In 1862, the firm of Alvan Clark and Sons, of New York, were completing a magnificent 18-inch refractor, and the younger Clark was trying it on Sirius, when he said: "Why, father, the star has a companion!" The elder Clark also looked, and sure enough there was a faint companion due east of the bright star, and in just the position required by theory. Not that the Clarks knew anything about the theory. They were keen-sighted and most skilful instrument-makers, and they made the discovery by accident. After it had once been seen, it was found that several of the large telescopes of the world were able to show it. It is half as big, but it only gives 1/10000th part of the light that Sirius gives. No doubt it shines partly with a borrowed light and partly with a dull heat of its own. It is a real planet, but as yet too hot to live on. It will cool down in time, as our earth has cooled and as Jupiter is cooling, and no doubt become habitable enough. It does revolve round Sirius in a period of 494 years--almost exactly what Bessel a.s.signed to it.

But Bessel also a.s.signed a dark companion to Procyon. It and its luminous neighbour are considered to revolve round each other in a period of forty years, and astronomers feel perfectly a.s.sured of its existence, though at present it has not been seen by man.

LECTURE XV

THE DISCOVERY OF NEPTUNE

We approach to-night perhaps the greatest, certainly the most conspicuous, triumphs of the theory of gravitation. The explanation by Newton of the observed facts of the motion of the moon, the way he accounted for precession and nutation and for the tides, the way in which Laplace explained every detail of the planetary motions--these achievements may seem to the professional astronomer equally, if not more, striking and wonderful; but of the facts to be explained in these cases the general public are necessarily more or less ignorant, and so no beauty or thoroughness of treatment appeals to them, nor can excite their imaginations. But to predict in the solitude of the study, with no weapons other than pen, ink, and paper, an unknown and enormously distant world, to calculate its...o...b..t when as yet it had never been seen, and to be able to say to a practical astronomer, "Point your telescope in such a direction at such a time, and you will see a new planet hitherto unknown to man"--this must always appeal to the imagination with dramatic intensity, and must awaken some interest in almost the dullest.

Prediction is no novelty in science; and in astronomy least of all is it a novelty. Thousands of years ago, Thales, and others whose very names we have forgotten, could predict eclipses with some certainty, though with only rough accuracy. And many other phenomena were capable of prediction by acc.u.mulated experience. We have seen, for instance (coming to later times), how a gap between Mars and Jupiter caused a missing planet to be suspected and looked for, and to be found in a hundred pieces. We have seen, also, how the abnormal proper-motion of Sirius suggested to Bessel the existence of an unseen companion. And these last instances seem to approach very near the same cla.s.s of prediction as that of the discovery of Neptune. Wherein, then, lies the difference?

How comes it that some cla.s.ses of prediction--such as that if you put your finger in fire it will get burnt--are childishly easy and commonplace, while others excite in the keenest intellects the highest feelings of admiration? Mainly, the difference lies, first, in the grounds on which the prediction is based; second, on the difficulty of the investigation whereby it is accomplished; third, in the completeness and the accuracy with which it can be verified. In all these points, the discovery of Neptune stands out pre-eminently among the verified predictions of science, and the circ.u.mstances surrounding it are of singular interest.

In 1781, Sir William Herschel discovered the planet Ura.n.u.s. Now you know that three distinct observations suffice to determine the orbit of a planet completely, and that it is well to have the three observations as far apart as possible so as to minimize the effects of minute but necessary errors of observation. (See p. 298.) Directly Ura.n.u.s was found, therefore, old records of stellar observations were ransacked, with the object of discovering whether it had ever been unwittingly seen before. If seen, it had been thought of course to be a star (for it shines like a star of the sixth magnitude, and can therefore be just seen without a telescope if one knows precisely where to look for it, and if one has good sight), but if it had been seen and catalogued as a star it would have moved from its place, and the catalogue would by that entry be wrong. The thing to detect, therefore, was errors in the catalogues: to examine all entries, and see if the stars entered actually existed, or were any of them missing. If a wrong entry were discovered, it might of course have been due to some clerical error, though that is hardly probable considering the care taken over these things, or it might have been some tailless comet or other, or it might have been the newly found planet.

So the next thing was to calculate backwards, and see if by any possibility the planet could have been in that place at that time.

