and the Theory of the Induction-balance. 131 



U being g - E( |~ R) (exp.) {(B) - (B + S) + (2B + S) 



;;.;' ~(2B+2S)}(-Q 



and ' 



^bemg| + :E ^5)(exp.){(S)-(S + R) + (2S + K) 



-(2S + 2E) + (3S + 2E)J- (-^) 



Accordingly., after a very large number of vibrations (which 

 will be accomplished in a few seconds) the current is either 



or else the same expression with E and S everywhere inter- 

 changed,, according as the last change of resistance was from 

 E to 8 or from S to ~R, t being the time which has elapsed 

 since the last change. 



' The law of variation of such a current is therefore just the 

 same as for a simple make and break (4) ; but the part depend- 

 ing on time is multiplied by a constant fraction always less than 

 unity, and which diminishes rapidly as r (the period of a semi- 

 vibration of the intermittence) diminishes. 



If t be infinitesimal compared with s , g . the fraction is 

 E xi + b 



and hence the current is 



S + B 



*=s( 1+ sTe* L > 



or, as of course t (being less than t) is itself vanishing, 



. . 2E ,a. 



Z= STE' ' * ' * • * ' (8) 



Hence the current tends to approach this constant value if 

 the vibrations are too rapid. Such a current as this is of 

 course inappreciable by a telephone ; but the above would be 

 its galvanometric indication . 



Tnis-must *be. something like the state of things in a coil 

 with a too rapid break. 



Query, whether any thing of the same sort happens when a 

 battery-current is passed through a vacuum-tube, the inter- 

 mittence being almost too rapid to be heard by the telephone. 

 Drs. De la Eue and Hugo Miiller have put a telephone in 

 circuit with a battery and vacuum-tube, and heard only a 

 faint rustling when the stratifications were steady. 



K2 



