the oxide of lead introduced into the composition of glass, augments to a considerable degree, its dispersive power; it augments likewise its refractive power, although in a smaller proportion. Of all the substances which were tried by M. Cauchoix and myself, the liquid known in chemistry under the name of sulphuret of carbon, appeared to have the greatest dispersive power. The dispersion produced by it was ten times that of water, under similar circumstances; the refractive powers of sulphur, and of solid carbon are also very considerable. Still this correspondence between the increments of refraction and dispersion is very far from being general, especially when the ratios of refraction differ but little. The essential oils of citron and turpentine, muriatic acid, pure or saturated with ammonio-muriate of mercury, disperse more than crown glass, but refract less, as has been well ascertained. The same is true in a number of other instances; so that the relation of the dispersive forces of bodies to their chemical composition, is even more difficult to be foreseen than that of the refractive forces. John Dollond, a celebrated English optician, was the first who proved, by experiment, the error of Newton, respecting the possibility of obtaining an achromatic compensation, preserving at the same time an excess of refraction. Euler supposed this to be possible, because it was realized, at least very nearly, in the construction of the eye, which is achromatic when well adjusted, and sensibly unites all the refracted rays in the image upon the retina, and paints the objects in their proper colours, as may be seen by taking the eye of an animal recently killed, and removing the outer coating from the back part, and examining the images formed there. But this remark, upon an organ thus composed, was not sufficient to develope the true principles upon which the compensation is founded. Euler proposed several hypothetical laws, which might produce this effect. It was in trying these laws that Dollond was lead to repeat some of the experiments of Newton, upon compensation by prisms of different refracting substances; and being led by chance, or a happy conjecture, to try some of a nature very different from each other, like crown glass and flint glass, he discovered that the refraction produced by crown glass remained predominant, when the angles of the prisms were such that the compensation was sensibly complete. By preserving the same relation between the prismatic borders of concave and convex lenses, made of these two substances, Dollond obtained achromatic object-glasses, which enabled him greatly to enlarge the apertures hitherto employed. Although great use has been made of this discovery, but little pains have been taken to perfect it, and opticians are still compelled to use the rules of compensation given by Dollond, even in instances where they are no longer applicable; and when under the necessity of deviating from them, on account of great difference in the substances, they have resorted to expensive and imperfect trials. These are the considerations which led M. Cauchoix and myself to seek an exact process, such as has here been given. Of the Dispersion which accompanies Extraordinary Refraction, and the Separation of the Axes of Double Refraction with respect to the different Simple Rays. 186. It has been mentioned, that in crystals endued with double refraction, the extraordinary image is generally coloured, as well as the ordinary. This phenomenon, therefore, proves that, at equal incidences, the extraordinary velocities are unequal for the different simple rays, as analogy alone would indicate; but it may be easily shown that the mode of dispersion resulting from it must generally be more complicated than that for images where the velocity is constant. Indeed, confining ourselves, for the sake of simplicity, to crystals of one axis, if we call the ordinary velocity v, and the angle formed by the extraordinary ray with the single axis U; we have seen that the extraordinary velocity v', is given by the formula, v2v2+k sin 2 U, in which k is a constant coefficient peculiar to each crystal, and which is positive in some and negative in others. Now, experiments show, that generally the values of this coefficient are sensibly different for the different simple rays, and increase with the refrangibility. Their variations, or rather those of the product k sin 2 U, which result from them, combine therefore with those of the square of the ordinary velocity to form v', and as the values of increase also with the refrangibility of the rays, it is manifest that if k is positive, as is the case in attractive crysals, the two causes of variation conspire in the extraordinary velocity; while on the contrary, if k is negative, as it in fact is in repulsive crystals, they counteract each other. In this last case, therefore, it is possible that they may nearly or entirely destroy each other; and then the extraordinary image may be sensibly white, although very powerfully refracted. Indeed, this singular phenomenon, is exhibited in the rhomboids of Iceland spar, when the incident ray SI, is directed towards the small solid Fig. 78. angle B'; because then the ordinary refraction tends to disperse the spectrum, by causing the most refrangible rays to approach the normal to the point of incidence; while the repulsive force, emanating from the axis IA', tends to disperse them in the opposite direction. Malus found that these two opposite causes counterbalance each other when the incidence is about 40°. Then the ordinary image only is dispersed; and the extraordinary image, although strongly refracted, is sensibly white. 