Velocity of Swiftly Moving Electrified Particles. 603 



the weight, and since the differences in the characteristic 

 frequencies will have a very much smaller influence for fust 

 /3 rays than for a rays, results of this kind should be expected 

 on the theory. 



If we assume that the formula (18) holds also for the loss 

 of energy suffered by /3 rays in penetrating a layer of matter 

 of greater thickness, we obtain for the " range " of the 

 ft particles 



\ Jo ***** ' 



where 2 denotes the last factor in (18) and (27). Con- 

 sidering 2 as constant, and using the above formula for AT, 

 we get 



R= WN2j (1-/^1 =2^Xv[(l-/3j*+ U-/5) -2] 



.... (28) 



Recently R. AY. Varder* has made some interesting ex- 

 periments on the absorption of homogeneous /3 rays. He 

 measured the variation in the ionization produced by the 

 rays in a shallow ionization chamber when sheets of different 

 thicknesses were introduced in the beam before striking the 

 chamber. Using aluminium sheets, he found that the ioniza- 

 tion varied very nearly linearly with the thickness of the 

 sheets, and his diagrams give a strong indication of the 

 existence of a " range " of the /3 particles. Varder compared 

 the ranges observed with the last factor S in the formula (28), 

 and found that the ratio between the ranges and S, though 

 nearly independent of the initial velocity of the rays, de- 

 creased slowly with this velocity. This should be expected 

 from the above calculations, as 2 will increase slowly with 

 the velocitv. Measuring R in gr. per cm. 2 Varder found 

 R/S = 0-35 - for £ = 0-8 and R/S = O30 for £ = 0'95. The 

 first factor in the theoretical formula is equal to 0*42 for 

 /3 = 0'S and 038 for /3 = 0*95. AYe see that the agreement 

 may be considered as very satisfactory. 



The distribution of the losses of energy, suffered by the 

 individual particles of a beam of initially homogeneous /3 rays 

 in penetrating through a sheet of matter of considerable 

 thickness, cannot be represented by the formula (12) used 

 in the former section, since — see section 2 — already the dis- 

 tribution of the loss of energy suffered in penetrating through 

 a thin sheet differs essentially from that given by formula (8). 



* Phil. Mag. xxix. p. 72-") (1915). 



