82 PEOCEBDINGS OF SECTION A. 



Substituting in these equations from section 18, and then equat- 

 ing separately to zero each set of vector terms of the same order, we- 

 obtain the two series of vector equations — 



rnq + qoilU^a,, + nqo)i2G,i ^ na,^ + ~{a,j ^ \ + a,, + i) >■ = 



TV ^ C y^ ^? 



pap -f pojA.' I 2<i-i, + '2^w (. 2" •< 1' Gr^, a,, + - (Gryj _ i Hp _ i 

 + G-p + i ap + i) > =0 



with a^ == 27^/p. 



where q is odd and p even. 



These reduce at once to the two series — 



a^^_l + iq Gr,, ^q + a,y + l = 



Gp-\a.p-\ + Tp a,, + G-,)+ia^,+i = 



or, after putting aVy for G^q a^, to — 



(j-q-i + ^g aV^ + a^y+i ^ 



a'p-i + T^> ap + a'p+1 = 



equations of exactly the same form as those for the simple case, but in 

 which the values of the t and t operators are now given by — 



2 C r TT ■) 



These operators having been calculated from known data, the 

 solution for a'„ a'j, a',, &c., a,, a^, &c., proceeds exactly as in the simple 

 case, and as a', =^ Gr,fii, a', = ^i^v ^^-i ^n ^3> ^s> <fcc., can theu be 

 obtained. 



20. In section 16 it was shown that the iron loss {i.e., energy 

 dissipated per sec. in the iron) in a magnetic circuit is — 



_2 



^MZq — sm 0,, 



hence the loss due to the flux A.,, section 18, is — 



, 2 



1 



>%qgq sin 8,, n^q + -^ (a,^-i + a,^+i) 



and that due to the flux A,, is — 



^ (^'^qgq sin ?>q - (tty-i — ",/ + i) 

 — 4 



Adding these, we find that the total iron loss in the generator is — 



— ojS'/yr/ilsin ?>q \ nHq + \ (a^-i + aq + {) -1- -- (a^_i — a,^ + i) 



2 ^2 4 



