42 674 67's O81 — 792 818 G08 S08 723 84 846 734 76 712 704 741 $0 go's 75 89 88:5 777 953 O86 G2 — 784 84 837 729 70 788 So4 9019 784 O27 — “No 93, O86 Tha O43. 8a OPN tad. Coad Gee CEVA Cle : (Flower aes oat 2 0 = . “ . 6 . 5 d A a . . A i . seca . t is - 7 . é ‘ x i Sir ciacece # 19 3 z i 0 ANcoley (een = Cel = oP ae =e 958 eee, 92 93°7 931 95°2 961 95°8 95°7 92°6 92 94°7 90°2 92° 92°8 90°6 96°1 90°5 93:9 — — 95:2 88:7 90:7 907 98'9 916 94'2 103" 96'9 90/a(92'4' (98 0; Bort) (Or. 190ld 310.0 Aino 7G oie Osama Org of Supra-Auricular—Total Transverse .........— 63°7 — _ 62°5 674 — 67'8 66°9 = — = ay, Dee ee om a ths aod 20 1 ye Ha rae) 20/5 oa 1819 ie Pre-Auvicular—Total Horizontal . — 51°7 47:6 43°9 459 — 46 46°8 — eS S = = a a ag Got We eats 6G o9'4 feed pay 67'9 70 (hen Frontal—Total Sagittal .. D343) 3357, 33) =) — 3407) = 330 air g3;n gua — — — 32:6) 32:9) 33:20 33'4: 34:2 = = PET AEG OMELET COM CeCe ercpcon ATT ATO EE ABT da aa SE on tn Total Sacrittal 2 Sete, a OU PEE COE ee ea 9 33:2 334 34° Ste 32°3 33° 331 38 33% 364 33'S 321 34'2 35'4 344 351 34°7 34°7 32'1 34'2 ga’ 33'2 Parietal giotel Sagit 331 35 35" 36 314 361 34 35°2 35 33°3 315 30:2 387 = = 5 30°9 29'S 33°1 38'9 30°2 35°9 321 36 2017 349 33'3 340 30% 34°7 35° 32° 34'8 349 Oceipital—Total Sagittal... 32'5 30°5 31°4 — — 29:3 — 32:2 32:8 328 3399 — — 29°7 32:1 35°2 3074 27°1 — 34 34°5 30°6 32°06 30% 27'7 34'1 31°9 36'1 29°7 32°2 30°3 34°9 30'S 32°1 33'2 30'5 319 7 8 Private Collections at 174 136 122 96 9 179 138 130 95 sence LO ee 19 30 «31 ollection ae 506 es Ti 7ee oe aa Ly) Lr 139) TAOhs Papers 79 nee Tage 127001 T2912 96 95 1 95 88 - — 108 109 _- — 104 108 _- — IOI 102 —_- — 18 18 128 115 ToT err 120 116 II4 108 SS 76 89 II0 140 120) 122 358 365 355 341 292 298 -—D 296 291 — — -8 404 401 SS 200210 500 505 + 517 487 37) 34h = gOre 36 30 325 — 29 30 91 915 9 98 96 86)787°55 5 93) 88 — — -+3 Io1r 98 mn a 94 92 114 — 10g 104 122 116 142 119 — — 83 102 89 —- — a 108 102 —- — a 86 85 65) 57 69 ~=«66 Tom 4 A) LO 7 Bo 38. de 38) 637 Gh 30K A. 3328-82 SRD) Bey 22)! .2R 48 445 4 50 50 ZO 3 ee eo are OOhrs p 52. eo) 51 46 4 47 46 se p00") =p. 59° 56 41 35 4 so) ae | 81°377°3 73 77°4 772 77°8 70'2 72°9 7371 95°7 90°7 98 94'2 94°7 533 491 49 58 — — — =a 72°3 —d 88°6 81 8d 84'2 86°5 45°8 44°9 7 42 40 80°4 761 8 83 67°4 94°5 95° 94 94°9 91°7 —- — 14°9 16°2 = = 3 73°3 72°6 = SS 39°83 4371 35°58 31 34°1 32°6 S510 othe 32:0 387 3025 S07 33°8 35°8 36 514 37 38 39 ! Royal Coll. of Surg. - 572 5734 5738 eS 180 144 127 Number... 1 2 3 4 5 6 q 8 9 MO) ah = py ey ae oS Gi? ST) ON) Oo RH 2 30. 31 82° 88 (84-36 86 <87> Sona MEASUREMENTS IN MILLIMETRES OF FEMALE SKULLS. | Museum. Catalogue Number x pane dge University Museum Private Collections at Basel, Santa Cruz and Orotava Barnard Davis Collection Royal Coll. of Surg. a eee ee 2 53 84 85 — 1716 mig m24 m28 493 495 496 497 498 499 500 501 502 504 506 509 SIE 512 513 514 572 5734 573B | Maximum Benet ec Gres I 8 Fomaen 2» on Ee GS SS » Maximum Breadth 7 19 175 171 183 181 164 188 174 179 171 181 182° 174 169 189 173°5 175 18375 185 188 177 178 182\ 172 183 172 163 180 170 177 171 175 -170 169 I8t 189 170 180 179 Basi-Bregmatic Hn 138 140 138 137 143 132 143 136 138 139 140 137 134 135 igh) 34 == == ko) IO) TEA TG) Te 136 146 140 14% 143 136 137 132 140 131 140 134 143 132 144 44 Minimum Frontal Breadi, 130 118 124 130 124 131 123 122 130 133 127 135 133 125 133 125 125 126 134 132 124 125 129 124 117 128 125 133 — 129 125 122 123 127 126 129 122 127 124 ares Se Sa 95'5 865 86 92 96 92 98 06 95 96 95 I00 93 89 107 92 96 IoI's 98 98 86 1 99 99 94 94 90 96 94 95 88 90 oF 27°80) 07 Oss no2maron 104 III III 119 108 Ti SIV OL) TD | WEE DWN) WG) HES OL) ae ORE te GIN my Hoy) ini 119 SS ES ee UNOS UCYL TNO. TR fie) OH |i) =. => sa oe — — — 112 108 I00 try 103 IIL 104 102 112 ro$ 104 108 105 103 109 104 112 YO4 109 I10 Asterion FS Siaisiniwivjureieiwiutncaieinie’elsis|sicinjeicie c/eie 106 102 100 108 IIo ee 120s = — oe a = ==, — — — 108 108 105 ee 104 99 IIt 106 106 ae To2 oa 102 100 103°5 110 to8 1 13 103 IO {OS BUCFEDT A Reece eae A) On BD 225. Gea eee Ss ee ee WS 23 BB I Tea 1S) 0729522) 722 ear 19 2 Total Frontal i Bl Bik IG) |) pe} ie) 22 Bi FO) De 5) 223 i 7 Z QO)” 19) eb — — 125 115 121 129 132 122 121 317 132 !I9 21 122 128 120 115 12t II 115 114 122 111 128 121 123 120 oe eee ee 127 120 125 127 121 114 120 114 127 128 115 I2l 122 123 122 132 124 123 134 122 125 115 114 109 124 13% 114 108 130 110 315 125 122 for Tar 137 SSSCoo Sao see SoUSH OBE OOS HOEOSEG 126 115 Il 110 122 129 112 100 126 120 116 Parietal = Resear taemerenecen ics J 3 83 OR SA” Cs Supra Occipital SA apc an ee SE 61 65 «(71 75 6 — 73 68 o1 76 89 70 66 70 66 80 8 65 (69 Curves zoe Occipital SOD SA ea NBO COS SHON CSED 116 126 122 131 120 107 121 131 116 110 140 — 132 110 III] 12% 124 130 116 — 111 114 126 109 108 127 — 120 122 110 114 107 I17 120 122 105 III SSE ES FAN goers aed 367 361 366 366 363 350 69 358 36 — 378 — 372 388 376 360 — 365358 362 345 345 371 — 355 341 355 338 344 353 373 344 352 368 3 35° 353 345 369 358 365 379 347 372 3 379 3 365 3 5 <8 ; Supra-Aurieular... o..0......cccss00:, 282 292 296 302 248 293 288 275 282 292 208 298 285 — — 292 288 281 296 315 | 303 299 294 290 305 260 296 291 291 288 308 287 jor 286 310 302 Total Transverse ........0..cc..00.., OS mOmE—areanroy ara passe = — — — 440 438 gor 420 431 413 413 411 419 434 398 404 401 406 410 422 405 428 396 430 425 Pre-Auricular ssc = 2 ==), eee Se np Se 2 | 216 222 219 209 211 210 206 210 226 228 231 206 240 21 5 231 240 = ia 09 193 221 224 262 210 268 264 260 227 210 23 ASN VGH FON GS) Gal Gi? Rn ies fan oP 500 326 46a Crate o OLZOn tale eee eee Be) Bjos) ey riy Gis} ass) lo) kos) Lfote) [yfofo) fof) ee Lol ne 512 525 490 510 § 4 2 Foramen Magnum Length ........................ SEE MC OMICS ESS IEESGHINGSIgng5. 36. 937° 41 —=- = ==, 3% 36-34 34 gg as gg 33 37 36 36 sola 8 36 34 33 34 36 36 33 36 2 Foramen Magnum Breadth..................0..... 39 JO Bf 35 BO BRS) BY As 3 go spy Sa Ps) I) OSsCéo) ss 3 Se oh aes 3 ae a8 ar 2 a : 3 5 3 d nce Nasal lyon ehh. ons ee ah ae OI 90° 8996 98 95') 08 06 OF Of O15 91 93 94 102 96 100 99 98 100 91 08? x 3 ae 2 23 ae 38 26 2 34 : 88 oa ae ins-Aevemlan mien wil ties ocean ca cnsicsse shea RO nO OME OME OO on ESS uerSS SO) S775) (87 (89) 84 93) 88) == On = = 85 82? + 76 5 7 5: 92s ee 98 10h. eee es Ey 93 ‘OC External Bi-Orbital Breadth ..................... OR} TO I WO WLS i OS yy 2 101 102 — 104 98 Jor 98 96 98 98 o4, Tox ~O7 ToAearaG Internal Bi-Orbital Breadth ..................... J OG G8 OF O88 O35 GS — = Se SS] SSS] By Os SS 88 93 95 — 94 95 94 92 90 — 92 98 95 88 94 99 CEES Pr TSS Les See ee cee ran PE2 013) 107, lO) UIs) 105 |ai5 123 112 114 — — — — -— — — — fir yr 107 — xr, — 105 112 — lo Tor 109) 1045) S07 s t4y One nLOmeanie = 3 — 126 121 — 124 — 119 — 124 — 125 128 127 120 124 125 Bi-Zygomatic Breadth ... -.............c.ececeee ces 12 //a5 0G L222 ORL OM 2 Il 2 ome 2 5 l22 eeTTONeI2 5 ell2 settOsr32\e027.50—— | eT oOmT 2 7a 23 seeIITA GT 4 4 Bi-Maxi Breadth CueCOMOS MESO mE umneS sue eer = 85 gon 88 = 66 99) — 88 == == son Sn. 80 87 89 99 87 102 89 — — 92 98) o4) (= scomemag i-Maxillary Breadth ..........--.:.sseseeseeceeeee 9 iB 2 OS Se ee ee eee ; Se 100 10s 107. — 110, 10] 108 oz = = prt uaa god We ate POAC Gere oon cc aot. oc etesaeanabaeeneae 106 113 107 104 103 103 107 IOI 108 105 9 6 828 ; Zo 63 86 8s 72 — (80 88) equ GhmRummnN Ophryo-Alveolar Height ................:scceee ee a Ce ee ee Blo o> AE aA = Bees 63 5? 69 66 59. —2 69) css cane mneemmmne Naso-Alveolar Height ................:::seeseeeeee CORSON mn Sian 2 O70 025 05) 57, (61 (G0\ 952-62) 63° 65, Gen | 17 i2 16 I§ “15 16 19 «7 Iq — cs 39 one are umCeete Spino-Alveolar Height.................2:sesseseeees ner; 2] 2) 1B WH IW Why Bo wey mw wh we iy TP NG 1} —5 Ao Ae) i} OR ie 7 34 36 «36 36 3d 38 gp as ge gt TSE isn 0 She eee BO MOMNEG MS noes ES SS 9308 85 35 «37 35 «9 36) «4D «40. — «391-37 86 6) 33 Sis nee 2 32 27 32 32 3 — 34 32 92 34 PLS Sen eee Om ees ee OS 2GOMPES4ueS Tg GO 31) 30 33°32 «29° «32, «340 gr 31 328 gomeaT ate ae amen ee te ais ra. Bi Dac Pee ee D2, Bil —«*I0)-— PB HS BN) OD YO) BO fo) PRE PAY A DWH) eon G 45 8 ai 50 a e — 47 50° 40 47 ees Oma a oe Tee eee SA 7 Te 5 ATe Ay 6481 4455\ a2 48°39 «50 fo —= 149 48 Fol Age 43 ae Be i at 23 2d. ai Bo, aa age Nasal Beek i eee 23 25 +24 22 22 22 23 24 23 22 20 25 25°5 22 i 20 5 24 24 Pee roe o aie 56 48 48 44 52 Sx — — 9 48) er Scola nen ce Nas ee ee - 3 meet ae ea ae : t = imteraalPalating engi, occu go G0 2 4 St 8 as SO Kw wo HH - Re “eS Be HE eB He 3 - Be Be Be POL ATSIC) gonnhadaenbe tenon eeesoan a [2+ So ee 2 Rane Cae = ome — 6 30 30 6emEg2 External Palatine Breadth .................. 63 64 57 57 45 ee ee ra ee me me ae 32 34 «31.=«i«36:'—«ig2t:s«2]tsi‘« yon 87°8 92"7 A 83 67"4 3s 7 — 72" 80 66°7 76°9 81:8 68'1 arsah eee owen nai sinamionrareisialaCe/eisis}72i8:0)2 oe 3 he 614 74°5 33-3 889 74 761 80°4 76°1 86:9 73°4 82°6 69°6 74°4 — 64 73° 77°3 83°3 69°8 646 ; Bee aie s : 96 : : Palatal (Virchow) J ee aasonO2 Pe 50 907s INOIODIGUIOO IED ue Reo 96° 91°77 — ~~! — 917 96°7 94°5 95 6 95°6 95°7 89°4 912 91°77 — 96 Se = 934 83 7 : : : 5 Alveolar (Flower) ...-.---.---s1s-nns ey Ae ces 68) 1655 174 167 (Caras Se ees 661 OER neat Tae Soa eae cei 2 — 1] BP ree eget eS ae, ahem 44 ep Me ee atalle ssc 4i't 38°9 44°6 43°8 50°6 43°5 S19 : ; ee Wek svi eye: Gil eee seit Le ae Pre-Auricular—Total Horizontal ..... 6 33°3 34:2 34°7 33°3 32° 34 33 344 35°8 31 331 33 34 347 3 sen ee se RG BS ee eS Parietal—Total Sagittal .........-.- 0" 343 39 333 35° 33% 30° 342 38 314 Occipital—Total Sagittal Se ndenceeqorgee 1896.] Mr Newall, On the Spectroscope, etc. 179 Monpay, 25 May, 1896. PrRoFEssor J. J. THOMSON, PRESIDENT, IN THE CHAIR. At a Meeting held at the Observatory the following com- munications were made: (1) On the spectroscope used in connexion with the 25-inch refractor. By H. F. Newatt, M.A., Trinity College. Mr Newall exhibited the spectroscope and shéwed some of the photographs of stellar spectra with terrestrial comparison spectra taken with the instrument. A general description of the spectro- scope has been published in the Monthly Notices of the Royal Astronomical Society, 1896, vol. LVI. p. 98. (2) On a suggestion for a form of spectroheliograph. By H. F, Newat., M.A., Trinity College. The results obtained by Mr Hale in photographing the sun’s dise with the light of some definite wave-length emitted by it are so full of interest and of promise of further development that it seems pardonable to make an untried suggestion which may lead to increased facility in taking such photographs. In a paper entitled “The Spectroheliograph” (Astronomy and Astrophysics, 1893, p. 241) Mr Hale has given a résumé of the earlier attempts to photograph prominences and of his own work in developing the spectroheliograph. (See also Astronomy and Astrophysics, 1892, pp. 407, 603.) M. Deslandres has in a paper entitled “ Appareils enregistreurs de latmosphére solaire” (L’Astronomie, June 1894), considered various forms of apparatus for researches similar to those carried out by himself and by Mr Hale. (See also Bulletin astronomique de lV Observatoire de Paris, Feb. 1894). The general principle of the method is as follows: An image of the sun is produced and allowed to fall on a slit ; the illuminated part of the slit is a chord of the sun’s dise. If the proper relative motion of the slit and the sun’s image is brought about, the slit can be illuminated successively by parallel chords of the sun’s disc. The slit is connected with some spectroscopic (or rather spectro- genic) apparatus which produces a monochromatic image of the slit, and this image is isolated from the neighbouring images by 180 Mr Newall, On a suggestion [May 25, letting it fall on a second slit. We can thus produce monochro- matic images of successive parallel chords of the sun’s dise. Photographic apparatus is then arranged so that the mono- chromatic images are laid side by side, and a complete photograph of the sun’s dise can thus be reconstructed. It is clear that there are many ways of bringing about the proper relative motions of the slits, the image of the sun and the photographic plate, but practical experience points to the desira- bility of reducing as far as possible the number of parts between which there is relative motion. Mr Hale has in the case of the spectroheliograph of the Kenwood Observatory attached a spectrogenic apparatus, con- sisting of collimator, diffraction grating and camera, to an equa- torial; and by driving the equatorial at the proper rate he keeps the sun’s image stationary relative to the spectrogenic apparatus, the whole being moved relatively to the earth. Then he moves the slit relatively to the collimator, and the second shit relatively to the camera, in which is a fixed photographic plate; the two slits move at different rates but are connected by carefully designed link-work. M. Deslandres has used a heliostat, which does away with the motion of the sun’s image relatively to the earth; and he advocates the relative fixity of slits and spectrogenic apparatus. Mr Hale, in using on Mount Etna a spectroheliograph designed by him for the late Mr Cowper Ranyard (Astronomy and Astro- physics, 1894, p. 662), made an advance in arranging that the camera and collimator should be parallel, so that the image of the sun and the photographic plate should be in parallel planes. ‘This method has been adopted by Mr Hale for the spectroheliograph designed for use in connection with the 40-inch Yerkes equatorial. The slits and the spectrogenic apparatus are relatively fixed, and the whole arrangement is bodily moved relatively to the sun’s image and the photographic plate. In this arrangement the resulting disc of the sun is round and undistorted, and there is no need for the rectification of the distortion which Mr Hale has had to deal with in his earlier investigations. It is perhaps worthy of note that there appears in Mr Hale’s photographs of detail on the sun’s dise much less per- spective foreshortening of detail near the sun’s limb than one would expect to find. In another arrangement, namely the “coronagraph” used by Mr Hale at Kenwood, 1893 (Astronomy and Astrophysics, 1894, p- 673), a modification of the Littrow spectroscope was used. But the spectroscope was fixed relatively to the sun’s image and to the photographic plate, and the slits were moved, the nature of the case being such that the slits move in opposite directions. 1896.] for a form of spectroheliograph. 181 Some modification of Littrow’s spectroscope with fixed slits would seem obviously the simplest one to use in these investiga- tions. Iam under the impression that Mr Hale has recorded his rejection of this form, but I cannot find such a reference. Recent work with a modification of Littrow’s spectroscope leads me to believe that the difficulty arising from reflexions from the lens- surfaces can be overcome by the use of suitable stops. The spectro- genic apparatus here suggested is accordingly a modification of Littrow’s spectroscope. Modification of Littrow’s Spectroscope. The essence of this form is that one tube and lens serve both for collimator and for camera or observing telescope. =; COT Focussing Screw il The tube 7' serves as collimator and camera; an object-glass Z is fitted in a tube 7” which slides in the main tube 7 for focussing purposes. A shit A is fitted at one side of the tube 7, its length being perpendicular to the axis of the collimator; a reflector B placed near the axis reflects light normally incident on the slit so that it passes along the axis of the collimator and so through the object-glass. A diffraction grating (or a train of prisms with a reflector at the end) is attached properly to the tube 7’ by means of a framework K. Light, after falling on the grating (or after a double passage through the prisms), falls on the object-glass again and passes along the tube 7’ till it falls on a second re- flector H, set so as to reflect the light out through the slit F, which is fixed opposite the first slit. The arrangement is in a certain sense direct vision; and the line joining the middle points of the two slits may be called the line of direct wsion; it is of course perpendicular to the axis of the collimator. (Such a form of instrument would be convenient for ordinary spectroscopic 182 Mr Newall, On a suggestion [May 25, purposes, an eyepiece being attached in place of the slit F. It might be preferable in such a case to have the slits parallel to the axis of the collimator, a corresponding change being made in the position of the grating.) For spectroscopic purposes an achromatic object-glass would be convenient, but for the use of the instrument in a spectroheliograph a single lens is all that is needed. A suitable small stop must be set on the inner surface of the lens near its centre to cut off stray reflected light. So far as I am aware, it has been the custom in all forms of spectroheliograph to move the slit slowly across the sun’s dase. Accurately equable motion is needed in order to avoid streaks in the resulting photographs—the streaks here referred to are those parallel to the slit, not those which are perpendicular to the slit and are due to dust on the slit—and even when the motion is equable, the effect of a cloud passing in front of the sun will be to diminish the density of the photograph only in that part of the disc over which the slit moves during the passage of the cloud. It often happens that the best definition in solar observations is obtained when there is considerable haze and even fog, which is necessarily of varying opacity. The necessary exposure for the whole disc may be attained either by moving the slit slowly once across the disc or by letting the slit pass comparatively quickly backwards and forwards over it often enough to get the necessary total exposure, the image of the sun being kept stationary whichever method is adopted. Mr Hale has adopted the first method, and I am not aware that the second method has been either tried or suggested. The oscillatory motion might be given to the slits and connected spectrogenic apparatus by properly suspending the apparatus and allowing it to swing like a pendulum. This method involves the use of a fixed beam of sunlight. The suggestion which I have to make may be summarized as follows :— 1. A celostat is to be used to throw a horizontal beam of sunlight. 2. An object-glass is to be inserted in the beam so as to form a fixed image of the sun—‘fized’ in the sense connected with the ccelostat as opposed to the heliostat. 3. The spectrogenic apparatus with fixed slits described and illustrated above is to be suspended like the bob of some forms of ballistic pendulums, and in such manner that (a) the slit A receives the image of the sun upon it, and bisects the circular disc of the sun when the apparatus is at rest; (b) the line of 1896.] for a form of spectroheliograph. 183 p nad direct vision as defined on page 181 is horizontal and coincides in direction with the axis of the horizontal beam of sunlight ; (c) the slits are vertical. This pendulum is to be set swinging with an amplitude slightly greater than the diameter of the sun’s image. 4. A photographic plate is to be set either all but in contact with the second (monochromatic) slit, or else considerably further back, with a lens placed between it and the second slit in such a way as to form an enlarged image of the second slit on the plate. The lens and photographic plate are to be fixed relatively to the earth and consequently also to the image of the sun. The resulting photographs will shew the average appearance of the disc during the whole exposure. The central parts of the sun’s disc would get less exposure in a given interval of swinging than those parts of the borders of the disc at the ends of a hori- zontal diameter of the image: but this would be no disadvantage if one considers the difference in brightness between the centre and the limb. The relation between the exposure at the centre and near the limb might also be controlled in their small limits by altering the amplitude of the swing. Loss of definition would arise either because of atmospheric disturbance, which would affect the whole disc, or because of violent motions on the sun’s surface, which would affect only restricted regions on the disc. The motions appear however to be seldom so great as to be likely to affect photographs taken with comparatively short exposures, and on such occasions local loss of definition would indicate the disturbed regions. I have hesitated to commit this suggestion to paper without giving it a practical trial ; my only excuse is that I am in hopes that some one may be induced to give the method a trial earlier than I see any prospect of being able to do myself. (3) On the Period of the Karth’s Free Eulerian Precession. By J. Larmor, M.A., F.R.S., St John’s College. 1. The main object of this note is to state a principle which allows us to estimate the effect of elastic yielding of a rotating solid on the period and character of the free precession of its axis of rotation. It has been suggested by the recent papers of Professor Newcomb and Mr Hough!, in which the discussion is chiefly confined to the case of an incompressible homogeneous spheroid. 1 §. Newcomb, Monthly Notices R.A.S., 1892; 8S. S. Hough, ‘‘ The Rotation of an Elastic Spheroid,” Phil. Trans., 1896. 184 Mr Larmor, On the Period of the [May 25, 2. In order to obtain a clear notion of the action of the internal forcive which causes the free precession, let us examine in a geo- metrical manner the well-known case of IL a perfectly rigid solid rotating round its C axis OC of greatest moment of inertia. When this motion is disturbed, let OZ represent the instantaneous axis of the O rotation w of the solid, and OL the axis of resultant angular momentum which is fixed in direction in space. In the case of a symmetrical solid OC, OI, OL lie in one plane. With reference to the solid itself, Of and OL will describe right cones round OC with common angular velocity ©, that of the free precession in the solid body of the instantaneous axis of rotation. The line OL being fixed im space, the point Z of the body will thus move away from the point Z fixed in space with velocity —Q.OLsiny, where y represents the angle COL; but as the body is rotating at the instant round the axis OJ with angular velocity w, the velocity of its point Z must also be w. OL sin (y — 4), where y—c represents the angle JOL. Thus we have the geo- metrical relation ha =O isiniy — @isiii (yi) sees eee (Dy The angular momentum of the rotating solid with respect to its centre of gravity O is at time ¢ made up of Cw cose round OC and — Aw sinz round OA. After an infinitesimal lapse of time 6¢, OC and OA have turned round the axis OL fixed in space through an angle ’dt say; thus OC has moved through an angle w’siny. dt, and OA through an angle w cosy.6t. These changes in the axes of the constant component angular momenta will introduce two reacting couples, acting round the same axis perpendicular to the plane COZ and equal to Co cost.@’ siny and — Aw sine. cosy: and in the steady precessional motion these couples must equi- librate each other, so that C cosesiny+A sine cosy = 0; that is, Ctany=A tans Combining equations (1) and (2), QO, = @ (cot y sin ¢ — cos ¢) 1896.] Earth's Free Eulerian Precession. 185 Thus the angular velocity of free precession, as seen by an observer partaking of the motion of the solid’, bears the ratio (C—A)/A secs to the angular velocity of the rotation: when the amplitude of the precession is small, the ratio reduces to (C — A)/A. 3. We have now to examine in what respects this argument is modified when there is elastic yielding to the centrifugal force of rotation, instead of absolute rigidity. As the period of relaxa- tion of a strain in the Earth is a fraction of a day, while that of the Eulerian precession is measured in hundreds of days, it follows that the distortion due to centrifugal force will follow with great exactness the movements of the instantaneous axis of rotation: and the same will usually hold good in other problems of slow and small free precessional motion. Thus if C’ and dA’ represent the moments of inertia, round OC and OA, of the configuration which the body would assume when the strain due to centrifugal force is removed,—or, what is the same thing, of the configuration it would assume under the action of an applied bodily forcive equal and opposite to the centrifugal force of the rotation—the angular momentum will now be made up of the components, C’w cose round OC, — A’w sine round OA, Io round OJ, where J is the increase of moment of inertia round OJ due to the centrifugal bulging. Thus the reacting couples, in the plane COZ, are C’w cost. w’ sin y, — A’wsini. w' cosy, Io. sin(y—2); and these must balance. When the axis OJ does not deviate far from OC, the moment of inertia round it is equal, to the second order of small quantities, to that round OC; thus J = C—C’, and the condition for steady precession is therefore C’ tan y + (C — C’) (tan y — tan ¢) = A’ tan o, that is, Ctany={C—(C’— A,)} tance; so that, by the geometrical relation (1) C’— A’ oi C02) COS bn) o\n vlalelolaleielele(ele=)siain) stele (4). 1 This is different from the precession of OC or OI in space, which is round the fixed axis OL, and of angular velocity Q', where 2’siny=w sinz. 186 Mr Larmor, On the Period of the [May 25, The validity of this result is also, as above stated, confined to the case in which 27/0 sine is large compared with the time of relaxation of elastic strain in the solid of revolution to which it belongs. Since C—C"’ is small compared with C and A, as the elastic deformation only slightly alters the shape of the body, the third of these balancing reacting couples can be neglected compared with the other two. Thus the free precession, under the influence of elastic yielding, will be the same as would belong to an absolutely rigid body, whose configuration is the one that the actual solid would assume were the centrifugal force removed, its elasticity being supposed unimpaired and the same as actually exists for smaller distortions. 4. In order that the principle stated in this form may hold good, it is not necessary that the solid should be symmetrical round the axis of rotation. The couple due to the elastic defor- mation by the centrifugal force can be similarly neglected when the moments of inertia of the solid are all unequal, provided, as above, the oscillation of its axis of rotation remains small, as will be the case if it is spinning round the axis of greatest moment and is but slightly disturbed. Thus, in accordance with Poinsot’s theorem, the motion may be represented by the rolling of the modified momental ellipsoid of the solid on a fixed plane; so that the axis of instantaneous rotation will trace out a small ellipse on the surface of the rotating body and the precession will there- fore be exactly periodic’. It follows easily from the Eulerian equations of motion of a solid free from external forcive, that the period of the free precessional motion of the axis of rotation round this ellipse is to that of the rotation of the body in the A'B 3 ntio ea OLE, ments of inertia, viz. those that would exist when the strain due to the centrifugal force is supposed removed as above; agreeing with the result already given where A’ and BP’ are equal. where A’, B’, C’ are the effective mo- > > 5. If when the centrifugal force is thus taken off, the rotating solid became dynamically symmetrical like a homogeneous sphere, there would be no free precession at all: if it became effectively prolate, the precession would be in the negative direction. In the actual case of the Earth, the precession is in the positive 1 Tt follows from Poinsot’s kinematic representation of the Eulerian motion, that for any solid rotating with no couples acting on it, the motion of the axis of rotation in the body itself is in all cases strictly periodic. It is not difficult to extend this result to the more general case in which there are fly-wheels or other sources of gyrostatic momentum attached to the solid. 1896. ] Earth's Free Eulerian Precession. 187 direction; which is in agreement with the accepted doctrine that the Earth assumed originally a form of fluid equilibrium, in which it has been gradually solidifying, so that were the centrifugal force now removed it would still retain an oblate form. 6. The practical outcome, as regards Astronomy, is that, as the precessional constant (C—A)/C of the actual Karth is deter- mined precisely by the periods of the ordinary astronomical precessions and nutations, so also the modified precessional constant (C’—A’)/A’ of the Earth us it would be were the centri- fugal force of the axial rotation removed, can be estimated from the period of the free Eulerian precession,—in so far, that is, as this period can be disentangled from the actual observations of changes of latitude, which are also affected by large irregular variations due to meteorological causes, and more or less of an annual character. As the value of C—A is determined by a knowledge of the variation of gravity at the Earth’s surface, the values of C and A are separately known; and therefore the value of 0’ — A’ is approximately known in terms of the Eulerian period, thus affording an additional datwm of somewhat precise character for investigations relating to the physical condition of the Karth’s interior. On the other hand, the forced nutations due to extraneous astronomical forcives, even those of short period, are of course not sensibly affected by the circumstance that the centrifugal part of the Earth’s ellipticity follows the movements of the axis of rotation. 7. The conclusions above stated are restricted to the case of a solid body, that is, one in which parts which were initially near together cannot wander far apart during the motion. If a large portion of the interior is fluid, other considerations will influence the result!. If the interior of the Earth were all fluid except an enclosing shell of moderate thickness, say a few hundred miles, there could be no sensible free steady precession at all, unless the rigidity of this shell were far beyond any that is actually known. The slight change of configuration due to transfer of the centrifugal force to a new axis of rotation, which is here contem- plated, need not be purely elastic, in order to make the conclusions valid. It may be in part viscous: but the wide discrepancy between the actual period of the Earth’s free precession and the one that would apply to a perfectly rigid Earth is evidence that this deformation is really in large part elastic. For if elasticity proportional to, or a function of, strain were entirely absent, then 1 Cf, Kelvin, Math. and Phys, Papers, Vol. ut. p. 132; Hough, Phil, Trans, 1895, 188 Mr Larmor, On the Period of the [May 25, viscosity proportional to, or a function of, rate of alteration of strain would (unless its coefficient were excessively large) be ineffective in preventing the assumption of the configuration of fluid equilibrium in the slow motions here considered, and free precession of periodic character would therefore be non-existent. 8. The influence of the mobility of the surface waters on the period of the free precession has however yet to be considered. For them also, if they are sufficiently deep, the time of sub- sidence of a disturbance will be small compared with the period of the precession: so that the principle already employed will still have an application. The simplest case to consider first is that in which the waters cover the whole surface. When the axis of rotation changes, the centrifugal strain will be shifted to the new axis; thus the ellipticity of the underlying solid Earth will be altered owing to its elastic yielding, while that of the ocean surface will be altered by a different amount easily calculated from the conditions of fluid equilibrium. If on the other hand the ocean consisted only of a thin layer, its law of depth would be changed considerably, and this may involve sensible currents in it. Taking the angular momentum arising from the velocity of these currents (which will diminish the correction due to the surface waters) to be negligible in the actual case, the precessional couple will be as before that of the configuration the Earth would assume if the centrifugal force were removed; it will be that of a spheroid of water with the free surface that would exist on the removal of that force, together with that of the underlying solid Earth with its centrifugal force removed, but with its specific gravity reduced by unity. If the underlying Earth were absolutely rigid, the effect of the layer of water on the precessional couple would be to diminish it by the couple arising from a spheroid of the same density as water, with ellipticity equal to that part of the ellipticity of the ocean surface which is due to centrifugal force alone: if the underlying Earth is yielding, the ellipticity of this effective water- spheroid must be that of the ocean surface less that of the solid Earth, both due to centrifugal force. In any case, it is clear that under these circumstances the free ocean will cause an increase in the precessional period. ‘This, as above stated, is on the sup- position that the ocean is on the average deep enough for the angular momentum of the currents created in the alteration of its free surface to be neglected: if for stance it were very shallow it could obviously have no appreciable effect, and that would be in part because the momentum of the currents would compensate the effect of altered ellipticity, im part because its surface would not then have time to attain the equilibrium form. 1896. ] Earth's Free Eulerian Precession. 189 9. The effect of the transference of masses of water by ordinary ocean currents and other causes has been considered long ago by Lord Kelvin and Prof. G. H. Darwin, and more recently by Prof. Newcomb, with the result that such disturbances are amply sufficient to originate displacements of the Earth’s axis comparable with the amplitudes of the observed changes of latitude. 10. If the Earth were absolutely rigid but covered throughout by surface waters, the momental difference C’— A’ which gives the free precessional velocity would thus be less than the one C—A which gives the forced astronomical precession, by that of a spheroid of water of the ellipticity e, (=;1,)! which is due to centrifugal force alone. This latter spheroid, of semi-axes a(1 — 2e,) and a(1+4¢,), has the moments of inertia C= 20H, (r+ 2€,), A,= 20K, bee 44)3 so that for it C,—A,=2a°E\e,, where EH, is the mass of a sphere of water of the dimensions of the Earth. 11. The potential of the attraction of the actual Earth at distant points is, by Laplace’s formula, E A+B+C-3. V=y/( == 2/3 tis where # is the Earth’s mass, @ its radius, and yH/a?=g. In the case of symmetry when A = B, we have thus Wad) Cad Y 7 Qr? (3co?@—1)+... @ being the co-latitude. The potential of the centrifugal force of rotation is V, =r sin’6. Over the surface of the ocean of ellipticity e, given by r=a(1+esin’6), the total potential V+ V, must be constant: thus = (1 —e sin?) — sii (3 cos?6 — 1) + 4@°a*y sin?@ = const., E 3C-A aoa so that Bie migaty gs OT do°a’y = 0, which gives C—A=2a7H(e—}3m); where m= oa/q, is the ratio of centrifugal force to gravity at the 1 Thomson and Tait, § 821. VON; 1D aN, hie 14 190 Mr Larmor, On the Period of the [May 25, equator, viz. 1S gg5. The value of e¢, the ellipticity of the sea- level, is about 5437: so that the value of C—A is just one half of that which would belong to the actual free surface in the absence of centrifugal force. [We observe, incidentally, that v=" s@K(e-hr Dee eau sl as Hae 2e sin?0) — 12 (e— 4m) (8 cos? — 1) — wa sin?@ = {1—(3m—e)sin?6}, where g, is the value of g at the Pole; which is Clairaut’s formula for gravity. Again, the value of (C— (0,0,0,8), where the quantities in the brackets denote the anharmonic ratios. On working out the relations they assume the simple forms Pa Cos (an) cos (Bn) + ede) cos (a&) = aug, Pa ely SB cos (an) ”°" ~~ cos (BE) where w,g denotes as usual the virtual coefficient of the two screws a and £. I had already given the second of these equations in the Tenth Memoir on the Theory of Screws, Trans. Royal Irish Academy, Vol. xxx., p. 571. I did not then know that there must be the further condition represented by the first. Nor was I then aware of the definite homography between the screws on two cylindroids which expressed the geometrical conditions under which alone one of these cylindroids could be the locus of impulsive screws cor- responding to the screws of the other as instantaneous screws. (5) On the maximum deviation of a ray of light by a prism. By Prof. A. ANDERSON, M.A., Sidney Sussex College. Let the great circle VV, be the principal plane of the prism, N, and NV, the normals to the faces. With NV, and J, as centres 196 Prof. Anderson, On the maximum [May 25, describe small circles with radii equal to the critical angle. These circles must intersect if it be possible for a ray to get through, and the point & representing the direction of the ray in the prism lies on the part of the sphere common to the areas of the circles. Draw a small circle whose distance from N,N, is 7’ the angle which any ray in the prism makes with the principal plane, and let it intersect the two small circles already drawn in # and F. Then for positions of R on HF, G the middle point 1s that which corresponds to minimum deviation and /, # are the points cor- responding to maximum deviation’. Hence to find the absolute maximum deviation we must examine the values of the deviation for positions of R on the small circle CA. Let R be one of these positions. Join V,R and take V,P a A A right angle. Join VR and produce so that sin V,Q =p sin N.R. Then P is the direction of the incident ray and @ that of the emergent ray, PQ being the deviation. Let PQ=6, V.R=¢, RQ =84; then if A be the angle of the prism it is easy to shew that j sin 0 cos 6 = (uw2—1) cos A GAG —p?+1+ pcos 6. The deviation is therefore stationary when sin 8 A ——; cosy cos A 5 + cos 0 18 stationary, which may be shewn to hold when cos A sin ¢ = tan y sin 0, a condition equivalent to 1 + cos?A 2 cos A Since 1 + cos?-A >2cos A, the necessary condition ¢ tan(2 tan y) the quantity in brackets is always negative and the absolute maximum deviation again corresponds to A with the same value as for the last case. As examples of the first case, which is of greater interest than the others, take two glass prisms one of 20° and the other of 50”, and assume the critical angle to be approximately 42°. With this value of the critical angle the angle of the prism must be < 60° 57’ for a stationary value of the maximum deviations to exist. For the first prism the deviation corresponding to the point A is found to be 22° 24’ and for the point C 35° 50’. The maximum deviation is accordingly 35° 50’. For the second prism, on the other hand, the deviation corresponding to A is greater than that corresponding to C, the values being respectively 56° 23’ and 46° 3’. It is easy to write down an inequality involving the angle of the prism and yu, separating cases where the absolute maximum deviation corresponds to the point A from those in which it corresponds to C, but it does not seem capable of concise expression. VOL, 1X. PART It, 15 198 Mr Dixon, On a method of discussing [May 25, (6) Ona method of discussing the plane sections of surfaces. By A. C. Drxon, M.A., Trinity College. The plane sections of surfaces are generally treated by examin- ing their projections upon one of the co-ordinate planes. It is possible however to find at once the equation to any section of any surface referred to any axes, or indeed to any triangle, in its plane. Let (a, 41, 21) (2, Yo, 22) (3, Ys, 23) be the co-ordinates of the three vertices of the proposed triangle of reference referred to the original axes. Let (u, v, w) be the areal co-ordinates of any point in the plane of the triangle referred to that triangle. Then the co-ordinates of the same point referred to the original axes are (Ua, + Vy + Ws, Wy + VYo + WYs, UZ + VZ_ + Ws). By substituting these for a, y, z in the equation to any surface we have the equation, in areal co-ordinates, to the section of the surface made by the plane of the triangle. As an application—if we write down the condition that this curve should have a double point and in this condition suppose £3, Y3, 2, to be current co-ordinates we have an equation which will represent the tangent planes that can be drawn to the surface through the straight line joining (a, y;, 2) to (#2, Yo, 22). Thus for a conicoid we have the equation to a pair of tangent planes in the form S50 Si5 Sb i=, Si, Sansa Sp Sia | (Sb S=0 being the equation to the surface itself, and (Si, Sing Shap Sin, Say Sa Od, oh PaO the areal equation to the section. If we wish to have Cartesian instead of areal co-ordinates in the plane, suppose (&, 7, €) to be the origin and (J, m, %) (ls, mo, Ne) the direction-cosines of the axes, rectangular or oblique. Denote the co-ordinates in the plane by (uw, v) and the co-ordinates of the same point referred to the old axes are (E+ ]Lut+ly, n+ mut mv, €+nuwt+ nv). For instance, let us consider a plane section of the surface aa? + by? + cz? =1. 1896.] the plane sections of surfaces. 199 Let (A, #,v) be the direction-cosines of the normal to the plane of the section. The equation is a(E+lu+ lw) + b(n +mu+ mv)? + ¢(€+nu+ny)?=1. As &,7, € do not enter into the highest terms, all parallel sections must be similar and similarly situated conics. Suppose the origin to be the centre; then a&l, + bnm, + cfr, = 0, a&l, + bym, + cn, = 0, so that = = a xe ; py ae Thus the locus of the centre of a section parallel to a given one is a straight line through the centre of the surface. If the axes of the section are the axes of w and v, we have abl, + bmyms, + enyns = 0, Ll.+ mym,+ N= 0, Ll, mM, __ NN or = = : b—c c—a a-—b Substitute for (,,m.,.) in the equation Al, + pm, + vn, = 0, and we find b—c c—a a—b Xr = v l, fe Mm, Ny as the equation that determines the directions of the axes of the section in terms of A, p, v. Or we may eliminate (/,, m., n.) by means of multipliers and write al, =pl,t+or, bm, =pm,+ op, cm =pn,+or. Thus p=al? + bm,? + cn,’, so that (1 — a&? — bn? — c&?)/p is the square of the semi-axis in the direction (0,, 7m, 1%); l, 7, m, are proportional to Xr pw v a—p’ b—p’ c—p’ dA? Va yp and ilies a—p b—p cp If the section is a circle we have a (0,7 — 1,7) + b (m,? — m2) + ¢ (n,? — n,”) = 0, all, + bmym, + cnn, = 0. 200 Mr Dizon, On a method, etc. [May 25, 1896. From these eliminate c. Thus & (Ml. — Nol1) (Ml, + Nate) = b (M,N, — Msn) (MN, + M i} J ° S S r—) = S S Geometrical |Shadow Bee aS ‘Ber r\ V/ As Viet Tae eee 1897.] near the focus of a Telescope. 267 its greatest maximum between v=1:2 and y=1°3 which will be within a small fraction of the radius, it then diminishes to its least minimum between y=1'8 and 1:9. Afterwards it passes through a series of maxima and minima until at length it becomes practi- cally constant and equal to unity. The appearance on a screen would be that of a bright ring surrounding a series of fainter rings, within a very small distance from it, these latter rings gradually disappearing into a uniformly illuminated space. The outer ring would be most conspicuous, not only by reason of its greater intensity but also because of its greater width. On a photographic plate exposed with a view to showing the existence of this outer ring the probability would be that the light from the inner rings would hardly affect the plate at all; in any case the maxima and minima would be so close together and differ so little from each other that they would be indistinguishable, except perhaps the first two or three. Moreover, unless the light used were of a single definite wave-length, the maxima and minima for different wave-lengths would overlap. If the light were confined to a small portion of the spectrum, this might not affect the outer ring very much, since it is separated from the next inner ring by a wider and darker interval than exists between any of the others, but a very small range of wave-length would be sufficient to fill up nearly all the other minima. The curve J? only represents the variation of the intensity for points which are near the outer ring in comparison with its radius, for points nearer the centre the terms which have been neglected would become more and more appreciable until the regularity of the curve was entirely destroyed. These terms were of order js (1 — «)? (2P? + 2Q— 1), and 1/Vz, of which however the first is always small, since P and Q become ultimately equal to 4; even the second would not make much alteration in the shape of the curve unless z were as small as 100, so that the curve will represent the intensity for a considerable distance towards the centre when y is large. At the centre itself, as is well known, 82M? = 4 sin? 7 ! or the intensity varies with the position of the plate from zero to 4. From the centre outwards the intensity varies irregularly until 1 — « and 1/7z become small enough to allow the application of the preceding results. The figure (Fig. 2) gives some idea of the shape of the intensity curve from the edge of the image up to the centre, the variation near the centre being quite irregular in the sense of varying rapidly with the position of the screen, while the constant-part and the variation at the edge are the same for all positions of the screen so ViO lex ET Vi 21 268 long as it is far enough away from the focus of the telescope to Mr Mayall, On the Diffraction Pattern make y large. 1:00 1:10 2:00 ‘7760 0365 6234 6863 7135 6975 6386 5492 “4509 3734 3434 _ TABLE I. ei? v 2551 2°] 2602 || 2:2 2655 || 2:3 2708 || 2:4 2763 || 2:5 2819 || 2:6 2933 || 2:7 2992 || 2:8 3052 || 2:9 3113 || 3:0 3372 || 3:1 3720 || 3:2 ‘4102 || 3:3 ‘4517 || 3:4 ‘4966 || 3:5 5450 || 3-6 5968 || 3:7 6518 || 3:8 ————————— || 339 ‘7099 || 4:0 “7707 "8327 Ay 8983 || 4:2 9635 || 4:3 1:0286 || 4:4 1:0920 AB | 11525 || 4:6 | 1:2088 || 4:7 1:2593 || 4:8 eee eS |e 7 1c) 1:3358 || 5:0 1:3696 13519 || 5:1 1:2803 || 5:2 1:1638 || 5:3 1:0274 || 5:4 8897 || 5:5 8018 7815 “8440 [Feb. 22, 1897. ] near the Focus of a Telescope. 269 TABLE II, vy | dM? | »v | em? || » | a2 || v | seat? 05 | -2262 | -30 | 1382 | -55 | 0865 || -80 | -0563 10 | -2008 | -35 | -1255 | -60 | 0791 || -85 | -0519 15 | -1854 | -40 | -1141 || -65 | 0703 || -90 | -o479 20 | -1679 || -45 | -1039 || -70 | 0665 | -95 | -0443 25 | 1522 || 50 | 0948 || -75 | -0611 || 1-00 | 0411 ! (2) On the marks made by stars on photographic plates ex- posed near the focus of a telescope. By H. F. Newatt, M.A., Trinity College. The appearances presented by some photographs of stars taken with the 25-inch visual refractor of the Cambridge Ob- servatory in the years 1893-4 were described and illustrated in a paper “On the formation of photographic star-dises” by the present writer, in the Monthly Notices of the Royal Astronomical Society, Vol. tiv. p. 515. In that paper attention was called to the existence of a considerable concentration of light in the boundary of the circle of diffusion for light of any wave-length ; and I was led by a series of observations and experiments, which gave much information as to the excellent performance of the object-glass, to express the view that “it may be a straightforward result in the theory of diffraction through a circular aperture,” that this annular concentration must exist. The extension of Lommel’s work (Bavar. Acad. Mem. 1886, Vol. Xv., p. 235), which Mr Mayall was good enough to undertake at my suggestion and has accomplished and described in the preceding paper (page 259), shows that near the focus of a perfect object-glass with circular aperture the circles of diffusion must exhibit an intensification of light of any given wave-length near the boundary. Mr Mayall has in fact found that the undulatory theory accounts for just such an effect as my experimental results led me to anticipate. A few more observations, and also some photographs taken since 1894, have only confirmed my view that whilst there are signs of some slight outstanding spherical aberration in the 25-inch refractor, the main factor in the production of the rings which I have measured in the star-marks obtained with special exposures of photographic plates has been the concentration of light near the boundaries of the circles of diffusion for different colours. 21—2 270 Mr Newall, On the marks made by stars etc. [Feb. 22, Of these photographs I propose only to speak of two. In the taking of one of them, the aperture of the object-glass was re- duced to 24 inches, and an opaque circular disc, 12 inches in diameter, was suspended in front of the middle of the object- glass, so that light was prevented from falling on the central part. The telescope was then pointed to a bright star and a photographic plate was exposed near the focus, at a distance 14 inches within the visual focus (ze. nearer to the object-glass). The appearance on the plate, which was sensitive to the yellow and green especially between 5900 and A 5200, is mainly due to the light focussed at the visual focus; and the mark produced consists of a circular disc, whose outer edge is brighter than the average and whose central part—that which corresponds to the obstructed part of the object-glass—is blank ; but round the central blank the intensity of photographic action is greater than the average. To put it in other words, the mark is a broad ring, whose external radius is twice the internal radius, and the in- tensity at the edges of the ring, both external and internal, is greater than the average within the broad ring; moreover the brightness of the internal edge is greater than when no ob- structing disc is used. The excess of brightness of the internal edge is the point to which I wish to call attention. The second photograph was taken under similar circumstances except that the obstructing circular disc was displaced from its central position, and set so that its centre fell halfway between the centre and edge of the full aperture. In this case also the marks on the developed plate exhibit an intensification of the light round the edge of what may be called the shadow of the displaced disc. In both of the photographs described there were several ex- posures of various durations on each plate. The effect of long exposures is to obliterate the differences of intensity in different parts of the marks. If the exposure is so short that the plate is barely affected by the average intensity, then the parts where the intensity is greater are seen with exaggerated distinctness. It is easy to pick out amongst the various marks made with different exposures, one or more that show the ring very plainly. The features seen in the photographs suggest the idea that the intensification of the light near the boundaries of these star-marks is a result which is to be expected with an object- glass of any shape of aperture, whether circular, square or tri- angular. [Some photographs lately taken with a triangular aperture show that this expectation is realized in fact. The triangular marks are bounded by edges of which the intensity is greater 1897.] Mr Newall, On the marks made by stars ete. 271 than the average intensity within the boundary. Note added 1897, Mar. 15.] The effects of spherical aberration would be distinguishable from the diffractional intensification near the boundary by the fact that the aberration effects would be different inside the focus from those outside the focus, but the diffractional effects would be the same on opposite sides of the focus. (3) Theorems on the contacts of spheres. By Mr W. M°F. Orr, M.A. Few, if any, of the following theorems are new. Theorem (1) is equivalent to the well-known theorem that all the generating spheres of one system of a cyclide touch all the generating spheres of the other system. Theorem (5) is proved analytically by Casey (Proceedings Royal Irish Academy, Vol. 1x.). I believe they are not generally known, however, and it may be worth while to bring them together. 1. The problem to describe a sphere touching four spheres may admit of an infinite number of solutions. For any four tangent planes from a point to a sphere are touched by an infinite number of spheres; by inversion from any point the four planes become four spheres touched by an infinite number of spheres. 2, Any two spheres and their inverses with respect to a third are touched by two infinite families of spheres. For if A, B be two spheres and d’, B’ their inverses with respect to another sphere O, the spheres which touch A and A’ are divided into two families each doubly infinite, all the members of one of which eut O orthogonally. Any sphere of this family which touches B must therefore touch B’ and belongs to one or other of two singly infinite families according as the natures of its contacts with A and B are the same or different. 3. Any three spheres and their inverses with respect to a fourth are touched in common by eight spheres and in general by no more. For if A, B, C be three spheres and A’, B’, C’ their inverses with respect to another sphere O, of the sixteen spheres which can be described touching A, B, C, A’ (in case the solu- tions of that problem are determinate), eight cut O orthogonally and therefore touch B’ and C’. 4. The sixteen spheres which can be described to touch four given spheres (in case the solutions of that problem be determinate), consisting of eight pairs of conjugates, the members of each pair being inverse to each other with respect to the sphere orthogonal to the original four, any two pairs of conjugates are touched by two infinite families of spheres. This follows from theorem (2). 272 Mr Orr, Theorems on the contacts of spheres. [Feb. 22, 5. Inthe same case any three pairs of conjugates are touched by four spheres besides the original four. This follows from theorem (3). 6. In the same case if the original four spheres be A, B, C, D, the four pairs of conjugates which belong to the same doubly infinite family touching any two of the given four as A, B are touched by two other spheres besides the original four, namely, the inverses of C, D with respect to one of the spheres of similitude of A and B. This is obvious as the eight spheres mentioned, touching C and D and cutting the sphere of similitude orthogo- nally, must touch the inverses of C, D with respect to that sphere of similitude. In this theorem as in the last we have a group of eight spheres touched by a group of six. (4) Change of the independent variable in a differential coefficient. By E. G. GAtuop, M.A., Gonville and Caius College. [This paper will appear in the Transactions, Vol. XVI. Part II.] Monday, 8 March, 1897. THE PRESIDENT, Mr F. Darwin, IN THE CHAIR. The following Communications were made: (1) On the wyection of the intercellular spaces occurring wm the leaves of Elodea during recovery from plasmolysis. By the President, Mr F. DARWIN, and Miss D. F. M. PErtTz. Hlodea continues to assimilate in salt solutions strong enough to plasmolyse the cells. On replacing the plant im water assimila- tion ceases, the gas disappears from the intercellular spaces, and the leaf is mjected with water. The disappearance takes place partly by the escape of bubbles at the open ends of the inter- cellular spaces, but chiefly by solution. The first of these phenomena depends on the surface tension of salt solutions being greater than that of water. The authors are not able to explain the solution of the air in the intercellular spaces. 