Moving Electrified Particles passing through Matter 17 



+ » 



where n , N \ C o,o§xz 7 



— 00 



is represented for all values of x by the convergent series 



, W1 1__3_V?Y 1 /3 _5\/?Y 



/W ~ 1.1.2 1.2 V2/ 1.2.1.2.3 Vl.2 + 2.3/ \2/ " 



1 /_3^ _5_ 2n — l\ (xX 2n 



~" (/i-l)rau.2 + 2.3 (^>JV2J '" 



+(^+»i^l-i)(g)V i: i 3 (;y+ 13! j g;g gy... 



+ (n-i)!niw -/ 



where 7 is Euler's constant, 7 = 0'5772. 



When <r is large, /(#) is represented by the asymptotic 

 series 



1.3.5...(2n-3).1.3...(2n-l) \ 

 1 lj 71 ! (8*)» / 



For the force acting on the electrons in the direction parallel 

 to the path of the particles we have now (see figure, p. 15) 



„ ^AB eftVt ,„, 



F2 = ' E At3 = (W+7)F =m -^ ) - 



For the energy transferred to the electron during the col- 

 lision we get in the same manner as above (ty{t) an uneven 

 function of t) 



+ 00 



Q 2 = 2 I 1 sin nz - ty(z) dz \ » 



— 30 



and introducing for yjr(z) 



21? 2 



q- 2 ^ 2 ^ 2 /!^\ 

 P/«7. ifiw. S. 6. Vol. 25. No. 145. Jan. 1913. C 



