ALTERNATING CURRENT MEASUREMENTS. 39 



force is proportional to the square of the current. The constant 

 deflecting force, due to a direct current C, is equal to kC 2 , the 

 instantaneous force due to an alternating current is equal to ki 2 , 

 where / is the value of the alternating current at a given instant, 

 and the average force due to the alternating current is equal to 

 k x average i 2 ; but, if the alternating current gives the same 

 deflection as the direct current, the constant force, kC 2 , must be 

 equal to the average force, k x average i 2 , so that average i 2 

 must be equal to C 2 , or y 'average i 2 must be equal to C. That 

 is to say, although the ammeter really measures the average 

 square of any current flowing through it, the scale numbers 

 (values of C) determined by direct-current calibration, are effec- 

 tive values of alternating current (V 'average i 2 C). 



12. The hot-wire ammeter and voltmeter. In these instruments 

 the current flows through a stretched wire, and the wire, heated 

 by the current, lengthens and actuates a pointer which plays 

 over a divided scale. 



The hot-wire instrument, when calibrated by direct current, indi- 

 cates effective values of alternating current, and when calibrated by 

 direct electromotive force it indicates effective values of alternating 

 electromotive force. This is evident in the case of the ammeter 

 when we consider that a direct current C and an alternating cur- 

 rent i which give the same deflection must generate heat in the 

 stretched wire at the same average rate. That is, RC 2 must be 

 equal to R x average i 2 , or C 2 average i 2 , or C = i/average i 2 . 



The hot-wire instrument has not been considered very satis- 

 factory hitherto on account of the tendency of the heated wire to 

 take a permanent set, that is, to become permanently elongated. 



13. The electrodynamometer. The electrodynamometer when 

 used as an ammeter or as a voltmeter consists of a fixed coil and 

 a movable coil connected in series. The current flows through 

 both coils, and the fixed coil exerts a force upon the movable coil 

 which deflects it and actuates a pointer which plays over a di- 

 vided scale. In some instruments the force action between the 



