11 



kri denoting the corresponding value of Sn. And eliminating 

 M between this and the former equation, we find 



CI ?l 



p = cotan 9 (2 - 3 sin 3 <j>) — — . 



"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 jr 3 dm, 



\r>dm, JVVm, &c, -^- , -^- , -^y,&c, the values of which, 



depending upon the distribution of free magnetism in the mag- 

 net and iron bar, cannot be known a priori.^ We may, how- 

 ever, determine the value of the coefficient 5 by experimental 

 means analogous to those already employed in the determina- 

 tion of jo. We have seen, in fact, that when the deflecting 

 magnet in that experiment was horizontal, and perpendicular 

 to the magnetic meridian, there was 



M 



— = XS hi. 

 a 6 



Now, let the iron bar be removed, and, the deflecting magnet 



remaining in the same position, let kn" denote the change of 



angle produced by its action. Then 



M „ 



— = Xkn ; 

 a 6 



and, dividing the equation last found by this, 



n 



The President exhibited to the Academy a map of Ire- 



* " It is obvious that this necessity does not arise in the adjustment of the 

 soft iron bars described in the commencement of this Paper." 



f "We may approximate to these values, and therefore to the value of Q, 

 on the assumption that the whole forces of the magnet and bar are concentred 

 in two points, or poles." 



