193 
1906-7.] Dr W. Peddie on Vibrating Systems. 
always unity, the excess of the radial over the transverse component of 
kinetic energy is 
tan 0 - 20 
tan 0 
where 0 is the angle which the path makes with the tangent plane at its 
extremity. The element of solid angle is 2w cos OdO , so that the average 
excess of the radial over the transverse component of kinetic energy is 
7 r 
p tan 0-20 
J tan 0 
o 
cos OdO , 
which can be put into the 
or, again, into the form 
2 x 2 2.4/ x 2 \ 2 2.4 • • • ■ (2 n) / x 2 \ n 
1+ 3lH^ 2 + OVrV^; + ' ' + 3.5 • • • • (2n + 1)\T+^/ _ * 
Evaluation of the first two terms of the integral shows that the whole 
quantity is negative ; so that, in the motion of a single particle throughout 
a sufficient time, there is excess of the transverse component of kinetic 
energy over the radial component ; or, in the motion of many non-colliding 
particles, there is, on the number-average, a like excess. 
VOL XX VII, 
„ , r 1 ax v 
3 ~ 4 /o rv? § 
form 
3 + 4 
n 
xddx 
+ e J 
13 
