A PHYSICO-PHYSIOLOGICAL STUDY.
CONTENTS.
INTRODUCTION:
Recent publications on telescope sights, advantages claimed for their use, cause of these advantages.
(Alger; American and English Handbooks of Telescope-Sights; Von Kodar; Korzen).
The essential difference between open sights and telescopic ones usually stated correctly but not exhaustively. No measurements given, except by Von Kretschmar, who indicates two separate sources of error.
Theme of the discussion; definition of the problem.
FIRST PART:
Uncertainty in aiming caused by the differences in distance of target, fore sight, and rear sight from the eye.
Mathematical computation of dimness of extrafocal (non-focused) objects in the plane of those seen distinct.
Photographic demonstration of the image of target and sighting apparatus with the eye focused on different distances. Image when aiming by telescope (or Grubb sight).
SECOND PART:
The error in direction caused by peculiarities of the human eye.
Peculiarity of the human eye in comparison with photographic camera. Scope of the eye.
Observations in regard to error in direction.
(Von Kretschmar's experiences with gunners; appearance of the moon's crescent; Helmholtz's and Rontgen's experiments).
Explanation of these experiences by the irregular astigmatism of the eye.
Definition of the difference between anastigmatic, regular, and irregular astigmatic vision.
Source of the latter appearance the construction of the crystal lens.
Influence on the vision of focused and non-focused objects.
Perception of non-focused objects improved by simultaneous error in localisation.
Application to the aiming with open sights, or telescope sights, or Grubb sight.
CONCLUSIONS:
Modern telescope sights.
Field of vision and brightness in modern telescope sights (illumination at night, magnifying power).
Influence of range of target on the parallax in the telescope.
Parallax, field of vision, position of the eyes with the Grubbsight.
Qualities of the prominent systems of prisms.
The question of keeping the sight line constant.
The advantages gained by the use of telescopes in aiming and laying guns have recently and repeatedly been the object of discussion, even before the general public.
P. R. Alger, Professor of Mathematics, United States Navy, strongly urges their application to naval ordnance, in a lecture before the U. S. Naval College, Newport, R. I., published in the PROCEEDINGS OF U. S. NAVAL INSTITUTE, 1897, XXIII, pages 125 to 140, and which contains a wealth of interesting remarks. In accordance with this the American "Handbook of Telescopic Sights" (Washington, 1899) expresses itself decidedly in favor of advantages reached by the adoption of telescopes, and so does the English "Handbook for Telescopic Sights, Land Service" (London, 1901). More recently E. von Kodar, 2d Class Naval Engineer, Austrian Navy, gave a lecture on this subject in the "Marine-wissenschaftlichen Verein" at Pola (published in "Mitteilungen aus dem Gebiete des Seewesens," Vol. XXXI, No. IX, August, 15, 1903, pages 713 to 734), where the characteristic peculiarities of construction and efficacy of telescope sights is clearly and accurately shown, with the exception of some inaccuracies which shall be mentioned later. This work also is highly in favor of the telescope.
Anton Korzen, engineer of artillery, Austrian navy, and teacher in the War College, in his valuable memoir on Die Richtmittel der Geschiitze in "Mitteilungen fiber Gegenstande des Artillerie-und Geniewesens," Nos. 5, 6 and 11, pronounces his opinion in a similar way in the chapter on telescopic sights.
After reading Korzen, however, it might be believed that the specific advantage in using telescope sights was the magnifying effect, as if the aiming by telescope could only be improved in proportion to its magnifying power. This is a very general mistake—may it be stated right here—the correction of which is the chief object of the following pages. The specific advantage in using telescopic sights is quite a different one, and is gained even if there is no magnifying at all. It is, indeed, a matter of free choice, to be decided on the ground of special argument, if a telescope for sighting shall have magnifying effect, and how much of it. With geodetic work, for example, non-magnifying telescopes are much in use, and very satisfactory.
In Alger's and Von Kodar's publications this specific argument is also more or less clearly given (indirectly also in the handbooks mentioned). So Alger says (page 125):
"It has long been recognized by those who have investigated the subject that it is physically impossible for the human eye to judge when three points at widely different distances are in one straight line." And Von Kodar (page 715) states even more pointedly: "There is no doubt that this method of aiming (i.e., with open sights) would be very perfect if the qualities of our eye would not make it impossible to simultaneously align three points situated at different distances. Everybody knows that in looking at a distant object our eye automatically accommodates itself to the long distance and then objects nearer us are only dimly visible, and vice versa. Therefore it is quite out of question for the eye to simultaneously and distinctly perceive the rear sight, quite near the eye, the fore sight, a small distance off, and the far-away target."
