OF ELECTRO-DYNAMIC FORCES. 



501 



in which the same notation is adopted as used by Gauss in his 

 Litensitas Vis Magnetlcce, &c. in the comparison of the mag- 

 netic observations. 



According to the fundamental principle of electro-dynamics, 

 we should be able to develope the tangents of the angle of deflec- 

 tion V and v' according to the diminishing odd powers of the 

 distance R, and we should have 



tan v = «R -k- b}i " 



tan u' = i a R~ -f- c R , 



where a, b and c are constants to be determined from the ob- 

 servations. If now in the present instance we make 



tan V = 0-0003572 R"" + 0-000002755 R~^ 

 tan v' = 0-0001786 R~' - 0-000001886 R~\ 



we obtain the following table of calculated deflections, and their 



difference from those found by observation : — 



Thus in this agreement of the calculated values with those 

 obtained by observation, we have a confirmation of one of the 

 most universal and most important consequences of the funda- 

 mental principle of electro-dynamics, viz. that the same laws 

 apply to electro-dynamic forces exerted at a distance as to mag- 

 netic forces. 



In this application of the laws of magnetism to electro-dynamic 

 observations, that case of the latter where the centres of the two 

 coils of the dynamometer coincide must be excluded. More- 

 over, in this extension of the laws of magnetism to electro-dynamic 

 observations, the values of three constants must be deduced from 

 the observations themselves, which is unnecessary when we have 

 recourse to the fundamental principle of electro-dynamics itself, 

 and calculate directly from it the results which the observations 

 should have yielded in accordance with it. Hence from the fun- 

 damental principle of electro- dynamics — 



1. In that case in which the straight line uniting the centre 



