when the Frequency is below a certain Critical Value. 401 

 From this equation curve III, Plate X., has been plotted; the 

 abscissae are values of a, and the ordinates values of y-, 

 expressed as percentages. For a transformer in which 



— = — = — - about, a second set of figures giving the fre- 

 r x r 2 500 ' & b & 



quency is also marked. 



The curve CCC, Plate X., is the ratio of C the primary 

 current when the secondary is closed to 1 the same secon- 

 dary open, and is evidently plotted from the equation 



C_„Ii__ 1 + * 2 



Cj ■ " I " */ 1 + 4* 2 ' 



Power Distribution in above Transformer. 



Let P be the power impressed on the primary when the 

 secondary is closed ; 

 P x the same when the secondary is open ; 

 H the heat-power developed in the primary when the 



secondary is closed ; 

 P 2 the power developed in the secondary. 

 Then 



2(a 2 + b 2 ) 



_ E 2 l + 2a 2 

 ~ 2?\ *l + 4a 



.2if 



(16) 



H=^.^4^f ? sin* pt.dt 

 ~2(a a + 6 8 ) 2r 1 'l + 4a 2 K > 



r.-fc' 1 ^]/ -*<!*+•>* 



_ fWWr 2 E 2 ; a 2 

 ~"2(a 2 + & 2 ) ~2r 1 'l + 4« 2 ' ' (1 ™ 



Obviously P = P 2 + H, unless there are masses of metal 

 present, in which eddy currents are developed, or the fre- 

 quency is so great that appreciable energy is radiated. 



