CHEMISTRY: MACINNES AND ABLER 
161 
the increase of solubility produced by the fine grinding of solids. An elec- 
trode in equilibrium with small bubbles will thus reach a higher potential 
than one in contact with undispersed gas. 
With the foregoing in mind we can proceed to an explanation of the voltage 
fluctuations. At a (fig. 1) a bubble has separated from the electrode, leav- 
ing a nucleus behind. As the electrolysis proceeds this nucleus will grow, 
obtaining hydrogen from the supersaturated solution or from the electrode. 
However, as the nucleus increases in size, the energy necessary to produce 
further increases in volume must decrease, as the ratio 
increase in surface 
increase in volume 
is continuously decreasing. If the bubble is growing slowly the hydrogen 
bearing solution surrounding the electrode will tend to get into equilibrium 
with the bubble. This accounts for the decrease in overvoltage from a to b. 
At h the buoyant effect of the electrolyte is sufficient to overcome the attrac- 
tion of the electrode for the bubble, which breaks away, leaving a nucleus 
behind. Bubbles are, however, seldom observed to come off at points corre- 
sponding to h] they probably remain in the pores of the electrode, and are 
pushed out by the growth of the following bubble. From b to a' the con- 
centration of dissolved hydrogen is increasing to a value such that the nucleus 
can again grow, when the processes described above are repeated. 
It is evident that it makes no difference, in so far as the absorption of energy 
is concerned, whether small bubbles are evolved, or a solution of hydrogen in 
equilibrium with the bubbles is formed. In the following paragraph it is 
assumed that all the hydrogen is liberated as bubbles. 
The number of bubbles of radius r that can be formed from a mol of hydro- 
gen of volume V is SV/^irr^. To obtain the surface energy of such a system 
this must be multiplied by ^ttt^ and the surface tension 7. Substituting 
RT/p for V (R, T and p are the gas constant, the absolute temperature and 
the pressure respectively) and equating the surface energy with the electrical 
