Distributions of Electricity, Magnetism and Galvanism. 193 



terra) by the flasneSj illuminated points^ and sparks which accom- 

 panv the transmission of the electricity from the glass of the 

 machine where it is first excited to the conductor which receives 

 it, the mechanical value of the electrification thus efi"ected would 

 be enormously over-estimated if it were regarded as equivalent to 

 the work that has been spent. Notwithstanding;, the mecha- 

 nical value of any electrification of a condv;ctor has a perfectly 

 definite chai'acter, and may be calculated with ease in any par- 

 ticular case by means of formulse demonstrated in this commu- 

 nication. The simplest case is that of a single conductor insu- 

 lated at a distance from other conductors, or with only miinsu- 

 lated conducting matter in its neighbourhood. In this case the 

 mechanical value of the electrification of the conductor is equal 

 to half the square of the quantity of electricity multiplied by the 

 capacity of the conductor*. 



In any case whatever, the total mechanical value of all the 

 distributions of electricity on any nuinber of separate insulated 

 conductors electrified with any quantities of electricity, is demon- 

 strated by the author to be equal to half the sum of the products 

 obtained by multiplying the " potential f " in each conductor by 

 the quantity of electricity by which it is charged. Each term 

 of this expression does not represent the independent value of 

 the actual distribution on the conductor to which it corresponds, 

 inasmuch as the " potential " in each depends on the jireseuce 

 of the others when they are near enough to exert any sensible 

 mutual influence ; but independent expressions of these inde- 

 pendent values are readily obtained, although not in a form con- 

 venient for statement here; and the author proves that their 

 sum is equal to the total value, as calculated by the preceding 

 expression. When a conductor is discharged without other me- 

 chanically valuable efieets being developed, as, for instance, when 

 the knob of a Leyden phial is put in communication with the 

 outside coating, or when a flash of lightning takes place, the 

 heat is equal in mechanical value to the distribution of electricity 

 lost. Hence, by what jn-ccedes, the amount of heat is propor- 

 tional to the square of the quantities discharged, as was flrst 

 demonstrated by Joule, in a communication to the Royal Society 

 in 1840, although it had been announced by Sir W. Snow Harris 



* Electrical capacity is a teiin introduced by the author to signify' the 

 proportion of the quantity of electricity that the conductor would retain to 

 that which it would communicate to a conducting ball of unit radius, insu- 

 lated at a great distance from other conducting matter, if connected with 

 it by means of a line wire. 



t A term first introduced by Green, which may be defined as the quantity 

 of mechanical work that would have to be spent to bring a unit of electricity 

 from a great distance up to the surface of the conductor, supposed to retain 

 its distribution unaltered. 



