this substance in the gaseous state, and the light emitted from the sodium in the nucleus, will be wholly or partially absorbed by the sodium gas contained in the atmosphere, and the dark lines D will be produced in the solar spectrum.

296. One of the most interesting astronomical applications of spectrum analysis, is the determination of the relative motions of the sun and the fixed stars. It is well-known, that the sun is moving at the present time in the direction of the constellation of Hercules. Now if a fixed star is observed to have a proper motion, it is evident on account of the enormous distances between the sun and stars, that the directions of motion of the sun and star must be nearly at right angles to the line joining them; but if the directions of motion are nearly parallel to this line, astronomical methods furnish no means of determining, whether the two bodies are approaching towards or receding from one another. It is at this point that spectrum analysis comes to our aid, and enables the direction of the relative motion to be determined, by means of the shifting of the fixed lines of the spectrum.

297. In order to understand how this is effected, we must explain a theorem originally due to Doppler, which is usually known as Doppler's Principle'.

Let us suppose, that a source S of light is emitting spherical waves, whose velocity of propagation is V; and that the source and the observer are in motion. Let the source be reduced to rest, by impressing upon the observer a velocity equal and opposite to that of the source; and let u be the component of the relative velocity of the observer towards the source, along the line joining him with the latter. Since the observer is unconscious of his own motion, the waves emitted by the source, will appear to be travelling with a velocity V+u; hence if λ be the wave-length, and 7′ the apparent period, that is the time which elapses between the passage of each successive crest of the waves,

DOPPLER'S PRINCIPLE.

291

Now the position of any line in the spectrum depends upon the number of waves, which fall upon the retina in a second. If therefore the observer be in motion, the position of any line will depend upon the apparent period, instead of upon the actual period. Accordingly if the observer is moving towards the star, so that u is positive, the apparent period will be less than the actual period, and any fixed line will be shifted towards the violet end of the spectrum. The converse is the case, when the observer is moving away from the star, so that u is negative, and the fixed lines are shifted towards the red end of the spectrum.

298. By the aid of this method Dr Huggins' ascertained in 1868, that in the spectrum of Sirius, the hydrogen line F is slightly shifted towards the red end of the spectrum; from which it follows, that there is a motion of recession between the earth and Sirius, and he calculated that the relative velocity is about twenty-nine miles per second.

299. Further observations made by Huggins' with improved instruments, not only confirmed his previous observations upon Sirius, but showed that many other stars are in motion, and that some are moving towards, and others from the earth. Thus Sirius, Rigel, Castor, Regulus and & Ursa Majoris, which are situated in that part of the heavens which is opposite to Hercules, are moving from the earth; whilst Arcturus, Vega, and a Cygni, which are situated in the neighbourhood of this constellation, are moving towards the earth.

300. The outer portion of the solar atmosphere consists chiefly of white-hot hydrogen gas, which is constantly agitated by storms of the most violent character; and by observing the peculiar alterations in the breadth and position of the hydrogen line F, Norman Lockyer has been enabled to calculate the velocity with which these masses of gas are moving.

The reader who wishes to pursue this subject further, is recommended to consult Roscoe's Spectrum Analysis, and the various memoirs and treatises relating to Spectrum Analysis, and to Solar and Stellar Chemistry. We must now pass on to the subject of absorption.

1 Phil. Trans. 1868.

2 Phil. Trans. 1872. In this paper a table is given of the stars, which are approaching towards or receding from the earth. See also Roscoe, Spectrum Analysis (fourth edition), pp. 329, 355, and pp. 400-410. ;

Selective Absorption.

301. From the preceding discussion on spectrum analysis, it will be readily understood, that the reason why sherry appears to be of an orange colour is, that this liquid absorbs blue and green light; whilst the colour of claret is due to the fact, that it absorbs yellow and green light, and transmits red and violet. The property which certain transparent substances possess of refusing to transmit light of certain colours, whilst allowing light of other colours to pass freely through, is called selective absorption. Even substances which are apparently transparent to light of all colours, exhibit selective absorption when sufficiently thick. Thus ordinary glass, such as is used for window panes, appears green when the thickness is sufficiently great, thus showing that glass is not perfectly transparent, but has a tendency to absorb certain kinds of light. Air also has a tendency to absorb blue and green light, and in a less degree yellow light; for the colour of the sun at mid-day is a whitish yellow, whilst at sunset or sunrise it is red, thus showing that a sufficient thickness of air refuses a passage to all but the red rays, and this fact has led many physicists to believe that the actual colour of the sun is blue. Silver leaf, which is opaque to luminous rays, transmits the ultra-violet rays, gold leaf transmits green rays, whilst glass which is transparent to luminous rays, absorbs the actinic rays, and also the rays of dark heat'. Quartz, on the other hand, transmits both the luminous and the actinic rays; and on this account it is customary to use quartz prisms when experimenting upon the latter rays. It therefore appears, that transparency and opacity must not be regarded as qualities, which form part of the intrinsic properties of substances, but which depend rather upon the periods of vibration of the ethereal waves.