This is the one argument clearly put against aiming with open sights, and further on it is also explained how by using telescopes (or the Grubb sight) the said errors are avoided.
But Von Kodar does not enter into discussing the amount of error to be expected in aiming with open sights. He is satisfied by characterizing the quality without determining the quantity of the error. In all the publications on the subject, known to the author, the only computation of an error in aiming is that of the difference in elevation by aiming with "fine sight" or "full sight" or "half sight," in the monograph by Colonel von Kretschmar on his level sight, July, 1890, of which a very abridged extract came out first in General R. Wille's book, "Das Feldgeschutz der Zukunft," Berlin, 1891, pages 253 to 256, and later, repeated in part, unfortunately not textually, in the same author's book, "Fried. Krupps Schnellfeuerkanone C/99," Berlin, istoo, pages 68 to 71. (From there it was taken into the discussion of Korzen's article, by Captain Wangemann, quite recently in Kriegstechnische Zeitschrift, VIIth year, 1904, pages 158 to 160.)
In Von Kretschmar's monograph, the original text of which he kindly lent to the author, there are remarks which, though short, seem to strike the true core of the matter. These remarks, according to Von Kretschmar, are founded on "observations made in actual shooting of four batteries in two years' courses and verified by the target reports." Von Kretschmar says (page 1 of his monograph): "Uniform and satisfactory aiming can only be obtained, if the apparatus for aiming attached to the gun furnishes the requirements and will not itself cause inaccurate and uneven aiming. The latter will and must be the case with all sighting apparatus allowing to the individuality and unreliability of the gunner a certain influence on the accuracy of every single aiming." Probably the authors of the American and the English handbook had something similar in mind when they described "the diminution or elimination of the personal error" as one of the advantages of telescopic sights.
Looking at these conditions somewhat closer shows that the problem consists in the discussion of and answer to two questions of widely differing character but equal importance for the practice, viz.:
1st. What uncertainty (inaccuracy) results with open sights from the fact that the human eye is unable to perceive at the same moment distinctly the sights and the target? and
2d. Are there factors in the human eye which, in aiming with open sights (i. e., looking simultaneously at objects at different distances), will produce a regular one-sided error as to direction of vision?
The difference in meaning of these questions is evident, considering that uncertainty may to a certain degree diminish through practice; but one-sided error in the eye will, through such practice, only be recognized more clearly, as is well known from the practice of astronomical and other art of measuring.
In the present case—not by far in all cases—it is very fortunate that the same means which relieves the uncertainty also eliminates the personal one-sided error.
I. UNCERTAINTY IN AIMING AS A CONSEQUENCE OF THE DIFFERENCE IN DISTANCE OF REAR SIGHT, FORE SIGHT AND TARGET FROM THE EYE.
It is easy to calculate the amount of this uncertainty.
A being a section through the middle (P) of the pupil (P' P") of the human eye focused and aiming at the target (Z). Distinct images on the retina will then appear only of objects near the target, i. e., relatively very distant objects. Points at closer range, for example the top of the fore sight, will give indistinct images. Instead of calculating how these are shaped on the retina it is simpler and more practical to find out how such indistinct images appear to the observer. Of course he perceives them as projected on the plane to which his eye is focused, and every point of the objects in the "extrafocal" plane as a "dispersion circle," a dim small disc whose center is in the connecting line of the object point and the middle of the pupil, or its prolongation, and whose circumference is determined by the geometrical projection of the Pupil on the focused plane, the object point as center of projection. So, if the top of the foresight (K) is connected with the rim of the pupil by lines KP' and KP" and these lines prolonged beyond K to the distant plane of the target, their dispersion there will show the size of the little disc representing the top end of K as it appears in an eye focused on the target.
This determination holds good in every sense. It gives in exactly the same manner the dispersion circle (disc) for every point of the rear sight as it appears in the plane of the target; also the dispersion images of target and rear sight, in an eye focused on the fore sight, and those of the target and fore sight in an eye focused on the rear sight. In the following the three cases, in which the eye is focused on target, fore sight and rear sight, will be called (a), (b), (c) respectively.
For instance, the same drawing which in case (a) gives the dispersion figure of K in the plane of the target, serves in case (c) to give the dispersion figure of K in the plane of the rear sight (V). The intersection of lines KP' and KP" with the vertical plane through V outlines the dispersion image of K when the eye is focused on V.
It may justly be objected that the parts of the sighting apparatus do not consist of separate points, being solid objects, and that the dispersion circles, covering each other to a great extent, will make a relatively clear impression on the eye with only indistinct outlines. This is correct and is easily proved by using the above equation for all points in succession. It is preferable instead of such calculation, to show to the reader its visible result by photographic representation.