1897.] Mr Blackman, The phenomena of Carbon Dioxide etc. 273 (2) The phenomena of Carbon Dioxide production associated with reduced vitality in plants, By Mr F. F. BLACKMAN. By the aid of an apparatus (which was exhibited), specially adapted for physiological research on very small outputs of carbon dioxide, several new phenomena of this nature have been brought to light in plants. These comprise the liberation of carbon dioxide produced in the following four cases. Firstly, that resulting from the action of temperatures between 40° C. and 50° C. on dry resting seeds : at temperatures below 40° C. no appreciable formation of carbon dioxide takes place, and at continued higher temperatures the amount, which is at first large, does not remain so but steadily falls off, indicating the decomposition of a definite limited quantity of some substance. Secondly, the large amount of carbon dioxide produced in the first few hours after wetting coarsely ground dry seeds. This cannot be attributed to the action of micro-organisms and is hindered by the action of chloroform and other poisons. Thirdly, the varying production of carbon dioxide by the action of volatile poisons and of fatal temperatures on living leaves. Finally, the post-mortem production of carbon dioxide brought about by subjecting recently killed leaves to the action of a temperature of 100° C. This amount was shewn to vary with the method of killing adopted, and evidence was forthcoming to shew that in this, as in the other cases, these substances which easily oxidise with liberation of carbon dioxide are in some way to be associated with normal respiratory processes. (3) On the leaves of BENNETTITES. By A. C. SEWARD, M.A., St John’s College. In the second volume of the British Museum Catalogue of Wealden plants!, I brought forward evidence in favour of including Williamsonia gigas Carr., Williamsonia Carruthersi Sew., and other species in the same family or even genus with the Lower Cretaceous Bennettites. Although we have not as yet discovered any example of Walliamsonia gigas showing internal structure, there are many reasons for believing that this Lower Oolite fossil represents an inflorescence very closely allied to that of Bennettites Gibsonianus Carr. The immediate purpose of this article is, however, to bring forward evidence in support of the somewhat discarded view that Williamsonia gigas is the inflorescence of the plant which bore the pinnate fronds known as Zamites gigas L. and H. It is by the gradual accumulation of facts and the cor- relation of various observations, that we are occasionally able to 1 “Catalogue of the Mesozoic plants in the Department of Geology” (Brit. Mus.) The Wealden Flora, Part ii. 1895, p. 134. 274 Mr Seward, On the leaves of BENNETTITES. [Mar. 8, surmount the difficulty presented by the almost constant occur- rence of plant fragments as isolated and imperfectly preserved fossils. We are now in possession of most of the data as to the essential features of the Bennettitean mflorescence, but we have hitherto had no satisfactory proof as to the nature of the vegetative organs which were borne by Bennettites. The juxtaposition of plant fragments in the same rock cannot as a rule be accepted as evidence of much value. There is no more serious difficulty in paleeobotanical work than that of piecing together detached portions of the same species, and the isolation of members of one individual has given rise to a multiplication of generic terms which, though a matter of necessity, has been a source of no little confusion. Anyone at all familiar with the method of occurrence of Williamsonia gigas in the Jurassic beds of the Yorkshire coast must have recognised its almost constant association with Zamites gigas. The association is so frequent as to naturally suggest an original union of the two fossils m one plant. In the classic work by Young and Bird—A Geological Survey of the Yorkshire Coast—published in 18221, a portion of a Zamites gigas frond is represented in Plate IT. fig. 2, and in fig. 6 of the same plate we have a typical example of Williamsonia. The authors do not give a name to either specimen, but express the opinion that “figs. 2 and 6 appear to belong to one plant; the former being a leaf, somewhat imperfect, and the latter the head or fruit of the plant?” Bird’s drawing of the frond does not do justice to the specimen which is fairly well preserved, and represents a perfectly characteristic example of Zamites gigas. The original fossils figured in Young and Bird’s work are preserved in the Whitby Museum. The late Prof. Williamson devoted a consider- able time during the earliest years of his scientific life to the investigation of the fossils to which Carruthers gave the name Williamsonia. No one has had opportunities of studying this genus as it occurs in the rocks near Scarborough equal to those enjoyed by Williamson ; and it is interesting to find that the most recent work has tended to support many of the conclusions arrived at by this observer. As early as 1834 Williamson’ expressed the opinion that Zamites gigas was connected with Willamsonia, and in his very able paper, published in 18704, this author is confirmed in the view of the organic connection of these two sets of fossils. This opinion was also shared by Brongniart®, who received an 1 Young, H. and Bird, J., A Geological Survey of the Yorkshire Coast, Whitby, 2 Ibid. p. 183. > Geol. Trans. [2] Vol. v. p. 230, 1834. 4 Linn. Trans. Vol. xxvi. p. 663, 1870. ° Tableau Vég. foss. p. 62, 1849. 1897.] Mr Seward, On the leaves of BENNETTITES. 275 unusually fine collection of English Williamsonias from the late Mr Yates. These specimens are now in the Natural History Museum, Paris, and many of them were drawn for Brongniart with a view to publication, but the work was unfortunately never completed. The drawings were afterwards made use of by Saporta in his compre- hensive work on Jurassic plants. In describing the Yates specimens Saporta expresses himself strongly against the generally accepted view as to the union of Williamsonia and Zamites. He does not hesitate to separate the Zamites fronds from any connection with the Williamsonias. There is he admits “une certaine conformité apparente entre les appareils floraux auxquels on peut laisser le nom de Williamsonia et le Zamites gigas, tel que le fait voir le remarquable empreinte de la collection du Muséum de Paris (voy. Pl.81, fig. 1). Nous avons tout bien de considérer les Williamsonia comme représentant l’inflorescence d’une monocotylédone primi- tive, révélant un type de Pandanées plus ou moins analogue aux Yuccites, aux Podocarya, aux Holirion de Andrae, ete.’” It is unnecessary to quote the various views advanced by different writers as the botanical affinity of W2llcamsonia, especially as these were in many cases largely influenced by Saporta’s decision as to the complete independence of this genus and Zamites gigas. Nathorst proposed a comparison of Williamsonia with the Balanophoreae?, but afterwards* reverted to the opinion of the earlier writers as to its connection with Zamites. A recent examination of the Yates collection in Paris, and a comparison of the numerous specimens in the museums of London, Cambridge, Whitby and Scarborough has led me without hesitation to regard the pinnate Cycadean fronds of Zamites gigas as the leaves of the plant which bore a Williamsonian inflorescence. One not infrequently finds a small bud or young Williamsonia borne on the end of a peduncle about 20 or 30 cm. long and 3 to 5 em. broad. Such an axis is covered with linear lanceolate scale leaves spirally disposed and often clothed with delicate hair-like ramenta, such as occur on the scale leaves of Dioon and other recent Cycads. Such a peduncle is figured by Saporta on Pl. XV. of Vol.iv.t The original is in the Paris Museum; the scale leaves are less prominent and not so thick as those shown in the drawing, and in this and other specimens one sees traces of the ramental appendages. The best example of a peduncle is included in the series of specimens of Wualliamsonia now in the possession of Mrs Crawford Williamson, to whom my thanks are due for an 1 Pal. Frang. Plantes Jurassiques, Vol. 11. 1875, p. 55. 2 Ofr. k. Vet.-Akad. Forh. 1880, No. 9, p. 33. 3 Ibid. 1888, No. 6, p. 359. 4 Pal. Franc. Plant. Jurass. Vol. tv. 1891. WAOIGS IDG aie 22, 276 Mr Seward, On the leaves of BENNETTITES. [Mar. 8, opportunity afforded me of examining the fossils figured im Prof. Williamson’s valuable memoir. Saporta alludes to the resemblance of the pedunele which he figures to the stem of Zamites gigas represented in his volume on Cycads, Pl. XI. fig. 1, but does not regard the similarity as evidence of relationship or identity. This specimen of Zumuites referred to in the above quotation from the second volume of the Plantes Jurassiques, is of exceptional interest and furnishes the most important lmk in the argument in favour of the connection between Williamsonia and Zanutes gigas. The figure in Saporta’s work is very imperfect and conveys but a poor and erroneous idea of the actual specimen. At the base we have a stem about 5 cm. broad with the surface features indistinctly preserved, but showing a number of imperfect scale leaves. To one side of the stem, 5 em. from the bottom of the specimen, are attached the petioles of two clearly preserved fronds of Zamutes gigas, and above these occurs part of a third frond apparently in its natural position but without the petiolar attachment. The stem is prolonged obliquely upwards to the left in the form of a branch about 3 cm. broad and 14 cm. long. This branch is thickly clothed with hairy leaf scales and terminates in numerous spreading leaf scales of a narrow linear lanceolate form. The position and surface features of this branch are very inadequately and incorrectly reproduced in Saporta’s figure. If we now turn to the specimen figured by the same author as a peduncle of Wzallaamsonia’, and which terminates in what appears to be a closed Wilhamsonian inflor- escence, we find the characters are identical with those of the branch of the stem bearing Zamites fronds. Specimens of peduncles in the British Museum, and others in the collections of Whitby and Scarborough, afford similar proof of the identity of the detached peduncles and the obliquely placed branch of the leaf-bearing stem. There can be little doubt that the terminal bud-like structure on these peduncles is a young and unexpanded Williamsonia, but even if this be disputed, there can be no question as to the identity of the typical Williamsonia scale leaves and those of the terminal bud on the peduncles. A specimen in the Whitby Museum shows a stem bearing two diverging peduncles, and evidence of the same habit of growth is afforded by an example in the British Museum. In all probability the stem figured by Saporta (Plantes Jurassiques, vol. 11. Pl. XI. fig. 1) bore another peduncle in addition to that shown in the figure; this is suggested not only by the examination of other specimens but also by the oblique position of the peduncle which 1 Pal. France. Plant. Jurass. Vol. 1. p. 55. ? loc. cit. Vol. Iv. Pl. xv. 1897.] Mr Seward, On the leaves of BENNETTITES. 277 is not brought out in the figure. The restoration of Zamites given by Williamson in his well-known paper (Pl. 53)! accurately represents what I believe to have been the manner of attachment of the inflorescence and foliage leaves to the main stem. The above description must necessarily lack completeness in the absence of figures, but it is intended to publish drawings in a monograph on British Cycadean plants now in preparation for the Paleeontographical Society. The precise relation between Williamsonia and Bennettites must be left for future discussion, but evidence is not lacking in support of the view that the two genera are both members of the same family, and if not included in one genus they must at least be placed in the same family of Bennettiteae. In the title to this paper I have used the term Bennettites in a wide sense as includ- ing plants of the Bennettitean type, though possibly generically distinct. The generic name Williamsonia, as expressing a more complete knowledge of the botanical affinity of the fossil than the provisional and comprehensive term Zamites, should be substituted for the latter in the case of Lindley and Hutton’s species, Zamites gigas. I am indebted to M. Renault for the opportunity of examining the specimens in the Paris Museum and for permission to have some of them photographed. My thanks are due also to Mr Newbitt of Whitby and Mr James Rowntree of Scarborough, for enabling me to examine the interesting examples of Walliamsonia and Zanutes in the museums of those towns. 1 Linn. Trans. Vol. xxv1. 1870. PROCEEDINGS OF THE Cambridge Philosophical Society. On Ine’s Solution of a Partial Differential Equation of the First Order. By A. C. Dixon, Se.D., Trinity College. §1. The present paper gives an account and a proof of Lie’s method* of solving a differential equation in one dependent and any number (including unity) of mdependent variables. The arrangement of the proof is such as to facilitate the examination of certain cases of exception. Such are afforded by the tac-locus and cusp-locus of the ordinary theory with one independent variable, and their analogues, and also by an extensive class of equations in which the linear partial form is included, and the integration of which has been discussed by Mayer+. Notes are added on the nature of a complete primitive, the complete solution of the auxiliary linear equation, and the satisfaction of limiting conditions. Method of Solution. § 2. Let z be the dependent variable, 2,, 2...a, the inde- pendent variables and p,, p.... p, the partial differential coefficients of z. If u, v are any two functions of these 2n+1 quantities, denote the expression r=n O(u,v) 7TS™ O(u, v) ne 0 (2, Pr) iu aaa Pr 0 (2, Pr) by the symbol (wu, v). * See Forsyth, Theory of Differential Equations, Part I. pp. 238—9; or Lie, Math. Annalen, Vol. vu. p. 242. + Math. Ann. Vol. vi. pp. 313—8. VOU. 1x, PL. VI. Ze 280 Mr Dizon, On Ine’s Solution of a Partial Then we know that the integration of any partial differential equation Ff Gig Os 2 2ny 25 Dis Pas >< Pn) =O eee eee depends on the solution of the linear equation CPD) S10 t ces seanseenah oe eee (2) for @ in terms of a, ... %n, Z, Pi --- Pn. ‘The general solution of this linear equation is derivable when that of the equation f=0 is known. § 3. With regard to the expression (f, ¢) two things are noticeable. In the first place it 1s indifferent whether we do, or do not, suppose that wherever p,, say, occurs in ¢ it is to be regarded as a known function of the other 2n variables, defined by the relation f=0. This is true for each term in the expression and therefore for the whole. Secondly, the following relation holds (u, (v, w)) +(v, (w, u)) + (w, (u, 2) ou du ow =—(v, W) AB (w, A (u, v) ag (3). Hence if u, v, w are all solutions of the equation (f/f, ¢) =0 it follows that the ratios (v, w):(w, uw): (u, v) are also solutions, unless they are constants. § 4. If now we suppose p, to be defined as a function of GP 36 big Fp f0n 500 {Opa by the equation f=0, and therefore not to occur in ¢ except apparently, the equation (f, ¢)=0, which is linear and homo- geneous in the 2n derivatives of ¢, is satisfied by 2n — 1 independent functions, say Uy, WU... Um 1, and the most general form of ¢ isa function of these. We take any such form, say w, and seek next a common solution of the equations (Ff, $)=9, (ch, $)= 0. This must be a function of u,, u.... Uen—, such that r=2n-1 od = (tt, Ur) the 0. The coefficients in this equation, or at least their ratios, are functions of u,, U2... Wen Since they satisfy the equation (f, $)=0. 1897.] Differential Equation of the First Order. 281 Hence the condition (m4, ¢)=0 gives a linear homogeneous equation connecting Op Op _ 0d f As] OU,” Og OUan—a’ the coefficients being functions of , w,... Uen+1. The full number of independent integrals of such an equation is 2n—2 and w is one of them; we may suppose without loss of generality that the FESt ATC Uy, Us ... Uon—o- The condition (w., 6)=0, when ¢ is a function of Ulay lee ten is similarly satisfied by 2n —4 forms of ¢ of which wu, is one and the rest may be taken to be us, wy... Uen—s- By carrying on this process we get a series of n expressions Uy, Uy ... Un, functionally independent of each other and such that ny 10) Cp Us) =O (Lo S— 1, A) We are now to shew how the integrals of the equation f= 0 depend on the functions w,, w, ... Up. du Ox; respect to x;, account being taken of the dependence of z, p,, po... Pn upon Z;. §5. Let us write for the differential coefficient of w with Thus Ox; 4 Ox; io 02 j=l On; ; Op; i and t=! (diy OUg Ag OUy\ sis 0 (Ur, Us) (dpi _ — i=1 (ae Op: Ou ap) ar ~. O( pis Pj) \ aa, Ou OT Nac, 5 Se ty 2. va enn erect (4). Putting f in the place of u;, we have Tit, OF - = = bya AUP rarcreracatarte ecatetatter 5), 2 an ane 0 @=12%..2) (5) since f = 0 by supposition. The system of 4n(n+1) equations thus found is, in virtue of the relation f = 0, an algebraical consequence of the system which contains the same number of equations. 23—2 282 Mr Dixon, On Lre’s Solution of a Partial §6. The n equations (5) offer three alternatives: (a) U;, Up... Up are all constants ; (B) U, Usp... Un are variable, but (i, Uy +++ Un) _ @ (Chg Bh don Gp) so that they are connected by one or more relations ; (y) se =0 GI ea): If we take (a) we may have an integral, the complete primitive, which is the result of eliminating p,, p.... Pn from f=90, h=G), Up =Ay... Un =p. If we take (vy) we may have an integral, the singular solution, which is the result of eliminating p,, p.... Pn from f=0 On Cin? GiDs Op), For (8), suppose the relations to be m in number, namely, OR Oh Oh aon Vine Oa Ib A 50 10) scosccscc0e- (6). Then only n—m of the equations (5) are independent—from (4) we may deduce that S Mey ogi & dd; Our _ 9 (ie ak vl ee ran Gy ODs e s=1 Oats : Ops Each value of 1 gives a set of n equations of which only n— m are independent and by comparison with (5) we deduce the n — m relations of of of Bp uenay a aGes QO). cas sheaeeeeee (7) Of. of. Og Opieit topes ODn Od» Bago moa Om Om By) Te ae Tf (8) leads to an integral it will be the result of eliminating Pr» Po++» Pn from f=0 by means of the n equations (6) and (7). The equation has thus n—1 distinct types of general integral 1897.] Differential Equation of the First Order. 283 since m may be any of the integers 1, 2, ... »—1, and the com- plete and singular integrals are extreme types for which m has the values n and 0 respectively. All solutions of the equation f=0 are included among those thus derived from any one system of functions Uy, Un «~s Un; but the system of functions is by no means unique, as is clear from their mode of formation. § 7. We may verify these solutions in the following way. Considering z, p,, p.... Pn as functions of 2, a... 2, we have at once, since f=0, ; s=n gee Oh Sc ates Ah Gee ae é sie Geer s=1 02, Op and also ou; dz ou; *%=" dp, Ou; du; (" Se Pa 6, 2s 3 ‘ : Oar, Oxy ° Oz sa1 OL, OP, Oi Thus r=n du; of = Hime oS Lae Ot S) = an, 4 yn tt ie eS Pr) 8=n T=Nn dps 0 (uw, f) SS pe Oty f) 5a), = fas al 02, 0 (ps, Pr) ( . and Ly ce ) 0 (wi, Uj) r=n (= Ou; = du; = = (U;, Uj) 2S Aaa say (2, Pr) —/ r id, Ae "Ses O(m, wy) (4a). Ox, Op, Ox, * Op, 6&=) r=) 0a, 0 (Ps; Pr) (In the double summations 7, s must be unequal.) | The first term on the right-hand side in each of the equations (5a) and (4 a@) vanishes, since f= 0. Now let these equations be multiplied respectively by the determinants of the matrix | Of Ou, OU, OUn | Op.’ Op,’ Op. Op, | r=1 eee essere 284 Mr Dixon, On Lne’s Solution of a Partial and the products added. We thus have on the right dz Of, Urs Ua «22 On) (in -) 0 (2, Drs Po +++ Pn)’ and on the left du, du, dus dun | » 04,’ Oa,’ Oa, °° Oa, of OU, Up OUn Op: ? Op; ) Op, so000ad 00006 On, of OU OUn ap,’ an es ANE ete ant In hike manner (S-p ) 0 (fy Uy +++ Un) Dip Fy) Oli ses fp) = the same determinant with x, written for z, in the first row. In these equations we may substitute for u,, w,...U, any n independent functions of them, say ¢,, ¢.... dn, the effect being to multiply each equation by the Jacobian O(di, be... hn) x @) (Dns Why one Qin)” We thus have (dz \ Cf bu bubs) _| 9 th db, didn Crs Pr) OZ pin ee pn) Wariner Geel Gue. of ody Opn Op, 5) Op: eeoreeeoeces Op, Of ody 4) 1D I Ope CO i i ea Of od Opn ) On ee ee _* If the relations among wu, u,... u, expressed by (6) are such that they cause this Jacobian to vanish for arbitrary forms of ¢,4,, ...¢,, then the equations (6) met be satisfied doubly by these relations, and this state of things can always be avoided. 1897.] Differential Equation of the First Order. 285 The right-hand side of this equation vanishes if the equations (6) and (7) are satisfied, m being zero or any whole number up to n inclusive. Thus in general the equations (6) and (7) give p, as the value of a and therefore afford a solution of the differential equation (1), which was to be proved. The relations (6) with f=0 form a ‘complete system,’ the singular solution of which is given by (7). Thus we may say that all the solutions of f= 0 are singular solutions of complete systems to which f=0 belongs. It is not necessary to form all such com- plete systems in order to have all solutions. Cases of failure. § 8. The proof will fail if OULU ne tn) Te En ie Te 8). OZ} Dis '2.2 Dn) (8) If we multiply the equations Gia) —0; ete: -(%,,.1,) — 0, ete: by the second minors of this Jacobian, formed by leaving out the derivatives with respect to z and p,, and add, we have, as other forms of the relation O Cf, tis <<: Un) _¢ 0 (2, Di ooo Dig) : Fe We. 3.5 UR) eat OG Diy. Dn) Hence it follows that all the determinants of the matrix | ef of OF 20f wOF Of ll some seeessehn Gn Or, 0%, 02 “Op, Op, | | Ou, Oy OU, Ou, Ou Ou, Ct Crue Ol, 02 Op, | OD, SUK oe Re) cacaetocce (9); jn] = a 286 Mr Dizon, On Lie’s Solution of a Partial vanish unless those of the matrix Sp ee a Ne (11) Op, : Op, of OD; of Un aps Vaan are all zero. There are therefore two kinds of exceptional cases, which we shall now examine*. §9. The equations (7) may be written a Sn ae =(), G=Hil, Zs.) Thus if (7) A i are both true it follows that ot 0d; ag Po Be unless the determinants (11) vanish. In the same way from (9), unless the determinants (11) vanish, =), of Odi — . = = Dae ofl). r An + Sy; Aa, O, (eal, n) * The proof also fails if O (brs Po -+- bn) _ =0 CNS hyaos CA) that is to say, since $,,4;, ... , may be chosen arbitrarily, if ee eee Cite NOt rots ; Bip, 7 Hopareesvone Cbm Ohm ay, ose cies These equations are n—m-+1 in number, and as u,...u, already satisfy the m equations (6) they will generally be inconsistent. If however any values satisfy them they will also satisfy (7). If the values are isolated then these relations afford a solution which is included in the complete primitive, since the values of U,...U, are given. If the values are not isolated then these relations are not numerous enough to enable us to eliminate p...pp- 1897.] Differential Equation of the First Order. 287 The values satisfying these conditions will occur twice in the oo *-™ determined by the m+1 equations (1) and (6) in the 2n +1 quantities 2, ...%p, 2, Pi -+- Dn- Thus if (8) is not a new relation this o”-”" must contain a double «”*, which will satisfy (7) but not be a solution of the differential equations (1) and (6). Any complete primitive of the system will define an «” on the «”~” and it will not generally happen that a complete primitive will, in geometrical ag meet the double o” in the same point on both sheets. The system of values of a,...%n, 2, Pi» Pn Will therefore be common to two complete primitives, which thus have contact with each other, so that the complete primitives of the system (1), (6) have a tac-locus. This is one of the cases of failure. The second is that in which the determinants (11) all vanish in virtue of a single relation. This relation will clearly be included in (7), at least as an alternative, and the other alter- native, if any, must be taken in order to find the singular solution of the system. In this case the complete primitive 0” has an "1 of cusps, that is of points where 2, ... #,, 2 are all the same for two consecutive points. The cusps of the system (1), (6) will form an o?—"—1 within which the equations (7) define an 2”. This will generally not satisfy the differential equations. The occurrence of a cuspidal ©” on the complete primitive ought perhaps to be considered as normal, since generally the vanishing of the determinants (11) will be secured by the vanishing of a factor of the left-hand side of (8)+. If we consider a singly infinite series of complete primitives of (1), regarding only the "+1 (z, a,,... #,), each primitive has the cuspidal oo” as part of its intersection with the consecutive. If we consider a doubly infinite series then each primitive has an 0” of points on the cuspidal x” as part of its intersection with two consecutives, and so on. Thus, whatever the value of m ( ( Le ae 0x, aes 0 & Pr> Pk +: Pn) and other such equations, each being linear and homogeneous in & of the quantities r=] a Opie lair): 1897.] Differential Equation of the First Order. 289 But the relations (6) and (7) are now only n —&+1 in number and therefore fail to determine 2, p,,...p, mn terms of a,... ap. They may be taken as determining 2, px, Prii--- Pn in terms of Ly, +++ Py, +.» Pea and it is then easily found that dz —= = .k-1 = ONG i.e 1), dz _ _O(f, di, bo--- Gm), OF, Gis a =» Pm) On, O(&;; Pr cpa) iMag (2, Pry 4D) eS 12a. 2). Thus the relations (6) and (7) yield an equation connecting Z, %, ... ® and leave k—1 of the quantities p,, p.... Py, un- determined. If then we suppose py, 2... Px to have the values just found for = (r=1, 2... &—1) it will follow from the equation (13) that dz Oa, 2 and in the same way 2 = pr (eas My bere n). Thus we may say generally that the equations (6) and (7) yield at least one relation among 2, #, ...#,, and when they yield only one, that is when m}n—k+1, that one relation satisfies the differential equation f= 0. Exceptional cases may arise here, again corresponding to the tac-locus and cusp-locus. In the one case all the minor determi- nants of order n —k + 2 formed from the matrix (10) vanish, in the other those of order n —k +1 formed from (11). § 13. We are thus introduced to classes of differential equations in which certain of the forms of solution are wanting. Lagrange’s linear equation is an extreme case, in which k=n. It is of course the only case that can occur when n=2. In general the class includes equations formed by eliminating the arbitrary constants and function from an equation of the form air (U1, Uz... UR) =0 where 2, v,... are known functions of z, 2... #, involving n —k arbitrary constants, and y is an arbitrary function. The differential equation is of such a form that it is satisfied by equating n-—k+1 of the quantities p,, p,... pn to linear functions of the rest, the coefficients involving z, 2, ... #,andn—k parameters. For instance 290 Mr Dixon, On Ine’s Solution of a Partial when n=3,k=2 the equation f=0 must so far as Pry Ps» Ps are concerned satisfy the condition for a ruled surface. This is neces- sary but not sufficient unless k = n. § 14. The number of complete primitives is unlimited, but it should be noticed that not every solution involving n arbitrary constants is a complete primitive in the sense that all other solutions can be deduced from it. It may be that an equation I (G; Ghy Broce Gay Crecos Gn) =U is such that from it and the n derived equations OF oF rag alien (GPs 1 AF ose 70) two or more equations can be deduced in which the arbitrary constants do not occur. Let these equations be fra, jeS0 cope: Then all the solutions derived from #’'=0 by the ordinary method of variation of parameters will satisfy this system of m equations, and therefore will not include all the solutions of any one of the system, say f, = 0. For instance the equation DZ = A,X? + AX XL, + AzXe? is a solution of 2 = PyLy + Pl. + P33 + Pi Peps containing three arbitrary constants, but since it satisfies the equation p,=0 also it is not a complete primitive in the true sense. §15. IZfany complete primitive of the equation f= 0 is known, the general solution of the auxiliary equation (f, ¢)=0 can be deduced * as follows. Let JOA REAR Os ea ian hy, Oy oon Ca) 0) be the complete primitive. Then from this equation and its n derivatives expressions can be found for a,, a)... @», in terms of Z, @...%n, P, -.. Pn; Otherwise it is not properly a complete primitive. Let these expressions be mm, ww... Un respectively. Then 2, %&s... Up, are n of the 2n — 1 solutions of Cid) 0) Another complete primitive can be found by taking An = a,b, + a,b, +... + An Dn— + bn, * See Mayer, Math. Ann., Vol. vit. p. 311. 1897. ] Differential Equation of the First Order. 291 and eliminating a,... d, by means of the equations oF oF lage eas (r=1,2...n—1). We still have a,=2,, d2= Uy... Gn =Un and the values of b,, b,...b, are solutions of the auxiliary equation. Thus the 2n —1 necessary solutions of the auxiliary equation are %,, Uz... Un and the ratios of au aU a Ou, ; Dus vee dun > where U denotes Dd CRF. ORE A oR) a It is easy to shew that these are independent, and thus we are in a position to write down the general solution of the auxiliary equation. $16. It would appear at first sight that the determination of the forms of the arbitrary functions to satisfy limiting conditions would involve the solution of differential equations, since the derivatives of the arbitrary functions occur in the solution; this is however not the case. Suppose for instance that the value of z is given when 2, = 0, say eS CRA Rens) } The values of p,, ps... Pn are therefore given when «#, =0, for then pra 2 (r=2,3...0) These values may be substituted for 2, 2, p., ps... Pn mn the equations f= 0, U, =A, Ug= Ag... Un = An, and the n quantities p,, 2... Z, may be eliminated. Thus one or more relations will be found among @, a... dp and these are what were required. More generally if the solution is to include all systems of values that satisfy the equations Xi (z, DY, Loos Ln) = 0, X2 (z, Hy, Vz «+. Xp) = 0, the values of p,, p.... Py, corresponding must satisfy the n—1 relations —1, Pi, Po. Pn ||=9. 02 i OL Vor iin Ly, a2? Da, oan 292 Prof. Anderson, On the Apparent [Apr. 26, The elimination of z, 2... 2, P: --. Pn from these n —1 relations, and Vi = 9, %.=0, f= 0, wy =a «1. Un = An, will give one or more equations connecting a,, a... d,, and these are what must be used to derive the particular solution sought. Monday, 26 April, 1897. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following were elected Fellows of the Society : R. Lachlan, Se.D., Trinity College. W. M. Coates, M.A., Queens’ College. S. 8. Hough, M.A., St John’s College. Rev. P. E. Bateman, M.A., Jesus College. The following Communications were made to the Society: (1) On the Apparent Electrification in an Electric Field at the Bounding Surface of Two Dielectrics. By Prof. A. ANDERSON, M.A., Queen’s College, Galway. In Maxwell’s Treatise on Electricity and Magnetism, Vol. I. 3rd edition, p. 100, the apparent surface charge o’ on the boundary of two media of specific inductive capacities K, and K, is defined Poe aad ; by the equation Te + ai + 4aro’ = 0. Maxwell then proceeds to state, giving a reference to Faraday, that if, durmg the action of the inducing force, the apparent electrification of the surface be discharged by passing a flame over the surface, then, when the inducing force is taken away, there will appear a true electrification opposite to o’. In an Appendix to the chapter in which this occurs the apparent electrification is described as acting on the conducting flame which is in connexion with the earth, attracting electricity of opposite sign, and repelling electricity of the same sign, the consequence being the production of a real electrification which masks the effect of the apparent one. Prof. Gray, in his Absolute Measwrements in Electricity and Magnetism, Vol. 1. p. 113, says that the action of the flame is to reduce the surface to zero potential, and that the real electrification is equal and opposite to the apparent electrification. In Mascart and Joubert, Vol. 1. p. 101 (English edition), it is stated that, though the layer of density o is a fictive layer, if its surface is brought to the neutral state by means of a flame, and if the sources of induction are removed, a real layer of density o will be found on the surface. 1897.] Electrification in an Electric Field, ete. 293 Again, Wiedemann, in Die Lehre von der Elektricitdt, Band 11., asserts that the flame removes the apparent electrification o’, and produces a real electrification of opposite sign depending on the action of the apparent electrification on the interior of the body. There seems to be some obscurity as regards what is meant by removing the apparent charge. Prof. Gray, however, clearly states, and I think the same thing is implied in the Appendix to the chapter in Maxwell above referred to, that it means reducing the surface to zero potential. It would, I think, be impossible to do this unless for the portion of the surface affected by the flame at one instant: if the flame be taken to another portion of the surface the real electrification produced there will alter the potential of all parts of the field and, therefore, of that part which has already been reduced to zero potential. To reduce the whole surface to zero potential, a flame large enough to affect all parts of it at once would be necessary. But, if this is what is meant by removing the apparent electrification, the real electrification, as will be shewn presently, is not necessarily either equal in amount or opposite in sign to the apparent electrification. Another way of putting it, used by Mascart and Joubert, is ‘reducing the surface to the neutral state.’ It is not clear what this means, unless it be making the electric stress zero at every point of the surface, on both sides of it. But this by Gauss’s theorem is impossible if a real electrification is produced by the flame. What seems to be properly implied by removing the apparent charge is making the surface density of this charge, as defined by Maxwell, zero; that is to say, a real charge must be given to the surface which will make the normal force at any point of it continuous. But, generally, this could not be done by means of a flame. Let o’ denote the apparent electrification, and o, the real electrification necessary to remove the apparent charge. Also let V denote the potential at any point before and V’ after the apparent charge is removed, and V, the potential due to the real electrification of the surface. Then, V’=V+V,, and we have dv aV dn, adn, dV dV gt May, 9 + 47ro’ = 0, d rrr also Ha, Wt toe Maras Ct V,) + 4aro, = 0, d d an, V+ Vi) + ay V+ Vi) =0. 294 Prof. Anderson, On Apparent Electrification, etc. [Apr. 26, Hence, Fea ie IU sail 1) Ny Ane GH, Gh, re and dm + dn, _ 40a = 0. To remove the apparent electrification is, then, equivalent to finding the actual surface density o, of a distribution of electricity on the bounding surface of two media of specific inductive capacities K, and K, which would produce an apparent surface density —o’, there being no other electricity in the field. This problem admits, in many cases, of an easy solution. As an example, consider the case of a charge e at the centre of a sphere whose radius is a and specific inductive capacity K,, the medium outside the sphere being of specific inductive capacity Qe paste K, K, iz = The surface density, o’, of the apparent 2 AS et inate wien 2 Inside the sphere the potential is ae +2 ( ip and outside it is : aL MA, é 1 1 electrification is, consequently, ree (Zz — = To find the real electrification which will remove all apparent electrification, we must find the distribution o, on the sphere which, of itself, would produce an apparent distribution of surface density e 1 1 a. : e KS aia ‘z — mal This is easily shewn to be Fuse (1 — =) ; and is, therefore, not equal to —o’ unless when K,=1. When this surface distribution is placed on the sphere, the potential both inside and outside is = , and the force is consequently the 1 same on both sides of the surface, as it ought to be when there is no apparent electrification. Suppose, on the other hand, we bring the surface to zero potential by means of a flame. The potential at all points outside will be zero, and the potential inside z (-- *). The surface 1 density of the actual electrification of the surface is, therefore, - rant which is not —o’ and not opposite to o’ unless when K,>K,. Besides, there is still an apparent electrification of surface density — roayee 1 1897.] Mr Newall, On Luminosity attending Compression. 295 (2) On Luminosity attending the compression of certain rarified gases. By H. F. Newatt, M.A., Trinity College. 1. Morrem (Pogg. Ann. 1862, Vol. 115, pp. 350—2, and 1865, Vol. 126, pp. 643—654) and Sarasin (Pogg. Ann. 1870, Vol. 140, p. 425) have given accounts of phosphorescence produced in rarified gases by the passage of electrical discharges. The pheno- menon itself was recognized in the earliest days of vacuum tubes. Morrem and Sarasin agreed in thinking that no pure single gas (as distinct from a mixture of gases) exhibits phosphorescence. Morrem found the phosphorescence very strong in a mixture of gases containing 200 parts of Oxygen, 100 parts of Nitrogen, and 150 parts of SO,. Sarasin regards the presence of oxygen as essential to the production of phosphorescence. J. J. Thomson (Recent Researches, 1893, p. 184) has described observations of such phosphorescence and has explained it in accordance with his view that the conduction of electricity by a gas is associated with decomposition. He states, “I have never detected any glow in a single gas (as distinct from a mixture) unless that gas was one which formed polymeric modifications, but all the gases I have examined which do polymerize have shown the afterglow.” 2. In the course of an investigation of the spectra of rarified gases rendered luminous by electrodeless discharges by Prof. J. J. Thomson’s method, I was dealing with the case of mixtures of Oxygen with other gases, chiefly Nitrogen and Carbonic Oxide in different proportions, and frequently obtained mixtures which at certain exhaustions phosphoresced so brilliantly that I was induced to devote some time to the study of the phenomena, in particular by means of the spectroscope. 3. A description of the apparatus used will make the con- ditions clearer. A glass tube, in which electrodeless discharges were to be passed, was connected with a Hagen-Topler mercury-pump, fused glass joints being used throughout. There was also attached to the pump a graduated tube in which mixtures of gases could be made in any desired proportions, and which served as a reservoir of such mixtures. Samples of the mixtures could be let into the pump by an arrangement very similar to that figured by Salet in his Traité de Spectroscopie (Masson, Paris, 1883), p. 209. In most of the experiments the electrodeless discharge was produced near the middle of a large tube, about 2 inches in diameter and 6 feet long. In a tube like this the phos- phorescence begins near the bright discharge and spreads along VOL. IX. PT. VI. 24 296 Mr Newall, On Luminosity attending [Apr. 26, the tube, in some cases quite slowly (about 1 foot per second), in other cases too quickly for any estimate to be made without special apparatus. The rate varies with the pressure and with the mixture used. 4. The colour of the phosphorescence is very varied ; I find among my notes that at various times the following colours have been observed :—white, silvery-grey, yellow, yellow-green, old gold, ruddy yellow, brilliant blue. The phosphorescence is undoubtedly diffused throughout the whole volume of the gas enclosed in the tube. There is an appearance of semi-opacity in the phos- phorescent gas, except in the case of a certain brilliant blue phosphorescence. The contrast in this respect between the yellow and the blue afterglows is as marked as that between a clear solution of copper sulphate and a liquid rendered turbid by a slight yellow precipitate in suspension. The blue phos- phorescence is marked, in my mind, as of an exceptional nature ; I have only seen it four or five times, but it has generally been of so short duration, that I have not been able to study it fully, nor can I say what conditions are necessary for its appearance, except that I connect it with oxygen and sulphur. Spectrum of the phosphorescent gas. 5. A careful and long continued spectroscopic investigation shows that the spectrum of the phosphorescent glows that I have examined is a continuous spectrum. Prof. Thomson records the observation of a few bright lines, if very high dispersion is used, but I have been unable to corroborate this observation. (In view of what follows in this paper, I should explicitly state that I refer here to the spectrum of phosphorescence which has been excited electrically in the rarified gas.) 6. An arrangement somewhat similar to a phosphoroscope was used. Between the spectroscope and the tube in which the phos- phorescence was produced, a sector or sectors of a circle were rotated by clockwork, which also drove a contact-break in the circuit that produced the bright discharge in the tube. It was arranged that the sector intercepted the light of the bright discharge, and allowed only the light from the phosphorescent gas to pass into the spectroscope. The spectra were observed visually and were also photographed. Both methods showed a continuous spectrum without any trace of bright lines, except on one occasion to which I refer later (§ 27). 1897.] the compression of certain rarified Gases. 297 7. The spectroscopic study of the phosphorescence itself has then given no evidence of its chemical origin. But the fact that a continuous spectrum is visible in a gaseous mixture of such tenuity as that dealt with (about 0™"3—0™™"1 pressure) is noteworthy. I was unable to detect diffuse bands or a maximum of brightness though the difference of the colours of the phos- phorescent hazes in different mixtures of gas would lead one to expect the existence of such bands. 8. The spectrum of the bright discharge which precedes the phosphorescence has only given results difficult to interpret when taken in connection with one’s knowledge of the care that has been taken in preparing the gases. For instance, a bulb had been carefully filled with electrolytic oxygen, after ‘rinsing’ the pump and tubes out with the gas, and after heating the tubes several times at very low pressure, and after leaving the pump and tubes exhausted for two or three days. The bright discharge gave only the band spectra of nitrogen and cyanogen, and it was only after continued sparking that the oxygen spectrum asserted itself. It seems to me that the spectrum of the bright discharge possibly affords no more certain evidence of the chemical origin of the phosphorescence than of the nature of the mixture of gases in which the discharge takes place. 9. The appearance of the phosphorescent gas led me to apply a test, which Sir G. G. Stokes has described as affording proof of the existence of solid particles in the flame of a candle. A beam of sunlight was concentrated by means of a lens upon the phos- phorescent gas: and the track of the beam in the gas, as also the scattering of polarized light, were looked for. But no evidence could be obtained that supports the idea that we might have to deal with the phosphorescence of solid particles momentarily set: free by decomposition accompanying the bright discharge. 10. In the course of my work with electrodeless discharges I have frequently found black or brown deposits on the inside of the glass tubes. In one or two cases the deposit has been thick enough to form a film which could be detached from the glass; the film was translucent and had a highly offensive smell. The formation of this film is a proof that permanent chemical changes are brought about by the discharge ; and there can be little doubt but that the phosphorescence is a sign that temporary chemical changes are also produced. 11. Taking into account the difference in the colour of different phosphorescent hazes and the difference in the condi- tions of their appearance, but setting only small weight on the 24—2 298 Mr Newall, On Luminosity attending [Apr. 26, indications of the spectrum of the bright discharge preceding phosphorescence, I am led to connect white phosphorescence with mixtures contaiming oxygen and carbon compounds, yellow phosphorescence with mixtures containing oxygen and nitrogen, blue phosphorescence with mixtures containing oxygen and sulphur. Pressure conditions. 12. So far as my experiments have gone, the phosphorescence appears in rarified gases between the pressures 0™6 and 0™™-01. It rises in brightness as the pressure is reduced and reaches a maximum at a pressure of about 0™™4, and fades away into invisibility as the pressure is further reduced. These pressures vary within small limits according to the nature of the gaseous mixture. 13. To measure the pressure, the pump has been calibrated in the well known method. The capacity of the pump-bulb is close upon 500 ¢.c.; and the bubble of air in the exit tube, measured at atmospheric pressure (or, at a pressure of one-tenth of the atmospheric pressure when very high exhaustion is to be dealt with), affords means of estimating the pressure of the permanent gases in the vacuum tube connected with the pump. A careful set of experiments on the indications of the gauge has shown within what limits they are trustworthy if certain precautions are attended to, the chief being that sufficient time should be given for the equalization of pressure throughout the tubes and bulb of the pump. Unless the connecting tubes are of large diameter the time required, when the pressure is of the order of 0°:1—0°01, is very great, something like 20 to 30 minutes, and it is consequently probable that if the pump is worked at a rate greater than one stroke in 20—30 minutes, the relative proportions in a mixture of permanent gases will be altered considerably by the inevitable differences in the rates of transpiration of the components. The connecting tubes used in my experiments are about 2 yards long and have an internal diameter of about + inch. 14. Striking effects may be observed if the pressure of the phosphorescent gas be altered whilst the gas is actually phos- phorescing after a bright discharge has been passed. Thus suppose the pressure of the gas is higher than that at which the maximum brightness for the given mixture occurs; then if during phosphorescence the pressure is reduced, a wave of increased brightness passes from the end of the tube near the pump to that remote from it. 1897.] the compression of certain rarified Gases. 299 Pressure-glow, or luminosity accompanying compression. Up to this point the present note deals with phosphorescence excited electrically and I now turn to the observations which suggested the title of the note. 15. The Hagen-Topler pump and tubes were filled with a mixture of gases capable of exhibiting the yellow phosphorescence that I attribute to oxygen with a trace of nitrogen in it. The pressure was reduced below the value for which electrically excited phosphorescence was a maximum for that mixture, namely below o™™-4 or 0™"3. Then the gas in the bulb of the pump itself was compressed in the usual process of pumping, preparatory to its being driven out of the pump. As the compression proceeded, the gas was observed to become luminous throughout that part of the pump-bulb which was not occupied by the rising mercury. Its brightness increased considerably and then gradually faded away. The maximum brightness was enough to enable one to read ordinary small print with ease. The amount of compression necessary for maximum brightness was found to depend upon the initial pressure. 16. After the gas has been compressed and has given out the ‘pressure-glow,’ then if it be allowed to return to its original large volume and low pressure and be again compressed in the pump-bulb, the gas does not glow, unless a certain operation has taken place at low pressure; it consists in (i) lowering the mercury in the pump-bulb enough to open connection between the pump and the tube used for the electrodeless discharge, and (ii) producing an electrical discharge in this tube. 17. It would appear that before compression the gas can be put into a state of combination or grouping, which is stable at the lower pressure; and when compression has raised the pressure to a certain value, the original grouping of atoms or molecules is no longer stable and the gas passes into a new state of grouping with an evolution of energy, part of which would account for the ‘pressure-glow.’ In some way the electrodeless discharge supplies the energy necessary to the formation of the combination which is stable at low pressure. Inasmuch as the mixture of gases, in which pressure-glow occurs, consists of oxygen with only a trace of nitrogen (and possibly some other gases which would _ ordinarily be treated as impurities), it immediately occurs to one that we have to deal with the formation of ozone at the low pressure. It is however not clear what part is played in the phenomena by the impurities, though it seems certain that their presence is of importance, if not essential for the production of the phosphorescence. 300 Mr Newall, On Luminosity attending [Apr. 26, 18. With reference to the amount of compression necessary for maximum brightness in the pressure-glow, a number of experiments were made under varied conditions and the results were found consistent with the idea that the maximum brightness of the compressed gas occurred at a pressure between 0™"’5 and 0™"3, fairly definite for a given mixture of gas. If the initial pressure of the rarified gas in the pump-bulb were small (eg. 0™"-01) the pressure-glow did not begin to take place with any brilliance until such a diminution of volume (e.g. about 20 or 30 fold) had been brought about as would increase the pressure to within the limits above stated. If, on the other hand, the initial pressure was comparatively high (e.g. 0""-1), then a much smaller diminution (two or three fold) of volume was required to produce the afterglow. 19. By regulating the rate at which compression was produced the brightness and duration of the glow could be controlled to a certain extent. The phenomena observed in this connection were all in conformity with the idea that in a given mixture and quantity of gas in the pump-bulb a definite amount of energy was to be got rid of by radiation for a given alteration of pressure, and that the time-integral of the intensity of the pressure-glow was approximately constant. 20. Attempts were made to obtain the pressure-glow without any electrical excitation like that described in § 16. The appa- ratus was left in complete working order one evening, and the next morning (i.e. after an interval of 15 or 16 hours), the rarified gas was compressed, but there was no glow:—that is to say, the energy requisite for the formation of the low-pressure-compound had not passed into the gas. A strong beam of light was passed through the gas, in the hope that this would communicate the requisite energy. But there was no glow. Electrical excitation was applied (as described in § 16), and the pressure-glow was as bright as before. 21. The actual distance between the tube for the electrode- less discharge and the pump-bulb was not more than 18 inches, but the connecting tubes were about 6—7 feet long. Very few electrodeless discharges in the tube were enough to put the gas in the pump-bulb into the state requisite for the production of the pressure-glow. The same gas was used again and again with apparently no uncertainty in the phenomena exhibited. 22. In order to make the conditions more simple, I sur- rounded the pump-bulb itself with a coil of thick wire and attempted to produce the electrodeless discharges in the pump- bulb: but though I have generally found it easier to produce the 1897.] the compression of certain rarified Gases. 301 discharges in large bulbs than in small tubes, I could not get the discharge to pass. The failure was attributed to the fact that the inner walls of the bulb were always wet with strong sulphuric acid, some of which floated on the surface of the mercury. 23. It may be noted here that the mercury in the pump was connected with earth through wires and the gaspipe system. This fact constitutes a difficulty in the way of explaining the pressure-glow as simply a phenomenon of electrical origin in which the compression plays a secondary part. 24. The explanation of the pressure-glow appears to me rather to be in general agreement with the explanation given by Sutherland (Phil. Mag. 1897, Mar.) of anomalies observed by Bohr and Crookes in the compression and rarification of oxygen. According to Sutherland, in the rarification of oxygen a point 1s reached (pressure 0™"-7) when oxygen begins to be converted into ozone, and below the pressure 0™™15 the gas is entirely ozone. Between the pressures 15™" and 0™ 7 the gas obeys Boyle’s Law as oxygen, and below 0™"15 it obeys Boyle’s Law as ozone. Between the pressures 0™™7 and O"™™15 the gas is a mixture of oxygen and ozone. Sutherland is led to the view that in the compression of ozone from the lowest pressures, the ozone begins, when the pressure reaches the value 615, to be knocked to pieces in virtue of the frequency of collision between ozone molecules being the same as that of some natural vibration in the molecule. 25. If Sutherland's views be correct in the case of ozone and oxygen, it is probable that there must follow a generalization of them to cases where mixtures of different gases are concerned. [Since the subject of this note was communicated to the Society, an abstract has appeared of a paper by Prof. Threlfall and Miss Martin (Nature, Vol. 56, p. 288) in which an experiment was made with the object of investigating whether oxygen can form ozone simply by virtue of a reduction of pressure, and the authors come to the conclusion that either no ozone is formed, or if such formation does occur, it is to an extent less than 0°005 per cent. of the volume of the gas employed. The nature of the indicator is not described in the abstract referred to. ] Spectrum of the ‘pressure-glow.’ 26. The spectrum of the gas glowing during compression 1s very marked and consists of a faint continuous spectrum with four conspicuous bright bands coinciding with those which Schuster has described as belonging to the spectrum of the nega- tive glow of oxygen. 