322 Mr CJtree, Changes in the dimensions of Elastic Solids. [Mar. 7, 



to be the same as in a sphere of the same material of equal 

 volume, and it is thence concluded that the spherical is a form in 

 which the reduction of volume due to gravitation is in general 

 either a maximum or a minimum. The reduction of volume is 

 calculated for a gravitating ellipsoid, and it appears that the 

 sphere is the form in which, when the volume is given, the re- 

 duction is a maximum. In a nearly spherical ellipsoid whose 

 principal sections through the longest axis are of eccentricities e x 

 and e 2 the reduction in volume is given by 



- Bvfv = (gpR/rok) {1 - (e* - e t V + e/)/45}, 



where R is the radius, and g the value of gravity at the surface, 

 in a sphere of equal volume and density. 



In a given volume of an aeolotropic material a very slight 

 assumption of an ellipsoidal form, insufficient to produce an 

 appreciable effect if the material were isotropic, increases or 

 diminishes the diminution in volume due to mutual gravitation 

 according as it consists in a lengthening or a shortening of those 

 material lines which are parallel to directions in which the 

 linear contraction under uniform normal pressure is above the 

 average. 



(6) On the law of distribution of velocities in a system of 

 moving molecules. By A. H. Leahy, M.A., Pembroke College. 



1. The following proof appears briefly to establish the fact 

 that Maxwell's law of distribution of velocities gives the only steady 

 distribution. The proof is a little shorter than the ordinary proof 

 as given by Boltzmann, even if Mr Burbury's variation of it as 

 published in the Philosophical Magazine for October 1890 be 

 adopted. 



Let a particle whose velocity is OP in magnitude and direction 

 strike a particle whose velocity is op. Suppose the particles to 

 belong to different systems, and let the number of particles of 

 the first kind which have velocity components lying between £ 

 and g+d];, w and w + dv, £ and £+d£, where £, n, £are the com- 

 ponents of OP, be F(0P)d^dnd^. Let f {op) d%dw' d£ have a 

 similar meaning when applied to the particles of the second 

 system. Then the number of impacts which particles with ve- 

 locity OP have with particles of the second system which have 

 velocity op will, in the interval dt, be per unit volume 



F(OP)d^d v d^.7rs' 2 udt.f(op)d^d v 'd^ (1), 



since each particle in the unit volume strikes, on the average, 

 7rs 2 udtf{op)d^'dn'd^' in the interval dt; the particles bejng re- 

 garded as hard spheres, the sum of the radii of two spnefes, one 



