LAW OF FORCE INFERRED FROM DEFLEXIONS. 63 



sion of magnetic masses is inversely as the square of the 

 distance between them ; Final Law of Magnetism. 



Let the' experiment of Article 26 be performed with 

 two values of c (the distance between the centers of the 

 magnets) which we shall call c x and c 2 . Let the cor- 

 responding deflexions be t and # 2 . Then we have the 

 two equations, 



sn 2 ; 



and nearly similar equations from Article 27, in each of 

 which the second term on the left hand is to be small. 

 And the question now to be considered is, What 

 numerical value for m will enable us to satisfy that 

 condition ? 



We shall approximately represent the state of the 

 case, by neglecting the small terms, and thus we get 

 the following approximate equations : 



c- m ~ l . AB = EB . sin t : c 

 c^ .mAB = EB. sin & : c~ m ~ l .mAB=EB. sin fa 



We must now appeal to actual experiment. A few 

 observations bearing on these points were made by 

 Gauss, but in the Greenwich Observations there are to 

 be found about one hundred observations in which the 

 disturbing needle was applied both broadside-on and 

 end-on, and a far greater number in which it was 

 applied end-on alone. We will take the observations 

 of 1860, January 16. 



