578 JAMES THOMSON, ESQ., ON THE EFFECT OF PRESSURE 
not be easily planned out or procured. Another, and a better, mode of proceeding 
has, however, occurred to me: and by it we can deduce, from the known expansion 
of water in freezing, together with data founded on the experiments of REGNAULT 
on steam at the freezing point, a formula which gives the freezing point in terms 
of the pressure ; and which may be applied for any pressure, from nothing up to 
many atmospheres. The following is the investigation of this formula :— 
Let us suppose that we have a cylinder of the same imaginary construction 
as that of the one described at the commencement of this paper ; and let us use it 
as an ice-engine analogous to the imaginary steam-engine conceived by Carnot, 
and employed in his investigations. For this purpose, let the entire space en- 
closed within the cylinder by the piston be filled at first with as much ice as 
would, if melted, form rather more than a cubic foot of water, and let the ice 
be subject merely to one atmosphere of pressure, no force being applied to the 
piston. Now, let the following four processes, forming one complete stroke of the 
ice-engine be performed. 
Process 1. Place the bottom of the cylinder in contact with an indefinite lake 
of water at 0°, and push down the piston. The effect of the motion of the piston 
is to convert ice at 0° into water at 0°, and to abstract from the lake at 0° the 
heat which becomes latent during this change. Continue the compression till one 
cubic foot of water is melted from ice. 
Process 2. Remove the cylinder from the lake, and place it with its bottom on 
a stand which is a perfect non-conductor of heat. Push the piston a very little 
farther down, till the pressure inside is increased by any desired quantity which 
may be denoted, in pounds on the square foot, by p. During this motion 
of the piston, since the cylinder contains ice and water, the temperature of the 
mixture must vary with the pressure, being at any instant the freezing point 
which corresponds to the pressure at that instant. Let the temperature at the 
end of this process be denoted by —t¢° C. 
Process 3. Place the bottom of the cylinder in contact with a second inde- 
finitely large lake at —¢°, and move the piston upwards. During this motion the 
pressure must remain constant at p above that of the atmosphere, the water in 
the cylinder increasing its volume by freezing, since, if it did not freeze, its pres- 
sure would diminish, and therefore its temperature would increase, which is im- 
possible, since the whole mass of water and ice is constrained by the lake to remain 
at—z°. Continue the motion till all the heat has been given out to the second 
lake at —¢°, which was taken in during Process 2, from the first lake at 0°.* 
* This step, as well as the corresponding one in Carnort’s investigation, it must be observed, in- 
volves difficult questions, which cannot as yet be satisfactorily answered, regarding the possibility of the 
absolute formation or destruction of heat as an equivalent for the destruction or formation of other 
agencies, such as mechanical work ; but, in taking it, I go on the almost universally adopted suppo- 
sition of the perfect conservation of heat. 

