EQUATION AND THE NATURE OK COHESION. 69 



a brief consideration, since it is diametrically opposed to common 

 assumptions. It will be noticed that in hydrogen and nitrogen b r , 

 by my figures for a and by the foregoing rule, makes a larger 

 fraction of V c than in such substances as octane. In one case wc 

 have VJ\.8Q and in the other V c j2.02. Now all are agreed, I 

 think, that this fraction will approach V ( .jS more closely the more 

 incompressible and unchangeable the molecule is. And it will deviate 

 from this in the- opposite direction the more compressible the mole- 

 cule. If the molecules were incompressible and constant in volume 

 then it should be, if a is constant, that b t , = V^JS. 



Now it has been generally assumed that the simpler molecules, 

 such as nitrogen and hydrogen, will be less compressible and more 

 constant in volume than the more complex molecules such as octane. 

 For example van Laar, while assuming that in most substances 

 b c is about V c j2. 1 as in benzene, believes that in hydrogen b c = VJ2.0. 

 I believe the view is erroneous that hydrogen and oxygen have 

 less compressible molecules than octane. I believe that just the 

 reverse of this is true and that these simple gases will deviate more, 

 rather than less than octane from the condition which should apply 

 to rigid molecules. It must be remembered that in these gases the 

 cohesion is very low, so that the pressure on the molecules is 

 greatly less than on a molecule of octane. For example at the critical 

 temperature of hydrogen the external pressure being, say, 13 atmos- 

 pheres, the total internal and external pressure will be 7.5 times 

 this, or 97.5 atmospheres. In octane the external pressure is 25 

 atmospheres and the total internal and external is 187.5 atmospheres. 

 Moreover the pressure within the molecule due to the atomic cohe- 

 sion must be very much greater in octane than in hydrogen. It is 

 with molecules just as it is with licjuids, the greater the internal 

 pressures the less compressible are they. The atoms must hence be 

 closer together in octane than in hydrogen and the molecule of 

 hydrogen will be actually more compressible, not less compressible 

 than octane. Consequently octane will behave more like a gas with 

 incompressible molecules than will hydrogen. Possibly the monatoinic 

 gases will be exceptional to the rule that the lower the cohesion 

 the more compressible the molecules. One. would anticipate that 

 they would bc exceptional unless the atoms are more compressible 

 than we think. 



The following calculation shows, I think, that the molecule of 

 hydrogen is in reality far more compressible than that of octane, 

 and not less compressible. 



This is shown by a comparison of the volume occupied by hy- 



