412 Scattering of Liylit by Atoms and Molecules. 



following properties : (i.) when # = 0, i. e. when r is infinite, 

 <£(#) = 1 • and (ii.) $(.#) must be o£ the form which will give 

 rise to the Balmer series in the hydrogen spectrum. These 

 conditions are not sufficient to determine $(#). We shall 

 show, however, that it is possible to write down an 

 expression for <f> which will satisfy these conditions, and 

 in addition lead to the scattering of polarized light in a 

 way consistent with Lord Rayleigh's experiments. 



Taking the case of a hydrogen molecule, we see from 

 equation (3) that if x 1 be the value of x in the hydrogen 

 molecule 



and if the electrons and positive charges are at the corners 

 of a square <9 = 7r/4, so that in this case 



., , 1 



vn-i; - 2 VY 





Since when x = w 1) d¥ _ /3 ^ 

 dr r 





where F is the force, we see, putting 





* = £+(«), 





^t /3= K (* + m) 



\ when x = x v 



Assume 



^ x ^dx r cos x+ ~ j 



This satisfies the condition that 0(#) = 1 when x = 0, and 

 it is of the form which would correspond to a Balmer's 

 series (see J. J. Thomson, Phil. Mag. April 1919). 



From the condition 



<j>(xi) = =, 



2 \/2 



I find by the method of trial and error that ^ = '58, and 

 substituting this value of x in the expression for /3, I find 

 /3='3 approximately. This gives a scattering of a little 

 less than 3 per cent. ; according to Lord Rayleigh's ex- 

 periments the scattering is a little less than 4 per cent. 



Other expressions for </> could be assumed which would 

 also be in agreement with experiment as far as the scattering 

 goes. 



