580 EFFECT OF PRESSURE IN LOWERING FREEZING POINT OF WATER. 



adopt a very large value for/m, the change of pressure during Process 2, still 

 the changes of volume (//« aadhn 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 efg h is extremely nearly 

 equal to that of the rectangle efmii, but/e is equal to F E, which is -087 feet. 

 Hence the work developed during an entire stroke is -087 x p foot-pounds. Now 

 this is developed by the descent from to-t of the quantity of heat neces- 

 sary to melt a cubic foot of ice ; that is, by 4925 thermic units, the unit Ijeing 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 imits descending from to-t is 4925 x 

 4-97 x t 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, 



/ = 00000355 p (1.) 



This, then, is the desired formula for giving the freezing point -r' 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 



(1.) t = -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 t, the lowering of the 

 freezing point in degrees centigrade, by the following formula — 



t = -0075 n (2.) 



* The atmosphere is here taken as being the pressure of a column of mercurv of 760 milli- 

 metres ; that is 29-92, or very nearly 30 English inches. 



