282 MEASUREMENT OF CURRENTS. 



is connected to the difference of potentials of the armature, by Ohm's 

 law E = IR, and we have Idt + C^E = 0. It follows that 



E being the difference of potential at the origin of the time. 



This is the principle of the method used by the late Mr. Sabine* 

 to determine very short intervals of time, and particularly the velocity 

 of projectiles. The armatures of a condenser are connected on the 

 one hand with a battery of small resistance, which maintains a con- 

 stant difference of potential ; and, on the other, with a wire of very 

 great resistance R. The two wires being at a given distance on 

 the path of a projectile, the first is cut and then after a time / the 

 second. The ratio of the residual difference of potential E to the 

 initial value E , is determined by discharges in a ballistic galvano- 

 meter. 



We may, moreover, graduate the instrument directly by the aid 

 of a rotating commutator, to which a given velocity is suddenly 

 imparted, and which, when once the condenser has been charged 

 and insulated, closes the circuit for an interval of time known by the 

 distance of two stops on the edge of a disc, the velocity of which 

 is known. Intervals of time can thus be estimated which do not 

 exceed 0*0001 of a second. 



897. MEASUREMENT OF A DISCHARGE BY THE ELECTRO- 

 DYNAMOMETER. When the same current I passes through the two 

 coils of an electrodynamometer (864), the couple for a deflection S 

 is equal to S'GI 2 cos 8. 



K being the moment of inertia of the movable coil, the angular 

 velocity w , imparted by a discharge the total duration of which is 

 very small compared with the duration of the oscillations, is given 

 by equation 



If the deflections are very small, and l] n represents the mean 

 square of the intensity of the current, we may write 



* R. SABINE. Phil. Mag. [5], Vol. I., p. 337. 1876. 



