DOPPLER'S PRINCIPLE.

1077

nate over a continuous spectrum being always nearly proportional to the width of the slit (§ 1061).

Of the nebulæ, it is well known that some have been resolved by powerful telescopes into clusters of stars, while others have as yet proved irresolvable. Huggins has found that the former class of nebulæ give spectra of the same general character as the sun and the fixed stars, but that some of the latter class give spectra of bright lines, indicating that their constitution is gaseous.

1059. Displacement of Lines consequent on Celestial Motions.According to the undulatory theory of light, which is now universally accepted, the fundamental difference between the different rays which compose the complete spectrum, is a difference of wavefrequency, and, as connected with this, a difference of wave-length in any given medium, the rays of greatest wave-frequency or shortest wave-length being the most refrangible.

Doppler first called attention to the change of refrangibility which must be expected to ensue from the mutual approach or recess of the observer and the source of light, the expectation being grounded on reasoning which we have explained in connection with acoustics (§ 898).

Doppler adduced this principle to explain the colours of the fixed stars, a purpose to which it is quite inadequate; but it has rendered very important service in connection with spectroscopic research. Displacement of a line towards the more refrangible end of the spectrum, indicates approach, displacement in the opposite direction indicates recess, and the velocity of approach or recess admits of being calculated from the observed displacement.

When the slit of the spectroscope crosses a spot on the sun's disc, the dark lines lose their straightness in this part, and are bent, sometimes to one side, sometimes to the other. These appearances clearly indicate uprush and downrush of gases in the sun's atmosphere in the region occupied by the spot.

Huggins detected a displacement of the F line towards the red end, in the spectrum of Sirius, as compared with the spectrum of the sun or of hydrogen. The displacement is so small as only to admit of measurement by very powerful instrumental appliances; but, small as it is, calculation shows that it indicates a motion of recess at the rate of about 30 miles per second.1

1 The observed displacement corresponded to recess at the rate of 41.4 miles per second; but 120 of this must be deducted for the motion of the earth in its orbit at the season of

1060. Spectra of Artificial Lights.-The spectra of the artificial lights in ordinary use (including gas, oil-lamps, and candles) differ from the solar spectrum in the relative brightness of the different colours, as well as in the entire absence of dark lines. They are comparatively strong in red and green, but weak in blue; hence all colours which contain much blue in their composition appear to disadvantage by gas-light.

It is possible to find artificial lights whose spectra are of a completely different character. The salts of strontium, for example, give red light, composed of the ingredients represented in spectrum No. 10, Plate III., and those of sodium yellow light (No. 3, Plate III.). If a room is illuminated by a sodium flame (for example, by a spiritlamp with salt sprinkled on the wick), all objects in the room will appear of a uniform colour (that of the flame itself), differing only in brightness, those which contain no yellow in their spectrum as seen by day-light being changed to black. The human countenance and hands assume a ghastly hue, and the lips are no longer red.

A similar phenomenon is observed when a coloured body is held in different parts of the solar spectrum in a dark room, so as to be illuminated by different kinds of monochromatic light. The object either appears of the same colour as the light which falls upon it, or else it refuses to reflect this light and appears black. Hence a screen for exhibiting the spectrum should be white.

1061. Brightness and Purity. The laws which determine the brightness of images generally, and which have been expounded at some length in the preceding chapter, may be applied to the spectroscope. We shall, in the first instance, neglect the loss of light by reflection and imperfect transmission.

Let A denote the prismatic dispersion, as measured by the angular separation of two specified monochromatic images when the naked eye is applied to the last prism, the observing telescope being removed. Then, putting m for the linear magnifying power of the

the year when the observation was made. The remainder, 29'4, was therefore the rate at which the distance between the sun and Sirius was increasing.

In a more recent paper Dr. Huggins gave the results of observations with more powerful instrumental appliances. The recess of Sirius was found to be only 20 miles per second. Arcturus was found to be approaching at the rate of 50 miles per second. Community of motion was established in certain sets of stars; and the belief previously held by astronomers, as to the direction in which the solar system is moving with respect to the stars as a whole, was fully confirmed.

breadth of slit

BRIGHTNESS AND PURITY OF SPECTRUM.

1079

telescope, m▲ is the angular separation observed when the eye is applied to the telescope. We shall call m▲ the total dispersion. Let denote the angle which the breadth of the slit subtends at the centre of the collimating lens, and which is measured by Then is also the apparent breadth of any absolutely focal length of lens' monochromatic image of the slit, formed by rays of minimum deviation, as seen by an eye applied either to the first prism, the last prism, or any one of the train of prisms. The change produced in a pencil of monochromatic rays by transmission through a prism at minimum deviation, is in fact simply a change of direction, without any change of mutual inclination; and thus neither brightness nor apparent size is at all affected. In ordinary cases, the bright lines of a spectrum may be regarded as monochromatic, and their apparent breadth, as seen without the telescope, is sensibly equal to 0. Strictly speaking, the effect of prismatic dispersion in actual cases, is to increase the apparent breadth by a small quantity, which, if all the prisms are alike, is proportional to the number of prisms; but the increase is usually too small to be sensible.

