AB representing the sound of the approaching whistle, BC representing the rapid degradation of sound as the engine rushes close past the hearer, and CD representing the sound of the receding whistle. When a bell is sounded on the engine, as in America, the effect is better recognized, as I had repeated occasion to notice during my travels in that country. Probably this is because the tone of a bell is in any case much more clearly recognized than the tone of a railway whistle. The change of tone as a clanging bell is carried swiftly past (by the combined motions of both trains) is not at all of such a nature as to require close attention for its detection.

However, the apparent variation of sound produced by rapid approach or recession has been tested by exact experiments. On a railway uniting Utrecht and Maarsen “were placed,” the late Professor Nichol wrote, “at intervals of something upwards of a thousand yards, three groups of musicians, who remained motionless during the requisite period. Another musician on the railway sounded at intervals one uniform note; and its effects on the ears of the stationary musicians have been fully published. From these, certainly—from the recorded changes between grave and the more acute, and vice versÂ,—confirming, even numerically, what the relative velocities might have enabled one to predict, it appears justifiable to conclude that the general theory is correct; and that the note of any sound may be greatly modified, if not wholly changed, by the velocity of the individual hearing it,” or, he should have added, by the velocity of the source of sound: perhaps more correct than either, is the statement that the note may be altered by the approach or recession of the source of sound, whether that be caused by the motion of the sounding body, or of the hearer himself, or of both.

It is difficult, indeed, to understand how doubt can exist in the mind of any one competent to form an opinion on the matter, though, as we shall presently see, some students of science and one or two mathematicians have raised doubts as to the validity of the reasoning by which it is shown that a change should occur. That the reasoning is sound cannot, in reality, be questioned, and after careful examination of the arguments urged against it by one or two mathematicians, I can form no other opinion than that these arguments amount really but to an expression of inability to understand the matter. This may seem astonishing, but is explained when we remember that some mathematicians, by devoting their attention too particularly to special departments, lose, to a surprising degree, the power of dealing with subjects (even mathematical ones) outside their department. Apart from the soundness of the reasoning, the facts are unmistakably in accordance with the conclusion to which the reasoning points. Yet some few still entertain doubts, a circumstance which may prove a source of consolation to any who find themselves unable to follow the reasoning on which the effects of approach and recession on wave-lengths depend. Let such remember, however, that experiment in the case of the aerial waves producing sound, accords perfectly with theory, and that the waves which produce light are perfectly analogous (so far as this particular point is concerned) with the waves producing sound.

Ordinary white light, and many kinds of coloured light, may be compared with noise—that is, with a multitude of intermixed sounds. But light of one pure colour may be compared to sound of one determinate note. As the aerial waves producing the effect of one definite tone are all of one length, so the ethereal waves producing light of one definite colour are all of one length. Therefore if we approach or recede from a source of light emitting such waves, effects will result corresponding with what has been described above for the case of water-waves and sound-waves. If we approach the source of light, or if it approaches us, the waves will be shortened; if we recede from it, or if it recedes from us, the waves will be lengthened. But the colour of light depends on its wave-length, precisely as the tone of sound depends on its wave-length. The waves producing red light are longer than those producing orange light, these are longer than the waves producing yellow light; and so the wave-lengths shorten down from yellow to green, thence to blue, to indigo, and finally to violet. Thus if a body shining in reality with a pure green colour, approached the observer with a velocity comparable with that of light, it would seem blue, indigo, or violet, according to the rate of approach; whereas if it rapidly receded, it would seem yellow, orange, or red, according to the rate of recession.

Unfortunately in one sense, though very fortunately in many much more important respects, the rates of motion among the celestial bodies are not comparable with the velocity of light, but are always so much less as to be almost rest by comparison. The velocity of light is about 187,000 miles per second, or, according to the measures of the solar system at present in vogue (which will shortly have to give place to somewhat larger measures, the result of observations made upon the recent transit of Venus), about 185,000 miles per second. The swiftest celestial motion of which we have ever had direct evidence was that of the comet of the year 1843, which, at the time of its nearest approach to the sun, was travelling at the rate of about 350 miles per second. This, compared with the velocity of light, is as the motion of a person taking six steps a minute, each less than half a yard long, to the rush of the swiftest express train. No body within our solar system can travel faster than this, the motion of a body falling upon the sun from an infinite distance being only about 370 miles per second when it reaches his surface. And though swifter motions probably exist among the bodies travelling around more massive suns than ours, yet of such motions we can never become cognizant. All the motions taking place among the stars themselves would appear to be very much less in amount. The most swiftly moving sun seems to travel but at the rate of about 50 or 60 miles per second.

