Before describing the proposed improvement, I shall quote Mr Bow's calculations regarding the unequal distribution of light throughout the picture, as given by a non-distorting lens. The rule, as laid down by him, is, that a doublet lens, fitted with a small stop between the lenses, will give an illumination of the image varying approximately as the fourth power of the cosine of the obliquity of the direction of the object; but as this rule does not give, at first sight, a very comprehensive idea of the variation in the illumination, it will be more easily understood by a reference to the results in figures, as in

To equalise this irregularity at the various points, I propose to increase the amount of opening in the stop, proportionally as the light or its effect diminishes, in order that the useful illumination may be nearly equal throughout; and to accomplish this, I first reduce the amount of light in the centre, by placing at a short distance, either before or behind the stop, a vertical bar, about half the width of the stop, cutting out more than half of the light, which would otherwise reach the centre of the plate, and forming the image there by the light which passes the two segments of the stop. By a proper arrangement of the size and position of the bar, the sum of these segments increases with the obliquity very nearly at the rate which is required for equal illumination; and if, as suggested by Mr Bow, the stop be made of a lozenge shape instead of a circle, with a bar onehalf of the width across the corners of the stop, and so placed that one-half of the stop is uncovered at an angle of 323°, or a width of view of 651°, the error at any point within that limit is reduced to less than 1 per cent.

The application of the bar will be seen by a reference to fig. 1, which represents a horizontal section of a Darlot's doublet lens. The stop is placed between the lenses at a, and the bar in front of it at b. c represents a pencil of rays

from a point in the centre of the view, which in its passage through the stop has its central part cut away by the bar at

d

Fig 1.

b, so that the image is formed by the union, at the focus, of the two segments dd of the pencil of rays. As the obli

Fig. 2.

quity increases, the two segments of the pencil vary in size, one diminishing until it disappears, and the other increas

Fig. 3.

ing, the sum of the two gradually increasing until at the side of the view, where the image is formed by the pencil e

partially reduced by the bar to the width shown at f, where it is of such an increased area, compared with dd, as to give about one-half more illumination than at the centre. The different appearances of the round stop in the centre and at the sides are seen in fig. 2, and of the lozenge-shaped stop proposed by Mr Bow in fig. 3.

Table II. exhibits the results of Mr Bow's calculation regarding stops and bars, adjusted to give equal illumination at the centre, and at certain definite angles, and shows the amount of error at intermediate angles.

This table shows that, with a round stop it is possible to obtain an illumination, as in example No. II., over a width of 60° with no greater error at any point than a loss of 1 per cent.; while in example No. IV., with a lozenge stop, the illumination over 65° has no greater error than an increase ofths per cent. for the 10° and 20° pencils.

The central portion of a lens will give good definition with a stop of any form, as is shown by the fact of the bar not preventing definition there, although the image is formed by two segments of the pencil of rays. But it may be of consequence to condense the pencil of oblique rays, so as to keep it as nearly circular as possible; and it may be an objection to the use of a circular or diamond-shaped stop, that in the one case we have nearly a semicircle, and in the

other a triangle, as the section of the pencil of extreme oblique rays. This evil, if it can be called one, may be partially corrected by using an ellipse for the shape of the stop, with the larger axis horizontal, and adapting the bar to it as if for a circle of that diameter.

In photographing clouds, it is useful to reduce the action of the light at the upper portion of the picture—that is, the lower portion of the plate in the camera, and the vertical bar gives the means of doing this in a very simple manner, to any required extent, by making the bar wider at top than at bottom, so as to allow a larger proportion of light to pass the stop from the foreground than from the sky. This arrangement is shown in fig. 4.

Fig. 4.

Although I have supposed the bar to be placed in front of the stop, it may be placed behind it; and as the section of the pencil of rays varies in relation to the side of the lens in the two cases, one having the straight side, and the other the curved side towards the edge of the lens, there may in some cases be a small difference in definition between the two methods, but it must be so small as to be of little or no consequence in practice. It will be observed, however, that in the tapered bar, its broadest end is at the top when in front of the stop, and at the bottom when behind it.

In adapting the bar to an existing lens, it will be seen, by a reference to fig. 1, that when the stop is in the ordinary position, the addition of the bar has the effect of keeping the useful portion of the oblique pencil further from the edge of the back lens than if the whole opening of the stop were used; so that if it be necessary to use the greatest possible width of the back lens to obtain flatness of field, the stop ought to be placed a little nearer the front lens when the bar is before it, or a little nearer the back lens when the

bar is behind it. In the former case, the alteration in the position of the stop will have the effect of slightly increasing the angle of view embraced by the lens.

Although of less consequence as regards single view lenses, the bar may be also applied to them with advantage.

Description of a Combined Optical Square and "Line Finder." By JAMES M. BALFOUR, C.E., F.R.S.S.A., Otago.*

In marine surveying especially, it is often very desirable to be able to run on a straight line between two objects, and the instrument submitted to the Society is intended to facilitate this. It consists simply of two mirrors at right angles to each other. Any two objects seen in contact in the two must, if the mirrors be properly adjusted, be in line with the observer, or rather with the instrument. The third mirror has been added to enable the same instrument to be used as an optical square also. It is convenient, but not essential.

I am aware that similar instruments have been already made, but none have been constructed in so compact and convenient a form, the absence of all external machinery, which so greatly increases the field of view, being, I believe, new. I have already made and worked with a little instrument of this form, and found it to answer well; but even in this form the small field was found to be an objection, as when off the line it was difficult to pick up the second object. To overcome this objection, it occurred to me to make one of the mirrors a portion of a convex cylinder, so that the coincidence of the images at the point of intersection would still indicate a straight line; but when off the line, even to some distance, the second object would still be seen in some part of the curved mirror, and its position in the mirror would also show on which side of the line the observer was.

* Read before the Society, and instrument exhibited, on 10th December 1866. Awarded the Society's Silver Medal.

VOL. VII.

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