by means of an obliquely situated Galvanometer Needle. 347 



Meritens) rather than by want of delicacy in the measuring- 

 apparatus. 



When the phase-difference is about a quarter of a period, 

 cos e is small, and its value is best found by observing the 

 effect of reversing the shunt-current while the main current 

 continues running. The difference is4AB cos e, from which, 

 combined with a knowledge of A and B, the value of cos e is 

 advantageously derived. If cose is absolutely zero, the re- 

 versal does not alter the reading. 



If the currents are in the same, or in opposite phases, it is 

 possible to reduce the joint effect to zero by suitable adjust- 

 ment of the coils or of the shunt resistance. 



The application of principal interest is when the shunt- 

 current may be assumed to have the same phase as the 

 potential-difference at its terminals, for then cos e is the factor 

 by which the true watts may be derived from the apparent 

 watts. We will presently consider the question of the 

 negligibility of the self-induction of the shunt-current, but 

 before proceeding to this it may be well to show the applica- 

 tion of the formulae when the currents deviate from the 

 sine type. 



If a be the instantaneous current, and v the instantaneous 

 potential-difference at the terminals, the work done is ^avdt. 

 The readings of the soft iron galvanometer for either current 

 alone may be represented by 



A 2 = h 2 $a 2 dt, B 2 = k 2 $v 2 dt, . . . .(2) 



where h, h are constants depending upon the disposition of the 

 apparatus. When both currents act, we have the readings 



Wor C 2 2 =§(ha±kv) 2 dt (3) 



Taking the first alternative, we find 



d 2 = h 2 $a 2 dt + 2hk$av dt + Pftdt, 



(V-A'-'B* Savdt 



or 



2AB {$jdtx$*dt} 



(*)" 



The fraction on the right of (4) is the ratio of true and 

 apparent watts ; and we see that, whether the currents follow 

 the sine law or not, the ratio is given by cos e, where, as 

 before, e is the angle of the triangle constructed with sides 

 proportional to the square roots of the three readings. 



