414 
CHEMISTRY: T. W. RICHARDS 
Leaving out of consideration tiie behavior of the liquids, which doubt- 
less is not fairly comparable with that of solids, we may compare these 
various quantities in parallel curves, each being plotted in relation to 
the increasing atomic weight. The accompanying diagram presents in 
the lowest line compressibiHties ; in the next above, atomic volumes; in 
the curve no. II, coefficients of expansion, and in the highest curve, the 
reciprocals of the absolute melting points. 
That essential relations exist between these data cannot be doubted. 
In each case a maximum is seen to occur with the alkali metals; and al- 
though the rest of the curves are less similar, nevertheless, distinct 
connection is traceable. The compressibility curve is most Uke the 
atomic volume curve, and the coefficient of expansion curve most like 
that of the reciprocals of the melting points. 
The attempt to find a mathematical relationship between these quan- 
tities is an interesting one. Such a relationship has already been sought 
by Griineisen, Einstein, Debye, and others, upon the basis of a specu- 
lative theory, without much experimental support. With the wealth 
of data herewith presented, however, an empirical attempt is possible. 
It is soon evident on studying the figures that in cases where the melting 
points and atomic volumes are nearly similar, as, for example, in the 
cases of gold and silver, the denser substance is the less compressible. 
On the other hand, with similar density and melting point, as in the 
case of sodium or potassium, the substance with the greater atomic vol- 
ume is the more compressible. Yet again, where the atomic volumes and 
densities are not very different, as in the case of sodium and calcium, 
the substance with the higher melting point has the lower compressibil- 
ity. Taking account of these general tendencies, one sees that the 
equation should take this general form: 
Compressibihty = K /j.!^^] -. 
J 2 {IJ)J3{1 m) 
in which K repr€sents a constant, V the atomic volume, D the density, 
the absolute melting point, fi, {2, fz, various as yet undetermined 
functions. 
The search for the nature of these respective functions is tedious and 
has not been carried very far; but the substitution in this equation of 
K = 0.00021, /i (F) = F,/2 (D) = D' '' and /a {TJ = {T^ - 50) gave 
results of about the right order with nearly all of the substances. For 
example, Hthium is thus calculated to be 8 instead of 9, sodium, 15.6 
(exactly its observed value), copper 0.66 instead of 0.75, silver 1.02 
instead of 1.01, tungsten 0.29 instead of 0.27, etc. Some of the cal- 
