14 Dr. N. Bohr : Theory of Decrease of Velocity of 



of the orbits gives * 



1 

 sm 2 S = 



+ e 2 & 2 \M + m) 



where 23 is the angle through which the direction of the 

 relative motion is deflected by the collision. For the sake 

 of brevity we shall in the folio win g use the notation 



gE(M + m) 

 V 2 mM * 



The velocity of the electron after the collision will make 



an angle equal to =- — $ with the path of the particle before 



the collision, and its value will be given by 



tf = V^-— 2 sind. 



The energy transferred to the electron by the collision is 

 consequently equal to 



~ 2wiM 2 V 3 . 9ev 



Qo= (^M)* Sm * 0) 



Further, we easily find that the displacement of the electron 

 in a direction perpendicular to the path of the particle, at 

 the moment in which the electrons and the particle are 



nearest each other, is equal to — r^cosS. We see that $ 



will be very small, and the velocity of the electron after the 

 collision very nearly perpendicular to the path of the particle 

 if p is great in comparison with X ; in this case the displace- 

 ment of the electron during the collision will further be very 

 small in comparison with p. 



Now proceeding to consider the effect of the forces on the 

 electrons from the side of the atoms, we shall for the present 

 assume that the frequency of the electrons is so small that 

 the time of vibration is very long in comparison with the 

 time of collision, for collisions in which p is of the same 

 order of magnitude as X; this will, in fact, be satisfied for 

 the lightest elements, as we shall see later. In this case 

 we shall consequently only have to consider the influence 



* Compare J. J. Thomson, ' Conduction of Electricity through Gases,' 

 p. 376, and Phil. Mag. xxiii. p. 449 (1912) ; C. G. Darwin, loc. cit. p. 903. 



