48 Captain Abney on Photographic Irradiation. 



Let r = the radius of the particle. 



0= the angle of incidence of R^ a ray of the pencil falling* 

 on it. 

 Let AE represent a section of the glass plate. 

 Let* ED=a? ; and / = thickness of the plate. 

 Since EGD = 20, 



.*. x: = rcos0-\- (t + r + r sin#) tan 20. 

 From the question before us it is manifest that caanot be 



greater than — . 



When r is small in comparison with t } 

 a}=t .tan 20, 

 dx__ \2t 

 W" cos 2 20' 



Now the quantity of light falling upon a very small surface at 

 G will be distributed on a small surface about D . 

 The small surface at G may be represented by 



r 2 sin cos .80 .hcj) 



(where cj> is the angular measure taken parallel to the surface of 

 the plate). 



The small surface at G will be 



<2&.6\£=:*.tan20x ~^L-J0 . Scj>. 



COS <vt/ 



If I and I' be respectively the intensities of the light reflected 

 from G and falling on D, 



T , Ir 2 sin cos Ir 2 „ _ - 



2 tan 20 4t 2 

 "l 2~zr 



COS Z C7 



Since %-=t . tan 20, 



r IrH 1 



4 (* 2 +a? 2 )f 



For the sake of illustration, the accompanying curve has been 

 constructed showing the general relation between the intensity 

 and angle of incidence on the bottom surface of the plate. The 

 ordinates represent the intensities. For the abscissae the thick- 

 ness of the plate has been taken as the unit of measure. 



The solid of revolution formed by the area rotating round 

 the axis of y would give the projection of the pencil of rays in- 

 cident on the particle multiplied by its intensity. Not all 

 these rays will be reflected back ; only those which fall at and 



* The refraction-index of collodion and the glass may he taken as equal. 



