470 Professor Thomson, On the Scattering of 



The conclusions drawn when the deflections were all in one 

 plane may thus be extended to the more general case. 



Although as yet we have no experiments in which the 

 arrangements have been such as to admit of an accurate applica- 

 tion of the formulae obtained in this paper, we have data by 

 which we can calculate the order of the quantity N^ the number 

 of corpuscles in an atom. 



Let us find the path of a particle which moves so that its 

 deflection is equal to the average deflection for the number of 

 collisions made by the particle, i.e. if ^ is the angle through 

 which the direction of the particle is deflected, n the number of 

 collisions made by the particle 



</) = Vn ^. 



If s is the length of path travelled by the particle, \ the 

 mean free path n = s/\ and </>^ = sd'^/\. 



If cc is the distance, measured parallel to the direction of 

 projection, travelled by the particle 



dx 

 ^=,cos<|,, 



X . <^- 

 or since s = ^^ , 



dx = -^^ cos ^,(f).d^, 



2A, 



or a; = -^ {<^ sin ^ + cos (p — 1], 



so that when = 7r/2, or the particle is bent at right angles to 

 the direction of projection, 



when X is greater than this the particle will begin to travel back 

 again, hence this value of x must be comparable with the distance 

 at which the number of particles crossing a plane at right angles 

 to the direction of projection is reduced to one half of those 

 projected. 



Substituting the value of X/^^ previously found we get 



25 



384i\^„ -^2 



i'-iy 



71 rv- 

 x= (tt — 2) -Tw- 



if we take the second of equations (B), 



putting ejm = 51 x 10", e = 5 x lO"", v = 10", iV - 2 x 3 x lO^", 



