CHEMISTRY: T. W, RICHARDS 
415 
culated values, to be sure, deviated much more widely than this, but 
none is of entirely a different order from the truth. It is possible to 
show a necessary relationship between this empirical equation and 
the outcome of recent work by Griineisen, and there is also some rela- 
tionship between this equation and the well-known formula of Dupre, 
but the full discussion of these relationships would occupy more space 
than is available in the present publication. It may be noted, how- 
ever, that the equation of Dupre is less satisfactory than the empirical 
equation just given as regards the elements, for density plays too large 
a role in the older expression. Moreover, the equation of Griineisen 
is designed only for presumably monatomic elements, and it gives a 
negative (and therefore absurd) result for bismuth, showing that its 
range is more limited than that of the equation just mentioned. 
No pretense is made, of course, that the empirical equation herewith 
communicated is a final statement of the relation of the quantities 
concerned. Nevertheless, because it gives the approximate order of 
magnitude of the compressibilities of widely different substances, one 
has a right to believe that the basis of the equation really refers to some 
of the more important tendencies which are at work. 
Attention may be called to the fact that these relationships are in 
accord with those which would be expected from the prediction of the 
theory of compressible atoms. An atom much distended because of 
its internal makeup might be supposed to be highly compressible, and 
so might one much distended because not greatly pressed upon by 
outside cohesive pressure. Both of these tendencies would cause small 
density, and, accordingly, large atomic volume, and the second of these 
tendencies would add low melting point. Therefore, the general form 
of the equation is plausible. 
A more complete discussion of the data and equation will soon be 
given in the Journal of the American Chemical Society. 
Summary. — This paper records all the recent work on the compressi- 
bihty of the elements performed at Harvard, reduced to the best avail- 
• able standard — the newly determined compressibility of mercury. 
It is pointed out that the reciprocals of the melting points are very 
closely associated with the coefficients of expansion, and that both of 
these properties seem to be essentially connected with atomic volume 
and compressibility. A preliminary empirical equation is proposed, 
which shows roughly the nature of this relationship. 
