SPHERICAL DISTORTION. 
focus, be viewed by an eye at e, an imaginary image will be seen 
at a certain distance, greater than that of the object. 
Fig. 29 . 
If the object be straight or fiat, such as o' o', the image will be 
curved with its convexity turned towards the lens, as shown at 
i' i', in the figure. If the object be concave towards the lens, the 
image will be less and less convex, until the object having a 
certain concavity, such as o" o”, the image will be straight or 
flat as shown at i" x". If the concavity towards the lens be still 
greater, as at o'" o'", the image will become concave towards the 
lens, but less so than the object. If the object be convex 
towards the lens, as at o o, the image x i will also be convex 
towards it. 
It follows, therefore, that a straight or flat object seen through a 
convex lens thus will appear curved or convex, and that a convex 
object will appear more convex. A concave object, provided it 
have a certain degree of curvature, will have a straight or flat 
image, and all objects more concave will have concave images. 
These results will be found to have considerable importance in 
the practical construction of compound microscopes. 
48. From what has been explained it follows, that if any 
expedient could be discovered, by which the focal length of a lens 
could be shortened without increasing its convexity, we could 
obtain a given magnifying power with a lens of a given 
diameter without increasing the aberration, a result which would 
be a most evident advantage. Now, there is only one way by which 
this could be accomplished, which is by finding some material for 
the lens, which without any countervailing disadvantages would 
have a greater refracting power than glass. A lens made of such 
a material would have a shorter focus, and consequently a greater 
magnifying power than a lens of glass with the same convexity. 
107 
