Scattering of a and.fi Particles by Matter. 671 



produce large deflexions of an a particle, and then compare 

 the deductions from the theory with the experimental data 

 available. 



Consider an atom which contains a charge ±Ne at its 

 centre surrounded by a sphere of electrification containing 

 a charge + N^ supposed uniformly distributed throughout a 

 sphere of radius R. e is the fundamental unit of charge, 

 which in this paper is taken as 4"65x 10~ 10 E.s. unit. We 

 shall suppose that for distances less than 10 ~ 12 cm. the central 

 charge and also the charge on the a particle may be sup- 

 posed to be concentrated at a point. It will be shown that 

 the main deductions from the theory are independent of 

 whether the central charge is supposed to be positive or 

 negative. For convenience, the sign will be assumed to be 

 positive. The question of the stability of the atom proposed 

 need not be considered at this stage, for this will obviously 

 depend upon the minute structure of the atom, and on the 

 motion of the constituent charged parts. 



In order to form some idea of the forces required to 

 deflect an a particle through a large angle, consider an atom 

 containing a positive charge Ne at its centre, and surrounded 

 by a distribution of negative electricity N# uniformly dis- 

 tributed within a sphere of radius R. The electric force X 

 and the potential V at a distance r from the centre of an 

 atom for a point inside the atom, are given by 



x=n,(; 2 -^) 



T7 XT Z 1 3 r ' \ 



Suppose an a particle of mass m and velocity u and charge E 

 shot directly towards the centre of the atom. It will be 

 brought to rest at a distance b from the centre given by 



W-M^-^ + g.) 



It will be seen that b is an important quantity in later 

 calculations. Assuming that the central charge is 100 e , it 

 can be calculated that the value of b for an a particle of 

 velocity 2*09 x 10 9 cms. per second is about 3*4 xlO -12 cm. 

 In this calculation b is supposed to be very small compared 

 with R. Since R is supposed to be of the order o( the 

 radius of the atom, viz. 10~ 8 cm., it is obvious that the 

 a particle before being turned back penetrates so close to 



