in Electricity and Magnetism. 375 



pared with what does pass, on account of the great length 

 and small section of the wire experimented with. 



Adopting, for brevity, the following notation : — 



L = length of wire. 



S = sectional area of wire. 



n = a multiple, or simply a number. 



Q = quantity of electricity which the battery can circu- 

 late, when the passage of the current is quite unimpeded ; 

 that is, the absolute power of the battery. 



q = that portion of Q, which passes through the wire ex- 

 perimented with, when it is included in the circuit. 



e = a constant, while L and S are constant; being 1, 

 when such a measure is taken for Q, that, on Q being re- 

 duced tO 1, (1 = —-. 

 2 



My object has been to obtain the law of conduction, giving 

 the values of q for all values of Q as well as of L and S. 

 In a wire of constant L and S, by varying Q, I find 



q = * yg (formula A). 



e + Q ' 



The quantity (q) of electricity which (from a given Q) will 

 pass through a length L, may be considered as a new avail- 

 able quantity, ox Q, for passing through another piece of wire 

 afterwards included in the circuit *. Hence for a wire of con- 

 stant S and of n x the length of another, we have (from 

 formula A) the new 



* = «M^b§TQ' or ' the new q = ?T^Q • • • (B 



When a copper wire having S = T ^ square inch, and 

 L = 58 feet, completes the circuit of a battery in such ac- 

 tion, that Q®is equal to the electricity circulated by the com- 

 bination of 0*1 grain of pure zinc per second, then q was 

 found to be \ Q, or the electricity arising from the combina- 

 tion of 0'05 grain of zinc per second. 



Now by applying this numerical datum, and the fact that 

 increasing S and Q together increases q in the same ratio, by 

 applying this to the above formula B, and reckoning L in 

 feet, S in square inches or fractional parts of a square inch, 

 and representing Q and q by grains of zinc used per second, 

 we may deduce the following formulae : — 



L=580.S.S=2, 

 Q.q 



* This reasoning will equally apply although the electric influence be 

 propagated by vibrations in any medium, or even by any simultaneous af- 

 fection or change of state in the particles of the conducting substance, but 

 the convenient analogy of a current rentiers the subject much clearer. 