For this purpose an artificial eye has been used, whose pupil opening could be adjusted to an accurately defined size, and whose retina is replaced by photographic plates, in other words, instead of the eye a camera was used. With this artificial eye photographs were taken of a sighting apparatus, which the Krupp Company in Essen, through Colonel von Kretschmar, lent to the author, and in which an open sight with cross-wires and another with a notch could alternately be put at exactly 1 m. distance from the point of the fore sight.
This instrument was aimed at an object, about moo meters away (spire of the "Landgrave House" near Jena) and photographs were taken with different focusing of the artificial eye—on the target, the fore sight and the rear sight—and with different pupil openings-2, 3, 4 mm. The photographs were made under a covered sky to avoid a one-sided illumination of the sights, and they have been reproduced in the following illustrations of such size that seen from a distance of 220 mm. they will give the same impression regarding the relative size of the objects represented, as when observed by the eye of the pointer. The illustrations show only the pictures obtained with 3 mm. pupil opening focused on target, fore sight and rear sight, for a notch sight and for a cross-wires sight. For comparison the drawing has been added by which aiming with an open sight is usually explained (Figs. 2 and 3). These illustrations, whose truth to nature is guaranteed, speak a language more eloquent than words.
Involuntarily the question arises, how is it possible to produce from such images, such visions, a direction of sight as distinct and accurate as actually obtained.
Two possibilities seem plausible. Either our eye focuses itself in rapid succession on target, fore sight and rear sight, and by comparing the remembered perceptions forms a judgment as to the direction; or our eye in aiming uses none of the pictures here shown, but unconsciously focuses itself on a mean distance between target and fore sight, at which the inaccuracies of all three of them is best equalized. It would be hard to find out which of these possibilities is the true cause.
In a correctly focused telescope, target, fore sight and rear sight are projected into the same plane. In the focus plane of the objective glass appears a sharp image of the target and is seen there together with the sharp image of the cross-wires through the magnifying ocular lens. Fig. d on the plate shows a photograph of these images as seen in a Krupp-Zeiss telescopic sight magnifying three times. d' is a picture of the same target as it appears in a telescope without magnification.
In Grubb's sighting apparatus, not the real image of the target is projected on a real cross, but, on the contrary, the virtual image of a real cross is projected on the target remaining in the distance; and through a semi-transparent, semi-reflectant glass plate they are simultaneously presented to the pointer's armed or unarmed eye. The appearance as to the distinctness is the same as in a telescope, only the cross is bright, and there is no enlargement for the naked eye. The above leaves no doubt any longer that aiming with either of these sighting apparatus is far superior to aiming with open sights. (The relative advantages and disadvantages of the Grubb apparatus and the Krupp-Zeiss telescopic sight do not enter the subject of the present article.)
II. THE ERROR IN THE DIRECTION OF AIMING CAUSED BY THE PECULIARITIES OF THE HUMAN EYE.
The peculiarities of the human eye as an organic apparatus have been ignored until now. In this theoretical deduction of the relative measures it has been assumed that our eye is a perfect Optical instrument, and accordingly optical instruments as perfect as at present obtainable have been used for graphic demonstration. In this way have been found the typical and general qualities of the phenomena under discussion, but not yet the particulars depending on the peculiarities of that special instrument, the human eye, which has to be used.
It may perhaps be claimed as the most general peculiarity of all human organs, or all organic apparatus, that though their special object is often reached in an admirable and marvellous way, they are suited for this only and no more. Their structure and functions, fit for their special purpose and just sufficient for it, does rarely satisfy further claims lying beyond their task.
Now the human eye is justly lauded and admired for its marvelous aptitude for the perception of visible phenomena. Taking this ability in its totality, nobody could think of artificially producing such an organ. But in its particulars certain defects are discovered which are avoided, even easily avoided, in an artificial apparatus. Helmholtz, on the basis of his own subtle investigations and those of earlier scholars, has stated that the refracting surfaces of the optical apparatus in our eyes are not perfectly spherical, not even parts of accurate rotation surfaces, that their axes do not coincide among themselves and with those of the diaphragms or with the line of vision, and that the entire composition of this optical apparatus does not satisfy those fundamental requirements as to the production of the image which are fulfilled by every artificial instrument (compensation of the chromatic and spherical inaccuracies of the image, and so forth).
