ALTERNATORS. 255 



long for readings to be taken. A curve of retardation (plotted 

 with time horizontally and the tachometer readings observed 

 vertically) is first obtained from the machine when allowed 

 to slow down from full speed to rest with the fields unexcited, 

 i.e., under the action of air and bearing friction only. A 

 second curve i? then taken in a similar manner, but with the 

 fields excited. The more rapid retardation which will occur 

 in this case is due to the effect of hysteresis and eddy 

 currents. 



The principle of this measurement is as follows : 

 The energy of rotation possessed by a rotating body is 



. / 2 T n \ 2 



where 7 is the moment of inertia of the body, 



n is its speed in revolutions per minute. 

 If the moment of inertia is measured in units of the 

 absolute C.G.S. system, i.e., in gramme-cm. 2 , the energy 

 is expressed in the same system as dyne-centimeters or 

 ergs. In order to bring the ergs to kg. metres we must 

 divide by9-81 x 10 7 , or if to watts-seconds by 10 7 ,orif to foot- 

 pounds by 1 -356 x 10 7 . Thus the energy of a rotating body in 

 watt-seconds or joules is 



(O TT \2 

 ^M x 10- 7 = -5457rc 2 10- 9 

 bu ' 



If the speed of the alternator when slowing down under 

 the influence of the frictional and other losses is observed at 

 successive intervals of time, the difference in the energy 

 possessed by the machine at two periods is a measure of the 

 work done in overcoming the losses. The amount of this 

 work divided by the time between the observations is the 

 mean power thus absorbed. The power absorbed will, of 

 course, grow less as the speed diminishes. By plotting a 

 curve of mean power for a number of speeds obtained as the 

 machine gradually slows down, the losses at full speed may 

 be obtained by continuing backwards the curve of losses to 

 cut the ordinate corresponding to full speed. 



Thus, for example, readings were taken every, half- 

 minute in obtaining the upper curve in Fig. 121 ; the reading 

 at full speed was 172 revs, per minute. The next reading 

 after half -minute was 164. The stored energy at full speed 

 was -545 / 172 2 x 10~ 9 watt -seconds. The energy lost during 

 the first half -minute was -545 7 (172 2 164 2 ) x lO" 9 . The 



