468 Professor Thomson, On the Scattering of 



under the conditions contemplated in equations A, but such are 

 now being made by Mr Crowther at the Cavendish Laboratory. 

 The observations we have are, however, sufficient to show that 

 Nq is of the same order as the atomic weight of the atom. 



We see from equations A that when the deflection is small 

 the thickness of the layer of a substance required to produce 

 a given deflection varies as 



m-V 1 (385 7r_^ ^ I 

 e' NNo 1 25 ^16 "I 



■i^F^ 1 385. 



or 



e^ NN, 25 



according as the positive electricity is uniformly distributed 

 through the atom or collected into separate units. We can 

 show that this result is true even when the deflection is not 

 small provided the velocity of the particles remains unaltered. 



For let f{z, ^) x 6 he the fraction of the particles which at a 

 distance z from the point of projection, measured parallel to the 

 original direction of projection, have a deflection cf), where <^ is 

 between md and {771 + 1) 6. 



Let A, be the mean free path of a particle, then f(z + X cos (p, md) 

 will be got from those particles which at a distance z had 

 deflections {m — l)6 or {m + \)6; each of these particles will 

 have made another collision, and if they are equally likely to 

 be deflected in one direction as the opposite, we see that 



f{z + \eo^^,me)^\f{z,{m-l)e] + \f[zXm+l)e], 



(compare Lord Rayleigh, Theory of Sound, vol. i. p. 35). 

 Expanding by Taylor's Theorem we get 



an equation which determines / as a function of / and 0. Since 

 the same value of z' will give the same value of ^, it follows that 