302 Mr Newall, On Luminosity attending Compression. [Apr. 26, 27. The contrast of this spectrum with that of the electrically excited phosphorescence (§ 6, 7) is very striking. In one case of the electrical phosphorescence the oxygen bands were seen, under circumstances however which led me to believe that they were really due to compression. The pressure in the tube for the electrodeless discharge was so low that the electrically excited phosphorescence was very faint, but whilst the phosphorescence was still persisting, more gas was let out of the reservoir into the pump and tube. Without any fresh electrical excitation, the phos- phorescence increased in brilliance and the oxygen bands were seen in the spectrum. In no other cases of electrically excited phosphorescence have I seen any but a continuous spectrum. It may be that the difference in the spectra in the two cases will suggest further investigation. I am not able to offer any explanation. It is to be regretted that the investigation of the pressure- glow is made so difficult by the apparent importance of what may be described as impurities. I am not able to recover with any certainty the mixture of gases capable of exhibiting the pressure- glow, and can only say that oxygen with traces of nitrogen and SO, is the mixture I should begin upon, if I wished to recover the conditions that obtained when I made the experiments about two years ago. Possible bearing of the phenomena of pressure-glow on astro- nomucal matters. 28. The origin and mechanism of the luminosity of nebule and the persistence of their general outlines and details are subjects that have occupied the attention of astronomers at various times ; and the idea of necessarily elevated temperature is losing ground. The mere fact that a rarified gas can be got into a state such that compression causes 1t to glow and emit a band spectrum is suggestive. If we admit a slow condensation going on in a gravitating mass of gas, whether it be gathered into globular form or irregularly extended like the nebula in Orion or’ surrounding stars like the Pleiades, then we should be led by the phenomena of the pressure-glow described in this note to conceive of the possible existence of a surface or layer of luminous matter, outside which luminosity would be inappreciable because the pressure was too low, and inside which the pressure was too high for luminosity of the kind considered. The gradual streaming in of rarified gas through the region when the conditions are favourable to the production of pressure-glow would account for the maintenance of the luminosity and the persistence of outline. 1897.] Mr Darwin, Observations on Stomata, ete. 303 Monday, 10 May, 1897, PROFESSOR LIVEING, VICE-PRESIDENT, IN THE CHAIR. The followmg Communications were made to the Society :— (1) Observations on Stomata by a new method. By FRANCIS Darwin, M.A. 16 Our knowledge of the behaviour of stomata is defective principally for want of good methods. The earlier workers simply stripped off the epidermis and examined the stomata microscopi- cally. This plan is obviously untrustworthy and has been replaced by a better method, ze. cutting surface sections. This is less inaccurate but is still open to the objection that it does not give evidence of the condition of the stomata in the uninjured leaf. Where the stomata are large it is possible with a microscope to see whether they are open or shut in the uninjured leaf; this is the method followed by Kohl*. The chief objection to this plan is that it can only be used in certain selected plants, e.g. Trianea, Caltha, and that it is laborious and requires considerable practice. Lastly, there is the method of N. Miiller+, in which the condition of the stomata is estimated by the rate of flow through them of a stream of air. Another set of methods are indirect in character and depend on the fact that in aerial leaves the loss of watery vapour takes place almost entirely by the stomata and not by the cuticle. In a leaf with stomata on the lower surface only, transpiration is all but confined to that surface. Such a leaf placed between two glass plates will bedew the lower but not the upper plate. Various methods have been founded on this basis. Merget{ used paper soaked in mixture of certain salts of palladium and mercury, the paper is applied to the surface of the leaf and becomes black or brown owing to the moisture coming off from the stomatal side. * Botanisches Beiblatt zur Leopoldina, 1895. + Pringsheim’s Jahrbiicher, Vol. v11t. $ Comptes rendus, 1878. 304 Mr Darwin, Observations on Stomata [May 10, In 1894 Stahl* introduced his cobalt method, in which he took advantage of the fact that paper impregnated with cobalt chloride is blue when dry, and becomes pink in damp air. Thus if dry cobalt paper is placed on each surface of a hypostomatal leaf, the paper rapidly changes to pink on the lower side, but remains blue on the upper surface. Whereas when the stomata are shut no such difference is seen. With this method Stahl has made out a number of most interesting facts. It is moreover a method especially applicable to demonstration and lecture purposes, since the effect is rapidly obvious, and clearly visible from a little way off. In the Practical Physiology, 1894, of Mr Acton and myself, I described a rough hygrometer in which the index was the awn of Stipa, and which I used to demonstrate that transpiration is ordinarily stomatal rather than cuticular. The method which I have to describe is like Merget’s and Stahl’s papers, and like my Stipa hygrometer, an indirect one, depending on the yield of watery vapour from the stomata. Two or three years ago I came across a toy consisting of the figure of a man cut out of a thin sheet of horn prepared in such a way as to be extremely hygroscopic. When placed on a damp surface it writhes and twists, curving away from the source of moisture. The toy had lain hidden in an old house for something like 100 years; 1t was made for fortune-telling purposes, the degree of movement on the hand indicating the disposition of the patient. The material was described as Chinese sensitive leaf; it is mentioned in Holtzappfel’s Turning and Mechanical Manipulation, Vol. 1, p. 123, 1846, as made from pressed horn. Similar toys in the form of fishes were described by Maria Edgworth, 1808, and appear to have come from Japan. Figures of women and also of fish, made apparently of gelatine or gold- beaters’ skin, are still sold for fortune-telling. But these are not so good for my purpose as horn sheets. Being unable to obtain any more of my original material I made use of shavings of horn and for a long time despaired of making them sufficiently sensitive. At last a chance observation showed me that the horn shavings are rendered sensitive by heat. The method of using the material is as follows. A strip of horn sheet 8 or 9 mm. long by 3 or 4 wide is fastened by one end to a small block of cork so that the horn lies flat on any surface on which the instrument is placed: the horn bears at its free end a bristle to serve as an index. When it is placed on a damp surface the index instantly rises to an angle of 20° to 50° or even more, whereas it remains flat on a dry surface. * Bot. Zeitung, 1894. 1897. ] by a New Method. 305 A paper-scale being fixed to the cork block serves to read off the movement: when applied to leaves, for instance a hyposto- matal leaf, the reading is zero on the upper side and varies on the other side according to the state of the stomata. It has been hitherto impossible to get any physical measure of what the readings indicate; from a large experience of various leaves it may be said that 50° means an extreme amount of transpiration, 30° fair degree, 10° a small degree. It is sometimes difficult to know how far the readings of the hygroscope can be taken to indicate the state of the stomata. Thus for instance in variegated leaves I get low readings on the white parts, high readings on the green parts. Is this due to partial closure of the stomata or to there being fewer stomata on the white patches, or is it because the absence of chlorophyll diminishes the yield of vapour? If the method fails in cases like this it is nevertheless applicable in broader, less critical issues. For instance, all microscopic observations from the time of Mohl agree that certain leaves close their stomata when they wither. It cannot be doubted therefore that the drop in the hygroscope readings in withering leaves corresponds with closure: the same argument applies to the effect of darkness. By taking readings on the uninjured leaf of Caltha and by looking at the stomata I have convinced myself that there is a rough agreement between the hygroscopic and microscopic methods. But I generally get a low hygroscope reading even when stomata look quite shut. If we may believe that broad differences in hygroscope readings represent differences in the openness of the stomata, we must not assume that where the hygroscope stands at zero there is absolutely no loss of vapour from the leaf. Thus there is no doubt that leaves lose some water by cuticular transpiration, yet the hygroscope always reads at zero on a surface free from stomata. Alsoa leaf whose stomata are apparently shut as indicated by the hygroscope, continues to lose weight by evaporation. Since the movement of the index depends on the difference between the moisture of the air on the two sides of the horn plate it might be supposed that a given surface would give very different readings in damp and dry air. But practically this is not so. I used a porous brick standing in a shallow layer of water; on the brick I placed a sheet of perforated zinc and on this the hygroscope; readings were taken in the dry air of the laboratory, in the less dry succulent house and in the various plant- houses, and I got no very serious differences in the readings. Another source of error is that the horn plate is affected by heat, ze. it curves away from a hot surface. This makes it difficult to experiment on the effect of heat, but otherwise is unimportant. 306 Mr Darwin, Observations on Stomata [May 10, It is impossible to make two instruments identical, so that the readings of one instrument are not strictly comparable with another. The chief use of the hygroscope, and for this it is admirably suited, is to compare the leaves of an experimental plant with those of a control, or to observe sudden or gradual changes of reading on a given leaf. Jif. In a forthcoming paper I shall give a full account of the results which I have obtained. In the present publication I give a brief statement of the facts which may be easily demonstrated with the hygroscope, together with some results which are believed to be new. 1. The hygroscope index remains at zero on the upper surface of a hypostomatal leaf, indicating that there is a low degree of transpiration from that surface. 2. There is active transpiration on the lower surface of a floating leaf (e.g. Nymphaea) when exposed to air. 3. In a terrestrial leaf with stomata on both surfaces, the behaviour of the stomata is different on the two surfaces. Thus the upper stomata are more sensitive to external conditions and are frequently shut when the lower ones are opened. 4, The typical stoma closes (either wholly or partially) in darkness. The process is not a sudden one, the readings of the hygroscope fall gradually to zero. It is difficult to generalise as to the time which closure in darkness or opening in light requires; half-an-hour would represent fairly rapid effect. 5. The natural diurnal course of the stomata can be easily followed by taking readings throughout the day and the behaviour of the stomata thus graphically represented. The rise in the early morning and the fall at night are both rapid, the inter- mediate region of the curve may be either more or less flat, or it may present a continuous rise and fall. 6. A certain degree of closure at night is almost universal in typical terrestrial plants and is generally absent in water-plants and marsh-plants*. Since the hygroscope does not distinguish between partial and complete closure, these results are not neces- sarily at variance with those of Leitgeb f. 7. The nocturnal closure is a periodic phenomenon: this is not so strongly marked as the nyctitropic movements of leaves, since the stomata of a leaf placed in a dark room at night are not found to be open in the morning. * Caltha and Trianea however close at night. + Mittheilungen aus dem Bot. Institut zu Graz, 1886. 1897. ] by a New Method. 307 The existence of periodicity may be best demonstrated by the method employed by Pfeffer in observing the “sleep” of flowers, namely, by seeing that they behave differently to a given change of temperature at different times of day. The case is the same for stomata. In the morning a much longer period of darkness is required to close the stomata than is necessary at night: on the other hand stomata which are closed, open in the light much more easily in the morning than in the late afternoon. 8. The well-known result that the stomata close when a leaf is cut from the plant and allowed to wither is strikingly demonstrable with the hygroscope, the readings sinking gradually to zero. In this way the fact observed by Stahl can be confirmed, namely, that the leaves of marsh and water-plants do not, as a rule, close their stomata on withering. The closure of the stomata produced by watering plants with dilute NaCl solution has also been confirmed *. 9. In some cases the process of withering is strikingly different. In Pointsettia, Tropaeolum, Campanula vidalit and some other plants the closure of the stomata is preceded by well-marked opening—as the following figures will show. hr min _ hygroscope 4.10 =10 12 =10 12:2 leaf cut off 13 =18 14 =15 15. -=22 18, )=20 23.5 | = 15 25 =10 I 12 5a) 0 The result is of some importance as bearing on the question of mechanism. The effect of cutting off the water supply must be to diminish turgescence—and diminished turgescence of the guard cells must mean closure. Therefore the opening of the stomata must be due to the loss of turgor in the other elements of the leaf, especially of the ordinary epidermic cells—the final closure being due to the withering of the guard cells+. This effect is especially well seen in plants with milky juices, eg. Campanula * See Schimper, Indo-Malayische Strand Flora, 1891. + On this subject see Leitgeb, loc, cit, 308 Mr Bateson, Notes on Hybrid Cinerarias. [May 10, vidaliz, Pointsettia. I imagine that the laticiferous vessels supply, . as it were, an efficient system of drainage by which a large quantity of fluid can at once escape, and therefore quickly alter the internal pressure in the tissues. My work also bears on the question of mechanism in another way. It has been assumed, I believe, incorrectly, that light opens the stomata because the assimilation of the guard cells leads to osmotic material being built up; the closure in darkness being due to loss of such osmotic matter. Schellenberg* has sought to uphold this view by placing leaves in air free from CO,, where he finds that the stomata are shut. In none of my experiments did I see any signs of closure being due to absence of CO,. But in any case, another of my results is unfavourable to this view. Many plants reopen their stomata if they are kept continuously in the dark for several days. Whatever is the explanation of this fact it is clearly not due to returgescence of the guard cells owing to assimilation. This fact was first observed by my assistant, Mr Elborn, to whom I am indebted for much valuable help. (2) Notes on hybrid Cinerarias produced by Mr Lynch and Miss Pertz. By W. Bateson, M.A., St John’s College. It is stated by many writers that the garden Cineraria arose as the hybrid offsprmg of several species of Senecio from the Canary Islands. This statement has been questioned by Mr Thiselton Dyer on various grounds. The author exhibited hybrids raised from S. cruentus, S. multiflorus and S. Heritieri (= lanatus) raised in the Cambridge Botanic Gardens by Mr Lynch and Miss Pertz which illustrated the great variability which appears in the offspring of the various crosses. In particular, specimens of Heritieri 2 x cruentus § and of the reciprocal cross were produced, showing excessive variability and proving how greatly the peculiar characters of Heritiert may be obscured in the offspring, even of the first cross. Five specimens of multiflorus ¢ x Heritiert § were exhibited, each of which was quite distinct from the rest. Experiments had entirely confirmed Darwin's ~ observation that Cinerarias are self-sterile in a high degree. They hybridize on the contrary with great readiness. An acci- dental hybrid between Heritiert 2 x garden Cineraria ¥~ and the reciprocal were also shown, the two plants being quite unlike each other, the former being an upright plant of a rather woody habit, resembling poor specimens of the garden Cineraria, while * Bot. Zeitung, 1896. 1897.] Mr MacBride, The Relationship of AMPHIOXUS, etc. 309 the reciprocal (illustrated by two specimens of independent origin) was a struggling plant with large pale flowers having almost a procumbent habit, differing considerably from both its parents. One seedling multiflorus $ x garden Cineraria § had been pro- duced which was almost entirely female, a few anthers only appearing in later inflorescences. These experiments were to be continued, but so far as they had gone they were entirely con- sistent with the view that the Cineraria was a hybrid between several species, cruentus, Heritiert and probably multiflorus being among them. The two first are named by most authorities as probable parents. It was proposed to publish details of the experiments when those of the next year should be completed. Monday, 24 May, 1897. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following were elected Honorary Members of the Society : Major Percy Alexander MacMahon, R.A. Prof. Charles A. Young, Princeton. Prof. Albert A. Michelson, Chicago. Dr Ludwig Boltzmann, Vienna. Prof. Augusto Righi, Bologna. Prof. Dimitri Ivanowitch Mendeleeff, St Petersburg. Sir Archibald Geikie. Prof. Edward Salisbury Dana, New Haven, Conn. Sir John Kirk. H. H. Albert, Reigning Prince of Monaco. Rev. Canon Alfred Merle Norman, Durham. Prof. Wilhelm Pfeffer, Leipzig. The following Communications were made to the Society : (1) The relationship of Amphioxus and Balanoglossus. By EK. W. MacBripg, M.A., St John’s College. In seeking for some light as to the origin of the great Vertebrate phylum, the only safe course is to examine with great care the anatomy and development of the least differentiated forms known to us which show traces of Vertebrate structure. 310 Mr MacBride, The Relationship of [May 24, The simplest animal which is universally recognised as a Vertebrate is Amphioxus, and the study of its anatomy and development has thrown a flood of light on the meaning and origin of many of the organs in the higher Vertebrates. If however we desire to trace the Vertebrates further back than Amphioxus, we find no consensus of opinion as to the direction in which we should prosecute our search. Dohrn supposes that we ought to go in the direction of the marine Annelid worms. This Society has recently had presented to it by a distinguished fellow, an elaborate paper, pleading for the affinity of Vertebrates with the Arthropoda; whilst, as we all know, Bateson’s view, that Balanoglossus is the lowest animal with traces of Vertebrate structure, has been widely accepted here, though it has not met with the same favour in Germany. It must be admitted that Balanoglossus is about as unlike a Vertebrate externally as one can well conceive, and it is difficult to imagine that the dominant Vertebrates should have taken their origin from a mud-inhabiting worm. One of the most prominent features in the organization of the lower Vertebrates is the division of their muscles into segments, a feature which they share with the Annelids, and to which it is hardly possible to compare the division of the body of Balanoglossus in three regions —head, collar and trunk. The main object of this essay is to show that there exists in the Amphioxus larva an analogous division of the body which precedes in order of development the. segmentation of the muscles. In a former paper on this subject, I showed that the ccelom in Amphioxus originated at three distinct points from the alimentary tube. (1) At the dorsal lateral corners a pair of hollow ridges become constricted off from the rest of the gut, and then by the obliteration of their lumen at various points, divided into a series of distinct sacs. These processes go on progressively as the animal grows in length—the ridges continuing to com- municate with the gut behind, long after they have been completely separated from it and divided into segments in front. (2) A pair of pouches grows out of the gut in front of the foregoing and nearer the mid-dorsal line, these give rise to the first pair of muscular segments and to other structures as well. (3) The most anterior portion of the alimentary canal becomes separated off from the rest, and becomes immediately divided into a pair of cavities of which the right becomes large and thin-walled, whereas the left becomes a small thick-walled sac which acquires an opening to the exterior. 1897.] AMPHIOXUS and BALANOGLOSSUS. 311 Now these sacs practically give rise to all that is contained between the skin and gut of Amphioxus with the exception of the notochord and the nervous tube. In the paper referred to I compared (3) to the head ccelom of Balanoglossus, and (2) and (1) to the collar and trunk ccloms respectively of that animal. It is & priori improbable that any form exactly like the ancestor of a living animal has survived to this day. For ew hypothest such a type of structure has been found to be unsuited to the environment and has been modified by the struggle for existence. If, however, whilst some of the ancestors of Vertebrates were undergoing evolution into higher forms under the stress of competition, others betook themselves to situations, like the mud, where they could escape the brunt of the struggle, such animals would preserve the general level of ancestral structure in a more or less degenerate form with special adaptations to a burrowing life, and this we suppose Balanoglossus to have done. In the higher Vertebrates the homologue of the head cavity has been detected in that bilobed head cavity which in the embryos of fish underlies the eyes, and from whose walls the majority of the eye muscles are formed, but the homologue of the collar cavity has not yet been sought for and naturally has not yet been discovered. In my former communication on this subject I alluded toa paper by Lwoff on the development of the germinal layers in Amphioxus. In this paper Lwoff not only maintains that the celom or body cavity does not originate from the alimentary canal, but that the whole mesoderm and the notochord itself originate from an ingrowth of the ectoderm. If this were true any possible comparison of Balanoglossus and Amphioxus would be rendered impossible; it would be a result of the most far- reaching character. It may be remarked that it used formerly in many cases to be asserted that the ectoderm gave rise to the mesoderm where later renewed research has shown that the mesoderm arose from the alimentary tube. I have now further evidence to offer in favour of this view. As I have said, the trunk ccelom becomes divided into separate muscular segments, these later become differentiated into a dorsal muscular and a ventral thin-walled portion; and then the dorsal portions become completely separated from the ventral parts, and simultaneously the latter become fused with one another to form two longitudinal coelomic canals. What I have designated as the collar coelom undergoes also differentiation into a dorsal muscular and a ventral thin-walled portion. The two do not however for a long time become con- stricted off from one another; and even when this occurs the VO, EX. PT. VI, 25 312 Mr MacBride, The Relationship of [May 24, ventral part does not become confluent with the ventral part of the trunk celom. The ventral part of the collar ccelom grows back externally to the trunk ccelom, forming two ventral lateral ridges which reach some little distance behind the last gill-slit which is formed. These ridges, which are traceable as soon as the mouth and first gill-slit have been formed, are really the first rudiments of the atrial folds, which later hang down over and cover the gill-slits. The ccelom contained in these ridges gives rise to the ventral muscle of the atrial cavity. Now in Balanoglossus the hinder end of the collar extends over and covers the first gill-slit, and the suggestion of Bateson that this re- presents the first beginning of the formation of an atrium like that of Amphioxus is borne out by the facts I have just narrated. I have said above that it was difficult to suppose that active Vertebrates were descended from a sluggish worm like Balano- glossus. It is however unnecessary to make such a supposition: when zoologists point to one existing animal as “representing” the ancestor of another, they often use loose and inaccurate language. The evidence that Lwoff brings forward in support of his position is exceedingly feeble. The first shape which the de- veloping egg of Amphioxus assumes is that of a hollow sphere— the so-called blastula: this then becomes converted into the well-known gastrula by the process of invagination, one half being pushed inside the other. Now Lwoff maintains that in the blastula certain cells are distinguished from the rest by their size, and that these alone represent the endoderm of other animals, they are first invaginated, and then the invagination of cells which are really ectoderm succeeds to this. Considering that the invagination is a continuous process which proceeds regularly to its completion, and that when it is completed no difference in the character of the invaginated cells can be detected, it will be seen that this is a most violent and arbitrary interpre- tation of the facts, which could only be entertained if it were shown that in the blastula the endoderm was clearly and sharply defined. I have cut about a hundred of invaginating blastule to examine this point and can meet it with a direct denial. It is true there are certain cells of the blastula distinguished by their larger size from the rest, but these merge gradually into the rest at the sides, and where the process of invagination just shows itself the smallest cells are found. This shows that the size of a cell depends on the rapidity with which division is going on, and as the process of invagination is connected and in fact caused by division and multiplication, it is natural that smaller cells should be found at the edges of the area which is about to be invaginated, 1897.] AMPHIOXUS and BALANOGLOSSUS. 313 As a matter of fact, although these small cells just appear at the spot which will become the dorsal lip of the blastopore, where Lwoff imagines the ectodermal invagination which is to give rise to the notochord to take place, it 1s the other lip which in the later stages exhibits it most clearly. It is true that in those higher Vertebrates in which the process of invagination can be clearly traced, the cells composing the upper wall of the primitive alimentary tube are small compared to those forming the under part of the wall, these being choked with yolk; and great stress is laid by Lwoff on this fact. The obvious and simple explanation is, that the processes of folding, which the dorsal wall has to undergo in order to give rise to the notochord and the mesoderm, would be rendered impossible were the cells composing it to be overcharged with yolk, and hence the yolk is confined to the cells forming the ventral wall of the gut. (2) On the degree of the Eliminant of Two Algebraic Equations. By R. Lacutan, Sc.D., Trinity College. The object of this paper is to show how the degree of the eliminant of two algebraical equations may be determined in a very simple manner by geometrical considerations. So far as I am aware the only method given in the ordinary text-books is that given by Serret,—Cours d’ Algébre supérieure, 4th edit. vol. 1, §§ 278—280, which method is due to Minding. Although not difficult to apply to particular cases, it does not seem to be so simple as that here given. 1. Consider two curves C,,, C, whose equations expressed in homogeneous coordinates are Fm (&, Yy, z)=0, Falt. y,2)=9%. If z be eliminated from these two equations we obtain an equation of degree mn, say Pian (x, y) = 0, which represents the lines connecting the point «=0, y=0 to the mn points of intersection of the curves Cy, Cn. Now of these mn points some will usually be found on the lines a, y, z forming the triangle of reference, and some will 314 Dr Lachlan, On the degree of the [May 24, usually be coincident with the vertices of the triangle. Excluding all these points let us suppose that there are r points of inter- section which do not lie on the lines a, y, z; and let ¢,(#, y)=0 be the equation which represents the line connecting these points to the point «=0, y=0. Then ¢,(#, y)=0 is what is usually called the z-eliminant of the equations Tin (® Y, 2)=9, fa(%s Y, 2) = 0. 2. It is obvious from this method of forming the eliminant of two equations, that, whichever one of the three variables be eliminated from two homogeneous equations, the result is of the same degree. This fact may often be used with advantage. As an example, suppose we require the degree of the eliminant when 2 is eliminated from two equations of the form Um + Uy = 0, Un + dug = 0, where Um, Up, Un, Wq denote functions of #, y of degrees m, p, n, q. Here if X be eliminated the eliminant is UmUg — Untlp = 0, and is of degree equal to the greater of the two numbers m+q or N+ Pp. Hence, if w be eliminated from the two equations the eliminant will contain > in the degree m+q or n+p, whichever is the greater. Similarly, it follows that the discriminant of Um + Mp = 0, will contain » in the degree m+p—1. 3. The degree of the eliminant of any two equations is to be found by arranging the equations in a homogeneous form, intro- ducing if necessary other variables. The equations are then to be considered as representing curves, and the number of points of intersection which lie on the lines forming the triangle of reference has to be determined. The degree of the eliminant is equal to the product of the orders of the curves diminished by the number just determined. 1897.] Eliminant of Two Algebraic Equations. 315 To illustrate the method let us take the example given by Serret. He takes the equations (a, 2) y' + (@, 2)y + (@, 4) y+ (@, 5)y + (#, 5)=0, (x, 8) y° + (a, 6) y+ (@, Ny +(@, 4) y¥* + (@, 3)y + (@, 4) = 0, where (a, 7) denotes an integral expression of the rth degree in «. Introducing z, so as to make these equations homogeneous, we have the equations of two curves, C,, C3; (a, 2). yi + (a, Z)2 y°2 + (&, 2) y+ (&, Z)sy + (a, 2)52 = 0, (a, Z)3 y° + (a, Z)g YZ + (2, Z)y YZ + (2, 2), Y72" + (H, Z)s Yo? + (a, 2),2°=0, where (a, 2), denotes a homogeneous expression of the rth degree. The only common points of the curves C,, Ci; which lie on the lines #, y, 2 coincide with the points s=z=0, and y=z=0. In fact, at the point e=z=0, C, has two branches, given by equating the coefficient of y* to zero, C,, has eight branches, given by equating the coefficient of y° to zero. Hence at this point there are 2 x : points of intersection of the curves. Again, at the point y= z=0, C, has one branch, given by equating the coefficient of * to zero, C; has two branches of the form y +arz=0 and y*a* + 628 =0. Hence at this point there are 4 points of intersection of the curves. Hence the order of the eliminant of the equations =6x13—2x8-—4=58, which agrees with Serret’s result. 4. The following examples are of some importance. Ezx.1. If @ be eliminated from the equations Di We ip +0" by + me ee Gn +0 An, he Af, Lean An En +0 a,+é@ On +6 the degree of the eliminant is n—1. =1, = 1, 316 Dr Lachlan, On the degree of the [May 24, Introducing &, 7 to make the equations homogeneous, we may write them in the form EX; is Ea, + ELn, = Jes —l= ayn + 0 ‘mee Ann +O Q A, &a A, £4; A, €a C= 1¢%1 2X2 pak eee OSPR Oe ant an +6 aan +6 ie C and ©’ are curves of the nth degree, having » common points on the line €=0, viz. ant+O0=0, an+0=0, &e., and (n—1) branches passing through the point »=0=0, and no branch of one curve touches a branch of the other. Hence the order of the eliminant is v—n—-(n—-1P=n-1. This result may also be inferred from § 2, for if & be eliminated, the result is obviously of degree (n—1) with respect to » and @. Ex. 2. The discriminant with respect to @ of the equation Ly L2 Ln G+0' tO Uo vance is of the degree 2 (n — 1). We have to find the degree of the eliminant of =i, Ex, Ex, i Ey st GaGa ad eaenen mm v x. Ln ue ee Uk ae Oe (an+ Of (an+0 "+ G@m+oy while the latter equation represents 2(m—1) lines through the point »=@=0, the degree of the eliminant must be 2 (n—1) (§ 2). Ex, 3. If @ be eliminated from the equations nn a oe § el GOR Gree) Gees a Aja, Ass A pln, GeO Gaon 1 GE Oe ; the degree of the eliminant is np — q (p > q). 1897.] Eliminant of Two Algebraic Equations. 317 This is obvious by eliminating & from Ea, oe. Extn ie (ayn a oye eee (Qn +0)? ‘oles A,a€ Anan at (an + 02 oe (Ann +6)2 ae Ex, 4, If 0 be eliminated from the equations av x 1 V n vs (q+ 0% * @+opt t@ top” Ayr, Ao Paes rail (a,+0)2! (ag 020 1 Can tO” the eliminant is of degree (n—1)p—q(p > q). Introducing & and 7 to make the equations homogeneous, we may write them in the form Ex, NX, NX Pe a he ae a ee = en () (aan + 8)? * (cam + BYP (ann + 8)? A, Ea, Ana, Anni (aan + 8)2* (ay £0)2 °° * Cay + 8 If now we eliminate & we get 1 A, a a Aen (an + 0)? (aan + 0)2 (tan + 02 1 Lo Zn Garren tort terres" If p >q, this result is of the (n —1) p—q degree with respect to » and @. Hence by § 2 the result of eliminating @ from the equations will be of degree (n —1) p —q with respect to & and ». Ex, 5. If « be eliminated from the equations Gyo + oO + +O, Ot. +a =, bya +... + bp ew + bet +... +b, =0; where a,, a,, b,, b,’ contain y in the rth degree, the eliminant is of degree 2mn. Consider the curves Com = Ug oe Up bt yp are +, +g 2 = 0, Can = Vyt™ +... Up A tate 4+ te =0; where w,, uy, Vp, Vy are homogeneous with respect to z and y of degree r, 318 Dr Lachlan, On Algebraic Equations. [May 24, These two curves have the point x=z=0 as a multiple point. In fact Cy, has m branches of the form z?+ kay =0 at this point, and C,, has n branches of a similar form. Hence the pomt #=0, z=0 counts for 2mn points of inter- section of the curves. Hence the degree of the eliminant = 2m x 2n —2mn = 2mn. Ex. 6. The discriminant with respect to # of the equation Qyt™™ +o. ty BOO +. + Oy B+... + ay =, where a,, a, contain y in the rth degree, is of degree 27? with respect to y. The discriminant is the same as the eliminant of the equations Qnayv" +...+(2n-—7) a0" 71+... 4 7ra,a' +... +a, =9, a0" +... trae +... + (2n — 1) aa" +... + 2na) =0. Consider then the curves Cy = 2nmyev"1 +... + (Qn — 1) UI +... + TU, ag +. tu, 241 = 0, Con = UO EU OO os +(2n— 1) ua" 2"—* +... + 2nu2"=0; where wu,, u, are homogeneous with respect to y and z of degree 1. The only common points of C,,_, and Cy, which lie on the lines x, y, 2 coimcide with «=0, z=0. Cy has n—1 branches of the form 2+kxzy=0 passing through z=0, z=0; and C,, has n similar branches passing through the point. Hence the point x=0, z=0 counts for 2n(n—1) points of intersection of the curves. Hence the degree of the eliminant = 2n x (2n — 1) — 2n (n — 1) = 2’ (3) Tides on the Equilibrium Theory. By C. CHREE, Sc.D., King’s College. [Published in Transactions, Vol. XVI. Part 11.] 1897.] Mr Henry, Experiments on Ultra-violet Light, etc. 319 (4) Haperiments on the Effect of Ultra-violet Light on the Conductivity of Iodine Vapour. By J. Henry, Trinity College, Cambridge (1851 Exhibition Science Scholar, Queen’s College, Galway). It is well known that ultra-violet light causes negatively charged bodies on which it falls to lose their charges, but it has not been tried so far as I am aware whether ultra-violet light, like Roéntgen rays, enables a gas through which it passes to conduct electricity ; the following paper is an account of some experiments made to test this point, the gases used being the vapours of Iodine and Amyl Nitrite. These vapours were used because it seemed probable that they would show this effect of light very readily if it existed, since they are sensitive to ultra-violet light in other ways*. The apparatus used in the experiments on iodine vapour con- sisted of an insulated copper disc, connected to a pair of quadrants of an electrometer and supported on a stiff copper wire inside a glass tube, which was closed at one end by a quartz plate, the other end being open. This tube was fixed in a sand bath so that it could be heated to a high temperature, the closed end being at the temperature of the bath ; the diameter of the tube was 3°8 cms., and the length about 20cms. The light was given by a carbon are and brought in a converging beam on the copper disc by a quartz lens (see fig. 1). to electrometer Ere. 1. a is a sand bath. b, a screen to protect insulated wire from hot gases. c, a brass cap holding quartz plate. d, a screen to cut off the scattered light, The copper disc had to be supported on a wire insulated out- side the tube at e, as the iodine always destroyed the insulation of any support inside, apparently by condensing on the insulating substance (discs of mica), even when its temperature was as high * Contributions to Molecular Physics, Memoir X. Tyndall. VOL) Ex. PT: VI 26 320 Mr Henry, Experiments on Effect of Ultra-violet [May 24, as 210° C., which was the temperature inside the tube during the experiments. The iodine was introduced at any time when re- quired in the end of a small glass tube and soon surrounded the dise with vapour, which gradually escaped at the open end of the large tube, but allowed sufficient time,—three or four minutes— for the necessary observations. Although a positively charged body is not discharged directly by ultra-violet light, yet I found that the disc, although positively charged, was discharged by the are-light when the disc was in the tube as shown above, and also that the rate of discharge depended on the distance “a” between the disc and quartz plate. Table I. gives the results of some experiments on this dis- charge, which show that it is due to the discharge of the negative electricity induced on the quartz plate by the positive charge on the disc, this mduced charge becoming very small as “#” in- creases. Column I. gives the distance “a” in cms. , IL. gives the leak per minute in scale divisions for the positive charge. , Il. gives the leak per minute in scale divisions for the negative charge. , LV. gives the total charge in scale divisions. Table I. If; II. III. IV. 0:1 cm. 35 76 110 i Bice, 9°5 76 110 Ds, A fe |) 120 x 3 7 | 10 In trying the effect of the arc-light on the conducting pro- perties of iodine vapour it was necessary to have the distance “a” small, otherwise all the effective light would have been absorbed by the vapour before reaching the disc, as was shown by experiments on the leak of the negative charge with iodine vapour present, so that it was not possible to get rid of the positive leak by increasing the distance of the disc from the end of the tube. 1897.] Light on the Conductiwity of Iodine Vapour. 321 Table II. gives the rates of discharge of the disc for different values of the distance “«,” the smallest being ‘1 cm. in experiment 4; the potential of the charged disc was in each case 12 volts. Column I. gives the sign of the charge on the disc. , IL gives the total charge on the disc in scale divisions. » III. gives the leak per minute due to light when there 1s no 1odine present. , IV. gives the leak per minute due to light when there is 1odine present. By placing a plate of clear glass in the path of the light the leak whether of the positive or of the negative-charge was at once destroyed. We see by these figures that the leak when iodine vapour is present is always much less than when it is absent, and also, as was to be expected, that the negative leak diminished more rapidly with the increase of the distance “2” when the vapour was present than the positive leak did, since in the latter case the light fell on the quartz plate before being sifted of its ultra-violet rays by the vapour; the diminution of the positive leak when the iodine is present seems to show that the vapour not only does not conduct, but even tends to prevent the escape of the negative Table II. | all lf ike IV. SHOVEO| | 50} £ }ogdvel! 58 a} eps d Baan 5 | 2 fe Meee.” | Gl af ve ieee 19 | 6 Mas. P60. | of | Exp. 3 meas) 27 | 15) Siesie ines. | a0p ee | electricity from the quartz plate, this effect may however be due to the absorption in the iodine vapour of the light reflected from the copper disc, back again to the quartz plate, this light in the absence of iodine increasing the discharge from the quartz. Owing to the leak of the positive charge, whether iodine 322 Mr Henry, Experiments on Ultra-violet Light, etc. [May 24. vapour is present or not, these experiments do not prove that there is absolutely no conduction of the charge through the vapour due to the light on it, but they do prove that if this conduction exists at all, it must be very small. In testing amyl nitrite, the vapour was allowed to rise round an insulated copper disc connected to an electrometer as before, - Fie. 2. but when the disc was charged positively, the arc-light caused no discharge whatever, whether the vapour was present or not. In another experiment on amyl nitrite, a beaker containing some of the liquid was placed in coil “a” (fig. 2), and a bulb for giving the electrodeless discharge in coil “b” which was in series with “a,” and the number of turns in the coils adjusted, until a substance of very small conductivity placed in “a” destroyed the discharge in “ b.” This arrangement showed the conductivity produced by the Réntgen rays in the air in coil “a,” yet it gave no indication of conductivity in the vapour of amyl nitrite, when the light from an electric arc placed over the open beaker fell on the vapour. In conclusion, I have to thank Professor J. J. Thomson for his many valuable suggestions in the course of these experiments. PROCEEDINGS OF THE Cambridge Philosophical Society. ANNUAL GENERAL MEETING. Monday, 25 October, 1897. Mr F. DARWIN, PRESIDENT, IN THE CHAIR. The following officers and new members of Council were elected :— President : Mr F. Darwin. Vice-Presidents : Prof. Newton, Prof. J. J. Thomson, Mr Larmor. Treasurer : Mr Glazebrook. Secretaries : Mr Newall, Mr Bateson, Mr Baker. New Members of Council: Mr Harker, Mr Hutchinson, Prof. Liveing, Mr Skinner. The names of the Benefactors were read. The following Communications were made to the Society:— VOL, IX. PT, VII. 27 324 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25, (1) Electrical Oscillations in Wires. By Mr H. C. Pock1ine- TON, St John’s College. 1. In this paper are discussed some problems relating to the propagation of electrical oscillations along wires. The wire is always supposed to be a perfect conductor, and to have a circular cross-section, the diameter of which is small compared with the other dimensions of the ees We have therefore to solve the equations V?(P, Q, R)= yas P, Q, RB), conv. (P, Q, R)=0, with q dt? the further condition that at the surface of the wire the vector (P, Q, &) is perpendicular to the surface. The method of solution used is to start with the simplest solution of the general equations and by adding an infinite number of such solutions together to obtain one of sufficient generality. The arbitrary function which represents the infinite number of arbitrary constants introduced into this last solution is then found from an equation deduced from the surface condition. This last part of the work is con- ducted by means of approximations. 2. The simplest solution of the general equations, that corresponding to the solution ¢=1/r of the equation V’p=0, is given by the formulae* Pil Qe Ail ape ~ dadz’ dydz’ — diz® in which 27r/p is the period of the disturbance, and 27r/a(= 27V/p) the wave-length corresponding in free ether to this period. This result can be expressed in words as follows. The electric force due to an elementary Hertzian oscillation with the element of length ds as axis, is compounded of two forces; the first of these +o7Il, where Il =e'e?*/r, a , and the second is a force o?II parallel to ds. This system of forces satisfies the equa- tions of propagation of electric force everywhere excepting at the element ds. If we place an infinite number of such elements consecutively so as to form a curve, of which ds will then be an elementary arc, and attribute varying strengths X to them, we shall obtain a system of forces which satisfies the equations of propagation everywhere except on the curve. The resulting system of forces is Gh Gh a a sie CEO) = ay ) Jas Fe +o [as (U, m, n) NII. “ Hertz, Wied. Ann. 1889, vol. 36, p. 4; Electrical Waves (tr. Jones), p. 140. is derived from a potential function — 1897.] Mr Pocklington, Electrical Oscillations in Wires. 325 If the curve is either closed or has its extremities at infinity, this is equivalent to Ch 0 5 i NA OLN, 0, hy) = (+ dy’ a) | ae +a? fas(l m, ”) AII...(1). This is a general solution containing an arbitrary function 2. 3. It now remains to consider the equation derived from the surface conditions. At a point at a small distance ¢ from the curve we have, neglecting all terms that are not large, dn dn fast 7 2 Ae loge. e?%, and similarly for fds/XII, etc., so that, to this order of approxima- tion, d dn _- — metry jenees bi oaks 2 upt = 1255 ae Be 2uTh Log el and similarly for Q and R. The component of force along the wire therefore is, to this order, ie ee —2|—— loge. e?*. 2 | ia +a) oge.é The force tangential to the cross-section of the wire =0 to this order. Hence the system of forces given by (1) is a solution of the problem (to this order) provided that ax ds? and the disturbance is propagated along the wire with velocity V and without diminution of amplitude. This is only what might have been expected from a knowledge of what happens in the case of a straight wire; for if in our case we take the electrical forces to be finite near the wire, at a finite distance they are zero. Lon — 0) or t=. 4, It is clear that in order to obtain results of much interest we must approximate more closely. We will now consider the equations obtained by neglecting only small quantities of the first and higher orders. As given by (1) the force at any point on the wire tangential to the axis is the same for all pomts on the same cross-section, and contains two terms, one containing log e, the other finite. The force tangential to the cross-section is finite and varies for a given value of s as the cosine of some azimuth angle. > 326 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25, Suppose now that we shift the curve formed by the Hertzian elements through a small distance of the second order. The effect is to change the value of the component tangential to the cross-section by a finite amount which varies as the cosine of some azimuth angle, and that parallel to the axis of the wire by an amount of the first order of small quantities. By making such a shift of appropriate magnitude and direction at every point, we can therefore eliminate the component tangential to the cross-section. At the same time, the component parallel to the wire is unaltered (to our order). Hence we may still derive the surface condition from (1) by taking the integration along the axis of the wire. The condition thus obtained is = 5 fas> — II +o? {1 fdsINII + m fdsmXII + n fdsnvIl}...(2). 5. Circular Ring. The simplest case that we can consider is that of a circular rmg. Let the radius of the ring be a, the radius of the wire ¢ as before, and let the axis of symmetry be chosen as the axis of z. We shall assume X= A cos rd, where } defines a point on the axis of the wire. This assumption will be justified later. At the point (a, 0, 2) [os a =-rA |" dll sin rd =-rA le do II, (sin cos rd + cos r@ sin r¢) e?", 0 where II, is the value that II takes when ¢ is put for (@ — d) and 0 for ¢, and is thus a function of ¢, a, z only, = — 2rAe”! sin rd | "dT, cos Tr ; 0 2 [asian =— 4 | adglIl cos ¢ cosrd 0 Alas 0s (r+1) 6 {apt cos(r+1)¢ 0 + cos (7 — 1) 6 {apt cos (7 — 1) 6| ; 0 as above; and fdsnrX II = 0. 1897.] Mr Pocklington, Electrical Oscillations in Wires. 327 Hence (2) becomes 0= |- 2rA ress? [" dp Il, cos rd +a°Aa cos 9 |” dp Il, {cos (r + 1) + cos (r — 14 Je ert, or ie do Il, cos rd (1? — aa? cos ) = 0.........08. (3), the disappearance of @ justifying the assumption made as to the form of X. In this equation for finding a we may give to a and z in II, any values which correspond to a point on ee surface of the wire. The simplest values are w=a+e, z=0, and these should therefore be chosen. 6. The special case r=1, which corresponds to the funda- mental node of the wire, is that of the most interest and will be investigated in detail. In this case, (3) becomes on substituting for II, its value (when z=0), gana? — 2a@ cos $+ W? il dd = {cos hb — xa°a? (1 + cos 2g)} = 0, Va? — Qacr cos h + ow or, putting w=A+e, zea? — cos 6 + F°a? cos 2 /2a (a+) (1—cos¢) +e Quaa sin $p Ls ik s we “ie 4 + [a Tne (3a°a? — cos d + $a°a? cos 2h) = 0...(4), where in the second integral ¢ has been put=0, since we are neglecting small quantities. The first integral in (4) is, calling 2aa=a, log "= L, and neglecting small quantities, 1 ne IE The second integral is, putting ¢/2 = W, | "ay oe = : {ea (bcos A) == * cos 2y| = Pay ee = (1+cos 4) — cos ar} + fay COs ee L = (1 + cos 4a) — — * cs apt (3): 328 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25, Now, n being an integer, 2 7 see) = | dip cos 2nrp cos (x~ sin Wr) = Jy, (2), 0 D2 sin (# sinvp) i = JOR OU ee Nee Pay Ete = [ day cos 2ny Shel ; diz I(x) SLOVENIA RU ae: | adie) 0 Therefore the first integral in (5) is CU. (Le iA ous a , at ssi ; eg e+ (2 ") J(o)+(4 1)[ deS()} ; and (4) becomes, on re-arrangement and multiplication by a, be Gin ltr x J (z 2 1) i ats eh) 3 +(2- *) J,(v)+(% 1) {. de JAo)} a eC | ay ee ae =e (1 — 2 cos 2ap + cos 4h) Oe 2, cos(#sin wv) — 1 +(¢-1) i, ty on 2} nO. This equation gives # and thence a with an error of the order of e/a. It can only be solved by trial. If however e¢ is so small that errors of the order of 1/Z? can be neglected, we may use an approximate solution of the above. A first approximation is 2 = 4 or «=2. A second is obtained by putting 2=2 on the right- hand side of (6). This gives (F x 1) L =485 — 70381, so that a= = (1 +(-243 — 3510)/D}. Hence the period of the oscillation is equal to the time re- quired for a free wave to traverse a distance equal to the circum- ference of the circle multiplied by 1 —-243/Z, and the ratio of the amplitudes of consecutive vibrations is 1 : e?*”¥ or 1 : 1—2°21/L. It is easy to verify from first principles that the decrease in amplitude of the vibrations is of this order, 1897.] Mr Pocklington, Electrical Oscillations in Wires. 329 7. Induced Vibrations in a Ring. We will now consider the case of a ring upon which plane waves are incident in a direction parallel to the axis of the ring. Let the coordinate axes be chosen as before, and let the incident vibration be given by Pi Oe eee The tangential force at the point @ due to this wave together with a disturbance induced in the wire of the fundamental mode and magnitude B, is to be equated to zero, giving 7 hts 0 = Ae?* cos 0 — 2 Be? — | d¢ II, cos p (1 — a7a? cos dh). 0 If we neglect e/a in comparison with unity, this becomes, as in § 6, 2B Ee bbe ) 0=A4+— |2-5+(¢-1) Li ur a Fie QZ % i |- = Js(a)+ (2 ma =) DEQ (7 2 1) i dad, @} a (2, cos(asin w)—1 +5] ay ae (1 — 2 cos 2 + cos 4p) + ([- 1) fray ae cos 24, Unless #= 2, this gives so that in general the induced vibration is small, and the thinner the wire the smaller the induced vibration. The phase is the same as or opposite to that of the electric displacement in the plane of the ring due to the incident wave. If, however, e=2=2+4 & where & is small, we may put # =2 in all the terms not involving L, and get Aad ae 2LE +970 —1:055.° The maximum amplitude of the imduced vibration is obtained when 2L£ = ‘970, or a= 2/2a= {1+ °243/L}/a, i.e. when the period of the incident wave is the same as the free period of the ring; the amplitude then is ‘948Aa?, and the phase is in quadrature 330 Mr Pocklington, Electrical Oscillations in Wires. (Oct. 25, with that of the wave. It is noteworthy that the amplitude of the induced vibration is independent of the thickness of the wire. If the incident wave is not proceeding in a direction — perpendicular to the ring, the problem can still be solved by a method similar to the above. The vibrations induced in the ring will however not be confined to the fundamental, but will include vibrations of all modes. 8. Helix. We will now consider the case of vibrations pro- pagated along an infinite wire wound into a uniform helix. Let the equations of the axis of the wire be e=acos ¢, y=asin 9, z=adtanw. We shall assume X= de**, This assumption is justified later. The value of the force tangential to the wire at the point (a, 6, Z) is e'** times that at the pomt (a, 0, z—aé tan @). Hence (2) gives 0= Ae! (as) ete | dpiBe'®? ll, + a? {eos wo | ddacos pe? II, 6=0 —2 -—2 hia sc + sin | doa tan we'®? u1 | 5 where II, is the value that II takes when ¢=0 and ¢ is put for p— 8. Hence 0 = de®? (aa? tan?w — B?+ aa? cos ) II)...(7). In obtaining this equation small quantities only have been neg- lected. If however e/a is very small, we may in this equation neglect all finite quantities in comparison with those of the order of loge/a. In this case we may with advantage find an approximate value of the right-hand side of (7). Assuming « any finite quantity, and neglecting terms that are finite, the right-hand side of (7) is -K Cart tan w y Speen ea aes en Ss 22 + 2 —s 2 242 | age eet {o?a? tan?w — 8? + aa? cos d} aa? sec?w — B? +{" d -K ? 2a (a + €)(1 — cos d) + ag? tan?o + & ag ae eraad tan w e 2a? tan?w — 8? 22 : +f pe Feta ao an’w — 8? + aa? cos d} The second integral is, neglecting finite quantities, cos — 2 (a’a? sec?w — ?) = log e. 1897.) Mr Pocklington, Electrical Oscillations in Wires. 331 The first and last can be reduced to sums of integrals of the 2) gab form | dd oO Phi integral* is — log y to our order, and thus the first and last integrals give 1 22 die Aly OS Dye) Tea ; Baan, oe tan?w — 8) log (aa? tan? w — 8?) + te°a? log {(1+ 8 +aa tan w) (1 —8+aa tan) (1+ 8 —aa tan w) (1 —B—aa tan w)}], and therefore the approximate form of (7) is 2 (aa? sec? w — £?) sin w log e = (4a? tan’ w — 8”) log (aa? tan?w — B?) + 30a? log (1 +8 + aa tan w)(1—8+ aa tan) (1+ 8 —aa tan o) (1 —8 —aa tan w)}...(8). Several cases may occur. (i) In general, if a is not small, the only term of importance is that on the left, so that aa? sec?w — 8? =0, or B=aaseca, and the velocity of propagation measured along the wire is P P_y -aseco === B a. the same result as that obtained in the case of a circle. (i) If however a and 8 are small, the first term on the right is also of importance. If a and 8 are so small that loge can be neglected in comparison with log (aa? tan? w — 8°), i.e. if the pro- duct of the wave-length of the disturbance into the radius of the wire is very large compared with the square of the radius of the helix, we have aa? tan*w — 6?