3rd,—Equality of illumination. Through m imagine a line mk drawn at right angles to m C, and cutting Cp in k. Now let a straight line passing always through this imaginary point k sweep round the circiunference of the stop at C and mark out with its end a circle on the front lens, in the neighbourhood of B, which would be its centre. Similarly, let a line passing through m sweep round the circumference of the stop and trace another circle on the front lens, the centre of which would be A. These two circles viz., that at A and that at B will be equal to another. But if instead of the point k we take the point 0, n6arer to C, the circle at B will then become. larger than before and consequently larger than that at A. Hence it follows that the area on the front lens covered by an oblique pencil is greater than that covered by the direct pencil. On the other hand the obliquity of the pencil occasions loss of light, as shown by the dotted lines across it. The gain from one cause does not entirely compensate for the loss from the other, and there is not perfect equality of illumination; but in the common view lens there is loss from obliquity of incidence without any set off to counterbalance it. The orthoscopic lens has therefore the advantage as regards equality of illumination.
4th,—Perfection of focus, and freedom from spherical aberration.
In the common view lens no attempt is made to cure spherical aber ration, or improve the focus, except by mean.s of the stop. Every thing is sacrificed to flatness of field. There would be much less spherical aberration in the central pencil if the lens could be turned with its convex side to the view. But in the orthoscopic combina tion spherical aberration may be, and is, completely remedied, and the quality of the focus, both of the direct and oblique pencils, greatly improved.
5th,—Coincidence of the visual and actinic foci. With four glasses instead of two, more lines of the spectrum may be united, and there fore the chemical focus improved, so that the orthoscopic lens has the advantage in that re,spect.
6th,—In lightness and convenience, and freedom from diffused light, the orthoscopic lens has greatly the advantage over the other. In copying, the common view lens cannot be used when the copy is to exceed one half the size of the original ; but when the focus of the orthoscopic lens is lengthened by bringing the object near it, it gives a sharp and good image up to full size. It is in fact the best copying lens that has yet been produced.
We have now discussed minutely the three forms of lens ntostly used by photographers. It only remains to describe the mechanical means by which lenses are ground and polished.