Generally, i. e., with sound normal eyes, these deviations remain within such limits, or compensate each other so favorably, that the task of our eye, viz., the perception of outside objects as visible phenomena, is reached in the satisfactory manner known to everybody. But the simultaneous perception of objects placed one behind the other in different ranges from the eye, as demanded in aiming, is beyond that task. Our eye is "not suited" for this purpose. Only by successive accommodation (focusing) on the several objects will our eye furnish us images of satisfactory sharpness without exertion and in rapid succession. Inaccurate pictures, consisting of dispersion circles, of objects on which our eye is not focused, aside from that inaccuracy, are possessed of certain specific defects which will occasionally be fatal to correct aiming, by one-sided errors in direction.
Before discussing the cause of this phenomenon, some facts must be stated, which in part are known to everybody, and in part can be easily experienced. As a most important fact, directly concerning our theme, is to be mentioned, what Colonel von Kretschmar states as a result of his observations on the shooting range, viz., that there are pointers who always, i. e., with every gun, whatever its aiming apparatus and its eventual inaccuracies may be, make an error in direction to one side. (An individual error in elevation can, of course, not be verified because of the possibility of using an open sight with a notch, at "full sight" or "fine sight" instead of "half sight.")
Furthermore, every nearsighted or very farsighted person knows that the moon's crescent, which ought theoretically to appear as one indistinct semicircle, is seen instead as an aggregation of several relatively clear semicircles displaced to right and left.
Simpler still, and therefore more convincing, is the result of a test which Helmholtz describes in his "Physiological Optics" (2d edition, Hamburg and Leipzig, 1885 to 1896, page 170), and which everybody may easily repeat: make a pinhole in a black cardboard and in a dark room hold it against a bright light at such distance from your eye that it cannot be seen distinctly; if nearsighted hold the card further away than your range of clear seeing; if farsighted approach it below that range; if normal make your eye artificially nearsighted by using a convex lens of several dioptries (f = 200 to 400 mm.; objectives of opera glasses usually have a convexity of 5 to 7 dioptries) and proceed as if nearsighted.
The theory of this experiment for a perfect optical instrument (photographic camera) is very simple; instead of the pinhole there ought to appear a smaller or larger disc of even brightness. In fact, as the picture (B) (Fig. 4) of a luminous point (L) appears before or beyond the sensitive plane (N N) (Retina, dulled glass, photographic plate) a dispersion figure (L' L") will appear on it, resembling in all parts the opening in the screen (pupil, diaphragm), and whose dimensions are in direct proportion to the focal difference (N B) and the size of the opening (P' P") in just the same way as shown above for the appearance of the fore and rear sights. As our pupil is approximately circular, we would be justified in expecting to perceive a small equally bright disc (E). We see this whenever we take a photographic camera with a reasonably good objective in place of the eye. Our eye itself, however, shows something different, varying from one individual to another and also from one eye to the other in the same individual. Helmholtz draws it for his left eye, as in fig. 5.
Fig. 5a, being the appearance with eye focused on a near object, Fig. 5b, with eye focused on a more distant one. Instead of the little disc of even brightness there appear several (usually 4 to 8) smaller ones grouped more or less symmetrically round a central one. The axes of symmetry of the figure differ with different persons, and are at different angles with the horizontal and vertical. The several luminous discs or specks show more or less of a tail. "As long as the light is faint, we see only the brightest parts of the phenomenon, and several images of the brightest point, one of them appearing brighter than the others. On the other hand, in case the light is very strong, for example, where direct sunlight falls through the pinhole, the rays of the star will flow together, and all around will appear a crown, much larger, of countless very fine lines in all colors." (Helmholtz.) (Anybody who should find it difficult to observe this phenomenon, which is beyond his range of accurate sight, ought to " glare " or look at it half dreamily. Otherwise desperate attempts of the eyes will ensue to see the cardboard clear, often causing pain and in all cases failing.)
As a third demonstration will serve the experiment, which W. C. Röntgen described in 1894 (Wiedemann's "Ann. der Physik und Chemie," N. F., Vol. 52, pages 589-92). Take an angular mirror of exactly 90 degrees with faces well meeting, i. e., with a very narrow, yet not quite disappearing edge (K) (Fig. 6). It will be best to use a good right-angle glass prism, through whose hypotenuse surface (H), one looks towards its side surfaces ( W' W") which act as mirrors with total reflection. The observer then sees his own eye and at first thinks it is a simple reflection, but on closer examination he finds that right and left are not reversed as in a mirror, but that he sees its correct image only turned around (K) by 18o degrees. It is easily understood that every point of the image is obtained by drawing a line at right angles from the object point to the edge K and doubling its length; in this way points P, P P, of the pupil are pictured in P'1 P' P’2.
The edge (K) of the angular mirror remains as a real object steady between the pupil and its image, independent of eventual movements of the eye sideways or forward and back, always exactly in the middle between pupil and image, and also exactly in the plane through both—the horizontal middle plane when the edge is held horizontal, the vertical, when vertical.