=0, or 8 =aa tan a, and the velocity of propagation measured along the wire is ie, Pp Be sec @ =~ cosecw = V cosec w, a so that the disturbance is propagated with a velocity V measured along the axis of the helix, If a and @ are small, but not so small that loge can be neglected, ie. if the product of the wave-length into the radius of the wire is comparable with the radius of the helix, the velocity of propagation has an intermediate value+. It is easy to see that a like result does not follow if we try to make (a?a? tan?» — 6?) small without making a and 8 small. * J. W. L. Glaisher, Phil. Trans., 1870, p. 369. + Hertz, Wied. Ann. 1889, vol. 36, p. 21; Electrical Waves (tr. Jones), p. 158, has proved experimentally that this is the case. 332 Mr Pocklington, Electrical Oscillations in Wires. [Oct. 25, (iii) If one of the factors, e.g. the last, of the term under the second log sign be small we have, since « and @ cannot then both be small, 2 (a?a? sec?w — 8?) sin w log e= da°a? log (1 — 8 — aa tan @). In this case we must have 8 V, given by (ai). No other cases arise by making a and 8 great, since we must then recur to (7), as (8) does not then hold; and here if a and B are great, we simply have a’a*sec’w — 6? =0, the case considered in (1). (2) On Circles, Spheres and Linear Complexes. By Mr J. H. GRACE. This paper is printed in the Transactions, Vol. xvi. Part 111. (3) Reduction of a certain Multiple Integral. By ARTHUR Buiack. Communicated by Professor M. J. M. Huu, M.A., Se.D., HARES This paper is printed in the Transactions, Vol. Xv1. Part 11. (4) On the Gamma Function. By Mr H. F. Baker. The Gamma Function could be defined for real values of « by the conditions (i) that T(1)=1, (2) that P(w#+1)=aP' (a), (iii) that, for a fixed finite h, as # tends to + 0, the difference IY@+h) I(s) T(a@+h) T(@) tends always to zero. The condition (11) was well known, being deducible from the result I’ («) ay gees orga at and was of suitable character for a definition; it was desirable however to deduce it immediately from the equation T(@)= | oe dt ; 0 this note dealt with such a deduction. 1897.| Mr Baker, On the lines of striction of a hyperboloid. 333 On the lines of striction of a hyperboloid. By Mr H. F. BaKeEr. It was a known fact that the lines of striction of a hyper- boloid formed two unicursal quartic curves. The most commonly given equation shewed that the curve was an octavic curve with six double points; such a curve on a surface of the second order could not be a proper octavic curve; for a cubic surface drawn through the double points and thirteen arbitrary points of the curve would otherwise cut the curve in 12+13=25 points. The question considered was what are the possible forms of such octavic curves. (5) On the Action of Uranium rays on the Condensation of Water Vapour. By C. T. R. Witson, M.A., of Sidney Sussex College, Clerk Maxwell Student. I have already (Proc. Roy. Soc., Vol. 59, p. 338, 1896; Phil. Trans. A. 189, p. 265, 1897) described experiments upon the effect of Rontgen rays on the condensation of water vapour. These experiments proved that the rays, in traversing moist air, in- troduce nuclei capable of acting as centres of condensation when supersaturation exceeding a definite limit is brought about by the sudden expansion of the gas. Nuclei, requiring exactly the same degree of supersaturation to enable condensation to take place upon them, are always present in very small numbers even without the action of the X-rays; but these rays enormously increase their number. To produce the degree of supersaturation necessary to bring these nuclei into play in air originally satu- rated, a sudden expansion is necessary such that v,/v,, the ratio of the final to the initial volume, exceeds 1:25; corresponding approximately to a fourfold supersaturation. In the absence of X-rays and other disturbing influences, no condensation is observed (after the removal of all foreign nuclei) if v,/v, is less than 1:252. If v,/v, lies anywhere between this and 1:37 a rainlike condensation results, the drops being few and scattered. Beyond this second limit dense fogs appear. The action of the X-rays is simply to increase the number of the drops which are formed when 2v,/v, lies between these limits; the minimum expansion required for condensation not being sensibly altered. The experiments described in the present paper show that nuclei of exactly the same nature are produced in moist air under the action of the Uranium radiation discovered by Becquerel. The form of apparatus used is represented in the accompanying figure. 334 Mr Wilson, On the Action of Uranium rays (Oct. 25, The thin-walled glass bulb A, about 5 centims. in diameter, contains the air to be exposed to the action of the rays. The tube, at the end of which the bulb is blown, is about 2°5 centims. in diameter. It has its open end ground perpendicular to the axis, and is wired tightly down in a vertical position against the flat surface of an indiarubber stopper. J Inside this tube there slides freely an inverted thin-walled test-tube P, with the lip removed and the open end ground smooth and perpendicular to the axis. The test-tube serves as a piston. Its open end is always immersed in the water which fills the lower part of the outer tube, in the way indicated in the figure. : By means of the arrangement B (described on p. 268 of the paper in the Phil. Trans. already referred to) the air-space in 1897.] on the Condensation of Water Vapour. 335 the upper part of the test-tube can suddenly be put in communi- cation with the exhausted vessel F. This causes P to fly till it strikes the indiarubber, thus causing a sudden expansion of the air in A. It remains tightly pressed against the surface of the indiarubber as long as the vacuum is maintained below it, thus preventing the lubricating water which surrounds it from escaping. While the piston is in this position, the extent of the next expansion is arranged for, by opening the screw-clip 7, and lowering the mercury reservoir f, till the pressure in A, as indicated by the gauge, is the desired amount below the atmo- spheric pressure. The clip is then closed and air readmitted to the interior of the piston P by opening the tap 7. The piston then rises till the pressure in A only differs from the atmospheric pressure by that required to support the weight of the piston,—a small fraction of a millimetre of mercury and negligible in these experiments. If B be the barometric pressure, then the pressure of the air before expansion is P,=B-rn, where 7 is the maximum vapour pressure at the temperature of experiment. The pressure of the air after expansion, when the temperature has risen to its former value, is P,=P,—p, where p is the reading of the gauge, taken before the previous contraction, as described above. Then the ratio of the final to the initial volume is V, Py B-ar y P, B-r-p Any condensation, in the form of drops, resulting from the expansion was made visible by the light of a luminous gas-flame, brought to a focus inside A by means of a condensing lens. The Uranium salt (the double sulphate of Uranium and potassium) was contained in a thin-walled glass bulb, forming a layer about 1 centim. in depth. The dust-particles originally-present having been removed by repeated expansions, observations were made of the result of a given expansion, with the bulb containing the Uranium salt alternately 2 or 3 millimetres above A (as in the figure) and removed to a distance. ile v/v, = 1-245. Result. No drops seen either with or without the rays. 336 Mr Wilson, On the Action of Uranium rays (Oct. 25, IT. a/v, = 1°260. Result. A dense shower was always seen when the expansion was made with the air in A exposed to the rays; only a few drops appearing when the Uranium salt was removed. III. Vo], = 1273. Result. Slight shower without the rays, a very dense shower under the action of the rays. IV. w/v, = 1-286. Result. The same as in III. The showers were not appre- ciably denser than in IIT. More exact measurements were now made of the minimum expansion at which the drops first begin to appear under the action of the rays. The experimental numbers are given in the following table. Pressures are all given in millimetres of mercury. Barometer = 769, ae — lib 7 = vapour-pressure = 13, P,=pressure of the air before expansion = B-7=169 — 13 =756. Gauge Pressure after | | reading, expansion, IPI), =|, Result P P,=P,—p 149 607 PONS i) 00 153 603 1-254 shower 149 607 1-245 | 0 151 605 1:249 shower Thus the minimum value of v,/v, required to bring about condensation under the influence of Uranium rays lies between 1:245 and 1:249. This agrees very closely with the value 1-252, found with very different apparatus for air under ordinary con- ditions (Phil. Trans. loc. cit.). 1897.] on the condensation of Water Vapour. 337 The Uranium salt shows a strong effect on the condensation, even when the thin glass vessel containing it is completely wrapped in tinfoil during the experiment and for many hours previously; showing both that this material is transparent to the agent which influences the condensation, and that the Uranium salt continues to be active when kept in the dark. There can be little doubt therefore that the effects on the con- densation are really due to the radiation studied by Becquerel. The nuclei introduced by the action of the Uranium rays, like those formed under the influence of the X-rays, persist for some seconds after the radiation has been cut off; for a comparatively dense shower can be obtained, by expansions of suitable amount, five or ten seconds after the removal of the tube containing the Uranium salt. If, however, an interval of one minute be allowed to elapse after cutting off the radiation, the drops produced on expansion are not appreciably more numerous than they would be, were the air not exposed to the radiation at all. The nuclei produced in moist air by Uranium rays appear, from the experiments described above, to be identical with those formed under the action of Réntgen rays, as well as with those always present in very small numbers in the moist gas. They require the air, originally saturated, to suffer sudden expansion such that v,/v, exceeds 1:25 in order that condensation may take place upon them; the density of the vapour at the moment when the expansion is completed being then approximately four times that of vapour in equilibrium over a flat surface of water at the same temperature (v. Phil. Trans. loc. cit.). The electrical properties of gases under the action of Réntgen and Uranium rays point to the presence of free ions. It is natural to identify with these the nuclei made manifest in the gas under the same conditions by the condensation phenomena described in this and previous papers. As early as 1887 R. v. Helmholtz (Wied. Ann., vol. 32, p. 1) and later the same author and Richarz (Wied. Ann., vol. 40, p. 161, 1890) accounted for the effect of electrification and chemical action in bringing about dense con- densation in a steam-jet by supposing free atoms or ions: to be produced by these processes. Prof. J. J. Thomson (Phil. Mag., vol. 36, p. 313, 1893) has explained how we should expect free ions, in virtue of the charge they carry, to have such an effect in helping condensation. Richarz has more recently (Wied. Ann., vol. 59, p. 592, 1896) found that a steam-jet reacts also with Roéntgen rays, and again explains the phenomenon by the hypo- thesis of free ions. The great advantage of expansion experiments over those made upon steam-jets is that we are able in the former to dis- tinguish between various kinds of nuclei, by means of the different 338 Mr Wilson, On the Action of Uraniwm rays, etc. [Oct. 25, degrees of supersaturation necessary to make condensation take place upon them. Whatever view may be held as to the nature of the nuclei introduced by X-rays and Uranium rays, they are shown in this way to be identical with one another, as well as with those existing in very small numbers in ordinary moist, dust- free air. Monday, 8 November, 1897. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following Communications were made to the Society:— (1) On Farmer's method of demonstrating assimilation. By Francis Darwin, F.R.S., President of the Society. The method here given is merely a simplification of the in- . teresting experiment described by Farmer in the Annals of Botany’. He there pointed out that the protoplasmic circulation ceases in an Elodea leaf kept in the dark, in a current of hydrogen: and that the circulation recommences if the preparation 1s illu- minated. The cessation of the movement is due to the absorption of the free oxygen, its reappearance to the oxygen produced by | the assimilatory activity of the chloroplasts. Farmer’s positive results should in any case I think outweigh Pringsheim’s? failure to observe a revival of circulation in illuminated specimens of Chara &c., and the results which I have obtained fully confirm Farmer's conclusions. My object in modifying Farmer’s method was to place an experiment of great educational value within the reach of those who possess no apparatus beyond a microscope. This can be done by mounting an Llodea leaf* in water and sealing the preparation by careful rmging it with melted “ wax-mixture.”* The prepara- tion is then placed in the dark, and the observer waits until the available oxygen has been absorbed and the circulation has come to rest, which takes place in from 3 to 6 hours. 1 Vol. x. p. 284. 2 Sitzb. k. Preuss. Akad. 1887. See also Vines’ interesting discussion Annals of Botany, Vol. 1. p. 371. 3 For reasons given below it is better to mount two or even three leaves under a single cover-glass. 4 Resin 15 parts, vaseline 50 parts, beeswax 35 parts. 1897.] Mr Darwin, On Farmer’s method, etc. eae It is easy to show that the cessation of circulation is due to want of oxygen by lifting the cover-glass with a needle and adding a drop of fresh water, when the protoplasm will begin to stream in a few minutes. The same result can—as in Farmer’s experi- ment—be produced by illumination. The length of the period of illumination required to start the movement varies : in a prepara- tion darkened for about 3 hours, in which the circulation has only recently come to a stand-still two or three minutes’ exposure to incandescent gas light will revive the movement in two or three minutes. When the period of darkness has lasted over 6 hours it may require 20—30 minutes... This clearly depends on partial inhibition! of the assimilatory powers of the chloro- plasts. If the period of darkness is still further prolonged it is easy to reach a condition in which it is apparently impossible to revive the circulation ; but my experiments not being especially directed to this point I cannot say what might be the effect of very prolonged illumination. It is to avoid the inhibition of assimilation that I mount several leaves under one cover-glass, so that the dissolved oxygen may be exhausted before the chloro- plasts fall into this condition. The method here described seems to me likely to be of value to teachers in putting an interesting experiment within the power of all. And it is worth noting that Farmer’s experiment has all the educational value of Engelmann’s bacterial method. For it demonstrates: (1) The evolution of oxygen by green. plants in the light. (2) The connection between movement and respira- tion and the fact that a chlorophyllous cell makes use for purposes of respiration of the oxygen evolved within itself. (3) It demonstrates in a rough way (what Boussingault showed to be true for aerial plants) that assimilation can begin in the absence of free oxygen. (4) It also demonstrates the inhibition of the assimilating function produced by prolonged darkness. For this last-named purpose it must be shown by the addition of oxygenated water that the failure to circulate does not depend on any loss of power in the protoplasm. The method also serves well to demonstrate the effect of light of different wave-lengths on assimilation. As a source of light I use incandescent gas, separated from the microscope by a glass trough through which cold water flows. For the different lights I use Landolt’s screen solutions? in flat-sided glass vessels. In this way the maximum effect in the red 718—639 wy can easily be shown. The circulation, as far as I have seen, does not begin in green? light unless the experiment is made after not more 1 See Ewart in Journal Linn. Soc. Vol. xxxt. 2 Berichte D. Chem. Ges. 1894, Vol. 27 (3), p. 2872. 3 The light is 540—505 up, @.e. it shows a narrow strip of blue. VOL, EX, PT, VIL 28 340 Mr Darwin, On Farmer's method, ete. [Nov. 8, than 2 or 3 hours of darkness, 7.e. when the assimilative function is not seriously inhibited. It should be possible to demonstrate a second maximum in the blue!, but I am here considering the question simply from the point of view of laboratory teaching, and in this connection I think it best to confine the demonstration to a comparison of red and green light. (2) Artificial Cultures of Stereum, a Timber-destroying Fungus. By Prof. MarsaaLL WARD. (3) On Encephalartos Ghellincki, ‘Lem., a rare Cycad. By A. C. SewarD, M.A., St John’s College. The subject of this note is one of the less known species of the African Cycadean genus Encephalartos. In 1895? I called attention to the unusual form of the fronds of Encephalartos Ghellinckia, Lem., and figured a small piece of a leaf from a specimen in the British Museum herbarium. A plant in the Royal Gardens, Kew, bearing a single frond, first attracted my attention to the species. The large and stout fronds of such species as Mncephalartos horridus, Lehm., E. Caffer, Mig., HX. Lehmanni, Lehm., £. Alten- steinit, Lehm., and others with broad and occasionally spinous pinnae represent the type of plant which is usually regarded as characteristic of the genus. Encephalartos cycadzfolius*?, Lehm. (= E. Frederici-Gualtelmt) forms a connecting link between species with narrower pinnae and H. Ghellinckw. The first account of H. Ghellincku was published by Lemaire‘ in 1867, the description being founded on a plant in the nurseries of Verschaffelt, by whom the Cycad was obtained from the central region of South Africa. The following is Lemaire’s diagnosis of the species :— “Caudex ut in praecedente (2.e. Hncephalartos villosus, Lem.). Frondes 5—12 erectae et illae ut praecedentis dispositae, totae gossypinae metrales et ultra (quas vidi solum in prima aetate frondationis sese evolventes; rhachi cylindrica serius siccata sub- plana) foliolis approximatissime oppositis v. rarius alternis omnino ob arctissimam marginum revolutionem lineari-filiformibus apice mucrone robusto aculeiformi pungentissimo terminatis, marginibus integris acus recte simulantibus. Coni ¥ et 2 nobis hucusque ignoti.” 1 Using a screen of ammoniacal copper sulphate which lets through a good deal of green as well as the blue end of the spectrum. 2 “The Wealden Flora”’ (Catalogue of the Mesozoic plants in the British Museum), vol. 11. 1895, p. 22, Pl. 111. fig. 3. 3 ibid. Pl. m1. fig. 6. 4 Lemaire, C., “L’illustration horticole,” Journal spécial des serres et des jardins, vol, x1v. 1867, p. 80. 341 Bisa res gears L Y 7, Vy Mr Seward, On Encephalartos Ghellinckuy, etc, 1897.] Nat. Size. 1 iat ARTOS GHELLINCKII, LEM. ENCEPHAL 2 28 4 i : ? SS aes preteen ee stem teens rem avrnsiw, 1897.] Mr Seward, On Encephalartos Ghellinckii, etc. 343 Lemaire describes both H. villosus and EF. Ghellinckii, and speaks of the two species as quite distinct from the other members of the genus. The two woodcuts and the coloured plate which accompany the above diagnosis convey an imperfect idea of the appearance of the latter species’. The plant reproduced in the Plate? was obtained by Mr Lynch, of the Cambridge Botanic Gardens, from Messrs Sander and Co., of St Albans, who received it from the interior of the Province of Natal. When sent to Cambridge the stem shewed no sign of life _ and bore traces of having been considerably charred, probably in a forest fire. After lying for some months in an apparently dead condition a fine crown of leaves was produced, and the accom- panying photograph was taken before all the fronds had attained their full development. The stem measures about 28 cm. in height and 70 cm. in circumference, and is covered with the characteristic armour-like investment of persistent and corky leaf- bases. The leaves are a little over 90 cm. in length, and in those which are not fully expanded the slender apices are bent over at the tip, and the linear-filiform pinnae are crowded together like the barbs of a goose-quill. The rachis of the mature frond bears two rows of opposite or alternate pinnae, about 11 cm. in length and 2 mm. broad, which are attached laterally to the leaf axis. - Both the rachis and pinnae present a woolly or tomentose appear- ance, especially in the young condition. The pinnae terminate in an acute spinous apex, and the margins are strongly revolute ; four parallel veins traverse each pinnae, but these are hardly visible in a surface-view. As shewn in the plate, the two rows of pinnae form a fairly wide angle with one another, and are not extended in one plane. In some of the fronds the rachis is slightly twisted in a spiral, as in Macrozamia spiralis, Maiq. The general appearance of Encephalartos (hellinckw suggests a distinctly xerophytic habit, and this is borne out by the thick cuticle and sunken stomata of the pinnae. The rachis is traversed by numerous vascular bundles of the typical mesarch form, characteristic of the petioles and peduncles’ of recent Cycads. Each bundle is surrounded by a more or less complete ring of large thick-walled fibres; the parenchymatous ground-tissue contains several large mucilage canals and the hypoderm consists of strands of fibrous elements alternating with parenchyma. The anatomical characters agree with those of other Cycads, and especially with other species of Hncephalartos. A transverse section near the tip of a rachis bears a striking 1 Lemaire, loc. cit., vol. xv. 1868, Pl. 567. 2 The photograph reproduced in the plate was taken for me by Mr Hayles of the Cavendish Laboratory. 3 vide Scott, D. H., Annals of Botany, vol. x1. 1897, p. 399. 344 Mr Seward, On Encephalartos Ghellinckii, etc. [Nov. 8, resemblance, in the scattered collateral bundles and large canals, to the fossil petioles known as Myeloxylon. ‘The hypoderm in the younger portion of a rachis consists in part of collenchyma, which afterwards developes into uniformly thickened fibrous tissue. The following points may be briefly noticed in the anatomy of the pinnae. In tranverse section a pinna has the form of a somewhat flattened crescent, the two edges bemg bent over towards the under surface. The upper surface is covered by a thick cuticle, and the epidermis is succeeded by two or three layers of thick-walled fibres, and internal to these there is exceed- ingly well-marked palisade tissue of one layer of long cells; internal to this the mesophyll consists of spongy parenchyma followed by one or two rows of fibres and the lower epidermis. There are numerous stomata on the lower surface, the two guard- cells being situated at the bottom of a fairly deep depression. The mesophyll is traversed by four collateral bundles surrounded by a ring of fibrous elements. The woolly appearance of the young fronds is due to the occurrence of numerous long unicellular hairs borne on a short and thick-walled stalk-cell as in Dzivon edule, Lind., and other Cycads1. The importance of such a species as Encephalartos Ghellinckia in connection with fossil Cycads has previously been discussed. The necessity of examining as many recent species as possible, especially the less known and rarer forms, cannot be too strongly urged. ‘There are several fossil fronds in which the rachis bears numerous long and narrow pinnae, which may well be compared with Encephalartos Ghellincku. Some of the Mesozoic fronds, which have been erroneously referred to the genus Cycadites?, bear a very close resemblance to those African Cycads with the narrow linear or linear-filiform segments. 1 My thanks are due to Mr A. W. Hill, of King’s College, for preparing several sections of the frond of Encephalartos Ghellinckii and other species. * For references to fossil fronds vide Wealden Flora, vol. 11. pp. 36 et seq. 1897.] Mr Townsend, Electrical Properties of Gases. 345 Monday, 22 November, 1897. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following communications were made to the Society :— Q) Partial Differential Equations of the Second Order. By Professor ForsyTH. This paper is printed in the Transactions, Vol. xvi. Part 11. (2) Electrical Properties of Newly Prepared Gases. By JOHN S. TowNnsEND, M.A., Cavendish Laboratory, Cambridge. (1) The experiments which are described in this paper form a continuation to those which have already been published in the Proceedings of the Cambridge Philosophical Society, Vol. 1x. Pt. v. It was there shown that the gases given off by the electrolysis of sulphuric acid or caustic potash carry with them an electric charge, a large percentage of which remains in the gas after it has been bubbled through a liquid, and passed through glass wool to remove the spray. Another property of these gases is their power of con- densing moisture to form a cloud. No such cloud could be observed in newly prepared gases unless they were charged, and further the weight of the cloud was found to be proportional to the charge on the gas. These results go to show that the condensation of the moisture is connected with the charge, and the experiments described in section 16 of the above paper, and in section 19 of this paper prove that when the cloud is formed in a charged gas the electrification resides on the drops forming the cloud. So that we have definite proof of the fact that the drops are formed round the carriers of the electric charge. (2) These results were used to find the charge on each carrier, and it was found to coincide with what we can calculate as being the atomic charge, on the supposition that at ordinary temperature and pressure there are 10” molecules in each cubic centimetre of a gas. The experiments giving the weight of the cloud corre- sponding to the charge being of importance, were repeated by the following method which gave the same proportionalities in the different gases between the charge per c.c. and weight of cloud per c.c., as were previously obtained. (3) The apparatus which was used is shown in figure 1. The positively charged oxygen and hydrogen given off from a dilute 346 Mr Townsend, Electrical Properties of [Nov. 22, sulphuric acid cell were first bubbled through a solution of potas- sium iodide in the small flask A and then through distilled water Fie. 1. Insulators are drawn with dotted lines and conductors with continuous lines. in B. Both A and B were immersed in a trough of water C so that they should remain at a fixed temperature while an experi- ment was being conducted. The charged gas thus formed a cloud and carried it along the delivery tube B, which led into the paraffin block P inside a large metallic screen S. The block P was arranged as shown in the figure in order that the moisture should not break down the insulation by settling on the paraffin. By this means the moist gas. entered the larger tube 7’ connected to three sulphuric acid bulbs F set up between the two paraffin tunnels P and Q. After the gas had bubbled through the acid it was not only cleared of the moisture, which under ordinary conditions it would have carried from B, but the cloud was also completely removed. The increase of weight in the bulbs thus arises from two causes, and when the weight of the moisture necessary to saturate the volume of the gas which passes through F is subtracted from the total, the weight of the cloud is obtained. The gas on leaving F entered one of the insulated inductors, the smaller one G being used for oxygen, and the larger one J for hydrogen. The inductor and the bulbs were both covered with tinfoil and connected to mercury cups in the paraffin block R, so 1897.] Newly Prepared Gases. 347 that either of them could be readily connected to the insulated quadrants of the eloctrometer. The experiments were conducted in the following manner. The sulphuric acid bulbs were carefully weighed and then con- nected by indiarubber tubing to the glass tubes which were imbedded in the paraffin blocks as shown in the figure. The current through the cell was switched on for a few minutes before joining the bulbs into the series, so as to drive the air out of A and B. As soon as the gas began to bubble through the acid in F a stop watch was started. By connecting the conductors F and G alternately to the quadrants of the electrometer the rate at which each was acquiring a charge was found. The sum of the charges acquired by #’ and G denotes the total charge passing out of B and that acquired by F# divided by the total is the dis- charging power of the bulbs. After the stream of gas from the cell had been running through the apparatus for a sufficient time the bulbs were removed, and dry air was drawn through them before weighing them a second time. In each experiment a current of 14 amperes was used which was kept constant by having an ammeter and an adjustable resistance in the circuit. In order to reduce the readings on the electrometer scale to absolute units it was found that when F was connected to the quadrants and the other conductors to earth, each scale division represented ‘0040 electrostatic units of quantity, and when G was connected to the quadrants the scale divisions each represented 0036 electrostatic units. The inductor J which was used with hydrogen had a larger capacity than either of the other two con- ductors, and when it was connected to the quadrants it required ‘0042 electrostatic units to make the spot of light on the electro- meter scale move through a division. The following tables give the results of the experiments which were made with the different gases, @ is the temperature in degrees centigrade of the water in B, W the increase in the weight of the sulphuric acid bulbs, and n, and n, the numbers of divisions that the spot of light on the electrometer scale moves per minute when F' and G [or J] are connected to the insulated quadrants ; w is the calculated weight of the moisture necessary to saturate the volume of gas uv at temperature @ which passes through Ff’ in the course of the experiment, ~ the weight of the cloud per c.c., v and p the charge per c.c. on the gas. The volume 2 is easily cal- culated as the gas is evolved by a known current. Table I. gives the results obtained with positive oxygen. In each experiment a current of 14 amperes was used, and the stream of the evolved gas passed through # for 20 minutes. 348 Mr Townsend, Electrical Properties of — [Nov. 22, Table II. gives similar results for positively charged hydrogen. Table III. refers to negatively charged oxygen from a caustic — potash cell, the stream of gas being passed through F for 15 minutes in each experiment. The experiments were performed with widely different densities of electrification p, in order to find how the weight of the cloud varied with the electrification. The ratio of the weight of the Dwein given in the last column for ‘cloud to the electrification each experiment. The variations in p were obtained by varying the temperature of the cell from which the gas was given off. Both in the case of a sulphuric acid electrolyte and a caustic potash electrolyte the charge on the gas which is evolved by a given current increases as the temperature of the electrolyte is raised. TABLE I. + Oxygen from H.SO, electrolyte. W-w v p pv l 22 31 | -0270 || 0050 | 22:3 x 10 §| 4:04 x 1077/55 x 10 1 13 20°, | :OTS87 1/0050 | T4511 1052 | 2-53) 1052-4 te 13 21 30 =| -0330 || 0118 | 20-8 x 107§|3°8 x 10°?|5:5x 10% 14 9 19 | :0240 || 0125 |11°5 x 10-°| 2:05 x 1073] 5°6 x 10°? TABLE II. + Hydrogen from H.SO, electrolyte. W-w W—-—w 2 oy) Pp pu O | 21:5 28-5 -0264 | 0092 | 8:8 105°) 2:1 x 105°) 4-25 alee Oo |) ae 34 | -0296 || 0092 | 10-5 x 10-°| 2:57 x 10°*| 4:1 x 10% 15 32 | 37 | 0486 || 0264 | 10°8 x 1075) 2°8 x10) 3-8x 10° | 15-3] 26 31 | -0445 ||-0271 | 85x 10°°|2:2 x10°%)39x 10% 1897.] Newly Prepared Gases. 349 Taste IIL. —Ozygen from KOH electrolyte. W-w W-w v P pv 0 15 266. | -OL8S8.)-0085. | 21x 105% |3°1 x 10-*| 6:8x 10% O | 22 32 | -0217 | 0035 | 25x 10-° | 4-1 x 107*/ 6-1 x 10-° 12 14°5| 24-5] -0230 || 0081 | 20x 10-6 | 2°86 x 10°*| 7:0 x 10° 11:5] 12:5] 22:5}-0206 | -0078 | 17x 10-* | 2-51 x 10-3| 6-8 x 10-8 (4) The numbers given in the tables show that in each case the weight of the cloud is proportional to the charge, and that this proportionality does not vary with the temperature of the water from which the cloud is formed, at least within the limits of 0° and 14°C. The ratio is not so exact in the case of the negative oxygen as it is for the other gases. The only chemical difference that was detected was that the former were slightly acid and the latter alkaline in their reactions. Since the vapour rising from hot caustic potash does not change red litmus to blue, the alkalinity of the gas must be due to small particles of caustic potash which are carried with the gas from the electrolyte and give it an alkaline reaction even after bubbling through sulphuric acid, this could easily be detected at all temperatures of the cell by letting the oxygen or hydrogen pass along a tube with red litmus. The oxygen given off by the electrolysis of caustic potash has no appreciable charge till the temperature of the cell is up to about 20° C. and the cloud begins to appear at the same time as the charge on the gas, so that the presence of the alkaline spray can have only a very small effect as no cloud is observed in the oxygen coming from the cell at a temperature 10° C. although the presence of the spray of caustic potash can be easily detected. (5) The following simple experiments show how intimately connected the charge on the gas is with the formation of the cloud. The apparatus used is shown in figure 2. The oxygen given off by a current of ten amperes from a caustic potash cell of specific gravity 1:3 was bubbled through a solution of potassium iodide in the flash A to remove any traces of ozone. Before entering the inductor J the gas bubbled through water in B. The inductor I was insulated and connected to the quadrants of the electrometer so that the charge on the gas that entered it could be read off on 350 Mr Townsend, Electrical Properties of [Nov. 22, the electrometer scale. The gas was not passed through any glass wool before entering J so that as much spray as possible should be carried from the cell. tee Fic. 2. The cell was at a low temperature, 11° to start with, and a current of 10 amperes was switched on which gradually warmed the electrolyte. During the first nine minutes that the current was on and the gas entering the inductor, no electrification what- soever was detected, and no cloud could be observed over the water in B. During these nine minutes the temperature of the cell © rose from 11° to 18°. During the next five minutes a deflection of 9 divisions negative was obtained and the temperature of the cell had risen to 21°5. At a temperature between 22 and 23 a thin cloud began to appear over the water in B and the spot of light was then moving at the rate of 4 divisions per minute, so that before the cloud becomes distinctly visible a small electrification of about 2 x 10 Electrostatic units per cc. is necessary. When the current is continued and the cell becomes hotter the electrification on the gas increases and the cloud becomes denser. (6) In order to show that the cloud disappears when the charge on the gas is removed the temperature of the cell was raised to 48° and, with the same apparatus as was used for the last experiment, the three following results were obtained. (a) When the gas passes from the cell to the inductor with- out filtering through glass wool a dense cloud was observed over 1897.] Newly Prepared Gases. 351 the water in A, and a deflection of 29 divisions negative per minute was obtained as the gas entered J. (b) The tube connecting A and B was removed and a tube containing glass wool was substituted. With the same current through the cell a slight cloud was seen over the water in B and the deflection was reduced to 6 divisions per minute. The elec- trification of the gas was thus reduced to 1 of its original value by passing through 15 centimetres of glass wool. The amount of spray carried through this length of wool must have been ex- tremely small but the cloud was distinctly visible. (c) The tube containing the glass wool was heated with a Bunsen burner, and its discharging power was considerably inereased as the spot of light then gave only 2 divisions per minute and no cloud was observed over the water in B. It is thus evident that the formation of the cloud and the presence of the charge are phenomena which accompany one another. (7) The clouds which are formed are slightly different in appearance and for equal electrifications those formed in oxygen are whiter than those formed in hydrogen. A difference is also to be noticed in the positive and negative oxygen clouds, that formed in the latter being the whiter. This would point to the fact that the drops formed in the negative oxygen are larger than those in the positive, and that those formed in either positive or negative oxygen are larger than those in the hydrogen. A fairly approximate value for the radius of the drop may be obtained by observing the rate at which the cloud falls in a vessel. The velocity of the drop through the gas was obtained by taking two photographs of the cloud allowing some minutes to elapse between the two exposures. Figure 3 represents two such photographs taken of the cloud formed by bubbling the charged oxygen from a sulphuric acid electrolyte through water. Three minutes were allowed to elapse between the two exposures, and the scale shows that in that time the cloud had fallen between 9 and 10 milli- metres. Similar experiments were made with the other gases, but in the case of the hydrogen the outline of the cloud never became so distinct as it did in the oxygen. The sizes of the drops were obtained from the formula paV = 47a'g (Lamb, Motion of Fluids, p. 229). This gives. for the radius of the drop in the positive oxygen 68 x 10~, the rate of fall being 10 millimetres in 3 minutes, and the radius of the drop in negative oxygen 7-9 x 10-* the rate of fall being 18 millimetres in 4 minutes, 352 Mr Townsend, Electrical Properties of — [Nov. 22, We thus know the weight of each drop and dividing this into the weight of the corresponding cloud, we obtain the number of drops per cubic centimetre. Fic. 3. When the number of drops is divided into the charge per cubic centimetre the charge on each is obtained. The charge on the positive carrier was thus found to be 2-4 x 10”, and that on the negative carrier to be 2°9 x 10™°. When we take into account all the experimental errors these two charges may be considered equal and approximately 3 x 10~". The charge on the hydrogen was found to be between one-third and two- thirds of this value but could not be arrived at very accurately owing to the difficulty of finding the size of the drop. For present purposes this charge will be taken as 3 x 107. 5 Velocity of the carrier when acted on by an electric force. (8) It has been shown that the radius of the drop forming the cloud is in the case of negatively charged oxygen 810~, so that its weight is 210~" grammes and when acted on by gravity, it moves at the rate of 18 millimetres in four minutes. The force acting on the drop is practically 210~°, so that it would require 210° 3x 10" velocity, or 2000 volts per centimetre. As we are only dealing an electric force of absolute units to produce an equal 1897.] Newly Prepared Gases. 353 with small electromotive forces it is evident that we may disregard the effect of mutual repulsion of the carriers when the gas is carrying a cloud. When the gas is bubbled through sulphuric acid the radius of the carrier is so much reduced, that the effect of the mutual repulsion of the particles carrying the charge is easily detected. (9) The following is a general method of investigating the motion of a gas in a vessel of any shape, the initial distribution being uniform. Let p be the density of electrification in any part of the gas, uv, v and w the velocities of the carriers along the axes of x, y and z. ; : ONE ERE) a! RPA ATs The equation of continuity is ; hanes es dy oe =0, the notation being the same as that used in Lamb, Motion of Fluids. Let ¢ be the electric potential; — a — ek and — Ste , are the da dy dz forces which act on the charged carriers, and their velocities w, v, and w, are given by the equations :— dg | dg | ‘4 (1) Kua ea: Ei — ae Kw=— e—* where e is the charge on the carrier and « is a constant to be determined experimentally. Substituting these values for w, v, and w, in the equation of continuity and we obtain :— ele = V2 = V2 ae. 54 é 1) 0, but ti) = Aap, therefore = St = — 4rre. Integrating and we obtain :— Po (2) Pp Ee ees eee 5 ies — where p, is the initial density, which is uniform throughout the space considered. Equation (2) shows that the motion takes place in such a way that the density p is a function of the time only and does not vary from point to point in the gas, on this account no variation in the pressure of the charged gas takes place and the terms = : = f BO4 © Mr Townsend, Electrical Properties of — (Nov. 22, and z : ing with the motion of gases, can be omitted in equations (1) since p does not vary from point to point. which have in general to be taken account of when deal- When the gas is in a closed vessel the mutual repulsion of the carriers of the electricity drives them to the sides where they either remain so close to the walls that they cannot be blown out, or else get discharged against the sides. The charged gas remaining in the vessel has a uniform density given by equation (2), and if the vessel which contains it is an insulated conductor connected to a pair of quadrants of an electrometer the deflection on the electrometer scale will be proportional to p when the charged gas is blown out of the vessel. (10) In order to investigate experimentally the rate at which the gas loses its charge to the sides of an inductor, or in other words to find how the density p will vary with the time, a metal Fic. 4. cylinder C, figure 4, 30°2 centimetres long and 1°6 centimetres in diameter, was used. The two ends of the cylinder fitted into paraffin blocks P, and P;, into which were also fixed the glass 1897.] Newly Prepared Gases. 355 tubes 7, and 7. The tube 7;, through which the cylinder was filled, had several layers of fine copper gauze across the broad end, which tended to distribute the gas evenly across the section. The whole apparatus was contained inside a screen S, the ends A and B of the tubes leading to the cylinder projecting outside the screen ; by this means the charged gas could be blown out of the cylinder, without stirring any apparatus or tubes inside S; so that the deflection on the electrometer scale, when C' is connected to the insulated quadrants, was solely due to the removal of the charge inside C. Any effect of gravity, on the motion of the carriers towards the sides of the tube, was prevented by placing it in a vertical position. (11) The gases that were examined were the oxygen and hydrogen given off by electrolysis of dilute sulphuric acid. The cell was raised to a temperature about 20° above the room, at which it could easily be kept by running the current. By means of an ammeter and variable resistance in the circuit the current could be kept constant. A method is thus provided of filling the cylinder several times with a gas having a constant electrification per c.c. When filling the cylinder with the hydrogen it is best to lead the gas in at the top, and when using oxygen at the bottom, in order that the air may be driven out in as short a time as possible, as it is not desirable to run the current for more than five minutes at a time, when a number of experiments have to be performed requiring the same electrification in each case. The gases were first bubbled through potassium iodide; and then through strong sulphuric acid, so that they should enter the tube D perfectly dry. The cylinder and tubing connected with it were thoroughly dried by heating them with a Bunsen burner and then blowing dry air through. This precaution is absolutely necessary as it only requires a very slight amount of moisture to form a cloud, and this would impede the motion of the carriers. (12) A series of experiments of the following type were then performed: The cylinder was connected to a pair of quadrants of the electrometer, which were kept to earth while the cylinder was being filled and insulated before blowing out the gas, so as to get the readings on the same part of the scale. The tube A was closed, and D connected to the delivery tube of the sulphuric acid wash-bottle, and a current of 14 ampéres sent through the cell. It only required the current to run for about five minutes to com- pletely fill C with the charged gas. The circuit was then broken and the tube B closed. At the same time a stop-watch was started. After the lapse of ¢ minutes the ends A and B are opened, and dry unelectrified air blown through C' to expel the VOL Lx, Pl Vill 29 356 Mr Townsend, Electrical Properties of — [Nov. 22, charged gas; this caused the spot of light on the electrometer scale to move n divisions, which is proportional to p the density of the electrification after the gas has remained in the cylinder for a time f. The numbers thus obtained for n and ¢ are given in Tables I. and II., the first being for charged hydrogen and the second for charged oxygen. nN t Selena a n t 32 0 mie AQ ~ 0 25:5 1 37:5 2 20:5 2 TABLE I. TABLE ik 29-5 4 175 3 24-5 6 15:5 4 22, 8 14 5 It will be seen that these numbers are nearly exactly the same as those given by the formula Dare if we put nm = 32 and 6 =-0043 in the case of the hydrogen, and n,=49 and @='00255 in the case of oxygen. The numbers calculated from this formula are given in the two following tables: n t SSS n t 32 0 Pohl be 49 0 25-4 1 37°5 2 21-1 2 TABLE IIT. TABLE LV. 30-3 4 18 3 25-5 6 15-7 4 Dy) 8 14 5 1897.] Newly Prepared Gases. 357 This shows that p=... Hence we have from equation (2)§ 9 ioe a), 4d Amr pve Dae (13) The velocity of the charged carrier when acted on by an electric force can be found from the above numbers. The electro- meter having been standardized, it was found that ‘0037 electro- _ static units of quantity would give a deflection of one division on the scale, so that we get 32 x 0037 ns pee poe 8K B02 Le in the hydrogen experiments, and 49 x ‘0037 = po ax xBODT in the oxygen experiments. Let «z and e;, denote the values of « and e for hydrogen and Ko and é, similar values for oxygen, and we get eile =°0043, where p, = 2°10-%, AT and apm 00255, where p)=3'10~. Ko Hence S56 atl als cane oopseneneeh (1). H 0 From the equation «V = Fe, which is similar to the equations (1) § (9), V being the velocity due to an electromotive force F, we obtain for the motion of the charged carrier in hydrogen F V= BG? and for the motion of the charged carrier in oxygen F = 5° Hence under an electromotive force of 1 volt per centimetre, : 1 ; the hydrogen carrier travels at the rate of 300 x56 centimetres 29—2 358 Mr Townsend, Electrical Properties of [Nov. 22, : é 1 1 2 per second, and the oxygen carrier at the rate of 300 * IB centi- metres per second. The conclusions arrived at from the above investigations are based on the assumption that in each case we are dealing with a gas containing carriers all charged with the same sign, either positive or negative. Experiments on conductivity have been carried out in order to test this point, and it has been found that we are in reality dealing with mixtures. Thus in the case of oxygen, or hydrogen, from a sulphuric acid cell having a positive charge equal to 8e, it is possible to obtain from the gas a positive charge of 4e and a negative charge of e. If we suppose the positive and negative to act independently the charge on the oxygen carrier would be 510-” instead of 310; also the velocities under a volt per centimetre would be smaller in the ratio of 3:4 than those given above. We can arrive at an approximate value to the size of the carrier if we assume that the viscosity of a gas effects the motion of a small sphere and a large one according to the same law 6rpaV = P. (Lamb, loc. cit.). Substituting 1 Vane NO for hydrogen, and igs HOt aceon ee = — = TS S= 1 712 300 2) aa we get the radius (a) for the hydrogen carrier 45107. Similar substitutions give the radius of the oxygen carrier 121077. Hence the carriers are large compared with molecular dimensions. JP The velocities obtained for the carriers in the conductivity due to Réntgen rays are far greater than the above. Thus for oxygen and hydrogen Mr Rutherford obtains velocities of 5:2, and 1°4 centims. per second under a volt per centimetre. [Phil. Mag., Nov. 1897. ] If we assume that the charges on the carriers are of the same order as those obtained in § 7 we see that the dimensions of the carrier are smaller than those with which we are here dealing. 1897. ] Newly Prepared Gases. 359 The discharging power of tubes. (14) It has been shown that, if the gas with a uniform charge po per c.c. be left in a tube for a time ¢, the density of the electri- fication falls to a uniform value p, given by the equation where a is a constant. Now if we suppose that the velocity of a gas as it passes along a tube be perfectly uniform and that no dis- charging takes place due to accidental circumstances, the values of t, p, and p,, would be connected by the same equation, where now t denotes the time that any portion of the gas takes to traverse the tube, p, and p being the densities of electrification on entering and escaping from the tube. When the gas is given off by a current through an electrolyte, the volume g which enters the tube per second is known when the : a é current is known; so that ¢=— where V is the volume of the tube, and the above equation becomes Po— Pp _ %p.V p q The values of p, and p are easily found and satisfy this equation roughly, so that a can be determined; its value however is greater than = found already. This is due to accidental discharging, as it can be shown that, even when the carrier is so large that the small E.M.F. driving it to the side of the tube could have no appreciable effect, still a measurable discharge takes place. (See § 21.) (15) If the gas be run into an insulated inductor after traversing the tube, var is the ratio of the charge gained per minute by the tube to the charge gained per minute by the in- ductor. These charges can be easily found by connecting the tube and inductor alternately to the insulated quadrants of an electro- meter. The tube C insulated in the manner described in § 10 was used in these experiments, the gas examined being the hydrogen given off by a current of 14 amperes from a dilute sulphuric acid electrolyte. The following deflections n, and n, were obtained, n, being the deflection per minute when the tube is connected to the 360 Mr Townsend, Electrical Properties of — [Nov. 22, insulated quadrants, and n, the deflection per minute when the inductor is connected to the insulated quadrants. fi |) Lene 9:5| 36 The relative value of n, and n, in absolute units of quantity was 12: 13°5, so that Po—p _ 12m on BSE We thus obtain the following numbers showing the connection Po P between and pp, so that PoP is (within 5 per cent.) pro- portional to the densities of the electrification. Po=P ose p ee PPo 30 He Meee 1510) Joel AO Oss) alo (16) Similar values were obtained for p)—p and p for the oxygen given off from the same electrolyte by a current of 14 amperes. A different method was used in this case, which did not require an inductor. When the tube C (experiment § 10) was being filled with a charged gas, which enters with an electrification p, and escapes with an electrification p, the quantity p, — p can be obtained by observing the rate (m, per minute) at which the spot of light moved on the electrometer scale, when the tube is full of the charged gas, and the stream kept running through it. The mean density of electrification in the tube is practically pe ; and was obtained by blowing out the charged gas, and observing the deflection », which is proportional to ore x V, where V is 1897.] Newly Prepared Gases. 361 the volume of the tube. The following values of n, pad MN, Were obtained : The rate q at which the gas is supplied to the tube is ‘85 c.c. per second: so that (p,—p) x 51 is the charge given to the tube per Aaa as the gas passes through it, and is proportional to ,, and Pot 2 Px Vis proportional to n,, where V, the volume of the tube, is 60°4 cubic centimetres. Thus we get the following values for ?°—? and Pu: (17) The ratio PoP was also found to increase when the current through the electrolyte diminished, thus showing that the ratio depended upon the rate at which the gas is supplied to the tube. Another tube of equal length and 1:12 centimetres in diameter was examined by similar methods, and it was found to have a far less discharging power than the larger tube; so that, when the supply g and density p, are given, the smaller the bore of the tubing that is used to convey the gas from one vessel to another, the less will be the loss of the charge. The above results showing the dependence of cai on p, are important as we see from the formula Eee ames opal P K q that the increase in the charge due to heating the cell arises from an increase in the number of carriers with the same charge, and 362 Mr Townsend, Electrical Properties of — [Nov. 22, not from an increase of the charge on the carriers already present ; for, if the increase in density were due to an increase in p, we would have found ?° : P to be proportional to the square of py. (18) It would be almost impossible to arrange to pass the gas along a tube in such a way that the discharging power would be as small as the theoretical value, calculated from the numbers given for «, section 13. Small differences in temperature between the gas and the sides of the tube, and other effects which would give rise to currents in the gas, considerably increase the dis- charging power, but have a comparatively small effect on the loss of charge when the gas is allowed to stand in the tube. The velocity of the carrier towards the sides of the tube, due to an electromotive force, will on this account be too large when calcu- lated from the formula 2°? = ie : pol p eer Thus, when we substitute the values given in §§ 10, 11 for Po and Po, We obtain for K the values: Keo. IK = NS 5 Oa: Causes which influence the discharging power. (19) Inthe above experiments the gases were always treated in the same way before entering the tube C, being bubbled first through a solution of potassium iodide and then through strong sulphuric acid. When the gases are bubbled through water instead of sul- phuric acid they will enter C carrying with them a cloud, the effect of gravity upon which makes itself very apparent by com- paring the charges acquired per minute by the tube, when in the vertical and horizontal positions. Thus in the case of a stream of highly charged hydrogen, which bubbled through water before entering C, it was found that the charge acquired was 14 scale divisions per minute as the gas passed through C’ in the vertical position; and 47 divisions per minute with C in the horizontal position. The electric capacity of the conductor, consisting of C and the quadrants, was vot altered by more than 3 per cent. by turning the tube round; so that the large increase in the dis- charging power must have been caused nearly entirely by the force of gravity acting on the drops forming the cloud. The experiment shows that the charge resides on the drops forming the cloud. 