Value of "a" of van der Waals' Equation 183 



It might also be imagined that the mass of cohesion was 

 a function of the number of atoms in the molecule, rather 

 than the number of valences, but a trial of this possibility 

 showed that this was not the case. 



After many trials in which the mass of cohesion, or the 

 factor M 2 K, was supposed to be a function of the first power, 

 the square, the square root, or the square of the cube root of 

 the product of the number of valences and the molecular 

 weight, it was found that only the last supposition yielded a 

 consistent result. In all the other guesses, the proportion- 

 ality factor " C " was far from being constant. Hence we have : 

 M 2 K -* C(Wt X Val.)*'*. 



With the values of M 2 K computed by the surface tension 

 formula it was found that the quotient M 2 K/(Wt. X Val.) 2/3 

 was indeed as constant as could be expected and C had a mean 

 value of 2 .98 X io~ 37 , when M 2 K is the square of the mass of 

 cohesion of one molecule multiplied by K and expressed in 

 absolute units. If "a" of van der Waals' equation is taken 

 for i cc. of gas under standard conditions and expressed in 

 atmospheres, the proportionality factor C would be 2 . 2564 X 

 io~ 4 . This gives values for "a" a little higher than those 

 generally accepted owing to my having used the coefficient 

 2.19 instead of 2.12 in computing M 2 K from the surface 

 tension. The computation of "a" for ether by the formula 

 2.2564 X io~ 4 (Weight X Valences) 2/3 gives the value 

 0.03669, whereas the value from the usual formula of van der 

 Waals is 0.03473; the coefficient 2.12 would have given the 

 value 0.03550. The fact that these values are throughout 

 proportionally somewhat higher than those usually assumed 

 does not affect the constancy of C. 



Table III shows that the quotient M 2 K/(Wt. Val.)*' 1 really 

 equals a constant when M 2 K is computed for the compounds 

 of carbon, hydrogen and oxygen of which the critical data 

 have been so carefully determined by Young. For the ele- 

 ments of these compounds there is no doubt of the valence 

 number. Carbon is always quadrivalent, hydrogen uni- 

 valent; and oxygen has been taken as bivalent. 



