MEASUREMENT OF A VERY SHORT TIME. 281 



Pouillet proposed this method for measuring a very short time, 

 such as that which a ball takes in traversing a gun-barrel. It 

 only applies provided the effects of induction may be neglected 

 that is to say, with rectilinear and very short circuits ; in other 

 cases the extra current on opening and closing must be allowed 

 for. The latter has generally a very slight influence ; for it is 

 produced only when the circuit is closed by the layer of air in 

 which the spark passes, and the resistance of which is very great. 

 If we assume that we can disregard the quantity of electricity 

 which corresponds to it, and if R and L are the elements of the 

 circuit (532), we have 



(54) 



r r L / *AI 



=\ Ut=lA B--1 i-*-i: \ . 



When the duration 6 is very great compared with the time necessary 

 to start the current, the value of the exponential may be neglected, 

 and this equation gives, at any rate approximately, 



We see that it is sufficient to add to the time calculated by 

 equation (53) a constant term equal to the quotient of the co- 

 efficient of self-induction of the circuit by its resistance. This 

 correction is, however, only sufficient for very shoit times. 

 Formula (54) shows that the impulse decreases then much more 

 rapidly than the time.* 



An experimental device enables us to get rid of all difficulties 

 with induced currents. Instead of opening the circuit after the 

 interval 0, the constant electromotive force is suppressed, a metal 

 wire of equal resistance being substituted for it. The two induction 

 currents follow then the same law (534) ; and, as they are in 

 opposite directions, the total quantity of electricity which traverses 

 the galvanometer in the time & is equal to I #. 



896. When the armatures of a condenser of capacity C, are 

 connected by a conductor of resistance R, which has no coefficient 

 of self-induction, the intensity I of the current at any given time 



* HELMHOLTZ. Pogg. Ann., Vol. LXXXIII., p. 505. 1851. Wissenschaft. 

 Abhandl., Vol. I., p. 529. 



