240 



In (12) we substitute for the mass i/ =: WV^ and for the resistance 



lo 

 w = -—, giving : 

 ncr 



. H* = 7.bjr\0' .gQN (13) 



which shows a simple relation between the allowable and 

 necessary strength of the magnetic field, the frequency and the 

 density and resistivity of the material. If we were at liberty to 

 choose any figure for iV, the length and the thickness of the string 

 would seem to be of no consequence. But we started from the 

 premise that the frequency should be as small as possible with a 

 string of predetermined length and thickness, and elasticity. Hence we 

 must put the value for xV taken from (1) in (13) giving 



H= 1.45 10' \^^ jl^gEQ' ..... (14) 



Now we can substitute this value for H in (5) and by likewise 



substituting ?f> =: — we arrive at a formula for the sensibility for 



potential differences: 



h I' 



— = 6040 



tw d\/d 





(15) 



This expression for h/iw gives the extreme limit for the sensibility 

 of a completely relaxed string in a magnetic field of a strength 

 exactly calculated to render the movements of the short-circuited 

 string critically damped. The volt-sensibility increases by /* and 

 decreases by d[/d. It also depends on the density, resistivity, and 

 elasticity of the material. In table III we find the constants for 

 different materials and in the fourth column the comparative 

 "material-factor" for each material. These have been multiplied by 

 10' so as to indicate defiections per microvolt with strings of 1 f* 



TABLE III. 



