Velocity of Swiftly Moving Electrified Particles. 561 



shown by noting that if the homogeneous equation admitted 

 a solution the boundary relation (23) would read 



— an v an v 7 



Multiplying by TJ(s) and integrating over £ we have 



J v — «/i v ' v aw? 



In this equation the integration may be extended over 

 <*) also, seeing that on the couductor side of those surfaces 

 the normal derivative is zero. But the potential U and its 

 derivative are continuous in the regions bounded by 2 and 

 €), so that the last equation makes the sum of two essentially 

 positive expressions equal to zero. U(p) must therefore 

 vanish identically and hence /jl(s) also. Thus since the 

 homogeneous equation has no solution except zero (24) 

 admits a unique finite and continuous solution /jl{s). From 

 this the potentials r(p) and vfp) are determined, and 

 therefore their sum U(/>). The final solution to our problem 

 is then 



V(p)=-0(p) + u ( P ). 



December 24, 1914. 



LX. On the Decrease of Velocity of Swiftly Moving Elec- 

 trified Particles in passing through Matter. By N. Bohr, 

 Dr. Phil. Copenhagen ; j>. t. Reader in Mathematical 



Physics^ University of Manchester* . 



Tf^IIE object of the present paper is to continue some 

 X calculations on the decrease of velocity of a and /3 

 rays published by the writer in a previous paper in this 

 magazine f. This paper was concerned only with the mean 

 value of the rate of decrease of velocity of the swiftly 

 moving particles, but from a closer comparison with the 

 measurements it appears necessary, especially for /3 rays, to 

 consider the probability distribution of the loss of velocity 

 suffered by the single particles. This problem has been 

 discussed briefly by K. Herzfeld J, but on assumptions as to 

 the mechanism of decrease of velocity essentially different 



* Communicated by Sir Ernest Rutherford, F.R.S, 



t Phil. Maer. xxv. p. 10 (1018). (This paper will be referred to as I.) 



X Phys. Zettschr. 1912, p. o47. 



