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a view of fulfilling the characteristics 

 which he had mentioned, and which 

 represented all cases of the follow- 

 ing problem : — Given two alternate-cur- 

 rent machines coupled in series, and 

 having given electromotive forces, and 

 the same known period of alternation, a 

 given resistance in the whole series and 

 a given coefficient of self-induction for 

 the whole series: how will any time- 

 interval between the corresponding 

 phases of the two machines (phase angle), 

 affect (1) The work to be put into the 

 system ; (2) The work to be got out of 

 the system ; (3) The stability of the 

 motion ; (4) Efficiency (or the relation of 

 (2) to (1)); (5) the work wasted in heat- 

 ing the circuit ? Proceed thus : — With 

 a pair of dividers lay down to any con- 

 venient scale, A B, proportional to the 

 electromotive force of the first machine, 

 and B C (in the same straight line but in 

 the opposite direction), proportional to 

 that of the second machine, and describe 

 a circle upon A B as diameter. Adopt- 

 ing as the positive direction of ro- 



