208 Mr. 0. Klein on Scattered Radiation from 



form of a divergent integral. Moreover, he never tried 

 to evaluate this integral, a fact which accounts for his not 

 observing the mistake. At the outset of the calculation I 

 have been guided completely by Ishino. There is nothing 

 new in what follows as regards the mathematics. 



Suppose a plate of thickness lis struck by a radiation, whose 

 intensity is I. The absorption coefficient may be k, the 

 scattering coefficient a. When the radiation has penetrated 

 the plate to the depth x, its intensity has been diminished to 

 j g -(/c+a)x^ rpj ie q lian tity of scattered radiation issuing from 

 the distance between x and x-\-dx is evidently o-Ie~ {K+ ^ z dx. 

 But it is not distributed alike at all angles. J. J. Thomson 

 has theoretically arrived at the following expression for that 

 part which is radiated from the solid angle dw, whose 

 direction makes the angle 6 with the incident radiation : 



d<r = k(l+ cos 2 0)dw. 



If this expression be integrated over all directions we 

 ought to have a. 

 Consequently 



=HT 



(l+coJd)smdd0=~L 



lb7T 



da = §<r(l+ cos 2 6) sin d$. 



This expression, according to experimental investigations, 

 does not seem to be quite correct. For what we have in 

 view, however, the error will scarcely be of any importance. 

 I therefore adopt the following expression for the radiation 

 that is scattered from the path dx between two cones, whose 

 generatrices form the angles 6 and 6 + dd with the incident 

 radiation when leaving the plate : 



|Lr(l + cos 2 6')^ ( ' c+<T)x sin6'^^. 



Owing to absorption and scattering, the intensity of this 

 radiation when leaving the plate will be 



(l-x) 



f 1*7(1+ cos 2 6) sin 6 e~ {K+<T)x e~ (<+a) cose d6 dx, 



l — x 



for the radiation must travel the distance ^ . The 



cos a 



radiation issuing from the whole plate and falling within a 



