EQUATIONS OF PROPAGATION OF ELECTRIC WAVES. 
15 
and suppose"^ that the fiuiction (f) is very nearly zero for all values of its argument C, 
except such as lie in the interval between — and where and two very 
small positive numbei-s; further, we suppose that between these values becomes 
so oreat that 
fV(erfj =1.(35). 
-?0 
We may then choose and Q so that, if ; ^ is the I’adius of the sphere cto, 
+ cQ < — Cu, ^’u + ; 
then -we shall ha\ e 
r'l I c'<> I 
J ~ 7 j 
U “^0 
“ C) 
and, provided r^ is sulticiently small, these will hold for any negative value of and 
any positive value of Q. 
With this choice of <^q, the second line of the expression (33) becomes — | 47r_/gO“‘ 
in the limit, w-dien Vq is indehnitely diminished, being the value of/’for the point <4 
and the time t = 0. 
In the first line of tlie expression (33) we develope v and w in such forms as 
«= (')■) + ^ ^ 
where ( )„ indicates that the value at t) is to be taken ; w^e observe that 
^0 
and find that, Avhen is diminished indefinitely, the limit i.»f tlie first line is the 
same as that of 
tn 
or it is - i Itt/’c f 
★ 
The pi'oees.s adapLed from Kna'iiiKjrr, ' Uplik,’ pp. L’ l, 25. 
