Current and Potential Difference Analogies. 211. 



therefore in all the nine cases 



Apparent watts cos (d — <j>) . cos <£ 

 True watts cos 



1 + tan 6 . tan <£> ,* ^ 



= 1 + tan 2 $ ; * * * V ) 



The circuit cd need only possess a self-induction /, even if 

 an ammeter or dynamometer form part of it, but the circuit 

 ah may have mutual induction and capacity as well as self- 

 induction. If therefore we write expression (1) in the form 



Lp lp 



1+ 1 



K r 



(2) 



as we did in 1888, where p equals 2w times the frequency, it 

 must be remembered that while I and r are the true values of 

 the self-induction and resistance of cd, L and E, are only 

 the effective self-induction and resistance of ab. Hence, as 

 Mr. Blathy suggested in the ' Electrician 3 for 1888, it is 

 better to leave our expression for the ratio of the apparent to 

 the true watts in the general form as given in (1) rather than 

 to put it in the derived form as given in (2). 



^ will generally be positive if the resistance of cd is small ; 

 but, if cd contains a doubly-wound high resistance-coil, as is 

 generally the case when cd, is the fine-wire circuit of a watt- 

 meter, then it is quite possible to make $ positive, nought, 

 or negative. 6 may, of course, be also positive, nought, or 

 negative, depending on whether the self and mutual induction 

 effects preponderate or not over the- capacity effect. It is 

 therefore possible to have either 6 or (/>, or both, positive or 

 negative. 



The apparent watts will therefore be : — 



too large if 6 and <j> be both of the same sign and 6 > (f> ; 



, 11 *f / (1) ^ and ^ be k°^ n °f the same sign and 0<<j); 



\ (2) 6 or <fi be of different signs ; 



correct if 1 C 1 ) 6 and * be ec L ual 5 

 conect n |^ £ benougllt 



Now (j) can be made very small in one or other of three 

 ways : — 



1. Use some method of testing, like that shown in figures 

 1, 3, 4, 5, 6, and 8, which does not require any 

 measuring instrument to be placed in the non- 

 inductive circuit cd. 



P2 



