448 PROCEEDINGS OF THE AMERICAN ACADEMY. 



water for this temperature. The piston displacement was plotted as a 

 function of the pressure for this temperature. The temperature of the 

 thermostat was then raised by a suitable amount, and the piston displace- 

 ment found as a function of the pressure for this new temperature. 

 This was done for four different temperatures, including zero. From 

 these four curves, with the help of an interpolation for temperature, the 

 piston displacement may be found for any temperature and pressure in 

 the region of the liquid water below zero. This displacement was 

 found at 5° intervals for several different pressures, increasing in steps 

 of 800 kgm. At each pressure, therefore, the thermal dilatation may 

 be found by taking the difference between the displacement at the 

 desired temperature and zero. 



If the experiment were performed in the simple manner described, 

 evidently several very serious errors would be introduced. No account 

 whatever has been taken of the thermal dilatation of the steel cylinder, 

 which is not very large, or of the gasolene transmitting the pressure, 

 which is comparatively more important. These two disturbing effects 

 were corrected for by two auxiliary experiments. In the first, the lower 

 cylinder was almost entirely filled with a cylinder of bessemer steel, 

 and the displacement found for any temperature and pressure of the 

 region in question, exactly as for water. In the second auxiliary ex- 

 periment, the lower cylinder was entirely filled with gasolene, and the 

 displacement found as before. In applying the correction, the entire 

 interior of the apparatus may be thought of as consisting of two parts ; 

 one portion is that which would be occupied by the bessemer cylinder, 

 and the second portion is all the rest, including the remainder of the 

 lower cylinder and the upper cylinder. It is to be noticed that this 

 " first part of the volume " is purely fictive : it need not be actually 

 occupied by the bessemer. In the auxiliary experiment in which the 

 lower cylinder is filled with gasolene, this " first part of the volume " 

 is filled with gasolene ; in the actual experiment with water, the " first 

 part of the volume " is filled partly with the steel of the shell, partly 

 with water, and partly with enough gasolene to make up the difference. 

 The advantage in thus thinking of the volume as split up into two 

 parts is that the second part remains the same in the three experi- 

 ments. The displacement of the piston at constant pressure due to 

 change of temperature of the thermostat will evidently include, for " the 

 second part," the thermal dilatation of the cylinder, and what is impor- 

 tant, will be independent of the position of the piston in the upper 

 cylinder, since only the lower cylinder is involved in the change of 

 temperature. By taking the difference of the apparent dilatations at 

 constant pressure for the three experiments we shall obtain, therefore, 



