METHOD OF DAMPING. 539 



the expression for the resistance may be put into different equivalent 

 forms 



G 2 M 7r 2 c rt _ A 



R = 7H" 



* 



The square of the galvanometric constant G appears in all cases. 

 Weber, and after him F. Weber, calculated this constant from the 

 dimensions of the frame; but in that case the multiplier should 

 have dimensions which are inconsistent with rapid damping, and 

 it will be seen that it is important to increase as much as possible 

 the effect to be measured that is to say, the difference of the two 

 dampings with open and closed circuit. 



It is better therefore to determine the constant G by comparison 

 with another galvanometer G' of known dimensions, using a shunt 

 if necessary. The deflections 8 and 8' produced by the same current 

 give 



G 2 _G' 2 tan 2 S 



H~" H^tan 2 a*' 



If this value be substituted in the expressions for the resistance 

 it will be seen that, besides the times of oscillations r and T O , the 

 logarithmic decrements A and A , and the constant G', we should 



determine either the ratios and (first form) or the moment 



ri ti 



of inertia K, and the horizontal component H' of the terrestrial 

 field (third form). 



The experiment amounts, in fine, to using either the first of the 

 values of R or the latter that is to say, we should know one of the 

 two expressions 



G 2 M_G' 2 H M tan 2 S 



2 H ~T~ if H f tan 2 8'' 

 G 2 K G' 2 K 



2 H 2 2 H' 2 tan 2 S' 



