9 : 
‘on. We are, therefore, unable to obtain the value of this 
moment, expressed as an explicit function of a and A, and 
must have recourse to a different development. 
‘‘ Let the distance of any point of the iron bar from the 
centre of the suspended magnet, CP’, be denoted by &, 
R? =a? + (h-r’)?, and p?= R?+r?- 2ar sin u. 
Expanding ih according to the inverse powers of R, and in- 
p 
3 
tegrating, observing that M, = 0, when n is even, 
dmd d d. 
eet = fame oS pt treaty 
~'2°4°6 
- 327 (M+ 124? sint w Me) [ “4+ Bees ; 
or, if we make 
ule -ims | + $$ Ms [Fhe ae 
ts (Ma| Fr - 4 Ms | Fh + &e.)=B, 
in which, on account of the smallness of the distance of the \ 
iron bar, the term containing sin? uw may bear a very sensible 
proportion to the whole. Accordingly, if we put, for abridg- 
ment, 
4a=MU, Ba’=MUQ, 
the moment of the force exerted by the iron bar is 
MU cos u (1 + Q sin? x) ; 
and the equation of equilibrium therefore is 
U (1 + Q sin? uw) = X tan wu. 
“Let Vd Y denote, as before, the change of U produced 
by a small change of the earth’s vertical force. Then, if we 
