Professor Challis to the Rev.

R. Main. [EXTRACT.]

"Cambridge Observatory, August 7, 1846.

"I have undertaken to search for the supposed new planet more distant than Uranus. Already I have made trial of two different methods of observing. In one method, recommended by Mr. Airy

* I met with a difficulty which I had anticipated. *** I adopted a second method."

From a subsequent letter (to be cited hereafter), it appears that Professor Challis had commenced the search on July the 29th, and had actually observed the planet on August the 4th, 1846.

At Wiesbaden (which place I left on September the 7th), I received the following letter from Professor Challis :

dressed the following very important letter to Greenwich:

J. C. Adams Esq., to G. B. Airy.

"St. John's College, Cambridge, September 2, 1846.

[This letter, which contains some very important and minute calculations, is too long for insertion, but it contains the following observations :-}

"I am at present employed in discussing the errors in latitude, with the view of obtaining an approximate value of the inclination and position of the node of the new planet's orbit; but the perturbations in latitude are so very small that I am afraid the result will not have great weight. According to a rough calculation made some time since, the inclination appeared to be rather large, and the longitude of the ascend

[EXTRACT.]

Cambridge Observatory,
September 2, 1846.

"I have lost no opportunity of searching for the planet; and, the nights having been generally pretty good, I have taken a considerable number of observations: but I get over the ground very slowly, thinking it right to include all stars to 10-11 magnitude; and I find, that to scrutinize, thoroughly, in this way the proposed portion of the heavens, will require many more observations than I can take this year."

On the same day on which Professor Challis wrote this letter, Mr. Adams, who was not aware of my absence from England, ad

am now treating the subject much more completely, and hope to obtain the result in a few days.

"I have been thinking of drawing up a brief account of my investigation to present to the British Association.

On the 31st of August, M. Le Verrier's second paper on the place of the disturbing planet (the third paper on the motion of Uranus) was communicated to the French Academy. I place the notice of this paper after those of September 2, &c. because, in the usual course of transmission to this country, the No. of the Comptes Rendus containing this paper would not arrive here, at the earliest, before the third or fourth week in September; and it does not appear that any earlier notice

of its contents was received in England.

It is not my design here to give a complete analysis of this remarkable paper; but I may advert to some of its principal points. M. Le Verrier states that, considering the extreme difficulty of attempting to solve the problem in all its generality, and considering that the mean distance and the epoch of the disturbing planet were determined approximately by his former investigations, he adopted the corrections to these elements as two of the unknown quantities to be investigated. Besides these, there are the planet's mass, and two quantities from which the eccentricity and the longitude of perihelion may be inferred; making, in all, five unknown quanti ties depending solely on the orbit and mass of the disturbing planet. Then there are the possible corrections to the mean distance of Uranus, to its epoch of longitude, to its longitude of perihelion, and to its eccentricity; making, in all, nine unknown quantities. To obtain these, M. Le Verrier groups all the observations into thirtythree equations. He then explains the peculiar method by which he derives the values of the unknown quantities from these equations. The elements obtained are,—

Semi-axis Major......... 36.154

It is interesting to compare these elements with those obtained by Mr. Adams. The difference between each of these and the corresponding element obtained by Mr. Adams in his second hypothesis is, in every instance, of that kind which corresponds to the further change in the assumed mean distance recommended by Mr. Adams. The agreement with observations does not appear to be better than that obtained from Mr. Adams's elements, with the exception of Flamsteed's first observation of 1690, for which (contrary to Mr. Adams's expectation) the discordance is considerably diminished.

M. Le Verrier then enters into a most ingenious computation of the limits between which the planet must be sought. The principle is this assuming a time of revolution, all the other unknown quantities may be varied in such a manner, that though the observations will not be so well represented as before, yet the errors of observation will be tolerable. At last, on continuing the variation of elements, one error of observation will be intolerably great. Then, by varying the elements in another way, we may at length make another error of observation intolerably great; and so on. If we compute, for all these different varieties of elements, the place of the planet for 1847, its locus will evidently be a discontinuous curve or curvilinear polygon. If we do the same thing with different periodic times, we shall get different polygons; and the extreme periodic times that can be allowed will be indicated by the polygons becoming points. These extreme periodic times are 207 and 233 years. If now we draw one grand

curve, circumscribing all the polygons, it is certain that the planet must be within that curve. In one direction, M. Le Verrier found no difficulty in assigning a limit; in the other he was obliged to restrict it, by assuming a limit to the eccentricity. Thus he found that the longitude of the planet was certainly not less than 321°, and not greater than 335° or 345°, according as we limit the eccentricity to 0.125 or 0.2. And if we adopt 0.125 as the limit, then the mass will be included between the limits 0.00007 and 0.00021; either of which exceeds that of Uranus. From this circumstance, combined with a probable hypothesis as to the density, M. Le Verrier concluded that the planet would have a visible disk, and sufficient light to make it conspicuous in ordinary tele

scopes.

M. Le Verrier then remarks, as one of the strong proofs of the correctness of the general theory, that the error of radius vector is explained as accurately as the error of longitude. And finally, he gives his opinion that the latitude of the disturbing planet must be small.

