OF AN ELECTRIC DISCHARGE. O 



where the sign of summation at the right-hand side refers to all 

 possible combinations of every single mass of the given system 

 with every one of the exterior systems. 



In like manner let a portion of the mutual action of the 

 masses of the given system itself be assumed to be inversely pro- 

 portional to the square of the distance, so that if r denote the 



distance of two masses m and m' from each other, + — ^ will 



denote the attraction or repulsion exerted between them. We 

 obtain for this portion S3 of the entire sum 



/23(X^^-fYt/2/ + Z^^)=S±-^r- + const, . . (4) 



where the sign of summation to the right refers to all possible 

 combinations of every two of the given masses. 



Now the quantity 2)3 + ^ — is the potential of the exterior 



system of masses upon the given system^, and S± the po- 

 tential of the given system of masses upon itself; and hence the 

 two last-mentioned portions of the work consist simply in the 

 increasing of these potentials. 



To these propositions, which indeed are those of ordinary 

 mechanics, but which it was necessary to premise here, let us 

 now add, that heat consists in a motion of the ultimate particles 

 of bodies, and is the measure of the vis viva of this motion ; so 

 that if in any portion of the given system heat be excited, this 



* The quantity -f ", where p denotes the distance of the mass /n from the 



point 0, is usually called, after the manner of Gauss, the potential of the said 

 mass at this point; the potential is, in this case, not referred to the actual 

 mass m which occupies the position o, but to an assumed unit of mass. This 



At 



quantity +- is certainly of such importance in mechanics as to need a special 



name; in like manner, however, the quantity +~ is of great import; so that 

 a short name is necessary here also, and it also is sometimes named potential. 

 This double use of the word can, however, easily load to error, and to distin- 

 guish one from the other I have applied to -f-- the old name potential func- 

 tion, used by Green, and applied the word jpo/e«<i«/ exclusively to the quantity 



P 



