IN LOWERING THE FREEZING POINT OF WATER. 577 
above 0°, by an infinitely small quantity, instantly becomes absolutely 0°; and 
afterwards, as the motion of the piston continues, the air absorbs heat from the 
mass of water in the second cylinder, part of the mass passing at the same time 
into the state of ice. Hence the whole mass expands; and therefore, on account 
of the resistance offered by the hand to the motion of the piston of the cylinder 
containing the mass, the internal pressure is increased, and a quantity of work, 
not infinitely small, is given out by the piston, and is received by the hand. To- 
wards the end of this process, let the resistance offered by the hand gradually de- 
crease till, just at the end (that is, when the piston of the air-cylinder has resumed 
its first position) it becomes nothing, and the pressure within the water-cylinder 
thus becomes again equal to that of the atmosphere. The temperature of the 
mass of partly frozen water must now be 0°, and the air in the other cylinder 
being in communication with this, must have the same temperature. The air is 
therefore, infinitely nearly at its original temperature, and it has its original 
volume. Hence it is now left in a state infinitely nearly the same as that in which 
it was at first. Farther, let the ice, which has been formed by the freezing of 
the water, be placed in contact with the lake till it melts, which it will really do 
since the lake is warmer than 0°, though only by an infinitely small quantity. 
Thus the mass of water is left in its original state, and it has been already shewn 
that the air is left infinitely nearly in its original state. Hence no work, except 
an infinitely small quantity, can have been absorbed or developed by any change 
on the air and water, which have been used. But a quantity of work not infi- 
nitely small has been given out by the piston of the water-cylinder to the hand ; 
and therefore an equal quantity* of work must have been given from the hand 
to the air-piston, as there is no other way in which the work developed could 
have been introduced into the apparatus. Now, the only way in which this can 
have taken place is by the air having been colder, while it was expanding in the 
second process, than it was while it was undergoing compression during the first. 
Hence it was colder than 0° during the course of the second process; or, in other 
words, while the water was freezing, under a pressure greater than that of the 
atmosphere, its temperature was lower than 0. 
The fact of the lowering of the freezing point being thus demonstrated, it be- 
comes desirable, in the next place, to find what is the freezing point of water for 
any given pressure. ‘The most obvious way to determine this would be by direct 
experiment with freezing water. I have not, however, made any attempt to do so 
in this way. The variation to be appreciated is extremely small, so small, in fact, 
as to afford sufficient reason for its existence never having been observed by any 
experimenter. Even to detect its existence, much more to arrive at its exact 
amount by direct experiment, would require very delicate apparatus which would 
* In saying ‘an equal quantity’’ I, of course, neglect infinitely small quantities in comparison 
to quantities not infinitely small. 
