336 EQUILIBEIUM OF HETEROGENEOUS SUBSTANCES. 



electrode. But whether the electrodes are liquid or solid, if the 

 external electromotive force V V" applied to an electrolytic com- 

 bination is varied, when it is too weak to produce a lasting current, 

 and the electrodes are thereby brought into a new state of polarization 

 in which they make equilibrium with the altered value of the electro- 

 motive force, without change in the nature of the electrodes or of the 

 electrolytic fluid, then by (508) or (675) 



and by (687), 



Hence 



d( V - V") = ^dcr' - ^-,d<r". (689) 



J- a *- a 



If we suppose that the state of polarization of only one of the elec- 

 trodes is affected (as will be the case when its surface is very small 

 compared with that of the other), we have 



d</ = ^(F'-F"). (690) 



**a 



The superficial tension of one of the electrodes is then a function of 

 the electromotive force. 



This principle has been applied by M. Lippmann to the construction 

 of the electrometer which bears his name.* In applying equations 

 (689) and (690) to dilute sulphuric acid between electrodes of 

 mercury, as in a Lippmann's electrometer, we may suppose that the 

 suffix refers to hydrogen. It will be most convenient to suppose the 

 dividing surface to be so placed as to make the surface-density of 

 mercury zero. (See page 234.) The matter which exists in excess 

 or deficiency at the surface may then be expressed by the surface- 

 densities of sulphuric acid, of water, and of hydrogen. The value 

 of the last may be determined from equation (690). According to 

 M. Lippmann's determinations, it is negative when the surface is in 

 its natural state (i.e., the state to which it tends when no external 

 electromotive force is applied), since cr' increases with V" V. When 

 V" V is equal to nine-tenths of the electromotive force of a Daniell's 

 cell, the electrode to which V" relates remaining in its natural state, 

 the tension &' of the surface of the other electrode has a maximum 

 value, and there is no excess or deficiency of hydrogen at that surface. 

 This is the condition toward which a surface tends when it is extended 

 while no flux of electricity takes place. The flux of electricity per 

 unit of new surface formed, which will maintain a surface in a 



*See his memoir: "Relations entre les phenomenes electriques et capillaires," 

 Annales de Chimie et de Physique, 5* se"rie, t. v, p. 494. 



