308 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
Writing 
it follows that 
^o/Rl — ^l5 Vo/^l — A*-!) Co/11'1 — 
{x-^o)/R = \ 2 , {y- 7 ]^>)IR = fl-j, {^-L)I^ = V 2 , 
I\i + m[Xi + 7 iv-^ = —cos(f), 
and the relations satisfied at the point Q are equivalent to 
K = ^1 + 2^ cos (f), 1^2 = 1^1 + 2m cos cf), V2 = vi + 2 n cos <f), 
whence the above values of may be written 
The principal parts of the components of the electric force at the point {x, y, z) due 
to the surface distribution are therefore given by 
Xo = -iK^ (R-^-/r^)-‘^’ e-(w-R.-B) ^cos (/> + 2n/}/RRi, 
Yo = {/rii.i + 2i.imcos(/) + 2mn}/RRa, 
Zo = {-V-pi" + 2vincos(/> + 2?i"}/RR,, 
and, writing 
X = \ 7 \ y — IX 7 \ z = Vl\ 
where 
= X^+Tf + Z^, 
the principal parts of the components of the electric force at the point {x, y, z) due to 
the oscillator are 
iK%\ iK^v - t/c" (X^ +e-^^^-'-yr; 
therefore the principal parts of the components of the total electric force at the point 
[x, y, z) are given by 
{vi\i + 2 v-J. cos </) + 2n/}/RRi, 
{uii/i + 2j/im cos + 2mw}/RRi, 
{ —Xi^—Pi^+2rin cos <^ + 2w^}/RRi. 
