Electrometer as a Wattmeter and Voltmeter. 



367 



Seeing from fig. 3 how great was the deviation from, the sine law, 

 it would have been necessary to analyse each carve by Fourier's 

 theorem, if the subject was to have been treated mathematically, 

 the phase difference being given. The current curve was continually 

 changing its form with different loads, and this would have neces- 

 sitated observing the curve in each case, so that nothing was to be 

 gained by this method of treatment. The potential curve 0, fig. 3, 

 has, however, been analysed,* and can be expressed by the equa- 

 tion — 



C = Bx sin — + B 3 sm — + 



The first five co-efficients are as follows : — 





B 3 



B 5 



B 7 



B 9 



540-1 



1-9 



31-5 



-6-5 



1 -3 













We see that B 5 is important, being about 6 per cent, of B x ; so that 

 from the analysis the cosine law could not be expected to hold. In 

 section (a), Table II, the cosine law is applied in two instances for 

 the purpose of illustration. It gives 18'54 as against 17*0 for the 

 Watts, per division of scale, for 60°; and 17"2 as against 17 for 30°. 

 For small angles the error does not appear to be so great. 



The conclusions arrived at from these experiments are that the 

 Kelvin Quadrant Electrometer can be used with accuracy as a 

 Wattmeter in the case of alternate currents having any phase rela- 

 tion, and that, as pointed out by Dr. J. Hopkinson,f it is necessary 

 to see that within the range of potentials applied, Maxwell's formula 

 is verified. This is, perhaps, best done by applying steady potential 

 differences to the needle and quadrants, and measuring these by 

 Poggendorff's method, employing Clark's standard cell as the unit of 

 comparison. It could also be tested by applying known alternating 

 potentials to the needle and quadrants, the curves being in phase. If 

 it is required to use alternating potentials of high value, such, for 

 instance, as 2000 volts or more, a suitable transformer could be 

 employed to reduce the potential on the needle. Such unloaded 

 transformer could have the primary and secondary electromotive 

 forces in phase, and of the same wave form, J so that no error would 

 be thereby introduced. 



* ' Electrician,' August 31, 1894, p. 517. 

 f ' Philosophical Magazine,' April, 1885. 

 X ' Electrician,' February 15, 1895, p. 463. 