Now let us consider how far a motion of 100 miles per second might be expected to modify the colour of pure green light—selecting green as the middle colour of the spectrum. The waves producing green light are of such a length, that 47,000 of them scarcely equal in length a single inch. Draw on paper an inch and divide it carefully into ten equal parts, or take such parts from a well-divided rule; divide one of these tenths into ten equal parts, as nearly as the eye will permit you to judge; then one of these parts, or about half the thickness of an average pin, would contain 475 of the waves of pure green light. The same length would equal the length of 440 waves of pure yellow light, and of 511 waves of pure blue light. (The green, yellow, and blue, here spoken of, are understood to be of the precise colour of the middle of the green, yellow, and blue parts of the spectrum.) Thus the green waves must be increased in the proportion of 475 to 440 to give yellow light, or reduced in the proportion of 511 to 475 to give blue light. For the first purpose, the velocity of recession must bear to the velocity of light the proportion which 30 bears to 475, or must be equal to rather more than one-sixteenth part of the velocity of light—say 11,600 miles per second. For the second purpose, the velocity of approach must bear to the velocity of light the proportion which 36 bears to 475, or must be nearly equal to one-thirteenth part of the velocity of light—say 14,300 miles per second. But the motions of the stars and other celestial bodies, and also the motions of matter in the sun, and so forth, are very much less than these. Except in the case of one or two comets (and always dismissing from consideration the amazing apparent velocities with which comets’ tails seem to be formed), we may take 100 miles per second as the extreme limit of velocity with which we have to deal, in considering the application of our theory to the motions of recession and approach of celestial bodies. Thus in the case of recession the greatest possible change of colour in pure green light would be equivalent to the difference between the medium green of the spectrum, and the colour 1-116th part of the way from medium green to medium yellow; and in the case of approach, the change would correspond to the difference between the medium green and the colour 1-143rd part of the way from medium green to medium blue. Let any one look at a spectrum of fair length, or even at a correctly tinted painting of the solar spectrum, and note how utterly unrecognizable to ordinary vision is the difference of tint for even the twentieth part of the distance between medium green and medium yellow on one side or medium blue on the other, and he will recognize how utterly hopeless it would be to attempt to appreciate the change of colour due to the approach or recession of a luminous body shining with pure green light and moving at the tremendous rate of 100 miles per second. It would be hopeless, even though we had the medium green colour and the changed colour, either towards yellow or towards blue, placed side by side for comparison—how much more when the changed colour would have to be compared with the observer’s recollection of the medium colour, as seen on some other occasion!

