was exchanged for a white wall, and the hairs were seen at a distance of 113 feet. Just about eleven o'clock the sun lit up the horizontal hair with a brilliant glow, and then an image, formed by it, was distinctly seen at the great distance of 173 feet, but the appearance was not at all hair-like. It was far too broad, and not sharp at the edges. The opera-glass did not make it look like a hair, but left no doubt that the hair caused the image, and that the image corresponded with it in position and length. A pencil was then held over the horizontal hair and seen with the opera-glass, without distortion. As soon as the sun's motion carried it from the most favourable position for lighting up the hair, it ceased to give any image visible at a long distance.

In experiments with hairs attached to a window-pane, it will be found that the quantity and direction of the sunlight, and the colour of the background, and its degree of illumination, all affect the apparent diameter of the hairs. A diffused rain-cloud with a good deal of white light in it, gives a small diameter, and very sharp definition. Taking this as the most correct aspect of the object, any change of conditions which makes it look broader must be regarded as introducing optical errors, and it may be remarked that when, after viewing a hair two or three feet off, it is viewed at 15, 20, or 30 feet off, it does not seem to have its diameter diminished, as would result from perfectly accurate vision.

So long as the image seen by the eye corresponds tolerably well with the true aspect of a hair, it is fair to say, "I see the hair;" but when such aspects are afforded as in the experiments with full solar illumination the hair is not seen, but only the effect of its reflexions and refractions on the solar beams.

If an observer, seeing this appearance, concluded that the frame had a band across it in a central position, he would be right; but wrong if he attempted to estimate its breadth, or to decide upon the nature of the substance composing it. This is a case of a kind of vision giving some information that corresponds with fact, coupled with other information that differs widely from fact; and an inquiry suggests itself whether a good deal of vision obtained with high powers and peculiar illumination does not partake of this character.

On the 12th November, the sunshine being brilliant and air clear, the experiments were repeated. At 10 A.M. both hairs were sharply seen at 105 feet, without distortion. At 10.12 the horizontal one was seen at 110 feet, and at about 115 feet twelve minutes later. The sky then became hazy, and the hairs invisible at the long distances.

About four o'clock on the 11th November, when walking up a hill two or three miles south-west of East Grinstead, the vanes standing above the angles of the four square towers caught the

sunlight and gave the appearance of a broad golden band suspended in the air above the tower. The vertical diameter of this band far exceeded the optical angle under which the vanes would have appeared if it had been possible to see them correctly with the naked eye; but there was no error of position, and the grouping of the vanes in one unbroken line simply arose from the distance being too great for the interspaces between them to be noticeable. In such a case what is seen? Certainly not the vanes, but a welldefined optical image differing considerably from them. The noncorrespondence of this image with fact was inferred partly from the observers having seen the vanes at a short distance, and partly from the improbability that anyone had suspended a broad gilt band in such a situation. Had there been no knowledge of the real structure and no improbability in there being a broad gilt band over the tower, the optical appearance might have led to a belief in its existence. May we not suppose that microscopists are sometimes in danger of being misled by appearances they have no means of bringing to any decisive test?

III.-On the Measurement of the Angle of Aperture of Objectives. By F. H. WENHAM, F.R.M.S.

(Read before the ROYAL MICROSCOPICAL SOCIETY, November 13, 1878.) IN arranging in the form of a paper, some recent investigations on this yet undecided question, I have no desire to maintain a controversy that has at times appeared as one of personal feeling instead of scientific reasoning. The facts cannot be established by a majority of opinions, but by actual experiments. It is to these principally that I now refer.

Professor Stokes, at the meeting of this Society held in July last, has brought forward a question, and shown in theory that by means of a front lens, with an emergent surface exceeding the hemisphere, a ray may be refracted within the substance of the glass in a direction at right angles to the axis or at an angle of 180°. He then remarks that if the reduction of the surface be to a hemisphere," the aperture in glass, though reduced from the extreme of 180, still remains very large.'

It is with front lenses having refracting surfaces less than a hemisphere that we have been dealing, and to such Professor Keith's paper on the Tolles refers. It may be stated that we are not seeking for foci within the front lens, or yet on its surface. An immersion lens is not useful for viewing diatoms in balsam only. Every lens that I have seen professing 180°, whether it has an adjustment or not, is expected, and does, in fact, focus upon dry mounted objects. This necessitates a correct focus at a little distance beyond the last surface, from a position which must include a less air angle than 180°, and is consequently within the critical angle of nearly 82° in the crown glass.

The referred to belonging to Mr. Crisp has considerable focal distance in air, and I am confident that when the axial angle is correctly measured it will be proved far short of 180°, and the whole of Professor Keith's calculations concerning it must fall to the ground. The practical obstacles which have hitherto prevented the construction of any objective reaching to an air aperture of 180° still exist.