1897.] Newly Prepared Gases. 363 A similar result was obtained in the case of charged oxygen carrying a cloud; the corresponding numbers of divisions of the _ scale being 4 and 20, showed that five times the charge is removed by the tube when it is turned from the vertical to the horizontal position. Rough values for the size of the drop might be deduced from these numbers; but the variations in density per c.c. (due to the cloud) are so great, that it would be impossible to arrive at satisfactory values, especially in the case of hydrogen, where the weight of the cloud can be as great as 4th of the weight of the gas in the same volume. (20) Even when the gas has been bubbled through sulphuric acid before entering C,a slight effect of this kind is still to be found. Thus, when the tube is turned from a vertical to a horizontal position, the charge acquired by it per minute increases from 16 to 19 divisions of the electrometer scale per minute. If the coefficient of viscosity can, even roughly, be applied as in section 13 to determine the size of the carrier, the effect of gravity could not exert on a carrier a force that would cause it to move through the gas surrounding it, with a velocity of the same order as z4, centimetres per second. In fact, if we take the density of the carrier to be unity, its radius should be as big as 3107, in Uae that the force of gravity should make it move with a velocity zap Centims. per second. But if, instead of considering a single carrier, we consider the case of a finite quantity of gas (occupying unit volume say), as differimg from the surrounding gas by ‘05 per cent. in density, which could arise from various causes, a vertical motion far greater than the above would ensue, which would affect the discharging power of a horizontal tube. The gases can be sent through a tube containing phosphorous pentoxide, after bubbling through sulphuric acid, so as to remove all traces of moisture; and if the powder is placed loosely in a horizontal tube, about 8 centims. long with glass wool at the end to prevent dust being carried along, not more than half the charge on the gas will be lost. The hydrogen when dried in this manner loses more of its charge, in passing along the vertical tube C, than if it had been dried by sulphuric acid alone; but the loss of charge was not found to be increased by turning the tube from the vertical to the horizontal position. (21) The discharging power of a tube in a vertical position is, as we should expect, greatly diminished by having the gas moist, as the electric force is then too small to have any appreciable effect in causing the drops to move towards the sides. 364 Mr Townsend, Electrical Properties of [Nov. 22, Thus, in an experiment similar to that explained in section 15, the hydrogen, instead of being bubbled through sulphuric acid before entering C; was bubbled through water, and it was found that when C acquired a charge of 14 per minute the inductor acquired 75 per minute, whereas if a similarly charged dry gas were used, C’ would have acquired a charge at the rate of 28 per minute, and the inductor at the rate of 62. The same property holds in the case of charged oxygen. Thus when the gas carries a cloud only 4 divisions per minute were acquired by C, whereas a similarly charged dry gas would have given 7 divisions per minute. The loss of charge of the clouded gas in passing through a vertical tube is due to the unevenness in the motion and the accidental contact of the cloud with the sides. Diffusion. (22) Experiments were performed on the diffusion of charged gases in order to find out whether any of the charge can pass ~ Fic. 5. through porous earthenware. The apparatus which was used in these experiments is shown in figure 5. It consists of two 1897.] Newly Prepared Cases. 365 cylinders, the outer Q was of tin, and the inner P was a porous porcelain vessel fixed by means of corks (C) to the tin cylinder. The porous vessel had one aperture which was fitted with an indiarubber stopper carrying two tubes projecting through the sides of Q@ at D, and D,. The tube Z was broken, and fitted with a paraffin tunnel for purposes of insulation, and the tube U dipped into a sulphuric acid bottle and so acted as a manometer. The outer cylinder had two apertures at H and F, the tube R from # led into a large insulated inductor, and the tube from F was connected through a paraffin tunnel to the delivery tube of a sulphuric acid bottle. e Before performing an experiment it is necessary to thoroughly dry the whole apparatus, this was done by blowing dry air through T and F. The charged hydrogen from a sulphuric acid electrolyte was dried and allowed to enter the cylinder P through 7. The bellows is connected to the tube S and a gentle current of air is blown into the cylinder through F. The cylinder Q is connected to earth, and the inductor into which R leads is con- nected to the insulated quadrants of the electrometer. By this means the hydrogen which diffuses through P is carried with the air current along the tube R into the inductor. The sulphuric acid in U during the course of the experiment rose in the tube showing that the hydrogen diffused as quickly as the tube 7 supplied it. Only a very small fraction of the original charge was found to be on the gas after diffusion as the deflection per minute, as the diffused gas enters 7, was found to be less than 2°/, of the deflec- tion obtained by allowing the gas to enter J directly. (23) Having seen that the hydrogen in diffusing carries with it no appreciable charge it is interesting to know whether the electricity is carried to the sides and gets caught in the pores of the porcelain or whether the carriers remain distributed through- out their original volume surrounded by the air which diffuses in to take the place of the hydrogen. In order to test this the whole apparatus was insulated and experiments were conducted as follows :— The outside cylinder Q was connected to the insulated quad- rants of the electrometer, and the hydrogen from the cell after bubbling through strong sulphuric acid was admitted into P by means of the tube 7. The draught of air between P and Q was maintained in order to make the diffusion as rapid as possible, no inductor was used so that the hydrogen after diffusion was carried 366 Mr Townsend, Electrical Properties of — [Nov. 22, into the atmosphere of the room through #. As the charged gas entered P, the conducting cylinder @ being connected to the quadrant, the deflection on the electrometer scale registers the total charge that enters P. When a sufficient charge had entered P, the tube 7 was closed and the sulphuric acid in the manometer U rose rapidly and showed a maximum difference of pressure between the atmosphere inside and outside P of about 3 centimetres of acid. As the blowing into # was continued the sulphuric acid in U began to fall gradually and in a few minutes the difference of pressure was reduced to one or two millimetres, which showed that practically all the hydrogen had diffused out. The question was then decided by observing what charge could be blown out of P by blowing through 7, and it was found | that a large fraction of the original charge could be thus removed from inside P. The charge which is thus blown out does not represent quite all the electricity left in the atmosphere in P after the hydrogen had diffused out as about 10 per cent. got discharged in bubbling through the sulphuric acid before escaping through v. The numbers obtained in three experiments which were per- formed in the above manner are given in the following table :— n, 1s the charge (in divisions of the scale) put into P, ¢, the time in minutes required to admit the charge, h, the maximum height in centimetres that the sulphuric acid rises in U after the tube 7 is closed, ¢, the time that elapsed while the manometer fell from h, to h,, and n, the charge that was blown out of P. Ny ty h, hy ty No 210 i 3 30 IL Ag 6 130 200 3 3°2 2 4) 125 132 5 30 2 4 98 The current through the electrolyte was in each case 14 amperes. In the last experiment the charge on the gas was reduced by passing it through a tube of phosphorus pentoxide before it enters 7’. We thus see that the carriers of the electricity in the charged hydrogen can with ease be transferred to an atmosphere of any 1897.] Newly Prepared Gases. 367 other gas by diffusion. Also, by continuing the stream of hy- drogen into P, the density of the charge in P increases, so that diffusion not only affords a method of removing the charge from a gas, but also gives us a means of increasing the electrification per unit volume. Experiments with hydrochloric acid. (24) When gases are given off by electrolysis both the quantity and sign of the electricity which they carry are affected by various causes. These changes which the charge undergoes are well illustrated by a series of experiments which were performed with a 20°/, solution of hydrochloric acid. The form of the apparatus used to generate hydrogen and chlorine by electrolysis from hydrochloric acid is shown in figure 6. It consists of two glass bulbs, joined together, from each of which project two tubes S,, 7; and S,, 7,. The tubes S, and S, acted as delivery tubes for the gases, which collected in the spaces immediately underneath them. The electrodes, 4, and #,, consisted of carbon sticks which fitted into the tubes 7; and 7; indiarubber tubing projecting over the ends of 7 and 7, prevented the apparatus from leaking when the bulbs were filled with a liquid. The carbon sticks had a thin layer of copper deposited on the ends A, so as to make good contact with the mercury in the cups C,, C,. These cups acted as terminals to which the leads, from the cells supplying the current, could be joined. The current through the electrolyte was given by an ammeter in the circuit, and was easily adjusted to any required value by means of a variable resistance. 368 Mr Townsend, Electrical Properties of — [Nov. 22, (25) The electric state of the gases was examined by leading them into an insulated inductor, connected to one pair of quad- rants of an electrometer. The other pair of quadrants, the case of the electrometer, and the screen inside which the inductor was placed, were connected to earth. The hydrogen was bubbled through a strong solution of caustic potash and the chlorine through water, before entering the inductor. (26) The charge carried by the hydrogen evolved from a hydrochloric acid electrolyte varies in a very peculiar manner. When new carbon electrodes are used and the current turned on, the electrometer shows that the gas, at first, has a positive charge, but although the current is kept constant, this charge diminishes gradually and after some minutes becomes negative, 1t soon reaches its maximum negative value and the charge then remains constant, except for a small variation due to temperature. When the electrolyte is cooled, and the same current again sent through the acid, the hydrogen begins to come off with a negative charge. (27) The chlorine, which has been evolved from the positive electrode, will be seen to have dissolved’in the acid not only round the positive electrode, but also round the negative, before the change of sign is observed in the hydrogen. If now this acid be removed from G, and the electrodes well washed, and a fresh quantity of acid used, it will be found that the electrometer will indicate charges on the hydrogen, exactly similar to those at first observed except that the positive charges are not so large. After washing the electrodes a second time, and experiment- ing again with a fresh quantity of acid, the same effect will be observed without any further diminution in the positive charges. The number of divisions of the scale obtained in an experi- ment of this kind are :— Ist minute 14 divisions positive, [en 29 1 1 9 bb) 3rd is 5 * after a few minutes the hydrogen came off with a negative charge, corresponding to 5 divisions per minute. The current through the electrolyte bemg 10 amperes, and the value of divisions on the electrometer scale in absolute units of quantity, being obtained by multiplying them by -003. bP) When the chlorine was similarly examined it was found to have a small negative charge, corresponding to 4 divisions of the 1897. ] Newly Prepared Gases. 369 electrometer scale per minute. It did not vary in sign like the charge on the hydrogen. (28) It is probable that the remarkable change of sign that occurs in the charge carried by the hydrogen is due more to the absorption of chlorine gas by the carbon electrode, than to the presence of chlorine gas in the electrolyte; for if the platinum electrodes were used the hydrogen was given off with a large positive charge and did not change when the chlorine got dissolved in the electrolyte. It is improbable that the effect is due merely to the change from platinum to carbon, as there was no corresponding change when similar experiments were performed with sulphuric acid ; the positive charge on the hydrogen evolved being large whether platinum or carbon terminals were used and no change occurred by running the current for half an hour, except a gradual increase in the charge which can be shown to be due to a rise in tempera- ture. It was also found that the charge on the hydrogen was increased by using a new carbon electrode, instead of that used with the hydrochloric acid. (29) In the case of direct electrolysis where no secondary action takes place, or other chemical effects at the electrode, con- siderations of polarization would lead us to expect that gases would come off carrying with them a charge of the same sign, as that which they carry in the electrolyte. Thus in the case of polarization due to a layer of hydrogen with a positive charge surrounding the electrode it is conceivable that, when the evolu- tion of hydrogen takes place, some of the gas composing this layer would come off without losing its charge. (30) In seeking to explain the changes of sign that occur, as in the case of the hydrogen evolved from hydrochloric acid, it must be remembered that, once the gas has acquired a charge, only a small quantity of electricity is lost by bubbling through liquids, so that causes which influence the sign of the charge should most naturally be sought for at the place where the gas is being evolved, and may be due to the state of the electrode or to impurities in the electrolyte in the immediate vicinity of the electrode. (31) There are some well known phenomena which point to an explanation of the results obtained with hydrochloric acid, namely: the electrification of gases by glowing metals*. The typical effects of this kind are, the positive electrification of * J. J. Thomson, Phil. Mag., Dec. 1896. 370 Mr Townsend, Electrical Properties of [Nov. 22, oxygen when a metal is being oxidized, and the negative electrifi- cation of hydrogen when blown past a hot oxidized metal; the metal in the former case uniting more readily with the negative oxygen atoms, and the oxygen in the latter uniting more readily with the positive hydrogen atoms. The only necessity for the high temperature of the metal is to break up some of the molecules of the gas into atoms, but in the cases we are dealing with the gases, at the electrode, are already in the atomic state. We should therefore expect somewhat similar effects to take place when the gases which are evolved can form chemical compounds with the electrode, or with bodies either dissolved in it, or in its immediate vicinity. (32) If the above principles are applied to the case of hydro- chloric acid we should expect, when the gases are evolved by electrolysis, that the hydrogen would carry a positive charge, and the chlorine a negative charge. The subsequent change from positive to negative, in the case of the hydrogen, can be explained by supposing a small quantity of hydrochloric acid to be formed at the negative electrode, due to the action of the nascent hydrogen on the chlorine, and that the positive hydrogen atom is more active in forming a compound with chlorine than the nega- tive. A similar explanation would apply to the change which occurs from negative to positive in the charge carried by the chlorine when platinum is used instead of carbon for an electrode, since a chloride of platinum is formed. (33) The charged hydrogen given off from a platinum elec- trode, in the electrolysis of hydrochloric acid, has the same property of forming a cloud when bubbled through water as the highly charged gases obtained by other methods. The chlorine - however has only a small charge, and moreover contains a quantity of hydrochloric acid vapour which would be difficult to remove, without making the charge too small to form a visible cloud. The hydrogen was treated in the following manner, in order to get rid of the acid vapour which would form a cloud when bubbled through water. The delivery tube from the cell was connected to the tube 7, which dipped into a strong solution of caustic potash contained in a flask H,, and the gas then passed along a tube containing glass wool soaked in caustic potash before it bubbled through the water in a flask H,. The hydrogen which was evolved from the platinum electrode, after passing through this apparatus, was led into an insulated inductor connected to the electrometer and, with 10 ampéres through the electrolyte, the spot of light on the electrometer scale was deflected 37 divisions per minute, and with 14 ampéres, 62 divisions per minute, the 1897.] Newly Prepared Gases. 371 temperature of the cell being 36°. In both cases a dense cloud was observed above the water in H,. In order to test the efficiency of the apparatus, for removing the acid vapour, and at the same time to show that newly pre- pared hydrogen does not form a visible cloud unless it has a considerable charge, the gas evolved from the carbon electrode was led into H,. It was found that the electrometer was giving only 3 divisions per minute and no cloud could be seen over the surface of the water in H,, although the temperature of the cell, and current through it, were the same, as when 37 divisions per minute were obtained by using a platinum electrode. In weighing experiments were performed in order to find the ratio of the weight of the cloud to the charge, but it could easily be seen that the cloud was less dense than that which would be formed in similarly electrified gas evolved from a sulphuric acid electrolyte. In addition to the above experiments, the effect of Rontgen rays in discharging the gas has been examined. It is hoped that the results of this investigation, and the experiments on con- ductivity alluded to in section 13, will be ready for publication in the near future. In conclusion I desire to express my thanks to Professor Thomson for the valuable assistance his suggestions have afforded. (3) Ona chemical effect produced by the impact of kathode rays. By Professor J. J. THoMSoN and Mr S. SKINNER. Aluminium is rapidly evaporated from the kathode by an electric discharge in a highly exhausted vacuum tube in which air has been replaced by mercury vapour. ‘he metal is con- densed over the walls of the tube in the form of a bright mirror. An iron kathode gives a similar mirror in a mercury vapour discharge tube. When the aluminium coating is dissolved off the wall of the bulb by hydrochloric acid a gelatinous membrane remains which gives the reactions of silica, and the escaping hydrogen has an unpleasant odour from the small quantity of silicon hydride which it contains. The iron mirror dissolves completely in hydrochloric acid. From these observations it appears that aluminium driven off from a kathode by an electric discharge acts on the glass, forming a silicide, which on solution in hydrochloric acid yields aluminium chloride, gelatinous silica and some silicon hydride. When potassium vapour is used in the place of mercury the glass opposite the aluminium kathode is roughened. In parts sheltered by screens from the discharge the glass is not attacked. VOUAEX. PT. VII, 30 372 Prof. Thomson & Mr Skinner, On chemical effect, etc. [Nov. 22, In potassium vapour the aluminium kathode is not evaporated to any marked degree. In this case the action on the glass may be attributed to the potassium which under the action of the discharge attacks the glass forming soluble potassium silicate ; so when the bulb is washed out with water and dried a frosted surface is left. Opposite the kathode both in the mercury vapour and po- tassium vapour bulbs a dark annular stain of the shape of the kathode is formed. This stain resists the action of strong hot hydrochloric acid, nitric acid, aqua regia and potash solution. The action of hydrofluoric acid removes it apparently by dissolving the glass. These tests indicate carbon rather than silicon, but the quantity of the stain is too small to make certain. The stain is also formed on screens of mica, quartz and calcite; and this supports the view that it is carbon fractionally evaporated from the aluminium and iron cathodes. The sheet aluminium and iron used for kathodes was not pure. For comparison some pieces of an old incandescent lamp which was blackened inside with carbon, evaporated from the filament by long use, were treated with hydrofluoric acid and examined: microscopically. The visible effects in this case were very like those observed when the stain was treated with the acid. The stain in each case was apparently in a state of tension and portions of it curled up when broken. Monatomic gases appear to permit the evaporation of alu- minium, as Professor Callendar has observed its evaporation in an argon vacuum tube. (4) On the effect of zine and other metals on a photographic plate. By Professor J. J. THOMSON. In the course of a discussion at the Cavendish Physical Society on Dr Russell’s paper on the photographic effect produced by certain metals, Sir George Stokes suggested that possibly light might be thrown on the question as to whether these effects were due to radiation or to the vapour of the metals, if photographs were taken with a stream of air flowing between the metal and the photographic plate. In consequence of this suggestion a series of the photographs made by zinc and amalgamated zinc (1) with nothing but air between the zine and the photographic plate, (2) when the zine was covered with a film of celluloid, were taken both with and without an air blast. The photographs with the air blast were found in both cases to be distorted, which is in favour of the view that the effects on the photographic plates are due to the vapour of the metals, . 1897.] Mr Perkins, Notes on some Hawaiian Insects. 373 Monday, 6 December, 1897. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following were elected Fellows of the Society : Mr A. S. Ramsay, M.A., Fellow of Magdalene College; Mr W. M. Fetcher, B.A., Fellow of Trinity College. The following were elected Associates of the Society : Mr J. Zeleny, Mr H. A. Wilson, Mr G. H. Shakespeare, Advanced Students of Trinity College; Mr J. H. Vincent, Advanced Student of St John’s College; Mr P. Langevin, Advanced Student. The following Communications were made to the Society : (1) Notes on some Hawanan Insects. By R. C. L. PERKINS. Amongst the most important representatives of the Order of Neuroptera in the Hawaiian Islands, are the dragon-flies of the genus Agrion. Several species are found on all the more import- ant islands of the group, and the range of many of them extends over several islands; wherein they ditfer from the greater part of the endemic insects, which are for the most part confined to a single island; or to one or two of those which le most closely together. At the same time, when a series of examples of a species from different islands is compared, certain more or less constant differences are often ‘observable, especially as regards size. But the most interesting facts relate to the earlier stages or nymphs, which are aquatic and carnivorous. Excluding these dragon-flies and a few water-beetles, the insect fauna of the streams and pools is almost non-existent. The Ephemeridae, Perlidae, and Trichoptera, usually so numerous, are entirely un- represented in the Islands, although the mountain streams, rising at high altitudes, with their superb waterfalls, and various temperatures, appear admirably adapted for many of these. It is therefore not a little surprising to find the group of dragon-flies so well represented, and that the individuals are so numerous, being on the whole the most conspicuous of all the endemic insects. In the absence of the groups above mentioned, I believe that their main food-supply comes from without, consisting of such creatures as accidentally fall into the water. Under ordinary circumstances this is not great, but after rain, when the streams rise very quickly, food becomes abundant. When the streams, as is often the case, become nearly dry, large numbers of creatures resort to 374 Mr Perkins, Notes on some Hawaiian Insects. [Dec. 6, the pools that are left, for the sake of the moisture, and the numbers that come to grief is often astonishing, the whole surface being covered with the drowned and drowning. There are, however, other species the nymphs of which live under very different circumstances. These have given up their aquatic life, and live hidden at the bases of the leaves of a liliaceous plant—Astelia veratroides. Sometimes a little water is held by the plant around the stem, but more often there is merely a collection of damp earth and dead leaves. These nymphs would even appear to dislike the collections of water, for in wet weather they often crawl halfway up the leaves, instead of remaining at the base, where the water accumulates. They differ in some points from those which frequent the water; they are shorter and stouter, and much more sluggish, and the caudal appendages are very short and thick, differmg therein greatly from some of the aquatic species, the appendages of which form beautiful tracheal gills. On the whole they are without doubt better off as regards a food supply than the aquatic species, for there is generally abundance of animal life around them. A number of interesting beetles breed only in this plant, and minute young of molluscs and earthworms are generally abundant in the same, as well as the larvae of small moths. Moreover nymphs of various sizes often frequent a single plant, and if hard pressed for food the larger, no doubt, devour the smaller individuals. In consequence of these habits, some of these species of dragon- flies, although their powers of flight are feeble, may often be seen in numbers in localities remote from water, and where they would not naturally be looked for. These terrestrial nymphs are able to endure extreme drought. On one occasion when out shooting, having no more convenient re- ceptacle, I carried a number for the greater part of the day in an envelope. In the evening, although very dry, they were still quite lively. They were then placed in a tumbler of water, where they remained on the bottom, not being able to crawl up the sides. Here they remained for a day, apparently as happily as on dry land, when they were taken out and preserved. To turn to the Order of Coleoptera, which is more richly represented in the Islands than any other, by far the most conspicuous are the species of the genus Plagithmysus. With the allied genera Callithmysus and Clytarlus they form a special _ group of Longicorns, and no nearly allied form is known from elsewhere. Hence the country from which they may have been derived is quite uncertain. About 40 species are at present known. These beetles are remarkable in many ways, more particularly for the manner in which the wings are folded, there 1897.] Mr Perkins, Notes on some Hawaiian Insects. 375 being no transverse folding, so that they project beyond the elytra; secondly in the small development of the hind-body, at least in the males; and thirdly as being furnished with three distinct sets of stridulating organs. With regard to the latter the thoracic arrangement for stridulation is of the usual kind. The second mode by which sounds are produced, is by rubbing the bases of the hind femora against the margins of the elytra. These margins are specially sculptured much like a file, and the parts which rub them are roughened with minute tubercles. Altogether the arrangement reminds one not a little of the stridulating organs of the grasshoppers, and the Plagithmysi themselves have some little resemblance in general appearance to those insects. The third set of stridulating organs, which were discovered and pointed out to me by Dr Sharp, are on the basal joint or coxae of the middle and hind legs, and they may really be considered as two distinct sets, since the middle pair operate on the adjoining edge of the thorax, the hinder pair on a ridge on the basal segment of the abdomen. Moreover, in a specimen of P. aequalis examined, the striation of the coxae on either pair of legs was different, being evidently coarser on the intermediate pair. It is highly probable therefore that by the use of these different organs a considerable variety of sounds can be produced, for the sound made by the legs when rubbing against the elytra is not the same as that produced by the prothorax rubbing on the scutellum, and the degree of pressure, or rapidity of movement, also causes a variation in the sounds. The insects run with extreme rapidity over the tree trunks, when the sun shines hotly on them, and often perform curious evolutions, running in short curves or zigzags and at times almost giving little leaps. It seems _ hardly possible that such movements can be made without stridu- lation, although the sounds are not audible unless the creature is held in the hand. The small size of the hind-body may be connected with the frequent great disparity of size between the sexes, for the females of many of the species are often relatively very minute, and probably in all the species many such individuals would be found were sufficient material available for examination. While the minute males are not affected by the almost rudimentary condition of the hind-body, were this of the usual length, many of the large males would be quite unable to pair with a large proportion of the females. As it is, this is not the case, and male and female will often pair though the former is several times the bulk of the latter. Moreover it should be mentioned that both sexes are polygamous and pair many times. It is possible however that the rudimentary condition of the hind-body is in some way connected with the stridulating organs. 376 Mr Perkins, Notes on some Hawaiian Insects. [Dec. 6, The extreme variation in size of a given species may be due to differences in the quality of the food of the larvae, which may be found in a tree which has only just fallen, or begun to die, while others are feeding on a tree the wood of which is in a much drier condition. One of the most interesting points in regard to the Plagi- thmysi is the extreme variability of most of the species, which affects not only the colour but also the structure. The variation in the latter, however, is not so readily appreciated as the colour-. variations, and I do not propose to refer further to it here. Variation in colour is shown in various parts of the insect but is more especially remarkable on the posterior femora. On the Island of Hawai there are four very closely allied species of the genus. Three of these, P. varians, darwinianus, and lamarckianus, are found in the same locality, but each is solely attached to the kind of tree on which its larva feeds. Where the different trees grow side by side the three Plagithmysi may be found side by side; but in some parts of the forest only one of the three trees is to be found, in which case only the one species whose larva feeds on it is also found. The fourth species, P. black- burnt, feeds on the same tree as darwinianus, but occurs on the other side of the island. All of these species are variable in the colour of the femora, but the variation as exhibited in a series is distinct in each. In some cases the variation is so great that the extreme forms would appear to be more distinct, than are some of the allied species from each other. I have examined a considerable number of individuals of each of these species which are here exhibited. Thus of P. darwinianus, which feeds on Sophora chrysophylla, an acacia, the 65 individuals all have the femora red, the apices being very rarely dark. Of P. blackburni which feeds on the same tree but not in the same locality, 68 have these parts black, only 5 red. Of P. varians, which feeds on Acacia koa, 41 have the femora black, 53 have the apices bright red, while 4 are nearly entirely of a reddish colour. Of P. lamarckianus, which feeds on trees belonging to the Urticaceze, the legs are wholly black or reddish, probably either variety being about equally numerous, the species being much less common than any of the preceding. Thus on the whole each species divides into two or three varieties without true intermediate forms. It is true that if some of the individuals of P. varians be closely examined, the apices of the femora are seen to be less dark (ie. slightly reddish), but these fall in naturally with the black-legged specimens, and are very far removed from the brightly coloured examples. 1897.] Mr Perkins, Notes on some Hawaiian Insects. BY a | The only other species examined is P. aequalis, a species very distinct from any of the preceding, found on the Island of Kauai. The variation in this species is similar in kind to that of P. black- burnt, but the relative numbers of each variety are very different, for while in that species the red-legged variety is extremely rare, in the present one out of 181 examined no less than 70 are of this form. The large amount of variation exhibited is the more remarkable on account of the limited distribution of the species, for not one of the genus is known to inhabit more than one island, and many of them are certainly confined to a very small area of the island on which they are found. It has been already mentioned that all the species are polyga- mous. Of selective pairing by the different varieties there is no trace. On one occasion when watching a number of P. varvans on a fallen tree trunk, I noted that a female of the black-legged form paired successively with the brightly coloured variety, which has the apices of the femora red, then with one of her own colour, and shortly afterwards with the extremely rare variety which has the legs entirely dull red—And instances of a similar kind can be noticed any day, where a species is plentiful. Were sexual selection operative there is no doubt that a much larger number of distinct forms would be produced. It is interesting to consider the conditions that have brought about the specific dis- tinctions in these species so closely allied. Taking into considera- tion the fact that no species is found on more than one island, either geographical isolation, or a difference in food, or a combina- tion of these two factors, seems to account sufficiently for the separation of the species. Of the species under consideration, three may be found side by side (although each of them is also found in places apart from the other two), yet each keeps entirely to the tree on which its larva feeds; and the other P. blackburni, although it has the same food as P. darwinianus, does not inhabit the same area. So far as the native fauna is concerned these Plagithmysi have few enemies. It is doubtful whether any parasites attack them ; if any do so, they are certainly of extreme rarity. Except on the Island of Maui, birds either leave them alone or perhaps are very rarely able to catch them. On that island, however, one of the Drepanididae—Pseudonestor—is extraordinarily modified in accordance with its habit of living on the larvae, pupae and immature beetles of this genus and the allied Clytarlus. Indeed its food consists chiefly of these creatures, which it is able to tear out from the hardest wood. The great scars, made on trees which are affected by the beetles, may often be seen as the result of the work of this bird, and when opened its stomach is usually filled with their larvae. 378 Mr Perkins, Notes on some Hawarian Insects. [Dee. 6, Like the other orders of Insects the Hymenoptera are repre- sented by a very few types out of the enormous number that exist elsewhere. ‘Thus the bees, excluding a few isolated forms, which have either certainly or probably been introduced by man, are represented by a single genus; the wasps also by a single genus, and the Fossors by two genera of Crabronidae, and two closely allied forms of Mimesidae. It is to the remarkable evolution of species of each of these types that the comparative wealth of the aculeate hymenoptera is due. Thus while there are a very few genera which can be looked upon as endemic, the average number of species to each genus is very great, this number being about 28. Most numerous of all in species is the genus Odynerus represented in the Islands by some 80 distinct forms. They are one of the most important elements in the fauna, and are sufficiently numerous to attract the attention of people not particularly interested in such things, the more so as one or two of the species abound around houses, and avail themselves of holes in woodwork or furniture for forming their cells. Although intimately related to one another, and extremely similar in general appearance, in reality they exhibit a very great variety of structure. If one collects these wasps over the Islands from Oahu to Hawaii, the general blackness of their colour is very remarkable. Some are more or less marked with red, the markings being rarely noticeable, unless the insect is caught and examined, and a few have one or two narrow bands of a pale yellow colour on the hind-body, which also are not as a rule easily noticed. Many are entirely black. If now one compares with these a collection of the species from the Island of Kauai a difference is at once seen. Excluding one or two species which frequent the coast and, scarcely modified, have a wide distribution over the Islands, all the species have two distinct yellowish abdominal bands, the second being nearly always evidently wider than the first. When the insects are on the wing, these bands are plainly seen. It so happened that im the course of my collecting over the Islands, Kauai was not visited until after the other islands had been collected over, so that it was no small surprise to find the wasps so distinct in superficial appearance. At the time I supposed that the Kauai species would turn out to be very closely related to one another, at least more closely than to those on the windward islands. This however proves not to be the case, for some of the most remotely allied species on the other islands, are represented on Kauai by species which are structurally only slightly modified forms of the same, although their superficial appearance is very distinct. For some reason or other it is clear that the Odyneri of Kauai have assumed an appearance almost unique amongst the great number of species occurring in the Islands—they have what are called ‘warning 1897.] Mr Perkins, Notes on some Hawanan Insects. 379 colours’. That these markings have any such significance is I think certainly not the case. There is no reason to suppose that the species on Kauai have any more need of their special coloration than the black species of Hawaii, but rather the reverse, as birds, which are their only possible enemies, are more numerous on the latter island. As a matter of fact, after the examination of the food of many individuals of nearly all the endemic birds, I have never found them to feed on any of these insects whether black or coloured, nor would the majority of them be the least likely to do so, on account of their habits and structure. For the most remarkable feature exhibited by the endemic land-birds is the specialization of form for the purpose of securing some special food, which has led to the extreme diversity of structure exhibited in a group so small as the Drepanididae. So extreme is this specialization of some of the birds, that their food is almost limited to one special form of plant or animal, as we have already seen in the case of Pseudonestor,; while even in less specialized birds the range of food is very small. It is just these most highly specialized birds that are the first to disappear when their natural surroundings are interfered with, as they have already done on the Island of Oahu, which has been more upset than the rest of the group, by foreign settlers. It is not exaggerating to say that the extinction of a few species of beetles would extermi- nate both Pseudonestor, and the various species of Heterorhynchus, while the disappearance of three species of trees would do the same for the three genera Rhodacanthis, Chloridops, and Lox- ioides, and many of the other birds are equally dependent on a particular section of either fauna or flora. The birds most lkely to feed on the Odyneri are the fly- catchers of the genus Chasiempis, which do not appear to do so, but confine their attention for the most part to small Lepidoptera and their larvae. If they did feed on these, one would expect the Odyneri of Hawai to have distinctive marks as well as those of Kauai, since the birds are equally common upon both. But there is every reason to believe that the colours of the insects have no such significance, and it is still further convincing to notice that the Odyneri of Molokai have a general tendency to red-markings— Molokai being an island where no fly-catchers exist,—while on Hawaii these insects, even in certain points of structure of secondary value, tend to greatly resemble each other. The distinct style of coloration of the Kauai species is a point of some importance, for it has long been known that in other - countries insects of this group have a great general resemblance to one another in the country they inhabit, as for instance the highly endemic species in Australia and Chili. No doubt, were they more widely known, these cases of Chilian and Australian WO. IDG, PaO 31 380 Mr Perkins, Notes on some Hawaiian I nsects. [Dec.6, 1897. insects would be referred to as good instances of what are called ‘warning’ colours, but from the study of the Hawatian species such a significance becomes very doubtful. It seems much more probable that they are due to the general condition of the country they inhabit—it may be climate or some such cause. (2) Remarks on a journey to investigate the habits and develop- ment of Lepidosiren paradoxa. By Mr J. Granam Kerr, B.A, Christ’s College. PROCEEDINGS OF THE Cambridge Philosophical Society. Monday, 24 January, 1898. Mr F. DARWIN, PRESIDENT, IN THE CHAIR. The following communications were made to the Society :— (1) A New Method in Combinatory Analysis with applica- tions to Latin Squares and associated questions. By Major P. A. MacManon, R.A., Se.D., F.R.S. This paper is printed in the Transactions, Vol. xvi. Part iv. (2) Abelian Functions in connexion with two-dimensional fluid motions. By H. F. Baker, St John’s College. 1. Consider the portion of the upper half plane of the complex variable ¢ which lies outside p circles, which do not intersect each other or the real axis. Then the function which gives the streaming motion in this portion of the upper half plane due to a doublet of arbitrary strength and position is already known (Joc. cit. (8), (@))*. * The references given to the literature are by the Greek letters, as follows: (a) Riemann, Ges. Werke (1876), No. xxy., p. 413 (or second edition, p. 440); (8) Schottky, Crelle, lxxxiii. (1877) ; (vy) Schottky, Crelle, ci. (1887) ; (6) Schottky, Crelle, evi. (1890); (0) Burnside, Proc. Lond. Math. Soc. xxii., xxiii., and Messenger of Mathematics, xx. (1891); (x) the writer’s Abelian Functions (1897), Chap. xii. ; (A) Kluyver, Acta Math. xxi. (1897). VOL. IX. PT. VIII. oe 382 Mr Baker, On Abelian Functions in connexion [Jan. 24, As we shall require the result, and to illustrate the pomt of view, we give a proof. Denote the real axis by C,; the points of the circles which are nearest to the real axis by Cy’, ..., C,’, and these circles themselves by the same letters, reckoning from right to left ; denote the region bounded by (, Cy’,... , Cp’ by Q); denote the circles which are the images of C,’,..., C,’ in the real axis by C;,..., Cp, the points of them which are nearest to the real axis being also denoted by C,,..., Gy; denote the region bounded by the 2p circles Cy’, ..., Cp, C,, ..., Cy by Q, the axis C, being then disregarded. Then it is known (loc. cit. (8)) that there exists a function, G, single valued in 0, save for real periods, real on O), Cy’, ... , C,’, and infinite at an arbitrary point €=¢ like (P+7Q)/(€—t), where P, Q are arbitrary real constants. Being real on (, this function will (Schwarz, Ges. Abh., 11. p. 66), have the same value at any point of the caircum- ference C, as at the point of the circumference C,’ which is its image in C,, and will be infinite in Q, beside at ¢, at €=#', where t’ is the conjugate complex of ¢, namely like (P—7Q)/(¢—?¢). Now the region © when considered as the locus for functions whose values at any point of one of the boundaries Cy’, ... , C,’ are equal - to the values at the conjugate complex point of the boundaries O,,..., Cp, is a p-ply connected Riemann surface, for which the fundamental functions are well known (loc. cit. (x)). It follows therefore from the theory of functions on such a surface that for proper values of the constants A,, ..., 4p, A, the function desired is given by @=—(P+iQ)T?*—-(P- iQ) Te" + Awe? +... + Awe + A; here A is an arbitrary real constant, and A,,..., A, are determined by Ayti» +... + Aptp,r = 270 [(P + 1Q) ob, (2) + (P — 20) 6, (DI), (7 = 1a 5 ee where ¢,,() denotes dv"/dé ; the point =a is supposed taken on Ch. By applying similar reasoning we find for the function giving the general circulatory motion in Q,, ON Paes $5 a $3 briny =Bor’ +... + Bu +B, where B,, ..., By are determined by the values of W on Qj, Cy,..., Cy’; and infer, by the way, that ye" is real when € and a are real, and that 7,,,is a pure imaginary, so that the constants A,, ..., Ay above are real (loc. cit. (), (X)). 3 1898. ] with two-dimensional fluid motion. 383 Therefore when €, a are real (P +iQ) 19+ (P — iQ) Te", is real; as can be shewn from the explicit formule. This function is single valued in ,; it has its imaginary part constant on each of the circumferences CY’, ..., C,’. 2. The problem of Riemann’s paper (loc. cit. (a)), in which however the boundaries are not necessarily circular, is the deter- mination of the solution, for the region Q,, of the potential equation ol Of 1? U Of * On? which is finite within ©, and takes on the boundary an assigned continuously varying value wv. This is given, at t = & + in, by U =/uP* =), where P%is the function real on the boundary of Q,, Nee only real periods, which is infinite at the interior point ¢ like 5— log (€—t). This function is known (loc. cit. (X)), or follows as rite from the theory of a Riemann surface, being given by 1 i a SS ple ae ake + A,v8 Al Pi = where ¢’ is the conjugate complex of t, a is real, A is a real constant, A,,..., A, are real constants determined by the equations 8 4 Ayr toe + Apty,r =O, (r=1, 2,..., p). 3. Among the single valued functions for the region 0, with rational infinities, there is one of particular interest—that namely which is real on the boundary and has a single pole of the first order at an assigned point of each of the (p + 1) separate boundary curves (,, Cy,..., C,. This function effects a conformal repre- sentation of the region ©, upon an infinite half plane (p + 1) times covered, and is thus the direct generalisation of the function giving the conformal representation of a simply connected region upon a simple half plane. In what follows we put down this function for the case when the circles .C/’, ..., C,’ are unrestricted (save by the inequalities which are necessary for the convergence of the series involved); and then give the very simple form taken by the function when the Abelian functions involved are those of hyperelliptic character. 32—2 384 Mr Baker, On Abelian Functions in connexion (Jan. 24, The construction of a function, single valued in the region Q, unchanged by the substitutions which transform the circles CY’,..., Cy respectively into C,, ..., Cp, and having p +1 poles of the first order within Q, of arbitrary position, is known—being as follows (loc. cit. («)); let the poles be at z, q, ... , cp, and let ae (Yr2 + 8)? : @ (Zz, ee Bo le ? let the additive arbitrary constant be determined by the condition that the function vanishes at =a; then, the function is given by 1G | WE, Oy Oy a) GiB Gh), sea OE Gs) |; OG, 6) O(GsQs DGsGh sa, OG, Gs) OE 56) QEGy@y OGpah) a5 OGa Gs) ey. iP I Na React i where # is an arbitrary constant, and a, ... , @, are the analogues of a by the p fundamental substitutions whereby the circles Cy, ..., Cy’ are respectively transformed into C),..., Cp. In the case under consideration the region © has the specialty that the circles Ci, ..., Cp are the inverses of C,’, ..., C, in regard to (,>— we proceed to prove that in this case, if z be upon the real axis C,, and ¢,, ..., ¢) be respectively upon the circumferences CY’, ..., Cy, then, for a suitable determination of the constant H, the function is real upon each of the curves C,, Cy, ..., Cp. The necessary value for # is that of the inverse of the minor of ®(z, f) in the determinant (or any real multiple of this)—when # is so determined the function may be denotod by W({, a; 2, G, ..., Cp). To prove this it is sufficient to prove that the function is real upon the real axis (Schwarz, Ges. Abh., IL p. 66). Now it follows from Riemann’s theory that the function, uniform in ©, unchanged by the p fundamental substitutions, with poles at z, q, ..., Gp, respectively on C,, Cy’, ..., Cp’, and vanishing at €=a, is given by P(E) = (Prt iQ) TE" +... + (Pp + 1Q)) PE" + (P+ 1Q) PES where P,, Q,, etc., are real constants whose ratios are given by (Pi + iQ,) bn (@) + +. + (Pp + 1Qp) dn (cp) + (P+ iQ) $n (2)=0, @ Sse where ¢,, (€) = dv® “[dé We have already seen that ¢, (£) is real when € 1s real; hence these equations involve also, if c,, c, be conjugate complexes, the equations, (P, — 10h) dn (G)+. aa (Py oF Wp) Pn (Cp oa (P a - Pn (z) =0, @=1) 2) Ree 2. See 1898. ] with two-dimensional fluid motion. 385 which, in turn, shew that, a being real, the function Ai (6) = (Pi =) Ve" +... + (Pp — 1Q,) TS + (P iQ) TE is a single valued function unaltered by the fundamental substitu- tions. The poles of f,(¢) in the ¢ plane are however the same as those of f (£), since ¢,’, c, are analogues of one another for the r-th of the fundamental substitutions—and the functions /,(f), f(£) vanish at the same place a. Wherefore, considering the residues at the pole z, we infer (P+ 1Q)7F(E) = (P10) AO); as we have already shewn that for conjugate complex values of ¢ the quantities a a ee 10) re", have conjugate complex values, it follows that the function (P+7Q)71 /(€) has the same property. This proves the theorem in question. 4. The same argument can be used to establish the further result: Take p +1 points entirely within the region Q, so situated that those which are not upon the real axis C, consist of pairs occupying conjugate positions in regard to this axis. The uniform function unaltered by the p fundamental substitutions which has these points for poles of the first order is necessarily real upon C,, Cy, ..., Cp’ (and C,, ..., C,), or can be made so by multiplication by a proper constant factor. For the region ©, this gives the theorem: take any m points within ©, or upon one or more of the circumferences Cy’, ..., C,’, and any & points upon OQ, so that 2m+k=p+1; there exists a function uniform in Q,, real on CY, ..., CG,’, G, and infinite to the first order at each of the m+k points taken in Q,. It may be of interest to give the functions of §§ 3, 4 for p=1. Let the fundamental substitution be (De =A) (SB) (eA) and v=|Vm|. Then if be any real quantity, ee | Sa lou pe alo (- = men = AG,| AC ° ae BY OO ae 8 io BS Ay? (forms which hold when (, becomes a circle, C, being the point where the straight line C/C, cuts the circle C,), the general and a particular form of the function of § 3 are given by errs Oe eae: ae) xe Ce Q(u)—e(v) eE(u)—-—@E(Wt+e’)’ O(u)—¢e’ 386 Mr Baker, On Abelian Functions in connexion [Jan. 24, where », w are real; and the function of § 4 by PM+EO PF WH+O'O) E(M)—eE%) e(u)—e)” where ¢ belongs to a point in Q,, and ¢, is the conjugate complex quantity. The function of § 1, which is real on C/’ and C), and has only real periods, and has one arbitrary pole of the first order in Q,, is given by oye OOO ps gy CORO ple eee COT p ote pape Te? EO —e) where P, @ are real quantities. 5. We consider now the case in which the circles G, Cy,...C,’ are all cut at right angles by another circle O. It is known that in this case the functions arising reduce themselves to hyper- elliptic functions. The figure (1) drawn for p =3, will explain the notation we adopt. In any case where the 2p circles C,’, C,, ..., C,’, Cp consist of pairs of circles inverse to one another in regard to the real axis Cj, 1898.] with two-dimensional fluid motion. 387 the singular points lie within the circles CY’, O,, ..., O,', Cp, and consist of pairs of points inverse to one another in regard to O). This is clear either because the substitution 5, is equivalent to an inversion in regard to the circle C, followed by an inversion in regard to the circle C;,, or, what is the same thing, by remarking that if P=. 9O9 PHM. be two substitutions in which the primary factors occur in the same order but are the inverses of one another, and, if z, 2’ be conjugate complexes, then also ¢(z) and ¢’(2) are conjugate complexes. But in the case in which the circles Cy, C’, ..., Cp’ are all cut at right angles by another circle, O, it follows further that the singular points all le upon this circle O. Hence follows immediately another consequence; we have already seen that the imaginary part of the function o ii > log So siCBn) 275° §—34 (An) is constant on each of the circles Cy’, ..., C,’, C), being zero on C; it can now be seen that the real part of v$ is constant on each of the arcs of the orthogonal circle O which are limited by the circles CY,...,Cp,C,,..., Cp. For ifj, 7’ denote two substitutions such as ¢@ and ¢’, we can put 1 6-9) (Bn) €-3) (By) $ —— > ] = Ra ATE i = 7 > On 20 i,j °8 o— ae (An) c ae aj (An) and 3; (Bn), 3; (An)—as also $j (Bn), 3; (An)—will be two singular points having conjugate complex positions upon 0. As the real part of v§ depends only on the arguments of the factors [S—3) (Bn)I/[E— Sy (An)], the result follows at once. ys n From this, if barriers be drawn in Q, consisting of the p straight lines joining CC, C,C,,...., Cp Cp, we find the equations yin Go = —4, or 0, as N=7, Or N=7. It will be sufficient to consider one case. Let D,’ be the inverse point of C,’ in regard to the circle O, and let A denote the real part of v%% at the point a,; then since the function — 1 is real on the are ac, it has conjugate complex values along the ares ¢,Cy’, c,D,/; so that we have on these arcs, respectively, = aoe Ja ots i a 08% = — $y, 1— My 388 Mr Baker, On Abelian Functions in connexion [Jan. 24, where yp is a variable real quantity; again, since —7(v2%— K) is real on the are a@,¢,, it has conjugate complex values on the arcs a,C,’, a,D,{; so that we have on these ares respectively ve ?