TO THE THEORY OF ELECTRICITY. 75 



produce a new polarity, whose direction and quantity will be 

 very nearly the same as those before determined. Now /having 

 been supposed resolved into two forces, one equal to b in the 

 plane of the body's equator, and another perpendicular to this 

 plane ; if {3 be very small compared with 5, the angle 7 will 

 be very small, and the direction of the new polarity will be 

 very nearly at right angles to the direction of , a result which 

 has been confirmed by many experiments : but by our analysis 

 we moreover see that when b is sufficiently reduced, the angle 

 7 may be rendered sensible, and the direction of the new polarity 

 will then form with that of b the angle JTT + 7 ; 7 being deter- 

 mined by the equation 



sin 7 = ^ . 



This would be very easily put to the test of experiment by em- 

 ploying a solid sphere of iron. 



The values of the forces induced by the rotation of the body, 

 which would be observed in the space exterior to it, may be 

 obtained by differentiating that of V before given, and will be 

 found to agree with the observations of Mr BARLOW (Phil. Tran. 

 1825), on the supposition of j3 being very small. 



As the experimental investigation of the magnetic pheno- 

 mena developed by the rotation of bodies, has lately engaged 

 the attention of several distinguished philosophers, it may not 

 be amiss to consider the subject in a more general way, as we 

 shall thus not only confirm the preceding analysis, but be able 

 to show with what rapidity the body approaches that permanent 

 state, which it has been the object of the preceding part of this 

 article to determine. 



Let us now, therefore, consider a body A fixed in space, 

 under the influence of electric forces which vary according to 

 any given law ; then we might propose to determine the elec- 

 trical state of the body, after a certain interval of time, from 

 the knowledge of its initial state ; supposing a constant coercive 

 force to exist within it. To resolve this in its most general 

 form, it would be necessary to distinguish between those parts 

 of the body where the fluid was at rest, from the forces acting 



