328 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
and the componeuts of the electric current distribution to be assumed on the lower 
side of the disc are 
a — 
2 k a 
^ _ 2 k d e 
^ “ Y dy) n ' 
7 
= 0, 
where rj, Zq are now the co-ordinates of a point on the disc. Therefore the 
components of the magnetic force at a point x, y, z due to this distril^ution are 
a = 
/3 
7 
1 A1 
27rV 1 i 02 V 0^ t’l 
K 
27rV J J 02 r dr] 'y\ 
= 0 , 
where 
writincr 
->.2 
= {x-^f + {u-yY + {z-z,)\ 
X = p cos <f), y = p sin (f), ^ = pi cos (^i, V = Pi shi </>i, 
the resultant magnetic force due to the distribution is 
^ cos (^-a sin (^ =^ [ [ siii{<f)y + 4>) '' 'Ylp^iJj)^, 
277 V 02 Jo Jo r 
02 Jo 
where 
— {z—ZqY+p^ + Pi^—2ppi cos ((^i —(/j), 
.. 2 _ ^ 2 , 2 
'1 — "0 I Pi • 
Now }\ + r is stationary when 
A = (p-pi)A’ = Pi An 
and, writing II, Hi for the corresponding values of r, and sin S- = pi/j’i, the principal 
value of the magnetic force is given by 
^ ( sin 2(^ A %R^-2p,-v.^^-iA-<eos^3(Hr‘+K-)p''^ 
277 V ,, 2 , 02 J —p, 
AVhen «—pi is not small, the principal value of the above expression is 
^ .tK(V(-K,-K) 
YYz Ki + II 
that is, when the point x, y, z is on the upper side of the disc 
— ^ sin sin 2(^ -^pr—» 
V Ri -1- II 
which is the value, with the opposite sign, of the resultant magnetic force due to the 