These peculiar relations, absolutely accurate, make this experiment well suited to explain the theory of aiming. The analogy is apparent the edge represents the fore sight which, from the fixed position of the eye, is projected on the reflected image of the eye representing the target. Again, it is easily computed how the edge ought to appear were the image of the eye seen distinctly, and how the image is seen in fact when in place of the human eye a camera is used in the experiment: Instead of a sharp (supposing it is bright) a diffused broad band would spread over the picture of the pupil, of uniform dim brightness and just as wide as the picture, exactly covering it.
Fig. 7 is the reproduction of such a picture as produced on the sensitive plate by a photographic objective. Again the appearance in the eye is quite different; instead of one band of diffused brightness several more or less clear lines parallel to each Other are seen, one of them, brighter than the others, absorbing usually the observer's attention, who, neglecting the others, takes this one for the only picture of the mirror's edge.
Now it ought to be expected for theoretical reasons that this prominent picture of the edge would exactly halve the picture of the pupil, horizontally or vertically, as the angular mirror may be held. This is, however, as Röntgen states, generally not so. With some persons the vertical line is nearer the nose, with others nearer the temples; the horizontal with some persons is too high up, with others too low &Am. This deviation is stated as of different size by different persons, and undoubtedly perceived so. With some persons the anomaly is nil. This test by Röntgen furnishes an excellent explanation of the theory of aiming by fore and rear sights, the conditions of the test being especially simple and to be determined with absolute accuracy and not to be disturbed. No kind of carelessness or lack of attention can influence the accuracy of the test; the angular mirror automatically corrects the conditions and even an inaccuracy in its angle '(more or less than go degrees) will only make the observation slightly more difficult, but will not diminish its accuracy.
The explanation of Rontgen's experiment—which its originator sought in vain 2—is, the author thinks, to be derived without difficulty and is perfectly consistent with and similar to that of Helmholtz's experiment from the so-called "irregular astigmatism" of the eye. The edge of the angular mirror is nothing but a linear repetition of Helmholtz's pinhole, the phenomenon in the one case only an integration of the one in the other.
The phenomena of "regular astigmatism" or simply "astigmatism," of the eye as well as of artificial optical apparatus, are well known. With our eye they are shown most conspicuously in that the rays of a star-shaped figure * do not appear equally sharp; one direction is specially favored, the one at right angles to it specially neglected. A change of the state of focusing of the eye makes these main directions or "meridians of astigmatism" reverse their parts: the meridian dimmest before changes into the clearest, and vice versa. The cause for this is that the refracting surfaces of the eye, especially the cornea, are not regular rotation surfaces around the axis of the eye as axis of rotation, but in one meridian have a greatest and normal to it a smallest curvature, like a rotation surface, say an egg of plastic material, which has been slightly deformed by one-sided pressure. Consequently the rays will meet sooner in the meridian of greatest curvature than in that of the smallest. Such an eye, strictly speaking, receives two images of every point (which explains the term "astigmatism," from a and arcria, literally "pointlessness.") Practically every eye is astigmatic in a small degree, because the refracting surfaces are in no eye perfect rotation surfaces. But astigmatism of less than one-half dioptry is hardly perceptible and oculists do not consider it as pathological.
Irregular astigmatism does not consist in a regular systematic deformation of the refracting surfaces in the eye, like an egg under one-sided pressure—mathematically speaking a three-axed ellipsoid—but in a relatively irregular one, producing accordingly a "scattering" of the rays which form the image, into several bunches more or less separate from each other. On close examination the crystal lens of the human eye shows a peculiar texture and condition of its surface (Fig. 8). While the cause for regular astigmatism is found nearly exclusively in the cornea, the texture of the crystal lens causes the irregular astigmatism.
The crystal lens does not descend uniformly from its center, but there are, so to say, hill ranges, six in number, separated by as many valleys—very shallow ones of course—running radially from it. These hills and valleys are not even quite smooth like well-polished glass lenses, but show fine grooves, the lens consisting of fine fibres. It is evident that every lack of uniformity in the shape of texture must result in adequate irregularity of the image. And so even an excellent eye will not perceive a bright star as one point of light, but with "tails," as a center of nimbus of rays; wherefrom we derive our definition of the word "star" and "star-shaped." With regard to these conditions, Helmholtz, whose thoughtfulness in judgment is as much beyond suspicion as his authority, made the statement, grown famous since and often quoted (Cfr. " Die neueren Fortschritte in der Theorie des Sehens," Preuss. Jahrb., 1868, reprinted in "Vortrage und Reden von H. Helmholtz"): "Now it is not saying too much, that dealing with an optician who would try to sell me an instrument having the last-named imperfections, I should believe myself perfectly justified in using the strongest words as to the negligence of his work and in refusing to accept his work."
