23 



point, come together at different intervals along 

 the central line or axis. By reference to Fig. ' 

 it will be seen that the outer, or marginal rays are 



refracted at c and / so that they will combine at 

 g and the inner, or central rays are refracted at 

 j and k so that they will meet at /. In the same 

 manner will the rays which enter between c Ji 

 and i d come together at intermediate points 

 between g I and those of the central portion 

 between // and i will fall beyond /. The amount 

 of spherical aberration depends upon the shape of 

 the lens and in different lenses of the same focus, 

 is greatest in the double convex form, less in the 

 plane convex and least in the so-called crossed 

 lens, in which the two surfaces are of different 

 radii and in the proportion of 1 to 0, on condition 

 however, that the surface of short radius is directed 

 toward the object. This form of lens however, is 

 seldom used, as it shows the greatest amount of 

 aberration if used in the reversed, position. The 



