16 Mr. A. Campbell on the Magnetic Fluxes in 



From this curve it is not possible to get the exact value of 

 the hysteresis loss, as the iron core is not a uniformly mag- 

 netized closed circuit. To get an idea, however, of the amount 

 of the power wasted by hysteresis, let us suppose that the 

 magnetic circuit is equivalent to a uniform iron ring of the 

 same cross-section as the core of the shant-coil, uniformly 

 wound with the same number of turns n x as the shunt-coil * 

 (carrying the same current) , and traversed by a flux equal to 

 that at the part of the meter-core for which the curve in fig. 6 

 was taken. 



Let c = current at any moment, 



anci s = section of ring. 



Then 



Hysteresis-loss in joules per cycle 



= §cdv = 10"% jc^ = W-\s§cdB 

 = lO" -8 ^ x (area of curve) 

 = lO" 8 x 1200 X 3-7 x area 

 = 0-00114. 

 .*. at 86^~ per second, 



Power spent = S6x 0*00114 = 0'098 watt. 



It was found by direct measurement that the actual power 

 spent in the meter (with the shunt-current alone) was far 

 larger than this. Accordingly measurements were made of 

 the rise of temperature of the iron core by means of an iron- 

 nickel thermopile. Three junctions of the pile were bound 

 against the iron, which had its surface well insulated with 

 paint. A pad of wadding was tied over the spot, and the 

 thermopile was connected with a suitable galvanometer. The 

 shunt-current was switched on for 120 seconds, the deflexion 

 being read at intervals, and on breaking the current the 

 cooling was observed for several minutes. The thermopile 

 and galvanometer were calibrated with a known difference of 

 temperature, and the curves of heating and cooling were 

 drawn. The curve of heating was then corrected by means 

 of the other curve, and thus the heating of the iron (cor- 

 rected for cooling) was found. 



At a spot just above the shunt-bobbin the corrected rise of 

 temperature w r as o, 87 C, whilst near the air-gap it was only 

 about half of this. Taking account of this last fact, we may 



* The exact value of n x was not known, but the value (1200) used 

 was estimated from the resistance and gauge of the shunt-wire and the 

 size of the coil. 



