

u-Partides with Hydrogen Nuclei, 489 



conservation of energy becomes inapplicable ; but the absence 

 of rotational change is made very probable by an argument 

 based on the quantum theory, similar to one that occurs in 

 the study of the specific heats of a gas. Let I be the 

 moment of inertia of one of the particles, and suppose that v 

 is a permissible frequency for rotation about the axis of I. 

 Then the energy of rotation is -^I(27rv) 2 , and by quantum 

 principles this must be equal to nliv, where n is zero or an 

 integer. Solving, we have 



v=~ . • • • • • (2-2) 



and so the possible energies are of the form 



w 2 /> 2 



A w 



We conjecture the a-particle to be not larger than a sphere 

 of radius about 2 x 10~ 13 cm., while its mass is known to 

 be 6-5xl0" 2i gr. This makes 1 = 1-04 x 10~ i9 gm.cm. 2 

 -and v = nx 3*2 x 10 2i sec. -1 , while the energy comes to be 

 7i 2 x2-lxl0" 5 erg. The energy of translation of an 

 ^-particle is l'3xl0~ 5 erg, and if n = l these quantities 

 are nearly equal. Thus if the collision set up a rotation in a, 

 there would be little energy left to produce the H-particle, 

 and it would not be detected. On the other hand, if 

 rotational energy were converted into translational, it would 

 force itself on our attention as an apparent breach of the 

 conservation of energy. As this has not been observed, and 

 ,as the first; case could not be observed, it appears correct to 

 neglect the possibility of changes of rotational motion. It 

 may be remarked that the validity of our assumption might 

 he tested by experiments which observed both velocity and 

 direction of the H-particles simultaneously. If particles of 

 different velocities were found going in the same direction, 

 the experiments would have to be described by a more 

 complicated collision relation, involving four instead of three 

 variables. 



The other quantity, which occurs in the experiments, is 

 the number of H-particles produced for the given angle of 

 projection 6. Now we can never control the particular 

 types of collision that will occur. So this number is a direct 

 measure of the probability of a collision that will produce 

 an angle 6, and this probability can be translated into the 

 area of a certain reoion in the following way. First consider 

 a set of collisions in which both particles have given orienta- 

 tions, and for which a has given initial velocity and 