But this is the least important of the difficulties affecting the application of this method by noting change of colour, as Doppler originally proposed. Another difficulty, which seems somehow to have wholly escaped Doppler’s attention, renders the colour test altogether unavailable. We do not get pure light from any of the celestial bodies except certain gaseous clouds or nebulÆ. From every sun we get, as from our own sun, all the colours of the rainbow. There may be an excess of some colours and a deficiency of others in any star, so as to give the star a tint, or even a very decided colour. But even a blood-red star, or a deep-blue or violet star, does not shine with pure light, for the spectroscope shows that the star has other colours than those producing the prevailing tint, and it is only the great excess of red rays (all kinds of red, too) or of blue rays (of all kinds), and so on, which makes the star appear red, or blue, and so on, to the eye. By far the greater number of stars or suns show all the colours of the rainbow nearly equally distributed, as in the case of our own sun. Now imagine for a moment a white sun, which had been at rest, to begin suddenly to approach us so rapidly (travelling more than 10,000 miles per second) that the red rays became orange, the orange became yellow, the yellow green, the green blue, the blue indigo, the indigo violet, while the violet waves became too short to affect the sense of sight. Then, if that were all, that sun, being deprived of the red part of its light, would shine with a slightly bluish tinge, owing to the relative superabundance of rays from the violet end of the spectrum. We should be able to recognize such a change, yet not nearly so distinctly as if that sun had been shining with a pure green light, and suddenly beginning to approach us at the enormous rate just mentioned, changed in colour to full blue. Though, if that sun were all the time approaching us at the enormous rate imagined, we should be quite unable to tell whether its slightly bluish tinge were due to such motion of approach or to some inherent blueness in the light emitted by the star. Similarly, if a white sun suddenly began to recede so rapidly that its violet rays were turned to indigo, the indigo to blue, and so on, the orange rays turning to red, and the red rays disappearing altogether, then, if that were all, its light would become slightly reddish, owing to the relative superabundance of light from the red end of the spectrum; and we might distinguish the change, yet not so readily as if a sun shining with pure green light began to recede at the same enormous rate, and so shone with pure yellow light. Though, if that sun were all the time receding at that enormous rate, we should be quite unable to tell whether its slightly reddish hue were due to such motion of recession or to some inherent redness in its own lustre. But in neither case would that be all. In the former, the red rays would indeed become orange; but the rays beyond the red, which produce no effect upon vision, would be converted into red rays, and fill up the part of the spectrum deserted by the rays originally red. In the latter, the violet rays would indeed become indigo; but the rays beyond the violet, ordinarily producing no visible effect, would be converted into violet rays, and fill up the part of the spectrum deserted by the rays originally violet. Thus, despite the enormous velocity of approach in one case and of recession in the other, there would be no change whatever in the colour of the sun in either case. All the colours of the rainbow would still be present in the sun’s light, and it would therefore still be a white sun.

Doppler’s method would thus fail utterly, even though the stars were travelling hither and thither with motions a hundred times greater than the greatest known stellar motions.

This objection to Doppler’s theory, as originally proposed, was considered by me in an article on “Coloured Suns” in Fraser’s Magazine for January, 1868. His theory, indeed, was originally promulgated not as affording a means of measuring stellar motions, but as a way of accounting for the colours of double stars. It was thus presented by Professor Nichol, in a chapter of his “Architecture of the Heavens,” on this special subject:—“The rapid motion of light reaches indeed one of those numbers which reason owns, while imagination ceases to comprehend them; but it is also true that the swiftness with which certain individuals of the double stars sweep past their perihelias, or rather their periasters, is amazing; and in this matter of colours, it must be recollected that the question solely regards the difference between the velocities of the waves constituent of colours, at those different stellar positions. Still it is a bold—even a magnificent idea; and if it can be reconciled with the permanent colours of the multitude of stars surrounding us—stars which too are moving in great orbits with immense velocities—it may be hailed almost as a positive discovery. It must obtain confirmation, or otherwise, so soon as we can compare with certainty the observed colorific changes of separate systems with the known fluctuations of their orbital motions.”

That was written a quarter of a century ago, when spectroscopic analysis, as we now know it, had no existence. Accordingly, while the fatal objection to Doppler’s original theory is overlooked on the one hand, the means of applying the principle underlying the theory, in a much more exact manner than Doppler could have hoped for, is overlooked on the other. Both points are noted in the article above referred to, in the same paragraph. “We may dismiss,” I there stated, “the theory started some years ago by the French astronomer, M. Doppler.” But, I presently added, “It is quite clear that the effects of a motion rapid enough to produce such a change” (i.e. a change of tint in a pure colour) “would shift the position of the whole spectrum—and this change would be readily detected by a reference to the spectral lines.” This is true, even to the word “readily.” Velocities which would produce an appreciable change of tint would produce “readily” detectible changes in the position of the spectral lines; the velocities actually existing among the star-motions would produce changes in the position of these lines detectible only with extreme difficulty, or perhaps in the majority of instances not detectible at all.

It has been in this way that the spectroscopic method has actually been applied.

It is easy to perceive the essential difference between this way of applying the method and that depending on the attempted recognition of changes of colour. A dark line in the spectrum marks in reality the place of a missing tint. The tints next to it on either side are present, but the tint between them is wanting. They are changed in colour—very slightly, in fact quite inappreciably—by motions of recession or approach, or, in other words, they are shifted in position along the spectrum, towards the red end for recession, towards the violet end for approach; and of course the dark space between is shifted along with them. One may say that the missing tint is changed. For in reality that is precisely what would happen. If the light of a star at rest gave every tint of the spectrum, for instance, except mid-green alone, and that star approached or receded so swiftly that its motion would change pure green light to pure yellow in one case, or pure blue in the other, then the effect on the spectrum of such a star would be to throw the dark line from the middle of the green part of the spectrum to the middle of the yellow part in one case, or to the middle of the blue part in the other. The dark line would be quite notably shifted in either case. With the actual stellar motions, though all the lines are more or less shifted, the displacement is always exceedingly minute, and it becomes a task of extreme difficulty to recognize, and still more to measure, such displacement.

