[ 229 ] 



XVI. On the Shape of the Atom. By R. D. Kleeman, 

 D.Sc, B.A., MacJcinnon Student of the Royal Society ; 

 Emmanuel College, Cambridge *. 



AT the absolute zero of temperature the molecules of a 

 substance would probably be in contact with one 

 another. From a knowledge of the density of different 

 substances at the absolute zero we could therefore determine 

 the real relative volumes of different atoms and molecules. 

 The density of a substance at the absolute zero cannot be 

 found directly, but it can be calculated with probably fair 

 accuracy. Such a calculation has been carried out by 

 Guldbergt for a number of substances. And Traubef has 

 shown, using these determinations, that the volume of an 

 atom is proportional to the square root of its atomic weight, 

 and the volume of a molecule therefore proportional to the 

 sum of the square roots of the atomic weights of the atoms 

 composing the molecule. A knowledge of the connexion 

 between the volume of an atom and its atomic weight does 

 not by itself furnish any information as to its shape, but this 

 relation in conjunction with the cross-section of the atom, 

 which can be obtained from the kinetic theory of gases, gives 

 us some information on this point, as will be shown in this 

 paper. 



The shape of the atom which suggests itself as the most 

 probable, and which is the one usually assumed, is that of 

 the sphere. Assuming then that the atom is spherical in 

 shape, we have that its volume is proportional to r' 6 and its 

 cross-section proportional to r 2 , where r is the radius of the 

 atom. Since its volume is also proportional to ??i 1/2 , where 

 m is its atomic weight, its cross-section is proportional to m 1/3 . 



In Tables I., II., and III. values of Q, the sum of the 

 diametrical sections of the spheres of action of the molecules 

 contained in unit volume of a gas at atmospheric pressure, 

 are given for a number of vapours. The values contained in 

 Tables I. and II. were taken from Meyer's c Kinetic Theory 

 of Gases,' pages 303, 307, and 308, and those in Table III. 

 were obtained from Landolt and Bornstein's Tables, 5th 

 edition. They correspond to a temperature of 0° C. The 

 sum of the sections Q is obtained from the equation 



where 5 is the mean radius of the sphere of action of a 



* Communicated by the Author. 



t Zeit. fur Phi/s. Chcmie, xxxii. p. 122 (1900). 



X Phys. Zeit. p.,667, Qct. 1909. . . : . 



