68 Proceedings of the Royal Society of Victoria. 



shaped windings, and the four sides jointed together to form the 

 completed transformer. 



Let us determine the proportions of such a transformer so that 

 T, and hence the efficiency, shall be a maximum. 



Let 26, 26, be the square opening in the laminae, 2yS, 2^' the 

 cross section of the magnetic circuit, 2/3 being measured in the 

 planes of the laminae, then, 



« = 46^ /=4(/3+/3' + i6) 



a = 4:^/3', \=8{b+/3) 



Proceeding as in § 56 we find, in order that 



A / , 



— and — shall be minima 



a a 



when aa is constant, 



that 2/3(/3'-2/3) = 6(3/3-;8') 



and if p' = -qjS, p = ub as before, 



j^3— 7/ _4/^4-3 



and the equation of the losses 

 ai _ pi 



becomes 



18?/ +16// + 2 _^pl 

 6?/(4«^ + 7?/+~3)~^QK' 

 from which, for any given values of s, />, Q, I and K, tc can be 

 found and hence rj. 



The equation of the output, 

 6V^=. ^-^ , 



gives b, which with ii and 77, determine the transformer. 

 For example, if we take as before 

 s^ = 1.029, P,= 12.5 K.W. 

 we find 



b=7.S, /3 = 4.5, /3'=11.09, 

 and the value of r is 7680, which is considerably larger and hence 

 better than for either of the two preceding types. 



Iron loss:=:copper loss = 176.7 watts. 



Efficiency = 97.26 per cent. 



