CONVERGENT SERIES 43 



of ordinary algebra are followed, and it must be remem- 

 bered that 



j X j =j 2 



= -i, 

 and, therefore, 



-JXJ =+i 



j 5 =+j, etc. 



Thus (4 +j 5) X (7 +73) is worked out as follows: 



4+7*5 

 7 



+ 28+^35 

 - 15 +712 



+ 13+747- 



In using the convergent series, E, P, and Q are the same 

 as used with the K formulas, E being expressed as a real 

 number without any j term. Z is equal to (r -\-jx) I, 

 where r and x are taken from Tables VII to XII, Part III, 

 for resistance and reactance per mile. F is equal to 

 (g -\-jb) I. The leakage conductance, g, per mile, should 

 be estimated from the most suitable test data available, 

 giving insulator leakage and corona loss under conditions 

 similar to those of the line considered. The capacity sus- 

 ceptance, b, per mile, will be found in Tables XIII to 

 XVI, Part III. 



After F and Z have been written down in the form of 

 complex numbers, the product FZ should be found, as 

 described above for the multiplication of complex quan- 

 tities. From this is obtained 



FZ FZ FZ 



, , and , 



24 6 