Examined in this way the tabulated observations of Flamsteed showed that he had unwittingly observed Ura.n.u.s five distinct times, the first time in 1690, nearly a century before Herschel discovered its true nature.

But more remarkable still, Le Monnier, of Paris, had observed it eight times in one month, cataloguing it each time as a different star. If only he had reduced and compared his observations, he would have antic.i.p.ated Herschel by twelve years. As it was, he missed it altogether. It was seen once by Bradley also. Altogether it had been seen twenty times.

These old observations of Flamsteed and those of Le Monnier, combined with those made after Herschel's discovery, were very useful in determining an exact orbit for the new planet, and its motion was considered thoroughly known. It was not an _exact_ ellipse, of course: none of the planets describe _exact_ ellipses--each perturbs all the rest, and these small perturbations must be taken into account, those of Jupiter and Saturn being by far the most important.

For a time Ura.n.u.s seemed to travel regularly and as expected, in the orbit which had been calculated for it; but early in the present century it began to be slightly refractory, and by 1820 its actual place showed quite a distinct discrepancy from its position as calculated with the aid of the old observations. It was at first thought that this discrepancy must be due to inaccuracies in the older observations, and they were accordingly rejected, and tables prepared for the planet based on the newer and more accurate observations only. But by 1830 it became apparent that it would not accurately obey even these. The error amounted to some 20". By 1840 it was as much as 90', or a minute and a half. This discrepancy is quite distinct, but still it is very small, and had two objects been in the heavens at once, the actual Ura.n.u.s and the theoretical Ura.n.u.s, no unaided eye could possibly have distinguished them or detected that they were other than a single star.

[Ill.u.s.tration: FIG. 93.--Perturbations of Ura.n.u.s.

The chance observations by Flamsteed, by Le Monnier, and others, are plotted in this diagram, as well as the modern determinations made after Herschel had discovered the nature of the planet. The decades are laid off horizontally. Vertical distance represents the difference between observed and subsequently calculated longitudes--in other words, the princ.i.p.al perturbations caused by Neptune. To show the scale, a number of standard things are represented too by lengths measured upwards from the line of time, viz: the smallest quant.i.ty perceptible to the naked eye,--the maximum angle of aberration, of nutation, and of stellar parallax; though this last is too small to be properly indicated. The perturbations are much bigger than these; but compared with what can be seen without a telescope they are small--the distance between the component pairs of [epsilon] Lyrae (210") (see fig. 86, page 288), which a few keen-eyed persons can see as a simple double star, being about twice the greatest perturbation.]

The diagram shows all the irregularities plotted in the light of our present knowledge; and, to compare with their amounts, a few standard things are placed on the same scale, such as the smallest interval capable of being detected with the unaided eye, the distance of the component stars in [epsilon] Lyrae, the constants of aberration, of nutation, and of stellar parallax.

The errors of Ura.n.u.s therefore, though small, were enormously greater than things which had certainly been observed; there was an unmistakable discrepancy between theory and observation. Some cause was evidently at work on this distant planet, causing it to disagree with its motion as calculated according to the law of gravitation. Some thought that the exact law of gravitation did not apply to so distant a body. Others surmised the presence of some foreign and unknown body, some comet, or some still more distant planet perhaps, whose gravitative attraction for Ura.n.u.s was the cause of the whole difficulty--some perturbations, in fact, which had not been taken into account because of our ignorance of the existence of the body which caused them.

But though such an idea was mentioned among astronomers, it was not regarded with any special favour, and was considered merely as one among a number of hypotheses which could be suggested as fairly probable.

It is perfectly right not to attach much importance to unelaborated guesses. Not until the consequences of an hypothesis have been laboriously worked out--not until it can be shown capable of producing the effect quant.i.tatively as well as qualitatively--does its statement rise above the level of a guess, and attain the dignity of a theory. A later stage still occurs when the theory has been actually and completely verified by agreement with observation.

Now the errors in the motion of Ura.n.u.s, _i.e._ the discrepancy between its observed and calculated longitudes--all known disturbing causes, such as Jupiter and Saturn, being allowed for--are as follows (as quoted by Dr. Haughton) in seconds of arc:--

ANCIENT OBSERVATIONS (casually made, as of a star).

