94 



SCIENCE 



[N. S. Vol. XXXVI. No. 916 



Having thus found M^K, the volume " h " 

 of the molecules in the liquid and vapor of 

 pentane at 180° vcas computed. In the vapor 

 it was 140.3 e.c, and in the liquid 124.24 e.c. 

 for gram molecular quantities. The volume 

 of the molecules in the vapor is, therefore, 

 certainly larger than in the liquid. 



4. r/ie Nature of Cohesive Mass. Belation 

 "between Cohesion and Gravitation and the 

 Number of Valences. A Method of Determin- 

 ing the Valence of Compounds. — The very 

 interesting relationship has been discovered 

 that the value M-K, the factor proportional to 

 the square of the cohesive mass of a molecule, 

 is equal to the constant 2.97 X 10"^^ multi- 

 plied into the two thirds power of the prod- 

 uct of the molecular weight and the number 

 of valences in the molecule. This relation- 

 ship holds in such a variety of substances that 

 it seems universally true. It gives a valuable 

 means of computing valences, vchen the critical 

 data are known. Van der Waals's constant 

 " a " can then be computed very exactly for 

 non-associating substances when the valence 

 is known by the formula : a = 2.97 X 

 10-" (Wt. Val.)V3iV2. The value is given in 

 absolute units. N is the number of molecules 

 in the volume taken. 



The short table illustrates the constancy of 

 c, the quotient, when the factor M'^K, com- 

 puted in the manner just mentioned from the 

 surface tension, is divided by the two thirds 

 power of the product of the molecular weight 

 and the number of valences per molecule. 



It will be seen from this table that the sub- 

 stances of which the valence is not doubtful, 

 and of which the critical data have been so 

 carefully determined by Young, give a con- 

 stant value of c. Associating substances, like 

 methyl alcohol, give a quotient higher than 

 the average. A higher mean molecular weight 

 and valence number must obviously be taken 

 for these substances. The high figure for 

 argon may indicate that at the temperature at 

 which its density was determined, there was a 

 slight association, a few two-atom molecules 

 being present. If this is the case, 39.9 would 

 be probably a mean molecular weight. If the 

 theoretical value of 2.97 be supposed to be 

 correct instead of 3.10, it would be necessary 

 for the mean valence number to be 1.06; and 

 from this the atomic weight of 37.5 instead of 

 39.9 would be computed. The critical data of 

 krypton do not fall in line with the formula; 

 and xenon, if the critical data are right, must 

 be taken as bivalent. In all the argon group, 

 the valence must be taken at least as unity. 

 These substances can not be considered as 

 having zero valence, as that would make the 

 value of c infinite, unless the cohesive mass 

 was zero also. But that this is not zero is 

 shown by the fact that the gases can be lique- 

 fied. The critical temperature of helium was 

 taken as 7° Abs. instead of 5° as given by 

 Onnes, and 8° as suggested by Dewar. 

 Hydrogen gives a constant close to 2.94, if 

 Sarrau's critical data are taken, but not when 

 those of Olszewski are used. Oxygen is taken 

 with a valence of 2 instead of 4. Even with 

 this assumption it is only by using the recent 

 determinations of density made by Mathias 

 and Onnes that a value near to 2.97 can be ob- 

 tained. These matters will be discussed in the 

 complete paper. It is possible that the coeffi- 

 cients for the computation of M'^K should be 

 different in these simple gases. 