= K— 37, +X, ve4= K —$7,,—2, where p is a variable real quantity ; therefore Oe ce; — uD Cy + Ope D,! —— vr C= Oe Cy, while, on the other hand, OD cu Oe 4 I + Ub» CY where II represents the value obtained in passing from one side to the other of the barrier through CY, =—1 when r=1 and =0 when 7+ 1, it being supposed that, as in the figure, the arc cq 1s in the counter-clockwise direction ; hence we have by addition Zu % = TT, giving the result enunciated. This equation is also easily seen to be the condition that the function v%“% be continuous at Dy’. For these results ef. Joc. cit. (@); the proof here given is de- signed to bring out the identity with some corresponding results in the theory of a hyper-elliptic Riemann surface; it is upon this identity that an important result deduced below is made to rely. Further, since the real part of v$ is constant upon the separate arcs of the circle O we obtain Oy @ — il by Oh a IL 1 CBee > ony ae IS St a OHA, OP Cx) Oh, —> A AL, GO; Gy — al. OS 2= OTr, Oana OTr, 3) UR 7= OTr, 3> of which for instance the value of v%% can be obtained by a method similar to that employed above, by adding the values obtained by passing from a, to ¢,, first directly along the circle O, and then along the path a,0{'C,a)'c,'0,C,'c,, where a, ¢, are the images of a,, c, on the circle C). These equations shew that, for the definition of the half periods, the points a, ¢, G1, C:, M2, ..., are exactly analogous to the branch places denoted by the same letters when the period loops of the hyperelliptic Riemann surface are drawn as in the annexed figure (2). Hence from the theory of hyperelliptic theta functions we infer that the theta functions © (v% %), O (vs °) vanish respectively in the FOUKEAS (Cin ace GY) BACH (Giz ooo5 Ga)) 1898. ] with two-dimensional fluid motion. 389 Consider now the function ? ne yak HERI? (f ) Si TST, where ¢,=(a,€+B;)/(y,€+6,), and the summation extends to every substitution of the group. When one of the p fundamental substitutions of the group, as given by the positions of the circles on the ¢ plane, is put into the form ¢°=(af+ )/(yf+ 8), with aS — By =1, there is an ambiguity as to the signs of the quantities a, 8, y, 6, which must be settled beforehand in order that the Fig 2. function .(¢, w) may be definite. There are then 2” functions r(¢, w), differing according to the conventions adopted in the case of the p fundamental substitutions. It is known (Camb. Phil. Proceedings, Vitt (1895), p. 332, or loc. cit. (x), p. 8368) that any one of these functions has, in the region Q, beside €=%, p zeros }41, +++, &p Which are given by the equations aw mot we “P= 4 (Gr oi hy), (r =1,..., Pp), where m,, ..., m, are the zeros of the theta function © (v>™), and (fi +h), «+> (Gp + hp) is an aggregate of p integers, each of which may be taken to be either even or odd according to the conventions, explained above, adopted for the signs of a, 8, y, 6 in the p fundamental sub- stitutions. Hence we deduce, if the conventions be taken so that each of Gr +h, is an even integer, the functions r(E a), r(G ¢) vanish respectively in (dy, ..., dp) and (c, .... Cp»). More generally, from the results developed above, such as v,“” “= — 4, we have, the 390 Mr Baker, On Abelian Functions in conneaion [Jan. 24, p finite zeros of any one of the 2” functions X (€, a) are (fy, «--, Mp), where 1, 1s either a, or c,, according to the convention adopted for the signs of a, 8, y, 6 in the p fundamental substitutions. A direct verification is given below. Therefore, from what was proved in the general case, a function which is uniform in the region O, unaltered by the substitutions of the group, real on the circles Cy, Cy, ..., G,, Cy, ..., Cy, and in- finite to the first order on each of these circles, is given by Z=2(E, a)/r(E, ¢); with the notations explained loc. cit. («), save that c, replaces b,, this can be put into the various forms following, where pm is an arbitrary place,-and a constant factor is disregarded, = 6) (v% ®) ell” Bw )) (us 3) C, a) _a(G0)a (bm)... #6 4) oS OYa(G G)) doo @ (SG) © Oe [v— ax (a,)| ... [ec —2(a,)] aX x(a—a«2(G)]... [e—x(c,)] In the elliptic case, with = pom Pane? fe nina a, € NH, Cy ap, Cp? Z ins We Oe log ( dtr €¢-B j;a-B ) c—A | a—A/’ we have, with the convention of sign here adopted, save for a constant factor, x(Ea)_ Ve@—e _ gt) M50) Ve(uta)—e 9(u)— es’ the points c,, a, c, a@ corresponding to the values @;, @, &, © of Q (wu), respectively. It is easy to verify that this function has the desired behaviour. Thus by the function (6 'a)/X(E c) the conformal repre- sentation required in Riemann’s paper referred to, is effected. 6. We explain now how to obtain a direct verification from the series itself of the statements that have been made as to the zeros of the function X (fa). For this purpose we suppose the circle O, which cuts the circles (, Cy, ..., Cp at right angles, to be the axis of imaginary quantities, the point a being the origin, ¢=0, and the left side of the imaginary axis being the interior of the circle O. Then we may put SSO, Ch SUir, CG Silin, C= dey on- 2 - —— 1898.] with two-dimensional fluid motion. 391 where k,, h,, ky, ho, ... are real positive quantities in ascending order of magnitude. It is then found that, for positive integral n, we have % aMe+ BO SE —h ky” are) = ar) NG) a yi? Sir where a6" — By” = 1, and () os (oe ag my “3 (ee = ey Ohl, Why — Vie) Wiig + Vd S mace ce) Vh, —Vk Vh,y + Vk; the square roots Vh,, Vk, k, being taken positively; here e,, = +1, is a quantity which is not determined by the positions of the circles, but must be assigned when the substitution 3, is put into the form i (gj== ae ye 8 with a6 — BMy” =1, From these it immediately follows that if z be a pure imaginary quantity, and 2 =—z be its conjugate complex, y,’2+ 6,” 1s real and equal to yz’ + 6”, while ay 2 + 8)” is purely imaginary and equal to the negative of al") 2! + B", Therefore if =e 21 Q No len eye) o (=. WIP. OTS, / —ny Ta a af+f8 Ei fet FO ee be two substitutions in which the factors formed from the primary substitutions follow one another in the same order, but for pty factor SY? in the first there enters, in the second, the factor Sz” follows, if z and 2’, =—4z, are conjugate complex quantities, ae $ (z)=— $' (2), and yz+ d= 9/'2'4+06. These facts are clear enough from a consideration of the figure. For our purpose another fact is also necessary, namely when ¢,=-+ 1, we obtain ac.+ 8 =—¢c,=¢,/, y%c,+80 =1, when ¢,=—1, we obtain aa, +B" =—a,=a,, ya,+6% = where ¢,, a, denote the conjugate ae of ‘c, and a, ‘re- spectively. 392 Mr Baker, On Abelian Functions, &c. [Jan. 24, Hence, retaining the notation for ¢ (£), ’ (6), if 8%. O= Grp so that AL+ Baad [aries BM] +8 [ye+ 8) we have when ¢, = 1, Ac,+ B=a'c,’ + B’ =— (ac, + B), when ¢,=— 1, Aa,+B=da, + B =—(aa,+ 8); we find also, in fact, in these two cases, $ (Cr) =— P'S; (Cr), & (Gr) = — $'Sy (Gy). Thus it follows, that when e, = 1, the series GEOn) 1 ME O= si YE + Om) aye ee (0) m Cm mms + Bm vanishes for €=c,; for when €=c, the term arising by the substitution $, of the group, is equal and opposite to the term arising by the substitution ¢’$,. Similarly when ¢,=—1, the series vanishes for =a,. In a somewhat artificial way this result may be included in the statement—the series, \ (§ a), has, beside = 0, the p zeros Ata A, — Cy Up + Cn _ An — Cy 5 Oe 5 eae eae where €, ..., €, each equal to +1, are the signs determining the p fundamental substitutions, as given by putting n=1 in the formulze written down above for the substitution S$”. (3) On the production of a cloud by the action of ultra-violet light on moist air. By Mr C. T. R. Witson, Clerk Maxwell Student. If the light from an arc lamp be brought to a focus, by means of a quartz lens, within a vessel containing moist dust-free air, a bluish fog becomes visible in the course of a few minutes along the path of the light. The cloud particles remain in suspension for hours after the light has been cut off. The phenomenon is shewn even in unsaturated air, but the faint blue haze which then developes takes much longer to form. When the radiation is not sufficiently intense to shew these effects a dense fog can still be obtained by bringing about slight supersaturation by expansion. These clouds, unlike those obtained by Tyndall (Phil. 1898.] Mr Wilson, On the production of a cloud, ke. 393 Trans., 160, p. 333, 1870) and by Aitken (EZdin. Trans., 39, 1. p. 15, 1897) by the action of light on various vapours, are due to the ultra-violet rays alone; for if a thin sheet of glass or mica (substances which are opaque to these rays) be interposed, not a trace of fog or rain is formed even when a high degree of super- saturation is brought about by expansion. It is possible that the small particles to which the blue of the sky is due are the result of this action of the ultra-violet rays, of which sunlight, when it first enters our atmosphere, doubtless contains a plentiful supply. (4) On the use of logarithmic coordinates in Physics. By Mr J. H. VINCENT. (5) On the Dine Reflection of Rontgen Rays. By J. J. THomson, M.A., F.R.S It is well known that when Réntgen rays fall on a solid or liquid surface there is a diffuse return of rays from the surface ; these diffusely returned rays we shall call secondary rays. The consideration of the nature and manner of production of these secondary rays suggests some interesting questions, as the experiments of Sagnac and Langevin show that these secondary rays differ in their properties from the primary rays which excite them. So that it would seem that bodies exposed to Réntgen rays can themselves emit rays which possess many properties in common with the ordinary Rontgen ray. Thus for example Rontgen has recently shown that air through which Rontgen rays are travelling sends out rays into regions carefully screened from the direct action of the primary rays. Sagnac, who has recently investigated the properties of the secondary rays diffusely reflected from metals, finds that though they resemble the primary rays in not being refracted, they are absorbed with very much greater rapidity, the secondary rays being practically extinguished after passing through a centimetre or so of air at atmospheric pressure. Sagnac found too that the penetrating power of the secondary rays depended on the nature of the metal from which they emanated; thus close to the surface of the metal the secondary rays were more abundant with zinc than with copper, at a short distance from the surface of the metal the proportions are reversed, showing that the rays from copper have more penetrating power than those from zinc. Sagnac arrived at his results by using the photographic method. Langevin 394 Prof. Thomson, On the Diffuse [Jan. 24, working at the Cavendish Laboratory has arrived at these and other results by the electric method. The following investigations were undertaken in the hope of throwing some light on the way in which the molecules of a substance might be conceived to give out Réntgen rays. Since there is no reflection of the Rontgen rays we cannot suppose that the secondary rays are produced by an action similar to that by which light is ‘scattered’ from small particles. If however we adopt the theory described by the author in the Philosophical Magazine for Feb. 1898, that the Rontgen rays are thin pulses of intense electric and magnetic intensity such as is shown would be generated by the sudden stopping of the cathode rays, then one way in which the secondary Réntgen rays might be produced is as follows. Let us suppose that the atoms of the substance carry electric charges, then when the pulse of intense electric intensity which constitutes a Rontgen ray falls on these atoms it will suddenly change their velocities, this sudden change in the velocity of a charged atom will generate a secondary pulse of electric and magnetic intensity which on the above theory would constitute a secondary Réntgen ray. The nature of this secondary ray is as follows: if a sphere of radius @ with a charge e is suddenly started with a velocity w parallel to the axis of X, then the state of the magnetic field can be shown to be as follows. If P is a point under consideration, O the centre of the particle, and OP=r, then H the magnetic force at P is zero when the time t which has elapsed since the particle was started is less than (r—a)/V, where V is the velocity of light through the medium surrounding the sphere: when t>(r—a)/V<(r+a)/V, then . _ ew sin 0 Hf ar where @ is the angle between OP and the axis of X; when t>(r+a)/V, | ew sin 0 =] Hf the lines of magnetic force are circles with their centres along the axis of X and their planes at right angles to it. Thus between | the times t=(r—a)/V and t=(r+a)/V a pulse of intense magnetic and electric force is passing over P. Now consider a primary Réntgen ray travelling along the axis of z; let the electric intensity im the pulse make an angle ¢ with the axis of X, this intensity will give an impulsive velocity parallel to itself to a charged particle in the path of the pulse, let this 1898. ] Reflection of Réntgen Rays. 395 impulsive velocity be w. The magnetic force in the secondary pulse will in a direction making an angle W with the axis of z and ~ at a distance 7 from the particle be equal to ew i ao — sin’ sin’ ¢, while the energy in the pulse will be proportional to (1 — sin? sin? ¢). Let us suppose that instead of there being only one ray there are a large number in which the electric intensity is in different directions, but uniformly distributed round z, then the energy will be proportional to arr? e*w? arr? (1 — }sin® ), thus the energy when w= 0 or zis twice that when y=7/2. So that if the secondary radiation arises solely from an action of this kind the intensity of the reflected radiation in the direction of the primary rays would be twice that in a direction at right angles to them. The intensity of the diffuse reflection in different directions was tested by the following method. ABCD is a box made of A FHM B FG 1 ake ees C Fic. 1, sheet lead, Réntgen rays pass into this through a small lead tube EFGH and are diffusely returned from the patch KL; pieces of photographic plates with screens of perforated zinc in front of them were placed at M and N, at equal distances from the middle of the patch HK; the diffusely returned rays from HK produced after an exposure of about two hours photographs on the plates N, M; the photographs at M and N did not show any appreciable difference in intensity though a large series were taken with exposures varying from 2 to 6 hours. Tests were made which showed that these photographs were made by rays coming from HK and not from the air through which the primary Rontgen rays passed. This was done by removing the bottom of the box, when the effect on the plates was very slight compared with that produced when the bottom of the box was in its place. Though the photographic method is not a very delicate test of the relative 396 Prof. Thomson, On the Diffuse [Jan. 24, intensity of the rays, the results show that the mtensity at M where wf is small cannot exceed that at NV where w is nearly 7/2 in anything like the ratio of 2 to 1, thus showing that the greater part at any rate of the effect does not arise in the way suggested. Some experiments were made to see if there was anything of the nature of selective absorption of these diffusely returned rays. In these a plate in the position M was covered with paper, on this paper two crosses were placed, one of these crosses was made of thin platinum foil, the other by painting red lead on the paper; the thickness of the layer of red lead was altered until when the diffusely returned rays came from the lead sheet at the bottom of the box the depth of the shadow cast by the red lead was very nearly the same as that cast by the platinum foil. The bottom of the box was then covered by a piece of platinum and photographs again taken: the depth of the shadows seemed to be in the same proportion as when the rays were reflected from lead, showing that there is no marked selective absorption. The absence of refraction in these diffusely returned rays was verified by the following experiment. A straight slit parallel to the bottom of the box was cut in the side BC of a lead box, the diffusely returned rays passing through the slit produced a bright line on a photographic plate placed outside the box, a thin wedge of alu- minium was placed between the slit and the photographic plate and photographs were again taken, the line of light on the plate was found unbroken by the prism though faint in the part where the rays were intercepted. The equality of the radiation in differ- ent directions shows that these secondary rays do not originate by the method of which the theory is given above. The primary Réntgen rays ionize the substances through which they pass, and the rapid ionization in an electric field of a molecule consisting of positively and negatively electrified atoms will be accompanied by an electromagnetic disturbance lasting for only a short time. The general character of this disturbance may be represented graphi- cally as in the following figures. In the first stage (a) the Faraday tubes in the external field and that connecting the atom in the molecule are uninfluenced by each other; in the next stage (b) the tubes bend towards each other, then they run together and break away as in fig. (c), and after this stage the atoms in the molecule are not connected by a Faraday tube and are dissociated. While these changes are im progress we have a very rapid movement of Faraday tubes in a space comparable with that between the atoms in a molecule. This movement of the tubes will give rise to an electromagnetic disturbance which in con- sequence of the intense radiation will be almost dead beat and so equivalent to a pulse of electromagnetic disturbance. The 1898. } Reflection of Réntgen Rays. 397 radiation emitted from ionization will be more symmetrically distributed than that previously investigated and so there will be less difference of intensity between the secondary radiation in the direction of the primary ray and that in a direction at right angles to it. Ionization (if sudden) may thus be expected to give rise to rays having properties similar to those of the secondary Rontgen rays. E. Wiedemann* has shown that an electric discharge gives rise to rays to which he has given the name “Entladungstrahlen ” ; these rays can pass through substances opaque to light and are not deflected bya magnet. Now the electric discharge is accompanied + Pee — A B a + = A Bt b bss 2 f A B c Fig, 2. by ionization of the gas through which the discharge passes and, though this ionization is probably not of so sudden a character as that produced by Réntgen rays, Wiedemann’s experiments seem to show that it is rapid enough to give rise to rays having properties analogous to the secondary Réntgen rays. It seems not impossible that in the case of a complicated structure like the uranium atom regrouping of the constituents of the atom may give rise to electrical effects similar to those which occur in ionization and might possibly be the origin of the uranium radiation. 1 Zeitschrift fiir Hlektrochemie, 11. p. 159, 1895. VOL, Lx. PT: Vill. 33 398 Mr Willey, Some Zoological Results of a [Feb. 7, Monday, 7 February, 1898. Mr F. Darwin, PRESIDENT, IN THE CHAIR. The following were elected Fellows of the Society : J. H. C, Datton, M.D., Trinity College. A. H. Ramsey, M.A., Magdalene College. W. M. FLetcHeRr, B.A., Trinity College. The following communication was made to the Society :— Some Zoological Results of a Voyage to Melanesia during the years 1894—1897. By ArtuHuR WILLEY, D.Sc., Balfour Student. I. Nautilus. 1. The deposited eggs of N. pompilius were obtained by me during the months July—September, 1897, in cages kept at a depth of some 50 to 60 fathoms in Blanche Bay, New Britain. They differ very slightly in the ornamentation of the outer capsule from the eggs of V. macromphalus, the pectinate _ ridges in those of the former species being more frill-like. 2. The otolithic contents of the otocysts of Nautilus were correctly described by Macdonald’ in 1855 as consisting of m- numerable minute otocones. Sometimes in preserved specimens the effect of the preservation appears to be to coagulate the fluid contents of the otocyst, so that the otocones cohere to form a solid otolith. This explanation will account for the erroneous interpretation recently published on this subject. 3. The region of the mantle which secretes the calcareous septa of the shell is marked off from the surrounding region by a thickened rim or contour line. The latter was described by me under the name of the septal contour and figured on p. 170 of the Quart. Journ. Micro. Sc., Vol. XXxXIx., 1896, together with a repre- sentation of the pallio-septal arteries. The septal contour has been redescribed by L. E. Griffin (loc. cit.) as the “ posterior ventral aponeurotic band” without referring to my account, al- though the paper containing it is included in his bibliography. 4. The animal of N. umbilicatus has not, so far as I am aware, ever been examined or even seen by a zoologist before. I was fortunate enough to obtain one specimen which had been taken from the surface in the neighbourhood of the D’Entre- 1 Phil. Trans. 1855, p. 277. Macdonald supposed his specimen, which was obtained off the Isle of Pines, to be N. umbilicatus; but that it was really N. macromphalus is abundantly evident from his description of the animal even if it were not already known that he had mistaken the species. 2. BE. Griffin, “‘ Notes on the Anatomy of Nautilus pompilius,” Zool. Bulletin, Vol. 1. p. 147. 1897 1898.] voyage to Melanesia during the years 1894—1897. 399 casteaux Group, to the east of New Guinea. While the animals of NV. pompilius and N. macromphalus are almost, if not quite, indistinguishable from one another, that of WV. wmbilicatus differs markedly from both, especially in the surface texture of the hood, which is coarsely areolated, the polygonal block-like areas being separated by deep valleys. 5. In any attempt to interpret the morphology of the tenta- cular appendages of Nautilus and the arms of the Dibranchiate Cephalopods, if function, innervation, and development are re- jected as evidence of their pedal origin, the only way left open to approach the subject seems to be by taking into consideration the general phenomena involved in cephalogenesis. In all other animals which possess a compound head, the latter is not pro- duced by elaboration of the pre-existing simple head with its preoral lobe, but by the incorporation of other parts of the body into the cephalic complex. Thus while in Arthropods we have the cephalothoraz, in the Cephalopod Molluscs we have, viewed from the standpoint here adopted, the cephalopodium. II. Ctenoplana. This remarkable animal appears to be the existing representative of the type from which the Ctenophora and the Plathelminthes diverged; the former being its pelagic and the latter its littoral descendants. The importance of Cteno- plana lies in the fact that it presents a transition from biradial to bilateral symmetry, the transitional feature being its dorso- ventrality. Some authorities consider Ctenoplana only as a slightly modified Ctenophore. From this point of view, however, Ctenoplana loses much of its interest and all of its importance; but I do not think that there is sufficient justification for such a depreciatory attitude. It may indeed be said that Ctenoplana is no more a Ctenophore on the one hand or a Planarian on the other than Peripatus is a Cheetopod or a Myriapod. For further details on Ctenoplana I may refer the reader to my paper in the Quart. Journ. Micro. Se. Vol. XXXIX., p. 323. III. Enteropneusta. In Spengel’s great Monograph of this group there are two theoretical conclusions to which I wish to refer. The first is that the Enteropneusta have no Chordate affinities; and the second, that the genus Balanoglossus (sensu stricto) is the most primitive type of the group. As this genus is the one which is least capable of beimg compared, in any detail, with Amphiowus, the latter conclusion, if true, would tend to confirm the former. In the section Chlamydothorax of the genus Ptychodera the gill-slits open freely to the exterior throughout the greater part of 33—2 4.00 Mr Willey, Some Zoological Results of a [Feb. 7, their length, in Pt. flava throughout their entire extent; in other words, the branchial sac is freely exposed to the surrounding water. Observations made on living specimens of Pt. flava at the Isle of Pines led me to suppose that this condition of the branchial sac, with its skeletal supports, which include synapticula or cross-rods, was more primitive than that in which the primary bars are fused with the body-wall and the external openings of the gill-slits are reduced to minute pores. This latter condition would naturally tend to render the skeletal structures more or less superfluous, and, in fact, as shown by Spengel, there are no synapticula in Glandiceps and Balanoglossus. That this is a secondary loss rather than a primary deficiency seems to me to be extremely probable, and this view is further confirmed by the organisation of an Enteropneust which I have described as a new genus, Spengelia’. This genus, apart from its own peculiar features, exhibits close affinity to Glandiceps, but it has synapticula. Another point which Spengel regarded as evidence of a primitive nature was the absence of a circular layer of muscles in the body wall of Balanoglossus. Spengel himself could not avoid calling attention to the improbability of this defect in the structure of a soft-bodied animal like Balanoglossus being primitive, even while vindicatmg his position. In a species of Ptychodera from Funafuti, recently described by J. P. Hill? as Pt. hedleyz, Hill found that there was no circular layer of muscles in the wall of the trunk-region, except at the extreme posterior end, where it forms the anal sphincter. As this species belongs to that section of the genus Ptychodera which bears most external resemblance to Balanoglossus, there is obviously every reason to suppose that the absence of circular muscles is also a secondary loss. Such considerations as the above are adduced for the purpose of proving that Ptychodera (Chlamydothoraz) is the most primitive and Balanoglossus the least primitive type of Enteropneusta. IV. Peripatus. Last year I obtained thirteen specimens of a species of Peripatus in New Britain, which constitutes a new (Melanesian) type equivalent to the types represented respectively by the Neotropical, Australasian and Ethiopian species. In the position of the generative orifice behind the last pair of legs it resembles the Cape species, in the absence of crural glands it resembles the New Zealand species, while the facts that the males have a less number of claw-bearing legs than the females (22 pairs in the former and 24 in the latter) and that embryos in all stages 1 Q. J. M.8., Vol. xu. p. 623. 2 Mem. Austral. Mus. 11. Pt. 5. 1897. p. 335. 1898.] voyage to Melanesia during the years 1894—1897. 401 of development are to be found in the uteri of one female, indicate a very striking correspondence with the Neotropical species. The embryos are provided with a large ectodermic trophoblastic organ apparently formed by the dilatation of the primary body- cavity. Of the thirteen specimens only two were males, but the examination of the older embryos taken from the larger females showed that the number of legs in the respective sexes was con- stant. It is probable that the embyros of this species will throw a side-light on the “placental” development of the Neotropical species as described by Kenmel. Monday, 21 February, 1898. Mr F. DARWIN, PRESIDENT, IN THE CHAIR. The following communications were made to the Society : (1) On some differential equations in the theory of symmetric algebra. By Professor FORSYTH. This paper is printed in the Transactions, Vol. xvi. Part iv. (2) The Discharge of Electrification by Ultra-violet Light. By E. RurHerrorp, M.A., B.Sc., 1851 Exhibition Scholar New Zealand University, and Coutts Trotter Student, Trinity College, Cambridge. The general action of ultra-violet light on the discharge of electrification has been investigated by many different experi- menters. Hertz’ in 1887 first drew attention to the action of ultra-violet light on a spark gap. Wiedemann and Ebert? showed that the kathode was the seat of this action and investigated the general effect on high potential discharges. Hallwachs*® and Righi‘ observed the fact that zinc and other metals became positively electrified under the action of ultra-violet light. These results were extended by Elster and Geitel®, who have published a series of papers on the effect of ultra-violet light in causing discharge under various conditions and have also® investigated 1 Wied. Annal. xxx1. p. 983. 1887. 2 Wied. Annal. xxx. p. 241. 1888. 3 Phil. Mag. xxvi. p. 78. 1888. 4 Phil. Mag. xxv. p. 314. 1888. 5 Wied. Annal, xxxvitt. p. 40, xxxvill. p. 497, xxx1x. p. 332, xu1. pp. 162, 166, Lit. p. 433, Lv. p. 684. 6 Wied, Annal. xu. p. 166. 1890. 402 Mr Rutherford, The Discharge of [Feb. 21, the action of a magnetic field on the discharge at low pressures. Stoletow? investigated in detail the relation between the current and electromotive force for the discharge at low voltages and at different pressures. Most of these papers have dealt with the general character of the discharge, but the subject of the nature of the conduction and of the carrier that discharges the electrification has not been specially attacked. In a very interesting paper Lenard and Wolff? investigated the effect of a surface, on which ultra-violet light fell, on the condensation of a steam jet in the neighbourhood, and their results led them to the conclusion that many bodies were disintegrated under the action of ultra-violet light and that the particles torn off became nuclei for the condensation of the steam jet. In the light of more recent experiments these results are however capable of other interpretations. R. v. Helmholtz? has shown that a steam jet is acted on when chemical action is going on in its neighbourhood. Richarz* has shown that Réntgen rays produce condensation in a steam jet, and Wilson® has recently observed that ions produced under the action of Uranium and Rontgen radiation become under certain conditions nuclei for the condensation of water around them. He has also demonstrated the important fact, which appears to have been overlooked, that ultra-violet light produces clouds in ordinary moist air quite independent of any solid body in its neighbourhood. The presence of this effect must have complicated the effects of Lenard and Wolff, and the more general results on the properties of ions in producing condensation seem to show that possibly their results may be ascribed to the presence of free gaseous ions rather than disintegrated particles of metal. It is the object of this communication to give results of investigations on the nature of the carriers of the negative electrification produced under the action of ultra-violet light, and to show that probably the greater part of the electrification is carried by gaseous ions produced at the surface of the negatively electrified plate. In order to obtain a discharge with ultra-violet light, the light must fall on a negatively electrified surface. There is no discharge produced by allowing the light to fall between two plates without impinging on either. In this respect the action of ultra-violet light is very different to Roéntgen and Uranium radiation, which produce a volume ionisation of the gas through 1 Journal de Russ. Phys. xx1. 1889. Journal de Physique, 1x. p. 468. 1890. 2 Wied. Annal. xxxvu. p. 443. 1888. 3 Wied. Annal. xxxu1. p.1. 1887. xu. p.161. 1890. 4 Wied. Annal. urx. p. 592. 1896. 5 Camb. Philos. Soc. Vol. 1x. Pt. vii. 1897. 1898. ] Electrification by Ultra-violet Light. 403 which they pass. The question whether there is any volume ionisation of a gas through which ultra-violet: light passes was investigated by Henry’ who tried the vapours of iodine and methyl iodide both of which are very powerful conductors under Réntgen rays but with a negative result. The result of Wilson that a cloud is formed in moist air with strong ultra-violet light renders it possible that there is a slight volume ionisation of the gas through which the light passes, but the effect appears to be too small to be determined by electrical means, and in all later experiments it is assumed that the surface of the negatively charged plate is the seat of the action of the ultra-violet light discharge. If we allow ultra-violet light to fall on a negatively electrified surface, e.g. a polished zinc plate, since the body is slowly dis- charged, it seems probable that if the discharge is due to the convection of the charged particles, these charged particles can be blown away by directing a sufficiently rapid blast of air across their path. This has been experimentally shown by Zeleny?, who showed that a negatively charged gas can be obtained by blowing past the negatively charged plate when the ultra-violet light was acting. This gas has similar properties to the charged gas? obtained by the separation of ions in Réntgen ionisation, for they readily give up their charge and refuse to pass through a plug of cotton-wool: I had independently observed the same fact, and had also investigated the effects of blowing currents of air by electrodes, especially from the point of view of determining the velocity of the carrier of electricity. Before entering on the general results it is necessary to draw attention to the phenomena observed by Blondlot and Bichat?. They found that if an insulated zinc plate was acted on by ultra- violet light, when all the conductors in the neighbourhood were connected to earth, the potential to which it could be raised was increased 6 or 7 times by allowing a blast of air to impinge on the plate. They found that this action was independent of dust and moisture. It is.easy in this way to raise the potential of a plate of amalgamated zinc to 15 volts in a few minutes, although the potential to which it could be raised under the action of the light alone was less than 2 volts. I have also found that the rate of leak of a body charged negatively is much more rapid when a blast of dust-free air is directed against it. A plate of polished zinc, charged to — 8 volts, 1 Proc. Camb. Phil. Soc. Vol. 1x. Pt. v1. 1897. 2 Phil. Mag. March, 1898. 3 Rutherford. Phil. Mag. April, 1897. 4 ¢. R. xvi. p. 29. 1888, 404 Mr Rutherford, The Discharge of [Feb. 21, placed at a distance of 10cm. from a neighbouring plate gave a rate of leak 12 times as fast as under the action of the ultra- violet light alone. The blast seems to assist the electromotive force in removing the negative charge. The presence of this action must be taken into account in all cases where currents of air impinge on negatively electrified surfaces. The following figure (Fig. 1) shows the general arrangement WS LZ g a NS EaArTA | | | of the experiment to show the effect of blowing a current of air by a negatively electrified plate on which ultra-violet light is allowed to fall. A blast of air from a bellows or a gasometer passed between two parallel plane electrodes B and C, and then through an in- sulated aluminium cylinder 7. The air before reaching the plates was free from dust as far as possible by passing through a bulb G tightly packed with cotton-wool. An are light A was used as a source of ultra-violet light. The light after passing through a quartz plate Q, which covered an opening in a metal screen LI surrounding the arc, passed through a second quartz plate Q,, through the fine wire-gauze B and then impinged on the metal plate C, which was generally of polished or amalgamated zine. The broken lines show the position of insulators by which the gauze B, the plate C, and the tube 7’ were all insulated from one another. An insulated wire W passed centrally down the tube T. In a particular experiment the plate C was 42 cms. long, 1-5 cms. wide and ‘8 cm. from the gauze B. Since the area of the rectangular orifice through which the air passed was only 1:2 sq. ems., velocities of the air of 300 or 400 cms. per sec. could be readily obtained. Fic. 1. eo. = TR il nie ot te 1898.] Electrification by Ultra-violet Light. 405 Experiment 1. C was connected to the negative pole of a battery of 8 volts, the other pole being connected to earth. The gauze B was connected to one pair of quadrants of an electrometer, the other pair being connected to earth. All other parts of the apparatus were earthed. When the arc light was acting the plate C lost a negative charge which passed over to the gauze B and the electro- meter needle showed a movement corresponding to 60 divs. per min. When a rapid current of air was directed between the plates, the leak to the electrometer was completely stopped. This showed that the carriers of the negative charge, which had left C, had been blown out by the rapid current of air. If C was charged to —24 volts the rate of leak from C cor- responded to 170 divs. per min., but where the blast was in action the rate of leak was reduced to 8 divs. per min., or less than 54, of the charge which escaped from C reached the gauze B; when CU was charged to higher voltages and the blast kept in action, a still greater proportion of the charged particles reached the gauze without being blown out. The number of carriers that reached the gauze could be raised or lowered by diminishing or increasing the velocity of the blast, the other conditions remaining the same. Experiment 2. We have seen that a whole or part of the charged carriers can be prevented from reaching the gauze B. It is now necessary to show what becomes of the carriers after being blown out from between the plates. The plate C was charged to — 24 volts and the gauze connected to earth. The aluminium cylinder 7’ was connected to one pole of a battery of 30 volts, and the wire W connected to the electrometer. There was no deflection of the electrometer if the arc alone was acting. If 7’ was charged nega- tively, then when a current of air was sent between the plates the wire W became charged negatively. If 7’ was charged posi- tively there was no appreciable leak to W. This shows that a negatively charged gas has passed into the cylinder which in the first case lost its charge to the central wire and in the other to the tube 7. A very convenient means of testing the whole charge conveyed with the current of air is to place a plug of cotton-wool inside the tube, which has the property of completely discharging the electrification carried with the air. 406 Mr Rutherford, The Discharge of [Feb. 21, Experiment 3. Discharging power of a metal tube. If the aluminium tube 7 which was 30cm. long and 1:1 cm. diameter was connected to the electrometer and the central wire removed, it was found that the gas gave up part of its charge to the tube in its passage along it. In an experiment where the velocity of the air along the tube was about 150 cm. per sec., 4 of the gas was discharged in passing along the tube. Since the electrified particles tend to repel one another to the side such a discharge is to be expected. If the volume density of the electrification were uniform over the cross section of the tube, an experiment of this kind on the discharging power would allow us to calculate the velocity with which the carrier moves under its own repulsion, but this condition is here not fulfilled. Experiment 4. All the electrification blown out between the electrodes C and B can be collected. In one experiment the rate of leak of C was observed with the blast in action. Part (1) of the charge which left C was given up to the gauze B, a part (2) was discharged on the tube 7’ and the part (3) which escaped was caught in a cotton- wool collector. The sums of the rates of leak to (1), (2) and (3) were found to be very nearly equal to the rate of leak of C. Velocity of the Carrer. The general experiments on the effects of a current of air between two electrodes when the ultra-violet light is acting may be simply explained by supposing that the negatively charged particles, which escape from the surface C, travel towards the gauze B with a velocity proportional to the electromotive force between the two plates. Let u= velocity of the charged particle for a potential gradient of 1 volt per cm., d= distance between the plates, 1 =length of the plates, y = difference of potential in volts between the plates. The time ¢ taken for the carrier to pass from one plate to the other is therefore given by 1898. ] Electrification by Ultra-violet Light. 407 Now if P=velocity of blast, the time ¢, taken for the current of air to pass between the electrodes is given by t = P . Assuming that the velocity of the air blast is constant over the cross section of the plates, if ¢, is less than ¢ none of the charged carriers which leave C can reach the gauze B, but they will be all blown out with the current of air. We may suppose the carrier describes a diagonal path between the plates due to the resultant of the two impressed velocities at right angles to each other, and unless this diagonal path cuts the gauze B the carrier will escape. Let AB, CD (Fig. 2) be the two plates. Suppose the carriers to be produced uniformly along CD by the action of ultra-violet light. A carrier starting from C' travels along the diagonal path CL and gives up its charge to the plate AB. Draw BP parallel to LC, meeting CD at P. We see that a carrier starting from P A iL B ye yee is —_ oa ue : a t ” a Pod Cc P D Fie. 2. will just reach B. All carriers starting from the right of P will not reach AB but will be carried out by the current, while those to the left of P will give up their charges to AB. The ratio p of the number of carriers blown out to the total number that leave CD is given by PD oD” the distance PD=P .t, where ¢ is the time taken for the carrier to cross over between the plates ; Cp. The ratio p is determined experimentally and P can be measured, therefore the value of u can be at once obtained. 408 Mr Rutherford, The Discharge of [Feb. 21, Experiments performed in this way give a value of the velocity of the carrier at normal pressure of about 1°5 cm. per sec. for a potential gradient of 1 volt per cm. This method is however probably not capable of accuracy, on account of the variation of the velocity of the air across the cross section of the plates and accidental disturbances due to the violent eddying motion of the air when velocities of the order of 300 or 400 cm. per sec. are used. The method is also practically restricted to the case of air on account of the large amount of gas required for an experiment, so that I was led to devise a more general and satisfactory method of determining the velocity of the carrier. In Fig. 3 the general arrangement is shown: a glass bell-jar j RQ a eae Se eT ree | 414 Fie. 3. was fixed on a base plate CD of zinc through which a circular opening HF was cut. In the top of the vessel there was fixed an ebonite stopper through which passed a rod L carrying at one end a polished metal plate AB. This plate AB was fixed to a ball-and-socket joint, and could be levelled by screws passing 1898.] Electrification by Ultra-violet Light. 409 through a plate fixed to the rod. The plate AB could be raised or lowered from the outside of the vessel by a screw. The bell- jar was fitted down to the base plate with sealing-wax, and the whole was placed on insulating blocks over a source of ultra-violet light S, which was either an arc light or a spark gap. The ultra- violet light first passed through a quartz plate Q,, fixed over an opening in a large metal screen, then through the quartz plate Q, covering the opening /F, and then fell on the metal plate AB. The wire-gauze performed the double function of allowing part of the light to pass through and yet acting electrically as a plane metal surface. The plate AB was generally of polished zinc and was accurately levelled to the base plate. A delivery tube 7’ was let into the base plate and the whole vessel was made air-tight to allow of exhaustion. In order to determine the velocity of the carrier, the rod L which was insulated by means of the ebonite stopper was con- nected to one pair of quadrants of the electrometer by the wire M, the other pair being to earth. The base plate CD was then connected to one terminal of a 100 volt transformer, worked from the town mains, the other terminal of which was connected to earth. When the base plate is charged positively, the plate AB is charged negatively by induction, and the negative carriers, set free under the action of the ultra-violet light, start travelling towards the base plate under the influence of the electromotive force acting between the two plates. If the plate AB is close to CD, a large number of the carriers are able to reach CD and give up their charge before the electromotive force is reversed. All the carriers distributed between the plates at the instant of reversal travel back to the top plate, and since the top plate is charged positively by induction no more carriers are produced during that half alternation. Experimentally it was found that there was no leak to the top plate when the base plate was negatively charged and the ultra-violet light was in action. We see therefore that when the plates are close together the plate AB loses a negative charge. This rate of leak will evidently decrease as the distance between the plates is increased, until a certain distance is reached, when the plate AB shows no loss of charge, although the ultra-violet light and alternating E.M.F. are both acting. When the plate is at this distance the first carriers liberated when AB becomes negative by induction are able to travel nearly to the base plate, but before any can give up their charge, the E.M.F. is reversed and they travel back to the plate from which they came. All distances greater than this give us no rate of leak, but it is the object of the experiment to determine the shortest distance between the plates for which AB shows no loss of charge. This point is in general fairly sharply defined, as 410 Mr Rutherford, The Discharge of [Feb. 21, the table below shows, which gives the rate of leak at different distances from the base plate. Turns of Screw aces ae ea 1 turn off scale 3 290 divn. 5 220 7 120 8 35 9 2 9:5 0 9 turns of the screw is approximately the shortest distance between the plates for which the loss of charge is negligible, and the numbers show how rapid is the decrease of deflection between 7 and 9 turns. Let w= velocity of the carrier for a potential gradient of one volt per cm. d=shortest distance between the plates for which the leak of AB is zero. T = time of complete alternation of the transformer. It is assumed that the E.M.F. at any time of the alternation is given by #,sin 27 a , where #, is the maximum value of the alternating E.M.F. The distance dz traversed by an ion in the time dt is given by ps Bed ee Bae d a Now the distance passed over by the carriers which first set out is equal to d in the time = : 1898. ] Electrification by Ultra-violet Light. 411 ‘, integrating both sides we obtain or i The distance d is determined experimentally, and /, and 7 are constants of the transformer circuit, so that wis known. Since the electrometer circuit is insulated before the E.M.F. is applied to the lower plate, the true potential difference between the top and base plate is less than the potential of the lower plate on account of the induction effect between the two plates. In consequence of the rapidity of the alternations the electrometer needle shows no movement due to the induction effect, so that it is necessary to determine the correction to be applied when the needle of the electrometer remains at rest. This may be simply done as follows : The two quadrants of the electrometer are insulated from each other, and then a steady E.M.F. is applied to the base plate. The electrometer needle is deflected, but is brought back to its original position by applying a suitable E.M.F. to the other pair of quad- rants. Let r be the ratio of the applied potential to the potential V of the base plate. The potential of the electrometer circuit 1s rV and the true difference of potential between the plates is (l—-r)V. The correction is thus made by putting (1 — 7) #, instead of E, in the equation that determines the velocity. The following is an example of a determination of the velocity of an air ion travelling through air, d=‘8cm., T = 4, sec. Reading of alternating voltmeter 95, the maximum value of the E.M.F. 4, is therefore given by II Wes GOT «hen. “= ET 1:37. The correction for induction between the plates was 5 per cent., so that the final value is wu = 1:44 cm. per sec. A large number of determinations have been made for the velocity of the air ion, and the mean of the results gives a velocity of about 1°45 cm. per sec. 412 Mr Rutherford, The Discharge of [Feb. 21, In these experiments two sources of ultra-violet light have been used, viz. an arc lamp and a spark between two zinc terminals. For the spark two large Leyden jars were charged up by a Rumkhorff coil and discharged through a spark gap of about ‘8cms. In order to get rid of electrostatic effects, the jars, coil, and spark gap were all placed inside a metal tank connected to earth. The opening above the sparking terminals was tightly closed by a quartz plate, on both sides of which fine wire-gauze, connected to earth, was stretched. This arrangement was found to screen thoroughly from electrostatic disturbances. For experiments on the velocity of the carrier the are light is not nearly so satisfactory a source of ultra-violet rays as the spark discharge. The arc as a rule gives out more intense radiation but it has the drawback of rapidly raising the tempera- ture of the plates and of the adjacent air. In consequence of this the velocity of the carrier is changed, and the determination of the least distance of no appreciable loss of charge cannot be made with certainty. In this respect the spark light is far more satisfactory and it is alsoa more constant source of rays, but it has the disadvantage of being an intermittent source of light. A source of error in the determination of the velocity, which is difficult to avoid, lies in the irregularity of the E.M.F. from the town supply. During the daytime, the load on the machines was light, and there were often rapid alterations in the E.M.F. and period of the alternations. Another source of error also lies in the assumption that the electromotive force curve of the alternator is a sine curve. It is mtended to continue these experiments and to use instead of the transformer an alternating electromotive force produced by reversing the sign of a steady E.M.F. by means of a suitable revolving commutator. It is hoped in that way to obtain a very accurate value of the velocity under varying condi- tions of pressure and temperature. Effects of different metals. If the theory that the discharge of electrification is due to the disintegration of negatively charged particles is true, we should expect to obtain different velocities of the carrier according to the metal on which the ultra-violet light falls. This point was tested by replacing the zine plates by similar sized plates of aluminium, lead, copper, amalgamated zinc and a zine plate covered with mercury sodium amalgam. Although there were differences in the rate of leak of these metals due to their different degrees of sensitiveness to ultra-violet light, it was found that the distance of no loss of charge was nearly the same in each ease. The are light was used for this series of experiments, and allowing 1898. | Electrification by Ultra-violet Light. 413 for errors of experiments it seems to be true that the velocity of the carrier is independent of the metal on which the light falls. This seems to show that the carrier is produced from the gas near the plate and not from the metal itself. Effect of electromotive force. The velocity of the carrier, i.e. the velocity for a potential gradient of one volt per cm. is independent of the potential of the surface from which the carrier sets out. Experiments were also made to determine the value of the velocity for different values of the E.M.F. To test this the ultra- violet light from an are was allowed to shine through a wire- - gauze on to a metal plate which was much larger than in the experiments in the bell-jar. By using a suitable transformer, potential differences, which were measured by a Thomson’s Multi- cellular Voltmeter, of 365 and 700 volts beside the usual 95 volts were obtained. Voltage | d | Correction for induction | 95 volts | ‘T75 cms. 14 per cent. BOD Fs. | oe les Ol. 700. , BOT 5; (ero When the corrections for induction are made, the radius of the velocities obtained for unit potential gradient are | Voltage Velocity | | i [Pye echipsey |W Rahs a as | | he hee3) sash de arte | 700 | 1:33 | We see from the above table the velocities are very approxi- mately proportional to the electromotive intensity between the VORA 1X. PIS Vill. 34 414 Mr Rutherford, The Discharge of [Feb. 21, plates. The actual velocity of the carrier when the »M.F. was 700 volts was 450 cms. per sec. From considerations based on the kinetic theory of gases it can readily be shown that a carrier of molecular dimensions carrying an atomic charge attains a limiting velocity in a uniform field after a very short interval of time and it then moves uni- formly. No correction therefore need be made for the interval that elapses before the carrier reaches its limiting velocity. Effect of pressure on the velocity of the carriers. The effect of pressure on the velocity was investigated by means of the apparatus shown in Fig. 3. The following table shows the results obtained for air : Pressure Velocity 765 mm. 1:4 cm. 323 3°36 162 73 140 78 95 Lites 58 203 34 33°6 These results show that down to a pressure of 34 mm. the velocity of the carrier is inversely proportional to the pressure. As Stoletow has shown, it was found that the rate of leak fora given E.M.F. increased with the diminution of pressure so that the results were capable of fair accuracy even at low pressures. The plates were never separated by more than 1°5 cm. but the electromotive force employed was much smaller for the lower pressures. In the experiment for the pressure of 34 mm. only 7 of the voltage of the transformer was used. If the law that the velocity is inversely proportional to the pressure holds for low pressures at a pressure of 1 mm. with a potential gradient of 1000 volts per cm. the carrier would travel with a velocity of 1-4 x 760 x 1000 = 108 cms. per sec. 1898. ] Electrification by Ultra-violet Lnght. 