SPHERICAL ABERRATION. 
image will be produced at a certain distance from tlie lens. Let 
this distance be called d\ 
If the border of the lens be now covered with a ring of card, 
and the central part with a card disc less in diameter than the 
ring, so as to leave an uncovered space between the disc and the 
ring, another faint but distinct image will be produced at a 
certain distance d"> a little greater than d\ 
If the border be covered with a broader ring of card, and the 
central part by a still less disc, so as to leave an uncovered ring 
of surface smaller than the last, another image will be produced 
still faint and distinct, and at a distance d'" greater still than d n . 
In fine, by continuing this process, it will be found that if the 
lens be resolved into a series of annular surfaces, concentric with 
each other and with the lens, a series of images will be produced 
at distances d', d\ d'", d"", &c., gradually increasing, that pro¬ 
duced by the external annulus being at the least distance, 
and that produced by the spot surrounding the centre at the 
greatest distance. 
On comparing the series of distances d ’, d", d’% d"" .... 
at which these images are placed, a very important circum¬ 
stance will be observed in their distribution. It will be found 
that while those produced by the central annuli are crowded very 
closely together, those produced by the annuli near the edge of 
the lens are separated one from another by much more sensible 
spaces. 
When the entire surface of the lens is uncovered and exposed 
at once to the object, it is evident that this series of images will 
be produced simultaneously. Some idea of their distribution 
along the axis of the lens may be found by referring to fig. 26. 
Fig. 26. 
L 
L 
The object being oo, and the image produced by the small 
central spot of lenticular surface being at 11, the images formed 
by the rings of surface immediately contiguous to this spot will 
be crowded together so closely in front of a screen held at n, 
that they will all be formed upon the screen with very little 
103 