When I first indicated publicly (January, 1868) the way in which Doppler’s principle could alone be applied, two physicists, Huggins in England and Secchi in Italy, were actually endeavouring, with the excellent spectroscopes in their possession, to apply this method. In March, 1868, Secchi gave up the effort as useless, publicly announcing the plan on which he had proceeded and his failure to obtain any results except negative ones. A month later Huggins also publicly announced the plan on which he had been working, but was also able to state that in one case, that of the bright star Sirius, he had succeeded in measuring a motion in the line of sight, having discovered that Sirius was receding from the earth at the rate of 41·4 miles per second. I say was receding, because a part of the recession at the time of observation was due to the earth’s orbital motion around the sun. I had, at his request, supplied Huggins with the formula for calculating the correction due to this cause, and, applying it, he found that Sirius is receding from the sun at the rate of about 29½ miles per second, or some 930 millions of miles per annum.

I am not here specially concerned to consider the actual results of the application of this method since the time of Huggins’s first success; but the next chapter of the history of the method is one so interesting to myself personally that I feel tempted briefly to refer to details. So soon as I had heard of Huggins’s success with Sirius, and that an instrument was being prepared for him wherewith he might hope to extend the method to other stars, I ventured to make a prediction as to the result which he would obtain whensoever he should apply it to five stars of the seven forming the so-called Plough. I had found reason to feel assured that these five form a system drifting all together amid stellar space. Satisfied for my own part as to the validity of the evidence, I submitted it to Sir J. Herschel, who was struck by its force. The apparent drift of those stars was, of course, a thwart drift; but if they really were drifting in space, then their motions in the line of sight must of necessity be alike. My prediction, then, was that whensoever Huggins applied to those stars the new method he would find them either all receding at the same rate, or all approaching at the same rate, or else that all alike failed to give any evidence at all either of recession or approach. I had indicated the five in the first edition of my “Other Worlds”—to wit, the stars of the Plough, omitting the nearest “pointer” to the pole and the star marking the third horse (or the tip of the Great Bear’s tail). So soon as Huggins’s new telescope and its spectroscopic adjuncts were in working order, he re-examined Sirius, determined the motions of other stars; and at last on one suitable evening he tested the stars of the Plough. He began with the nearest pointer, and found that star swiftly approaching the earth. He turned to the other pointer, and found it rapidly receding from the earth. Being under the impression that my five included both pointers, he concluded that my prediction had utterly failed, and so went on with his observations, altogether unprejudiced in its favour, to say the least. The next star of the seven he found to be receding at the same rate as the second pointer; the next at the same rate, the next, and the next receding still at the same rate, and lastly the seventh receding at a different rate. Here, then, were five stars all receding at a common rate, and of the other two one receding at a different rate, the other swiftly approaching. Turning next to the work containing my prediction, Huggins found that the five stars thus receding at a common rate were the five whose community of motion I had indicated two years before. Thus the first prediction ever made respecting the motions of the so-called fixed stars was not wanting in success. I would venture to add that the theory of star-drift, on the strength of which the prediction was made, was in effect demonstrated by the result.

The next application of the new method was one of singular interest. I believe it was Mr. Lockyer who first thought of applying the method to measure the rate of solar hurricanes as well as the velocities of the uprush and downrush of vaporous matter in the atmosphere of the sun. Another spectroscopic method had enabled astronomers to watch the rush of glowing matter from the edge of the sun, by observing the coloured flames and their motions; but by the new method it was possible to determine whether the flames at the edge were swept by solar cyclones carrying them from or towards the eye of the terrestrial observer, and also to determine whether glowing vapours over the middle of the visible disc were subject to motion of uprush, which of course would carry them towards the eye, or of downrush, which would carry them from the eye. The result of observations directed to this end was to show that at least during the time when the sun is most spotted, solar hurricanes of tremendous violence take place, while the uprushing and downrushing motions of solar matter sometimes attain a velocity of more than 100 miles per second.

