I regret this deeply, for many

reasons.

While I was expecting more complete information on Mr. Adams's theory, the results of a new and most important investigation reached me from another quarter. In the Compte Rendu of the French Academy, for the 10th of November, 1845, which arrived in this country in December, there is a paper by M. Le Verrier on the perturbations of Uranus produced by Jupiter and Saturn, and on the errors in the elliptic elements of Uranus, consequent on the use of erroneous perturbations in the treatment of the observations. It is impossible for me here to enter into details as to the conclusions of this valuable memoir: I shall only say that, while the correctness of the former theories, as far as they went, was generally established, many small terms were added; that the accuracy of the calculations was established by duplicate investigations, following different courses, and executed with extraordinary labour; that the corrections to the elements, produced by treating the former observations with these corrected perturbations, were obtained; and that the correction to the ephemeris for the present time, produced by the introduction of the new perturbations and the new elements, was investi gated, and found to be incapable of explaining the observed irregularity of Uranus. Perhaps it may be truly said, that the theory of Uranus was now, for the first time, placed on a satisfactory foundation. This important labour, as M. Le Verrier states, was undertaken at the urgent request of M. Arago.

In the Compte Rendu for the 1st of June, 1846, M. Le Verrier gave his second memoir on the

theory of Uranus. The first part contains the results of a new reduction of nearly all the existing observations of Uranus, and their treatment with reference to the theory of perturbations, as amended in the former memoir. After concluding, from this reduction, that the observations are absolutely irreconcilable with the theory, M. Le Verrier considers in the second part all the possible explanations of the discordance, and concludes that none is admissible, except that of a disturbing planet exterior to Uranus. He then proceeds to investigate the elements of the orbit of such a planet, assuming that its mean distance is double that of Uranus, and that its orbit is in the plane of the ecliptic. The value of the mean distance, it is to be remarked, is not fixed entirely by Bode's law, although suggested by it; several considerations are stated which compel us to take a mean distance, not very greatly differing from that suggested by the law, but which, nevertheless, without the suggestions of that law, would leave the mean distance in a most troublesome uncertainty. The peculiarity of the form which the investigation takes is then explained. Finally, M. Le Verrier gives as the most probable result of his investigations, that the true longitude of the disturbing planet, for the beginning of 1847, must be about 325°, and that an error of 10° in this place is not probable. No elements of the orbit or mass of the planet are given.

This memoir reached me about the 23rd or 24th of June. I cannot sufficiently express the feeling of delight and satisfaction which I received from it. The place which it assigned to the disturbing planet

was the same, to one degree, as that given by Mr. Adams's calculations, which I had perused seven months earlier. To this time I had considered that there was still room for doubt of the accuracy of Mr. Adams's investigations; for I think that the results of algebraic and numerical computations, so long and so complicated as those of an inverse problem of perturbations, are liable to many risks of error in the details of the process: I know that there are important numerical errors in the Mécanique Céleste of Laplace; in the Théorie de la Lune of Plana; above all, in Bouvard's first tables of Jupiter and Saturn; and, to express it in a word, I have always considered the correctness of a distant mathematical result to be a subject rather of moral than of mathematical evidence. But now I felt no doubt of the accuracy of both calculations, as applied to the perturbation in longitude. I was, however, still desirous, as before, of learning whether the perturba tion in radius vector was fully explained. I therefore addressed to M. Le Verrier the following letter:

G. B. Airy to M. Le Verrier. "Royal Observatory, Greenwich, June 26th, 1846.

"I have read, with very great interest, the account of your investigations on the probable place of a planet disturbing the motions of Uranus, which is contained in the Compte Rendu de l'Académie, of the 1st of June; and I now beg leave to trouble you with the following question. It appears, from all the later observations of Uranus made at Greenwich (which are most completely reduced in the Green wich Observations of each year, so

as to exhibit the effect of an error either in the tabular heliocentric longitude or the tabular radius vector), that the tabular radius vector is considerably too small. And I wish to inquire of you whether this would be a consequence of the disturbance produced by an exterior planet, now in the position which you have indicated?

"I imagine that it would not be so, because the principal term of the inequality would probably be analogous to the moon's variation, or would depend on sin 2 (v-v'); and in that case the perturbation in radius vector would have the sign for the present relative position of the planet and Uranus. But this analogy is worth little, until it is supported by proper symbolical computations.

"By the earliest opportunity I shall have the honour of transmitting to you a copy of the Planetary Reductions, in which you will find all the observations made at Greenwich to 1830 carefully reduced and compared with the tables."

Before I could receive M. Le Verrier's answer, a transaction occurred which had some influence on the conduct of English astro

nomers.

On the 29th of June, a meeting of the Board of Visitors of the Royal Observatory of Greenwich was held, for the consideration of special business. At this meeting, Sir J. Herschel and Professor Challis (among other members of the Board) were present; I was also present, by invitation of the Board. The discussion led, incidentally, to the general question of the advantage of distributing subjects of observation among

sup

different observatories. I spoke strongly in favour of such distribution; and I produced, as an instance, the extreme probability of now discovering a new planet in a very short time, provided the powers of one observatory could be directed to the search for it. I gave, as the reason upon which this probability was based, the very close coincidence between the results of Mr. Adams's and M. Le Verrier's investigations of the posed planet disturbing Uranus. I am authorized by Sir J. Herschel's printed statement in the Athenæum of October the 3rd, to ascribe to the strong expressions which I then used the remarkable sentence in Sir J. Herschel's address, on September the 10th, to the British Association assembled at Southampton: We see it [the probable new planet] as Columbus saw America from the shores of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis, with a certainty hardly inferior to that of ocular demonstration.' And I am authorized by Professor Challis, in oral conversation, to state that the same expressions of mine induced him to contemplate the search for the suspected planet.

