November ii, 1897 J 



NATURE 



47 



SOCIETIES AND ACADEMIES. 



Cambridge. 



Philosophical Society, October 25. — Mr. F. Darwin, 

 President, in the chair. — The following elections were made : 

 President — Mr. F. Darwin. Vice-Presidents— Prof. Newton, 

 Prof. J. J. Thomson, Mr. Larmor. Treasurer— Mr. Glaze- 

 brook. Secretaries— Mr. Newall, Mr. Bateson, Mr; Baker. 

 New Members of Council — Mr. Marker, Mr. Hutchinson. Prof. 

 Liveing, Mr. Skinner. — The following communications were 

 made : Electrical oscillations in wires, by ^Ir. H. C. Pock- 

 lington. In this paper are discussed some problems relating to 

 electrical oscillations about wires made of perfectly conducting 

 material and of circular cross-section. The first step is to find 

 an expression for the electrical forces which satisfies the space 

 differential equations, and gives infinite values for the forces 

 near the wires. It is then shown that the arbitrary function 

 contained in that expression can be so chosen as to make the 

 value of the component of the electric force tangetial to the sur- 

 face of the wire vanish if small quantities of the first order be 

 neglected. The value of this arbitrary function is found in the 

 case of a circular wire, and equations are found for the period 

 of oscillation and the decrement of the oscillation. These equa- 

 tions are solved in the case when the wire is so thin that it is 

 permissible to neglect not only its radius in comparison with 

 the circle, but even the square of the reciprocal of the logarithm 

 of is radius in comparison with unity. In this case the altera- 

 tion in period and the damping depend on the logarithm of the 

 ratio of the radii of the wire and the circle. As a corollary, the 

 problem of the resonance of a complete circular resonator is 

 discussed. It is found that when accurately tuned, the magni- 

 tude of the current induced is independent of the thickness of 

 the wire, and that the thinner the wire the more sensitive it is 

 to accuracy of tuning. The case of waves propagated along a 

 helical wire is next considered, a general equation being found 

 in which small quantities are neglected. The case when the 

 reciprocal of the radius of the wire can be neglected is discussed 

 in detail. For this case it is found that when the period 

 is not great, there are two velocities of propagation pos- 

 sible, one with a velocity {v) measured along the wire, 

 equal to that of light, the other with a greater velocity. 

 If, however, the period is greater than a certain finite 

 value, the former mode of propagation only is possible. If, 

 however, the period is very great, the velocity of propagation 

 may be greater than v, and if the period is so great that the 

 product of the wave-length in free space into the diameter of 

 the wire is very great compared with the square of the diameter 

 of the helix, the velocity attains a limiting value equal to v when 

 measured along the axis of the helix. — On circles, spheres, and 

 linear complexes, by Mr. J. H. Grace. Clifford in his paper on 

 Miquel's theorem gave an infinite series of theorems commenc- 

 ing with the fact that, given four lines, the circumcircles of the 

 triangles formed by them meet in a point. The present paper 

 contains a more general series of theorems in two dimensions, 

 and a somewhat analogous series in three dimensions. Also the 

 first theorem of the set for four dimensions is proved. Then 

 the method of Klein (" Linien-Geometrie und metrische 

 Geometric," Math. Ann , v. ) is used to transform these results 

 into theorems regarding linear complexes and straight lines ; 

 and the transformation of Lie {Math. Attn., v.) is used to obtain, 

 from properties of straight lines and linear complexes, results 

 concerning spheres and their angles of intersection. — Theorems 

 relating to the product of two hypergeometric series, by Mr. W. 

 McF. Orr. This paper deals with such theorems as that stated 

 by Cayley, /%//. Mag., November 1858 (Collected Papers, vol. 

 iii. p. 268). — Reduction of a certain multiple integral, by Mr. 

 Arthur Bla[ck. The integral dealt with is one in n variables ; 

 the suhject of integration is one involving an exponential of 

 which the index is a general quadratic function of « -t- i 

 variables. — On the gamma function, by Mr. H. F. Baker. This 

 note deals with the uniform convergence of a certain limiting 

 process.— On the lines of striction of a hyperboloid, by Mr. 

 H. F. Baker. This note remarks on the known fact that the 

 line of striction belonging to either system of generators is a 

 unicursal quartic curve, and considers the parametric expression 

 of more general forms of octavic curves with six double points. 

