of Edinhiirgh, Session 1883-84. 
555 
Hence, neglecting terms involving (Sa)^, the potential 
V = inScI 4cos"^ — - _ OttI . 
dV 
da 
dV (fr 
dr da 
, . g 8 a abc(Zr‘^ + ^h‘‘ ) 
“ ,.4(J2 + ,.2)f > 
F.= 
_,4afe(3a-J + 2i2 + 3c2) ,, 
nhahc 
{d^ + c^Y{d^ + 
This result can also be arrived at by finding the solid angle sub- 
tended by the whole rectangle 2a, 2& at the point m. Multiplying 
this by mSc we have the potential due to the whole shell 2a, 26, 8c, 
and differentiating with respect to a we obtain the force at m in the 
direction of a : this will evidently be zero. But differentiating this 
again with respect to a, and multiplying the result by 8a, we obtain 
for the action of the magnetic strip a value which agrees with the 
above result. 
Differentiating the coefficient respect 
(a2 + c2)2(a2 + 62_|_(.2)t ^ 
to c to find the maximum value of the deviating force, we obtain un 
equation which is cubic with respect to c^, from which it can be 
proved that the maximum value of the coefficient lies between 
c = — and c = 
2 
n/3 
for all real values of h 
In fig. 8, the values of the above coefficient for various values of 
c are represented in curves, the length being expressed in centi- 
meters. 
Curve I gives the values of the coefficient when a =10 and 
h = Sb (that is when the strip is indefinitely short). In this case, 
12ac 
(a2 + c2)i 
inSaSbSc . 
The curve may be interpreted as a diagram representing the deviat- 
ing force exerted by a magnetic particle, whose moment is 4 (in 
C. G. S. units) upon a unit magnetic pole at m. 
Curve II is for the case a = 10 6 = 2; 
Curve III „ „ a = 10 6 = ^; 
Curve IV ,, ,, a=10 6 = qo . 
