8 The Rev. H. Luoyp on the Determination of the Intensity 
by the deflecting magnet, upon any element of free magnetism, m, of the sus- 
pended magnet, in the direction of the line connecting it with the centre of the 
deflecting magnet, and in the line perpendicular to it, respectively, their moment 
to turn the magnet round its point of suspension will be 
r{xsin(@+ ¥) + y¥ cos (d+ ¥)}5 
r denoting the distance of the particle m of the suspended magnet from its centre, 
and @ the angle which the line connecting this particle and the centre of the 
deflecting magnet makes with the axis of the latter. Now, I have elsewhere 
shown* that, if we include the terms involving the fifth power of the distance, 
the values of x and y are 
2 
x= Theos {au + “2 (5 cos’ » — 8)}, 
m . M 5 
¥ = Gsin o {M+ 578 (Seog —1)} 5 
a being the distance of the particle m of the suspended magnet from the centre 
of the deflecting magnet, and m and M, denoting, respectively, the integrals cor- 
responding to \mrdr, (mr"dr, for the deflecting magnet, taken between the limits 
r=+i length. Now 
‘ ae 
sin d= —siny; 
a 
so that, extending the approximation to the term involving the fifth power of 
the distance only, we must make sin @ = 0, cos @ = 1, in the coefficient of that 
term. ‘The preceding expressions are thus reduced to 
——— 
m 
a 
2M ihe oe 
(ucosp+ =), Y=-—mMsing; 
a a 
and, substituting, the moment of these forces to turn the magnet is 
mr { 
aM (3 sin $ cos @ cos + + (2 — 3 sin’) sin ¥)+ See y} : 
a 
or, eliminating @ by the relation between it and y, 
mr . r Ts: 4m 
sin y [at (2+3 cosy —3 7 sin y) +h. 
* Transactions of the Royal Irish Academy, vol. xix. p. 163. 
