Electrometer as a Wattmeter. 505 



for if the resistance is made low the instrument is not sensi- 

 tive enough, and if it is made high the electrometer no longer 

 reads in watts. If the instantaneous pressures are 0, x, and y, 

 the force exercised hy the first quadrant a in the positive 

 direction is k y 2 , where k is the constant of the instrument. 

 This constant may be omitted, and the force denoted hy y 2 . 

 The force exercised hy b is— (y — x) 2 ; hy c, — (y — x) 2 ; and by 

 d, y 2 . The total force is thus 2 (2y — x) x. The needle contact 

 may now be moved from y to x and another reading taken. 

 This is of course 2 x 2 . Subtracting this from the first readme;, 

 we get 4 (y — x) x, which is the power taken by W. This is 

 the arrangement that was adopted by Dr. Hopkinson in his 

 measurements of the Gaulard and Gibbs transformer in 1884. 

 During the first reading the instrument is really two idio- 

 static voltmeters, one being in shunt to both the resistance 

 and W, and the other in shunt to W alone. During the second 

 reading it is a voltmeter in shunt to the resistance alone. 



Professor Ayrton arranges the instrument so that the quad- 

 rants are in shunt to W, and the needle is first connected to x 

 and a reading taken, and the needle is then connected to 

 and a second reading taken. During the first reading, the 

 instrument is a voltmeter in shunt to W, and during the second 

 it is two voltmeters, one in shunt to the resistance and one 

 in shunt to the whole circuit. The difference again gives the 

 power spent in W. Mr. Smith uses a discharge-key for 

 making a change quickly. The discharge-key can be used 

 in either arrangement, but the first is more accurate. For 

 instance, suppose y — x, the pressure on W, is 2000 volts, and 

 x, the pressure on the resistance, 20, and suppose the instru- 

 ment one per cent, low at one reading. The first reading by 

 the second method is 8,000,000, the second 8,160,000. Suppose 

 the latter is read one per cent, low, viz. 8,078,400, the result- 

 ing determination is 78,400 instead of 160,000 ; that is to say, 

 the power is more than 100 per cent, greater than that given 

 by the instrument. In the arrangement used by Dr. Hopkin- 

 son, however, the readings are 160,800 and 800, so a mis- 

 reading of one per cent, in the first makes one per cent, error 

 only, and in the second makes no sensible difference. 



The quadrant electrometer may, however, be arranged so 

 as to read power directly without any change of connexions. 

 This is shown in fig. 2. A second resistance equal to the 

 first is put on the other side of W, and the quadrants are con- 

 nected up as shown. The first quadrant a then has a force 

 y 2 , the second b, — (y — x)~. So far the instrument is like that 

 shown in fig. 1 , but with only half its quadrant utilized. Quad- 

 rant c has a force — x 2 , and dis inactive ; so that quadrant c 



