Alternate Current Transformer. 39 



which corresponds to 25 lbs. of iron core for each kilowatt of full 

 load activity. 



It is worth noting that, for transformers of the same type 

 made of similar iron, the percentage iron and copper losses and 

 the weights of copper and iron per kilowatt of full load activity, 

 are inversely proportional to the fourth root of the product of 

 the output into the frequency. 



Section III. 

 Transformer Leakage. 



42. In addition to the magnetic lines forming the main flux F, 

 produced by the combined action of G\ and C.^ and looped on both 

 circuits of a transformer, there are other lines, the leakage lines, 

 that are only partially looped on the two coils and that traverse 

 the space occupied by the coils, in some cases completing their 

 circuits in the iron. It will be shown that, after the transformer 

 is somewhat loaded, the effect of these leaknge lines on its opera- 

 tion is the same as would be produced l)y two fluxes ; one, the 

 primary leakage flux, supposed to consist of lines in phase with 

 the primary current that are looped on the primary and miss the 

 secondary circuit, and the other, the secondary leakage flux, 

 suppposed to consist of lines in phase with the secondary cui'rent, 

 that ai-e looped on the secondary and miss the primary circuit. 



43. Let Lj and L.j be the inductances of the two coils when the 

 leakage lines only are considered, Mj.^ the mutual inductance of 

 the primary on the secondary, that is the number of leakage 

 lines looped on the secondary arising from unit current in the 

 primary, and M21 the mutual inductance of the .secondary on the 

 primary. (Mj^ will not in general be equal to Mji). 



The e.m.f. e^ generated in the primary coil by variation of the 

 leakage lines due to C^ and Cj will be represented by the vector 



zt/LiCj + K'M^iC.j 

 after it has been turned through a right angle in the negative 

 direction : but since the vector 



which represents the magnetising ampere turns, is, after the 



