304 
continuously. For naphthalene this point 
would lie in a region of several thousand 
atmospheres and several hundred degrees 
Centigrade—therefore, in a region too re- 
mote to admit of actual approach. 
Again, the breadth of the cycles, meas- 
ured along the pressure axis, decreases 
from the center of the field both in the 
direction of increasing and decreasing pres- 
sures. The tenor of these results is an ad- 
ditional indication of the recurrence of a 
lower critical temperature at which cycles 
must necessarily vanish. The decrease of 
the bréadth of the cycles in the direction of 
decreasing pressure suggest the possible oc- 
currence of a point in the region of nega- 
tive external pressure, so circumstanced 
that beyond it the substance would solidify 
at a lower pressure than that at which it 
fuses. This may be interpreted as follows: 
The normal type of fusion changes contin- 
uously into the ice-type of fusion through 
a transitional type characterized by the ab- 
sence of volume lag. 
An independent discussion more search- 
ing in character has quite recently been 
given by Tammann. Tammann points out 
that for the normal case of fusion and for 
increasing pressure the two determinative 
factors of the Clapeyron equation—the vol- 
umes and latent heat of fusion—will not in 
general simultaneously become and remain 
zero. He argues that the volume constant 
will at the outset decrease with pressure 
passing through zero to negative values. 
Hence the curve representing the relation 
of melting point to pressure must initially 
rise to a maximum when the melting point 
pressure ratio is zero, and then decrease. 
Contemporaneously, the latent heat of fu- 
sion, decreasing continually with pressure, 
eventually also reaches zero, but at a much 
later stage than the volume constant. At 
this stage, therefore, since the melting point 
and the volume constant now have definite 
values (the latter negative), the melting 
SCIENCE. 
[N.S. Vou. VI. No. 140. 
point and pressure ratio is negatively infi- 
nite. Hence the curve expressing the re- 
lation of melting point to pressure decreases 
with increasing pressure from the maxi- 
mum specified, as far as the pressure at 
which latent heat is zero, and there drops 
vertically downward. Thus Tammann’s 
melting point pressure curve, with its ini- 
tial and final ordinate in the direction of 
temperature, maps out a field of pressure 
and temperature within which the body is 
solid. Outside of this region the body is 
liquid and cannot by pressure alone be con- 
ceivably converted into the solid state. 
Any thermo-dynamic change involving a 
march through the boundary of this region 
is accompanied by the discontinuity of fu- 
sion, of viscosity, etc. A march through 
the final ordinate (for which latent heat is 
zero) is probably not accompanied by such 
discontinuity. For a given temperature 
there may be two fusion pressures. At a 
temperature sufficiently below the melting 
point the continued increase of pressure 
should, therefore, move the normally fusing 
body from the solid into the liquid state 
continuously. This is a somewhat anoma- 
lous result of close reasoning, but it must 
not be forgotten that in the depth of our 
ignorance of the actual occurrences above 
several thousand atmospheres the term 
anomaly isa misnomer. Indeed, if we re- 
gard the melting pressure curve beyond the 
stated maximum as characterizing the ice 
type of fusion (which Tammann does not 
do) our difficulties would in a measure be 
reconciled. 
Tammann finally points out that the 
term lower critical temperature is not justi- 
fied by the character of the phenomenon. 
Data for melting point and pressure due to 
Damien seem directly to corroborate the 
occurrence of zero values in the ratio of 
melting point and pressure increments, but 
Damien’s tests are restricted to a pressure 
interval much too small to be trustworthy. 
