344 Prof. J. J. Thomson on 
We can easily show that 
{td eo dR 
iil Pade Par dx dy dz= a ae 
rite anbe sir Bobi) i oe 
{i Zu oP af dx dy 1 ae 5 
where R is the distance OQ between the fixed and moving 
points, and #9, yo, 29 are the coordinates of Q. Using these 
values for the integrals we find 
ie ee Bae _ \ 
Pike da, dz," daydyy  ‘\dyy * de). 
pee’ ad’R aR d?R u 
tay (aaa. ° asda dag) * MOR 
ips pee’ d,; dR, dR. dRy . /u 
—— > de, \" de, +o twa.) tHe oe 
Similarly, 
en aR, aR fe Be! 
v ay At dx, 3 dys *- ” die bit. R 
_' mee dg dR, dR dk ,w 
W= ae " ast dy TO de, tHe RK: 
We notice that 
au. dV. aw 
da, * dy. * dzz 
We shall now show that the line of the resultant momentum 
passes through Q the fixed point. Take Q as origin, let 
x,y,z be the coordinates of any point in the field. Then 
the moment of momentum of the field about the axis of < is 
equal to 
uM {Quy —Bh\y—(ah—yf)e}da dy de 
= w\\\y (a7 +yg+ch)dax dy dz 
—p\\\h (ca --yB+zy) dx dy dz; 
each of the integrals is equal to 
/ 
2 _ (va;— Wy), 
where R is the distance OQ between the fixed and moving 
2 ee 
