February 4, 1892] 



NATURE 



335 



and estimates for the erection of the Sedgwick Memorial 

 Museum of Geology on a site within the Old Botanic area, con- 

 tiguous to the new Chemical Laboratory. 



Dr. Forsyth, F. R.S., is appointed an additional member of 

 the Mathematical Board for one year. 



In consequence of the lamented death of Sir George E. Paget, 

 Sir G. M. Humphry and Dr. D. MacAIister have been ap- 

 pointed to act for the Regius Professor of Physic, in reference to 

 Acts for medical degrees during the vacancy in the professorship. 



SOCIETIES AND ACADEMIES. 

 London. 

 Mathematical Society, January 14. — Prof. Greenhill, 

 F.R. S., President, in the chair. — The President drew the atten- 

 tion of the members present to the loss the Society had sustained 

 by the recent death of Prof. Kronecker, who was elected an 

 honorary member on January 14, 1875. — The following com- 

 munications were made : — The harmonic functions for the ellip- 

 tic cone, by E. W. Hobson. The harmonic functions for the 

 circular cone were introduced by Mehler ; an account of them is 

 given in Heine's Kiigelfiinctionen. In this communication the 

 more general functions are considered, which are required for 

 potential problems connected with the elliptic cone. It is shown 

 that the normal functions are of the form 



where r is the radius-vector, and yu, v are elliptic co-ordinates, 

 the functions A, B satisfying differential equations which differ 

 from Lame's equation only in having - h + p\ - i instead of n ; 

 thusthe functions A and B are Lame's functions of complex degree. 

 The forms of these functions as required for the potential prob- 

 lem are considered, and some examples of their application are 

 given. — Some theorems relating to a system of coaxal circles, by 

 R. Lachlan. This paper is based en a suggestion contained in a 

 short note by Dr. A. S. Hart in the Quarterly Journal {wo\. ii. 

 p. 143), who indicated a simple and elementary method of ob- 

 taining Poncelet's theorem. In the present paper this method 

 is discussed in detail. Poncelet's theorem may be thus stated : 

 If A I, An, A3, Ai, . . . A,„ be n points taken in order on the 

 circuinference of a circle S, so that any (« - i) particular con- 

 nectors of the poly stii^m A^A^ . ■ . A,i touch fixed circles coaxal 

 ivith S, then the remaining connectors of the figure will envelop 

 circles -which belong to the same coaxal system. If now S^, 5 de- 

 note the circle which is touched by "the chord A^A„ it is proved 

 that if {n - l) connectors of the polystigm touch any (« - i) of 

 the circles Sj, 2. Sj, 3, . . . , . . . S«_i, «, the remaining con- 

 nectors of the polystigm will envelop the remaining circles. 

 A few special cases are then discussed, among which the most 

 interesting is the case of zn points Aj, Aj, . . . Aj,,, taken in 

 order on a circle S, so that the chords Aj Aj, A2A3, . . . AjxAj, 

 touch another circle S' : it is then proved that the n chords 



A,A„4.i, AjA. 



must intersect in a limiting point 



of the circles S and S', and that the remaining 2«(« - 2) con- 

 nectors may be divided into (« - 2) sets of 2«, each set being 

 tangents to a circle coaxal with S and S'. Further, it is proved 

 that the 2«(« - i) connectors which do not intersect in the 

 limiting point may be arranged in «(« - 1) pairs, each pair 

 touching two circles of the system. — Note on the formula for 

 the number of classes of binary quadratic forms of a given 

 determinant, by Prof. G. B, Mathews. — Researches in the 

 calculus of variations (third paper), by E. P. Culverwell. — Mr. 

 E. B. Elliott, F.R.S., made a short oral communication on a 

 generalization of De Morgan's method of duality in partial 

 differential equations. He exhibited schemes of linear substitu- 

 tion for one set of variables in terms of another set of first 

 derivatives, which have the self-dual property, discussing the 

 cases of two and of three independent variables. — Major Mac- 

 Mahon, F.R.S., mentioned the "stamp-folding" problem, at 

 which Prof. Schoute, of Groningen, has been working. For a 

 strip of stamps (one stamp width), the following results, when 

 the strip is folded so that the face (or back) of one stamp only is 

 exposed, were given : (i) = i, (2) = 2, (3) = 6, (4) = 16, 

 (S) = SO. (6) = 144, (7) = 462, (8) = 1398 (?), (9) = 4527. For 

 squares, the results given were (2) = 8, (3) = 296, (4)= 13007 (?). 

 (9) is found to give more than i\ billions. The law of formation 

 of the numbers is sought. — Messrs. Basset, Love, Kempe, 

 Hobson, Prince C. de Polignac, and the President spoke upon 

 the papers. 



