11 
hn’ denoting the corresponding value of gu. And eliminating 
M between this and the former equation, we find 
, an 
m 2-3 sin? ¢) — —. 
p=cotan 0 ( sin? @) re he 
-«¢ We must likewise have recourse to experiment, to deter- 
mine the value of the coefficient S.* In fact we have seen that 
the quantity, Q, which enters into the expression of this coeffi- 
cient, is the ratio of two series containing the integrals {r°dm, 
dm (dm (dm 
BR’) RB’ | R’ 
depending upon the distribution of free magnetism in the mag- 
frdm, fridm, &e., | &e., the values of which, 
net and iron bar, cannot be known a priori.| We may, how- 
ever, determine the value of the coefficient S by experimental 
means analogous to those already employed in the determina- 
tion of p. We have seen, in fact, that when the deflecting 
magnet in that experiment was horizontal, and perpendicular 
to the magnetic meridian, there was 
A = XS hn’. 
Now, let the iron bar be removed, and, the deflecting magnet 
remaining in the same position, let An’ denote the change of 
angle produced by its action. Then 
ae Xhkn" ; 
and, dividing the equation last found by this, 
” 
ya 
_ n 
The President exhibited to the Academy a map of Ire- 
= eee 
* «It is obvious that this necessity does not arise in the adjustment of the 
soft iron bars described in the commencement of this Paper.” 
+ “We may approximate to these values, and therefore to the value of Q, 
on theassumption that the whole forces of the magnet and bar are concentred 
in two points, or poles.” 
