tuting for the plane mirror, a small concave mirror mm, which re- 209. Cassegrain further modified this construction, by substituting in place of the small concave mirror, a small convex mirror mm, in order that the aberrations of sphericity produced Fig. 134. by the two mirrors, might mutually compensate each other. In this case, that the second image may be formed on the side of the observer, it is necessary that the first should not be actually formed; but that its imaginary place should fall beyond the small mirror, between its surface and the principal focus. This result which was not considered in article 15, because it supposes the incident rays convergent towards the mirror, is easily demonstrated by the general method of article 13. 210. In figures 130, 131, 133, and 134, for the sake of simplicity, we have only represented a simple eye-glass. But, it is in fact necessary, in order to render the last image colourless, that the eye-glass should consist of two lenses, arranged according to the principles laid down in articles 200, 201. We have also been obliged, in the figures, to increase very much the true dimensions of the eye-glass, compared with those of the mirror MM, that we might be able to represent the mass of rays and succession of images, in a conspicuous manner. It is hardly necessary to remark, that in these telescopes, the mirrors are firmly fixed in the axis of a tube, sufficiently long to permit only those rays which are nearly perpendicular, to fall upon them. Indeed, we often contract this opening by means of diaphragms, for the express purpose of interrupting those rays which would fall on the borders of the mirror, this being never so well executed as the centre. The tubes ought to be blackened on the inside, like those of refracting telescopes, for the better absorption of the light irregularly reflected from their sides. In fine, they must be mounted in such a manner that they may be directed at pleasure, towards the different points of space. Method of M. Arago for determining the Magnifying Power of Optical Instruments. 211. It has already been observed, that in instruments intended for viewing distant objects, the magnifying power is equal to the ratio of the visual angles, under which the same object is seen with the naked eye, and through the system of glasses of which the instrument is composed. If the object is sufficiently near the eye to allow its distance, in these two cases, to be compared, it is necessary to combine the ratio of the visual angles with the ratio of the real and apparent distances of the object, in order to deduce the ratio of its real and apparent magnitudes, both taken at the distance of distinct vision. The process of M. Arago gives immediately the ratio of the visual angles. For this purpose, we take a double prism of rock crystal, similar to those whose construction is represented in figure 92, and which serve for double-image micrometers. We measure the angle O c E or C, at which it divides the light. This can be done in a very simple manner, as we shall soon see. We next place the double prism behind the eye-glass of the instrument under examination, which we first suppose to be either a reflecting or refracting telescope. If we view, through this system, a distant circular object, of a known diameter, we shall see it double, and in general its two images will be separated from each other. Then we remove it further or bring it nearer until these two images touch each other by their opposite edges. When this takes place, we know that the rays proceeding from the borders of this.object, after having traversed the instrument, emerge from it, making with each other an angle precisely equal to C. Now, since we know the diameter M of the object, and its distance which we call 4, we can easily calculate the visual angle a, under which the same rays cross each other at their cal tangent. The ratio of these angles or press the magnifying power of the instrument. will therefore ex Now, in order to determine exactly the angle C, we can view the object through the double prism alone, and carry it farther off or bring it nearer, until its two images appear to touch each other. Then, from the known diameter of the object and its Fig. 135. distance, we can calculate the visual angle which it subtends, and this will be the value of C. But M. Arago rendered this observation more exact by viewing the two images through a small telescope, before which, in contact with the object-glass, was placed the double prism which gave more distinctness without altering the coincidence of the images. Moreover, instead of a single object, he substituted several of different diameters, at the same distance, and even gave them a triangular form, in order to be able, without displacing them, to choose, in each experiment, the visual angle suited to the double prism, whose amplitude he wished to determine. 