Flamsteed 1690 +612 " 1712 +927 " 1715 +738 Le Monnier 1750 -476 Bradley 1753 -395 Mayer 1756 -457 Le Monnier 1764 -349 " 1769 -193 " 1771 -23

MODERN OBSERVATIONS.

1780 +346 1783 +845 1786 +1236 1789 +1902 1801 +2221 1810 +2316 1822 +2097 1825 +1816 1828 +1082 1831 -398 1834 -2080 1837 -4266 1840 -6664

These are the numbers plotted in the above diagram (Fig. 92), where H marks the discovery of the planet and the beginning of its regular observation.

Something was evidently the matter with the planet. If the law of gravitation held exactly at so great a distance from the sun, there must be some perturbing force acting on it besides all those known ones which had been fully taken into account. Could it be an outer planet? The question occurred to several, and one or two tried if they could solve the problem, but were soon stopped by the tremendous difficulties of calculation.

The ordinary problem of perturbation is difficult enough: Given a disturbing planet in such and such a position, to find the perturbations it produces. This problem it was that Laplace worked out in the _Mecanique Celeste_.

But the inverse problem: Given the perturbations, to find the planet which causes them--such a problem had never yet been attacked, and by only a few had its possibility been conceived. Bessel made preparations for trying what he could do at it in 1840, but he was prevented by fatal illness.

In 1841 the difficulties of the problem presented by these residual perturbations of Ura.n.u.s excited the imagination of a young student, an undergraduate of St. John's College, Cambridge--John Couch Adams by name--and he determined to have a try at it as soon as he was through his Tripos. In January, 1843, he graduated as Senior Wrangler, and shortly afterwards he set to work. In less than two years he reached a definite conclusion; and in October, 1845, he wrote to the Astronomer-Royal, at Greenwich, Professor Airy, saying that the perturbations of Ura.n.u.s would be explained by a.s.suming the existence of an outer planet, which he reckoned was now situated in a specified lat.i.tude and longitude.

We know now that had the Astronomer-Royal put sufficient faith in this result to point his big telescope to the spot indicated and commence sweeping for a planet, he would have detected it within 1-3/4 of the place a.s.signed to it by Mr. Adams. But any one in the position of the Astronomer-Royal knows that almost every post brings an absurd letter from some ambitious correspondent or other, some of them having just discovered perpetual motion, or squared the circle, or proved the earth flat, or discovered the const.i.tution of the moon, or of ether, or of electricity; and out of this ma.s.s of rubbish it requires great skill and patience to detect such gems of value as there may be.

Now this letter of Mr. Adams's was indeed a jewel of the first water, and no doubt bore on its face a very different appearance from the chaff of which I have spoken; but still Mr. Adams was an unknown man: he had graduated as Senior Wrangler it is true, but somebody must graduate as Senior Wrangler every year, and every year by no means produces a first-rate mathematician. Those behind the scenes, as Professor Airy of course was, having been a Senior Wrangler himself, knew perfectly well that the labelling of a young man on taking his degree is much more worthless as a testimony to his genius and ability than the general public are apt to suppose.

Was it likely that a young and unknown man should have successfully solved so extremely difficult a problem? It was altogether unlikely.

Still, he would test him: he would ask for further explanations concerning some of the perturbations which he himself had specially noticed, and see if Mr. Adams could explain these also by his hypothesis. If he could, there might be something in his theory. If he failed--well, there was an end of it. The questions were not difficult.

They concerned the error of the radius vector. Mr. Adams could have answered them with perfect ease; but sad to say, though a brilliant mathematician, he was not a man of business. He did not answer Professor Airy's letter.

It may to many seem a pity that the Greenwich Equatoreal was not pointed to the place, just to see whether any foreign object did happen to be in that neighbourhood; but it is no light matter to derange the work of an Observatory, and alter the work mapped out for the staff into a sudden sweep for a new planet, on the strength of a mathematical investigation just received by post. If observatories were conducted on these unsystematic and spasmodic principles, they would not be the calm, accurate, satisfactory places they are.

Of course, if any one could have known that a new planet was to be had for the looking, _any_ course would have been justified; but no one could know this. I do not suppose that Mr. Adams himself could feel all that confidence in his attempted prediction. So there the matter dropped. Mr. Adams's communication was pigeon-holed, and remained in seclusion for eight or nine months.

