248 MEASUREMENT OF CURRENTS. 



the ratio of the distance 2x of the fixed coils to their mean radius #, 

 and the ratio of the mean radii a and a'. This latter ratio may be 

 reduced to a comparison of the two resistances, and may be deter- 

 mined electrically with the greatest precision (876). ' 



Instead of circular coils, Cazin* used two parallel rectangular 

 coils. The calculation for this action was given in (492). 



Mascartf also used, with the same object, the action (791) of 



^ two equal and parallel coils on a long coil with the same axis as 



V the first, and the lower plane of which is in the plane of symmetry 



of the two fixed coils. The movable coil A' is suspended to the 



plate of a balance, and the current is conveyed there by very flexible 



platinum wires. The reciprocal action being near the maximum, the 



equilibrium is perfectly stable. 



As the intensity of the current is almost always subject to con- 

 tinual variations, it is difficult to obtain an exact balance ; but small 

 differences may be estimated by observing the displacement of the 

 index. If we want to observe in the position of equilibrium itself, 

 and the current is diminishing, for instance, the action being 

 attractive, weights which are slightly too small are added, and the 

 moment of the passage of the needle through zero is observed. 

 The same operation, repeated from time to time, would enable us 

 to fix points for constructing the curve of intensities from which 

 the value of the current is deduced at a given time, or the in- 

 tegral in respect of the time. This integral will give the total 

 quantity of electricity which has passed. 



A similar device may be applied with all apparatus, whether 

 of torsion or depending on the time, which require the return of 

 a movable part to a fixed position. 



We may, in conclusion, cite an arrangement of Von Helmholtz,| 

 which, though not suited for absolute measurements, is very con- 

 venient. To the pans of an ordinary balance are suspended two 

 identical coils, the diameter of which is equal to the height, and 

 which can move freely inside two fixed coils of the same height. 

 These are supported by a horizontal metal arm, which may be 

 fixed on the pillar of the balance. One acts by attraction and the 

 other by repulsion on the corresponding movable coil. The 

 position of the fixed coils is regulated by the condition that the 



* CAZIN. Ann. de Chim et de Phys. [4], Vol. I., p. 257. 1864. 

 t MASCART. Journal de Physique [2], Vol. I., p. 109. 1882. 

 % HELMHOLTZ. Proceedings of the Roy. Soc., 1881. Wissenschaftliche 

 Abhandlungen, Vol. I., p. 922. 



