" the Transformation of Energy. 115 



from which it appears, that if the principles which we have laid 

 down as experimental data be rigorously correct, electrical actual 

 energy and chemical energy are simply proportional to each 

 other, and the amount of electrical actual energy produced in a 

 circuit is the exact equivalent of the chemical potential energy 

 which disappears. 



Let us next examine the transformation of electrical actual 

 energy into the potential energy of magnetism by means of soft 

 iron ; and for this purpose let a horse-shoe bar be magnetized by 

 means of a coil encircling it, in which is a current of the energy 



Let the keeper be at a fixed distance x from the bar, and let 

 the amount of their mutual attraction be 



Then it is known by the experiments of Messrs. Joule, Lenz, 

 and Jacobi, that within certain limits the coefficient P is propor- 

 tional, for a given length and arrangement of coil, to the square 

 of the quantity of the current, all other things being supposed 

 constant j that is to say, it is simply proportional to the elec- 

 trical actual energy ; therefore, within those limits, the electrical 

 actual energy which disappears in producing magnetic potential 

 energy is the exact equivalent of the magnetic energy developed. 



When the electric current exceeds a certain quantity as com- 

 pared with the transverse section of the bar, Mr. Joule has proved 

 that the magnetic attraction no longer increases in the exact 

 ratio of the electrical energy, but more slowly. The conclusion 

 to be drawn from this is somewhat remarkable. The total attrac- 

 tion between the bar and its keeper being proportional to P, the 

 portion which causes electrical energy to disappear when it acts 



dY 



is proportional to Q -^, which being smaller than P, the difi'er- 



ence, represented by P — Q -^, is the coefficient of a portion of 



magnetic attraction which acts in raising weights like that of a 

 permanent magnet, without causing electrical actual energy to dis- 

 appear. It is probable that the action of this portion of mag- 

 netism is accompanied by some peculiar variations in the mole- 

 cular condition of the iron. 



(9.) In order to apply the general law of the efficiency of 

 machines to the mechanical action of electro-chemical energy, we 

 have only to conceive for the purpose of this calculation that the 

 reception and discharge of actual energy, which really take place 

 at the same instant, are performed during alternate instants. 

 Then Qi will represent the energy corresponding to the chemical 

 action in the battery in unity of time, and Qg that corresponding 



