GENERAL THEORY OF THE TRANSFORMER. 



243 



magnetomotive force qiri' x x\X xN'*. Ignoring the reluctance 

 of the iron, the magnetic reluctance of the path of the leakage 

 flux d$ is the reluctance, //(X<^r), of the air gap aa y of which 

 the sectional area is \dx (counting both legs of the coils each 

 of length X/2 as shown in Fig. 207) and the length is /. 

 Therefore, placing d$ equal to magnetomotive force divided by 

 reluctance, we have 



t^\. 



but this flux dj> encircles the fractional part xjX of the pri- 

 mary turns, therefore the fractional part xjX of d$ should be 



j*-" ~- L ~"" "~~~~~ ^^_ 





iron 



iron 



Fig. 209. 



counted as encircling the whole primary coil. Representing by 

 d<& ? this flux, xj X Y. d$, which is to be thought of as encircling 

 the whole primary coil, we have 



Therefore the value of <!>' is 



_ 



IX* 



_ 



3/ 



(iii) 



Similarly, remembering that N'i* equals N"i n ', we may 

 find 



* All quantities in this article are understood to be expressed in c.g.s. units. 



