348 Mr. T. H. Blakesley's Further 



Suppose 



Z = A.c 1 '* + Bc 1 c 2 + Cc 2 2 



at any instant; then the mean value of Z will be 



A. 1 D 1 + B 1 D 2 + C 2 D 21 



where ]D 2 is the reading of a dynamometer one of whose coils 

 carries C\ and the other c 2 . 



If Z is power, A, B, C are of the order resistance. If Z 

 is E.M.F.'^, A, B, C are of the order (resistance) 2 . It is neces- 

 sary that A, B, C should not be functions of the time. Hence 

 power and E.M.F. , the latter being merely power per unit of 

 conductivity, are very appropriate quantities for the method. 



To take the simple case of two machines working in parallel 

 into a third inductionless circuit. The equations are 



^2—f=r 2 c 27 



f=r 3 c 3 , 



and c 1 ^-c 2 =c s ; 



where e x and e 2 are the total E.M.F. s of the generators in the 

 two loops 1 and 2 (including all induction); c v c 2 , and c B are 

 the three instantaneous currents, the two former positive 

 towards the same point of junction, the latter positive towards 

 the other, so that Ci + c 2 = c 3 always ; and/ is the potential 

 difference at the points where the circuits join. 

 Then, since 



g 1 c 1 = r 1 c 1 2 + r 3 c 1 C3 or r } + r z c x * + r 3 c x c 2 , 



e 2 c 2 = r 2 c 2 2 + r 3 c 2 c 3 or r 2 + r 3 c 2 2 + r&Cs, 

 we have power of 1st generator 



=nil>i+^ , 3il > 3, or n + ni^i+r 3l I> 2 ; 



power of 2nd generator 



= r 22 D 2 + r 32 D 3 , or r 2 + r 32 D 2 + r 31 D 2 , 



where D refers to a dynamometer-reading. 



Here we appear to require four dynamometers ; but the 

 expression for the instantaneous power may be written in the 

 2nd form given, which necessitates only three dynamometers. 

 Either generator here becomes a motor if the second term as 



