23 



(ii.) Where r is such that />+ W -\-r is greater than /?, the 



-^ D 



limits of ^ are cos and zero, and the limits of r are R - D 



R-r 



and R-D-D'. 



Hence 



iV/Tz^ J7?_/)_/)'( \R-rl J ( ) 



R-D-D rfj)^D'\ f D 



= -(/e-/)+c^)'--(/?-/:>-Z>'+rf)'-2Z>V^ 

 3 fj 



D' ^(D + D')[^{R+d) + ^{R + d-D)} 



+ -^- — - los- 



y{R + d) " VZ^{ ^(A' + rf)+ J(R + d-D-D') 



D"-^2DD' ^R\v{R + d) + ^{R + d-D- D') 

 ■loe.- 



V{R + d) ^ ^{^D + D')\V{R + d)+ x^d\ 



Curve C is plotted from this formula for the case when R = 3'5 

 and D' ='b. As usual, d is taken equal to 1'33. 



The following co-ordinates have been used in drawing the 

 curve : — 



DjR '057 -143 -200 -257 -380 -500 -714 

 i/I -833 -642 -539 -449 -288 -174 -044 



CASE (d). 



The radio-active material in the forim of small spheres. 



This case is not realised in any of the experiments des- 

 cribed in this paper, but is introduced in order to show how 

 greatly the effects depend on the mode of arrangement of the 

 radio-active material. 



Suppose the sphere to be of such a size that its diameter 

 is a few times greater than the range of the a particle in the 

 radio-active material itself. It may then be supposed that the 

 sphere emits equal numbers of a particles in all directions 

 and at all ranges up to the maximum. Neglecting the varia- 



