332 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
and the principal parts of the components of the electric force cine to the distribution 
are 
that is 
X = - 
K^VlXl 
27r J J 
if {IK 
+ m/ri + wri)-;-c?S, 
Y = if(ZX,+mfi,+»,) 
Z = 
r7\ 
,iK(yt-r^-r) 
rr 
dS, 
, tK(Vt—rj —?■) 
ff + -__ dS, 
ZTT Jj 7 Ti 
X = 
27rIliR J 
,r 
k-YjPi f 
27rE.iR J 
.r 
gC(c(V« r, 0 
27rllill J 
YYdiere OP = R], QP = P, and da is the projection of an element of the surface on a 
plane perpendicular to OP. 
The integral involved in these expressions has been already evaluated and gives 
when the point Q is not near to the curve of contact of the tangent cone from O to 
the surface of the obstacle 
that is 
X = -X', Y = -Y', Z = -Z', 
and therefore at points inside the boundary of the geometrical shadoYV and not close 
to it the principal part of the electric force vanishes and consec)[uently the principal 
part of the magnetic force vanishes. In the second case when OQ, QP made ecjual 
angles with the normal at Q the coefficients 
— r'o (Xi + X 2 ) (/A-i + W/fXi + TlVi^ + 71 X 2 (^-1^2 ■t'P'iP'2't r'lC'a) — ftXi + (Jfii — mXi) (g2^i — 
— V 2 (/U .1 + P 2 ) {lXi + mixi + nvi) + njji2 {XiX2 + P'iP'2 + *^i^^2)~'^^/^i + (^/^i~'^^V) 
{X 2 (Xi + X 2 ) + /X 2 (gi+ga)} {lXi + miix-\-nV]) + nv 2 (XiXa + p.i/Xa + i'iVa) — 
-\-{Jl^\—mX^ {X2[j.i — Xi[X2), 
vanish at Q and therefore the principal parts of X, Y, Z vanish at P, provided the 
point Q is not near to tlie curve of contact of tlie tangent cone. These residts might 
