of the oc Particles from Radium C and Thorium C. 547 



Returning to the results of the present investigation, an 

 inspection of figs. 3, D, and 6 (PL XVII.) will show that there 

 is no sign of a "hump" on the ionization curves of the three 

 types of particles considered, although an effect of the magni- 

 tude of that found for polonium by Lawson and Rothensteiner 

 should make itself manifest, being well outside the margin 

 of experimental error. 



Indeed, it is difficult to see how such a "hump" could 

 come about, if account be taken of the slope of the curve 

 before probability effects begin to become appreciable. In 

 the next section we shall proceed to calculate the effect on 

 the ionization curve of these probability variations. 



§ 6. Theoretical Interpretation of the End of the 

 Ionization Curve. 



It has been pointed out in § 4 that, near the end of the 

 range of the a. particles of radium C, the equation of the 

 ionization curve is 



I -353 (6-592- a?) . 



How much this part of the curve is due to the variation 

 of ionization along the path of the a. particle and how much 

 to a possible variation in the individual ranges of the 

 a particles due to some unknown cause, is immaterial 

 for the present purpose ; it is sufficient to say that this 

 equation approximately represents the facts over that portion 

 of the range lying roughly between 64 and 655 cm. 



Let us assume that, were it not for probability variations 

 due to electronic encounters as considered by Flamm and 

 Bohr *. this straight line would represent the ionization 

 curve up to the extreme end of the range, i. e., until the 

 ionization current bad fallen to zero. We assume a parallel 

 bundle of rays comprising a definite large number of <x 

 particles per second and neglect the thickness of the ioniza- 

 tion chamber. 



Let N be the number of a particles which get beyond x. 

 Then the average ionization at x due to one a particle is 



3-53 (6-592 -.r)/N. 



If, owing to its meeting with an unusual distribution of 

 electrons, one of these particles has its range increased by £. 

 it seems reasonable to suppose that the ionization at x due 

 to this a. particle will be 



3-53 (6-592 + f-. r )/N. 



* Loc. cit. 



