310 Capt. E. Henderson on 



below is a continuation of his investigation, the same nota- 

 tion being used throughout. The subject-matter dealt with 

 by Professor Perry opens out a large number of problems, 

 but it will be sufficient for the present if we consider the 

 simplest case only, that of two alternators coupled up in 

 parallel to a non-inductive resistance, and if we deal with the 

 following points : — ■ 



(a) To prove that the law for alternators in parallel is the 

 same as that for cells in parallel. 



(b) To deduce the relation between self-induction, fre- 

 quency, and resistance, for maximum control under given 

 conditions. 



The problem is complicated further if we take into con- 

 sideration the condenser effect of a long cable, in addition 

 to the self-induction due to transformers in the external 

 circuit. 



When two alternators are running together in parallel, 

 they give out equal power when in phase, but directly they 

 are out of step the leading machine gives out more power, 

 and so may be said to drive the lagging machine, which gives 

 out less, as a motor. 



This extra power, together with that supplied by the 

 engine, tends to bring up the lagging machine and retard 

 the leading machine, and the two come thus into phase 

 again. 



It is requisite, then, that for as small a difference in phase 

 as possible, the difference in power given by the two alter- 

 nators should be as large as possible. 



But the total power given by the two varies as the dif- 

 ference in phase increases. 



Therefore, for any particular difference in phase the ratio 

 of the difference to the sum of the powers would be a measure 

 of the controlling force between the two. 



When the two machines are in phase this ratio is zero, 

 and the ratio should increase as the angle of phase increases, 

 being a maximum when the lagging machine is doing no 

 work, but is running altogether as a motor. 



The problem to calculate Pi and P 2 , the powers of two 

 alternators having electromotive force 



tf!=E sin (n/+«) and e 2 =^ sin (nt—a), 



internal resistance r, and self-induction I, coupled up in 

 parallel to a non-inductive resistance R, can be easily, 

 deduced. 



Employing the data given in Perry's ' Calculus for 



