134 Mr. L. Simons on the Beta-Ray Emission from 



of the speed of the particles from Whiddington's law,. 

 \i A =z constant *. 

 But the operation 



£lofrtf (W(*)) 



ax 



performed on the exponential curves would also yield — X„ 

 meaning that only if the original curves were exponential, 

 plotting the slope of the logarithms of residues such as BC, 

 fig. 5 (PL III.), would result in the same constant, repre- 

 sented in figs. 8 and 9 (PL III.) by a horizontal straight 

 line. 



In this work involving unknown functions, in which the 

 operations have to be performed geometrically, the latter 

 process involving one differentiation is possible, although 

 the physical interpretation of the resulting curves is not so 

 clear as if the former process had been adopted. Figs. 8 

 and 9 (PL III.) show the results of operating by the latter 

 method on the carves of figs. 5 and 6 (PL III.). As these 

 curves are roughly logarithmic, it was thought that this 

 shorter method would show up just as accurately as the 

 method involving two differentiations where the function 

 represented by the one part of the curve changed, if at all,, 

 into that represented by the remainder of the same curve- 

 Pigs. 8 and 9 show, of course, that none of the curves of 

 figs, o and 6 are exponential. Portions of the curves seem 

 to be represented by the same function, definite changes 

 taking place at the points marked. 



It is not claimed that the resulting lines are true in their 

 smaller detail. A large portion of the end has been omitted 

 in consequence of the impossibility of performing the 

 graphical operation, whilst there can be little accuracy at 

 the beginning because of the difficulty of measuring the 

 small ionization currents. It is claimed that the largest 

 features of the curves are fairly correct. It is presumed 

 that the positions of the minima on these curves give the 

 range of*the sub-group of electrons f. 



* Proc. Roy. Soc. A. vol. ixxxvi. p. 375 (1912). 



f A little consideration will show that if there were two homogeneous 

 groups of electrons emitted from a given screen and superposed, each 

 following an exponential law of absorption, the curve in this case, 

 drawn in the manner of figs. 8 aud 9 (PL III.), would fall gradually to 

 a minimum, marking the range of the slower group, after which it 

 would run on horizontally. If, on the other hand, the logarithmic 

 absorption coefficient, as it appears in these experiments, increases with 

 distance from the screen, the resulting curve, drawn in the same manner ? 

 would still show a minimum or a decided change in direction approxi- 

 mately at the range of the slower group. 



