ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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point q , the image of c ; draw the line m x q on which prolonged will be 
found the image of o. From the point o draw through q x the line o q , 
until it meets the first face of the lens in m. Through m and c x draw 
the line c x m, which prolonged will pass without deviation out of the 
lens, and will meet m x q in a point o x ; the point o x will be the image 
of o. 
If from the point o the perpendicular o g be let fall on the axis, and 
from o x the line o x g x , the point g x will be the place of the image of the 
point g seen through the lens. 
Iu order to obtain the principal foci of a given lens, draw a radius 
l c (fig. 10) to the centre of its first face, and draw its corresponding 
refracted ray m x q, then through the point q x draw q x m parallel to l c, 
drawing m c x and prolonging it till it meets m x q 2 prolonged in S. 
Fig. 10. 
The point S will be the image of a point situated at an infinite distance 
in the direction of c m l. Drawing from S a normal to the axis we 
obtain in p x a principal focus of the lens. The same construction 
repeated for the other face will give the second principal focus p, or 
the point of the principal distance of the lens. 
We can obtain the second focus more quickly when once the first is 
known, profiting by a very simple relation which exists between the two 
distances q p x and q x p of the two principal foci from the centric points. 
Representing by r the radius of curvature a c x of the first face of 
the lens l x , by r the radius b c x of the other face, by x the distance 
b q of the centric point q from the second face of the lens, by x x the 
distance a q x of q x from the first face, and denoting by F the distance 
q p x and by F x the line q x p we readily obtain the following relation : — 
F — r x + x 
Fj - r + x x 
which gives directly F, if we know F 1? or F! when F is known. 
