600 Mr. G. F. Becker on the Gudermannian 



The first group lias a fair photographic action, the second a 

 strong action. Taking into consideration the intensity of 

 their photographic action and the variation of ionization 

 with velocity, these two groups should contain a relatively 

 large number of /3 rays. Consequently, a magnetic field was 

 used which would direct all /3 rays of velocity less than 



2'8 x 10 10 — -' on to the plate P, and a balance obtained 



see. i ' 



Then the usual field was excited, and a balance again ob- 

 tamed. Some slight but rather uncertain evidence of the 

 excitation of 7 rays was obtained, but the decay of the 

 emanation during the course of the observations made 

 measurement of such small effects very difficult. Even had 

 a constant source of /3 rays bean available, the difference in 

 amount of excited 7 radiation was too small to measure with 

 certainty. 



If it be supposed that the 7 rays from radioactive matter 

 are produced by the /3 i'ays, these experiments bring out 

 clearly the high efficiency of the transformation of /3 rays 

 into 7 rays during the disintegration of the atom of 

 radium C compared with the efficiency of the conversion of 

 /9 rays into 7 rays when the former fall on matter of high 

 atomic weight As Gray has shown, lhe exact converse 

 holds for the product radium E. 



Similar experiments have been made, using emanalion 

 contained in a glass tube sufficiently thin to let out the 

 a rays, and it has been found that a measurable amount of 

 7 rays is apparently produced by the impact of a rays. The 

 discussion of these experiments is reserved for a later paper. 



I desire to express my best thanks to Prof. Rutherford 

 for suggesting this research, and for his help and interest 

 throughout the course of the experiments. 



LV. The Gudermannian Complement and Imaginary 

 Geometry. By Georue F. Becker*. 



IN applications of the gudermannian to physical problems, 

 it is in many cases convenient to employ the complement 

 of this angle rather than the angle itself. This slight modi- 

 fixation also helps to bring out interesting analogies. 

 Let the gudermannian complement be denoted by 



G(«) = 7r/2~gch ( ; 



then the familiar relations between the gudermannian and 



* Communicated bv the Author. 