302. Some of the dynamical theories which have been proposed to explain absorption will be considered in the next chapter, but the following example will assist the reader to understand how it is, that a medium can be opaque to waves whose periods lie between certain limits.

The mechanical properties of a substance, which is incapable

1 Lecher and Pernter, On the Absorption of Dark-heat Rays by Gases and Vapours, Sitz. der K. Akad. der Wissen. in Wien, July 1880; translated, Phil Mag., Jan. 1881. In this paper references are given to the investigations of other experimentalists.

SELECTIVE ABSORPTION.

293

of transmitting waves whose periods lie beyond certain limits, may be illustrated by supposing that for waves travelling parallel to x, the equation of motion of the ether is

If in this equation we put b=0, we obtain the ordinary equation which is furnished by Green's theory; and the last term may be conceived to represent the action of the substance upon the ether. Putting

=

When T∞, μ= 1; as 7 diminishes, μ increases but remains real as long as T>b/a. When 7b/a, μ and V=0; and when T<b/a, μ is negative and V is imaginary. The medium is therefore incapable of propagating waves, whose period is less than b/a; and an equation of the form (1) might therefore be employed to illustrate the action of a medium, which is opaque to the ultra-violet waves.

303. The theoretical explanation of the absorption of certain colours, depends upon the dynamical theorem to which allusion has been made. The molecules of all substances are capable of vibrating in certain definite periods, which are the free periods of the substance. The number of different free periods depends upon the molecular structure of the substance; and in all probability, the more complex the substance is, the more numerous are the free periods of the molecules. If therefore any of the free periods lie within the limits of the periods of the visible spectrum, absorption will take place. Suppose, for example, that the velocity of light in an absorbing medium were given by an equation of the form

where A is a positive constant, 1, K2 are the free periods of t matter, and K > K1. When 7> K, V is real; but when 7

between 1 and K2,

TK,

V will be imaginary; and when 7< K1, V

be again real. Hence a medium, in which the velocity of light is represented by (2), would be transparent to waves of light, whose periods lie between and 2 and between, and 0, but would be opaque to waves whose periods lie between x and x; and (2) might therefore represent a medium, which has an absorption band in the green.

Colours of Natural Bodies.

K2

304. The colours of natural bodies are due to two distinct causes; first, because they absorb certain rays of the spectrum, secondly, because their structure is irregular. That the colours of natural bodies do not arise from their being unable to reflect light of the same colour as that which they absorb, can be shown by examining the surface of a solution of sulphate of copper, enclosed in a vessel whose sides are painted black; for it will be found that the solution appears to be black instead of blue, as would be the case if it reflected light of the same colour as that which it transmits. Moreover the image of a white object reflected at the surface, appears white instead of coloured. If however the solution be rendered turbid by the addition of a little powdered chalk, the liquid immediately appears to be of a brilliant blue. The addition of the chalk produces what is equivalent to an irregularity in the structure of the liquid, and its colour is thereby made manifest.

When white light is incident upon a substance having an irregular structure, a small portion of the light is reflected at the surface, but by far the greater portion will enter the substance. Of this latter portion, a part will pass between the particles, and another part will be refracted by them. The refracted portion will become coloured owing to the absorption of certain kinds of light, and will then be reflected in an irregular manner at the surfaces of the different particles. Hence the light, which taken as a whole, comes from the surface of the substance, exhibits the colour of the particular kind of light, which the substance does not absorb. The red colour of the poppy is due to the fact, that the leaves of its flowers contain a juice, which absorbs blue, green, and a portion of the yellow rays; and if this flower be held in the red end of the spectrum it appears to be of a brilliant red, whilst if it be held in the green or blue it appears to be black,