412 
MR. S. H. BURBURY OR THE COLLISION OF ELASTIC BODIES. 
(1), (2), (3), (4). Four tangential components of velocity. 
(5). The angular velocity 0 of the spheroid round an axis perpendicular to OZ in 
the plane of the paper. 
And if u, U he normal components of velocity, and co the angular velocity round an 
axis through 0 perpendicular to the plane of the paper, the following two, viz. :— 
By conservation of momentum, 
(6.) mu + MU = (M -b to) V = mu' + MU'. 
By conservation of moment of momentum round the axis through 0 perpendicular 
to the plane of the paper, 
(7.) - McU + Aw = S = - McU' + Ao>'. 
We then form the equations 
m(u-u') + M(U-U') =0, 
— Me (U — U') + A(o)-o/) = 0, 
and by conservation of energy, 
to (u + v!) (u - u) + M (U + U') (U - U') + A (w + c o') (co - co') = 0; 
and equating the determinant to zero we obtain, neglecting common factors, 
U — U — Cco = p, 
u — U — Cco = — p, 
and, using Y, S, and p for S : . . . S„_j and It in the general equations, we see that if 
the Maxwell-Boltzmann distribution of energy exist, it is not disturbed by colli¬ 
sions between spheres and spheroids. 
III. Professor Burnside’s problem (see his paper, Bo}n Soc, Edinburgh, July 18, 
1887). He supposes a number of similar and equal spheres, each of unit mass, but 
each sphere, instead of being homogeneous, has its centre of inertia at a distance c 
from its centre, c being supposed very small compared with the radius. The principal 
moments of inertia are for each sphere A, B, C, and the direction cosines of c referred 
to the principal axes through the centre of inertia are for each sphere the same, viz., 
a, (3, y. The direction cosines of the line of centres at impact referred to the principal 
axes are for one sphere L, M, N, and for the other l, to, n. 
Further the normal velocities are U, u, and the angular velocities round the 
principal axes are 12^ I2 3 , fl 3 , w 1 , co 2 , <o 3 for the two spheres respectively. 
Finally we write, 
N/3 — My = P v/3 — my = p. 
Ly — Na = Q ly — net — q. 
Ma — L/3 = R TOa — 7/3 — r 
