364 Electromotive Forces in the Voltaie Cell. 
Take a gramme-equivalent of any metal, say 65 grammes of 
zinc, and imagine it rolled out into a thin sheet of foil of 
area A. The difference of potential between it and the air 
being V in electrostatic units, ;,~ in volts, its charge will be 
oN 300 
— where w is the distance between it and the air, a quan- 
Ww 9 
tity of molecular magnitude. ‘The electrical energy of this 
s 
which must therefore have been the electrical 
Makeat: AV 
charge 1s 5; 
work done (2. e. the amount of potential chemical energy trans- 
muted into electrostatic energy) in spreading out the zine 
over so much surface. [Capillary tension is part of the 
mechanical work done. | 
Now let it be rolled so thin that every atom of it is in con- 
tact with air, 2. e. let its thickness be also of molecular mag- 
nitude « We can regard its potential energy in two ways: 
either as chemical or as electrical. Chemically its energy, 
measured by heat of combination, is 
46,000 VJ, 
where V is expressed in volts. Hlectrostatically its energy is 
PME ORE 
Equating these two values, and writing for the quantity of 
metal m= Auwp, we have the general relation 
mu Vi = O20 come ax os 
whence, taking m=65, p=7, and V=1°8, we get, as our esti- 
mate of linear molecular dimensions, 
oi xO 
The data in this calculation are all very definite; hence if 
the reasoning is legitimate, this estimate ought to be a pretty 
good one. It is trae that another metal would give a rather 
different estimate, unless ne were constant for all; but for 
ordinary metals—e. g. zinc, iron, copper, mercury, silver—this 
is not so outrageously far from being the case; though discre- 
pancies arise with such metals as sodium on the one hand, 
and platinum on the other. But it is very doubtful whether 
platinum could be regarded as an oxide, however thin it were 
beaten ; and sodium would probably take fire long before the 
proper molecular thinness was reached. 
‘The several estimates of Sir William Thomson for the size of 
atoms were given in ‘ Nature,’ March 1870, and are reproduced 