It was this success on the part of an English spectroscopist which caused that attack on the new method against which it has but recently been successfully defended, at least in the eyes of those who are satisfied only by experimental tests of the validity of a process. The Padre Secchi had failed, as we have seen, to recognize motions of recession and approach among the stars by the new method. But he had taken solar observation by spectroscopic methods under his special charge, and therefore when the new results reached his ears he felt bound to confirm or invalidate them. He believed that the apparent displacement of dark lines in the solar spectrum might be due to the heat of the sun causing changes in the delicate adjustments of the instrument—a cause of error against which precautions are certainly very necessary. He satisfied himself that when sufficient precautions are taken no displacements take place such as Lockyer, Young, and others claimed to have seen. But he submitted the matter to a further test. As the sun is spinning swiftly on his axis, his mighty equator, more than two and a half millions of miles in girth, circling once round in about twenty-four days, it is clear that on one side the sun’s surface is swiftly moving towards, and on the other side as swiftly moving from, the observer. By some amazing miscalculation, Secchi made the rate of this motion 20 miles per second, so that the sum of the two motions in opposite directions would equal 40 miles per second. He considered that he ought to be able by the new method, if the new method is trustworthy at all, to recognize this marked difference between the state of the sun’s eastern and western edges; he found on trial that he could not do so; and accordingly he expressed his opinion that the new method is not trustworthy, and that the arguments urged in its favour are invalid.

The weak point in his reasoning resided in the circumstance that the solar equator is only moving at the rate of about 1¼ miles per second, so that instead of a difference of 40 miles per second between the two edges, which should be appreciable, the actual difference (that is, the sum of the two equal motions in opposite directions) amounts only to 2½ miles per second, which certainly Secchi could not hope to recognize with the spectroscopic power at his disposal. Nevertheless, when the error in his reasoning was pointed out, though he admitted that error, he maintained the justice of his conclusion; just as Cassini, having mistakenly reasoned that the degrees of latitude should diminish towards the pole instead of increasing, and having next mistakenly found, as he supposed, that they do diminish, acknowledged the error of his reasoning, but insisted on the validity of his observations,—maintaining thenceforth, as all the world knows, that the earth is extended instead of flattened at the poles.

Huggins tried to recognize by the new method the effects of the sun’s rotation, using a much more powerful spectroscope than Secchi’s. The history of the particular spectroscope he employed is in one respect specially interesting to myself, as the extension of spectroscopic power was of my own devising before I had ever used or even seen a powerful spectroscope. The reader is aware that spectroscopes derive their light-sifting power from the prisms forming them. The number of prisms was gradually increased, from Newton’s single prism to Fraunhofer’s pair, and to Kirchhoff’s battery of four, till six were used, which bent the light round as far as it would go. Then the idea occurred of carrying the light to a higher level (by reflections) and sending it back through the same battery of prisms, doubling the dispersion. Such a battery, if of six prisms, would spread the spectral colours twice as widely apart as six used in the ordinary way, and would thus have a dispersive power of twelve prisms. It occurred to me that after taking the rays through six prisms, arranged in a curve like the letter C, an intermediate four-cornered prism of a particular shape (which I determined) might be made to send the rays into another battery of six prisms, the entire set forming a double curve like the letter S, the rays being then carried to a higher level and back through the double battery. In this way a dispersive power of nineteen prisms could be secured. My friend, Mr. Browning, the eminent optician, made a double battery of this kind,13 which was purchased by Mr. W. Spottiswoode, and by him lent to Mr. Huggins for the express purpose of dealing with the task Secchi had set spectroscopists. It did not, however, afford the required evidence. Huggins considered the displacement of dark lines due to the sun’s rotation to be recognizable, but so barely that he could not speak confidently on the point.

There for a while the matter rested. VÖgel made observations confirming Huggins’s results relative to stellar motions; but VÖgel’s instrumental means were not sufficiently powerful to render his results of much weight.

But recently two well-directed attacks have been made upon this problem, one in England, the other in America, and in both cases with success. Rather, perhaps, seeing that the method had been attacked and was supposed to require defence, we may say that two well-directed assaults have been made upon the attacking party, which has been completely routed.