415 These experiments on the variation of the velocity with the pressure afford very strong evidence that the carrier of the charge is of molecular dimensions. According to the kinetic theory of gases the velocity of a charged particle of molecular dimensions varies inversely as the pressure’. If however the particle is large compared with a molecule, the velocity of the carrier is dependent only on the viscosity of the gas which is independent of the pressure within limits. The conclusion to be drawn from these results is that the carriers must be very small and comparable in size with a molecule. Many of the interesting results of Stoletow® on the relation between the current and the E.M.F. for different pressures on ultra-violet light conduction can be generally explained on the hypothesis that the rate of production of the carriers is a function of the pressure, and that the rate of escape of the negative ions is dependent on the velocity of the carrier. It is not my intention here to enter into a detailed discussion of his valuable results but the fact that the current through the gas at very low pressures (about ‘002 mm.) is independent of the pressure seems to show that either there is a slight disintegration of the electrodes by ultra-violet light or that the presence of mercury vapour is responsible for the action. Velocity in different gases. The velocity of the carrier depends on the gas surrounding the plates. Hydrogen and carbonic acid were used and were well dried before passing into the apparatus. Gas Velocity | Ratio, Air—1 Atay oS Aekrsisttwsce 1-4 1 Hydrogen. ........ 3°9 2°8 Carbonic acid .. ‘78 56 These results were obtained with the use of the arc ight when the heating of the gas prevented the velocities being obtained with as much accuracy as desired. The hydrogen ion in hydrogen 1 J.J.Thomson. Brit. Assoc. Report, 1894. 2 Journ. de Phys. 1x. p. 468. 1890. 34—2 416 Mr Rutherford, The Discharge of Electrification etc. [Feb. 21, travels nearly three times as fast as the air ion im air, and 5 times as fast as the carbonic acid ion in carbonic acid. It has been shown that the carriers which are produced under the action of ultra-violet light have very similar properties to the ions which are produced by Réntgen radiation. It is also an interesting result that the velocity of the air ion m Rontgen conduction is not very different from that obtained in ultra-violet light conduction. In a previous paper’ it has been shown that the sums of the velocities of the positive and negative ions in air, hydrogen and carbonic acid are 3:2, 10-4 and 2:15 cms. respectively. Assuming for the purpose of comparison that the velocities of the positive and negative ions are equal, the table below shows the relative values of the velocities for the negative ions: Velocity in | Velocity in Ul- Gas Roéntgen tra-violet light Conduction Conduction SANG UR eae i tert 1:6 cms. 1-4 Hydrogen ...... Oy 3°9 Carbonic acid ...| UO ee 78 = = — Considering the widely different methods used for the deter- mination of the velocities in the two cases, the comparative agreement shows that possibly the carrier is the same in the two cases or in any case not greatly different. The results obtained in this paper seem to show that the gas near the surface of the negatively electrified plate is ionised under the action of ultra-violet light. The positive ion gives up its charge to the plate and the negative ion is repelled from the plate. This ion travels through air at normal pressure and tem- perature with a velocity of about 1-4 cms. per sec. for a potential gradient of one volt per cm. The velocity of the ion varies in- versely as the pressure and is different for different gases. It is intended to continue these investigations on the velocity of the ions and on the general phenomena of ultra-violet light conduction. ! Phil. Mag. Nov. 1897. CAVENDISH LABORATORY, Feb, 21, 1898. 1898.] Messrs Heycock & Neville, Rontgen photographs. 417 (8) Rontgen photographs of metallic alloys. By Mr C. T. Heycock and Mr F. H. Neville. The authors exhibited and described photographs taken by means of the Réntgen rays through plates of alloy. As the two metals forming the alloy possess different degrees of transparency to these rays the photographs show the separation of the metals that has taken place during the solidification of the alloy. For example, alloys of gold and sodium containing less than 30 per cent. of gold are seen to consist of well-developed, very transparent crystals, which must be pure or nearly pure sodium, imbedded in a mother substance which solidified last, and which from its com- parative opacity evidently contains the gold. On the other hand, alloys containing more gold show very opaque needles of gold im- bedded in a less opaque mother substance. This mother substance was the same as that in the first-mentioned alloy; it solidified after the needles of gold had been formed. Photographs of alloys of aluminium and gold and of aluminium and copper were shown which exhibited similar phenomena. The crystals of aluminium in the alloy with copper were perfect rectangular crosses several millimetres in diameter. The gold-aluminium alloys showed a precipitate of Roberts-Austen’s compound of the formula AuAl, ; the crystals were well-marked cubes and octahedra. Monpay, 7 March, 1898. PROFESSOR NEWTON, VICE-PRESIDENT, IN THE CHAIR. The following Communications were made to the Society :— The Coral Reefs of Funafuti, Rotwma and Fiji together with some Notes on the Structure and Formation of Coral Reefs in general. By J. STANLEY GARDINER, M.A., Gonville and Caius College, Cambridge. INTRODUCTION. HAvING been enabled by means of a grant from the “Balfour Fund” to join the “Coral Reef Boring Expedition” to Funafuti, I had the pleasure of spending upwards of three months on that atoll with Prof. Sollas, who suggested to me the propriety of comparing its reefs with those of Fiji and other islands in the vicinity. To Prof. Sollas I am under deep obligations, and any value that my observations may have is largely due to him. 418 Mr Gardiner, The Coral Reefs of [Mar. 7, I am also much indebted to Capt. Field and the officers of H.M.S. Penguin for their great courtesy and assistance at all times. Returning to Fiji in the middle of August, I left in the Penguin at the end of the month for Rotuma, where I remained until the middle of December. Here I was much beholden to Mr Leefe, the Resident Commissioner, for his assistance and especially for the loan of his boat and crew. Coming back to Fiji the second time, after a tour round Ovalau, I proceeded along the north coast of Viti Levu to Nathilau. Crossing from there to the Rewa river, I obtained two canoes and in five days reached Suva, where I remained for some days, making excursions to the Navua river, the Mbenga barrier reef and into the neighbouring country. I then spent a fortnight in Wakaya on the kind invitation of Capt. Langdale, late R.N. Having received from the Hon. J. Stewart, Colonial Secretary, an offer of a passage round the Lau Group in the government 8.S. Clyde, I gladly accepted, visiting the Exploring Group, Lakemba, Fulanga, Ongea, Namuka and Kambara. On returning I went to Taviuni, where I spent a fortnight, riding or walking round the greater part of that island. Ratu Lala, the native chief, then sent me in his whaleboat to Rambi and on to Lambasa, which we reached in four days. I next crossed to Nateva Bay, down which I proceeded, partially by canoe, and reached Savu-Savu Bay on the third day, whence I proceeded to Levuka, where I obtained ship to Sydney. In Fiji I was greatly assisted by Capt. W. W. Wilson, Harbour Master of Levuka, who took the Clyde round the Lau Group especially to help and direct me. As Capt. Wilson probably knows more than any man living about the reefs and anchorages in the Central Pacific, and most generously placed freely at my disposal his journals and the mass of imformation he has collected, I cannot sufficiently express my indebtedness to him. I wish also to express my thanks to the Hon. W. L. Allardyce, Native Commissioner; Mr Berry, Commissioner of Works; Mr Turner, Chief of Customs, Levuka; Capt. Langdale, late R.N.; the late Capt. Puttnam; Ratu Lala; Mr C. Thomas; Mr W. Reay; Mr W. Chalmers and many others for their hospitality and aid. In England I am under great obligations to Prof. Newton, Mr Adam Sedgwick, Mr W. Bateson, Mr A. C. Seward and especially to Prof. Hickson, for their encouragement and counsel. In particular I must thank Mr J. J. Lister for much valuable criticism and advice. 1898.] Funafuti, Rotuma and Fiji. 419 CONTENTS. Part LI. The Atoll of Funafuti. Part II. Rotuma. Part III. The Reefs of Fiji. Part IV. The Raised Reefs of Fiji. Section 1. Viti Levu. Section 2. The Lau Group. Section 38. Summary and Conclusions. Part V. Special Features in the Natural History of Corals. Section 1. The Structure of a Reef. Section 2. The Bathymetrical Limits of Coral Growth. Section 3. The Food of Corals. Section 4. Conditions affecting the Growth of Coral Reefs. Section 5. The Rate of Growth of Corals. Part VI. The Formation of Coral Reefs. PART L THE ATOLL OF FUNAFUTI. THE atoll of Funafuti was chosen as a typical atoll by the Coral Reef Boring Committee of the Royal Society in 1896. It belongs to the Ellice islands, which he to the north of the Fiji Group, and extend in a broad line from lat. 11° S. to lat. 5° 30’S., running almost north-north-west and south-south-east. In the same line to the north at a distance of about 150 miles lie the Gilbert islands, which are themselves continued north by the Radack and Ralick chains of the Marshall islands. All are of coral origin and many of atoll form. In the bathymetrical charts, published in the Report of the Challenger Expedition, the Ellice islands are seen to lie on a plateau of about 1500 fathoms with the Fijian, Tongan and Samoan Groups, the whole in a deep of over 2000 fathoms. The soundings of Captain Field, H.M.S. Penguin, in 1896 proved, however, that the Ellice islands are separated from this plateau by depths of over 2000 fathoms, and showed also that Funafuti rises as an isolated reef in this deep. Further soundings of the Penguin by Nui, Nukulailai and towards Nukufetau from Funafuti indicate that these atolls probably rise in a similar manner so 420 Mr Gardiner, The Coral Reefs of [ Mar. 7, that there appear to be in the Ellice Group a number of isolated islands rising separately from a depth of over 2000 fathoms. The atoll of Funafuti (Fig. 1) has a lagoon 12 miles long by 8 miles broad, lying almost north and south. It is of a roughly oval shape, extending south into a “pocket” about 3 miles deep, much of the bed of which is uncovered at low tides. Round this lagoon is a more or less continuous reef, varying in breadth from + to 4 a mile in accordance largely with the portion, which has been turned into land. On the east side is an island 64 miles long, continued north by two more small islands, Amatuku and Mulitefala, with narrow breaks in the land between; this main island bends to the westward about 2 miles from its south end. Continuing it to the south-west are three other islands, Fatata, Funangongo and Funamanu, jomed to one another and to the main island by the reef, which can easily be crossed at low tide. The next island to the west, Falefatu, is separated from these by a broad ship’s channel with a minimum depth of four fathoms ; on the west side of this island there is another similar channel with a depth of five fathoms. The reef is here continued into the “pocket,” which extends about 34 miles to the south, and is largely surrounded by land. On the west side of the atoll the reef is very broad, nevertheless it has only a few small islands. To the north-west is another broad ship’s channel through the reef with a minimum depth of 44 fathoms. On the west side there are also three channels of 4 fathoms and two narrow some- what tortuous passages of 11 and 23 fathoms. The north side of the lagoon has two small islands, Fualifeke and Pava, but while surrounded by the reef has otherwise no land. The direction of the wind from March to November is from the east-south-east, veering completely round in the three summer months, December, January and February, to the west-north- west; but while the easterly wind is steady during the greater part of the year, the westerly wind in the summer is more irregular and less strong with considerable periods of calm. The current is due probably entirely to the wind and accordingly comes from the same direction; I was informed, however, by several trading captains in Fiji that the set in the summer months westward is never very great and in calms is lost, giving place to a slow set eastwards. In agreement with the wind the reef is, save for the two ship’s channels to the south, continuous round the east and south sides of the atoll and largely converted into land. The “pocket,” the projecting southern horn of the atoll, is exposed fully to the south and east and is almost completely surrounded by land. The flood tide into the lagoon sets in strongly through the ship’s channels; but at the same time a large amount of water is received from the breaking of the sea over the reefs 1898. ] Funafuti, Rotuma and Fiji. 421 WH Pocket”: FUNAFUTI ATOLL F LG. 1. 422 Mr Gardiner, The Coral Reefs of [Mar. 7, between the different islands. The ebb tide, however, can receive little assistance by the sea water of the lagoon escaping in this way, so that the out-going currents are much stronger; for some time indeed after low tide there is still a noticeable current outwards in these channels. The current too in the southerly channels naturally sets in stronger, and goes out weaker than in the westerly ones, as it is to some extent the resultant of the forces of the tidal and wind currents. The islands on the reef are generally covered with loose blocks of reef-rock between which coconut and other trees have taken root; in most places there is little or no soil. In some parts the surface shows a flat platform of hard rock with scanty, or no vegetation ; the largest lies in the middle of Fualifeke, and there is another on Funafara to the east of the “pocket.” Usually the presence of this flat smooth platform is concealed by boulders, among which the trees grow, but I found it existing very generally on all the islands to the south of the atoll, and by the sides of the “pocket.” To the east such a flat does not exist, the whole surface seeming simply to be a mass of loose blocks, the skeletons of different species of corals and masses of reef-rock. The breadth of the islands varies from 50—3800 yards, but of course at their ends they narrow down to mere ridges; their general breadth is scarcely more than 120 yards. The main island in its extreme eastern part is considerably broader than any of the other islands of the atoll, by the village being about 600 yards across. Here there is, however, for the greater part of the breadth on the lagoon side a deep sandy soil, formed of the ordinary beach sand, which is found in the lagoon in the vicinity, mixed with a certain amount of mould from the vegetation, which grows especially luxuriantly on it. Here too there is what Professor Sollas has called the “mangrove swamp,” a bare area in the middle of this part of the island, covered with water at high tide; to it the sea gains access from the seaward face of the atoll through three tunnels at its northern end. Its south end is covered by a fine mud, varying up to 3 feet in depth, with boulders imbedded in it; these are often of large size and project in places above the surface of the mud. Partially imbedded in this mud Professor Sollas has traced a crescent-shaped’ ‘dead coral reef, constituted almost entirely of two species, one a massive Porites and the other Heliopora coerulea. For a great part of the day this floor les bare and dry, the frayed ends of the Heliopora standing like broken reeds 6 inches above its surface, and the great clumps of Porites forming a series of stepping stones of equal height. Neither of these corals stands long 1 Report on the Coral Reef at Funafuti. Nature, Vol. tv. 1897, p. 376. 1898.] Funafuti, Rotuma and Fiji. 423 exposure to the air; on Funafuti they require constant sub- mergence and we are thus led to regard their upper surface as marking what was at one time the level of low tide in the swamp.” The species of Porites, referred to, very closely resembles Porites arenosa (Esper), a very common species on the shoals in the lagoon; living Heliopora was only obtained once at Funafuti, and then from a depth of over 35 fathoms off the southern reefs of the atoll. The rest of the swamp is sparsely covered with mud, being formed of a hard consolidated rock, which closely resembles the rock forming the reef. North of the mangrove swamp is a marshy pool more or less filled with brackish water, and there are in the middle of the south end of the same island a number of such pools; they seem to me to be directly comparable to the “ barachois” of Diego Garcia’, described by Bourne. From the sea the mangrove swamp is separated by the “hurricane beach,” a structure which extends to some extent round the seaward face of all the islands, but varies considerably on account of the position of the islands in respect to the atoll, and possibly from other causes. It is the extreme edge of the land against which the sea, after passing over the reef, expends its force. The height of its summit above the sea level at high tide varies up to 7 feet, but a greater height than 4—5 feet is un- common. Its top is covered with boulders torn from the reef facing it, often much rounded and worn by the water. Near its summit this beach slopes down to the sea at an angle of about 30°, but towards its base, where it is washed by the tide, and formed of a hard consolidated coral-rock, it passes gradually into the flat reef. Its formation along the whole of the main island is precisely similar to the above, but in the islands to the south-east of the “pocket” there can scarcely be said to be any such beach at all, and the land is broken into, and in places partially submerged at spring tides. On the leeward side of the atoll generally this beach, or a sudden fall from the land to the high tide level, exists, but at its base the solid rock cannot be seen; instead the whole is covered by small rounded fragments of reef-rock, coral, shells, etc., forming in fact a pebbly beach. From the hurricane beach the land usually slopes towards the lagoon with a drop of two or three feet in a few yards, and then a very gradual slope. To windward of the atoll the islands on their lagoon sides have usually no sharp fall, the high-tide level at “springs” being marked by the extension of the vegetation. By the village, however, the wash on the sandy shore has caused a well-defined drop of one to two feet. To leeward of the atoll 1 «The Atoll of Diego Garcia and the Coral Formations of the Indian Ocean,” by G. C. Bourne. Proc. R. Soc. 1888, xi. p. 440. 424 Mr Gardiner, The Coral Reefs of (Mar. 7, there is a very distinct beach on the lagoon sides of the islands similar to the hurricane beach of the same islands. A hurricane beaeh, such as is found on the windward face of the atoll, could indubitably have been formed by masses of coral and reef-rock, thrown up by the waves, subsequently consolidating underneath by the deposition of carbonate of lime on the evapora- tion of the water at low tide, but under such circumstances the strata should dip towards the ocean, which piled up the fragments in the first place. The stratification is not generally visible, but at the ends of the islands, especially to the south-east of the atoll, it appears rather to be horizontal. At the north end of Amatuku there is a section clearly visible of a small cliff about 6 feet high; the strata are horizontal, but this island is here rather broad and the cliff stands well back from the sea, continuing for about 50 yards along the lagoon shore. The three islands, Funamanu, Funangongo and Fatato, have the hurricane beach much steeper than the main island; indeed the centre one, Funangongo, has towards the ocean a precipitous fall, in places almost a cliff, of 5 feet, succeeded by a steep boulder-covered beach. On the top it is not formed of a firmly consolidated rock, but of somewhat loosely aggregated blocks of coral and reef-rock; the extreme height here above high tide I measured at 6 feet. The action of the sea on the coast is plainly visible in fallen shrubs and trees, undermining the beach, and from the loose nature of the land above continually causing slips. The beach is strewn with boulders, which extend considerably below high tide level, and between tide marks these seem to be joining on to the rock below by the deposition of carbonate of lime on the evaporation of the water left on the beach, when the tide falls. On the islands lying north-east of the “pocket,” a somewhat similar hurricane beach is found, but it is not so steep; it is, however, consolidated to a higher level than in these islands, and the horizontal character of its strata is more distinctly visible. Under the hurricane beach on the windward side of the atoll there is an area, rarely more than 15 yards broad, of very rough, ragged rock with shallow pools of water here and there at low tide. Outside this is the flat of the reef and its raised outer edge; these latter parts vary on this face in combined width from 40— 80 yards. As I shall have occasion to refer to these zones constantly, I shall call them the rough zone, the reef-flat and the rim. The rock of all these three zones consists of a consolidated mass of the skeletons of corals and nullipores with shells, sand and the remains of various marine animals; it is exceedingly hard and rings to the hammer. On the surface where, exposed to the air between tide marks, it has time to dry, it is almost structureless to the unaided eye, but pieces, obtained from under 1898. ] Funafuti, Rotuma and Fr. 425 water by means of a chisel, show clearly its constituents. In the pools of the rough zone, referred to above, and on the reef-flat slabs may be here and there raised by a crowbar, used as a lever. These are found to have been fixed on to the rock below by means of the living bodies of Tunicata and Porifera, growing to both, while the spaces between them abound with Polychaeta Gephyrea, Mollusca and Echinodermata. These slabs, and indeed the solid rock elsewhere, are in most places much bored by worms, so that this formed perhaps my most prolific collecting ground for animals; a considerable amount of muddy sand, formed by these animals, under the rocks is a general feature. Some of these slabs have been but recently thrown into their present positions, and are being consolidated on to the rock below them. Many others, on the contrary, which could only be raised by breaking the rock itself, seemed to be due rather to the inwash of the sea, perhaps removing from under the harder coral, or nullipore remains, a layer of sandy or softer rock, which had formerly fixed them to the rock below. Probably both actions are going on at the same time, the former in the pools of the rough zone, lying immediately under the hurricane beach, and the latter on the reef-flat outside its limits. That the effect of this latter may in time be very considerable was indicated by the whole beach on the weather side, after a strong easterly gale, being to some extent strewn with slabs, which, on investigation, I found to have come from the reef-flat close to the rough zone. The ordinary range of the tide at springs is 64 feet. At high tide the hurricane beach at its base is covered with 4 feet of water; in the rough zone there is a fall of about one foot, and a sharp fall from this zone of one foot to the reef-flat. The reef-flat is itself hollowed out to some extent so that it usually has about 8 inches of water on it, but is at the same time cut off from the sea by the rim of the reef, which stands up about one foot above low tide. The outer edge is much broken up by fissures (Fig. 2), which often run for 20 yards or more straight into the reef: these are joined together to some extent by cross fissures, so that the rim at low tide appears to consist of a number of great more or less rectangular flat masses projecting 1—2 feet above the reef-flat. These are arranged so that there is a distinct edge running along fairly evenly, but there are outside this on the weather face of the atoll a number of similar masses extending outwards for 8—10 yards with a depth over them of 2—3 feet at low tide. These masses can be clearly seen at low springs, after the backwash which precedes a breaker, and form the proper edge of the reef. Off this line there is a sudden fall to a depth of 3—4 fathoms; in places, however, there is no such fall and no proper edge, but a succession of masses and buttresses at 426 Mr Gardiner, The Coral Reefs of [Mar. 7, greater depths further and further seawards. Such a succession was clearly visible off the south end of the “ pocket,” and in many places to windward a gradual slope, such as the above, was indicated by the waves breaking at considerable distances outside the rim. The fissures (Fig. 2) vary greatly in breadth and shape ; some are only a few inches broad while others are five or six _ yards. Their depth varies up to 3 fathoms, the average being at low tide about 14 fathoms where they run through the mm of the reef. In all, the edges overhang the sides considerably, and are very thin; indeed, the fissures seemed as if they were being enclosed by the edges growing out above and meeting one another, while the channel below was being kept open by the scour of the tide. In some the edges have absolutely met, and the presence of the fissure is merely indicated by one or more blowholes, out of which at low tide is driven a cloud of spray with each in-rushing wave. Although I carefully examined a number of these fissures after storms, I never saw any signs of their edges being broken, and I think that there is no doubt that the flat surface of the reef extends by their means. The blowholes can be found almost completely closed, and indeed every intermediate stage, from what might be termed a boat channel to the solid reef, formed in such a manner as I have suggested, can be seen (Fig. 2). At the bottom of these fissures a few small boulders often lie with a certain amount of sand around and between them. Occasionally the sides are found to approach one another, and even to have fused, cutting off from the fissures pools, which, when the tide recedes, are left full of water. At the edges of these fissures the reef shows a somewhat sharp rise of 1—14 feet from the reef-flat (Fig. 2, a). It is here much pitted on the surface and has a somewhat mammillated appearance; in the smaller pits Kchini live in large numbers, and crabs and other animals take refuge in them. Over the surface there grow small green seaweeds a few inches high, and a small - slate-coloured species of Zoanthus. Both of these might have to be carefully searched for, as generally nearly the whole is covered by white, grey, brick-red and dark green coloured in- crusting nullipores. The importance of these cannot be over- estimated; the lime they secrete is always very dense, and apparently structureless. Its thickness for a single plant is often very considerable, and nearly the whole reef at the rim I consider to have been formed by them. It is by means of the growth of these nullipores that the fissures are bridged, and indeed, by the use of the chisel, small spaces of a few mches in diameter can be easily found completely surrounded by these organisms. The reef-rock of the surface in this position, when broken into, shows no trace of a coral origin, but simply consists of the lime formed 1898. ] Funafuti, Rotuma and Fijt. 427 by these nullipores. Generally the horizontal thickness of the lime formed by each plant, as it were, does not seem to be very great while the total mass is enormous; the thickness of the lime of some large massive nullipores, obtained by the use of Priest- man’s grab outside the reef, was between 3 and 4 inches, but from the reef itself I never saw a nullipore with a greater thick- ness than 2 inches. What I have termed before the rim of the reef is really then an area 3—4 feet broad at the sides of these fissures, but facing the sea about 5 yards across. The waves break a short distance outside the rim and rush over it, or to some extent wet it every time they break; the water also rushes up the fissures, and so great is the momentum behind it, that it wells over their sides in every direction. The rim generally extends back all round the fissures, but from the ends of some, which run especially deeply into the reef, it is absent, these serving to take the return water, which is poured over the edges of the others, back to the sea. Between these several fissures, and between the rim and the rough zone under the hurricane beach, the reef-flat, before mentioned, lies. The surface of this zone is very flat and smooth and covered over completely in its outer parts by nullipores and other algae. Its level is such that at ordinary low tide the greater part of its surface is covered over by 8 inches to a foot of water; its level below the rim round even the most open fissures is also such that at the lowest spring tides most parts of it are concealed by a few inches. Nullipores do not thrive on it well, perhaps on account of the hot sun at low tide, and most of it is covered by small, delicate, filamentous algae, which give it a very smooth slippery surface. Holes in it a few inches to several feet below its general level occur, and in these and on its outer part a few species of corals are sparingly found. Of these Pocillopora and Stylophora are by far the most numerously represented, and in many parts were the only corals obtained from this area. The species of these genera represented were Pocillopora suf- fruticosu, P. brevicornis, P. clavaria, P. squarrosa, P. meandrina, P. glomerata, Stylophora palmata, S. pistillata, S. digitata and three species which I have named S. compressa, S. lobosa and S. rugosa. These grow for the most part in clumps, and in this situation are rarely more than 6—7 inches in diameter, while 3—4 inches with a height of 1—2 inches for the clump is more usual. Their distribution nowhere is such that they could for a moment be considered to have any effect practically on the growth of this part of the reef. The only other species of coral at all common was a Prionastraea, which was however very local in its distribution. The fissures for the reef present the most abundant signs of 4.28 Mr Gardiner, The Coral Reefs of [Mar. 7, coral life; their sides, where they do not overhang excessively, often have growths of Pocillopora grandis which markedly shows positive heliotropism, growing outwards at first from the sides and then straight towards the light. Their bottoms in any parts, where they are raised above the general level, and so are above the scour of the sand, may be covered with corals. From this position I obtained, as well as various species of Pocillopora, two species each of Coeloria and Fava and one species each of Prionastraea, Heliastraea, and Montipora; in addition to the above, I also obtained Madrepora surculosa and Madrepora haimei from the north end of the main island, but did not find any other species of this genus on the windward side of the atoll, although in Fyi I subsequently found it to be by far the most abundantly represented on the outer reefs. It would be a misnomer to speak of any of these corals as being abundant on the outer reef, the conditions requisite in the fissures being by no means common ; in any area to be visited there could only be anticipated with any certainty a few species of Pocillopora and Stylophora and Mon- tipora incognita (Bernard). Mullepora, which is generally supposed to grow where the break of the waves is strongest, I only obtained in this area in a well-protected situation on the leeward side of the atoll. Under the overhanging sides of the fissures corals do not grow, though the conditions as to food supply should be eminently favourable; this may be due to the scour of the water along the sides, but I think it may also be partially accounted for by the absence of direct sunlight, the growth in general of the species of Madreporaria found in these seas showing, according to my observations, markedly positive heliotropism. The lagoon shores of the islands on the rim of the atoll have either a hard pebbly beach corresponding in position, though not in height or extent, to the hurricane beach with a platform running off from it into the lagoon, or else a sandy beach usually tailing off with a similar lagoon platform, or reef. Opposite to the village there is no such reef, but the sand beach slopes off gradually into the lagoon, the bottom of which is here covered by a dense coating of sand. Professor Sollas, in his report’ to the Royal Society, especially draws attention to the sand: “As regards the nature of this sand it is important to observe, that it does not consist of coral débris; this material and fragments of shells forming but an insignificant part of 1t; calcareous algae are more abundant, but its chief constituents are large Foraminifera, which seem to belong chiefly to two genera (Orbitolites and Tinoporus). It covers a considerable area of the islands, and has accumulated during the memory of the imhabitants to such an 1 Loe. cit. p. 378. 1898. ] Funafuti, Rotuma and Fi. 429 extent as to silt up certain parts of the lagoon. This and the abundant growth of corals and calcareous algae, such as Halimeda, lead to the belief that the lagoon is slowly filling up.” I shall have occasion later to refer again to this paragraph; here I am merely drawing attention to it as showing the nature of the sand. It is only in this one situation that I failed to find a solid gently sloping platform of rock extending from the islands into the lagoon; in some places its nature is to some extent disguised near the shore by a deposit of sand, but its presence is everywhere clearly indicated. Its surface is smooth, but somewhat broken up into holes, which generally increase in size with the distance from the land; it is also in places strewn with boulders. After a gradual slope, to a depth of about 6 feet at low tide, it commonly ends in a cliff, or wall, soundings from the edge of which give depths of 2—5 fathoms, or even more. Such parts of it, as lie below the low tide level, are covered with green algae, Sar- cophytum, sponges and foliaceous nullipores; corals too are fairly abundant on its extreme outer edge. Denser nullipores are also found belonging for the most part to species with upright plates, or round mamillated projections; great bunches of the genus Halimeda are very common. Sarcophytum is found in great flat spreading masses, but its distribution and that of corals over this area depend largely on the position of the lagoon-reef in respect to the openings in the atoll-reef, currents, etc. The outer reef varies to an extraordinary extent, but every- where the rim and the reef-flat present similar features to those already described for the windward side. The inner rough zone on that side is generally narrow and fairly even in height, but in places on its inner part just at the base of the hurricane beach isolated pinnacles of rock occur. These clearly form part of the reef- rock below them, and consist of similar constituents. The largest have a diameter of 6 x 6 feet with a similar height; their tops often to some extent overhang their bases. At high tide they are washed by the waves, but stand up for 1--2 feet above the tidal level. By this wash of the waves they are sometimes eaten into in such a way that the softer rock between the harder coral skeletons has been removed, leaving the corals freely ex- posed. The genera Millepora and Madrepora can commonly be identified ; I also found the laminae of Heliopora. The branches or laminae of these corals generally grow straight upright in any position, in which they are well covered at low tide. Their skeletons, in the few places where I could trace them satisfactorily, I found invariably standing on these pinnacles in the same position. Such would not be the case were these pinnacles formed in a hurricane beach by the consolidation of fragments and the subsequent solution of the parts of the beach round them. VOL. EoPr, Vill, 3D 430 Mr Gardiner, The Coral Reefs of [Mar. 7, Hence I can only conclude that these pinnacles are really due to an elevation, and are the remains of a part of an old raised reef, which formerly extended for some distance outside the present hurricane beach. If this same zone is examined, on the three islands to the south of the main island, it will be seen to get progressively rougher with more pinnacles. The middle island, Funangongo, has no pinnacles, but across this zone there run out from the hurricane beach great buttresses of coral with fissures between, up which the waves rush at high tide. These buttresses are essentially a part of the hurricane beach behind them, and run out almost to the edge of the rough zone: at ordinary high tides the crests of most are just awash. The scour of the tide between these buttresses is very considerable, and accordingly they are to some extent undermined at their sides and bases. On the next island to the south, Funamanu, the same characters are still further accentuated, cross channels sometimes occurring between these fissures leaving pinnacles outside the buttresses. Corals in the position of growth are found plentifully on the tops of these buttresses. The rock forming their greater part is to the eye structureless, but im places sand and slabs may be seen, indicating horizontal stratification. The buttresses are continuous with the lower part of the hurricane beach behind, the upper part of which is formed by piled-up fragments from the reef in front. The resemblance of this part of the dry reef to the extreme outer edge of the living reef, as it at present exists, is very extra- ordinary. Every stage, from the pimnacles on the extreme windward face to this structure, can be traced, and I do not think there can be any doubt but that these pinnacles once formed part of a similar structure on the weather face, the greater portion of which has been washed or dissolved away. On Mateika, Luamotu and Funafara, an almost exactly similar rough zone to that of Funamanu was found; but to the south of the “pocket” this zone is about 70 yards broad and very much as described for the windward side of the atoll, save that it is rougher and more strewn with boulders, which the seas have apparently not been powerful enough to roll up. together to form a hurricane beach, as in fact none such can be said to exist. On the outer sides of the leeward islands the same zones are found, but generally the outer rim is less well defined, while the rough zone is exceedingly broad and rugged. Commonly the reef-flat is 30—40 yards across, the rough zone being about twice as broad. Horse-shoe island, or Fuafatu, on the leeward side exhibits all these characters in its reef very well. The rim is distinct, but its fissures are less numerous and deep than to windward; the reef- flat is about 35 yards in breadth and the rough zone about double 1898.] Funafuti, Rotwma and Fiji. 431 that amount. Then there is a steep beach of rounded pieces of coral-rock, shells, etc. On the island itself there is a considerable amount of sand with a very small, though distinct, sandy cliff by the lagoon with a steep beach of shingle and sand. The lagoon reef has a maximum breadth of about 120 yards with a steep drop into about 4 fathoms of water. The sandy beach is not nearly so well marked in the bay, which gives it the name of Horse-shoe island, here being formed rather of a consolidated breccia, which is not on the surface very firm. It can be seen to consist of coral fragments, sand, and a large number of Y’ridacna and other shells. Neither the coral skeletons nor the shells are in the position that they naturally live in, but both dip towards the lagoon, and no doubt there is a formation of rock going on here between tide marks by the consolidation of these fragments. The greater part is not exposed even at the lowest spring tides, so that we have here the consolidation of a breccia both between tide marks and under the water. Small pinnacles are by no means uncommon on the outer rough zone to leeward: they are exactly similar to those of the windward face, but are situated generally close to the outside of the zone, which differs also in being much broader and often strewn to a great extent with massive boulders. Some of the pinnacles are not so well defined as belonging essentially to the rock, of which this zone is composed, and seem to be rather masses of the conglomerate, now being formed outside the reef, thrown up on it by strong gales or hurricanes; such are commonly called “negroheads,” and have been well described by Dana. One part of the reef between two of the islands, which I was un- fortunately prevented from visiting owing to a rough sea, appeared to have a considerable number of such fragments. It is remark- able that if there are “negroheads” on the leeward reefs, there should be none on the reefs to windward, against which the force of most of the gales is broken. Either they are only thrown up in bad cyclones, or hurricanes (which always strike to leeward), an almost impossible supposition, or the growth of these masses is firmer to windward. I consider that such masses would be worn away, and broken up much quicker to windward of the atoll than to leeward, and I think, too, that the growth of the reef outwards goes on faster likewise, so that the masses of reef forming outside should be fixed more strongly, and be more firmly built to windward. To the north of the atoll, are the two islands, Pava and Fualifeke, separated by a narrow channel from one another, but at low tide thew rough zones are continuous. Towards the other each sends out a sand bank, but these are separated by a pool with about three feet of water at low tide. Off these islands 35—2 432 Mr Gardiner, The Coral Reefs of [Mar. 7, (Fig. 3), the rough zone is extremely broad being rarely less than 100 yards, while the reef-flat is only about 30 yards. There is here practically all along a sudden drop of two feet from the rough zone to the reef-flat, and along this edge there is a line of small pinnacles. The -hurricane beach is formed of coarse shingle and shows very distinctly in its abrupt fall the height to which the tide rises. Towards the lagoon the beach is sandy ; below this the lagoon platform is distinct. In the small lagoonlet, between the two islands, there is found a sandstone, the strata of which dip slightly towards the lagoon. It is apparently a true beach sand- rock formation and only occurs in this position. I have appended a section (Fig. 3) across the island of Pava, showing the general features of the rim of the atoll here. The reef, except where it is broken by the deep channels before mentioned, is continuous round the whole lagoon, and connects all the islands with one another. The rim and reef-flat show no discontinuity, the reef-flat, continuing between the islands, and a little lagoonwards ending in a straight cliff exactly similar to that of the lagoon platform of the islands. The reef between the islands slopes a little towards the lagoon, so that, even at extreme low tide, a small quantity of water makes its way over it into the lagoon instead of flowimg out again through the fissures, which run through the rim. Probably owing to the difficulty of fixation found by the larvae, few corals grow on the reef in such a position. To leeward the reef is often very broad, as indeed are the inter- spaces between the several islands, and is generally exposed slightly at extreme low tides. Often its lagoon edge extends continuously with that of the lagoon platform of the islands, and is much broken up into knolls and patches, on which corals and nullipores flourish luxuriantly. South of Fuafatu, the reef has a distinct channel in its middle a few fathoms deep, extending along for some distance it consists of an outer reef with a distinct row of pinnacles marking its position at low tide, and an inner reef, a broad flat platform, a continuation of the lagoon reef of the island itself. South of this both reefs have a distinct but narrow passage to the ocean beyond; this passage through the outer reef is nothing more than a long fissure with a depth of about 24 fathoms, and is just broad enough to take a boat through. North again of the same island and generally to the westward, the reef has a depression in the centre, but it is not usually more than a few feet deep. The shoals in the lagoon commonly on their upper surface, resemble very closely the inner parts in relation to the atoll of the lagoon reef, and the same species of coral are found on both. About the centre of the lagoon is one large shoal, and there are many others, which lie mostly on the windward side and towards 433 Funafuti, Rotuma and Fiji. s}R109 SUIMOIF) “p . pus pau siapjnog ‘9 soo ae NO at ‘o'Ol4 Ty JOON 4 2514 ESET 00) Gis 0} est Ueppng ‘Te aanssy aq) panos panuntos wry & ana jo edojs junpery -% 3 wey Jey 'P ‘your 1 07 spavk ZT ‘a]B0g your [ 07 spank p jeoI9A — your | 07 spuwk g :jR,UOZIIO}] ‘a]EIg ‘Wnyeuny JO j991 1ajnO 943 UI SAaINssy 9e1Y4} SsOIDe UOIYIIG peszejue — Sy ur ou aqy, ]242] eply MoT ; : = [esa] apr ga 6e Te q ¥ MOT adojs 193NnQ sy J auoz sapfnog 0 °9 wy 8 [aqueys ywog 'q q Wey VOY PP youag 't your [ 09 epred ZT :[eoqseA — "qour ] spivd QZ] :[RIMOZWI0H ‘a]KOg ODIs BUINJOY JO 4Sve oy} 0} JooxT 94} JO uOoag 1A9] Opy MOT wuoyyed noosey 4 9 ajocunid yrtm auoz ySnoy 9 puvy 3 wey Joy ‘© Dls i qovaq aurouiny ‘p my oF your | 0 spre gy :jeoysa, — yout | 04 spavd gg] where 6,, b, are any two of ¢,, Gd), C:, M2, c, the singular tangent planes which pass through this point being DB) D) Py, JE. Jee L b3D4> eer I b3b5? where b;, b,, b; are the three of the set ¢, @, ¢, a2, ¢ other than 1) b.. Still supposing A,=0, A, = 4, the expressions for the partial differential coefficients of the third order in terms of a, y, 2, referred to in §1, can be taken so that the squares and the products of twos of Qo», @m, Mer, Mim are rational integral cubic polynomials in a, y, z. I have obtained the ten equations, of which for instance three are Qoon = No + Ag + Aye? + 4a? + day + 42, Qon = No + Ay? + Aay? — 4yz, 2 Orm(Oon = a + Asy + 2r.LY + Bary + Ay? — az. The first of these equations shews that all the functions @, @on, Qo, Yim can be expressed rationally in terms of the three &= On, Y= On, €=@om, (a remark easily generalisable to higher values of p). It is known that there exist cubic surfaces touch- ing the sixteen-nodal quartic surface along sextic curves ; denoting the right-hand sides of these equations momentarily by X, Y, Z, the equation of the quartic can be put into the form AX VY = Z?, which shews that each of the cubic surfaces X, Y touches the quartic along a sextic curve lying on Z=0. There are also irrational forms for the equation of the quartic; for instance one arises from the verifiable identity Qs = QxQ@o2— xP: Further, in the form ?=¥ (a, y), to which the equation is reducible bi- rationally, y (a, y) is the product of the five expressions Pp. 1898.] differential equations defining periodic functions. — 519 The expressions for uw, u as linear integrals can now be obtained as in § 1. The result can be brought into a familiar form ae 3 ean ? Li STAN ee aw 0g 0g where Y=0 is what the equation of the sixteen-nodal quartic becomes when we substitute for z in terms of a, y and €, where €= @.,, and L, M, N are rational integral polynomials Tih yy 1G. From the point of view of the theory of functions it is the surface V=0, rather than the sixteen-nodal quartic, which is to be regarded as fundamental. (8) Coming next to a certain symbolical form of which the differential equations are capable, we notice that we have 2 Ca a Ze 3 Aico’, Qn = — = A,A,oo'’, Qu =— = Aico’, and similarly Qo — 602 —— OO 2202 — ee atk Bom =— = Aico’, etc., where Shy 0 CoN a Mas = (= _ = o (Uy, Uy) a (Uy, Uy ), etc., the variables w,’, ws’ being replaced after differentiation by a, ws. Now let k., k,, %, w, , m be arbitrary constants, let us take . Klein’s invariantive form for the polynomial F(a, z), and Eve [ Art p)de xa =| "2 + pw’) dx Oy = ee ee Ve a NGS then the differential equations are summed up by 1 0 @ ae iil aga 3 | (& Ov, + le; =) Coxe @ dvs s= k, 5a”) | oo = (Au — Np). (db ) bith, oo" = i ZN?) ht oO = oO 0 = 0 ) gee Ow’ =n). $5] (55, bezy) — (bean Sane) | 2m where o is regarded as a function of v,, v,, and, after differentiation, V2, ¥, are to be replaced by 2, %. d= bik, + ok, = < This form shews, by equating terms of the same dimension on the two sides, that the equations can be used to obtain the expan- sion of the o-functions in integral powers of the arguments, and gives an immediate proof of the known theorem as to the invariant and integral character (in the coefficients of $%) of the 520 Mr Baker, On a certain system of [May 2, terms; as a practical example I have obtained the expansion of the function o,(%, U2) up to terms of the ninth order, assuming only the terms of the first order to be u,. It is probably better however that the linear partial differential equations, which for any specified function are more convenient than these, should first be deduced from them *. From either point of view it is clear that the differential equations, regarded as given, are sufficient entirely to define the theta functions. (4) The case of three variables may be dealt with more eursorily. Putting ©= Ox, Y= Ox 2= Pn, €= Yn, 1= Pa, $= On, A= 9221 — PnPx2 + Pa — PsPn, SF (@) = Mt MEH... + Ages + 427, iG, DS Soe Pa en al the fifteen differential equations are (1) @ss33 — 653 = brs + Age + 4Y, (2) @s352 — 6530s = Aey — ZE + 62, (3) @sss1 — 6053s = Agz — 2m, (4) @s32 — 405. — 205300. = $Asy + Nez — 2m, (5) @s3 — 40320 — 20230n = $252, (6) @ssn — 405 — 2@s30n = 2A, (7) @s20 — 6 soon = — No — FAL + gy + Agz — OC, (8) @s1 — 403202 — 2021Qo = — $A + AZ — 2A, (9) @san — 4s — 2s =o + ZA22, (10) @si1 — 6Qn@r1 = Aye — Er + vz, (11) Qs — 6m = —} Ae t+Aghs—SAge + Agsy + AE + Asn — BAGG +12A, (12) Qa — 6 err = — Zo — EMyAg — B Aw + Ags + As — EASE, (13) Qn — 4@n — 2QnQn = — brAdg — ZAge— Ary + Ags + bArgn, (14) @on — 6@n@n = — FAs — 2Zragy + $2 — SAUE+ Ay, (15) @un — 6@), = ENA — EApAy + ANZ — BAKE + A] + AE. From the first twelve of them we find the three independent equations S=B/P, T=QR/P, U=QYP, * For the case of p=1, see Weierstrass, Werke, 1. p. 7. 1898.] differential equations defining periodic functions. 52 where P = 2a? + bru? + 2Qay + br,w — 224+ 2E+ EA,, Q) = 2x°y + bevy + 2xz — E+ YP + Ersy + N+ drs, R = 2072 + brguz + yz — an + 452 — €, S = 2x2? + r,2?-— 22y + Er, T = 2ayz + drgyz + 22— yn — 2E + 4d, U = 2ay? + drgy + 4yz — 2yE4+ 264+ 4r. Each of the three relations is, when reduced, of the fourth degree in the aggregate. We find other relations, also of the fourth degree, which are deducible from the three above. Of these two have forms which deserve to be recorded :— ”; E — 2z, y+tnr;, 2a +4r, | =9, 6 —(n+4nr,;), 2€-22+48d,, ytHr, tM, 26 +420, —(n+ dAs), E— 22 No; ih, g, ui} z, Y, — 4, i = 0; & —(7+4rs) 2€-22t+35m, ytsrs th, 26+ 4r., — (9 + 4s), E — 2z No, iM, g Y] if in the first of these determinants we omit #, y, z and replace E, n, € by «a, y, 2, it becomes identical with the Kummer nodal quartic obtained in §3; an independent set of three of these equations is indeed to be regarded as the generalisation of the Gopel relation to the hyperelliptic case p=3. For any value of p the generalisation should consist similarly of a set of $p(p—1) equations in 4p(p+1) Abelian functions. There is a generalisa- tion in another direction in which there enter 2?—1 Abelian functions—holding however for the general case of p variables. (3) On the Total Helipse of the Sun 1898 Jan. 22. By H. F. Newatt, M.A., Trinity College. A general account was given of the observations made during the recent eclipse, and photographs were exhibited, shewing (i) the general appearance of the corona, (11) the spectrum of the sun’s limb as photographed with prismatic cameras by Sir Norman Lockyer’s party, and by Mr Evershed, (11) the spectrum of the sun’s limb as photographed with a slit-spectroscope by Mr Newall, and a diagram was shewn illustrating the distribution of glowing ‘coronium’ as observed by Mr Newall with a slitless grating spectroscope. Capt. E. H. Hills, R.E., exhibited and described the photo- 522 Mr M°Clelland, On the figures produced [May 16, graphs obtained by him of the spectrum of the corona, and also the two series of photographs of the spectrum of the sun’s limb at the beginning and end of totality. Monday, May 16, 1898. Mr F. Darwin, PRESIDENT, IN THE CHAIR. At a Meeting of the Society held at the Cavendish Laboratory, B. Cookson, Trinity College, was elected an Associate. The following Communications were made to the Society : (1) On the figures produced on photographic plates by electric discharges. By J. A. MCCLELLAND, M.A., Trinity College. Several experimenters have lately drawn attention to the figures produced on photographic plates on development, after an electric discharge has taken place on to or near the surface of the plates. The figures are very interesting and well defined, and differ in a marked degree according as the discharge is positive or negative. The manner of the production of these figures seems to be imperfectly understood, and it has not been shown whether they are due to a direct chemical action of the discharge on the plate, or whether they are simply produced by the light of the discharge. If the figures are produced by a direct chemical action on the plate it would point to a difference in the manner in which the positive and negative discharges spread over the plate ; if produced by the action of light on the plate the figures would be explained by the different forms of the discharge in the air close to the plate. In this paper the effect of the gaseous medium surrounding the discharging point on the form of the figures is investigated, and also the effect of interposing thin plates of different material between the film and the discharge. In this way we vary the form of the visible discharge in the gas close to the plate and can compare it with the figure produced, and we test the trans- parency of various substances to the action. It will appear from the figures given that the effect on the films is produced principally by the light of the discharge. The discharge passes through the air quite close to the film and the sharpness of the lines on the figures is explained by the nearness of the source of light to the plate, only the part of the plate just beneath the lines of discharge being affected. On this explanation the difference in the positive and negative figures corresponds to the difference in the discharges in air; and the photographic action brings out these differences very clearly. 1898.] on photographic plates by electric discharges. 523 The figures Nos. 1 to 6 were taken in air at different pressures as given below. Positive Negative No. Pressure. No. Pressure. 1 1 atmosphere 5 1 atmosphere 2. 