change of 3.5" to produce the same variation in the decimal.

430. If, in achromatic object-glasses, the aberration produced by the unequal refrangibility of the differently-colored rays ought to be destroyed; then, since the focal lengths of the lenses of flint and crown-glass ought to be nearly in the ratio of the dispersion of the two kinds of glass; and since, on the other hand, the ratio of dispersion for the different colors is not the same, it is evident that some aberration must still remain; and we must, therefore, determine this ratio, in order that this aberration may be a minimum for the distant vision of objects. This cannot take place, if the difference between the focal lengths for the rays of different refrangibility in the same object-glass is a minimum; for the different colors have not the same intensity: the aberration of the yellow rays, for example, which have the greatest brightness, will produce in the ratio of their intensity a worse effect than the violet ones, if the aberration for the latter is of the same magnitude. Hence we must know the intensity of each color in the spectrum, or in what ratio the impression of any color of the spectrum is stronger or weaker than that of another color. In order to measure this intensity, M. Frauenhofer constructed the following apparatus. 431. To an eye-glass, constructed for that purpose, for the telescope of the theodolite, he applied a small plain metallic mirror, the edge of which being well defined, cut the field of the telescope in the middle, as shown at a in fig. 15. It was placed before the eye-glass E, at an angle of 45°, and at the place of the image formed by the object-glass A. The eye-glass E is pulled out till the edge of the mirror, which ought to be vertical, is distinctly seen. At the side of the eye-glass, and in a direction perpendicular to the edge of the mirror a, and to the axis of the telescope AE, he fixed a tube c B, cut in the direction of its length at b; and in this cut he placed a narrower and a shorter tube MN, fig. 16, which crossed the larger tube c B perpendicularly. In this narrow tube was a small flame, in the axis of the larger tube, which was supplied with oil from an external vessel. The narrow vertical tube b, fig. 15, or M N fig. 16, had in the axis of the larger tube a small round aperture, turned towards the mirror a, by which the light of the flame fell upon it. By this contrivance, we perceive, in half of the field, the mirror a illuminated by the flame, and in the other half one of the colors of the spectrum formed by a prism placed before the objectglass A. The nearer the tube b is brought to a, the more will the flame illuminate the mirror,

Experiment I.

Intensity of Light.

and consequently we can obtain, at the same time, an impression produced on the eye by the light of the mirror (as seen by the eye-glass) of the same intensity as that which is produced by a color of the spectrum in the other half of the field. The squares of the distances of the flame from the mirror, for the different colors of the spectrun., are then inversely as the ratios of their intensity. Though at first it appears difficult to compare the light of two different colors, yet it becomes easy by a little practice. The intensity of the light of the mirror approaches more to that of any color in the spectrum, if, at the same position of the eye-glass, its vertical margin is less distinct. If the mirror is adjacent to a part of the spectrum, more or less illuminated, the edge of the mirror becomes, in both cases, more distinct; because, in the first case, the mirror appears to be placed in the shadow, and, in the second case, it is the color of the spectrum that is found there. The experiment with the mirror is a little difficult and uncertain, if we perceive clearly the lines of the spectrum, because the brightest and the darkest lines touch one another almost in every color. On this account the aperture in the window-shutter is made so broad that only the strongest lines are just visible, and the fine ones not at all. In place of the mirror outside of the shutter, by which the light entered, he put a white plane surface illuminated by the sun, because by any imperfection of the mirror the light is irregularly dispersed, which renders the observations more dubious.

432. In order to vary the experiments, he at one time enlarged the round aperture before the flame, and at other times contracted it. He placed at the end c of the wide tube, a piece of ground glass, through which the mirror received its light. In this case he measured the distances of the flame from the ground glass. To avoid all illusion the aperture before the eye-glass ought to be small, and to be at the place where the principal rays, or the axes of the rys coming from the edge of the field, cut the axis of the telescope. With the prism of flint-glass, No. 13, having an angle of 26° 24′ 5′′, he obtained the following results. Though the experiments were made in clear weather, and at noon, he sometimes perceived, in the course of the observations, a slight change in the density of the light which the prism received. The differences of the four sets of experiments may have been partly owing to this change, and the flame may also have changed its intensity in the course of the observations. If we call the intensity of the light at the brightest part of the spectrum 1, we shall then have―

B 0.010

433. The brightest part of the spectrum is nearly at one-third or one-fourth of DE from D. Its position cannot be determined more exactly, nor is it of any great importance.

