PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
297 
then at the surface 
H= — 
and 
1 7 rap 
>19 9 9 , O : 
47 T“C0~p“ + a-w 
2irctp 
2 [27 rap sin pt + an cosp£] [M cos n6 + N sin n6"\ 
47r 2 a 2 _p 2 + crn- 
— [27 rap cos pt — an sinp£] [Q cos n6 + R sin iiff]. . . (v), 
n 
W = ^ H - 
4. We now proceed to find the components of magnetic force. When there is no 
magnetic matter (as we assume to be the case) the equations in cylindrical connecting 
a, (3, y with F, G, H, are 
3G 
IO GL —— 60 r\ ? 
C0 OZ 
~ 9F 0 H 
^ _ a j a»’ 
a 3 f 
= di (sr&) ” Be' 
With the distribution that we have chosen, F = 0, G =£. 0, and hence 
1 0H ^ 
“ _ w de 
fi = 
_3H j>. 
003 
7 = 0 J 
When the value of H 0 at the surface is 
then just outside, 
so that just outside, 
H 0 = Ae in6 sin pt, 
H« = A (- 
L ° —- L| e sin pt, 
— 1 
a Q = in A e ine sin pt 
Y 
/3 0 = — nA -- n - e ine sin pt J 
or* 
(vi.). 
Now when we consider the mechanical effects, since, on Ampere’s theory the 
mechanical effects of two elements of currents upon each other are equal and oppo¬ 
sitely directed in the straight line joining them, the field, due to the induced currents, 
MDCCCXCH.—A. 2 Q 
