4 8o SCIENCE PROGRESS 



to be the specific volume or volume of one gram of the sub- 

 stance. It is impossible to follow van der Waals' train of 

 reasoning in arriving at this conclusion. Its general reason- 

 ableness may be shown, however, in the following way. We 

 are already familiar in the phenomenon of gravitation with 

 the fact that any two pieces of matter attract one another, 

 and that this attraction is the greater, the greater the masses 

 of material and the closer they are together. In the case of 

 molecular cohesion we are apparently dealing with a phenome- 

 non of a different kind, one of far greater intensity when the 

 particles are close together, but dying off much more rapidly 

 than gravitational attraction does, as we draw the two mole- 

 cules apart. It is unlikely that molecular cohesion and 

 ordinary gravitation have anything in common, except that 

 they both represent forces of attraction. In the phenomenon 

 of cohesion it seems reasonable to assume that the cohesion 

 will be the greater the more closely packed are the molecules. 

 That is, the cohesion it across any unit plane is some function 

 of the density of the substance, for the more closely packed 

 are the molecules the greater is the density, tt, therefore, 

 increases with the density, but what is the proper function 

 to employ ? In expressing forces of attraction, gravitational 

 or electrostatic or magnetic, we find in general that the expres- 

 sions have something in common as regards their form. What is 

 common to them is the occurrence of a product of two quantities, 

 masses or charges, or pole strengths. In the present case, since 

 density or close packing seems to be the significant thing, we are 

 led by a very rough analogy to think of cohesion as depending 

 upon the product of the densities of the substance on the two 

 sides of the unit plane. Since the substance is the same in 

 every respect on both sides of the plane, we conclude that the 

 cohesion is proportional to the square of the density. But the 

 density is simply I/V, where V is the specific volume, so that ir 

 is proportional to I/V 2 . Denoting the proportionality factor 

 by a, we can write 7r = a/V 2 . It must be clearly borne in mind 

 that the above reasoning is by no means rigid. The density 

 term enters into the expression not in virtue of the mass of 

 each molecule — for that would be equivalent to identifying 

 cohesion with gravitation as regards nature, though not neces- 

 sarily as regards degree — but in virtue of the fact that the 

 greater the compression, the greater the number of molecules 



