Study of Transformers. 171 



9 



nation with — . Hence, instead of saying that my tables 



show the effect of diminishing frequency in a given trans- 

 former, I might say that they really show the effect of 

 keeping frequency constant and diminishing the section or 

 increasing- the length of the iron magnetic circuit. 



27T 



Thus, for example, the table for — = 100 may mean 

 — = 100 and L = 10, M = l, L f = 'l ; 



T 



but this table is correct for 

 2tt 



T 



= 1000, and L = 1, M = 'l, L' = '01. 



I shall only assume, in fact, that in any table the ratios of 

 L to M and L f remain constant. 



For the sake of beginners it is well to state that, using 

 amperes, volts, and ohms, if P and S are the numbers of 

 windings of the primary and secondary respectively ; if a is 

 the cross section of the iron in square centimetres, and \ the 

 average length of the complete iron magnetic circuit and fi 

 the permeability (being about 1500 in ordinary transformer 

 Working), we may take it that 



L=s± xIo' I 



\ 10 



> (3) 



I 

 J 



and if there were no magnetic leakage — that is, if all the field 

 due to a primary current through every winding of the 

 primary passed through every single winding of the secondary, 

 then 



M= VLL', orM = PS^f I Q. 

 If two or three tables be compared for which the values 



27T 



of — L differ even greatly, it will be noticed that A', e', // 



are practically the same from the very smallest to the greatest 

 loads. Also, except for small loads A, e, P, and E, are prac- 

 tically the same. This is the more striking as the frequency 

 is greater. Now this is really the same as saying that if the 

 ratios of L, L' ; and M remain constant, considerable changes 