My analysis of this paper has necessarily been exceedingly imperfect, as regards the astronomical and mathematical parts of it; but I am sensible that, in regard to another part, it fails totally. I cannot attempt to convey to you the impression which was made on me by the author's undoubting confidence in the general truth of his theory, by the calmness and clearness with which he limited the field of observation, and by the firmness with which he pro

claimed to observing astronomers, "Look in the place which I have indicated, and you will see the planet well." Since Copernicus declared that, when means should be discovered for improving the vision, it would be found that Venus had phases like the moon, nothing (in my opinion) so bold, and so justifiably bold, has been uttered in astronomical prediction. It is here, if I mistake not, that we see a character far superior to that of the able, or enterprising, or industrious mathematician; it is here that we see the philosopher. The mathematical investigations will doubtless be published in detail; and they will, as mathematical studies, be highly instructive but no details published after the planet's discovery can ever have for me the charm which I have found in this abstract which preceded the discovery.

I understand that M. Le Verrier communicated his principal conclusions to the astronomers of the Berlin Observatory, on the 23rd of September, and that, guided by them, and comparing their observations with a star-map, they found the planet on the same evening. And I am warranted, by the verbal assurances of Professor Challis, in stating that, having received the paper on the 29th of September, he was SO much impressed with the sagacity and clearness of M. Le Verrier's limitations of the field of observation, that he instantly changed his plan of observing, and noted the planet, as an object having a visible disk, on the evening of the same day.

*

observations would have shown me the planet in the early part of August, if I had only discussed them. I commenced observing, on the 29th of July, attacking first of all, as it was prudent to do, the position which Mr. Adams's calculations assigned as the most probable place of the planet. On the 30th of July, I adopted the method of observing which I spoke of to you. In this way I took all the stars to the 11th magnitude in a zone of 9' in breadth, and was sure that none brighter than the 11th escaped me. My next observations were on the 4th of August. On this day I took stars here and there in a zone of about 70' in breadth, purposely selecting the brighter, as I intended to make them reference-points for the observations in zones of 9' breadth. Among these stars was the planet. A comparison of this day's observations with a good star-map would most probably have detected it. On account of moonlight I did not observe again till the 12th of August. On that day I went over again the zone of 9' breadth which I examined on the 30th of July.

*

* *

* The space gone over on the 12th of August exceeded in length that of the 30th of July, but included the whole of it. On comparing [at a later time] the observations of these two days, I found that the zone of the 30th of July contained every star in the

if

of the 12th of August, except one star of the 8th magnitude. This, according to the principle of search, which in the want of a good star-map I had adopted, must have been a planet. It had wandered into the latter zone in the interval between the 30th of July and the 12th of August. By this statement you will see that, after four days of observing, the planet was in my grasp, only I had examined or mapped the observations. I delayed doing this, partly because I thought the probability of discovery was small, till a much larger portion of the heavens was scrutinized, but chiefly because I was making a grand effort to reduce the vast number of comet observations which I have accumulated; and this occupied the whole of my time when I was not engaged in observing. I actually compared to a certain extent the observations of the 30th of July and the 12th of August soon after taking them, more for the sake of testing the two methods of observing adopted on those days than for any other purpose; and I stopped short within a very few stars of the planet. After the 12th of August I continued my observations with great diligence, recording the positions of, I believe, some thousands of stars: but I did not again fall in with the planet, as I took positions too early in right ascension.

On the 29th of September, however, I saw, for the first time, Le Verrier's last results, and on the evening of that day I observed strictly according to his suggestions, and within the limits he recommended; and I was also on the look-out for a disk. Among

Before terminating this account, I beg leave to present the following remarks:

First. It would not be just to institute a comparison between papers which at this time exist only in manuscript, and papers which have been printed by their authors; the latter being in all cases more complete and more elaborately worked out than the former.

Second. I trust that I am amply supported, by the documentary history which I have produced, in the view which I first took, namely, that the discovery of this new planet is the effect of a movement of the age. It is shown, not merely by the circumstance that different mathematicians have simultaneously but independently been carrying on the same investigations, and that different astronomers, acting without concert, have at the same time been looking for the planet in the same part of the heavens; but also by the circumstance that the minds of these philosophers, and of the persons about them, had long been influenced by the knowledge of what had been done by others, and of what had yet been left untried; and that in all parts of the work the mathematician and the astronomer were supported by the ex

hortations and the sympathy of those whose opinions they valued most. I do not consider this as detracting in the smallest degree from the merits of the persons who have been actually engaged in these investigations.

Third. The history presents a remarkable instance of the importance, in doubtful cases, of using any received theory as far as it will go, even if that theory can claim no higher, merit than that of being plausible. If the mathematicians, whose labours I have described, had not adopted B de's law of distances, (a law for which no physical theory of the rudest kind has ever been suggested,) they would never have arrived at the elements of the orbit. At the same time this assumption of the law is only an aid to calculation, and does not at all compel the computer to confine himself perpetually to the condition assigned by this law, as will have been remarked in the ultimate change of mean distance made by both the mathematicians, who have used Bode's law to give the first approximation to mean dis-`

tance.

Fourth. The history of this discovery shows that, in certain cases, it is advantageous for the progress of science that the publication of theories, when so far matured as to leave no doubt of their general accuracy, should not be delayed till they are worked to the highest imaginable perfection. It appears to be quite within probability, that a publication of the elements, obtained in October, 1845, might have led to the discovery of the planet in November, 1845.