igo/f\ Mills — Molecular Attraction. 91 



approached and d approaches D in value, the diminishing 

 difference of their respective cube roots would enormously 

 increase the proportional errors of the observations. This is, 

 however, not the case. Substituting- for L its value from 

 equation 4 and for E, its value from equation 1, we have, 



0.0 4 31833 (V - v) (|^- T - P) 

 [11] flT-i/iy — = constant. 



Next putting ^=l/z;andD = l / V, and simplifying, we get, 



[12] 0.0 4 31833 (VvYs + V% v% + V%*0 (|^- T — p) = con. 



On inspection of the factor, VvVs -+- V%z>% + V%z;, we see: 



1. That errors of observation occurring in the density of 

 the liquid have at low temperatures little effect on the con- 

 stant, but as the critical temperature is approached and v 

 approaches V in value, a percentage error in the density of 

 the liquid will cause about 2 /i of the same percentage error in 

 the constant. 



2. That errors of observation occurring in the density of 

 the vapor cause at low temperatures about the same percent- 

 age errors in the constant, but as V approaches v the percent- 

 age error caused in the constant is decreased to about 2 /i of 

 the error of the observation. 



To determine the error caused by an error in the vapor 

 pressure, we transform equation 12 into the form 



[13] |£-T-P= C ° nstant 



8T 0.0 4 31833 (Vz/% + V%v%+ YVzv) 



The right-hand side of the equation is very small at low tem- 

 peratures, but increases with rise of temperature until as the 

 critical temperature is approached the function of the vol- 

 umes approaches 3V%. 



The relative magnitude of the terms on the left-hand side 

 of the equation must be considered. Taking water at 0° C as 