Arrangements were made not very long ago, by which the astronomical work of Greenwich Observatory, for a long time directed almost exclusively to time observations, should include the study of the sun, stars, planets, and so forth. Amongst other work which was considered suited to the National Observatory was the application of spectroscopic analysis to determine motions of recession and approach among the celestial bodies. Some of these observations, by the way, were made, we are told, “to test the truth of Doppler’s principle,” though it seems difficult to suppose for an instant that mathematicians so skilful as the chief of the Observatory and some of his assistants could entertain any doubt on that point. Probably it was intended by the words just quoted to imply simply that some of the observations were made for the purpose of illustrating the principle of the method. We are not to suppose that on a point so simple the Greenwich observers have been in any sort of doubt.

At first their results were not very satisfactory. The difficulties which had for a long time foiled Huggins, and which Secchi was never able to master, rendered the first Greenwich measures of stellar motions in the line of sight wildly inconsistent, not only with Huggins’s results, but with each other.

Secchi was not slow to note this. He renewed his objections to the new method of observation, pointing and illustrating them by referring to the discrepancies among the Greenwich results. But recently a fresh series of results has been published, showing that the observers at Greenwich have succeeded in mastering some at least among the difficulties which they had before experienced. The measurements of star-motions showed now a satisfactory agreement with Huggins’s results, and their range of divergence among themselves was greatly reduced. The chief interest of the new results, however, lay in the observations made upon bodies known to be in motion in the line of sight at rates already measured. These observations, though not wanted as tests of the accuracy of the principle, were very necessary as tests of the qualities of the instruments used in applying it. It is here and thus that Secchi’s objections alone required to be met, and here and thus they have been thoroughly disposed of. Let us consider what means exist within the solar system for thus testing the new method.

The earth travels along in her orbit at the rate of about 18? miles in every second of time. Not to enter into niceties which could only properly be dealt with mathematically, it may be said that with this full velocity she is at times approaching the remoter planets of the system, and at times receding from them; so that here at once is a range of difference amounting to about 37 miles per second, and fairly within the power of the new method of observation. For it matters nothing, so far as the new method is concerned, whether the earth is approaching another orb by her motion, or that orb approaching by its own motion. Again, the plant Venus travels at the rate of about 21½ miles per second, but as the earth travels only 3 miles a second less swiftly, and the same way round, only a small portion of Venus’s motion ever appears as a motion of approach towards or recession from the earth. Still, Venus is sometimes approaching and sometimes receding from the earth, at a rate of more than 8 miles per second. Her light is much brighter than that of Jupiter or Saturn, and accordingly this smaller rate of motion would be probably more easily recognized than the greater rate at which the giant planets are sometimes approaching and at other times receding from the earth. At least, the Greenwich observers seem to have confined their attention to Venus, so far as motions of planets in the line of sight are concerned. The moon, as a body which keeps always at nearly the same distance from us, would of course be the last in the world to be selected to give positive evidence in favour of the new method; but she serves to afford a useful test of the qualities of the instruments employed. If when these were applied to her they gave evidence of motions of recession or approach at the rate of several miles per second, when we know as a matter of fact that the moon’s distance never14 varies by more than 30,000 miles during the lunar month, her rate of approach or recession thus averaging about one-fiftieth part of a mile per second, discredit would be thrown on the new method—not, indeed, as regards its principle, which no competent reasoner can for a moment question, but as regards the possibility of practically applying it with our present instrumental means.