 — On the action of the radiation from uranium salts on the 

 formation of clouds, by Mr. C. T. R. Wilson. It has been 

 shown in previous papers (Proc. Roy. Soc, vol. lix. p. 338, 



NO. 1463, VOL. 57] v., - 



1896; Phil. Trans., vol. clxxxix. A, p. 265, 1897) that under 

 the action of Rontgen rays, nuclei are produced in moist dust- 

 free air, capable of acting as centres of condensation, when the 

 air, initially saturated, suffers a sudden expansion such that 

 7'../t/,, the ratio of the final to the initial volume, exceeds I'ac. 

 Nuclei requiring exactly the same degree of supersaturation are 

 present in very small numbers in moist dust-free air under 

 ordinary conditions. Recent experiments show that the radia- 

 tion from uranium salts introduces nuclei, again requiring 

 exactly the same degree of supersaturation, in order that con- 

 densation may take place upon them. The nuclei are many 

 times more numerous than in the absence of the rays. 



Paris. 



Academy of Sciences, November 2. — M. A. Chatin in 

 the chair. — Actinometry in balloons, by M. J. Violle. Actino- 

 metric observations from balloons should possess many ad- 

 vantages over those taken on the earth, as the complete absence 

 of dust is a.ssured, and the air layer is also reduced. A trial 

 ascent in the Balaschoff, by MM. Hermite and Besan9on, 

 showed that the radiation from the balloon itself was a neglig- 

 able quantity ; but from the results obtained, it would appear 

 that there was still above the balloon such a quantity of water 

 as in the liquid state would form a column of several centi- 

 metres in thickness. — On the preparation and properties of the 

 borides of calcium, strontium, and barium, by MM. H. Moissan 

 and P. Williams. The boride of calcium is formed by heating 

 a mixture of dry calcium borate, aluminium, and sugar charcoal 

 in a carbon crucible in the electric furnace for seven minutes 

 (900 amperes and 45 volts). The duration and regularity of 

 heating has a great influence upon the yield. The boride is 

 obtained as 'a black crystalline powder, so hard that it readily 

 scratches rock crystal. Chemically it is not easily decomposed, 

 dry hydrogen at a red heat, nitrogen at 1000°, and water at 

 ordinary temperatures being without action upon it. Fluorine 

 attacks it in the cold with incandescence, but the other halogens 

 only destroy the boride at a red heat. The borides of strontium 

 and barium are prepared in the same way, and possess analogous 

 properties. The formula of these compounds, RBg, is identical 

 with that of the hydrozoates of Curtius, RNg. — Occultation of 

 the group of the Pleiades by the moon on October 13, 1897, 

 at Lyons, by M. Ch, Andre. — Observations on the Perrine 

 comet (November 2, 1896) made at the observatory of Rio de 

 Janeiro, by M. Cruls. — New demonstration of the fundamental 

 theorem of projective geometry, by M. H. G. Zeuthen. —On the 

 determination of the integrals of a partial differential equation 

 by certain initial conditions, by M. E. Goursat. — On the problem 

 of M. Bonnet, by M. C. Guichard. — Compressibility of gases 

 at different temperatures at pressures near that of the atmo- 

 sphere, by M. A. Leduc. — On the atomic weights of argon and 

 helium, by M. H. Wilde. — On the stannic acids, by M. R. 

 Engel. A resume of the work on the stannic acids, with an 

 explanation of some of the apparent contradictions. — Use of 

 fluorescine for the detection of traces of bromine in a saline 

 mixture, by M. H. Baubigny. The bromine is set free by a 

 mixture of potassium permanganate and copper sulphate, and 

 the vapours evolved allowed to impinge upon fluorescine paper. 

 The presence of as little as •001 gr. of bromine in 10 gr. of 

 common salt is shown by a reddish coloration of the paper due 

 to the formation of eosin. —On the crystallographic identity of 

 the dextrorotatory and laevorotatory asparagines, by M. P. 

 Freundler. The accuracy of Pasteur's law having been called 

 in question by M. Walden from certain experimental deter- 

 minations of M. Grattarola on the two asparagines, these 

 angular measurements have been redetermined, with the result 

 that the deviations found are well wiihin the limits of experi- 

 mental error. — Study of the transformation of sugars occurring 

 in olive oil, by M. C. Gerber. — Mixed grafting, by M. L. 

 Daniel, A description of a new mode of grafting which gives 

 better results when the two plants present marked physiological 

 differences. — On the evolution of the black rot, by M. A. 

 Prunet. Injection may take place through the leaves of the 

 vine at a certain stage of development, after which the leaves 

 lose their susceptibility to black rot. It is just before this 

 critical period that remedial measures should be applied to the 

 leaves. — On the age of the grits containing Sabalites ande- 

 gavensis in the west of France, by M. Jules Welsch. — New 

 researches on the Ostioles, byM. J. J. Andeer. 



