SEPTEMBER 3, 1897. ] 
would here again be given by corresponding 
increments of about .1° per atmosphere. 
For solid metals the isometries are of a 
different order. 
Another line of research for liquids to 
which I attach supreme importance has 
only just been begun: I refer to the system- 
atic study of the entropy of liquids. 
Among the first results on the heat pro- 
duced in suddenly compressing a liquid are 
those of Tait. They are of too limited a 
range, however, and not in good accord 
with the more recent and extended data of 
Galopin. Generally speaking, the change 
of temperature produced per atmosphere of 
compression increases with temperature in 
a marked degree, as one may infer from 
Kelvin’s equation. For organic bodies this 
inerement at ordinary temperatures is of 
the order of +;° = .020° per atmosphere. 
In case of liquid metals the order of values 
is decidedly different, being about =, this 
value, recalling correspondingly divergent 
results observed for the isometrics of vol- 
ume. Quite recently (1896), the same 
subject has been taken up by Tammann (to 
whom we also owe results for the correla- 
tive compressibility) particularly for solu- 
tions and with reference to the theory of 
solutions. Tammann’s data are of the 
order .001° per atmosphere at 0°, and in 
better keeping with the thermo-dynamics 
of the subject than the earlier experiments. 
Much more, however, must be done before 
anything like a degree of critical accuracy 
is approached or a broad survey taken. 
Pressure intervals are to be chosen wider 
and the temperature measurement given 
with greater certainty. 
Finally, I wish to touch upon the rela- 
tions of melting point and pressure in their 
more recent development. Obviously, the 
classical work of Andrews on the continu- 
ous passage of a liquid into the gaseous 
state will find some counterpart in the 
manner in which the analogous passage 
SCIENCE. 
303 
from the solid into the liquid state takes 
place. The character of these phenomena 
may be shown from direct observations of 
melting point and pressure, as was done by 
the earlier observers. Full knowledge, 
however, can be obtained only by mapping 
out the isothermals throughout the region 
of fusion very similarly to the method pur- 
sued by Andrews himself for vaporization. 
This has thus far been attempted for a 
single body only, naphthalene, within 130° 
and 2,000 atmospheres. Six isotherms (63°, 
83°, 90°, 100°, 117°, 130°) were traced 
within these intervals, along each of which, 
excepting the first, the body passed from 
the liquid to the solid state under the in- 
fluence of pressure only. An exhibit of 
these data shows strikingly that in all cases 
the change of physical state takes place in 
accordance with a cyclic law, 7. ¢., a larger 
pressure is necessary to change the body 
from the liquid to the solid state, at a given 
temperature, than the pressure at which 
the body at the same temperature again 
spontaneously melts. Freezing almost al- 
ways seems to take place at once; the cor- 
responding fusion is apt to be prolonged, 
and in its gradual occurrence traces the 
contours of James Thomson’s well-known, 
doubly-inflected isothermals much more 
fully than does the allied case of vaporiza- 
tion. 
The appearance of the cyclic parts of 
these isothermals is suggestive, and may be 
described in terms of their dimensions in 
the direction of volume and of pressure re- 
spectively. The former dimensions indi- 
cate the probable fate of the volume incre- 
ment. They show that, as pressure and 
temperature increase, the volume increment 
tends more and more fully to vanish, and 
they thus imply a lower critical tempera- 
ture at which the solid would change into 
the liquid continuously as far as volume is 
concerned. It does not follow that other 
properties of the body would here also vary 
