of the Conditions of Maximum Efficiency. 



Li 



35 



equal to CAE, i. e. its tangent is equal to 7^-, and therefore 



its magnitude is independent of the angle of phase-difference 

 {tt-ABC}. 

 Let D be in the F circle, and join DE. 



Now it is easy to see that the two triangles EAD, CAB are 

 similar, and their sides homologous in the order of the letters 

 given. For 



EA=CAcosEAC, 



D A = B A cos D AB = B A cos E AC, 



and the angle 



EAD=EAC + CAD = DAB + CAD = CAB. 

 Hence the third side 



DE = BCcosEAC, 

 and therefore is invariable, whatever the phase-difference 

 between the lines AB, BO. 



But D is also fixed ; therefore E lies upon a circle whose 

 centre is D, and whose radius is BO cos EAC, or BC cos DAB. 

 I call this circle the E circle. 



We have now reached the following state of things : — 

 F must lie upon a fixed circle, 



•^ J7 JJ V JJ 



and AEF are in one straight line. 



With these prefatory remarks I now proceed to the solu- 

 tion of the questions particularized at the beginning of the 

 paper; which will now be seen to be merely the finding out of 

 the particular position of E upon its circle, which will make 



FE 



the ratio -^ as large as possible, or, which is the same thing, 



AE 



that of -p™ as small as possible. 



9. Let e and f be the two electromotive forces. Take 

 D2 



