340 Mr. L. St. C. Broughall on the Frequency 



is led to this arrangement by a consideration of the -valency 

 of the elements, and also his hypothesis shows that the pro- 

 perties of neon should be similar to those of helium and 

 argon. 



There is also considerable evidence that the atom or 

 molecule of neon is spherical, and the diameter of the atom 

 has been calculated b'y two methods. It has been found by 

 means of the viscosity of the gas, and secondly, W. L. Bragg 

 has given a value for " d " the diameter of the atom of neon 

 after consideration of the diameters of the atoms of elements 

 which have atomic numbers near that of neon. 



Representing the diameter found by viscosity measure- 

 ment by " a " we obtain the following values for neon : 

 o- = 2"35 x 10~ 8 , d=l-30 x 10" 8 cm. Now the value for " d " 

 is very much less than the value for " a' 9 and it is supposed 

 that when two molecules collide they do not come into 

 contact. W. L. Bragg considers 'that his value for the 

 atomic diameter is the distance between the outside electrons. 

 In consequence of this we shall use the value d=l'30 

 x 10 ~ 8 cm. for the real diameter of the neon atom. 



In order to obtain a spherical atom by the rotation of 

 eight electrons at the corners of a cube there are several 

 possible axes of rotation, but the simplest case is to assume 

 that the atom rotates about three perpendicular axes XX', 

 YY', ZZ'. YY' is determined by the mid points of .the 

 surfaces of any opposite pair of sides of the cube. In a 

 similar manner XX' and ,ZZ / are determined by taking- 

 different pairs of sides. Using these axes of rotation the 

 atom will have a radius equal to one half the diagonal of 

 the cube, and this will be represented by " c." Further, for 

 simplicity the lengths of the edges and of the surface 

 diagonals will be represented by "21" and c [2s" respec- 

 tively, since the representation of u I ,J and " s" as functions 

 of " c ,} tends to make the work obscure. 



We see that these axes of rotation give all the electrons in 

 the outer shell or octet similar velocities, and it is for this- 

 reason of symmetry that these axes have been adopted in 

 preference to all others. 



The question now arises as to what will be the positions 

 of the other two electrons. We desire if possible to make the 

 forces acting on the other electrons the same for all of them, 

 and the only possible positions for the electrons e 9 and e 10 is 

 to place them on one of the axes XX', YY', or ZZ'. It 

 is quite immaterial which axis we take, but the electrons are 

 assumed to be upon the axis XX' throughout this paper, and 

 are at a distance "r" cms. from the nucleus, which latter is 



