409. It would be of great importance to determine for every species of glass the dispersion of each separately-colored ray. But, since the different colors of the prism do not present any precise limits, the spectrum cannot be used for this purpose. More precision would be obtained if we possessed glasses or colored fluids which permitted only light of the same color to pass; the one, for example, permitting only the blue light to pass, and the other only the red. M. Frauenhofer was not, however, fortunate enough to procure either a glass or a fluid which possessed this property. In every case the white light which passed through was still decomposed nto all its colors, with this difference only, that in the spectrum the color peculiar to the glass or the fluid was more brilliant than the rest. Even the colored flames obtained by burning alcohol, sulphur, &c., seen through a prism, do not yield a homogeneous light corresponding to the color. These flames, however, such as that of a lamp, particularly that of a candle, and, in general, the light produced by the flame of a fire, exhibit between the red and yellow of the spectrum a clear and well marked line, which occupies the same place in all the spectra. This line appears to be formed by rays which are not decomposed by the prism, and which consequently are homogeneous. In the green space we perceive a similar line, but it is weaker and less distinct, so that it is often very difficult to find.

410. It was, however, absolutely necessary for M. Frauenhofer to have homogeneous light of each color, and the following was the method which he employed:- Behind an aperture in a shutter, 1-5 of an inch wide and 007 wide, he placed a prism A, fig. 12, of flint-glass, with an angle of about 40°; and at BC, a distance of about thirteen feet, he placed six lamps, whose light fell through narrow apertures on the prism A. The width of these apertures was 0:05 of an inch, their height nearly 1.5, and the distance of one lamp from another 0-58. The light of the lamps which fell on the prism A was refracted by it, and decomposed into colors, and afterwards passed through the aperture in the shutter. From the lamp C, for example, the red rays came in the direction of E, and the violet in that of D. From the lamp B the red rays passed towards F, and the violet rays towards G, &c. At the window of another house, 692 feet from A, and at the same height of the plane BA C, he placed the theodolite already mentioned, before the telescope of which, on the horizontal plane, was set the prism II, whose index of refraction for the different colored rays he wished to determine. The prism H could only receive from the lamp C the red rays, the others, for example the violet, going to a side at D, did not fall upon the prism. In like manner, from the lamp B, it was only the violet rays which fell upon the prism H. In this way the prism relieved from each lamp rays of a different color, setting out from the same point. If the prism H, or the aperture of the object-glass, was not too broad, some rays of the six lamps, for example those between the violet and the blue, between the blue and the green, &c., will not fall upon the prism H, but will be entirely wanting. In this case the spec

trum of rays passing by the small aperture A, and seen by the prism H, and by the telescope of the theodolite, will appear as in fig. 13, where I is the violet, K the blue, L the green, &c., and each color will appear separate. The distances ON, N M, &c., will increase as the dispersive power of the glass with the same angle of the prism H is greater. Since these distances, and the angle formed by the incident ray with an emergent ray, may be measured by the theodolite with a great degree of accuracy, it is easy, by means of this mechanism, to determine the index of refraction of each colored ray for every kind of refracting substance. Above the prism A, at the distance of one foot and a half, he made another aperture in the shutter, in the same vertical line with A, behind which he placed a lamp, from which the prism H likewise received light. The spectrum produced by the lamp ought then to appear by the prism before the telescope of the theodolite, and below the colored points as P, R, Q. shining orange or reddish line which appears in every spectrum of the light of the fire is shown at R. This line enables us, in the present case, to be certain that, on different days of observation, we have always the same color in the colored points, which would not take place if the table on which the lamps are placed suffer the least change in relation to the prism. On this account we ought to place the table so that the point N may always be found in the same vertical line with R. When this is not the case it is easy to bring it to the position by the adjusting-screws B and C. Since the distance of the lamps, or rather that of the small apertures by which the light falls on the prism A is invariable, we are sure, on different days of observation, to have always the same color in the colored points.

The

411. The distances of some of these colored points, for example the violets, the blues, and the reds, whose light is weak, cannot be measured without illuminating the micrometer wires of the telescope. These colored points, however, lose, by the ordinary method of illuminating the field, as much light as the wires receive, and therefore this method cannot be employed. It was necessary, therefore, to have a mechanism by which the wires alone could be illuminated, while the rest of the field remained dark. Such a mechanism M. Frauenhofer applied to his micrometer The illuminating of the wires may thus be modified at pleasure, and always with facility. This is effected on the side of the eye-glass by means of a small lamp enclosed in a hollow globe, from which the light falls upon a lens, and throws it in a parallel manner on the wires. At the inner margin of the eye-glass, constructed for the purpose, the rest of the incident light is absorbed without falling on the lens. With this apparatus he has measured the angles of refraction of the different colored rays for several refracting substances, the results of which are given in the following table. With all the substances the angle of the incident ray is equal to the angle of the emergent ray N. Each angle was measured four times. Since the light which sets out from A does not fall in a parallel manner on the prism H; or rather, since the plane in which the prism II is placed is not in the axis of the theodolite

414. From these results it is obvious that there are great anomalies in the ratio of the dispersion of the differently-colored rays in some refracting media.