187. It has likewise been remarked that, according to a very ingenious discovery made by the son of the celebrated Sir William Herschel, the axes of double refraction in crystals, are not always the same for all kinds of simple rays, but have different positions, and different inclinations to each other, for these different rays. This dispersion has as yet been observed only in crystals of two axes. Indeed, it is easy to see that it is not possible in others, simply from the condition of symmetry of faces, which is necessary for the existence of a single axis. For the same reason, in crystals with dispersed axes, all the pairs of axes are comprehended in the same plane, and have the same intermediate line common. But the direction of the dispersion is subject to no rule. In some crystals, such as the sulphate of barytes, the nitrate of potash, aragonite, sugar, and hyposulphate of strontian, the axes of the red rays are less inclined to each other than those which correspond to the violet rays. The reverse takes place in borax, siberian mica, sulphate of magnesia, white topaz, and tartrate of potash and soda. The phenomenon is particularly excessive in the last salt. According to Mr Herschel, the inclination of the axes in this, is 55° 14' for the violet rays, and 750 42′ for the red rays, each being taken at the extremity of the spectrum. It is obvious that these differences as to position and angles must affect the course of the refracted rays, calculated Opt. 24 118. 120. 116. according to the general law, and therefore in crystals where they are sensible, we are obliged to specify the particular species of rays to which the formulas are to be applied. These phenomena must evidently render the laws of dispersion very complicated, in the crystals under consideration. But it was not in this way that Mr Herschel made the discovery of the separation of the axes. The tartrate of potash and soda, where it is so considerable, has a double refraction, so very feeble, that it is hardly capable of being measured; and in crystals hitherto observed, where the double refraction is most powerful, the axes are generally very little dispersed. But the phenomenon of their dispersion is rendered very evident, independently of the doubling of the images, by certain phenomena of colour to be explained hereafter; and it was by these that Mr Herschel was led to the discovery. Dioptric Instruments consisting of several Glasses. 188. THE most complicated dioptric instruments may be considered as consisting essentially of two glasses. The first, called the object-glass, receives the light immediately from the object, and forms an image of it at its focus. The second is called the eye-glass, and is placed near the eye for the purpose of viewing this image, which, according to the relative focal distance of the two glasses, and the position in which they are placed, will appear erect or inverted, magnified or diminished. This system may be greatly improved by making the eye lens to consist of several glasses, properly disposed, and rendering the object lens achromatic when it is possible. By this means greater distinctness and a higher power may be obtained. All the varieties, however, may be reduced to the same principle. Whatever be the number and curvature of the glasses, they must all have their axes in the same straight line and be firmly fixed in a tube, consisting of several pieces that slide within each other, for the purpose of varying the distance of the eye-glass from the objectglass. This tube should be blackened on the inside for the purpose of absorbing all the light which strikes upon its sides; for no rays but those which come nearly in the direction of the axis, common to all the lenses, can be of use in vision. Hence, in order to insulate these rays completely, a number of transverse partitions with circular openings, called diaphragms, are placed in the interior of the tube, being coloured black, in order to arrest by their opacity the rays which are too oblique. In general, all instruments of this kind may properly be considered as cameræ obscuræ, or dark rooms, of small dimensions and a field of view of little extent. This last limitation is required in order to the enlargement to which it is to be subjected in the image; for it would appear distorted if it were not reduced to very small dimensions. 189. Each kind of instrument is appropriated to a particular purpose; some are employed in examining very minute objects at a short distance by enlarging their image; these are called microscopes; others are used in viewing distant objects, under a greater angle than they present when seen by the naked eye, they being seen with equal distinctness at the same time; these are called telescopes. In both these kinds of instruments, the same principles are employed; and they are adapted to their respective objects by introducing some peculiarities in the construction. This will be seen as we proceed to examine successively those which are the most common and most useful. 1 Compound Microscope. 190. THE object-glass of this instrument is a small lens A, of Fig. 121. a very short focus, before which are placed minute objects Sz, at a distance A ̧P or 4, which exceeds very little the distance A,F, of the principle focus. Behind this lens is formed an inverted image ƒ, 1, at a distance Л,P, or S, much greater than 4; and if the magnitude of Sz is expressed by I, that of ƒ11, will 1 IS 1 be expressed by ; hence this image is likewise much greater than the object Sz. If this degree of magnifying power were sufficient, the image might be received upon ground glass, placed at f11, and viewed in this situation by the naked eye. But it is evident, that the effect would be increased still more if the |