M. Le Verrier's answer reached me, I believe, on the 1st of July. The following are extracts from it:

M. Le Verrier to G. B. Airy.
Paris, 28 Juin, 1846.

** Il a toujours été dans mon désir de vous en écrire, aussi qu'à votre savante Société. Mais j'attendais, pour cela, que mes recherches fussent complètes, et ainsi moins indignes de vous être offertes. VOL. LXXXVIII.

Je compte avoir terminé la rectification des éléments de la planète troublante avant l'opposition qui va arriver; et parvenir à connaître ainsi les positions du nouvel astre avec une grande précision. Si je pouvais espérer que vous aurez assez de confiance dans mon travail pour chercher cette planète dans le ciel, je m'empresserais, Monsieur, de vous envoyer sa position exacte, dès que je l'aurai obtenue.

"La comparaison des positions d'Uranus, observées dans ces dernières années, dans les oppositions et dans les quadratures, montre que le rayon de la planète, calculé par les tables en usage, est effectivement très-inexact. Cela n'a pas lieu dans mon orbite, telle que je l'ai déterminée; il n'y a pas plus d'erreur dans les quadratures que dans les oppositions.

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Le rayon est donc bien calculé dans mon orbite; et, si je ne me trompe, M. Airy désirerait savoir quelle est la nature de la correction que j'ai fait subir à cet égard aux tables en usage?

"Vous avez raison, Monsieur, de penser que cette correction n'est pas due à la perturbation du rayon vecteur produite actuellement par la planète troublante. Pour s'en rendre un compte exact, il faut remarquer que l'orbite- d'Uranus a été calculée par M. Bouvard sur des positions de la planète qui n'étaient pas les positions elliptiques, puisqu'on n'avait pas pu avoi régard aux perturbations produites par la planète inconnue. Cette circonstance a nécessairement rendu les éléments de l'ellipse faux, et c'est à l'erreur de l'excentricité et à l'erreur de la longitude du périhélie qu'il faut attribuer l'erreur actuelle du rayon vecteur d'Uranus.

"Il résulte de ma théorie que

2 H

l'excentricité donnée par M. Bouvard doit être augmentée, et qu'il en est de même de la longitude du périhélie; deux causes qui contribuent, à cause de la position actuelle de la planète dans son orbite, à augmenter le rayon vecteur. Je ne transcris pas ici les valeurs de ces accroissements, parceque je ne les ai pas encore avec toute la rigueur précise, mais je les aurai rectifié avant un mois, et je me ferai un devoir, Monsieur, de vous les transmettre aussitôt, si cela vous est agréable.

Je me bornerai à ajouter que la position en quadrature, déduite en 1844 des deux oppositions qui la comprennent, au moyen de mes formules, ne diffère de la position observée que de 0"-6; ce qui prouve que l'erreur du rayon vecteur est entièrement disparue.

"C'est même une des considérations qui devront donner plus de probabilité à la vérité de mes résultats, qu'ils rendent un compte scrupuleux de toutes les circonstances du problème. Ainsi, bien que je n'aye fait usage dans mes premières recherches que des oppositions, les quadratures n'ont pas laissé de se trouver calculées avec toute l'exactitude possible. Le rayon vecteur s'est trouvé rectifié de lui-même, sans que l'on l'eut pris en considération d'une manière directe. Excusez-moi, Monsieur, d'insister sur ce point. C'est une suite du désir que j'ai d'obtenir votre suffrage.

"Je recevrai avec bien du plaisir les observations que vous voulez bien m'annoncer. Malheureusement le temps presse; l'opposition approche; il faut de toute necessité que j'aye fini pour époque. Je ne pourrai donc pas

cette

comprendre ces observations dans mon travail. Mais elles me seront très-utiles pour me servir de vérifications; et c'est ce à quoi je les employerai certainement.'

It is impossible, I think, to read this letter without being struck with its clearness of explanation, with the writer's extraordinary command, not only of the physical theories of perturbation, but also of the geometrical theories of the deduction of orbits from observation, and with his perception that his theory ought to explain all the phenomena, and his firm belief that it had done so. I had now no longer any doubt upon the reality and general exactness of the prediction of the planet's place.

On the 13th of July, I transmitted to Professor Challis "Suggestions for the Examination of a Portion of the Heavens in search of the external Planet which is presumed to exist and to produce disturbance in the motion of Uranus," and I accompanied them with the following letter:

G. B. Airy to Professor Challis.

Royal Observatory, Greenwich,
July, 13, 1846.

"I have drawn up the inclosed paper, in order to give you a notion of the extent of work incidental to a sweep for the possible planet.

"I only add at present that, in my opinion, the importance of this inquiry exceeds that of any current work, which is of such a nature as not to be totally lost by delay.'

On August the 7th, Professor Challis, writing to my confidential assistant (Mr. Main) in my supposed absence, said