Observations have been made at Greenwich, both on Venus and on the moon, by the new method, with results entirely satisfactory. The method shows that Venus is receding when she is known to be receding, and that she is approaching when she is known to be approaching. Again, the method shows no signs of approach or recession in the moon’s case. It is thus in satisfactory agreement with the known facts. Of course these results are open to the objection that the observers have known beforehand what to expect, and that expectation often deceives the mind, especially in cases where the thing to be observed is not at all easy to recognize. It will presently be seen that the new method has been more satisfactorily tested, in this respect, in other ways. It may be partly due to the effect of expectation that in the case of Venus the motions of approach and recession, tested by the new method, have always been somewhat too great. A part of the excess may be due to the use of the measure of the sun’s distance, and therefore the measures of the dimensions of the solar system, in vogue before the recent transit. These measures fall short to some degree of those which result from the observations made in December, 1874, on Venus in transit, the sun’s distance being estimated at about 91,400,000 miles instead of 92,000,000 miles, which would seem to be nearer the real distance. Of course all the motions within the solar system would be correspondingly under-estimated. On the other hand, the new method would give all velocities with absolute correctness if instrumental difficulties could be overcome. The difference between the real velocities of Venus approaching and receding, and those calculated according to the present inexact estimate of the sun’s distance, is however much less than the observed discrepancy, doubtless due to the difficulties involved in the application of this most difficult method. I note the point, chiefly for the sake of mentioning the circumstance that theoretically the method affords a new means of measuring the dimensions of the solar system. Whensoever the practical application of the method has been so far improved that the rate of approach or recession of Venus, or Mercury, or Jupiter, or Saturn (any one of these planets), can be determined on any occasion, with great nicety, we can at once infer the sun’s distance with corresponding exactness. Considering that the method has only been invented ten years (setting aside Doppler’s first vague ideas respecting it), and that spectroscopic analysis as a method of exact observation is as yet little more than a quarter of a century old, we may fairly hope that in the years to come the new method, already successfully applied to measure motions of recession and approach at the rate of 20 or 30 miles per second, will be employed successfully in measuring much smaller velocities. Then will it give us a new method of measuring the great base-line of astronomical surveying—the distance of our world from the centre of the solar system.

That this will one day happen is rendered highly probable, in my opinion, by the successes next to be related.

Besides the motions of the planets around the sun, there are their motions of rotation, and the rotation of the sun himself upon his axis. Some among these turning motions are sufficiently rapid to be dealt with by the new method. The most rapid rotational motion with which we are acquainted from actual observation is that of the planet Jupiter. The circuit of his equator amounts to about 267,000 miles, and he turns once on his axis in a few minutes less than ten hours, so that his equatorial surface travels at the rate of about 26,700 miles an hour, or nearly 7½ miles per second. Thus between the advancing and retreating sides of the equator there is a difference of motion in the line of sight amounting to nearly 15 miles. But this is not all. Jupiter shines by reflecting sunlight. Now it is easily seen that where his turning equator meets the waves of light from the sun, these are shortened, in the same sense that waves are shortened for a swimmer travelling to meet them, while these waves, already shortened in this way, are further shortened when starting from the same advancing surface of Jupiter, on their journey to us after reflection. In this way the shortening of the waves is doubled, at least when the earth is so placed that Jupiter lies in the same direction from us as from the sun, the very time, in fact, when Jupiter is most favourably placed for ordinary observation, or is at his highest due south, when the sun is at his lowest below the northern horizon—that is, at midnight. The lengthening of the waves is similarly doubled at this most favourable time for observation; and the actual difference between the motion of the two sides of Jupiter’s equator being nearly 15 miles per second, the effect on the light-waves is equivalent to that due to a difference of nearly 30 miles per second. Thus the new method may fairly be expected to indicate Jupiter’s motion of rotation. The Greenwich observers have succeeded in applying it, though Jupiter has not been favourably situated for observation. Only on one occasion, says Sir G. Airy, was the spectrum of Jupiter “seen fairly well,” and on that occasion “measures were obtained which gave a result in remarkable agreement with the calculated value.” It may well be hoped that when in the course of a few years Jupiter returns to that part of his course where he rises high above the horizon, shining more brightly and through a less perturbed air, the new method will be still more successfully applied. We may even hope to see it extended to Saturn, not merely to confirm the measures already made of Saturn’s rotation, but to resolve the doubts which exist as to the rotation of Saturn’s ring-system.

Lastly, there remains the rotation of the sun, a movement much more difficult to detect by the new method, because the actual rate of motion even at the sun’s equator amounts only to about 1 mile per second.

In dealing with this very difficult task, the hardest which spectroscopists have yet attempted, the Greenwich observers have achieved an undoubted success; but unfortunately for them, though fortunately for science, another observatory, far smaller and of much less celebrity, has at the critical moment achieved success still more complete.

The astronomers at our National Observatory have been able to recognize by the new method the turning motion of the sun upon his axis. And here we have not, as in the case of Venus, to record merely that the observers have seen what they expected to see because of the known motion of the sun. “Particular care was taken,” says Airy, “to avoid any bias from previous knowledge of the direction in which a displacement” (of the spectral lines) “was to be expected,” the side of the sun under observation not being known by the observer until after the observation was completed.

