e= )i - = «wt ^ 2(7/^ 



80 PKOCEEDINGS OP SECTION A. 



ctirrent-turns na., in any magnetic circuit, we have always a relation o£ 

 the form — 



y^ ^ Gr, nHj 



— ^ 

 where G-j is an operator of the form ff^ c , which can be determined. 



Hence, following the assumption already made, if the magnetizing 

 current-turns — 



nx = n (a, + aj + a. + &c.) 



produce in a magnetic circuit a flux F =/j + j^ + f^ + &c., then ^ = 

 nG^a,^,f. = iiGr^a,^,/^ =■ nG^a,^, &c., where the G's are operators of the 



type given by Gtq — g,, i '' ' 



In the above the back e.m.f., e say, in the magnetizing coils due 

 to change of flux is — 



dF _ 



dt ~ ' 



and the power absorbed, that is the total iron loss in the magnetic 

 circuit, is the mean value of ex^ that is of — 



dY . ^ ■ "^ 



vx — - , that is of ^w^a,, into t '-i '%q^f(i 

 dt 



which is =■ \ n(jji%q Nfq a,/ {See Section 11.) 



= ico2<7-^-'' sinS,, . 

 9" 



17. As an example, let us determine the G operator for a mag- 

 netic circuit of uniform cross section = 100 cm' made up of 40 cm 

 length of laminated iron and two air gaps each 1 m.m. when B maxi- 

 mum = 5000 and the frequency 30. 



In the paper already quoted we find for a sample of No. 26 iron, 

 with good insulation between the lamin<T, when B max. = 5000 and 

 frequency ^ 30 q.p. that 



IJL = 2500 I '''' (q.p.) 



Now — 



and- 



Hence — 



G= 59681 . 



