362 On Mr. Grove's "Experiment in Magneto- electric Induction." 



denser C. Let the plates of the condenser be connected by the 

 additional conductor y. 



y 



Let M sin 6 be the value of the potential of the magnets on 

 the coil of the armature ; then if the armature revolves with the 

 angular velocity n, the electromotive force due to the machine is 

 Mw cos nt. 



Let R be the resistance of the wire which forms the coil of 

 the armature M and that of the fixed electromagnet. 



Let L be the coefficient of self-induction, or the " electromag- 

 netic mass " of these two coils taken together. 



Let x be the value of the current in this wire at any instant, 

 then La? will be its "electromagnetic momentum." 



Let C be the capacity of the condenser, and P the excess of 

 potential of the upper plate at any instant, then the quantity of 

 electricity on the upper plate is CP. 



Let p be the resistance of the additional conductor, and y the 

 current in it. We shall neglect the self-induction of this current. 



We have then for this conductor, 



p=«/- • • • ■ (i) 



For the charge of the condenser, 



of =.-„.. ........ ® 



For the current w, 



Mflcosw* + Btf+L^ + P = 0. ... (3) 



If. we assume 



a? = A cos (ft/ -j- a), 

 we find 



A2 __ MV(i+cyv) 



~ ps{(l-LC» 2 ) 2 + R 8 CV}. +21ty + R 2 + Lrc 2 ' 



, = cot -, 1 ^ B + p-LCK 

 Cpn RCpn + Ln 



