228 



that the changes of the induced force of the bar are propor- 

 tional to those of the inducing action, and then compare them 

 with the changes of deflection observed. The calculated and 

 observed results of many series of observations, taken in this 

 manner, were found to accord as nearly as the accuracy of 

 the observations themselves allowed. 



In making this comparison, however, it is necessary to 

 take into account the effect of the direct action of the fixed 

 magnet upon the suspended one. The axis of the former 

 magnet being not far from the vertical passing through the 

 centre of the latter, its action upon it and upon the iron bar 

 follow, nearly, the same law ; so that its direct effects upon 

 the position of the suspended magnet are, very nearly, pro- 

 portional to those which it produces through the medium 

 of the induced force of the bar. On this principle the ob- 

 served results may be cleared, approximately, of those parts 

 of the changes which are foreign to the question. Still it 

 must be admitted that such a complication of the results 

 tends to weaken their evidence ; and it was therefore de- 

 sirable to obtain further proof, in a manner less exception- 

 able. 



The object being to alter the inducing action according 

 to a known law, and to observe the changes of the induced 

 force, as shown by the position of the suspended magnet, it 

 is manifest that it may be attained by simply varying the 

 angle which the iron bar makes with the direction of the 

 earth's magnetic force, the distance of its pole from the sus- 

 pended magnet remaining unchanged. In fact, it will be 

 seen, by pursuing the same reasoning as before, that if r 

 denote the total force of the earth, and ip the angle which 

 the bar makes with its direction, the equation of equilibrium 

 of the suspended magnet is 



pR cos i// + 5" = X tan u ; 

 the line connecting the pole of the bar with the centre of the 



