278 
CHEMISTRY: HARKINS AND WILSON 
will result if these two particles are brought very close together, is 
suggested by Lorentz,^ but he calculates neither the sign nor the magni- 
tude of the effect, nor does he indicate how the calculation may be made. 
The symbols used are G = electromagnetic momentum per unit volume, 
H = magnetic intensity vector, E = electric intensity vector, S = 
Poynting's vector for magnetic flux, c is the velocity of light, and [AB] 
represents the vector product. 
Now G = [EH]/c = S/c^, and for the field due to a system of 
charges ^ 
c c c c 
where the summation Sd/) is the vector product of each i with each j. 
The first summation gives the electromagnetic momentum which would 
be due to the particles if their fields did not overlap, and the second 
term gives the effect of the overlapping of the fields. This may be 
called the "Mutual electromagnetic momentum," and is designated 
by G. 
(1 - u')ei 
47r/'2(l-w2 sin^^j)' 
(1 — sin^ ^i) = /3i. The transverse component of E due to the two 
particles 1 and 2 is 
_ K^e r sin di sin 62] 
where the sign is positive if the charges have the same sign, and 
negative if they are of opposite sign. As only the longitudinal compo- 
nent of the vector G is desired, only the transverse component of E 
is needed. Then H — uE sin 4>/c, where 0 = the angle between E and 
the direction of u. 
If El is used, 0 = 90"", and H = u (Ei smOi ^ E2 sme2)/c. Hence 
[E Hi u 
G = = — (El sin di ± E2 sin ^2) {Ei sin di ^ E2 sin ^2), 
For point charges Ei = - — ^TTT^TWs* "^^^ ~ 
c 
and G = - - J E.E2 sm 0. sm Mr = "TFPW"^" 
Now r^^^ = - (r^ sin^ d) and sin^ d = y\ Let a = | distance 
between ei and ^2. Neglecting all terms in u^, and placing dr = Iwydydx, 
we have 
~ poop CO yHydx 
G = =t — — — 47r 
8cV JoJo\/{[(x - aY [{x ay -\- y""]}^ 
