60 G. F. Firzazratp—On the Mechanical Theory of Crookes’s Force. 
as it must be of this form we get on putting our other quantities into the forms 
of spherical harmonics 
eae Be ae oF 
w—=3MNv,%( mE 5 P) 
1 
P..=gMNv,(B,- 75 5 bt ZB.) 
P= 
= TpMNes B=P,, 
215, P 
“15 6 yx 
Similarly for the quantities of energy transferred we get 
ae 
= rei C, pdpdg 
oy aNe kf C, V1 —p2 sin $ dude 
aa 
om 
Kk LG V1 =? cos ¢ dudo 
so that if we assume as we eee, may 
Oe, + ¢.V1 =p? sin 6 + ¢,9/1 — 2? cos ¢ 
We get 
Q, _SMN»; 36, 
Q,=aMNe? o, 
Q.=sMNv3 6 
Even in this most general form we can see that there will in general be a differ- 
ence of pressure in different directions. For itis evident that the pressures in the three 
directions cannot be equal unless 6, and 6, both vanish, which will not in general be 
the case. Withouta knowledge of the nature of the distribution of the velocities 
and numbers of molecules moving in the different directions, it would be impossible 
to calculate the values of b,, b., b;, b,, and 6,, but I think we can see that they will 
in part at least vary as the square of the quantity of heat passing. This can be 
seen from the following considerations. No matter what the distribution of the 
velocities and number of molecules moving in the different directions may be, it is 
plain that terms occurring in the coefficients of “1—,? sin - ¢ VW1—,? cos ¢ Ze. In 
the spherical harmonics of the 1st order in uw and v will occur in the terms of the 
same order in nv n v’and n v* and that linearly, while these same terms will occur 
squared in the spherical harmonics of the 2nd order innvnv’, and nv’. Hence we 
see that terms occurring linearly in the spherical harmonics of the 1st order in nv* 
