604 Dr. N. Bohr on the Decrease of 



In addition, the transverse scattering of the rays due to 

 deflexions suffered in collisions with the electrons as well as 

 with the positive nuclei must be taken into account. This 

 scattering; will cause the mean value of: the actual distances 

 travelled by the particles in the matter to be greater than 

 the thickness of the sheet. If, however, we for a moment 

 neg.'ect all collisions in which the particles suffer either 

 abnormally big losses in their energy or big deflexions, we 

 may, as in section 2, expect that the rest of the rays will 

 behave in a similar way to a beam of a rays and that they 

 will show a range of a similar degree of sharpness. There- 

 fore the distribution of the energy of a beam of initially 

 homogeneous ft rays emerging from a thick layer of matter 

 must, as for a thia sheet, be expected to exhibit a well- 

 defined peak sharply limited on the side of the greater 

 velocities, bat falling more slowly off towards the smaller 

 velocities. The further the rays pass through the matter the 

 greater the chance that the particles will suffer a violent 

 collision, and the smaller will be the number of particles 

 present at the peak of the distribution. A simple calculation 

 shows that by far the greater part of this effect is due to the 

 deflexions suffered in collisions with the positive nuclei. 

 An estimate of the effect of these collisions may be obtained 

 in the following way. 



The orbit of a high speed ft particle colliding with a 

 positive nucleus has been discussed by 0. G. Darwin'*. From 

 his calculations it follows that the angle of deflexion (j> of a 

 ft particle of velocity Y = ftc is given by 



6 



cot' 



(^ (^^^(i-jsv)- 



where ne 2 (l — ft 2 )* 



^~ pft i c*m~' 



ne is the charge on the nucleus and p is the length of the 

 perpendicular from the nucleus to the path of the ft particle 

 before the collision. Let pr be the value of the p corre- 

 sponding to yjrz=r. The probability that a ft particle will 

 pass through a sheet of matter of thickness ISx without 

 suffering a collision for which ^t>t is equal to 1 — g>A#, 

 where 



2 KJ 7mV(l-/3 2 )N 

 1 T T 2 ftWin 2 



Since (D&x is small, this probability can be written e- w ^ 

 * Phil. Mag. xxv. p. 201 (1913). 



