April 23, 903] 



NA TURE 



599 



striking curve of diurnal variation, the early morning- maxi- 

 mum being most pronounced ; the afternoon one is also 

 present, but is much less protracted and of far less ampli- 

 tude than the former. Minima occur about mid-day and 

 in the evening. The author concluded by giving an account 

 of Halli well's float pattern self-recording rain-gauge. 



Mathematical Society, April 16. — Dr. E. W. Hobson, 

 vice-president, in the chair. — Mr. C. S. Jackson exhibited 

 the logo-logarithmic slide-rule constructed from a design 

 prepared by Colonel Dunlop and himself, and gave an 

 account of the history of the invention. In principle it 

 goes back to the early part of the nineteenth century. — The 

 following papers were communicated : — Prof. A. Lodge, 

 Relations between points (in a plane) having conjugate 

 complex coordinates. This is an addition to a paper read 

 at the meeting in January, 1903. — Prof. A. E. H. Love, 

 Note on exact solutions of the problem of the bending of 

 an elastic plate under pressure. The method given by 

 Michell in Proceedings, vol. xxxi., yields exact solutions of 

 the problem, which can be determined completely when the 

 plate is bent by uniform pressure applied to one face, or by 

 pressure varying uniformly over the face, and the (clamped) 

 edges are circular or elliptic. For any form of clamped 

 edge the deflexions produced by such pressures are deter- 

 mined by the same differential equations and boundary con- 

 ditions as arise in the ordinary approximative theory. 1 he 

 principles on which the ordinary theory is founded are true 

 to a certain order of approximation only. The small cor- 

 rections which must be made do not affect much the calcu- 

 lation of the strength of the plate to resist bending, but 

 they account rationally for the existence of the shearing 

 stresses and of the tension (analogous to that of a mem- 

 brane) by which the pressure is balanced. Under uniform 

 pressure the median plane of the plate is unstrained, but 

 under varying pressure this surface undergoes a small ex- 

 tension. — Mr. E. T. Whittaker, On those functions which 

 are defined by definite integrals with not more than two 

 singularities. Among the functions included in this class 

 are the Bessel functions, the error-function, the logarithm- 

 integral, the cosine-integral. A definite integral containing 

 two numerical parameters is discussed, and it is shown 

 how, by specialisation of the parameters, the above-men- 

 tioned functions and many others can be obtained. The 

 functions defined by the definite integral satisfy a linear 

 differential equation of the second order which is a general- 

 isation of Bessel 's equation ; they possess Asymptotic ex- 

 pansions, and are connected by recurrence-formulae and 

 integral-formulae analogous to those which hold in the case 

 of Bessel functions. Attention is drawn to new functions 

 included in the class defined by the general definite integral. 

 — Mr. H. MacCoii, On the validity of certain formulae. 

 The paper contains a criticism of certain formulae in the 

 algebra of logic. — Mr. A. Young, On covariant types. — 

 Mr. R. F. Gwyther, On the deduction of Schlomilch's series 

 from a Fourier series, and its development into a definite 

 integral. The paper presents a demonstration of the con- 

 nection of Schlomilch's expansion of an arbitrary function 

 in a series of Bessel functions of order zero with Fourier's 

 expansion of the same function in terms of cosines. Both 

 expansions can be represented by the same surface integral, 

 and the one is transformed into the other by change of the 

 variables in the double integral. — Messrs. H. W. Richmond 

 and T. Stuart, The inflexion-conic of a trinodal quartic 

 curve. It is known that the six points of inflexion of a 

 trinodal quartic curve lie on a conic. The paper contains 

 two simple proofs of this theorem, and the equation of the 

 conic is obtained explicitly in various systems of coordinates. 



Edinburgh. 



Royal Society, February 16. — Lnrd M'Laien in the chair. — 

 Dr. J. Beard communicated a paper on the embryology 

 of tumours, in which, after a critical examination of the 

 theories which had been brought forward, he gave a detailed 

 description of his own views. The continuity of germ cells 

 from generation to generation was now becoming generallv 

 accepted among embryologists. The fertilised egg did not, 

 however, give rise directly to an embryo, but rather to a 

 set of germ cells, every one of which had the power, with 

 appropriate environment, of developing into an embryo. 



