GRADUATION OF GALVANOMETERS. 253 



points A and B, A' and B', the two pairs of quadrants are connected 

 with A' and B' separated by a resistance R. If the needle is con- 

 nected with the point A, the deflection a observed satisfies the 

 equation 



l -XkIi 1 ; 



if the needle is connected to the point B, the deflection /? gives 

 also 



Subtracting these two equations from each other, we get 



as V's-V'^RI, and V 2 -\\ = E, it follows that 



FT /? -" 



= - 



We may, finally, make use of an electrodynamometer the fixed 

 coil of which is in the principal circuit, and the movable coil, which 

 is of great resistance, is placed as a shunt at the two points A and 

 B. The deflection observed is in that case proportional to the work 

 of the electricity between these two points.* 



870. GRADUATION OF GALVANOMETERS. In mirror instruments, 

 where the deflections are very small, the intensity of the current is 

 proportional to the tangent of the angle of deflection, or to the angle 

 itself, and this is also the case with all galvanometers in which the 

 deflections are within certain limits. This proportionality ceases, 

 however, to hold if the needles are long in comparison with the 

 dimensions of the coil; an empirical graduation is then necessary. 



If we have at command a galvanometer with a systematic 

 graduation, such as a sine or a tangent galvanometer, the same 

 current is passed through the standard instrument and the gal- 

 vanometer under trial, using a shunt if necessary, so as to bring the 



* M. DEPREZ. Comptes rendus, Vol. xc., p. 592. 1880. 