But Professor Young, at Dartmouth College, Hanover, N.H., has done much more than merely obtain evidence by the new method that the sun is rotating as we already knew. He has succeeded so perfectly in mastering the instrumental and observational difficulties, as absolutely to be able to rely on his measurement (as distinguished from the mere recognition) of the sun’s motion of rotation. The manner in which he has extended the powers of ordinary spectroscopic analysis, cannot very readily be described in these pages, simply because the principles on which the extension depends require for their complete description a reference to mathematical considerations of some complexity. Let it be simply noted that what is called the diffraction spectrum, obtained by using a finely lined plate, results from the dispersive action of such a plate, or grating as it is technically called, and this dispersive power can be readily combined with that of a spectroscope of the ordinary kind. Now Dr. Rutherfurd, of New York, has succeeded in ruling so many thousand lines on glass within the breadth of a single inch as to produce a grating of high dispersive power. Availing himself of this beautiful extension of spectroscopic powers, Professor Young has succeeded in recognizing effects of much smaller motions of recession and approach than had before been observable by the new method. He has thus been able to measure the rotation-rate of the sun’s equatorial regions. His result exceeds considerably that inferred from the telescopic observation of the solar spots. For whereas from the motion of the spots a rotation-rate of about 1¼ mile per second has been calculated for the sun’s equator, Professor Young obtains from his spectroscopic observations a rate of rather more than 1? mile, or about 300 yards per second more than the telescopic rate. If Young had been measuring the motion of the same matter which is observed with the telescope, there could of course be no doubt that the telescope was right and the spectroscope wrong. We might add a few yards per second for the probably greater distance of the sun resulting from recent transit observations. For of course with an increase in our estimate of the sun’s distance there comes an increase in our estimate of the sun’s dimensions, and of the velocity of the rotational motion of his surface. But only about 12 yards per second could be allowed on this account; the rest would have to be regarded as an error due to the difficulties involved in the spectroscopic method. In reality, however, the telescopist and the spectroscopist observe different things in determining by their respective methods the sun’s motion of rotation. The former observes the motion of the spots belonging to the sun’s visible surface; the latter observes the motion of the glowing vapours outside that surface, for it is from these vapours, not from the surface of the sun, that the dark lines of the spectrum proceed. Now so confident is Professor Young of the accuracy of his spectroscopic observations, that he is prepared to regard the seeming difference of velocity between the atmosphere and surface of the sun as real. He believes that “the solar atmosphere really sweeps forward over the underlying surface, in the same way that the equatorial regions outstrip the other parts of the sun’s surface.” This inference, important and interesting in itself, is far more important in what it involves. For if we can accept it, it follows that the spectroscopic method of measuring the velocity of motions in the line of sight is competent, under favourable conditions, to obtain results accurate within a few hundred yards per second, or 10 or 12 miles per minute. If this shall really prove to be true for the method now, less than ten years after it was first successfully applied, what may we not hope from the method in future years? Spectroscopic analysis itself is in its infancy, and this method is but a recent application of spectroscopy. A century or so hence astronomers will smile (though not disdainfully) at these feeble efforts, much as we smile now in contemplating the puny telescopes with which Galileo and his contemporaries studied the star-depths. And we may well believe that largely as the knowledge gained by telescopists in our own time surpasses that which Galileo obtained, so will spectroscopists a few generations hence have gained a far wider and deeper insight into the constitution and movements of the stellar universe than the spectroscopists of our own day dare even hope to attain.

I venture confidently to predict that, in that day, astronomers will recognize in the universe of stars a variety of structure, a complexity of arrangement, an abundance of every form of cosmical vitality, such as I have been led by other considerations to suggest, not the mere cloven lamina of uniformly scattered stars more or less resembling our sun, and all in nearly the same stage of cosmical development, which the books of astronomy not many years since agreed in describing. The history of astronomical progress does not render it probable that the reasoning already advanced, though in reality demonstrative, will convince the generality of science students until direct and easily understood observations have shown the real nature of the constitution of that part of the universe over which astronomical survey extends. But the evidence already obtained, though its thorough analysis may be “caviare to the general,” suffices to show the real nature of the relations which one day will come within the direct scope of astronomical observation.