16 ELECTRICAL MEASUREMENTS 



used for the entire coil, this being the size which would be most 

 advantageous if the coil were uniformly wound.* 



Relation between the Galvanometer Constant and the Resist- 

 ance of a Thomson Galvanometer. The magnetic effects ob- 

 tained by using coils having the same dimensions but wound 

 with wires of different sizes are proportional to the ampere-turns; 

 the galvanometer constant, G, is therefore proportional to the 

 total number of turns in the coil. Let A be the area of the cross- 

 section of the coil, and n' the number of turns which thread 

 through a square centimeter of the cross-section. Suppose first 

 that the thickness of the insulation is zero and that the diameter 

 of the wire is B\. Then 



G = kAn' = Kri = ~ 



&i 



where k and K are constants. 

 The resistance per unit volume of the coil, w, will be 



and the galvanometer resistance, if V is the volume of the coil, 

 will be 



(2) 



So if the thickness of the insulation is zero, the galvanometer 

 constant is proportional to the square root of the galvanometer 

 resistance. 



Suppose the bobbin to be filled with an insulated wire, the 

 diameter outside of the insulation, designated by C, being the 

 same as that of the bare wire just considered. Let the diameter 

 of the wire itself be B. As the number of turns has remained 



! Same ' G not changed but the resistance will be increased 

 in the ratio ^; call this ratio y\ then to keep G the same if the 

 new value of R be used, 



(3) 



ing 

 phy. 

 ,, vol. 1, 1MO, p. 244, where all the necessary formula, are 



- f J a , graded coil of a definite resistance and having 



* by - G " ABBOT in the 



