924 . Dr. J. Chadwick and Mr. E. S. Bieler on the 



the counting of the weak scintillations produced by these 

 H particles much easier and more certain. The micro- 

 scope used consisted of a Watson holoscopic objective of 

 16 mm. focal length and '45 numerical aperture combined 

 with a low-power eyepiece. Compared with the old system, 

 this increased greatly the brightness of the scintillations 

 and gave at the same time a larger field of view, i. e. a larger 

 number of particles, other conditions remaining constant. 

 This system was found to be the most suitable for these 

 experiments ; further increase of the numerical aperture 

 with corresponding increase in brightness of the scintil- 

 lations could only be obtained with a 'smaller field of view. 

 Careful tests showed that with the above system, H particles 

 with a range of more than 2 cm. could be counted with 

 certainty under good conditions of experiment. The counts 

 of both observers were found to be consistent over an interval 

 of some months. 



In this way, the more direct method of experiment 

 described in this paper was rendered possible. These 

 experiments were carried out in the hope that a detailed 

 study of these collision phenomena would give definite 

 information as to the size and shape of the & particle or 

 helium nucleus, and as to the field of force around it. 



§ 2. The Collision Relation. 



Experiments of the kind described here can only give 

 a statistical account of the numbers of hydrogen nuclei 

 projected in various directions and with various velocities 

 by a pencil of a particles of known velocity. If there is no 

 loss of energy in the collision, all the hydrogen nuclei 

 projected in any one direction have the same velocity. The 

 experiments then lead to a relation between three variables 

 which has been called by Darwin * the Collision Relation. 



Let E, M, and V be the charge, mass, and initial velocity 

 of the a particle. Let <?, m be the charge and mass of the 

 hydrogen nucleus, initially at rest, and let u be the velocity 

 after collision, in a direction making an angle 6 with the 

 initial line of motion of the a. particle. 



If the law of conservation of energy holds, it follows 

 that ,, 



u = 2 1 rf*- V cos = f V COS 0, 

 M 4- m ° 



since M = 4m. 



* C. G. Darwin, Phil. Mag. vol. xli. p. 486 (1921 ). 



