580 EFFECT OF PRESSURE IN LOWERING FREEZING POINT OF WATER. 
adopt a very large value form, the change of pressure during Process 2, still 
the changes of volume gm and hn in Process 2 and Process 4 would be ex- 
tremely small compared to the expansion during the freezing of the water; and 
from this it follows evidently that the area of the figure ¢fg h is extremely nearly 
equal to that of the rectangle efmn, but fe is equal to F E, which is -087 feet. 
Hence the work developed during an entire stroke is ‘087 < p foot-pounds. Now 
this is developed by the descent from 0° to—¢ of the quantity of heat neces- 
sary to melt a cubic foot of ice; that is, by 4925 thermic units, the unit being the 
quantity of heat required to raise a pound of water from 0° to 1° centigrade. 
Next we can obtain another expression for the same quantity of work; for, by 
the tables deduced in the preceding paper from the experiments of REGNAULT, 
we find that the quantity of work developed by one of the same thermic 
units descending through one degree about the freezing point, is 4-97 foot-pounds. 
Hence, the work due to 4925 thermic units descending from 0° to—¢ is 4925 x 
4:97 x ¢ foot-pounds. Putting this equal to the expression which was formerly 
obtained for the work due to the same quantity of heat falling through the same 
number of degrees, we obtain 
4925 x 4:97 x t = 087 x p. 
Hence, 
¢=00000855 p.0 ob aoe et 
This, then, is the desired formula for giving the freezing point —¢ centigrade, which 
corresponds to a pressure exceeding that of the atmosphere by a quantity p, 
estimated in pounds on a square foot. 
To put this result in another form, let us suppose water to be subjected to one 
additional atmosphere, and let it be required to find the freezing point. Here 
p = one atmosphere = 2120 pounds on a square foot; and, therefore, by 
(r) = 00000355 x 2120. 
or ¢ = ‘0075. 
That is, the freezing point of water, under the pressure of one additional atmo- 
sphere, is—-0075 centigrade; and, hence, if the pressure above one atmosphere 
be now denoted in atmospheres,* as units by n, we obtain ¢, the lowering of the 
freezing point in degrees centigrade, by the following formula— 
t= -0075 n. cong yee 2) 
* The atmosphere is here taken as being the pressure of a column of mercury of 760 milli- 
metres ; that is 29-92, or very nearly 30 English inches. 

