388 Scientific Proceedings, Royal Dublin Society. 
diagram, but may be a contraction as in the familiar case of ice. 
The amount of this volume change varies greatly according to 
the substance under examination. In the extreme case the corners 
B and C may be so much rounded off that there is no longer any 
vertical line (fig. 3). We can include both these cases if we 
define the melting point of a simple substance as “ that tempera- 
ture at which its coefficient of expansion isa maximum.” ‘This 
definition only breaks down in the extreme case when the curve 
flattens out to one continuous line. But this is only the usual 
difficulty of applying a general law to the limiting case; and 
it is doubtful if such a limiting case occurs in nature (¢.e. among 
actual substances), and if it did occur, it would be legitimate to say 
that such a substance had no melting point. As examples of the 
behaviour of a number of different substances I may refer to the 
beautiful curves of Kopp.1 Barus says they are too seldom quoted. 
Similar descriptions will apply to the above curves (figs. 1 to 
4), if we let the ordinates represent quantities of heat. The 
do 
for that particular temperature, and the vertical height of the 
steeper portion measures the “latent heat” of fusion. From this 
point of view we might define the melting point as “ that tempera- 
ture at which specific heat is a maximum.” So far as I know, 
these two definitions are consistent, 7.e. they would both lead to 
the same melting temperature for the same substance. This 
seems to me to be the only satisfactory way of drawing a sharp 
line of distinction between solid and liquid; and I can see no 
objection to drawing such a sharp distinction in theory, at least, 
even though our imperfect means of working may render it im- 
possible to do so in practice for some time to come. 
Now it is extremely probable, and in the absence of any data 
to the contrary it seems fair to assume, that many other physical 
properties also change suddenly, and in a similar manner, at the 
same temperature. If we say that a substance does not melt 
suddenly at any one temperature, we mean that its coefficient of 
expansion and specific heat increase gradually as it approaches 
its melting temperature, and finally attain a maximum at that 
slope of the curve at any point now shows the specific heat (SF 
1H. Kopp, ‘‘ Ueber die Volumanderung einiger Substanzen beim Erwarmen und 
Schmelzen,’’ Liebig’s Ann. d. Chem. u. Pharm., vol. xciii. (1855), pp. 129-232. 
