92 



Messrs. Ayrton, Mather, and Sumpner 



VIII. Self-induction of Galvanometer- Coils. 



We have already seen that the sensibilities of two precisely 

 similar galvanometers, which differ only in resistance, cannot 

 easily be predicted from their resistances, since, in consequence 

 of the varying thickness of the insulating covering of the 

 wire, there is no simple connexion between resistance and 

 the number of convolutions of wire occupying a given space. 

 It therefore occurred to us to consider whether, since the self- 

 induction of a coil of a given size and shape depends mainly on 

 the square of the number of convolutions, and but little on the 

 thickness of the wire or of the insulating covering, the square 

 root of the self-induction would be proportional to the mag- 

 netic constant of the coil. The following table gives the 

 results of the tests on the three astatic reflecting-galvanometers 

 already referred to : — 



Galvanometer. 



Eesistance, 



in ohms. 



r. 



Self-induction, 



in secohms. 



L. 



Time Constant, 

 in seconds. 



D. 



A 



26 

 2457 

 6410 



0-052 



1-75 



4-72 



0-002 



0-00071 



0-00074 



349 

 2160 

 3360 



B 



C 





D, as before, standing for the number of scale-divisions of 

 deflexion produced by the same current with the same 

 distance of the scale, the same system of mirror and magnets 

 being used in each case, and the controlling magnet adjusted 

 to give the same periodic time of oscillation. The following 

 gives the ratio of the values of D, of the square roots of the 

 self-inductions, of the square roots of the resistances, and of 

 the resistances to the power § : — 



5? = 6-190 

 -L'a 



5° =1-555 



-L'b 



' Viz**™* \/h 



9*721 



1-615 





^ = 9-627; a /^ = 9-526; \/'-^ = 

 D A V L A V r A 



From the preceding list it appears that the ratio of the 

 square roots of the self-inductions gives the ratio of the 

 galvanometer-constants of coils, not only much more accu- 

 rately than the ratio of the square roots of the resistances, 



9-051. 



