66 G. F. Fivzcrratp—On the Mechanical Theory of Crookes’s Force, 
If V2 and V,? be the total mean squares of the velocities of agitation V,?=v,?+w, , 
V2=v.2+u,* and the quantity of heat transferred is 
Q=k(p, VP, Ty p2V ou?) 
k being as before the coefficient by which the vis viva of translation has to be 
multiplied in order to get the total energy of the gas. 
From these we easily obtain 
K=p,ti,(u,+%2) 
Q=hou,(V? re 5) 
V;-V; 
Uf Ug 
We have besides p,-+e,=e where e is the density of the gas. Hence there are 
six equations between the six unknowns 
”, Q=kK: 
Pi Pz Vy Vz % Us 
and in order to eliminate them and obtain an equation between K and Q it is 
necessary to make one further assumption. I assume then that 4=\% and %=)», so 
that Vi=(2+1)u? and V’=('+1)u%, I assume this because if the streams did not 
interfere with one another at all we should have 
udagVi so that if °+1=a* we should have o’=6 and a=2°5 q.p. 
Our equations then become 
V, —V/=a'(u,7—4u;) 
7. Q=—kKa*(u, — ue) 
from these we can eliminate “p.p: and putting V:\—V.’=X* we get 
22 
3 K°Q?— a®k*X* ‘ K4—0, 
Which is a quadratic for Q? or a biquadratic for K. 
Solving for Q we get 
Qi+4 
ckKVa 
ih ae 1 
; y X4p? + 4a2K? 20K} ; 
as evidently the other solutions are inadmissable. 
From this we may get an approximate value for Kin terms of Q for unless 
« be very large or the density or difference of temperature very small X%p is 
much greater than 2aK. For instance if V, and V,. correspond to a difference of 
10°C 
Ti at 
V,—48500 nf = V,=48500 4/375 
and consequently 
(48500)2 } 
“5 *, X=9700 
while p=, for air at atmospheric pressure 
. X%=107600 
