when the Frequency is below a certain Critical Value, 399 

 these values in (12) it becomes 



f 1 Y- 1 J. flV4{g-"."i(8-i8»)} M « 



W + " "(i+^xi+aiT"' • • ( } 



To make |- greater than unity, obviously 



2 

 a x a 2 must be less than - — -=g, 



or the critical value of 



ai %(2-/8*) ; ^ given); 

 and that of 



When the primary and secondary are identical or have the 

 same shape and coil- volume *, and the secondary when closed 

 is short-circuited, 



oc 1 = a 2 = a. 

 Then 



lu;^ 1+ — ot^p — >• • • (U) 



and the critical value of «=■* 



2 — p 2 



When /3=1, or there is no magnetic leakage, the critical 

 value of a= \^2. 



Jo ymd the value of a x that ivill make j a maximum, a 2 and 

 /3 being given. l 



I /I\ 2 . 



Obviously from (13) j- is a maximum when f =p ) is a 



« 1 {2-« 1 « 2 (2-/S 2 )} 



maximum, that is, when z z is a maximum, 



1 + &i 



since « 2 an d /3 are constants. 



Differentiating with respect to a x and equating to zero 

 gives 



^/4 + ^(2-/3 2 ) 2 -* 2 (2-/3 2 ) 



«!= g . . . {10) 



If /3=1, or there be no magnetic leakage, 



* Relative difference of thickness of insulation being supposed negli- 

 gible, if different-sized windings are used. 



