result; and this would, in fact, be the case (though the alteration would, under any conceivable conditions, be wholly inappreciable) if the source of light emitted rays of a certain order only. But in the case of such a source of light as a star-or the Sun-no change of colour could be produced, because though-to take the case of approach--the red light would be shifted towards the orange, while a portion of the violet would disappear, yet heat rays from beyond the red end would become visible as red rays through being shortened, and so the spectrum would be complete as before. A similar result would follow in the case of recession.

But the presence of dark lines in a spectrum gives the observer a far more effective means than mere change of colour would supply of determining the approach or recession of a source of light. If some recognised dark line in the spectrum of a star-say, for instance, the F line-is found not to agree exactly in position with the corresponding line in the spectrum of

the fact that the approach of a star at a given rate produces a greater relative effect on wave-lengths of any order than the recess of the star at the same rate would produce.

Of course, in the interesting case of stellar approach or recess, the problem is somewhat complicated by the Earth's own motion, which does not take place in the direction of the star, nor necessarily in the same plane. The successful measurement of the velocity with which Sirius is receding from us is a problem of such interest that I may be permitted to note a very small contribution of mine to the work, in the determination of the formula for eliminating the effects of the Earth's motion (v) viz.-Earth's motion towards starv cos λ sin (l—l') where and are the respective longitudes of the star and the Earth, and a is the star's latitude. The contribution has no particular value, but, such as it is, it chanced that I made it.

a fixed source of light-as a hydrogen flame, for instance -then the difference of position must be ascribed to a motion of recess or approach on the part of the star, and the rate of such motion may be determined by noticing the amount by which the line is displaced.

Now, this method admits of being applied under exceptionally favourable conditions to the examination of solar cyclonic motions-if only these motions are sufficiently rapid to fall within the province of this special mode of research. For we have in the lines appertaining to parts of the Sun which are relatively at rest the means of determining very surely, and

measuring somewhat exactly, the displacement due to such motions as we are considering.

Let us take as an instance the case represented in fig. 39. Here s s', as before, represents the portion of the prominence P P' which is under examination. Only a small part of the spectrum is shown, that, namely, near the F line; and the bright line of the prominence which under normal conditions coincides with the dark line F of the solar spectrum is seen to be displaced towards the violet. It thus appears that, owing to a motion of approach affecting the portion of the prominence included within the narrow space s s', the light-waves producing the F line seem shortened.

The general fact of a motion of approach is thus ascertained. But the rate of approach can also be measured; for we know the length of the light-waves corresponding to the line F, Van der Willingen and Ångström having independently determined the wave-length corresponding to the principal lines in the solar spectrum. So that if we measured in any way the distance of the bright F line of the prominence from the dark F line of the solar spectrum, we should be able to calculate the amount of the apparent change. A better plan, however, is available. For the bright solar spectrum (fig. 39), as also the atmospheric spectrum above, is crossed by other dark lines besides the F line, and these enable us to see at once how far the bright line has shifted. Suppose 1, for example, to be another dark line of the solar spectrum, and that the bright prominence-line has moved half-way from proper place towards 7, then we know that its wavelength is changed to a value midway between the wave-length corresponding to the lines F and 1.* The change of value thus indicated gives us at once the rate of the motion of approach which affects the portion of the prominence-matter corresponding to the space st-because, though the wave-length corresponding

its

*This is true for such small displacements as are here considered. For greater differences of refrangibility, no such simple proportions exist, partly because the actual change of wave-length (for given differences of refrangibility) diminishes towards the violet end, and partly on account of the irrationality of dispersion for all known media, when the spectra they give is compared with what Ångström has called the normal solar spectrum.

†The general rules on which the calculation proceeds are sufficiently

to the line will not be indicated in the tables of

Ångström or of Van der Willingen (which only include the principal lines), yet it is readily determinable, and indeed may be regarded as a known quantity. And, in a similar way, if the line is shifted towards the red end, the velocity of recession of the prominence-matter can readily be determined.

But as a general rule the whole line would not be shifted bodily as in fig. 39; since indeed this would imply that the whole of that portion of the prominence which is seen within the space s s' was travelling bodily towards the observer; whereas obviously such a motion could very seldom be expected to occur. Ordinarily, then, we may expect to find a configuration of the bright line indicating varieties of motion. The same holds also in the case of portions of the solar photosphere, or spots, lying near the edge of the Sun's disc (so that ordinary cyclonic motions within them may be capable of being recognised by the method we are considering), or in the case of more central portions of the Sun's disc where ascending and descending motions are taking place, resulting in motions of recess or approach with reference to the terrestrial observer. In all such cases we may expect to find peculiarities in the affected lines, corresponding to simple. Suppose the wave-length corresponding to the line to be 485.89 millionths of a millimeter, that corresponding to the line F being 486-39 such millionths. Then, since the prominence F-line appears half-way between F and 7, the wave-length has been reduced to 486 19 millionths of a millimeter, or diminished by 0-2 such millionths. Hence the velocity of approach of the prominence matter is ths of the velocity of light, or some 80 miles per second.

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varieties in the motion or rates of motion of the parts examined.

I give a few examples, illustrating the way in which such peculiarities are to be interpreted. I consider, for convenience, motions taking place in that coloured envelope (whence the solar prominences seem to spring) which has been called the sierra or chromatosphere:Suppose ss to represent the portion of the Sun and chromatosphere under examination, s s' being the Sun's limb, c c' the (invisible) outline of the chromatosphere. Now, if the F line appeared as in I., we should conclude that the hydrogen in the part of the sierra under

examination was quiescent near the Sun's surface, as far as motions of approach or recess are concerned (though it might be moving very rapidly in a direction square to the line of sight), but that at some distance from the Sun's surface it was moving very rapidly towards the eye, the rate of motion increasing with the vertical height above the Sun. If, on the other hand, the spectrum appeared as at II. (fig. 40), we should come to a similar conclusion, substituting only a motion of recession for one of approach. If the spectrum appeared as at III. we should conclude that to a certain level above the Sun's limb there was a gradually