Capacity of the Microsco^^e, By Prof. Helmholtz. 
Then cos. (r, ri) = 1, and S . cos. (r, N) is the projection of S 
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 s = tt . . a^. 
L = J . TT . . . COS. (r, N). [6*] 
The same amount 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', d S', N', 
then 
L = J' . TT a"^ d S' . COS. (r, N'). [6^] 
Now, S' is the image oi ds, and its projection— normal to the 
axis — d S' . cos, (r, N') is the image of the corresponding projection of 
d S. We have therefore the proportion 
d S . COS. (r, N) : S' . COS. (r, N') = /32 : 
From which follows 
J . . /32 = J' . a'2 . ;8'2 ; 
and by equation [5], 
J : J' = n2 : [62] 
This gives the brightness with which the surface of image 
included within the outline of the illuminating cone shines, inde- 
pendent of the direction which d S and d S' have in relation to the 
axis, and of their distances from the surface of the curve (of lens). 
From this image (<iS') we might pass on to consider a second, 
£^S", and so forth. It is obvious that between each following image 
and S a similar equation would arise. 
If we suppose the object and the image to lie in the same 
medium, then the brightness of the optical image jproduced by rays 
which incline at very slight angles to the axis and perpendicular 
ivill always be equal to (i. e. neither more nor less than) the bright- 
ness of the object, except in so far as loss of light by reflexion and 
absorption may occur. 
But this law should hold good without limitation of divergence 
angle. For if it were possible to throw an image of any bright 
point sending forth its light according to the conditions above 
expressed (namely, of rays circumscribed by a diaphragm aperture), 
which image should shine with greater intensity than the rule 
above given admits ; then we could cause this bundle of rays to pass 
on as parallel rays through a plane end-surface into the air, and to 
fall into the eye of an observer ; and in such case it would happen 
that an object would be seen more brightly illuminated through an 
