494 Mr. 0. G. Darwin on the Collisions of 



4cos 3 0(r — lot), since theory tells us that the range is the 

 same as for an a-particle of the same velocity. It then 

 travels through the gas a distance AB = ly and then through 

 a metal foil. Let the stopping power of this foil be t cms., 

 measured in hydrogen. It traverses the foil obliquely at 

 angle yfr, and so, when through, it will have residual range 

 4 cos 3 [r — Iw) — ly — t seo/r, and only if this quantity is 

 positive will the H-particle make a scintillation. 



The quantities y and ty are determinate in terms of x 

 and 0, so that the inequality 



A cos* (r - Ix) >ly + t sec ^ . . . (3'1) 



fixes a limiting value of for every value of x. Under 

 conditions where I is a considerable fraction of r, the equation 

 may not give a solution at all for values of x near unity. 

 This means that the a-particles, when they have got to x = l, 

 have lost so much velocity that even their most favourable 

 encounters are incapable of producing a scintillating particle. 

 We shall not need to consider this case here, but shall find 

 that the case where I is only a small fraction of r is the 

 important one. In the experiments it ranged between 10' 

 and 20 per cent., and the former belongs to the most 

 important experiments. Neglecting l/r, we have 



cos 3 #>-^sec^ (3-2) 



Substituting the value of i|r, 



cos 3 > £7<x/(l -A' 8 sin 2 0), 

 or in a form convenient for computing 



x< cosec0A ■{}-{£) se c 6 o\ • • • (3-3) 

 The terminal values are 



for<r=0 cos# =a/j-, 



for* = l cos^y^l. 



Thus 1 <0 O , and so fewer particles near x = l give scin- 

 tillations than near x = 0. This is not because of the reduction 

 of velocity of the a-particles, but because those thrown off 

 at a given angle strike the stopping foil more obliquely. 



