240 The Mathematical Electricians of the 



this which determines the electromotive force of the cell.* 

 The amount of energy which is changed from the chemical to 

 the electrical form in a given interval of time is measured by 

 the product of the strength of the chemical affinity into the 

 quantity of chemicals decomposed in that time, or (what is the 

 same thing) by the product of the electromotive force of the 

 cell into the quantity of electricity which is circulated. This 

 energy may be either dissipated as heat in conformity to 

 Joule's law, or otherwise utilized in the outer circuit. 



The importance of these principles was emphasized by 

 Hermann von Helmholtz (b. 1821, d. 1894), in a memoir which 

 was published in 1847, and which will be more fully noticed 

 presently, and by W. Thomson (Lord Kelvin) in 1851f; the 

 equations have subsequently received only one important 

 modification, which is due to Helmholtz.:}: Helmholtz pointed 

 out that the electrical energy furnished by a voltaic cell need 

 not be derived exclusively from the energy of the chemical 

 reactions : for the cell may also operate by abstracting heat- 

 energy from neighbouring bodies, and converting this into 

 electrical energy. The extent to which this takes place is 

 determined by a law which was discovered in 1855 by Thomson. 

 Thomson showed that if E denotes the " available energy," i.e., 

 possible output of mechanical work, of a system maintained 

 at the absolute temperature T, then a fraction 



TdE 

 fidT 



of this work is obtained, not at the expense of the thermal or 



* The heat of formation of a gramme-molecule of ZnS04 is greater than the heat 

 of formation of a gramme-molecule of CuSO* by about 50,000 calories ; and with 

 divalent metals, 46,000 calories per gramme- molecule corresponds to ane.m.f. of one 

 volt ; so the e.m.f. of a Daniell cell should be 50/46 volts, which is nearly the 

 case. 



t Kelvin's Math, and Phys. Papers, i, pp. 472, 490. 



J Berlin Sitzungsber., 1882, pp. 22, 825 ; 1883, p. 647. 



Quart. Journ. Math., April, 1855 ; Kelvin's Math, and Phys. Papers, i, 

 p. 297, eqn. (7). 