434. The curve in fig. 14 represents the intensity of the light in the different colors. The above values are the ordinates, and the measured arcs BC, CD, in the table containing the measures of the angles obtained from different kinds of glass, &c., from flint-glass, No. 13, the abscisWe may suppose that the quantity of the light in the different colored spaces is represented by the areas of the curve BC, CD. If we call this quantity 1, for the area of the space DE, then we shall have

sæ.

435. Having several object-glasses of the same aperture, the same focal length, and the same kind of glass, we may determine in which of them the aberration produced by unequal refrangibility is the best compensated, if we cover one-half of each of them by a screen passing through the centre of the object-glass in a straight line. In those where the margin of a distant object is most distinct the aberration is best compensated. In making this comparison we must attend only to the distinctness of the object, and not be deceived by the colors, because one object-glass may show less color than another, and yet its distinctness be less. This detailed method of finding the best ratio of dispersion is useful only for determining how much the aberration of the faintest rays ought to exceed that of the brightest rays. This result will be still more accurate if it is obtained by trials made with greater object-glasses, whose apertures are in the ratio of the greatest possible focal length. It is scarcely necessary to add, that the aberration of sphericity was corrected in all the object-glasses employed in these experiments. There is still another aberration which takes place in the eye itself, and to which we ought to pay attention if we wish to find the best ratio of the colorific dispersion.

436. On placing the red color of the spectrum in the middle of the field of the telescope of the theodolite, and on adjusting the eye-glass so as to be able to distinguish the fine micrometer wires, these wires will be no longer seen when the violet rays enter the field, the eye-glass remaining fixed. In order to see the wire in this color, we must bring the eye-glass much nearer the wire; that is, more than double the aberration produced by the unequal refrangibility of the two kinds of rays in the eye-glass. This proves that the differently colored rays in the eye have not the same focal distance, and that the eye is not achromatic. The distance to which the eye-glass ought to be displaced in different colors, in order to see the wire distinctly, enables us to calculate this aberration of the eye, which is by no means small; but we must take into account the aberration produced by the eye

glass itself. It is scarcely necessary to state, that, in observations of this kind, no other light but that of the spectrum ought to enter into the field of the telescope, and that the wire should not receive any foreign light. M. Frauenhofer has found, with a lens of crown-glass, No. 13, with a focus of 0.88 Paris inches, that the eyeglass, in passing the wire from the ray C to G, ought to be displaced 0-054 of an inch, in order to see the wire with equal distinctness in both colors. A lens of crown-glass, No. 13, of 1.33 Paris inches focus, requires to be displaced 0.111 for the same colors; a lens of flint-glass, No. 30, with a focus of 0-867, requires a displacement of 0.074; and another of flint-glass, No. 30, and a focus of 1.338, required to be displaced 0-148 of an inch. In these experiments he looked with one eye at a fixed object, whilst with the other he observed at the wire through the lens, in order that he might be certain that, with the different colored rays, the eye was always equally susceptible of uniting on the retina white rays of a given divergency; and, consequently, that it did not change, in that respect, for the different colors. Even with that precaution, however, the results did not differ greatly from the preceding.

437. The result given by the first lens is, that, if the red rays fall parallel on the eye, the blue rays ought to diverge from a point 23.7 inches distant, in order to have in the eye the same focal distance. With the second lens this distance was 21:3; with the third 19-5; and with the fourth 17.9. In this calculation he has taken into account the influence produced on this displacement by the unequal refrangibility of the two kinds of rays in the lens. This aberration in the eye cannot be fixed more rigorously, but by varied and repeated trials. It would be desirable to have the experiments repeated on the eyes of different persons in order to obtain a mean result. In order to determine this aberration with still more precision, we must also take into account the diameter of the luminous cylinder formed by the rays which go from the eye-glass to the eye. The diameter of this cylinder varies, and depends on the aperture of the object-glass, and the focus of the lenses of the eye-glass. It is easy to conceive that this aberration increases with the diameter of the cylinder. Great care is therefore requisite, in the calculation of object-glasses, to attend to the aberration of the eye, and to make it disappear from the ob ject-glass.

438. If, in the calculation of achromatic objectglasses for the spherical aberration, we wish to make this aberration disappear entirely, the indices of refraction for the flint and crown-glass ought to belong to the same colored ray; for if these indices belong to different rays the aberration can never be extinguished, notwithstanding the most rigorous calculation. As the discovery of the lines on the spectrum enables us to determine these points with accuracy, they must be considered of great utility in removing this aberration.