Meanwhile, and quite independently, something of the same sort was going on in France. A brilliant young mathematician, born in Normandy in 1811, had accepted the post of Astronomical Professor at the ecole Polytechnique, then recently founded by Napoleon. His first published papers directed attention to his wonderful powers; and the official head of astronomy in France, the famous Arago, suggested to him the unexplained perturbations of Ura.n.u.s as a worthy object for his fresh and well-armed vigour.

At once he set to work in a thorough and systematic way. He first considered whether the discrepancies could be due to errors in the tables or errors in the old observations. He discussed them with minute care, and came to the conclusion that they were not thus to be explained away. This part of the work he published in November, 1845.

He then set to work to consider the perturbations produced by Jupiter and Saturn, to see if they had been with perfect accuracy allowed for, or whether some minute improvements could be made sufficient to destroy the irregularities. He introduced several fresh terms into these perturbations, but none of them of sufficient magnitude to do more than slightly lessen the unexplained perturbations.

He next examined the various hypotheses that had been suggested to account for them:--Was it a failure in the law of gravitation? Was it due to the presence of a resisting medium? Was it due to some unseen but large satellite? Or was it due to a collision with some comet?

All these he examined and dismissed for various reasons one after the other. It was due to some steady continuous cause--for instance, some unknown planet. Could this planet be inside the orbit of Ura.n.u.s? No, for then it would perturb Saturn and Jupiter also, and they were not perturbed by it. It must, therefore, be some planet outside the orbit of Ura.n.u.s, and in all probability, according to Bode's empirical law, at nearly double the distance from the sun that Ura.n.u.s is. Lastly he proceeded to examine where this planet was, and what its...o...b..t must be to produce the observed disturbances.

[Ill.u.s.tration: FIG. 94.--Ura.n.u.s's and Neptune's relative positions.

The above diagram, drawn to scale by Dr. Haughton, shows the paths of Ura.n.u.s and Neptune, and their positions from 1781 to 1840, and ill.u.s.trates the _direction_ of their mutual perturbing force. In 1822 the planets were in conjunction, and the force would then perturb the radius vector (or distance from the sun), but not the longitude (or place in orbit). Before that date Ura.n.u.s had been hurried along, and after that date it had been r.e.t.a.r.ded, by the pull of Neptune, and thus the observed discrepancies from its computed place were produced. The problem was first to disentangle the outstanding perturbations from those which would be caused by Jupiter and Saturn and all other known causes, and then to a.s.sign the place of an outer planet able to produce precisely those perturbations in Ura.n.u.s.]

Not without failures and disheartening complications was this part of the process completed. This was, after all, the real tug of war. So many unknown quant.i.ties: its ma.s.s, its distance, its excentricity, the obliquity of its...o...b..t, its position at any time--nothing known, in fact, about the planet except the microscopic disturbance it caused in Ura.n.u.s, some thousand million miles away from it.

Without going into further detail, suffice it to say that in June, 1846, he published his last paper, and in it announced to the world his theoretical position for the planet.

Professor Airy received a copy of this paper before the end of the month, and was astonished to find that Leverrier's theoretical place for the planet was within 1 of the place Mr. Adams had a.s.signed to it eight months before. So striking a coincidence seemed sufficient to justify a Herschelian "sweep" for a week or two.

But a sweep for so distant a planet would be no easy matter. When seen in a large telescope it would still only look like a star, and it would require considerable labour and watching to sift it out from the other stars surrounding it. We know that Ura.n.u.s had been seen twenty times, and thought to be a star, before its true nature was by Herschel discovered; and Ura.n.u.s is only about half as far away as Neptune is.

Neither in Paris nor yet at Greenwich was any optical search undertaken; but Professor Airy wrote to ask M. Leverrier the same old question as he had fruitlessly put to Mr. Adams: Did the new theory explain the errors of the radius vector or not? The reply of Leverrier was both prompt and satisfactory--these errors were explained, as well as all the others.

The existence of the object was then for the first time officially believed in.

The British a.s.sociation met that year at Southampton, and Sir John Herschel was one of its Sectional Presidents. In his inaugural address, on September 10th, 1846, he called attention to the researches of Leverrier and Adams in these memorable words:--