in the Wire of a Voltaic Circuit, 193 



greater than that of an inch in length of the thinner in the 

 ratio of the square of radius ; so that if the rise of temperature 

 is inversely proportional to the fourth power of diameter or 

 radius, the heat-force engendered in an inch length of the wire 

 is inversely proportional to the square of the diameter; and if 

 the elimination takes place on the surface of the wire, the force 

 engendered on a square inch of that surface is inversely propor- 

 tional to the cube of the diameter. 



Assuming that the heat evolved in the wire of a voltaic cir- 

 cuit is also produced on its surface only, we may compute from 

 Ohm's formula the ratio between the diameter of the wires 

 and the heat evolved on a square inch of their surfaces respec- 

 tively. I have made this calculation (see the appended note), 

 and find that the ratio is precisely the same as the above. 



It seems difficult after this to believe that there can be any 

 difference in the modus operandi : if it is the surface alone that 

 is primarily affected in one case, it must be the same in the 

 other. 



I am, Gentlemen, 



Your most obedient Servant, 



John James Waterston. 

 Inverness, July 22, 1865. 



Note as to the Heat-generating Faculty in the Voltaic Circuit. 



W= heat-work performed in constant element of time. 



E = electromotive power of battery. 



Assume that the resistance in the metallic part of the circuit is 



incomparably greater than in the liquid portion. 



d 2 

 C = conducting-power of circuit = — , in which d is diameter and 



I length of wire. 



W=EC=Ey 



Suppose W and E to be invariable, and the circuit to be composed 

 first of a wire whose surface is s v diameter d it and length l v and 

 afterwards of a wire whose surface is s 2 , diameter d 2 , and length l 2 , 



r d* d? .d? 



C = -=^; hence / 2 =/ 1? , 



d 3 

 To find the ratio of s x to s 2 , we have s^irdJi and s z =irdj z =7rl l ~ ; 



hence 



d* c? 3 



Sl :s 2 :: icl x d t : ttI, -± : : d x : ^ : : d* : d 2 \ 



If the invariable work W of the circuit or heat-force is engendered 

 Phil. Mag. S. 4. Vol. 30. No. 20.2. Sept. 1865. 



