528 REroKT — 1884. 



a 



28. Let us try -whether we cannot do better with a single metal 

 ■exposed to air, not troubling about the contact of two metals, which is 

 unnecessary, but simply considering one metal in contact with air. 



Take a gramme-equivalent of any metal, say G5 grammes of zinc, and 

 imagine it rolled out into a thin sheet of foil, of area A. The difference of 



V . 

 potential between it and the air being "V in electrostatic units, tt^q m volts, 



its charge will be — , where re is the distance between it and the air, 



•a quantity of molecular magnitude. The electrical energy of this charge 



is , which must therefore have been the electrical work done (i.e., the 



2irx 

 amount of potential chemical energy transmuted into electrostatic energy) 

 in spreading out the zinc 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 contact with air, 

 i.e., let its thickness be also of molecular magnitude, x. 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. Electrostatically its energy is 



— • (-Y- ' 



2 it x y.mj 



Equating these two values, and writing for the quantity of metal m= A xp, 

 we have the general relation 



mV=-S28-pa- 2 JxlO 10 ; 



whence, taking m = Go, p = 7, and V = 1-8, we get, as our estimate of 

 linear molecular dimensions, 



8 = 4 X 10- 9 . 



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 true 



that another metal would give a rather different estimate, unless > 



were constant for all. For ordinary metals, e.g. zinc, iron, copper, 

 mercury, silver, this is not so outrageously far from being the case ; 

 but discrepancies 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 in 'Thomson 

 and Tart,' Part II., Appendix F. In a lecture on the size of atoms 

 delivered at the Royal Institution in February 1883, he re-states these 

 estimates with slight modifications thus : — 



If atomic dimensions are comparable with 10~ 8 centimetre, brass 

 would rise 02° 0. at the instant of formation ; while if atoms are so 

 small as 2:5 X 10" 9 , it would rise 1000° C. Hence 10-s is to be regarded 

 as a limit of smallness. 



A soap-film so thin as 10~ s centimetre would raise itself 280° by 

 collapsing; therefore there are not several molecules in this thickness. 



