THE MAGNETIC MEASUREMENT OF CURRENT. 33 



22. The Weber electrodynamometer. In order to measure a 

 current by means of the Siemens electrodynamometer, the reduc- 

 tion factor of the instrument must be determined by observing 

 the value of < for a known value of the current / [see equation 

 (i) of Art. 21], The Weber electrodynamometer, on the other 

 hand, is so constructed that the value of k can be calculated 

 from the dimensions of the coils A and B and their positions 

 relative to each other. The Weber electrodynamometer is 

 sometimes called an "absolute" electrodynamometer because the 

 measurement of current by the Weber instrument involves only 

 geometrical and mechanical measurements. 



Imagine a large circular coil of radius R, and having Z f 

 turns of wire, to be placed with its axis along pp and its plane 

 along cc in Fig. 27, and let us think of the magnetic field H of 

 Fig. 27 as due to a current of I abamperes in this large circular 

 coil. Then 



H-*j! (D 



according to equation (i) of Art. 14. 



Let the coil which is shown in Fig. 27 be a comparatively small 

 circular coil of radius r and having Z" turns of wire, and sup- 

 pose this small coil and the large coil to be connected in series so 

 that the current / flows through both. Then the torque exerted 

 on the small circular coil placed as shown in Fig. 27 will be: 



T = 7rr 2 Z'7#cos0 (2) 



according to equation (5) of Art. 20 as modified by the note at the 

 end of that article. Therefore, substituting the value of H 

 from equation (i) in equation (2) we have: 



2<**r*Z'Z"I* cos 



t ~^r (3) 



from which the value of I in abamperes can be calculated when 

 r (a mechanical quantity), r, R and < have been measured, 

 Z' and Z" being known. 



4 



