118 TREATISE ON ALTERNATING CURRENTS. 



equal to the product of their respective coefficients of self-induc- 

 tion. That is 



M 2 = 

 or 



As, however, there is always some leakage, we may write 



where \ is less than unity, and is a measure of the leakage. 



Leakage causes, then, a diminution of the mutual induction, 

 and, consequently, a drop in the induced secondary E.M.F. At 

 the same time, it causes an increase in the equivalent self-induc- 

 tion of the primary circuit (see 60, Chap. XL). Now, it is the 

 equivalent self-induction of the primary circuit which causes the 

 primary current to lag behind the applied P.D., and, consequently, 

 produces a larger primary current than corresponds to the secondary 

 current in the ratio of their respective turns. 



The principal effects of magnetic leakage are, therefore 



(1) The production of an excessive wattless primary current. 



(2) A consequent increase in the primary copper loss. 



(3) An increased drop of the secondary terminal P.D. 



(4) A diminution in the efficiency of the transformer, owing to 

 the increased primary copper loss. 



CORE LAMINATIONS. 



71. We have seen (see 61, Chap. XL) that the loss in the 

 core of a transformer, due to eddy currents, is proportional to the 

 square of the thickness of the core stampings. This would make 

 it appear that the thinner the stampings the better would be the 

 results obtained. 



So far as eddy-current losses alone are concerned, this is 

 correct ; but there are other considerations which impose a minimum 

 thickness of the plates. Suppose that with stampings 18 mils, 

 thick the insulation between the stampings occupied 15 per cent, 

 of the whole volume of the core ; then, with the same kind of 

 insulation and stampings 9 mils, thick, the insulation would 

 occupy about 26'1 per cent, of the volume of the core, and so, by 

 making the stampings thinner and thinner, the ratio of the volume 