75 - Sad i Od » »”? The figures were taken with all other conditions the same but the pressure varied. The photographic plate was laid on a piece of ebonite and put under a bell-jar in which the air could be exhausted or compressed; a pointed metal rod just touched the surface of the film and was connected to the outer coating of a Leyden jar set on the table, the inner coating of which was joined to one of the knobs of a Wimshurst machine; the distance between the knobs was the same in all the figures. The marked change in the figures produced by a change in the pressure of the air shows that the form of the figure depends to a great extent on the form which the discharge takes in the air near the film; even when the discharging point touches the film the condition of the air near the film is the principal factor in determining the nature of the figure. With the intensity of discharge used the negative figure shows little detail at atmospheric pressure, while the positive shows its characteristic fine tapering lines. As the pressure diminishes both positive and negative figures increase in size and the negative breaks up into branching feathery lines. At the lowest pressure given (4 atmos.) the lines in both the positive and negative figures have broadened out until nearly all the plate is affected (the negative figure for this pressure is not reproduced but it was very similar in appearance to the positive). Figures were also taken for pressures greater than atmospheric, and as the pressure increases the figures get smaller and smaller, the positive still showing its fine tapering lines and the negative becoming a circular spot in which no lines can be detected. Now when we do the experiments in a dark room and watch the discharge carefully the form of the visible discharge is the same, as far as can be judged by the eye, as the form of the figures; in the positive we see the sharp branching lines and in the negative we see less distinctness of outline. As the pressure is lowered the lines broaden out until at the lowest pressures we see only a continuous flash all over the plate round the dis- charging point. The photographic figures are the same, but showing more detail than we can notice with the eye. In the figures given above the intensity of the discharge is small; it is interesting to increase the intensity and produce larger figures. 524 Mr McClelland, On the figures produced [May 16, Figures 7 and 8 are positive and negative taken by placing the photographic plate on a metal plate connected to the outer coating of a Leyden jar; the outer coating of a second jar was joined to a metal rod which just touched the film. The jars were then charged until a spark passed between their inner coatings. Here we have the discharge running out in heavy lines, from each of which at various points branch off small discharges similar to those in the smaller figures. In the positive the potential rose high enough to break down the air to the edge of the plate and on to the metal base, and the greater part of the discharge passed this way. Even the heavier lines in the negative are less bent about than in the positive. To test whether the effects on the film are due to the light of the spark a number of experiments were made with thin plates, some transparent to light and some opaque, placed between the film and the discharging point. _ With a thin plate of mica on the film the branching lings of the positive figure are only slightly less distinct than when the film is uncovered. Figure 9 is taken with a small circular piece of glass } mm. thick placed on the centre of the photographic film, and the discharging point touches the glass. The lines of the positive figure beneath the glass are quite distinct but broader than they otherwise would be; we would expect this broadening as the light is further from the film by the thickness of the glass. For figure 10 the same piece of glass was used but half of it was rendered opaque to light by a thin coating of Brunswick black on the side next the film. Here again the figure comes out distinct through the transparent part but not through the opaque part. In figure 11 part of the film was covered with a piece of ebonite 4mm. thick; the opaque ebonite entirely shielded the film although not much thicker than the glass which had little shielding effect. These figures seem to prove that the light of the discharge is necessary to produce the figure on the plate. As it is well known very perfect impressions of coins or any metal dies can be obtained by placing them on a photographic plate and passing a discharge to them. Here again the light of the discharge from the coin appears to be sufficient to explain the effect produced. Around the edge of the coin we have a discharge and also minute discharges from the edges of the raised portions of it, where the film is affected. Where the coin touches the film it is not affected. Figure 12 is taken by weak sparking on a coin laid on a photographic plate; the edge of the coin is brought out by the Plate IV. To face p. 524, 43 * ae _" ym tah? Levee w Phil, Soc. Proc. Vol. 1x. To follow Plate IV. i atom mee Be ine tee meh ati t - f Seis De . Se liad ¥ cu ease nn item Raha Be Lin DERE ta = a tee nese eter remit: we os \ ty Ab sen a \ 0 bE Soot a 1898.] on photographic plates by electric discharges. 525 discharge from it and the letters by the minute discharges from their edges. Under the parts which touch the film there is no action, and under the level parts which did not touch there is weaker action. We also get a very good impression of the coin if it is laid on the film and covered with an ebonite plate and the discharge allowed to pass to the ebonite; with this arrangement we have an induced discharge around the coin which gives the impression. If the ebonite is between the coin and the film no effect is produced. All these effects on photographic plates would seem to be due, in great part at least, to the light of the discharge, although the amount of light may be very small indeed. That the positive and negative figures differ so radically is due to the different forms of discharge in air in the two cases ; the positive is more in the form of a brush and the negative of a low. 3 Why the nature of the discharge into air from a positive and a negative point should be so different is a property as yet not understood. It is interesting to compare these photographic figures with the figures produced by sprinkling a mixture of sulphur and minium on an ebonite plate on which a discharge has passed. The negatively electrified sulphur adheres to the plate if the discharge has been positive, the positively electrified minium if the discharge has been negative. The positive and negative figures thus produced are very similar to the photographic figures, only the latter show more detail. Here again when the pressure of the air surrounding the plate is reduced the effect is similar to that with the photographic plate; the radiating lines in the positive become fainter and broader as the pressure is diminished. This effect of the pressure of the air has been observed by Joly (Proc. Roy. Soc. Vol. 47) who concludes that the figures owe their form chiefly to the manner in which the discharge spreads in the surrounding air. In experiments with these dust figures one often gets a secondary positive in the centre of the primary negative or vice versa, but this is simply due to a secondary discharge back from the ebonite to the point used to convey the discharge to the plate. In fact if we touch with an earthed metal rod a plate of ebonite which has been electrified by a discharge having passed to it, we get a figure around the point touched opposite to the sign of the charge on the plate. In conclusion I wish to thank Prof. Thomson for the assistance afforded by his suggestions. 526 Mr Wade, Method of facilitating the measurement [May 16, (2) On a Method of facilitating the measurement of tem- perature by means of Platinum Thermometry. By E. B. H. Wabdk, B.A., Trinity College. S1. Object of the Paper. The method of measuring temperatures by finding the resistance of a platinum wire, claims a high degree of accuracy and is also widely applicable. Probably one reason why it is not more frequently used, is that equal increments of resistance do not represent equal increments of temperature, so that inconvenient calculations are required to deduce the latter. The object of this paper is to describe a means of avoiding these calculations. It is assumed that the formula employed by Callendar and Griffiths is exact, and if the directions contained in the paper are followed every unit of resistance will represent the same interval of tem- perature, which may be 1° Centigrade or any other. It is hoped that this will lead to the adoption of platinum thermometry by those who have hitherto been deterred by the calculations. § 2. Description of a modification of Wheatstone's Bridge, which gives direct readings with platinum thermometers. Fig. 1 represents a form of Wheatstone’s Bridge in which P is a platinum thermometer having resistance R; at temp. t. A, B, are coils of equal resistance of a galvanometer. If a single adjustable resistance were situated between points C, D, Jip the whole arrangement would be that in ordinary use. But in the suggested modification this interval is occupied by two adjustable resistances in parallel forming a shunt. And these coils are to be manipulated according to the following rule. 1898.] of temperature by means of Platinum Thermometry. 527 “ By whatever amount the resistance of one arm of the shunt is increased, that of the other is to be diminished.” Thus the sum of the resistances of the arms of the shunt is constant. Let it equal S. It will be shewn that if S is chosen rightly at the outset, and if the above rule is obeyed, then the condition that the bridge is balanced is that the arms of the shunt are linear functions of the temperature. By suitable choice of con- stants we may make the resistance in one arm numerically equal to the temperature. ‘The rule is most easily followed by connect- ing two ordinary resistance boxes in parallel and transferring plugs from one to the other, so that one box gains in resistance what the other loses. § 3. Demonstration of the accuracy of the Method suggested. Since the equation connecting resistance and temperature is that of a parabola with axis inclined, any of the following equa- tions may be used in which &; is the resistance at ¢, R, the resistance at 0°, @ is the change of resistance between 0° and 100°. 1 Pi eeet| EES 1 AY 0) /g Rae a ea SEND REG (1), TPs Gt (TUE a 624 (Oe) ae a (2), R,— R, ees t ) re db 100 =6 (1002 a 100} eee rseeeresresense (3). The constants in the three equations are connected as follows: C—a2— 07 — ly, _ (100 + 8) ¢ a= 4 — 28z = ~~ 1002 5 op SS 2 = 7008" Now equation (2) can be written as follows : 1 1 i ; ; qeere = ee) yaa tte) R= which will at once be recognized as the expression for the effective resistance of two conductors in parallel whose individual resistances are a’ (t+ 2) and a —a’(t+ 2) respectively. Since these two are each linear functions of the temperature and since their sum is 528 Mr Wade, Method of facilitating the measurement {May 16, 13, a B constant = will in future be called S. constantly — , the method of § 2 is shewn to be justifiable. The In order to make this result practically serviceable, it must be remembered that at the present day it is usual to find the values of the constants ¢, 5, Ry, (see § 3 equation (3)), in preference to any three others, and it will be necessary to shew how to obtain z, a, and S from these quantities. To find z, a— a — 27, Ji, = OG = [BF ya h, — Cia RNA OO OD gob putting a= GOOe ° B= 1002” we easily get 22 Coe OOD Sy ey one pli te (BE A ao Again a Po 100: Ry + 2 ee, oe as a control of the accuracy of the calculations we may use at a’ fy =2— ° Messrs Neville and Heycock have kindly furnished me with the constants of several pyrometers and from these I have calculated the values of S, a’, z, which would convert them into direct reading instruments. 1898.] of temperature by means of Platinum Thermometry. 529 Example 1, Pyr. 22. d= 99°786, 2= 245771, o=— (£490) (a2 =— E0858 15: R, = 257°885, S=7929°71, [a = 1012728]. ate’ ° a“ Test: 2 257°885, but Hy = 25:70:885; Example 2. Pyr. 25. @= 99-206, 2= 246°765, S6= 1°5135, a = 1081240, R= 251000, 8 = 118618, [a = 1:0070850]. ate = 957-666. 2 but Ry = 257°666. I have calculated what would be the resistance of these pyrometers at the melting point of gold (960°), using first equation (3) of § 3, secondly the rule Test: z Rage ere: S The exact agreement only proves of course that the arithmetic and algebra has been correctly performed, but this it seems to me is all that need be proved. The conclusion is that by using this form of bridge the same temperature can be arrived at without calculation as would have been arrived at by the 6 formula. Whether this method of calculating the temperature is itself correct is of course outside the object of this paper. In concluding this note it may be well to point out a curious analogy between the action of the shunt and the action of the impurities in the wire. It is regarded by many as not improbable that in a wire of perfectly pure platinum the resistance might be a linear function of the temperature, and then no shunt would be required to give direct readings. If so we may regard the action of the impurity in the wire as similar to a shunt in providing an alternative path to the flow of electricity. It seems hardly worth while to push the idea further in a paper whose object is entirely practical. J am greatly indebted to Mr Griffiths and also to Messrs Neville and Heycock for the assistance received from them. VOES Ux. PT. VIE 49 530 Dr Willey, The Development of Peripatus, etc. [May 16, (3) The development of Peripatus novae-britanniae. By Dr A. WILLEY (Balfour Student). The ova are without yolk and the nutrition of the embryo is effected by the development of a large trophic vesicle which occupies the entire dorsum of the embryo and projects far in front of the embryo as a head-fold and behind as a tail-fold. The trophic vesicle is thus a hollow closed cylinder lined internally by endoderm and externally by ectoderm, the cells of the latter being adapted for absorption of nutriment. The trophic folds were compared with the amniotic folds of insects. The trophic cavity becomes the gastral cavity of the adult and in the transformation from one to the other the endoderm undergoes certain changes. It secretes a basal membrane and a cuticular membrane simul- taneously with a great increase in thickness; and between the two membranes the endoderm contains numerous small and large yolk-like globules which are probably to be regarded as reserve nutrient matter to tide the embryo over the first few days of its independent life. This late deposition of reserve nutrient matter derived ultimately from the maternal organism, as opposed to foreign ingested matter, is probably of some significance with regard to the question of the lecithality of the ovum. The embryo lies outside on the ventral surface of the trophic vesicle just as an insect embryo lies upon the yolk. (4) On the possibility of deducing magneto-optic phenomena from a direct modification of an electro-dynamic energy function. By Mr J. G. Leatuem, M.A., St John’s College. [Printed in the Transactions, Vol. xv. Pt. I.] The method initiated by Maxwell for the explanation of the Faraday effect depended on the direct insertion of a magneto- optic term in the energy. This method was extended by Fitzgerald and others to the explanation of Kerr’s effect, namely the modification introduced im the circumstances of optical reflexion by magnetisation of the reflector. A difficulty occurred however in satisfying all the interfacial conditions, which virtually showed that such a scheme was not formally self-consistent. The origin of the discrepancy has been traced by Mr Larmor (Report on the Action of Magnetism on Light, Brit. Assoc. 1893) to omission to secure what may for shortness be called the electromotive incompressibility of the medium: in the ordinary problem of optical reflexion there is no tendency for this to be disturbed, but when Maxwell’s magneto-optic energy terms are included the reaction against compression introduces what may be termed an electric pressure, which must appear in the equations. 1898.] Mr Leathem, On the possibility of deducing, etc. 531 It was necessary to compare the modified scheme thus obtained with experimental knowledge: and the calculations given in this paper show that in fact it does not represent the phenomena. The paper is only a summary of the actual calculations, because since they were completed the author has shown (On the Magneto- optic Phenomena of Iron, Nickel and Cobalt, Phil. Trans. 1897) that the other rigorous theory formulated as an alternative by Mr Larmor (loc. cit.), which leads to an analytical scheme practically the same as those advanced on various hypotheses by Fitzgerald, Goldhammer, Basset, Drude, and others, is in much more satis- factory agreement with experiment. This brief history of the subject shows the desirability of the examination of the conse- quences involved in the former method of explanation: the result is however what was to be expected by those who adhere to the more recent formulation (Larmor, A Dynamical Theory of the Electric and Luminiferous Medium, Part 11., Phil. Trans. 1898) of optical theory which treats a material medium as free ether pervaded by discrete molecules involving in their constitution electrons considered as nuclei of intrinsic zthereal strain. On such a view a continuous energy function is not the starting point, and the influence of these discrete nuclei could hardly be conceived to modify the propagation in the intervening ether in so fundamental a manner as an electromotive pressure would demand. (5) On the solutions of the equation (V? + x?) = 0 in elliptic coordinates and their physical applications. By R. C. MACLAURIN, B.A., St John’s College. [Printed in the Transactions, Vol. xv. Pt. I.] (6) On the interpretation of divergent solutions of the hyper- geometric equation. By Mr W. M°F. Orr, Professor at the Royal College of Science, Dublin. 532 Mr Hargreaves, The Harmonic Expression of the The Harmonic Expression of the Daily Variation of Solar Radiation, and the Annual Variation of its coefficients. By R. Harcreaves, M.A., formerly Fellow of St John’s College, Cambridge. [Read 22 November 1897. Revised 1898. ] A harmonic series, applied to express the intermittent daily supply of heat from the Sun, consists of a series of terms with the day, half-day, one-third of a day &c. as periods, and an opening term on which the total supply for the day depends. Each coefficient depends on the latitude of the place and on the Sun’s declination, and through the latter is subject to an annual variation. This annual variation for the opening term was discussed in @ previous communication to the Society*. The present paper contains the solution for the general case, and tables are appended giving numerical values for latitudes up to 60°, at intervals of 10°. A corresponding analysis of the daily variation of temperature, and the yearly variation of its coefficients, will be found in a volume published by the Meteorological Council, under the title ‘Harmonic Analysis of hourly observations of Air Temperature and Pressure at British Observatories’; and an account of the method and general results in a paper, bearing the same title, by Lieutenant-General Strachey, published in the Transactions of the Royal Society for 1893. I understand that this is practically the only case in which the Harmonic Analyser has been applied to the second stage, ze. to express the annual variation of co- efficients of the daily expansion. The preliminary comparisons - which I have made of these results of observation, with the calculations of the present paper, are sufficiently promising to justify a detailed study, should time permit. But the time and labour required are very serious, and the reader who gives a casual glance at the collection of numerical tables appended here, will hardly realise the weeks of laborious calculation involved. These tables, with explanations in sections 1 and 5, are all that is needed for meteorological purposes. Section 3 gives a brief réswmé of properties of the coefficients, which in the more general form of the mathematical problem, bear a curious resemblance to the Associated Functions of Laplace. §1. With a diathermanous atmosphere, the amount of solar radiation reaching a unit area of the earth’s surface, depends on * «Distribution of Solar Radiation on the Surface of the Harth, and its depen- dence on Astronomical Elements,’ printed in Transactions, 1896. Daily Variation of Solar Radiation, ete. 533 the distance of the sun and the angle of exposure to the sun’s rays. The element of heat-supply may be written a cos I, in which dt is time-element, r the distance of the sun from the earth, and J the sun’s zenith distance. In latitude X, when the sun’s declination is 6, cos J=sin sin 6 + cosd cos 6 cos; > the hour-angle varies in the course of the day from —y, to +, where y, the hour-angle at sunset is given by sin A sin 6 + cos X cos 6 cos Yr, = 0. The factor cos J is positive during the day, and at night is replaced by zero. In lieu of this discontinuous expression, we propose to write the quasi-continuous expansion in cosines of multiples of y, in which y varies from — 7 to + 7, embracing the whole twenty-four hours. Fourier’s method gives for this pa Bg COM SUP: te necun tats coats (1), 7? in which Vv Xs =| (sin A sin 6 + cos A cos 6 cos W) cos si dp ...(2). 0 The factor 2 is to be omitted for the opening term (s=0), on which depends the day’s integral heat-supply, and so the element of the annual variation discussed in the previous paper. The other terms express the daily variation divided into harmonic components, whose periods are the day and its exact sub- multiples. Integrating by parts, for the general case ee cos A cos 6 (= (s—1)y, _ sin(s ae aS s—l ST and for the case s=1, ---(3). cos A. cos 6 : = ian (hy, — 3 sin 2) As W, is known in terms of » and 6, these formulae give numerical values of the coefficients for an assigned latitude and date of the year. But a general expression for y, may be obtained in a series of associated Laplace’s functions with sin ) and sin 6 as arguments, applicable to the whole globe and taking proper account of the discontinuity that occurs in arctic regions. For greater generality this is found for vi Xop,s =| (sin A sin 6 + cos A cos 6 cos YW)? cos sp dip...(4), 0 534 Mr Hargreaves, The Harmonic Expression of the the resemblance of which to the mtegral expression for an associated function, viz., [ (2 + Va —1 cost)” cos sy dip, strikes the eye at once. Physically this corresponds to an absorbing atmosphere in which the fraction of light or heat transmitted is (cos/)?—, depending on the angle between the zenith and the sun’s direction; one factor cosZ being due to the oblique exposure of a surface. § 2. First notice that the conditions for arctic and non-arctic regions are embraced in the statement that all values yr between 0 and zw, which make sind sind+cosAcos dcosy positive, are admitted in the integration. During the period of total day Wy, is continuously 7, and during the period of total night it is 0. Now if we expand in zonal harmonics a function which = az? for positive values of 2, and vanishes for negative values, the coefficient of P,, (#) in the expansion is 1 Ann oie : | aPP,, (@) da 4 Jo ean p(p—2)...(p—n+2) 2 * (p+) (p+3) Vote aie sagas 0 ()) = 2n+1 v (p=!)(p=3)-..(p=n + 2) oa 2 (p+2)(p+4)...(p+tn+1) ? ”» » (See Todhunter’s Functions of Laplace, pp. 18 and 19.) Introduce this expansion in (4), writing sin) sin 6 + cos) cos 6 cos W for w, and we get Mea i ; LApyn Pn (sin A sin 6 + cos A cos 6 cos Yr) cos sp dy, 0 the integration being now from 0 to 7, because we have re- placed the original expression, with its discontinuity and variable limits, by the quasi-continuous expansion. With w=sina, w’ = sin 6, we have P,,(sin \ sin 6 + cos A cos 6 cos yr) [=s n—s & = mee Tey ey Pe) En lee where P,5(“) = che and the factor 2 1s to be omitted for s = 0. be — > Daily Variation of Solar Radvation, ete. 535 Hence the expansion sought is \2 ae y)? Pit (0) Py (nu!) » (6). Xp, SS TrA », n The formulae quoted for A, ,, though correct, are rather misleading for the case in which p is an integer ; they suggest that differences in type turn on x being odd or even, whereas in reality they depend on p—n being odd or even. Whether n is odd or even, the group of terms for which p — n is even terminates with n=p, and the formula is au WAP se! yt eee (7a). 2 1.3...a~+tp+1).2.4...(p—n) When p — 1 1s odd and positive, the form is 2n+1 |P Ron Sa hig aie oes aoe oe When n=p +1, it is ila cp bee a 2 aa mie (Tc). 2/) 2210p) When n — p is odd and greater than 1, it is 2n + 1 - (a — p — 2) ae ESC EE .(p+n4+]1) (—1)!-P- (7d). Thus up to n=p-+1, all terms odd and even occur and all are positive, beyond this only terms for which n— p is odd occur, alternately positive and negative, the first negative term being that for which n=p+3. All the terms for which n ~ p is odd are embraced in the single formula an +1 bi 3G a). |p (1p mes (2° 2.4... (n+p41)(n—p) (n— pt+2)...(n+p) which will be found to give correctly the three cases (b), (c) and (d). The result (6) was obtained for s=0 in the previous paper by a much more troublesome method. § 3. Various sequence formulae may be established directly from the definition (4). Obviously Mo a= Xp-1, Si A SIN 6 + 4 cos A cos 8 (Y¥p-1,6-4 + X%p—isi)-+ (8): 536 Mr Hargreaves, The Harmonic Expression of the Also +p cos X.cos & (Cgpatnen = i ny) =["> sin W sin sv. cos X cos 8 (sin eo 6 + cos A cos § cos yw)? dyp = E sin sy (sin X sin § + cos X. cos 8 cos | ‘i +" sx (sin \ sin 6 + cos A cos § Be eee sidyp, or SXp,8= FP - COSA CoS 8 (Yip 5 — Xp1, G4) > ceeeae (9). From (8) and (9) we get 2P Cos cos 6 {(s — 1) Xp—-1,sa — ($+ 1) Xy4, 543} = (8 — p) Xp,s + PXp—,s8in Asin S...... (10), which is wanted below. Again i (sin cos sap (sin X sin 8 + cos X. cos 6 cos ye} = (cos cos sv — §. sin sin sip) (sin X sin 6 + cos A cos 8 cos ypyP4 —(p—1)cos2rX cos 8 sin? ap cos syr(sin X sin § + cos X. cos 8 cos pe. Hence, writing cosWcossp—s.sinwsinsy=1{(s+ 1)cos(s+1)p—(s— 1)cos(s—1)yp}, and integrating (p—1)cosr cos sin W cossy (sin X sin 6 + cos X cos 8 cos WP dap = 4 {(s F 1) Ge = (s = 1) Xp—1,3—i}, or by (10) a P(p—1) cos? cos? § | sin’ycossyr(sin \sin 8-+cosd.cos8 cos Wr)? dar 0 = (P — 8") Xp,s — PXp—i,5 SiN D sin 8. But evidently vA cos’ A cos? 6 | cos’ yr cos sy (sin A sin 6 + cos X cos 8 cos yp)? dy 0 = Xp,s — 2X p—1,5 SIN A Sin 6 + Xp—2,3 SIN? A sin? 6. Hence, multiplying this by p(p—1), and adding to the previous equation, P(p—1)Xp-»,5 Cos? X cos? § = (p? — 8°) Xp, — p (2p —1)xp-a,,8in Nsin 8 + p (p —1) Xp», 5 Sin? A sin? }, Daily Variation of Solar Radiation, ete. 537 or P(p—1)(cos?rA —sin®d) Xp ~2, s=(p?—S"). Xp,s— p(2p—1) Xp-a,5 Sin Sind a sequence equation in which only the letter p changes. The elimination of y,, from (8) and (9) gives an equation in which only p — 1 occurs, and if we raise by 1 the value of p this is ¥cosr cosd {(s +p +1) Xp, s41 +(S — p—1) Xp, sa} + 5xXp,s8in A sind = 0 the sequence equation in which only the letter s changes. Further differentiating y,,; with regard to X, we easily obtain cos X MXee + DX p,s Si A= PY p-1,2 81D 4 .........(18), and differentiating again cos X 228 d? a + (p — 1) sin X To. + PXp,s cos A = P sin 8 Signe : Multiply this by cos), and substitute for psin Xcosd “Aes and for pcos) sin 3 Sens from (13) (in the latter case with p reduced to p—1), then cos* i Ehe.s —sin X cos x Xo + PXp,s COSA = p’ sin? dX — p (2p — 1) x%p-1,5 Sin Asin 6 + p(p—1)yxpy_-»,,sin? 6. Simplify the right-hand member by the sequence equation (11) and divide by cos? X, Un, : AX rs — pa nA tt Piet )- a Xv.s=P(P—1)Xp—+,5 (14). The left-hand member of this equation has the form of Laplace’s equation for ©, In this case the function is linked to the alternate one by the right-hand member, which is zero for the Laplacian. § 4. The result (6) for the case in which sin 6 or w= 0, gives the P expansion of (1 — »’) in associated functions, an extension of the es known expansion of (1 — p2)2 in zonal harmonics. With == ()0 wT m.|pcos?r Oe =cosr af cos? yp. cos sda = Sy "IE (p —s) [s (p +8) 538 Mr Hargreaves, The Harmonic Hupression of the when p—s is even and = 0, ’ = () when p—s is even and < 0, |p. cos? rX (— jjP@rst-19 ~ (s—p) (s— p+2)...(8+p) when p ~ s is odd. On the right-hand of (6) the terms of the series which do not vanish are those for which n — s 1s even, in which case Jn +s (— Ware ce 2" |i (w—s) |k(m +8) Taking p—s even, p—m is also even, and the expansion is finite, terminating with n=p. ‘Thus s being not greater than p, n ranges from s to p, and = Ip Ge we)? BDae Ty (2n +1). |p Bes (ae 24/4 (p —s) E (p +s) 8 21.3...(p+n+1).2.4...(p—n) |n+s 4) z(m—S) n+ s x See (1 — y?)2 P,* (u) 2” |4 (mn —s) |3(m +8) 4 or an Bo nap (GIy 2? @p £1). Ju —s |3(p—s) |3 (pts) (L5H) = Pn: on Biel) 2 Sep =n) hors) S One (ie LE) oceccmoee| (15) With p ~ s odd, n ~ p is odd and the series infinite. Thus p.a- 2)2(— 1} (p+s+ —11°) (s—p)(s—p+2)...(8 +p) n=0 7 (2n +1) |p.1.3...(n + p) (— pF tet iy n=s 2.2.4...(p+n+1)(n—p)(n—pt+2)...(n+p) es DO? nts es Gees) ge) ee mM » (=p naw ™(2n+1)1.3...(n+p)(s—p)(s—p+2)...(s+p) |n—s n=s 229 4. (nt p+1)(n—p)(n—p+2)..(n+p) [E(m=s) |k(n+s) (AP Gee (16). = Daily Variation of Solar Radiation, ete. 539 Remembering that 1 1 \n +8 ee ANS s 2 an ae [=e ewrde= sq (15) implies pts ds P Fo 8) Op Tee i 32) yt ae fds Sea |jzo Se \3 ( pe?) 2 dy 8 du = Qn —s)|b(n+s) AS. (17), with n, p, s odd or even together, n2s, p2s, p Zn; but if with n, p, 8 odd or even together, s > p, then the integral vanishes. In the same way (16) gives for n and s odd or even together and p the reverse, and either n or p the greater, [a- pyr “de a 7.1.3...(0+p)n+s(s—p)(s—pt+2)...(s +p) GA. (nt prD Mod tw —p\a—p+2)...nep) For the ® notation the connecting formula is ln 35 Cl = te) lie (H) =1.3...(2n—1) Or s. Two particular cases may be noted, viz. those for which s = 0; (16) then gives for p =—1, 0, and all positive integers * (p = — 1, opening term 5) : ee cle ape sic. vise ane ae (4n+1)1.3...(2n—1)1.3...(2n+2p+ 1) 9.4...In.2.4...(2n4+2p +2)(2n—2p —1)(2n—2p+1)...(2n+2p+1) Pn(u) vehinens (ES) 3 and similarly (15) gives (= 1)" (4a +1) Pan (#) on P— POD, Ste Dp = UNE son $14 Das 2 So ora ga (2u+1)(2n +3)... (Qn + 2p +1) |p pen PNW (20). , - * This expansion was obtained directly in Messenger of Mathematics, “Oct. 1896, p. 92, but the reduction there given is only true for 2n>2p+1. The form above suits ‘either case. ve \ ve 540 Mr Hargreaves, The Harmonic Expression of the §5. Returning now to the particular case of the functions x required for a diathermanous atmosphere, p= 1, and we need only 1.3...(2n—1) a write the s suffix; accordingly with a, = abbreviation, 7 Ne) ae = We (oar) Or P'm(sind) Pon (sind) ) i= Zcosrcosdt 5 coshcosd > (@n—1)@n+2) ° an (OnE) | Xa= - zeosheosdZ Ga Son aD) | Vs= cos Acos*oS ‘s . | Pn (Sin) P”'on(sin 8) (2n—Z)(2n—1) 2n(2n+1)(2n+2)(2n4+8) Yu= 5 cos hcos'dS - 4 es PP, (sind) PP”, (sin 8) (2n—3)(2n—2)(2n—1) In (Qn4+1)(Qn+2)(Qn4+3)(2n+4) ) First notice that all these coefficients vanish at the poles, as they should do, for there is no daily variation proper at the poles. Again, sind, sind change signs, one in passing from northern to southern hemisphere, the other in passing through the equinoxes ; cos A, cos 6 do not change sign. 7 4, remaining odd terms, y;v;... are entirely odd, y.y,... entirely even, conclusions which may be drawn directly from (3). When sin 6 is expressed in terms of solar longitude by the relation sin 6 =sinesin 0, Hence we see that x, has a single even term = cos X cos 6, the X3X5--- and the odd part of x, have the form a, sin 0+ a;sin 30 +a;sin 50 +..., X2X, and the even part of yx, have the form My + a cos 20 + a,cos 40 +.... Where ar.odd power of cos 6 occurs, an elliptic integral is wanted to complete the harmonic expression, thus the even part of y,, viz. T cos dcos = cos 0 (5 + E, cos 20+ EF, cos 40...) = cos X. (‘7533 + ‘0324 cos 20 — 0003 cos 4@...), Daily Variation of Solar Radiation, ete. E.,, being used for the integral Tv [0s 5. cos 2n6dé, 0 2 or | /1 —sin?e sin? @. cos 2nOdé. 0 The series (21) converge only slowly; they have been used to confirm other work for the latitude of Greenwich and for latitude 60°, but in the absence of tables of associated functions calculated with reference to angle, the labour entailed is absolutely pro- hibitive. Accordingly in the case of the even functions yx, 4... the formula (3) was used to give particular values for 6 = 0°, 30°, 60°, 90°. Knowing the form of the expansion, these are sufficient to determine a) a,a,a,; on the assumption that as and subsequent coefficients are negligible. The tabulated results for y, obtained in the previous paper (Q there) were obtained directly from finite formulae involving elliptic integrals, and shewed a rapid con- vergence in the numbers a, a,..., although in that case also the convergence of the zonal harmonics was slow. The expectation that this would also prove to be the case for y,... was confirmed by the small values obtained for ag, so small that although a, was always included in the work, its values are not tabulated, as they only just come into the 4th place of decimals for latitudes 50° and 60°. For the odd functions y;y;... and the odd part of y, only the values for 30°, 60°, 90° are available ; sufficient to give a, a, a; on the assumption that subsequent terms may be neglected. Here also the values of a; turned out very small. The calculations were made to 6 places, and two are suppressed. As regards the tables it should be mentioned that when _ a0 a dt is used, formula (1) becomes 2Hdé FO hyn + En c08 9H in which the y’s depend on @ as shewn in table (A). With one year for the unit of time h=2zab, also d@ =27dt [1 + small quantities depending on eccentricity]. The transformation to mean time is made as in § 17 of the previous paper, the product x,d@ becoming 27yx,'dt, so that formula (1) then stands 2H a dt [4x + Xx cos sr], 542 Mr Hargreaves, The Harmonic Expression of the and accordingly the y, functions tabulated in (B) contain the correction for the varying distance of the sun. For abbreviation ¢ is written for 27t. The even terms give no difference between northern and southern hemispheres, for y; the sign is to be changed throughout for the southern hemisphere, for x with both odd and even terms, the effects are more complicated and results given for both hemispheres, (A) Table of y’s expressed as harmonic functions of sun’s longitude measured from the vernal equinox. Xi = a) + a, sin 6 + a, cos 20 + a, sin 30 + a, cos 40 + ... A= O 7533 ‘0 0324 0 — 0003 10° ‘7419 ‘0691 0319 “0 —-0003 20° ‘7079 1357 ‘0305 ‘0002 — 0003 30° 6524 ‘1976 0280 ‘0008 — ‘0003 40° sonal 2516 ‘0248 ‘0015 — 0002 50° “4842 2946 0208 ‘0038 — ‘0002 60° ‘3767 3190 ‘0162 0095 — 0002 Yo = Ay + dy cos 20 + a, cos 40. Vs = a, sin @ + a; sin 36. A= O° 3197 +:01388 —-0001 N= 10> 50229) 20 10° 3140 0144 — -0006 20° —-0441 —-0004 20° +2952, (0183 —-0002 30° —:0618 —-0016 30° :2648 0242 — -0003 40° — 07338 —:0042 AOS © ON ‘0330 — 0004 50° — 0737 —-0097 50° -1689 0455 —-0002 60° —-0531 —-0204 60° 1037 ‘0616 +0017 Xs = Ay + a, cos 20 + a, cos 40. w= OF — 0639 — ‘0028 =P 10° — 0618 — 0039 + 0001 20° — 0550 — 0078 — 0001 30° — 0439 — ‘0139 + 0000 4()° — ‘0289 — 0217 — ‘0001 a0 — 0115 — -0290 — 0025 60° + 0025 — 0272 — 0087 545 Daily Variation of Solar Radiation, ete. (Fr + PF) 809 2 TOO. + (2% + PE) S00 ZEOO-— CL .@6 + PZ) 8099190.—( _.¢ +P) 809 GEOO. + LEOT. (FF + Ph) $09 ZOO0. — (ZZ + PE) $09 ZOO. — (Z_ BS + PZ) 809 CCFO. — CFE .Z + P) 809 F900. + GSOT- (FF + PF) 809 F000. — (.6Z + PE) 800 S100. -—CF ZZ + PZ) $00 6EEO. — C1E .1 + P) 809 OSOO. + LZZS- (PF + PF) $00 E000. — (.2Z + PE) 800 Z100.— CL .6G + PZ) 800 SFZO- — CLF .0 + P) 809 1600. + SF9Z (FF + PF) 809 ZOO: — (cE + PE) 809 6000. — COT .2% + PZ) $09 ZSTO. — (OF .0 + P) $09 ZOTO- + SS6E. (FF + PF) S09 9000. — ‘ 6 + + $§) 809 1000. — CET .@6 + PZ) 809 SFO. — COS .0 + P) 809 SOLO. + OF TE: (FF + PF) 809 1000- — (Zz + PE) 809 1000: — GFT .2% + PZ) 809 LETO- — (0% .0 + ) 809 OTTO. + LETS 2X c Pr + PF)S00 1000: —GF_ GE + PE) S809 6610. + CFE .h + PZ) 809 6C00. — (EE .OL + P) 809 OTE. + (Fp + PF) 800 1000. — Cae .z¢ + + $€) 809 [1Z0.— (69 LT + PZ) $09 98Z0- — (LZ oEL + P) 809 Z9OE — LOLS: (Fp + PF) 809 ZOOO. — COE . 1S + PE) 809 CEOO- — CFS .6E + PZ) 809 OLLO- — (9% OL +P) Soo goTs.+ “ (FF + PF) S09 Z000. — CIE .6€ + PE) 809 ZOO. + COE ST + PZ) 809 GOGO: — GLE oT + P) 809 Z81Z- — GHSF- (pF + Pp) 800 2000. — CFF .6z + GE) 800 6Z00-—CL .86+$Z) 800 F910.-CFL OL +) S00 1T1G.+ “ (Hp + $F) 809 Z000. -CL .29 — PE) 809 £000. — (Zz .6T + $2) 809 GEO: — CFS LL + $) 809 TRS. — TLLS- (PP + PF) 800 Z000- — CIE .G¢ + PE) 809 CO00. + (EF .66 + PZ) 809 Z1ZO-— (9.6 +P)s80096TZ-+ “ (Pp + PF) S09 £000. — CET .9% + PE) 800 ZE00:-—CF 06 + PZ) 800 ZFHEO. — 0B .GL + P) $09 NEL. — FEO. (rp + PF) 800 £000. — Cal FZ + PE) S00 9100. —CZT Fz + $Z) 809 T9ZO.— COG .8 +%)8092G6EL-+ “ Ge PF) 809 £000. -—( .9T + PE) S99 FLOO- — COF .0Z + PZ) 809 EFEO- — CLT 1 + P) 800 GILT: — 6102: (FP + PE) S00 GO00. — CIE .22 + PE) 809 C100. — (8 .€%+ PZ) 800 S6Z0:-—CIT.8 +9)8008F60.+ “ : oh + PF) 809 S000. — CLE .TZ + PE) 809 LTO. — (8% .1Z + PZ) 809 6EE0.—( LL + P) $00 SEED. — GIPL- Fr + PF)S09EQ0O: —( E+E) S00 9100. — GOS .1Z + PZ) 809 1ZE0:— CEP 0 +4) 8090120. + SEL. 1X ‘meoX T ou qiun ‘uotjeytsed woay pornsvout 7 uz =p ‘sully Uva ul posseidxe §X jo afqey, (q) 2 006 Mr Hargreaves, The Harmonic Expression, ete. 544 ( ) $09 1800. — (.6 + PE) 800 F100-+( .ZE + PZ) 800 T1Z0. + (OF .9B + P) $09 $000. — 2200. ( ) 809 G00. — (.66 + PE) 809 €T00-.+( ZS + $Z) 800 06ZO. + COL .ZL + P) 809 G00. — ETTO. ( ) 809 €000. — (,66 + PE) 809 L100. +( 6 + HZ) 800 2TZO.+ CFG .¢ +)809 ET00. — 68Z0. (FF + PF) 809 E000. — (.26 +S) $09 1000-+( 3 +. OZ) 800 GET. FCO. +)802 L100. — GEFO. (FP + Ph) 809 1000. — (23 + PE) 809 F000. +( 23 + $Z)8098700.+ (OF .E +#)809 6100. — 0240. (FP + PF) S09 0000. —(.26 + PE) 809 1000. +( 2S + Z) 800 GE00. + (8E.0 +)809 TZ00.— 8T90. (PF + PF) 809 0000. — (6% + PE) $09 1000. + CT .2% + PZ) 800 9Z00. +0 .0 +) 809 ZZ00. — 6E90- Xx 4 EE + PE) S09 ZFEOO. — (LL + $Z) 809 ZOO. + CTI + $) 800 Gez0). o&E + PE) 809 9100. — (, LT + $Z) 809 OOO. + GIL + $) 809 8190. 268 + PE) $00 F000. — (IT + $Z) $09 E100. + (IT + &) 809 LPFO. s6E + PE) 809 000. — (, LT + $Z) 809 B00. + (IT + P) $00 GZZO. eX / ( ( ( ( ( ( + o68 + PE) 809 FOTO. — (LT + $Z) 809 STOO. + (LT + $) 809 TEGO. 2&6 + PE) 809 1600. — (.1T + $Z) 809 GZ00. + (. ET + ¢) $09 1E 10. INDEX TO VOLUME IX. Abelian functions (BAKER), 381. Alloy, Superficial colour of a silver zinc (HEycock and NEvILLE), 222. Roéntgen photographs of metallic (Heycock and NEvILue), 417. Amphioxus, Formation of germinal layers in (MacBripe), 150. and Balanoglossus, The relationship of (MacBripr), 309. ANDERSON, A., On the maximum deviation of a ray of light by a prism, 195. On the apparent electrification at the bounding surface of two dielectrics, 292. Annual General Meeting, 1895, 1. Bee ea. 1806. 201. 1897, 323. Assimilation in aquatic plants, Effects of water currents on (DARWIN and Pertz), 76. —— Farmer’s method of demonstrating (DARWIN), 338. Associates elected, 215, 258, 373, 522. Astronomical elements, Solar Radiation and its dependence on (HARGREAVES), 61. Atomic weight of oxygen (Scorr), 143. Baker, H. F., On the Gamma Function, 332. — On the lines of striction of a hyperboloid, 333. — Abelian functions in connexion with two-dimensional fluid motions, 381. —— On a certain system of differential equations defining periodic functions, 513. Balanoglossus and Amphioxus, Relationship between (MacBripe), 309. Batt, Sir R. §., On a point in theoretical dynamics, 193. Bariow, Dr Lazarus, On an osmometer, 72. BatEmMay, Rev. P. E., Elected Fellow, 1897, Apr. 26, 292. Bateson, W., Discussion of Dr Gaskell’s paper, 39. —- Notes on hybrid Cinerarias produced by Mr Lynch and Miss Pertz, 308. Bennettites, On the leaves of (SEWARD), 273. VOL. IX. PT, VIU, 43 546 Inder. Brack, A., Reduction of a certain Multiple Integral, 332. BuackMAN, F. F., Phenomena of Carbon Dioxide production associated with reduced vitality in plants, 273. Bigs, E. J., Discussion of Dr Gaskell’s paper, 42. —— Communication between peritoneal cavity and renal veins through nephrostomial tubules, 73. BuiytHE, W. H., Forms of cubic surfaces containing 27 real straight lines, 6. BorRADAILE, L. A., Elected Fellow, 1895, Nov. 25, 17. Brappsory, Prof. J. B., Elected Fellow, 1896, Apr. 27, 141. Brain with the chrome-silver method, Results obtained by staining the (HILL), 235. Britt, J., Generalization of certain properties of the tetrahedron, 98. BurKILL, I. H., Collection of plants from New Britain (Neu Pommern), 90. Cathode Rays (THomson), 243. Cavs, CHARLES, Elected Fellow, 1896, Feb. 24, 97. CureEB, Dr C., Equilibrium of isotropic elastic solid ta 61. —— Tides on the equilibrium theory, 318. Cinerarias, Notes on hybrid (BATEson), 308. Coatss, W. M., Elected Fellow, 1897, Apr. 26, 292. Compression of certain rarefied gases, On luminosity attending the (NEWALL), 295. Connecting threads in the cell wall, Method for demonstration of (GARDINER), 504. Coral reefs (GARDINER), 417. Crania found at Girton in 1881 (Horton-SmitnH), 111. —— From Teneriffe (SHRUBSALL), 154. Cubic surfaces containing 27 straight lines, Forms of (BLYTHE), 6 Darton, J. H. C., Elected Fellow, 1898, Feb. 7, 398. Darwin, F., and Miss D. F. M. Prertz, Effect of water currents on the assimilation of aquatic plants, 76. — On the injection of the intercellular spaces occurring in the leaves of Elodea during recovery from plasmolysis, 272. —— Observations on stomata by a new method, 303. —— Farmer’s method of demonstrating assimilation, 338. Dewar, Prof. J., Experiments on liquid air, 97. Differential equation of the first order, On Lie’s solution of a (Dixon), 279. Differential equations defining periodic functions, On a certain system of (BAKER), 513. Diffraction pattern near the focus of a telescope (MAYALL), 259. Dioxymaleic acid and its derivatives (FENTON), 142. Drxon, A. C., On a method of discussing the plane sections of surfaces, 198. — On Lie’s solution of a partial differential equation of the first order, 279, Dixon, E. T., On the theory of order, 513, Index. 547 Duckwortu, W. H., Elected Fellow, 1896, Feb. 10, 72. Dynamics, On a point in theoretical (BALL), 193. EASTERFIELD, and T. B. Woop, The constituents of Indian hemp, 144. Echinid larvae, On the continuity of Mesenchyme cells in (MAcBripg), 153. Eclipse of the Sun, 1898 Jan. 22, Total (NEWALL), 521. Elastic solid shells, Equilibrium of (CHREE, C.), 61. Electric discharge, Expansion produced by (Marttn), 11. In vacuo (MoncKMAN), 216. —— On the figures produced on photographic plates by (M°CLELLAND), 522. —— Waves and Réntgen Rays, Longitudinal (THomson), 49. Electrical oscillations in wires (PocKLINGTON), 324. Properties of newly prepared gases (TOWNSEND), 345. Electrification at the bounding surface of two dielectrics, On the apparent (ANDERSON), 292. Eliminant of two algebraic equations, On the degree of (LACHLAN), 313. Encephalartos Ghellinckii (Sewarp), 340. Expansion produced by electric discharge (MARTIN), 11. Farmer’s method of demonstrating assimilation (DARWIN), 338. Fenton, H. J. H., On dioxymaleic acid and its derivatives, 142. FuetcHer, W. M., Elected Fellow, 1898, Feb. 7, 398. Flints from Plateau gravel at Salisbury, Chipped (HuauHss), 120. ForsytH, Prof. A. R., Partial differential equations of the second order, 345. On some differential equations in the theory of symmetric algebra, 401. Frog, Communication between peritoneal cavity and renal veins through nephrostomial tubules in the (BuEs), 73. Gapow, H., Discussion of Dr Gaskell’s paper, 39. — On the supposed relationship of Birds and Dinosaurs, 204. Gau.op, E. G., Change of the independent variable in a coefficient, 272. Gamma Function (BAKER), 332. GARDINER, J. STanLEy, Elected Fellow, 1898, May 2, 513. — Coral Reefs of Funafuti, Rotuma and Fiji, 417. GARDINER, WALTER, Method for demonstration of connecting threads in the cell wall, 504. Gases, Electricity in gases and the formation of clouds in charged (TownsEND), 244, — Electrical properties of (TowNsEND), 345. GasKELL, Dr W. H., The origin of Vertebrates, 19. Geological history of monocotyledons (SEWARD), 110. Grack, J. H., On circles, spheres and linear complexes, 332. GriFFitHs, E. H., On thermometric “Fixed points,” 224. Happovy, A. C., Elected Fellow, 1897, Feb. 8, 243. HarcGrEAVES, R., Elected Fellow, 1896, Mar. 9, 110. 548 Index. Hareruaves, R., Distribution of solar radiation and its dependence on Astronomical Elements, 69. Harmer, Dr S. F., Discussion of Dr Gaskell’s paper, 38. —— On cyclostomatous Polyzoa, 208. On the casts of Iguanodon bernissartensis, Boulenger, 202. Hawaiian Insects (PERKINS), 373. Henry, J., Effect of ultra-violet light on the conductivity of iodine vapour, 319. Heycock and NEVILLE, Superficial colour of a silver zinc alloy, 222. — R®éntgen photographs of metallic alloys, 417. Hit, Dr A., Some results obtained by staining the Brain with the chrome- silver method, 235. Hits, Capt. E. H., On the Total Eclipse of the Sun, 1898 Jan. 22, 521. Honorary Members, Elected 1897, May 24, 309. Horton-Smita, R. J., Description of crania found at Girton in 1881, 111. Hovuau, S. S., Elected Fellow, 1898, Apr. 26, 292. Huaues, Prof. T. M°K., Exhibition of specimen of Travertine lining wooden pipe, 17. —— Symmetry in the foliage of Mulberry with asymmetry in individual leaves, 18. — On the Recurrence of Ice Ages, 114. — Chipped Flints from the Plateau gravel of Salisbury and elsewhere, 120. Horst, G. H. J., Elected Fellow, 1896, Nov. 23, 222. Hysteresis, Method of measuring loss of energy in (SEARLE), 2. Ice Ages, Recurrence of (HuGHEs), 114. Iguanodon bernissartensis, Boulenger, On the casts of (HARMER), 202. (GapDow), 204. Indian hemp resin, On the constituents of (HASTERFIELD and Woop), 144. —— Pharmacological action (MARSHALL), 149. Iodine vapour, Effect of ultra-violet light on the conductivity of (Hmnry), 319. Kathode Rays (THomson), 243. —— (THomMsON and SKINNER), 371. KERR, J. GRAHAM, 380. Lacu3an, R., Elected Fellow, 1897, Apr. 26, 292. —— On the degree of the eliminant of two algebraic equations, 313. Larmor, J., On the absolute Minimum of optical deviation through a prism, 108. —— On the period of the Earth’s free Eulerian precession, 183. On the theory of osmotic pressure, 240. Leakage of electricity through dielectrics traversed by Réntgen rays (THom- Son and M°CLELLAND), 126. Index. 549 LeatHem, J. G., On the deduction of magneto-optic phenomena from an electrodynamic energy function, 530. Lie’s solution of a partial differential equation of the first order (D1xon), 279. Lister, J. J., Quinqueloculine arrangement of the chambers in the young of Triloculina and Biloculina, 236. LivEine, Prof. G. D., On photographing the whole length of a spectrum at once, i141. LiversipG£, A., Elected Fellow, 1897, Feb. 22, 258. Longitudinal Electric Waves and Réntgen Rays (THomson, J. J.), 49. MacBripg, E. W., Discussion of Dr Gaskell’s paper, 37. —— Note on the formation of the germinal layers in Amphioxus, 150. —— On the continuity of Mesenchyme cells in Echinid larve, 153. The relationship between Amphioxus and Balanoglossus, 309. M°CLELLAND, J. A., and THomson, Leakage of electricity through dielectrics traversed by Réntgen rays, 126. M°CLELLAND, J. A., On the figures produced on photographic plates by electric discharges, 522. Macponatp, H. M., Elected Fellow, 1896, Nov. 23, 222. MAc.LaAuRIN, R. C., On the solutions of the equation (y?+.«?) ~=0 in elliptic coordinates, 531. MacManovy, Major P. A., A new method in Combinatory Analysis, 381. Magneto-optic phenomena, On the deduction of (LEATHEM), 530. MarsHat.t, C. R., Note on the pharmacological action of cannabis resin, 149. MarsHALL Warp, Prof. H., Elected Fellow, 1896, Feb. 10, 72. —— Artificial cultures of Stereum, a timber-destroying fungus, 340. Martin, Miss, Expansion produced by electric discharge, 11. Maximum deviation of a ray of light through a prism (ANDERSON), 195. Mayatt, R. D. H., On the diffraction pattern near the focus of a telescope, 259. Melanesia (WILLEY), 398. Mesenchyme cells in Echinid larve (MacBrips), 153. Minimum of deviation through a prism, Absolute (LARMOR), 108. Monckman, Dr J., On certain cases of discharge in vacuo and on the zigzag path of lightning, 216. Monocotyledons, Geological history of (SEwarRD), 110. Mulberry, symmetry in foliage of a branch of (HucHEs), 18. Nephrostomial tubules in frog, Communication between peritoneal cavity and renal veins (BLES), 73. NrviILLE and Hrycock, The superficial colour of silver zinc alloy, 222. New Britain (Neu Pommern), Collection of plants from (BURKILL), 90. Newatt, H. F., Spectroscope used in connexion with the 25-inch refractor, 179. —— A suggestion for a form of spectroheliograph, 179. 550 Index. Newatt, H. F., On the marks made by stars on photographic plates near the focus of a telescope, 269. — On luminosity attending the compression of certain rarefied gases, 295. — On the Total Eclipse of the Sun, 1898 Jan. 22, 521. Origin of Vertebrates (GASKELL), 19. Orr, W. M°F., Theorems on the contacts of spheres, 271. — On the interpretation of divergent solutions of the hypergeometric equation, 531. Osmometer (Dr Lazarus BAaRLow), 72. Osmotic pressure, On the theory of (LAaRMOR), 240. PARKIN, J., Elected Fellow, 1896, Feb. 24, 97. Peripatus nove britanniz, On the development of (WILLEY), 530. PERKINS, R. C. L., Notes on some Hawaiian Insects, 373. Pertz, Miss D. F. M., and Mr F. Darwty, Injection of intercellular spaces in leaves of Elodea during recovery from plasmolysis, 272. —— Effects of water currents on assimilation of aquatic plants, 76. Phosphorescence in gases (NEWALL), 295. Photographic plate, Effect of zinc and other metals on a (THOMSON), 372. Figures produced by electric discharges on (M°CLELLAND), 522. Platinum Thermometry, On a method of facilitating (WADE), 526. Pocxiineton, H. C., Electrical oscillations in wires, 324. Polyzoa, Cyclostomatous (HARMER), 208. Precession, On the period of the earth’s Free Eulerian (LARMor), 183. Prism, Absolute minimum of deviation through a (LARMoR), 108. Maximum deviation of a ray of light through a (ANDERSON), 195. Quinqueloculine arrangement (LISTER), 236. Ramsry, A. 8., Elected Fellow, 1898, Feb. 7, 398. REYNOLDS GREEN, Dr J., Elected Fellow, 1896, Feb. 24, 97. Rosson, H. C., Elected Fellow, 1897, Feb. 22, 258. f Réntgen Rays, Longitudinal Electric Waves and (THomson, J. J.), 49. — Leakage through dielectrics traversed by (THomson, J. J., and M°CLELLAND, J. A.), 126. — On the nature of (SToKEs), 215. — On the diffuse reflection of (THomsoN), 393. — Photographs of metallic alloys (Hrycock and NEVILLE), 417. RUTHERFORD, E., The discharge of electrification by ultra-violet light, 401. Scort, A., On the atomic weight of oxygen, 143. —— On the combining volumes of carbon monoxide and oxygen, 144. Index. 551 SEARLE, G. F. C., Method of measuring the loss of energy in Hysteresis, 2. Sections of surfaces, Method of discussing plane (Dixon), 198. SEDGWICK, A., Discussion of Dr Gaskell’s paper, 37. SEDGewWICK, W. F., Elected Fellow, 1898, May 2, 513. SEwarp, A. C., Notes on Geological History of Monocotyledons, 110. — On the leaves of Bennettites, 273. — On Encephalartos Ghellinckii, Lem., a rare Cycad, 340. Surerey, A. E., Discussion of Dr Gaskell’s paper, 40. SHRUBSALL, F. C., Crania from Teneriffe, 154. SKINNER, S., and THomson, Chemical effect of kathode rays, 371. Solar Radiation, Distribution of, and its dependence on Astronomical Elements (HARGREAVES), 61. Spectroheliograph, A suggestion for a form of (NEWALL), 179. Spectroscope used in connexion with 25-inch refractor (NEWALL), 179. Spectrum at once, On photographing the whole length of a (LivEtrNe@), 141. Spheres, Theorems on the contacts of (ORR), 271. Stoxss, Sir G. G., On the nature of the Réntgen Rays, 215. Stomata by a new method, Observations on (DARWIN), 303. Surfaces, Method of discussing the plane sections of (Drxon), 198. Symmetry in foliage of mulberry (HuGHEs), 18. Teneriffe, Crania from (SHRUBSALL), 154. Tetrahedron, Generalization of certain properties of the (BRILL), 98. Thermometric fixed points (GRIFFITHS), 224, Tuomson, Prof. J. J., Longitudinal Electric Waves and Réntgen Rays, 49. —— On the cathode rays, 243. —— HEffect of zinc and other metals on a photographic plate, 372. -—— On the diffuse reflection of Réntgen Rays, 393. — and J. A. M®Crienianp, Leakage of Electricity through Dielectrics traversed by Réntgen Rays, 126. — and S. Skinner, A chemical eftect produced by the impact of kathode rays, 371. TownsEnD, J. S., On electricity in gases and the formation of clouds in charged gases, 244. Electrical properties of newly prepared gases, 345. Travertine lining a pipe, Specimen of (HUGHES), 17. Triloculina and Biloculina, Quinqueloculine arrangement of chambers in the young of (LISTER), 236. Ultra-violet light on the conductivity of iodine vapour, Effect of (HENrRy), 319. — On moist air, Production of a cloud by action of (WILsoN), 392. The discharge of electrification by (RUTHERFORD), 401. Uranium rays on the condensation of water vapour, Action of (WILSON), 333, 552 Index. Vertebrates, The origin of (GASKELL), 19. Vincent, J. H., On the use of logarithmic coordinates in physics, 393. Wane, E. B. H., A method of facilitating the measurement of temperature by means of Platinum Thermometry, 526. Watts, A. J., Elected Fellow, 1896, April 27, 141. Wittey, A., Some zoological results of a voyage to Melanesia 1894—1897, 398. — The development of Peripatus novee britanniz, 530. Witson, C. T. R., Elected Fellow, 1896, April 27, 141. — On the action of Uranium rays on the condensation of water vapour, 333. — On the production of a cloud by the action of ultra-violet light on moist air, 392. CAMBRIDGE: PRINTED BY J, AND C. F. CLAY, AT THE UNIVERSITY PRESS, OD ey ere” PROCEEDING OF THE i 4 CAMBRIDGE PHILOSOPHICAL 7 SOCIETY. VN OL: 5EX4). PARTOL [MicHAELMAS TERM 1895.] Annee te Cambridae : PRINTED AT THE UNIVERSITY PRESS, AND SOLD BY DEIGHTON, BELL & CO. AND MACMILLAN & BOWES, CAMBRIDGE. G. BELL AND SONS, LONDON. 1896 Price Three Shillings. xe ware cs OF THE “i CAMBRIDGE PHILOSOPHICAL — SOCIETY. VOL: EX? PARTITE. [Lent TERM 1896.] Cambrivae : PRINTED AT THE UNIVERSITY PRESS, AND SOLD BY ; DEIGHTON, BELL & CO. AND MACMILLAN & BOWES, CAMBRIDGE. : G. BELL AND SONS, LONDON. 1896 > f Qe ce - sc . = A Price Three Shillings. LDPE FE, PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. VOL: IX:.; PARP, LT. [EasteER TERM 1896.] Cambridee : PRINTED AT THE UNIVERSITY PRESS, G. BELL AND SONS, LONDON. AND SOLD BY DEIGHTON, BELL & CO. AND MACMILLAN & BOWES, CAMBRIDGE. 1896 Price Three Shillings. gait UR Sa Ped PWaheealt t » OF THE CAMBRIDGE oi woman a SOCIETY. VOL. IX. PART IV. [MicHAELMAS TERM 1896.} Cambridae : PRINTED AT THE UNIVERSITY PRESS, AND SOLD BY DEIGHTON, BELL & CO. AND MACMILLAN & BOWES, CAMBRIDGE, G. BELL AND SONS, LONDON. 1897 Price Two Shillings and Sixpence. February 5, 1897. SA OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. aa VOL EX: dae ant ne ae: Me) a y Me? fs ‘ - PROCEEDINGS OF THE WF. é : Oe es aS CAMBRIDGE PHILOSOPHICAL S br lety & ANAS Hy eta) mo x a any SNS eity cet au Sota Mishse | So ine W Hh Sine ish : i coe ay yy ara Se MICE COL Ray dpa tod de bie the DAH Use ay ree ab bt pe bie bee ab te ee et : ‘ ape wih F ti hh) Wi Keg \ i RAE MR Pane ' ruiy tlh east “ Ate f ‘i pyre yay eet Wale Hee ‘ \ Nee H EID cle Mat ented dys ; ‘i \ ; Se ae BC TN, bree eke CRA ea ' Sarat ie re YE ‘ he . va i . rier es a Aes 1a Oth ares at bide Lehre ‘ ithe vate hee Aas ee ee Wate as i hn, ah hae Pear a " yb ee rere vb oop '