As much importance, both theoretically and practically, appears to have been attached to the last few degrees of extreme angle of aperture verging upon 180°, I repeat that the value of aperture in theory, considered as a question of rays collected, is palpably as the chord of the arc including the angle, or, in other words, in proportion to the sine of the half angle; for large angles so small is the comparative increase, that the difference between 170° and 180° is only as 99 6 to 100. But setting theory aside in this question as not always working harmoniously with practice, let it be considered, experimentally, what is the probable importance to definition

from rays proceeding at extremely oblique angles from flat surfaces having a raised configuration or structure. Take, for the first example, a piece of coarse-grained canvas or other fabric. Throw light upon or through this obliquely, and examine it at various angles with a shallow magnifier. At visual incidences greater than 45° or 50° no advantage will be gained; on the contrary, there will be a positive loss of definition. The same effect is seen on a different surface consisting of uniform glistening particles, such as bird-seed. To this dissentients will say, "You are comparing observations under a low magnifying power or with none at all to those made with the microscope," but relatively the conditions do not differ. Perhaps the most trying work for a hand magnifier is in examining the polish of glass surfaces in order to ascertain if all the "greys" are worked out. For small lenses a half-inch achromatic is used, held at an angle of about 45°; at a greater angle the extremely fine specks cannot be discovered. Light is directed at a great obliquity on the surface or is transmitted. Uneducated workmen do not reason about any theory of angles, but adopt the one that gives the best result, simply because they find out at once that it does so.

My argument is that the angular aperture of microscope objectglasses has hitherto been erroneously measured by all the usual means, in which the outer oblique rays extending to the margin of the field of view have been in all cases included, and, in fact, constitute the false measurement. The true angle is the cone of rays diverging from an atom or point in the centre of the field. Other pencils of greater obliquity defining atoms at the margin, are exclusive and independent of the central rays as much as the different objects themselves, yet it is the direction of these exterior rays that we have hitherto been measuring. There seems to be an absence of experiment, or disinclination to admit the evidence of such an error. For one proof of an example wherein angle of direction is erroneously measured as angle of aperture, unscrew and remove the back lenses of high-power objectives, and measure the apparent apertures of the fronts alone by any of the usual methods, such as the traversing sector, or by the angle of direction to two distant images. The angle of the front lens alone of a thus measured came out as 83°, simply because the back lens included nearly a hemisphere, which admits lateral rays from a wide angular direction. The aperture of the front of a appeared as 110°, and that of a as 122°, because more rays entered sideways, as the back surface in these last lenses is almost a hemisphere. This exemplifies the absurdity and utter inaccuracy of the usual mode of measuring angle of aperture, as we know that these single lenses have in reality an angle of aperture of a few degrees only.

In order to define more clearly the direction of these outer rays, that cause indications of false aperture, I tried the following expe

riment. I selected a which worked as an immersion, as this position prevents confusion concerning other points of adjustment. The full aperture, as measured by the 'sector through a slide with water between that and the front lens, was 120°. The focal distance as immersion was 041. The diameter of transmission on the surfaces of front lens was 07, ascertained by allowing a drop of milk to dry on the front and measuring the diameter of the light spot from parallel rays entering from the back, using a low-power object-glass and micrometer eye-piece for the measurement.

The field of view included a diameter of 03 on a stage micrometer. With the exact focal distance from the front lens as a starting point, it remained to ascertain what were the apparent apertures taken through various stops of definite diameter set close to the front, that could only admit the base of a cone of rays from an angle proceeding from the axial focal point up to a known diameter of stop. The arrangement that I use is a form of adjustable slit, consisting of two strips of very thin platinum foil; one piece is cemented on to a slip of thin plate glass, which is made to slide under two staples by a micrometer screw acting against a counter spring. The fixed strip of foil is attached to one of the staples, so that when the screw is quite home the edges meet. The various widths at which the instrument was set were measured under the microscope with an eye-piece micrometer. Having got the desired width, the object-glass to be measured was attached, and the body of the microscope lowered till the slit came in contact with the front lens, a drop of water having been placed over the slit to prevent undue refraction, and obtain more light.

The apparent angles included by these limiting edges or stops were measured by the usual sector method, of rotating the microscope on a turn-table graduated into degrees, and ascertaining the vanishing point of a distant light; or, preferably, by means of an examining lens at the eye-piece, for observing the disappearance from the field of an actual image.

The real or true angles were estimated from the distance of the focal point, up to the known measure of the edges of the stop. Avoiding fractions of degrees, the following table gives the comparative results:—