438 PROFESSOR G. G. STOKES OR MR, CROOKES’S EXPERIMENTS ON 
glass fibre be treated as perfectly elastic, as it doubtless may be in considering the 
correction to be made for the inequality of the times of vibration, even though its 
defect of elasticity might not, possibly, be absolutely insensible in its influence on 
the main motion. Then if there were no fluid the equation of motion of the lamina 
would be 
l|?+n*l!9=0. 
As in the cases treated of in the paper of mine already referred to, the resultant 
pressure of the fluid on the lamina (the term “ pressure” here including the tangential 
action), will partly agree in phase with the displacement or force of restitution, partly 
with the velocity of the lamina. The first part will have the effect of adding to the 
mass of the lamina an ideal mass depending on the density, viscosity, and time of 
vibration. From the dimensions of the quantities involved with respect to time and 
density, this ideal mass must be of the form pf 
flT 
There is no need to express the 
dependence of the function f on the scale of lengths. In a similar manner the part of 
cW 
the resultant pressure which is multiplied by — must be expressed by p multiplied by 
LLT 
some other function of — and divided by a time. We may express it therefore by 
( ult\ t lit 
—J where n is —. Denoting the two functions of — by A and B respectively, 
we have accordingly for the equation of motion 
rlf) 
(I+Ap)^+2Bpnf+^=0 
dt 
( 5 ) 
The integral of this equation is 
where 
0=e qt (c cos mt-\-c sin mt) 
B pn 9 _ « 2 I _ By# 
q ~I+Ap’ m ~~ 1 + Ap (I + Ap) 2 
and since by definition of n, m—n, we have 
a 2 I 
n ~+'l-I + A P ’ 
and then by eliminating A between the last equation and the last but two we have 
a~Jq 
B= 
pn(n~ + j 3 ) 
( 6 ) 
