a-Particles ivitli Hydrogen Nuclei. 



509 



they always lie in the plane in which the orbit is described. 

 It is next necessary to see whether this is at ail a reasonable 

 assumption. To do so we take a model nucleus and compare 

 its equipotential surfaces with those of the bipole. The 

 recent evidence indicates that the nucleus of helium is made 

 up of two electrons and four protons, to adopt the name 

 suggested by Rutherford for the unit positive nucleus, which 

 in its isolated state is hydrogen. It was therefore natural 

 to choose a model composed out of these parts, and for 

 simplicity of calculation they were supposed arranged with 

 the protons one at each corner of a square and the two 

 electrons together at the centre. It was not intended that 

 this should really represent the structure of the nucleus, (and 

 indeed there is very great difficulty in any model of this 

 type in connexion with the theory of the relation of mass to 

 energy,) ; it was merely adopted as giving a convenient form 



Fig. 10 a. 



Fijr. 10 6. 



1 2 3 4 1 2 



Equipotentials of Bipole (a) and Square Nucleus (6). 



The potentials are measured with eja as unit, where a, the unit of length 

 in the figures, is the half distance between the poles of the bipole, 

 or the radius of the square. The dotted lines are the equipotentials 

 in a plane inclined at 45° to the others. 



for examining the differences between the equipotentials o£ 

 a real model and those of the bipole. Fig. 10 a shows the 

 equipotentials of the latter. In fig. 10 b the firm lines are 

 the equipotentials in a plane through the centre of the 

 square containing two of the protons, and the dotted lines 

 show those in a plane at 45° to the others ; in the outer 

 parts the two are indistinguishable-. Now the inner parts of 

 the figures are very different and some calculations o( the 