212. The method of M. Arago may be applied also to the microscope, under all the different forms of the eye-glass. Only the observation through the instrument, must be made upon an object very near and divided into small portions, like the objectglass micrometer, for example, already described. When we 193. have placed this micrometer before the object lens, at a conven- Fig. 136. ient distance for seeing distinctly through the eye-glass, the image the dimensions of which are traced upon it, we place the double prism between the eye-glass and the eye; and directing the double refraction perpendicularly to the series RR of marks traced upon the glass, we count the number RR', of divisions, embraced by the divergence of the two rays. Suppose it equal tom lines. This then will be the real magnitude of the object, which, being seen through the instrument, and brought by it to the distance D, of distinct vision, subtends at the eye the constant angle C; its apparent magnitude, as it is seen through the instrument, will therefore be equal to the distance D, multiplied by the trigonometrical tangent of the angle C; that is, equal to D tang. C; an expression which may be reduced to if we sup- Top.149. DC 206265 59. pose the angle A converted into seconds. It only remains, then, to divide this apparent magnitude by the real magnitude m of the 61, 62. object, as in the case of a simple magnifying glass, and the quotient DC will express the magnifying power. It is hardly ne 206265 m cessary to remark, that the distances D and m must be expressed in units of the same kind. Instruments employed in Optical Experiments. 213. AFTER having described the instruments which serve to enlarge the power of vision, it is proper to say a word concerning certain other kinds of optical apparatus, remarkable for the beauty or singularity of their effects. Camera Obscura. A CONVERGING object-glass adjusted to the shutter of a dark room, will concentrate the rays which come from external objects; and if these objects are very distant, compared with the focal distance of the glass, and situated nearly in the direction of its axis, it will give distinct images which may be received upon a white screen. These images are inverted; but in order to render them erect, it is sufficient to bring to the object-glass, instead of the direct light of the object, that of the image, already reFig. 137. flected and inverted by a metallic mirror MM. This apparatus is called a camera obscura. We may substitute for the screen a plate of ground glass; and for the room, a box fitted by means Fig. 138. of a curtain to receive the head. It can then be transported with ease, for the purpose of landscape painting. Dr Wollaston has remarked, that the best form for the objectglass of a camera obscura, is that of a meniscus convex towards the image, and concave towards the object, as represented in the figure. And some fortunate experiments, made by Cauchoix, seem to indicate that the ratio of curvatures the most favourable, is that of 5 to 8. The shortest of the two curvatures belongs to the surface turned towards the image, because the lens must be converging. Megascope. 214. HERE, as in the preceding case, an object-glass is adjusted to a window shutter; but, instead of causing it to produce the images of distant objects, we place without the room, at a small distance, in the direction of the axis an object strongly illuminated by the light of the sun, either directly or by reflection from several mirrors. If this object is not one of too great dimensions, a distinct image will be formed in the room, the distance and magnitude of which will depend upon the focal distance of the objectglass, and the distance at which the object is placed before it. In proportion, therefore, as we bring the object nearer to the principal focus, we can obtain larger images; but as these will also be thrown at a greater distance, we must be guided in this respect by the dimensions of the room, and must limit ourselves to such distances as will give images sufficiently magnified and at the same time well defined. The images will appear inverted, but may be made erect by inverting the object. Such is the megascope. Instead of a single object-glass, we may employ several combin- Fig. 139, ed, so as to become achromatic. Then the limits within which the images are distinct, are sufficiently great to enable us to form, in this manner, magnified or reduced representations of pictures and statues, or even of natural figures, M. Charles, who invented this instrument, contrived to magnify objects from 2 to 20 times. In this state, it may be very usefully employed in numerous researches relating to natural philosophy and natural history, where it is necessary to determine with precision the forms and outlines of objects whose smallness or delicate texture prevents their being measured directly. In this case, we receive the image on a plate of ground glass, and sketch the outlines on the opposite surface of the glass or on transparent paper applied to this surface. This process, although graphic, is susceptible of very great accuracy. 215. The magic lantern is simply a portable megascope, in which transparent objects are illuminated by the light of one or several lamps. The term phantasmagoria, or the raising of spectres, has been given to the exhibition of an optical apparatus, similar to the magic lantern, in which the distance of the object from the con |