reach us of every possible length between the limits already referred to, and vibrating in every possible plane, so that, even if our lens would make the wave-fronts emerge spherical, it would be found that the long red waves would come to a focus considerably farther out than would the short violet waves, and confusion of the image and colored fringes would result. It is also found impossible to construct lenses with surfaces of any other shape than spherical; consequently the optician has quite a complicated problem to solve before he can construct an object-glass which will not only make the wave-fronts emerge strictly spherical, but which will also make the red, green, and violet waves unite at the same focus, and thus cause all the waves from each luminous point like a star, which is a sun, like ours, too distant to have visible dimensions, to agitate but a single rod of the retina.
In practice, this is almost perfectly accomplished by combining a convex lens of crown-glass (the optical name for plate-glass) with a concave lens of flint-glass (the kind used for the finest cut-glass for table-ware), placed close together; but, to arrive at this result when the lenses are of large aperture, requires an amount of skill and patience attained by few.
Diagram 9 shows the two most approved forms of object-glasses.
Diagram 9.
The first is that used by Alvan Clark, in the largest and most perfect telescopes ever constructed. It consists of a double-convex lens of crown-glass, combined with a plano-concave lens of flint-glass, the crown-glass lens being placed in front. Both surfaces of the crown-glass lens and the first surface of the flint-glass lens have the same curvature. The focal length of this object-glass is nearly equal to