Helmholtz adds prudently: "Concerning my own eyes, of course, I should not act that way, but on the contrary be glad to keep them with all their shortcomings as long as possible. But the fact that though defective they cannot be exchanged for better ones, evidently does not diminish the amount of what from the viewpoint, one-sided but justifiable, of the optician, we must call their defects."
With less marked objects, not standing out as bright and isolated on a dark background as the stars, the irregular astigmatism does not interfere with distinct perception and localisation, i. e., with the task of the eye, as long as it is well focused on these objects—either by the natural accommodation of the eye, or by the assistance of spectacles. However, in such cases where an object, on which the eye has not been focused, must still be observed, as in the above experiments of Helmholtz and Röntgen, and especially the "experiment" of aiming with fore and rear sights, the effect of irregular astigmatism is fully recognized and changes the normal character of the result. A bundle of rays emanating from a luminous point, in the shape of a cone, because entering the eye through the circular pupil, will if "stigmatic," or as called in optotechnics "anastigmatic," unite after refraction in one point, the focus. When caught before its union upon a screen, wherever the screen is placed will mark a regular, uniformly illuminated circle. The same bundle deformed by irregular astigmatism (as long as not at the same time influenced by regular astigmatism) will in general also unite in one image point, the focus (F). But caught before or beyond the focus it shows an irregularly shaped and unequally illuminated figure. This dispersion, not being regular and uniform around the center, produces an irregular effect, varying from person to person. Sometimes it is one part of the bundle, sometimes another, which prevails in the final effect, often none of them, so that the strongest illumination will remain in the center.
The perception of objects on which the eye is not focused is often facilitated by irregular astigmatism. If the object consists of lines, wire et sim., the effect of the single secondary images of each point will accumulate so that several full images will appear—the moon's crescent, the mirror edge with Rontgen's experiment—and if one is found among these predominating in brightness and clearness, that one will be perceived as the image of the insufficiently focused object, and all the others ignored. In this way a much more distinct and clearer impression is obtained than from an image consisting of equally dim dispersion circles. Perhaps this might be considered by some as a "useful defect" of our optic. But the reverse of this usefulness lying too near, the distinctness of perception is to be paid for by more or less of an error in localisation, unless, so to say by accident, the prevailing picture lies in the "optical center of gravity" of the bundle of rays. Such is undeniably proved by the Röntgen experiment.
The mere fact that dimly seen points will not appear in the center of their geometrical dispersion circle does not yet constitute an error in the direction of aiming. For, if a lateral movement would affect all objects in the line of vision uniformly (i. e., by an equal value of angle), the foundation of the usual theory of aiming would remain, viz., that 3 points lying actually in the same line would so appear to an eye in the prolongation of that line. The direction of vision only would be slightly altered.
But unfortunately the lateral movement is not uniform. Helmholtz's dispersion images of a point in and outside the focus show that the distribution of light in the dispersion image is considerably altered. The texture of the bundle of rays between the lens of the eye and the retina is by no means regular, or, to word it more accurately, the deviations from the fundamental cone are so irregular, that the rays group themselves in a steadily changing manner into a number of partial bundles. In consequence, in one cross-section of the bundle—corresponding to one distance of the object—one partial image prevails, in others—corresponding to another distance—another will prevail; and these partial images, which, as said above, are perceived, as the images, are perceptibly deviated from each other in direction as well as elevation. The amount of the error in direction of vision certainly depends on the shape of the sights. With massive objects the one-sidedness in general will appear less distinctly than in the alleged tests with mere points and lines. Strictly speaking, for every separate shape of the sights an integration of all the points of the image ought to be made to get at the whole. But in practice the conditions of illumination will have very great influence. In an open notch-sight the horizontal upper edge and one of the oblique edges of the notch will be brightest and therefore of more influence on the total appearance. The reflection of the sky from the fore sight will make one side of it appear brighter. (The fact that this uneven illumination of parts of the aiming apparatus is an additional source of error will not be further discussed here; it has often been justly pointed out by others.) With a crosswire sight, even under diffused light, the individual lateral error of the eye will also influence the result.
Vision under conditions such as in aiming with rear and fore sights is so to say against nature. Our eye is only made, only fit to see objects clear and at the same time in their correct place at one distance; those at perceptibly different distances will be seen either dimly, inaccurately, or less dimly in a wrong place, a wrong direction. The telescopic sights (and the Grubb sight) avoid this defect in principle by placing the target and the parts of the sighting apparatus (reduced to cross-wires or similar marks) in the same plane, the same distance from the eye. The natural defects of the eye are thus eliminated, its ability to see and aim are used rationally. Therefore these instruments are preferable to the open sights even if, as in Grubb's instruments, there is no enlargement of the image. For optotechnical reasons essentially an enlargement of more than one has been chosen; it seemed so to say unnatural to make telescopes without enlargement.
