170 



Prof. J. Perry on the 



at the terminals of p. Let P be the average power given to 

 the primary, and P' that given out by the secondary. Then, 



taking 



V = asm — t, 



T 



C = A' sin f^t -<:'), 



(1) 



(t'-4^ 



P = la A cose, P' = i/>A' 2 , 



p/ 



Percentage efficiency = 100 -p=E, say, 



it is known that to calculate all the necessary values, the 

 simplest plan is to calculate the following magnitudes first : — 



l'=r. 



= L 





r = Li + — ar 



M2R/ 

 I* 



p 2 



Then 



A = 



., 2tt M 

 A-^a^, 



tan e ; 



2tt/ 



4tt 2 / 2 



T 2 ~ 



4tt 2 



L7-RV 



tan e f = 



2tt' LV + R'Z 



(2) 



As an example of a transformer with which we have 

 experimented electrically and arithmetically, take R = 10 

 ohms, R' = *l + p, a =1000 volts, L = 10 secohms, 1/ = -] 

 secohm, and take as is usual M = l secohm. That is, assume 

 no magnetic leakage. We have the following interesting 

 results obtained by altering r, beginning with a frequency of 

 160 per second and ending with the rather absurd case of t== 

 more than 6 seconds. It is to be observed that when I say 



2-7T 



in any case that — = 1000, or 100, I really mean that 



2tj- 



— L = 10000 or 1000 respectively. It will be observed 



that L, M, and L/ only enter into the calculations in combi- 