NO. 1747, VOL. 67] 



The number of germ cells in a particular species was 

 always some power of two; for example, eight in the frog, 

 thirty-two in the lamprey, 128 in the dog-fish, &c. Of 

 these one went to form the embryo, and the remainder 

 migrated or wandered about in the embryonic body to- 

 furnish the foundation of the reproductive products. A 

 certain percentage would get hopelessly wandered, and 

 never find their way to the normal position. It was in these 

 aberrant or " lost " germ cells that Dr. Beard found the 

 origin of tumours. In short, a tumour was a more or less 

 reduced, more or less incompletely differentiated sterile Meta- 

 zoan organism. It started by the abnormal development of a 

 vagrant germ cell, and growing under conditions unfavour- 

 able to the complete and normal differentiation of all its 

 parts, it unfolded and developed those things for the growth 

 of which the nidus was suitable, the rest degenerating. 

 Exactly as identical twins were the offspring of two sister 

 or brother germ cells identical in ancestry from the same 

 primitive germ cell, so any animal and a tumour within it 

 stood in the same relation of ancestry from one primitive 

 germ cell. — Sir John Murray communicated some pre- 

 liminary observations on seiches in certain Scottish lochs, 

 and exhibited a seichometer with which he hoped in the 

 coming season to get a more definite and precise record 

 of these oscillations. — Prof. Chrystal then gave an account 

 of the theory of seiches, touching on the work that had 

 been done by the Swiss and American investigators, and 

 developing the mathematical theory in a form convenient 

 for application. The theory was illustrated by a series of 

 experiments in a rectangular trough, carried out with great 

 skill by Mr. E. Maclagan Wedderburn, the characters of 

 the uninodal and binodal seiches and the influence of a 

 shelving bottom being well brought out. — A short paper 

 was presented by Prof. Anglin on the equation of a pair 

 of tangents to a conic. 



Dublin. 

 Royal Dublin Society, March 17.— Mr. Samuel Geo 

 ghegan in the chair. — On the petrological examination of 

 paving sets, by Prof. J. Joly, F.R.S. By examination of 

 the worn surfaces of many different sorts of paving sets, in 

 conjunction with petrological examination of the rock, it is 

 found possible to connect the qualities of the set with the 

 nature and relative amounts of the mineral constituents 

 present in the rock. The petrological examination of the 

 rock now becomes a very sure guide in the examination of 

 an untried set ; its degree of durability and roughness under 

 wear can be foretold with a high degree of certainty. — Mr. 

 William Tatlow exhibited and described an aluminium 

 rectifier for alternating electric currents, and a three-phase 

 rotary converter. 



Paris. 



Academy of Sciences, April 14. — M. Albert Gaudry in 

 the chair. — On certain algebraic surfaces for which the 

 integrals of the total differentials, reduce to algebraical 

 logarithmic combinations, by M. Emile Picard. — On the 

 discussion and integration of differential equations of the 

 second order with constant coefficients, by M. E. Vallier. — 

 The catalytic decomposition of alcohols by finely divided 

 metals; primary alcohols, by MM. Paul Sabatier and J. B. 

 Eenderens. The reactions previously described for ethyl 

 alcohol have been extended to higher alcohols of the same 

 class, and it has been found that, with reduced copper 

 between certain limits of temperature, the alcohol is split 

 up into the corresponding aldehyde and hydrogen, without 

 any secondary reactions of importance. With reduced 

 nickel the reaction is more violent, the aldehyde formed 

 being further acted upon. — The sounds emitted by sand in 

 motion, by M. Lortet. — On the projection of matter round 

 the electric spark, by M. Jules Semenov. From the experi- 

 ments described it would appear that gases and vapours, 

 traversed by a spark, are thrown out by it in all directions, 

 as a consequence of the sudden elevation of temperature. 

 The direction of the current does not appear to have any 

 effect upon the sense of this projection. — The action of radio- 

 active bodies on the electric conductivity of selenium, by 

 M. Edmund von Aubel. The radio-active bodies examined 

 acted upon selenium in a manner resembling light or the 

 Rdntgen rays, but the effect is produced much more slowly. 

 — On the electric and magnetic dichroism of liquids, by 