As to the advantages of telescopic sights, probably all experts agree that the suspicions which were formerly expressed against too great weight, great length, and particularly too small field, are void since prismatic telescopes were introduced.
"It must not be supposed, however," says Alger, "that all these great advantages can be attained at once and without accompanying disadvantages and sometimes mistakes. In the first place it was very difficult to obtain a telescope of large field and yet otherwise satisfactory, and those first issued had a field of only 4° which is entirely inadequate. With such telescopes, the ordinary rolling and pitching throw the target completely out of the field of view, as does also a small relative lateral motion, and this makes it extremely difficult to get the image of the target at the cross-wires. The telescopes now issued, however, have a field of 17°, which makes pointing easy, since the target remains in the field of view when the rolling is very heavy." Von Kodar, page 718, expresses himself similarly: "The field of a telescope ought to be at least large enough to prevent the gunner from losing the target from his field of view while the ship is rolling, as long as in the mean position of the ship the optical axis meets the target. The limits of rolling within which artillery can be used to advantage are not very wide; 6° to each side may be considered the extreme. An instrument with from 12° to 14° field therefore will be sufficient, although with modern arrangements angles of view up to 200 and more can be obtained." Beside the chief ad vantage of a large field, that the target may always be kept in view, there is the further important advantage, that the gunner can observe the hits of projectiles through the telescope, enabling him to judge of the place and effect of the hits, etc., better than with his naked eye." Also, page 724, he says: "The field of view of the ordinary terrestrial telescope is very small, considering its great length and small ocular glass. The latest designs, however, show astonishing improvement in this respect." And pages 733 to 734: "The adoption of telescope sights means an essential progress in ordnance, because by this means only, full use of modern guns regarding precision, efficiency and rapidity of fire can be obtained. Aiming in itself will be facilitated, therefore correct aiming will be easier, and the results of firing increased in consequence."
"It is probable that on the strength of such experience the ranges for firing will grow, yet, with guns provided with telescope sights, a range of say 6000 m. will not mean more than does now a range of from 2000 to 3000 m. A new era confronts us, in which sea fights instead of being decided at close range, will be fought, if not decided, on ranges hitherto not thought of."
Even the perfectly free field, with only its cross-wires, has indisputable advantages over the use of the open sight, where the notch covers half of the field. The easily effected illumination at night (by changing the black cross-lines into white ones appearing on perfectly dark ground) is another advantage. And such is the enlargement in the telescope, although limited (from 2 to 6), by which a more distinct perception of the target is gained, (see the illustrations d and d' on the plate) and a better observation of the hits and results of hitting.
The intensity of light in a modern sighting telescope with a "pupil of egress" of 5 to 7 millimeters will answer to all requirements.
The opinion is often beard that, beside the ocular, the objective glass also ought to be focused on objects at different ranges. Regarding this Von Kodar says in his book, page 717: "With smaller ones" (meaning telescopes) "the focal distance of their objectives being short, such an appliance is unnecessary because the images of objects at different ranges always fall in practically one plane, the focal plane of the objective." Indeed, with an objective of too mm. focal distance, a difference of 0.1 mm. would only result, if the object was as near as 100 meters; with an objective of 150 mm. focal distance, only at 225 m.; with one of 200 mm., only at 400 m. distance. Focal differences of 0.1 mm. cannot be recognized with the usual oculars (one dioptry in field glasses corresponds to 0.4 mm. displacement of the ocular), so with hand telescopes a change of focus is not needed as long as they are not used for considerably shorter distances than given above. Whether with guns the telescopic sights should have a focusing apparatus to help abnormal (nearsighted or farsighted) eyes of the pointers is a mere question of practice, on which opinions of military authorities differ. From the maker's viewpoint it must be said that the less there is adjusting movement, the less any disarrangements are to be expected.