439. Before the discovery of the lines in the spectrum, M. Frauenhofer determined the identity of the refracting powers of two kinds of

glass by cementing them together, and forming them into a single prism. If the two specula seen by this prism appeared on the same place, and without any reciprocal displacement, he concluded that their refracting power was the same. After the discovery of these lines, however, he found that two pieces of glass might still have a different refractive power, without that difference being perceived by the above method. This difference in refracting power was not only found in pieces of glass taken from different parts of the same crucible, but even in pieces taken from the two extremities of opposite sides of the same piece of glass. By repeated experiments on the manufacture of flint and crown glass, he has succeeded to such a degree, that in a crucible containing 400 lbs. of flint glass, two pieces, one of which was taken from the bottom, and the other from the top, have the same refractive power.

440. In observing the great quantity of lines in the solar spectrum, we might be led to believe that the inflexion of light at the narrow aperture in the window-shutter had some connexion with them, though the experiments described do not give the least proof of this, and, indeed, establish the contrary opinion. In order to put this beyond a doubt, and also to make some other observations, he varied the experiments in the following manner :

441. If we make the sun's rays pass through a small round aperture in the window-shutter, nearly 15" in diameter, and cause it to fall on a prism placed before the telescope of the theodolite, it is obvious that the spectrum seen by the telescope can only have a very small width, and consequently will form only a line. In a line, however, of almost no breadth, it is impossible to see the fine and delicate lines which transverse it; and, on that account, the fixed lines are not seen in a spectrum of this kind. In order, however, to see all the lines in this spectrum, it is necessary only to widen it by an object-glass, without altering its length. He obtained this effect by placing against the object-glass a glass having one of its faces perfectly plane, and the other ground into a segment of a cylinder of a very great diameter. The axis of the cylinder was exactly parallel to the base of the prism. The spectrum could not, therefore, change in its length, and was therefore only widened. In the spectrum thus altered he recognised all the lines occupying the very same position that they had when the aperture was long and narrow.

442. He employed the same apparatus for examining in the night time the planet Venus, without allowing the light to fall upon a small aperture.

443. In the spectrum formed by this light he found the same lines, such as they appeared in the light of the sun. That of Venus, however, having little intensity compared with that of the sun reflected from a mirror; the brightness of the violet and the exterior red rays is very feeble. On this account we perceive even the strongest lines in these two colors with some difficulty; but in the other colors they are easily distinguished. M. Frauenhofer has seen the lines D, E, b, F, fig. 14, very well terminated; and

he has recognised that those in bare formed of two, namely, a fine and a strong line. The weakness of the light, however, prevented him from seeing that the strongest of these two lines consisted of two; and, for the same reason, the other finer lines could not be distinguished.

444. With the same apparatus he has also made several observations on some of the brightest fixed stars. As their light was much fainter than that of Venus, the brightness of their spectrum was consequently still less. He has nevertheless seen, without any illusion, in the spectrum of the light of Sirius, three large lines, which apparently have no resemblance with those of the sun's light. One of them is in the green, and two in the blue space. Lines are also seen in the spectrum of other fixed stars of the first magnitude; but those stars appear to be different from one another in relation to these lines. As the object-glass of the telescope of the theodolite has only thirteen lines of aperture, these experiments may be repeated, with greater precision, by means of an object-glass of greater dimensions.

445. The electric light is, in relation to the lines of the spectrum, very different from the light of the sun and of a lamp. In this spectrum we meet with several lines, partly very clear, and one of which, in the green space, seems very brilliant, compared with the other parts of the spectrum. Another line, which is not quite so bright, is in the orange, and appears to be of the same color as that in the spectrum of the light of a lamp; but, in measuring its angle of refraction, M. Frauenhofer finds that its light is much more strongly refracted, and nearly as much as the yellow rays of the light of a lamp. Towards the extremity of the spectrum we perceive in the red a line of very little brightness; yet its light has the same refrangibility as that of the clear line of the light of a lamp. In the rest of the spectrum we may still easily distinguish other four lines sufficiently bright.

446. In making the light of a lamp fall through a narrow aperture, from 15" to 30" wide, upon a prism of great dispersion, placed before the telescope, we perceive that the red line of this spectrum is formed by two very delicate bright lines, similar in size and in distance to the two dark lines D, fig. 14. Whether the aperture through which the light of the lamp passes is wide or narrow, if we cover the point of the flame, and the lower blue extremity of it, the red line appears less clear, and is more difficult to be distinguished. Hence it appears that this line derives its origin principally from the light of the two extremities of the flame, particularly the inferior one.

447. The reddish line is, in relation to the other parts of the spectrum, very bright in the spectra of light produced by the flame of hydrogen gas and alcohol. In the spectrum of the flame of sulphur it is seen with difficulty.

448. Optical instruments in general have within the last century been brought to so high a degree of perfection that it may almost be doubted if there remain any real improvement to be made in them; nevertheless Dr. Goring states, that in the humble part of their con