INVESTIGATION OF CURRENTS IN THE VARIABLE STATE. 295 



908. We shall cite, in the first case, as more simple, the method 

 used by Mr. Sabine* for determining the form and velocity of pro- 

 pagation of the electrical wave produced in a cable, one end of 

 which is connected to the earth, and the other A is at a potential 

 which varies according to any given law (294 et seqq.}. 



The end A of the cable is insulated, and any given point of its 

 length is connected with a condenser the second armature of which 

 is to earth. A rotating commutator (896) first connects the point A 

 with a battery, and after a known time /, insulates the condenser 

 from the point M, and discharges it through a galvanometer. The 

 swing of the needle is proportional to the potential acquired by the 

 point at the moment of breaking. In this way the law of variation 

 of the potential during the closing of the circuit is determined. 



By arranging the contact studs suitably on the rotating com- 

 mutator, the length of contact of the point A with the battery 

 may be limited, or it may be successively raised to different 

 potentials of either sign for intervals of known length; so that 

 electrical waves alternately positive and negative may be sent 

 through the cable. If the contact stud relative to the point M 

 is then arranged so that the charge of the condenser is null, it 

 will determine the period at which the point M is in the neutral 

 state between two successive waves. 



It is, however, supposed that the presence of the conductor at 

 the point M does not change the original conditions of the experi- 

 ment, which necessitates that its capacity is very small in comparison 

 with that of the cable. 



909. The experiments of Von Helmholtzf on the variable period 

 of the current of closing refers to a more complicated phenomenon. 



The total quantity of electricity, which corresponds to the extra 

 current of making (533) or of breaking, for a current I in the 



permanent condition, is equal to I - . 



Jx 



It may be observed that if the channel of the coil is given as 

 well as the current, this quantity of electricity only depends on 

 the weight of the wire ; for the coefficient of self-induction L (780) 

 and the resistance R (726) are each proportional to the weight 

 of the metal. It is therefore advantageous, in studying the phe- 

 nomenon, to use a thick metal wire of good conducting material. 



* R. SABINE. Phil. Mag. [5], Vol. n., p. 321. 1876. 



t HELMHOLTZ. Pogg. Ann., Vol. LXXXIII., p. 505. i%$\. Wissen$chaft. 



Abhandl., Vol. I., p. 429. 