Let I denote the intrinsic brightness of the source as regards any one of its (approximately) monochromatic constituents; in other words, the brightness which the source would have if deprived of all its light except that which goes to form a particular bright line. Then, still neglecting the light stopped by the instrument, the brightness of this line as seen without the aid of the telescope will be I; and as seen in the telescope it will either be equal to or less than this, according to the magnifying power of the telescope and the effective aperture of the object-glass (§ 1038). If the breadth of the slit be halved, the breadth of the bright line will be halved, and its brightness will be unchanged. These conclusions remain true so long as the bright line can be regarded as practically monochromatic.

The brightness of any part of a continuous spectrum follows a very different law. It varies directly as the width of the slit, and inversely as the prismatic dispersion. Its value without the observing telescope, or its maximum value with a telescope, isi, where i is a coefficient depending only on the source.

The purity of any part of a continuous spectrum is properly measured by the ratio of the distance between two specified monochromatic images to the breadth of either, the distance in question being measured from the centre of one to the centre of the other.

This ratio is unaffected by the employment of an observing telescope,

and is.

ΔΙ

The ratio of the brightness of a bright line to that of the adjacent portion of a continuous spectrum forming its back-ground, is θε assuming the line to be so nearly monochromatic that the increase of its breadth produced by the dispersion of the prisms is an insignificant fraction of its whole breadth. As we widen the slit, and so increase 0, we must increase A in the same ratio, if we wish to preserve the same ratio of brightness. As is increased indefinitely, the predominance of the bright lines does not increase indefinitely, but tends to a definite limit, namely, to the predominance which they would have in a perfectly pure spectrum of the given source.

The loss of light by reflection and imperfect transmission, increases with the number of surfaces of glass which are to be traversed; so that, with a long train of prisms and an observing telescope, the actual brightness will always be much less than the theoretical brightness as above computed.

The actual purity is always less than the theoretical purity, being greatly dependent on freedom from optical imperfections; and these can be much more completely avoided in lenses than in prisms. It is said that a single good prism, with a first-class collimator and telescope (as originally employed by Swan), gives a spectrum much more free from blurring than the modern multiprism spectroscopes, when the total dispersion m▲ is the same in both the cases compared.

1062. Chromatic Aberration.-The unequal refrangibility of the different elementary rays is a source of grave inconvenience in connection with lenses. The focal length of a lens depends upon its index of refraction, which of course increases with refrangibility, the focal length being shortest for the most refrangible rays. Thus a lens of uniform material will not form a single white image of a white object, but a series of images, of all the colours of the spectrum, arranged at different distances, the violet images being nearest, and the red most remote. If we place a screen anywhere in the series of images, it can only be in the right position for one colour. Every other colour will give a blurred image, and the superposition of them all produces the image actually formed on the screen. If the object be a uniform white spot on a black ground, its image on the screen

will consist of white in its central parts, gradually merging into a coloured fringe at its edge. Sharpness of outline is thus rendered impossible, and nothing better can be done than to place the screen at the focal distance corresponding to the brightest part of the spectrum. Similar indistinctness will attach to images observed in midair, whether directly or by means of another lens. This source of confusion is called chromatic aberration.

1063. Possibility of Achromatism.-In order to ascertain whether it was possible to remedy this evil by combining lenses of two different materials, Newton made some trials with a compound prism composed of glass and water (the latter containing a little sugar of lead), and he found that it was not possible, by any arrangement of these two substances, to produce deviation of the transmitted light without separation into its component colours. Unfortunately he did not extend his trials to other substances, but concluded at once that an achromatic prism (and hence also an achromatic lens) was an impossibility; and this conclusion was for a long time accepted as indisputable. Mr. Hall, a gentleman of Worcestershire, was the first to show that it was erroneous, and is said to have constructed some achromatic telescopes; but the important fact thus discovered did not become generally known till it was rediscovered by Dollond, an eminent London optician, in whose hands the manufacture of achromatic instruments attained great perfection.

1064. Conditions of Achromatism.-The conditions necessary for achromatism are easily explained. The angular separation between the brightest red and the brightest violet ray transmitted through a prism is called the dispersion of the prism, and is evidently the difference of the deviations of these rays. These deviations, for the position of minimum deviation of a prism of small refracting angle A, are (1) A and (μ”—1) A, μ' and μ" denoting the indices of refraction for the two rays considered (§ 1004, equation (1)) and their difference is (u" -μ) A. This difference is always small in comparison with either of the deviations whose difference it is, and its ratio to either of them, or more accurately its ratio to the value of (μ-1) A for the brightest part of the spectrum, is called the dispersive power of the substance. As the common factor A may be omitted, the formula for the dispersive power is evidently ""

μ-1

If this ratio were the same for all substances, as Newton supposed, achromatism would be impossible; but in fact its value varies greatly,