Von Kodar's saying that the Grubb sight avoids "the influences of parallax which eventually are felt with telescopic sights" is as incorrect as his similar statement regarding "the limitation of the field." The distance between the mirror or objective, which changes the bundles of rays diverging from the cross into parallel rays, to the cross itself, is just as influential for an eventual parallax in Grubb's sight as the distance between the telescope objective and the cross-wires which should be mounted exactly in its focal plane. Also regarding the field, "it is provided that the trees shall not grow into the skies," which is easily shown. Probably a larger field than in the Grubb sight has never been reached, though a number of patents try to furnish means for a large field. It is true that the eye of the observer may freely move within certain limits without causing the slightest inaccuracy in the sighting. But this is equally true for the telescope, for here as well as there, not more nor less, "the eye is bound to one certain point in the optical axis of the instrument." For the mere perception of the target with the Grubb sight the eye has, though not complete, yet very ample freedom; but to see the cross at the same time, the eye must be reached by the bunch of rays issuing from it, and its opening is equal to that of the lens or mirror projecting the cross into the distance.
Ignoring the great analogy in the composition of Grubb sight and telescope, expectancies as to the merits of the former have evidently gone too far.
Among the several proposed designs of prisms the oldest, Porro's crossed prisms (amply described by Von Kodar, page 727 to 9), recommends itself by its simplicity and corresponding cheapness. The use of two separate elementary prisms results in a loss of about 8% of light, which may in most cases be ignored. It might also result in an inconstancy of the adjustment. But it has been shown by careful tests under high strain, for instance by the Swedish artillery, that such is not to be feared.
The so-called "pentaprism" which Von Kodar recommends as the best, does not deserve its praise for reliability and constancy; it is "of one single body" on paper only. In practice it can only be made of two pieces; there is perhaps a small gain in brightness (avoiding that 8% loss mentioned above) because the two parts touch and can be cemented; but no gain in rigidity. Cementing gives hardly any security for invariability of mutual position, when under such strains as in the present case.
The same is true of the system of prisms used in the telescopic sights of the United States navy.
A distinct progress in this direction was only made when the firm of Carl Zeiss produced those prisms actually consisting of one single piece which are used in the telescopic sights of the Krupp Company.
As a last objection against telescopic sights, it has been said that, although the perception of the target is improved, there is not the same stability of the correct sight line.
The sight line of open sights is determined as the line between the rear and fore sight; that of a telescope as the line from the center of the cross-wires to the rear focus of the objective lens. (Only this line can be called the "optical axis," or rather takes its place, in all telescopes for aiming or fixing a direction.) In the former case the two points whose connection indicates the direction, are 60 to 100 cm. or even more apart, in the latter case often less than mo mm. It is argued by some that the security against error in direction is in direct proportion to this distance. From a merely geometrical viewpoint such reasoning is undoubtedly correct. A lateral change of rear or fore sight, say for I mm. will alter the direction only about one-tenth as much as the same change in the relative position of cross-wires and objective lens. Yet the conclusion from the argument is erroneous; for, the probability of a lateral change of position of the said parts in a telescope is less than one-tenth of that in an open sight. And this is proven, not by argument, but by experience and explained by referring to the fact, that a small closed instrument is much better protected than one whose parts have to be fixed separate. Experience of rather long standing has made it evident that the adjustment of telescopic sights, even when fast on the gun itself and remaining in place during the firing, not only has kept as well, but according to the greater strain by enlargement, several times better than that of open sights. This is also indirect proof that the connection of the telescope with the sight and of the sight with the gun will, if properly made, satisfy all requirements.
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While the above was written there appeared another article treating of the same subject: Rosthoten, first lieutenant in the German 58th regiment of field artillery ("Jahrbacher far die deutsche Armee und Marine," No. 392, pages 571 to 581), speaks in the same sense, saying: " Spirit level and sighting telescope are bound to be the foundation for all future designs of aiming apparatus for field guns."
On page 580 the same author mentions that doubts have been expressed as to the solidity of telescopes, and states, against such objections, that they have been introduced in the German siege and fortress material after the severest tests, and also after exhaustive trials in the artillery of Switzerland, Sweden, Denmark, and Turkey. Roskoten draws from his arguments the following Conclusions:
"The aptitude for war use of the telescopic sights now offered by the makers is beyond all doubts.
"In spite of the apparent complication of the apparatus the drill of the pointing gunners is simplified and the quality and uniformity of sighting brought to high perfection."
The results of careful practical tests of the comparative accuracy of aiming with and without telescope would be more interesting and convincing than all the more or less theoretical arguments above. The programme for such test offers no difficulty; but the author thinks he himself lacks one condition for making such tests—finding it necessary that the pointers in the test ought to have full practice in both kinds of aiming and to be ignorant of the object of the test. Perhaps these lines will induce an officer in actual service to make the test. It will only be necessary to find the average error, and the probable error, easily computed from a number of single aimings towards the same target by the same pointer, using the one and the other sighting apparatus. Of course, a variety of targets, of illuminations, etc., will be tested and different persons serve as pointers to obtain results free from objection. The enlargement by the sighting telescope ought to be considered separately.