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Mr. C. G. Darwin : A Theory of the 



of the rays. Putting in the value of p from (4) or (5) 

 we have 



'**''* .__-** i 1/2 





w{ log (! + «)-/(«)} J 



Now A^ was obtained on the assumption that o- 2 ?; 4 /\ 2 is large, 

 and so here the second factor of the denominator may be 

 replaced by log it? —a, a being the limiting value of /, 

 2/3 f or /i and 2 for / 2 . When this change is made the 

 integration can be performed and gives 



~ <7 2 V 4 



log — r -a 

 X=iSkTrv. I log * . . . (13) 



§ 6. Comparison with Experiment. 



Of the substances whose absorption has been discussed, 

 Geiger * made experiments with gold, tin, and aluminium. 

 I apply (13) to foils of these substances of thickness 

 equivalent to 1 cm. of air, and I apply (12) to thin gold 

 foils as well. The assumption that a 2 v 4 /X 2 is large is hardly 

 justified for gold, especially for the values corresponding to 

 a small radius of the air atom. Indeed for gold, even in the 

 most favourable case an application of (13) to a thin foil 

 gives a value differing by 10 per cent, from that deduced from 

 (12), and (12) is only superior to (13) in that cV/A 2 h as 

 been supposed large once instead of twice. 



Table II. gives, for comparison with the experimental 





Table II. 



Most probable Angles of Scattering. 









Observed. 



Volume Distribution. 



Surface Distribution. 



<t for air . 







10 _ 8 10 - 8 -5 10 -9 



io- 8 



10-8-5 



10 -9 





1 Au foil 



2 „ „ 





10' 



23' 

 2°-l 

 l c -5 



0°-6 



13' 17' 27' 

 19' 25' 38' 



22' 

 31' 



30' 

 42' 



45' 

 64' 





Au equiv. 

 Sn „ 



Al „ 



to 1 cin. air ... 



l°-24 l°-63 2°-8 

 0°-79 1°05 l°-74 

 0°-35 0°-48 0°-80 



2°-63 

 l°-43 

 0°-53 



4°4 



2°44 



0°-79 



5° -9 

 l°-58 



* H. Geiger, Troc. Roy. Soc. A. vol. lxxxiii. p. 492 (1910). 



