492 Dr. J. E. Mills on the 



I am deeply indebted to Dr. Young for the assistance 

 which he has most kindly given me during the progress of 

 my work. The casual reader will hardly appreciate the 

 immense labour involved in locating and removing the errors 

 mentioned in this paper. But I hope that he will understand 

 that their discovery and removal was not the result of 

 accident and could not have been accomplished had the 

 relation which served as my guide been a mere approxi- 

 mation — itself the result of an accident. 



Is the equation exactly true ? It agrees with the facts at 

 present known as accurately as the corresponding measure- 

 ments have been made, and it is fortunate that they have 

 been made with wonderful accuracy. But in my opinion, 

 the equation has a theoretical significance and could only 

 be exactly true with absolutely stable and absolutely non- 

 associated substances. We have liquids nearly fulfilling 

 these conditions from 0° C. to their critical temperature, but 

 the esters and some of the other substances measured will 

 probably not be found exactly to fulfil this condition through- 

 out so wide a range of temperature. 



Considering the constant of Kleeman's equation, 

 L-E 



d 2 -W- 



■ constant, 



more closely, it will be noted that for isopentane, certainly 

 one of the most carefully measured of the substances, the 

 constant increases from 194-8 at 10° to 206-6 at 150° (the 

 high value at 0° is due to the use of the calculated vapour 

 density), or an increase of 6 per cent. There is a similar 

 increase with the other substances. 



Now if a diagram of the L — E e and density lines for 

 isopentane be made, it will be seen that the L — E e line is 

 approximately straight to 120° C. as is also the line for the 

 density of the liquid. Now at 120° d 2 for isopentane is 0'2491 

 and D 2 is 0-0010. Therefore up to and below 120° D 2 is 

 practically negligible compared with d 2 . Throughout this 

 temperature interval Kleeman's equation practically reduces 

 to 



— =— * = constant. 

 d 2 



Now while there are small individual errors in L — E 6 the 

 trend of the line is certainly most accurately established. 

 The errors in d, and consequently in d 2 , are very small. 

 Hence the steady increase shown by the constant of 



