PiiOFESSOii Thomson on the Distribution of Ekclridty. 281 



January 1.9, 1853. — TJie President in tlie Chair. 



Mr. Geosge Donaldson and 3Ir. James Taylor were elected members. 



The discussion on Mr. Rankine's paper " On the General Law of 

 the Transformation of Energy," was resumed, and Professor William 

 Thomson and Mr. James Reid expressed their opinion on the subject. 



A paper " On the Mechanical Values of Distributions of Electricity, 

 Magnetism, and Galvanism," and another "On Transient Electric Cur- 

 rents," were then read by Professor William Thomson. 



XXXV. — On the Mechanical Values of Dislribulions of Electricitij, 

 Magnetism, and Galvanism. By Professor W. Thomson. 



I. Electricity at Rest. 



To electrify an insulated conductor (a Leyden phial, for instance, or 

 any mass of metal resting on supports of glass,) in the ordinary way by 

 means of an electrical machine, requires the expenditure of work in turning 

 the machine. But inasmuch as part, obviously by far the greater part, 

 of the work done in this operation goes to generate heat by means of 

 friction, and of the small residue some, it may be a considerable propor- 

 tion, is wasted in generating heat (electrical light being included in the 

 term) by the flashes, illuminated points, and sparks, which accompany 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 effected would be enormously overestimated if it 

 were regarded as equivalent to the work that has been spent. Notwith- 

 standing, the mechanical value of any electrification of a conductor has 

 aperfectly definite character, and may be calculated with ease in any parti- 

 cular case, by means of formulae demonstrated in this communication. The 

 simplest case is that of a single conductor insulated at a distance from 

 other conductors, or with only uninsulated 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.* 



Id any case whatever, the total mechanical value of all the distribu- 

 tions of electricity on any number of separate insulated conductors electri- 

 fied with any quantities of electricity, is demonstrated 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 



* A term introduced by the author to signify the proponion of the quantity 

 of electricity that the conductor would retain to that which it would communicate 

 to a conducting ball of unit radius, insulated at a great distance from other conduct- 

 ing matter, if connected with it by means of a fine wire. 



t A terra 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 distribu- 

 tion unaltered. 



Vor.. III.— No. :,. 3 



