282 Pkofessok Thomson on the DislrUiul'wn of EkclricUij. 



it is cbarged. Each term of tbis expression does not represent the inde- 

 pendent value of the actual distribution on the conductor to which it 

 corresponds, inasmuch as the "potential" in each depends on the pre- 

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

 mutual influence ; but independent expressions of these independent 

 values are readily obtained, although not In a form convenient for state- 

 ment 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 mechanically valuable effects being developed, 

 the heat generally, as for instance in the sparks produced when the 

 knob of a Loyden phial is put in communication with the outside coating, 

 or when a flash of lightning takes place, is equal in mechanical value 

 to the distribution of electricity lost. Hence, by what precedes the 

 amount of heat is proportional to the square of the quantities discharged, 

 as was first demonstrated by Joule, iu a communication to the Royal 

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

 Harris as an experimental result, to be simply proportional to the 

 quantity. Mr. Joule's result has been verified by independent experi- 

 menters in France, Italy, and Germany. The author pointed out other 

 applications of his investigation, some of a practical kind, and others in 

 the Mathematical Theory of Electricity. He mentioned, that although 

 he had first arrived at the results in 1845, and used them in papers 

 published in that year, the first explicit publication of the theorem re- 

 garding the mechanical value of the electrification of a conductor appears 

 to be in 1847, in a paper entitled " Ueber die Erhaltung der Kraft," 

 by Helmholz. 



II. Magnetism. 



If a piece of soft iron be allowed to approach a magnet very slowly 

 from a distant position, and be afterwards drawn away so rapidly that 

 at the instant when it reaches its primitive position, where it is left at 

 rest, it retains as yet sensibly unimpaired the magnetization it had 

 acquired at the nearest position, a certain amount of work must have 

 been finally expended on the motion of the iron. For during the approach, 

 the iron has only the magnetization due to the action of the magnet on 

 it in its actual position at each instant, but at each instant of the time in 

 which the iron is being drawn away, it has the whole magnetization due 

 to the action of the magnet on it when it was at the nearest. Hence it 

 is drawn away against more powerful forces of attraction by the magnet, 

 than those with which the magnet attracts it during its approach ; from 

 which it follows that more work is spent in drawing the iron away than 

 had been gained in letting it approach the magnet. The sole effect due 

 to this excess of work is the magnetization which the iron carries away 

 with it ; and consequently, the mechanical value of this magnetization 

 must be precisely equal to the mechanical value of the balance of work 

 spent in producing it. 



