310 Dr. Sumpner and Mr. Phillips on a 



currents generated in the ordinary way. The construction of 

 the indicating instrument constitutes the real obstacle. The 

 reflecting instrument for alternate current circuits described 

 in this paper is the result of an attempt to overcome this 

 difficulty. The instrument is like a moving coil galvano- 

 meter in almost every respect, except that its field is due to 

 an electromagnet excited by an alternating voltage. The 

 theory of non-reflecting instruments of the same type has 

 already been fully explained *, but it may be convenient to 

 briefly refer to it. 



If an alternating voltage V be applied to an electro- 

 magnet whose winding consists of m turns, the core flux N 

 will be such that 



V = rA + mN, (1) 



where r is the resistance of the coil and A the current 

 traversing it. If the coil and electromagnet be so designed 

 that for currents of the frequencies used the resistance is 

 negligible in comparison with the impedance, we can neglect 

 the term rA. It follows that the rate of change of N will be 

 at each instant a measure of V, and this will be true what- 

 ever the permeability or hysteresis of the core. We thus 

 have a magnet whose strength is accurately determined by 

 the applied voltage whatever the physical properties of the 

 core. Such an electromagnet can easily be made very 

 strong. Moreover, the shorter the air-gap between the poles 

 is made, the denser is the magnetic flux due to a given 

 current, and the greater is the ratio of impedance to resist- 

 ance for a given winding. Thus the stronger the electro- 

 magnet is made by improving its magnetic circuit, the more 

 accurate it becomes, provided this electromagnet is excited 

 by the voltage of the circuit. 



Fiff. 1. 



The instrument here described has a laminated electro- 

 magnet formed, of stampings shaped like figure 1. These 



* Proc. Roy. Soc. vol. lxxx. (1908), ''Alternate Current Measurement," 



