1847.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



13 



disturbing planet (the third paper on the motion of Uranus) was communi- 

 cated to the French Academy. I place the notice of this paper after those 

 of September 2, &c. because, in the usual course of transmission lo this 

 couut'-y, the number of the Com^t^s Rendas conlainins; this paper would 

 not arrive here, at the earliest, before the third or fourth week in Septem- 

 ber ; and it does not appear that any earlier notice of its contents was re- 

 ceived in England. 



It is not my design here to give a complete analysis of this reniarlcable 

 paper; but I may advert to some of its principal points. JI. Le Verrier 

 states that, considering the extreme difhcnlty 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 

 quantities depending solely on the orbit and mass of the disturbing planet. 

 1 hen there are the possible corrections to the mean distance of Urarius. 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 thirty-three equations. He then explains 

 the peculiar method by which he derives the values of the unknown quan- 

 tities from these equations. The elements obtained are, — 



Semi-axis Major 



3G 154 



= 531 



Periodic Time . 217y-387 



Eccentricity . 0*10761 



Longitude of Perihelion 281° 45' 



Mean Longitude, 1 Jan. 1847 318 47 

 Mass^Jj5 = 0001075 

 True Heliocentric Longitude, 1 Jan. 1847 326° 32' 

 Distance from the Sua . . 33-06 



It is interesting to compare these elements wilh those obtained by Mr. 

 Adams. The dilfereace between each of theFe and the corresponding ele- 

 ment obtained by Mr. Adams in his second hypothesis is, in every instance, 

 of that kind which corresponds to the fui-ther change in the assumed mean 

 distance recommended by Mr. Adams. The agreement with observations 

 does not appear to be belter than that obtained from Mr. Adams's elements, 

 with the exception of Flamsteed's first observation of I6!I0, for which (con- 

 trary to Mr. Adams's expectation) the discordance is considerably dimi- 

 nished. 



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 revoluiion, 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 tlie 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 

 oo. 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 

 carvilinear polygon. If we do the :/ame thing wilh ditferent periodic 

 times, we shall get different polygons ; and the extreme periodic limes 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 

 carve, circumscribing all the polygons, it is certain that tiie 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 tliat the longitude of the planet 

 was certainly not less than 321°, and not greater than 335° or 345°, accord- 

 ing as we limit the eccentricity to 0-125 or 2. And if we adopt 0'125 

 as the limit, then the mass will be included between the limits 0'OU007 and 

 0'00021 ; either of which exceeds that of Uranus. From this circumstance, 

 combined wilh a probable hypothesis as to the density, M. Le Verriercon- 

 duded that the planet would have a visible disk, and sufficient light to 

 make it conspicuous in ordinary telescopes 



M. Le Verrier then remarks, as one of the strong proofs of the correct- 

 ness of ihe 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 uuist be small. 



My analysis of this paper has necessarily been exceedingly imperfect, 

 83 regards the astronomical and mathematical parts of it ; but I am sensi- 

 ble 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 un- 

 doubling confidence in the general trutli of his theory, by the calmness and 

 clearness with which he limited the field of observation, and by the firm- 

 ness with which he proclaimed to observing astronomers, '* Look in the 

 place which 1 have indicated, and you will see the planet well." Since 

 Copernicus* declared that, when means should be discovered for improv- 

 ing the vision, it would be found that Venus had phases like tlie moon, no- 

 thing (in my opinion) so bold, aud so justifiably bold, has been uttered in 

 astronomical prediction. It is here, if I mistake not, that we see a charac- 

 ter far superior to thai of the able, or enterprising, or industrious mathe- 



• I borroiv tliis history from Smitli's Optics, sect. 1050. Since reading lllis Memoir, 

 I bare, however, been iutornied by Professor I^e Rlurtjaii, that the printed worlis of Co- 

 pernicus do not at all support this history, auti that Copernicus appears to have believed 

 tliat the planets are self-luminous. — G. B. A 



matician ; it is here that we see the piiilosophor. The mathcinatical in- 

 vestigations will doubtless be published in detail ; and they will, as ma- 

 thematical studies, be highly instructive : but no details published after 

 the planet's discovery can ever have fur 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 September 23, and that, 

 guided by them, and comparing their observations with a star-map, they 

 found Ihe planet on the same evening. And I am warranted by the verbal 

 assurances of Professor Challis in staling that, having received the paper 

 on .September 29, he was so much impressed with Ihe sagacity and clear- 

 ness of M. Le Verrier's limitations of the field of observation, that he in- 

 stantly changed his plan of observing, and noted the planet, as an object 

 having a visible disk, on the evening of the same day. 



My account, as a documentary history, supported by loiters written dur- 

 ing the events, is properly terminated; but 1 think it advisable, for the 

 sake of clearness, to annf-x extracts from a letter which 1 have received 

 from Professor Challis since the beginning of October, when I returned to 

 England. 



[In this letter Professor Challis details his labours in search for the 

 planet, and states that on September 29, he singled out one star of 300 ob- 

 served that evening, for which he noted, "seems to have a disk." This 

 turned out to be the planet.] 



Before terminating this account, I beg leave to present the following re- 

 marks ; — 



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 aud 

 inure elaborately worked out thau the former, 



.Second. I trust that I am amply supported, by the documentary history 

 which I have produced, in the view which 1 first took, namely, that the 

 discovery of this new planet is the efl'ect of a movemeut of the age. It is 

 shown, not merely by the circumstance that different mathematicians have 

 simultaneously but independently been carrying on the same investigations, 

 aud that different astrouomers, acting without concert, have at the same 

 time been looking for the planet in the same part of tlie heavens ; but also 

 by the circumstance that the minds of these philusophers, and of the per- 

 sons 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 exhortations and the sympathy of those whose opinions they valued 

 must. I do not consider this as detracting in the smallest degree from the 

 merits of the persons who have been actually engaged in these investiga- 

 tions. 



Third. This 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 Bode's 

 law of distances (a law for which no physical theory of the rudest kind 

 has ever been snggesti-d), 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 tliis law, as will have been re- 

 marked in the ultimate change of mean distance made by both the mathe- 

 maticians, who have used Bode's law to give the first approximation to 

 mean distance. 



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 witliin probability, tbat a publication of the elements 

 obtained in October 1845 might have led to the discovery of the planet in 

 November 1845. 



I have now only to request the indulgence of my hearers for Ihe appa- 

 rently egotistical character of the account which I have here given ; a 

 character which it is extremely difficult to remove from a history that is 

 almost strictly confined to transactions with which I have myself been con- 

 cerned. 



THE GOVERNMENT SCHOOL OF DESIGN. 



Though a considerable time has elapsed since Ihe following report on the 

 French Schools was presented by Mr. Poynter to the Council of this In- 

 stitution, it has remained unpublished. The Council have since sanctioned 

 its publication, and as the subject of the document is not of temporary 

 interest, it is well worthy of perusal. 



" My Lords aud Gentlemen, — Previously to entering upon Ihe exercise 

 of the office to which Ihe Council have done me the honour to appoint me, 

 I considered that a more iutimate knowledge of the system of instruction 

 adopted in the French Schools, and its results, would enable nie to judge 

 mure advaulageuusly ul the condition aud prospects of our own. I have, 

 therefore, visited Paris with a special view to this subject; and would 

 willingly have extended my jouruey to Lyons, had time permitted, But, 



