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XLIII. On the Shape of the Molecule. By 11. D. Kleeman, 

 D.Sc, B.A., MacJdnnan Student of the Royal Society *. 



I^HE shape or a molecule is usually assumed to be spherical 

 and its diameter calculated on this supposition. One 

 of the formula? used is L = ^Nwa-^, where L denotes the 

 mean free path of the molecule, a 1 the radius of its sphere of 

 action, and N the number of molecules per c. c. at standard 

 temperature and pressure. The value for en is usually taken 

 as the diameter of the molecule. L is usually obtained from 

 experiments on diffusion or viscosity, and N from a knowledge 

 of e, the electric charge on an ion. 



But the assumption that the molecule is spherical in shape 

 is not admissible. Thus Meyer in his ' Kinetic Theory of 

 Gases'' shows that the cross-section of an atom, which is 

 proportional to o^ 2 , is an additive quantity relating to the 

 atoms composing the molecule. Meyer shows that this is 

 only possible if the atoms of the molecule lie approximately 

 on a plane. It is difficult to see how under the circumstances 

 the molecule can be spherical in shape. Especially since 

 using the values of the cross-section of molecules given by 

 o^ 2 , and the fact that the volume of an atom according to 

 Traube t is proportional to the square root of the atomic 

 weight, it has been shown by the writer J that the atom 

 must be approximately spherical in shape. 



The object of this paper is to give a method by means of 

 which direct information as to the shape of the molecule 

 may be obtained. 



At the absolute zero of temperature the molecules have no 

 motion of translation, and the apparent space occupied by a 

 molecule or atom is its true volume. Now the densities of 

 liquids at corresponding states are the same fraction of their 

 density at the critical state to within a few per cent. The 

 densities may therefore also be said to be the same multiple 

 of their densities at the absolute zero. The relative molecular 

 volumes of the molecules of* liquids at corresponding states 

 are therefore the same as the relative volumes at the absolute 

 zero. 



Further it is probable that the relative values of oy or a l 

 given by the above equations can only be legitimately com- 

 pared at corresponding temperatures. The value of <t x does 

 not represent merely the real cross-section of the molecule, 

 but the cross-section modified (usually increased) by the 

 field of force surrounding the molecule. 



* Communicated bv the Author. 



t Phys. Zeit. p. ml, Oct. 1909. 



t " On the Shape of the Atom," Phil. Mag. July 1910, p. 229. 



