10 
a the equation of equilibrium under the abbreviated form 
= Xfu, and differentiate, and divide by Y= X tan 0, 
= = fudu t+ fu Be 
tanw ane ee 1-—Q sin? u 
1+Qsin? wu’ eos? u (1+ Q sin? u)? 
electing the term 2 Q sin‘ w in the numerator, as inconsiderable ; 
> ne- 
But fu = 
wherefore putting, for abridgment, 
. cotan 6 eae | 1-Qsin® u 
Ae VUi+Qsin?w)’ ~  costu 1+Qsin?u’ 
there is finally, 
es on ox 
p (Sau+tanu =): 
c The os p, in this formula, is obtained by the me- 
thod already explained. It has been shown that when a mag- 
net is placed vertically, above or aries the suspended magnet, 
its inducing action on the iron bar = Ste 3 sin? ¢), eand @ 
denoting as before; and, as this ad has the same effect asa 
small change of the earth’s vertical force, the effect upon the 
suspended magnet is obtained by making 6 Y = = (2-3sin?¢), 
6X = 0, in the preceding equation. Wherefore, kn denoting 
the corresponding change of angle, 
=o sin? ¢) =p YS hn. 
Again, when the deflecting magnet is horizontaJ, and per- 
pendicular to the magnetic meridian, its effect is the same as 
that produced by a small change of the earth’s horizontal 
force, whose magnitude is given by the equation 
3X sin w+ cosu=0. 
a 
Putting, therefore, for §X the value thus given, and making 
oY=0, 
<- XS kn’; 