NO. II 62, VOL. 45] 



Linnean Society, January 21. — Prof. Stewart, President, 

 in the chair. — On a motion by the President, it was unani- 

 mously resolved that an expression of respectful sympathy should 

 be conveyed to Her Majesty the Queen, and to H.R.H. the 

 Prince of Wales, on the loss sustained by the death of H.R.H. 

 the late Duke of Clarence and Avondale.— Mr. M. F. Wood- 

 ward exhibited microscopic sections illustrating the develop- 

 ment of the teeth in the Marsupialia. He drew attention to 

 Prof. Kiikenthal's recent discovery of supposed rudimentary 

 successors in all the teeth, thus showing that the adult set of 

 teetli must be regarded as belonging to the first or milk series, 

 and not, as generally supposed, to the second or successional 

 dentition. These statements he was able to confirm for the 

 incisors and second upper molar of Didelphys. In the 

 Phalanger ( Trichosaurus) he found no trace of these structures 

 in connection with the molar teeth, but they were present 

 with the upper incisors. In no case did these rudimentary 

 successional teeth pass beyond the condition of simple down- 

 growths from the enamel organs of the functional teeth. — Mr. 

 J. W. Willis Bund exhibited a supposed hybrid between the 

 common and red-legged partridges, but in the opinion of 

 ornithologists present it was regarded as merely a variety of the 

 former species. — Mr. J. C. Mansel Pleydell exhibited a pair of 

 malformed horns of the roebuck found at Whatcombe, Bland- 

 ford, Dorset, their peculiar growth resulting from exostosis con- 

 sequent upon injuries sustained while in the sensitive condition. 

 — Mr. D. Morris communicated some further notes upon the 

 tick-pest of Jamaica, upon which an animated discussion took 

 place. — A paper was then read by Mr. F. E. Weiss "on the 

 development of the caoutchouc-containing cells of Eucommia 

 ulmoidcs, Oliver." He found that the bark and leaves of this 

 tree, used medicinally by the Chinese, and called by them "Tu- 

 chung," contain numerous elastic threads of silky appearance, 

 which proved to be of the nature of caoutchouc. They are con- 

 tained in long, unbranching cells, somewhat like latex cells, 

 which are found in the cortex and in the secondary phloem, 

 and accompany in large numbers the ramifying bundles of the 

 leaf and the pericarp. Unlike the ordinary latex cells, they are 

 not derived from specialised cells of the embryo, but originate 

 in all new growths, and can be seen forming in the cortex, the 

 pith, and the parenchyma surrounding the bundle of the petiole. 

 They originate in twos, by longitudinal division of a very 

 granular cell, both daughter cells growing out at their two 

 extremities into a long tube, which makes its way along the 

 intercellular spaces by sliding growth. They never contain more 

 than one nucleus, and the large granules of caoutchouc, which 

 soon make their appearance, finally coalesce into a single solid 

 mass, which has, when the tissues are broken, the appearance 

 of a silky thread. Mr, Weiss regards these cells as a primitive 

 form of latex cells, similar to those from which the more 

 elaborate ones of the ordinary Euphorbiaccts may have been 

 derived. — The meeting was brought to a close with a paper by 

 Dr. Jean Miiller on the Lichens of Manipur. 



Royal Meteorological Society, January 27.— Annual 

 General Meeting.— Dr. W. Marcet, F.R.S., Vice-President, in 

 the chair. — The Report of the Council for the past year showed 

 the Society to be in a very satisfactory position. In May the 

 library and offices were removed to more commodious premises 

 at 22 Great George Street. After defraying the cost of fitting 

 up the new offices, and the increased rental, there still remained 

 a balance in hand of ;[f224. Thirty-four new Fellows were 

 elected during the year, the total number on the roll of the 

 Society now being 552. Owing to the absence of the President^ 

 Mr. Baldwin Latham, through an attack of infliitWia, his 

 address on " Evaporation and Condensation " wa's read by the 

 Secretary. The question of evaporation is of as great im- 

 portance as the study of the precipitation of water on the face 

 of the earth, as the available water supplies of the country 

 entirely depend upon the differences between these two sets of 

 observations. The earth receives moisture by means of rain, 

 dew, hoar-frost, and by direct condensation. It loses its 

 moisture very rapidly by evaporation. Afthough evaporation 

 mainly depends upon the difTerence between the tensional force 

 of vapour due to the temperature of the evaporating surface, 

 and the tensional force of IJie vapour already in the atmosphere, 

 yet it is largely influenced by the movement of the air and by its 

 dryness, or the difference between the dew point and the actual 

 air temperature. Evaporation goes on at night so long as the 

 water surface is warmer than the dew point. With sea-water the 

 , evaporation is ^bout 4^ per cent, less than with rain water, while 



