Momentum in the Electric Field. 345 
points and 2, y; <; the coordinates of O when Q is taken as 
origin. Thus the moment of momentum about the axis of z 
vanishes. Similarly we may show that it vanishes about the 
axes of « and y, and thus the resultant momentum passes 
through Q the fixed point. 
This is only a particular case of the much more general 
proposition that the resultant of the momentum due to a 
stationary electrified point and a magnetic field passes through 
the fixed point when the magnetic field is continuous and 
derivable from a vector potential. For, taking the fixed 
point as origin, [the moment of momentum about the axis 
of z is given by the equation 
T=p\\\ {( (ya. —Bhy) y — (ahi —y/f,)e}-da dy dz, 
where 7, g,, 4, are the components of the electric polarization 
due to the charge, and are respectively equal to 
a 
= da’ dy’ dz I 
Substituting these values we find 
pe a 1 ae, =o 
et a Ydy v7 (Va 
=a eae |e dy dz. 
Integrating by parts, we find if a, @, y are continuous, and 
if at great distances from the origin they vary more rapidly 
than 1/7’, 
rte { a0) + 35 ay) — 5. (By +a0) da dy dz 
= He (iN { y (7 ce 1) } ate dy dz. 
Putting 
GED 0G) NI ae AD 
Gt Wee) nde ednesday. dy’ 
pe (qs dG oe aE 
ne Z pov G42 a —yVv'k eee 
-(0% ae 1) andy ae 
Shere ies = dG dH 
we have 
hyp de 
