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FETRUANY 20, 1885.J THE PHOTOGRAPHIC NEWS. 115 A TALK ABOUT LENSES. BY w. II. WHEELER.* As we have seen, the direct converging pencil from the front lens is incident first on the convex anterior surface of the flint lens, and the direct action is slight, that sur face having generally for its centre (that is, the centre of a sphere of which the convex surface is a part) a point not far from that to which the pencil is converging at incidence. But the oblique pencils have the effect of their obliquity exaggerated by that convexity. For, spreading out from the stop or centre ot the whole combination, their oblique direction is made more oblique in its incidence by the form of the surface. So also at emergence, and the depth of the concavity adds extremely to the effect. From what has been already said of aberra'ion, it will be under stood that its effects at one deep curve miy outweigh the sum of several contrary effects at other surfaces. And this effect, being of a diverging obliquity at a concave surface, is negative oblique aberration; which, lengthen ing the oblique pencils by an action increasing with the obliquity, flattens the field. For while positive aberration, direct or oblique, tends to shorten the focus, negative aberration tends to lengthen it. It is important to notice here that this oblique action, being largely dependent on the obliquity of incidence, as well as on the form of the surface, can exist where the direct aberrations are accurately balanced, thus flattening the field without injury to central definition. Other means of flattening the field are, an over-correction of aberration generally, so that with a small stop margi nal pencils are lengthened, and also an effect which this carries with it, the abnormally increased marginal action of the flint lens over-correc'ing the marginal dispersion And this effect, becoming more sensible as the obliquity increases, produces a want of coincidence in the foci, the actinic image being formed further from the lens than the visual, and the resulting field of view being thus flatter, as formed on the plate, than it appears on the focussing glass. We may thus see partly how flatness of field is obtained at the expense of the central part which can better spare it—a small stop equalizing the whole. To continue, the oblique aberration at the front lens is fairly favourable. Its anterior convexity harmonises with the relative positions of the pencils which converge to it from the subject wc are photographing. (Of course it is under stood that we are considering the relative directions of the various pencils which start from each point in the object, to be converged by the lens to corresponding points in the image. We must keep the idea of these relative direc tions quite separate from those of rays in the same pencil, which start from a point and come to a point. The pencils, as a whole, converge from an extended natural view, and diverge, after crossing at the stop or centre of the lens, to an extended artificial image. Then comes a partly unfavourable positive action ; for although the anterior convex surface of the flint has little effect on the converging rays as such, yet as regards obliquity the effect is strong, because the relative directions of the pencils are divergent, while the surface is convex. At the next surface, where they emerge, the concavity renders the surface still discordant with those relative directions, and the form of each oblique pencil, being generally mode rately divergent as it emerges,! is, as we have seen,strongly affected with negative oblique aberration. The greatest positive oblique aberration is evidently at the next anterior convex surface—that of the second lens—the relative directions of the pencils, as well as their moderately di vergent form, being discordant with it; though har monious with the posterior convexity, which again is dis cordant with the form of each separate pencil. ... .... * Continued from page 98. an’A nE.,5 °* incidence and emergence must always be reckoned by their anz.8 nI i a Perpendicular to the surface (called the normal} before inei- denee, and ajter emergence. To sum up, the first surface is positive and discordant to relative direction, and neutral as to form ; at the second surface, greatly discordant in both respects, but entirely negative; at the third surface, positive and discordant, greatly as respects direction, but generally less so as to form ; at the fourth, harmonious or neutral as to direc tion, but discordant as to form, yet in general not strongly so. This is, of course, a most rough and inadequate presenta tion of this beautiful arrangement, and, the curves being all mutually interdependent so as to combine achromatism and aplanatism with a very remarkable flatness of field, and freedom from confusion and astigmatism, considering the great aperture usually given, there will remain a consider able latitude in the curves and distances adopted by differ ent makers, the double convex lens, for instance, being sometimes more convex at its posterior than at its anterior surface, though oftener quite the reverse. But in general we may see how the flatness of field depends on the excess of negative oblique aberration, and the distinctive peculi arity of the Petzval construction is that both the surfaces of the flint lens are discordant with the relative directions of the pencils, and the second one extremely so. Now, as the proved efficiency of this principle is so great with a front lens whose convexity of field, oblique aberra tion, and astigmatism are distinctly more than with the front lens of an ordinary doublet, and that even with the much greater aperture usually given, one might be led to hope that to substitute that form, and use a Petzval back combination with it, would be an improvement, especially with a greatly reduced aperture, cutting off by far the worst part of each lens, and reducing the cost.* Some years ago, 1 wanted a lens which should cover well a plate of dimension rather over its focal length, and of large size (30 by 25). By using for front lens one from a wide-angle combination by Tench, of about 42 inches focus and 3 inches diameter ; and for back lens, the Petzval back combination from a Ross’s 4A, the separate focus of which was over 90 inches, and 5 inches diameter, it could be done, and leave very little distortion. But on putting them together, both were found so much over-corrected for aberration that they would not define well enough in com bination. It then occurred to me that if the double con vex posterior lens were placed next the stop, and the flint concave behind it, with its deep concavity next the plate, the balance of aberrations would be favourably altered, while the peculiar flattening power would remain. The result was that the back combination now distinctly im proved the definition of the front lens (which, when used alone, required to be stopped down extremely), and the flatness of field was something extraordinary. I may re mark that two pictures taken with this lens were exhibited at Paris in 1878, and may be presumed, therefore, to have been fairly successful. One might naturally expect that lenses constructed and calculated for this form would do better still, and I may remark that in a back combination so placed (as in Dallmeyer’s B and D lenses), the pencils having their most convergent form while traversing the interval separating the two lenses of the back combination ; an adjustment of that distance has its maximum effect on the balance both of aberration and dispersion, which is a practical facility in construction. Mr. Dallmeyer, indeed, specially sought this maximum effect for another purpose, and in his constructions the original aberrations are both much larger, while the distinctive peculiarity of the Petzval form is absent. Again, some eighteen months since, I desired to copy some engravings with minute accuracy, and to a large size (24 by 18). A lens of over 50 inches focus, of an ortho- scopic form, but modified to correct distortion, was tried, but the marginal definition was insufficient, 'This I con sidered owing to the comparatively violent curves of a * It is possible this may have already been done without my knowledge. Living iu the country, I have never seen Ross’s group lenses, and of cqurse do not know their construction.