394 PROCEEDINGS OF THE AMERICAN ACADEMY. 



cal computation with graphical construction already used in finding 

 the compressibility. A straight line was passed through the point at 

 9640 and 9°. 92, and the departure of the observed pressure values 

 from those calculated by the linear relation plotted on a large scale. 

 A smooth curve was then drawn through the midst of these points, and 

 the final values calculated by applying to the smooth values the 

 small correction determined from the smooth curve. 



The points of 1911, except for the two bad ones mentioned above, 

 lie on a smooth curve within the possible errors in reading the gauge. 

 The departure from linearity, although slight, is pronounced in the 

 direction of concavity toward the pressure axis, that is, less rapid rise 

 of freezing temperature at the higher pressures. 



There seems no reason why the points of 1909 are not just as valu- 

 able in indicating the manner of departure from linearity as those of 

 1911, since all the pressure readings are affected alike by the incom- 

 plete calibration of the gauge. The error in the gauge readings of 

 1909 is simply due to inaccurate knowledge of the cross-section. The 

 following correction was applied, therefore, to the gauge constant of 

 1909. The best straight line through the points of 1911 was deter- 

 mined (graphically from the smooth correction curve) and also that 

 through the points of 1909. The former gives a change of pressure of 

 197.1 kgm./cm.*^ per degree rise of temperature ; the latter 199.2. The 

 observed pressures of 1909 were all reduced in the ratio of 197.1 to 

 199.2. A smooth curve was then passed through these corrected 

 values by the method described above. Finally, to determine the 

 most probable departure of the freezing curve from linearity, the mean 

 of the two correction curves, those for the data of 1909 and 1911, was 

 taken. These curves differ nowhere by more than the possible errors 

 in reading the pressure gauge. From this curve it is possible to find 

 immediately the tangent to the melting curve at the origin. 



Finally, all these results may be collected into the following form. 

 At any given temperature the melting pressure is to be found by add- 

 ing to the pressure given by the formula p = 196.5 (t + 38.85) the 

 small correction term given graphically in Figure 16. The initial rise of 

 pressure per degree rise of thefreezing point is therefore 196.5 kgm./cm.^ ; 

 at 12,000 kgm. this has become only 1/2 per cent greater, so slight is 

 the departure irom linearity. The value of the initial slope, 196.5, 

 has no more certainty than the single series of observations of 1911, 

 but the departure from linearity shown in Figure 16 has the greater 

 weight which should be given to the mean of two independent series 

 of observations with different apparatus. 



A number of data collected incidentally in the course of the work 



