Popular Scientific Recreations in Natural Philosphy, Astronomy, Geology, Chemistry, etc., etc., etc. Gaston Tissandier

show clearly by experiment the connection existing between double images and radiated images from points, it is sufficient to make in a dark sheet of paper a small rectilinear slit, and at a little distance from one end, on a line with the slit, a small round hole, as shown at a in fig. 102. Looking at it from a distance we shall see that the double images of the line have exactly the same distance between them that the most brilliant parts of the starred figure of diffusion have from the point, and that the latter are in a line with the first, as will be seen at b (fig. 102), where in the image of diffusion of the luminous point, we only see the clearest parts of star a of the figure.

      On lighted surfaces, to which the eye is not exactly accommodated, multiplied images are often remarked through the passage from light to darkness being made by two or three successive steps.

      A series of facts which have been collected under the title of irradiation, and which show that brightly-lighted surfaces appear larger than they are in reality, and that the dark surfaces which surround them appear diminished to a corresponding degree, explains this by the circumstance that the luminous sensation is not proportional to the intensity of the objective light. These phenomena affect very various appearances, according to the form of respective figures; they are generally seen with the greatest ease and intensity when the eye is not exactly accommodated to the object examined, either by the eye being too near or too far off, or by using a concave or convex lens, which prevents the object being seen clearly. Irradiation is not completely wanting, even when the accommodation is exact, and we notice it clearly in very luminous objects, above all when they are small; small circles of diffusion increase relatively the dimensions of small objects much more than of large ones, with regard to which, the dimensions of the small circles of diffusion which the eye furnishes, when properly accommodated, become insensible.

      Fig. 103.—Experiment 1.

      1. Luminous surfaces appear larger. We can never judge exactly of the dimensions of a slit or small hole through which a bright light escapes; it always appears to us larger than it really is, even with the most exact accommodation. Similarly, the fixed stars appear in the form of small luminous surfaces, even when we make use of a glass which allows of perfect accommodation. If a gridiron with narrow bars—the spaces intervening being exactly equal to the thickness of the bars—is held over a light surface, the spaces will always appear wider than the bars. With an inexact accommodation, these phenomena are still more remarkable. Fig. 103 exhibits a white square on a black foundation, and a black square on a white foundation. Although the two squares have exactly the same dimensions, the white appears larger than the black, unless with an intense light and an inexact accommodation.

      Fig. 104.—Experiment 2.

      2. Two adjacent luminous surfaces mingle together. If we hold a fine metallic wire between the eye and the sun, or the light of a powerful lamp, we shall cease to see it; the lighted surfaces on all sides of the wire in the visual range pass one into the other, and become mingled. In objects composed of black and white squares, like those of a draught-board (fig. 104), the angles of the white squares join by irradiation, and separate the black squares.

      3. Straight lines appear interrupted. If a ruler is held between the eye and the light of a bright lamp or the sun, we perceive a very distinct hollow on the edge of the ruler in the part corresponding to the light. When one point of the retina is affected by a light which undergoes periodical and regular variations, the duration of the period being sufficiently short, there results a continuous impression, like that which would be produced if the light given during each period were distributed in an equal manner throughout the whole duration of the period. To verify the truth of this law, we will make use of some discs, such as that represented in fig. 105. The innermost circle is half white and half black; the middle circle has two quarters, or half its periphery, white, and the outer circle has four eighths’ white, the rest being black. If such a disc is turned round, its entire surface will appear grey; only it is necessary to turn it with sufficient force to produce a continuous effect. The white may also be distributed in other ways, and provided only that on all the circles of the disc the proportion of the angles covered with white is the same, they will always exhibit the same grey colour. Instead of black and white we may make use of different colours, and obtain the same resultant colour from all the circles, when the proportion of the angles occupied by each of the colours in the different circles is the same.

      Fig. 105.—Disc which appears uniformly grey by reason of its rotation.

      If we paint on a disc a coloured star, which is detached from a foundation of another colour (fig. 106), during the rapid rotation of the disc the centre affects the colour of the star; the outer circle assumes that of the background, and the intermediate parts of the disc present the continuous series of the resultant colours. These results are in accordance with the theory of the mixture of colours.

      Fig. 106.—Disc with a star painted on the background of another colour.

      Rotative discs, which are so much used in experiments in optical physiology, were employed for the first time by Müsschenbroeck; the most simple is the top. M. Helmholtz ordinarily uses a brass spinning-top, which fig. 107 represents at a third the natural size. It is set in motion by the hand, and its quickness may be increased or moderated at will; but it cannot be made to spin quicker than six rounds in a second; this motion will be kept up for three or four minutes. Thus, with a feeble movement of rotation, a uniform luminous impression can only be obtained by dividing the disc into four or six sections, on each of which we repeat the same arrangement of colours, light, and shade. If the number of repetitions of the design is less, we obtain, with a bright light, a more or less shot-coloured disc.

      Fig. 107.—M. Helmholtz’s top for studying the impression of light on the retina.

      It is easy to place designs on the disc, even when in motion, or to make any desired modification, by superposing on the first disc another disc with sectors, of which we can vary the position by slightly touching it, or even blowing on it, thus producing during the rotation of the disc very varied modifications. If, for instance, we place on a disc covered with blue and red sectors of equal size, a black disc, of which the sectors are alternately filled in or empty, the disc, as it turns round, will appear blue if the black sectors of the upper disc exactly cover the [red] sectors of the lower disc; and it appears red, if, on the contrary, the blue sectors are covered with the black; while in the intermediate positions we obtain different mixtures of red and white, and during the rotation of the disc may vary the colour insensibly by a gentle touch. By dividing the different sectors with broken or curved lines, instead of straight ones, we can produce an arrangement of coloured rings of great variety and beauty. To give the top greater speed, we set it in motion by drawing a string twined round its stem. The simplest method, as shown in fig. 108, consists in the employment of a handle similar to that of the German top. It is a hollow cylinder of wood set into a handle with two circular holes; and at right angles with these is a groove for the passage of the string. The stem of the top is passed through the holes of the cylinder, one end of the string is fixed in the small hole in the stem, and is rolled round by turning the top in the hand. The part of the stem on which the string is twisted becomes sufficiently thick for the top to remain suspended to the handle; then holding it a little above the table, and giving the string a powerful pull, we set the top in motion, and as the string unrolls it falls on the table, where it will continue its rotation for some time. The top represented in fig. 109 is constructed so that the discs may be firmly pressed by the stem, which is necessary in experiments for demonstrating Newton’s theory of the mingling of colours. We make use for this purpose of a variety of discs, made of strong paper of different sizes, having an opening in the centre and a slit, as in fig. 110; each of the discs