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July 31, 1891,] THE PHOTOGRAPHIC NEWS. 545 SPHERICAL ABERRATION, DIFFUSION OF FOCUS, ETC. BY w. K. BURTON, JAPAN. I REAR that your readers must, for the most part, be very sick of the subject of diffusion of focus, but I hope that they will have patience with me for a little if I bring the matter up once more, and I think it is but justice that the editor should let me say a few words in connection with a communication that appeared in the Photographic News by Mr. T. R. Dallmeyer, now a good many months ago. The circumstances were these. Perhaps I ventured on unsafe ground in criticising certain utterances of Mr. Dallmeyer’s anent diffusion of focus. I have now to admit, at all events, with all candour, that at the time I wrote I had not thoroughly understood Mr. Dallmeyer. I hope to be able to show that I had not entirely failed to understand the subject,* as Mr. Dallmeyer generously stated at the time. Immediately I read Mr. Dallmeyer’s communication I wrote to him saying that I had begun a set of farther investigations of the subject, and intended to write about the results later on. I did so begin, and had nearly finished what I had set myself to do, when my work was interrupted by an occurrence which, as it was of an entirely personal nature, need not be farther spoken of here. It is only within the last little time that I have been able to gather up the threads of the work again. 5, &c. I have not yet noticed that Mr. Dallmeyer acknowledged this correction. Even the axial line shown by Mr. Debenham in his dia gram accompanying the above-mentioned communication should, I consider, be left out, as it gives the impression that there is 50 per cent, more of light enclosed within the limits of the smallest cone than there really is. The drawing that I send is within the ordinary limits of hand drawing, and, allowing for the thickness of line necessary to permit of reproduction, a correct representa tion of spherical aberration, the lines representing the boundaries of cones, the diameters of whose bases are as 1, /2, /3, This drawing shows very distinctly the greater diameter of the cone of light at a given distance behind the plane of average focus representing the distance when a near object is focussed. It also shows not only the smaller diameter of the cone at a like distance in front of the plane of chief focus (repre senting the foreground), but shows the comparative definiteness of the boundary of this part of the cone. But Mr. Dallmeyer’s contention now is, that there is inward concentration behind the plane of average focus, and it may be said that even this drawing shows distinct inward concentration. I do not deny the appearance of such concentration, nor absolutely the existence, but I suspect that the appearance is produced more from the fact that the lines near the axis are nearly parallel before and after they intersect behind the average focus, whereas Mr. Dallmeyer, in the first part of the communication referred to, regrets that we live so far apart, that it is diffi cult to carry on a discussion. He is right so far. It is not possible to carry on a discussion with any satisfaction when several months must elapse between the printing of any two communications, and this even if the language used is always temperate. For this reason I propose to discuss no farther, but, in this communication, to give merely the result of certain experiments and calculations, letting anyone who likes draw his own conclusions. In the first place, although we have had so many draw ings representing spherical aberration already, I wish to bring one more before your readers. It was drawn long before I saw the article by Mr. W. E. Debenham, appear ing in the Photographic News for September 19th, 1890, in which he pointed out that it is not a fair representation of the concentration, or otherwise, of light, where there is spherical aberration, to draw lines representing cones of light, the diameters of the bases increasing by equal incre ments. The areas of the bases should increase by equal increments. That is to say, that diameters of these bases should be not as 1, 2,3, 4, 5, &c., but as 1, /2, 3, 4, * I have lost the number of the PMOTOGIAPHIC News containing the first part of Mr. Dallmeyer’s answer to my communication, and cannot, therefore, quote exact words. they cross at considerable angles in front of the focus, than because of much real central concentration. At any rate, I tried to find some other measure of central concen tration than the mere appearance of a diagram, however correctly drawn—not that I by any means despise such — and it seemed to me that a fair measure would be the intensity of the light on the axis of the lens, at different distances from the lens between that point where the cen tral rays intersect, and that where the extreme marginal rays intersect. This intensity, again, can be measured by finding the length, along the axis of the lens (where that axis is the focus of a point formed by the intersection of rays from different anuli of the lens), through which the light from anuli of the lens of equal areas crosses the axis. Thus, referring to the diagram, we take diameters ab, cd^ef, gh, &c., having the ratios 1, /2, /3, /4, &c., and calculate mathematically the distance between the two points where the lines from a and b intersect each other, and that where the lines from b and c intersect each other, then do the same for the point where the lines from b and c intersect each other, and that where the lines from d and e intersect each other, and so on. These are calculable without much difficulty by trigonometry, as suming a certain index of refraction. If the distance becomes less from without inwards (from a greater to a