415. These experiments led him to make some observations on the influence of heat upon the refraction of fluids. By the least change of temperature, the refraction of all fluids becomes stronger in the lower part of the prismatic spectrum than it is in the upper part: and hence every fluid acquires a kind of undulation, which prevents the colored points of the spectrum from being precisely distinguished. In making these experiments during the night, when the temperature continually changes, M. Frauenhofer was

obliged to stir the fluid every five or ten minutes, in order to render it homogeneous. These differences are not great in water, but in other fluids they are so considerable that all the spectrum is dispersed and confounded, even if the vessel is shut up from the air. Hence it follows that we ought not to expect good object-glasses by substituting fluids in place of flint-glass. We see also, from these experiments, how difficult it must be to melt flint and crown glass of a perfect homogeniety, since in every furnace of a glass-house the heat of the upper part of the crucible is almost one-third stronger than that of the lower part.

416. In order to obtain the indices of refrac

tion of the differently-colored rays with more exactness, and in order to determine if the action which refracting substances exert upon the light of the sun is the same as upon artificial light, he adopted the following method :

417. Into a dark room and through a narrow vertical aperture in the window-shutter, about 15′′ broad, and 36" high, he introduced the rays of the sun upon a prism of flint-glass placed upon the theodolite. This instrument was twenty-four feet from the window, and the angle of the prism was nearly 60°. The prism was placed before the object-glass of the telescope, so that the angles of incidence and emergence were equal. In looking at this spectrum for the bright line, which he had discovered in a spectrum of artificial light, he discovered, instead of this line, an infinite number of vertical lines of different thicknesses. These lines are darker than the rest of the spectrum, and some of them appear entirely black. When the prism was turned, so that the angle of incidence increased, these lines disappeared; and the same thing happened when the angle was diminished. If the telescope was considerably shortened, these lines re-appeared at a greater angle of incidence; and, at a smaller angle of incidence, the eyeglass required to be pulled much farther out, in order to perceive the lines. If the eye-glass had the position proper for seeing distinctly the lines in the red space, it was necessary to push it in to see the lines in the violent space. If the aperture by which the rays entered was enlarged, the finest lines were not easily seen, and they disappeared entirely when the aperture was about 40". If it exceeded a minute the largest lines could scarcely be seen. The distances of these lines and their relative proportions suffered no change, either by changing the aperture in the shutter, or varying the distance of the theodolite. The refracting medium of which the prism is made, and the size of its angle, did not prevent the lines from being always seen. They only became stronger or weaker, and were consequently more or less easily distinguished in proportion to the size of the spectrum. The proportion even of these lines to one another appeared to be the same for all refracting substances; so that one line is found only in the blue, another only in the red, and hence it is easy to recognise those which we are observing. The spectrum, formed by the ordinary and extraordinary pencils of calcareous spar, exhibit the same lines. The strongest lines do not bound the different colors of the spectrum; for the same color is almost always found on both sides of a line, and the transtion from one color to another is scarcely sensible.

418. Fig. 14, shows the spectrum with the lines such as they are actually observed. It is, however, impossible to express on this scale all the lines and the modifications of their size. At the point A the red nearly terminates, and the violet at I. On either side we cannot define with certainty the limits of these colors, which, however, appear more distinctly in the red than in the violet. If the light of an illuminated cloud falls through the aperture on the prism,

