THE MICROSCOPE. 
still more clearly intelligible by reference to figs. 6 and 7, where 
two lenses, l l and l' l', baying equal focal lengths, are repre¬ 
sented ; the same object, o and o', is placed 
at the same distances from them, and equal 
images of it, 11 and i' I', are produced at 
equal distances from the lenses. The 
angular aperture of L L, being i o I, is 
greater than that of l' l', which is i! o' l' ; 
and it is evident that a greater number of 
rays issuing from the object, will fall upon 
the lens L L, than upon l' l', in the 
proportion of the square of the angular 
aperture of the former to that of the latter ; 
thus, if the angular aperture of l l be 
twice that of L' L', the number of rays 
which fall on n will be four times the 
number which fall on l' i/. 
Supposing, then, that all the rays which 
fall upon each of the lenses, pass through 
them, and are made to converge upon corre¬ 
sponding points of the images 11 and i' i', 
it is clear that each point of the image 1 1 
will be more intensely illuminated than the 
corresponding point of I' i', in the propor¬ 
tion of the square of the angular aperture 
of L l to that of l' i/; and if these apertures 
be in the proportion above supposed of two 
to one, the several points ,of the image 1 1 
will be four times more intensely illumi¬ 
nated than those of i' i'. 
15. As a practical example of the effect 
of the angular aperture upon the image, 
we here give seven drawings made by the 
late Dr. Goring, of the appearance of a 
particle of dust, or a scale, as it is called, 
of a butterfly’s wing, viewed with the same 
magnifying power, the angular aperture of 
the lens being successively augmented. 
When the aperture was reduced to the 
smallest limit, the object appeared as re¬ 
presented at A, fig. 8; when the aperture 
was increased in the proportion of 2 to 3, 
the object assumed the appearance repre¬ 
sented at b, and, in short, by successively increasing the aperture, 
it assumed the appearances shown in c, i), e, e, and e. It will be 
12 
