LAW OF MOLECULAR FORCE, 41 



limits of present experimental possibility in the variation of L 

 and a. Let E be the translatory kinetic energy, then 

 TT A p log. L/a = E 



dp, L d (m E) 

 77 A m^ log. - = - 77- 

 at a at 



But A m -r^ has been shown to be the same for most liquids, so 

 dt 

 that d{m'E)jdt, or the temperature rate of variation of the 

 translatory kinetic energy of nearly all molecules, is the same 

 when measured at low constant pressure. This is an important 

 result in molecular dynamics ; its similarity to the law of Dulong 

 and Petit as to the constancy of the molecular heats of the 

 elements is obvious and suggestive, while its bearing on the 

 piiysical meaning of temperature is worth noting. 



To obtain the relative values of A for a large number of liquids, 



1 have used the fine abundance of experimental measurements of 



surface tensions made by Robert Schiff (Annalen der Chemie 223, 



Wiedemann Beiblatter 9), whose remarkable discovery of a 



definite law connecting chemical constitution and the number of 



molecules raised in a standard capillary tube, opened up the 



possibility of finding tlae relation of the parameter A to chemical 



constitution. 



■5 J^ . 

 By means of the formula a =- kAp^ m^ it is possible to find ^A 



as Schiff" has determined a c& p at the boiling point for a large 

 number of organic liquids. Arranging the value of kA in 

 descending order and studying them, one soon sees law among 

 them ; for example the values are '707 for Cg H14 -706 for Cg H,,, 

 and 'lOo for Cg Hg and these suggest that the number of hydrogen 

 atoms in a molecule exercises little eftect on the value of 

 kA, this holds throughout the whole of Schifi''s determi- 

 nations. Other things remaining the same, an increase in the 

 number of carbon atoms reduces the value of kA, and a study 

 of the whole series of values for ^'A shews that the introduction 

 of a single-bound atom of O exercises the same influence as that of 



2 atoms of C, and a double-bound O atom is equivalent to 3 atoms 

 of C ; we can state these facts briefly by saying that the parameter 

 equivalent of C being I, that of H is 0, of O' is 2, and of O" is 3. 

 If, then, the parameter-equivalents of the molecules are evaluated 

 according to these values for the elements, we can find a mean 

 value of k A, corresponding to each value of the molecular 

 parameter-equivalent n. The following little table contains in 



the first row the value of n, in the second the mean value of A A 



2 

 corresponding, and in the third the products k A n'-^ : — 



n 5 6 7 8 9 10 12 13 14 15 16 



1000^ A 794 700 620 567 525 468 485 414 387 379 365 

 2 

 100 ^ A n^ 232 231 227 227 227 217 228 229 225 231 232 



