420 



LIMITS OF OPTICAL CAPACITY OF THE MIOEOSCOPE. 



quantity of light sent forth from the luminous point d S upon 

 another point d s, whose distance is r as follows where (r,iV") and 

 {r,n) represent the angles formed between the line r and the normals 

 iVand n. 



L = J \ . cos (r,iV) . cos (r,w) 



(6) 



If now we understand \>^ d s the circular aperture of the cone of 

 rays at one of the refracting surfaces, and by fZ /S a luminous point 

 intersected by the axis so that r falls in the axial line. 



Then cos. (r,;z) = l, and d8 . cos. (r,^) is the 

 projection of rZ aS on a plane normal to the 

 axis. 



Let a be the angle of divergence of the rays 

 directed to the periphery of d s, then d «= 



TT . r. a^ 



Z=zJ. TT . a: . d S . cos, (r,iV) 



(6>) 



The same amoant of light must also be contained in the same 

 cone of rays continued through the following medium. And if we 

 indicate the corresponding quantities by the signs J', a', dS'j JN', 

 then 



Z=J' . wa" . dS' . COS. {r,N') (6*') 



Now, dS' is the image of d s, and its projection — normal to the 

 axis — dS' . cos {r,N') is the image of the corresponding projection of 

 dS. We have therefore the proportion 



dS . cos (r,A) : dS' . cos (r,iV')=/3' : /3" 



Jrom which follows 



J . a^ . /3'=/' . a'l /3'2 and by equation (5) 



(6^) 