the spectrum appears to be bounded on one side. between G and H, and on the other at B. The light of the sun, too, of great intensity, and reflected by a heliostate, lengthens the spectrum almost one-half. In order, however, to observe this great elongation, the light between C and G must not reach the eye, because the impression of that which comes from the extremities of the spectrum is so weak as to be extinguished by that of the middle of the spectrum. At A, we observe distinctly a well-defined line. This, however, is not the boundary of the red, which still extends beyond it. At a there is a mass of lines, forming together a band darker than the adjacent parts. The line at B is very distinct, and of a considerable thickness. From C to D may be reckoned nine very delicate and well-defined lines. The line at C is broad, and black like D. Between C and D are found nearly thirty very fine lines, which, however, with the exception of two, cannot be perceived but with a high magnifying power, and with prisms of great dispersion; they are besides well-defined. The same is the case with the lines between B and C. The line D consists of two strong lines, separated by a bright one. Between D and E we recognise about eighty-four lines of different sizes. That at E consists of several lines, of which the middle one is the strongest. From E to b there are nearly twenty-four lines. At b there are three very strong ones, two of which are separated by a fine and clear line. They are among the strongest in the spectrum. The space b F contains nearly fifty-two lines, of which F is very strong. Between F and G there are about 185 lines of different sizes. At G many lines are accumulated, several of which are remarkable for their size. From G to H there are nearly 190 different lines. The two bands at H are of a very singular nature. They are both nearly equal, and are formed of several lines, in the middle of which there is one very strong and deep. From H to I they likewise occur in great numbers. Hence it follows that in the space BH there are 574 lines, the strongest of which are shown in the figure. The relative distances of the strongest lines were measured with the theodolite, and placed in the figure from observation. The faintest lines only were inserted from estimation by the eye.

419. Various experiments and changes, to which M. Frauenhofer has submitted these lines, convinces him that they have their origin in the nature of the light of the sun, and that they cannot be attributed to illusion, to aberration, or any other secondary cause. In transmitting the light of a lamp through the same aperture, we observe only the light shown at R, in fig. 13. It occupies, however, exactly the same place as D in fig. 14; so that the index of refraction of the line D is the same as that of R.

420. It is easy to understand why the lines. are not well marked, and why they disappear, if the aperture of the window becomes too large. The largest lines occupy nearly a space of from 5′′ to 10". If the aperture is not such that the light which passes through it cannot be regarded as a single ray, or if the angle of the width of the

aperture is greater than that of the width of the line, then the image of the same line will be projected several times parallel to itself, and will consequently become indistinct, and disappear when the aperture is too great. The reason why, in turning the prisms, we cease to see the lines, unless the telescope is lengthened or shortened, may be thus explained :

421. The emersion of the rays, in respect to their divergence, is similar to their immersion only in the case where the angles of incidence and emergence are equal. If the first angle is greater, the rays after refraction will diverge, as it were, from a more distant point, and, if it is smaller, from a nearer point. The reason of this is, that the path of the rays which pass nearer the vertex of the prism is shorter than that of those which pass at a greater distance from the vertex. Hence the angles of the refracted rays are not changed, but the sides of the triangles for the emergent rays ought to be in the one case greater, and in the other smaller. This difference ought to vanish if the rays fall in parallel directions on the prism, which is also proved by experiment. As the violet rays have, by the object-glass of the telescope, though a chromatic, a focal distance a little shorter than the red rays, we see clearly why it is necessary to displace the eye-glass, in order to perceive the lines distinctly in the different colors.

422. As the lines of the spectrum are extremely narrow, the apparatus must be very perfect, in order to avoid all aberration, by which the lines may be rendered indistinct, and even dispersed. The sides of the prism ought consequently to be perfectly plain, and the glass of which the prisms are made ought to have neither scratches nor striæ. With English flint-glass which is never entirely free of these striæ, we can only see the strongest lines. Common glass, and even the English crown-glass,

contains many striæ, though they are not always visible to the eye. Those who cannot procure a perfect prism of flint-glass should use a fluid of great dispersive power, such as oil of aniseseed, in order to see all the lines. In this case, the prismatic vessel ought to have its sides perfectly plane and parallel. In general, the sides of all the prisms should form an angle of 90° with their base, and this base ought to be placed horizontally before the telescope, if the axis of the telescope is horizontal. The narrow aperture by which the light passes ought to be exactly vertical. The reason why the lines become indistinct, if any of the conditions now mentioned is neglected, may now be readily understood.

423. As the lines of the spectrum are seen with every refracting substance of uniform density, M. Frauenhofer has employed this circumstance for determining the index of refraction of any substance for each colored ray. This could be done with the greater exactness, as most of the lines are very distinct and well marked. For this purpose he selected the largest lines, because with substances of low refractive power, or with prisms of small refracting angles, the lines of less magnitude could scarcely be perceived with a strong magnifying power. The lines which he preferred were those marked B, C, D, E, F, G, H, in fig. 14. He made no use of the line b because it is too near F, and he endeavoured to use the middle one between D and F. It is not practicable to measure larger arcs, such as BH, but only small ones like BC, CD, because, in order to see the lines of the different colors distinctly, the eye-glass requires to be displaced.

424. The following table contains the measures of the angles obtained from different kinds of glass, and other refracting substances: