The actual difference between CO and Cm in the No. 1 lens, with the extreme oblique pencil, is about the one tenth of an inch. If then we multiply Mr by 18 and divide the product by their difference, we get ins. The difference between and Cm, (np,) is therefore nearly one-third of an inch. This is of course in favour of flatness of field, because it brings p nearer to the plane through q.
In the common view lens, presented to extremely distant objects, the field is very approximately a sphere the centre of which is the centre of the convex surface of the lens. On taking the exact dimen sions of the orthoscopic lens, and working the problem out completely, we find that, as regards flatness of field, the common view lens has a little the advantage ; and this result of theory is also borne out by the experiments we have made with both forms of lens differing but little in their focal length. In what follows, however, we shall show that in other respects the orthoscopic lens has many and great advan tages over the common view lens.
So much for flatness of field. Next, with respect to the angular extent of the field of view. It might be supposed that the common view lens having the advantage in flatness of field, it ought to include a wider angular field ; but that is not the case, because the distortion produced by the common view lens is so great, and becomes so un bearable when a certain small angle of field is exceeded, that it is necessary from this cause to restrict that angle to about In the case of the orthoscopic lens, the distortion is not only different in character, but much less in amount, and therefore, although the field is not absolutely so flat, still an angle as great as 47° may be included. This is a great merit of the orthoscopic lens, and one which should recommend it particularly to the notice of the landscape photographer ; because the bad effects of curvature of the image may be remedied by using a small stop, but for distortion there is no such remedy. A small stop gives a finer point to the pencils, but does not affect the curvature of the lines of the picture.
We now come to the 2nd topic, viz : Freedom from distortion.
In the common view lens with the stop in front, the oblique pencils do not pass straight through the margin of the lens, but are bent out of their course, inwards, towards the centre of the picture. This produces distortion, in a way in which we will endeavour to explain.
Suppose the stop extremely small, and the lens removed ; a perspec tive view would then be formed on the focussing screen, but larger than the picture produced by the lens, and quite free from distortion. Suppose a plain irregular polygon to be the figure represented, the angles of which on the screen are points A, B, C, D, &c., and let 0 be the point where the axis of the camera cuts it. Draw radial lines 0 A, 0 B, 0 C, 0 D, &c. Now introduce the lens. In consequence of the deflection of the axes of the pencils which pass through the margin of it, towards the point 0, the image of the poly gon will be smaller than before, and its angular points a, b, c, d, &c., will lie on the lines 0 A,O K, 0 C, &c., nearer to O. Now if the decre ments aA, bB, cC, &c., were exactly proportional to the radial lines OA, OB, 0 C, &c., the small polygon abed would be exactly similar to the large one AB CD—and there would be no distortion ; but no such law is observed in the production of these decrements as that of direct proportionality to the radial line, and the greater the radial line may be, a fortiori greater the decrement becomes. This produces distortion, and causes all straight lines which do not pass through the centre of the picture, to be bent inwards at their extremities. See "Distortion." Now let us turn to the orthoscopic lens. Here we see that the axes of the oblique pencils are bent outwards out of their course, and a larger picture produced than if a small hole, without lenses, were put at C. Instead of decrements we have now increments of the radial lines—and the production of these increments depends upon a different law from that of the decrements in the former case, and produces less distortion. What little distortion there is, has the effect of rendering straight lines convex to the centre of the picture, by bending their extremities outwards, but this defect is so inconsiderable as to be scarcely appreciable, and so far as it exists it has the good effect of increasing the comparative size of the side objects, and therefore throwing the central objects apparently further back ; while the common view lens has the opposite effect to such an extent as to interfere greatly with the aerial perspective, by diminishing the objects at the sides of the picture, which are generally the nearest, and thereby bringing the central and generally most distant objects apparently too much forward.