250 



NATURE 



{Jan. 28, 1875 



the end of this long discussion, to present a precise but 

 succinct r'csuDii, of them. 



In 1849, after I had ah-eady been engaged for ten years 

 in the work, and the better able to estimate the difficul- 

 ties, I presented its essential conditions in terms in which 

 I have no alteration to make. 



None of the tables, let us say, intended to represent the 

 movements of the planets, accord rigorously with the 

 observations. The most precise, those of the Earth and 

 Mercury, are not so accurate as could be wished. I do 

 not speak of those irregular discrepancies which the un- 

 certainty inseparable from every physical measurement 

 necessarily introduces between observation and calcula- 

 tion, but rather of those systematic errors whose variation 

 follows a determined law, the real existence and regu- 

 larity of which are prominent in the ensemble of the work 

 of the different observatories, and for which theory alone 

 can bo blamed. These inaccuracies ought to engage our 

 earnest attention ; no doubt they are inconsiderable, but, 

 on the other hand, they are everywhere present, and their 

 smalhiess does not authorise us to neglect them. 



It would assuredly not be very serious in itself that our 

 astronomical tables should make an error of half a second 

 in the time of the passage of a star on the meridian, if 

 the importance of this error did not lie in its degree of 

 certainty rather than in its magnitude. Every discre- 

 pancy betrays an unknown cause, and may become 

 the source of a discovery. If these errors should in- 

 crease considerably with the time, we may, it is true, 

 await their complete development in order to read with 

 greater certainty, in their onward progress, the cause 

 which produces them ; but, first, we should thus leave to 

 posterity the task of perfecting science and the advan- 

 tage of discovering new truths. Moreover, certain ex- 

 traneous influences may manifest themselves by eflects 

 always slightly sensible ; and if we neglect these effects, 

 the cause on which they depend will remain for ever 

 unknown. 



The theory of the motion of a planet rests upon the 

 hypothesis that each planet is subject only to the actions 

 of the sun and of the other planets, and, moreover, that 

 these actions are exercised conformably to the principles 

 of universal gravitation. 



But the consequences of the Newtonian law have not 

 been, in many respects, deduced with sufficient rigour ; 

 and, on this account, we are not in a condition to decide 

 if the disagreements evident between observation and 

 calculation are due solely to analytical errors, or rather if 

 they are partly due to the imperfection of our knowledge 

 of celestial physics. 



It will be necessary, then, to take up again the 

 mechanical theories of the motions of the planets, and to 

 rigidly e.xamine them to their most remote consequences, 

 before we are able to effect a decisive comparison with 

 observations. This is what has been done. 



Let us rapidly state that the general developments have 

 been the subject of five memoirs, presented and published 

 in 1S40, 1843, 1849, ^nd '855. 



The formuki; relative to secular irregularities have been 

 treated particularly in the memoirs of 1840 and 1S41. 



The same subject has been handled, in a more general 

 and more complete manner, in the paper communicated 

 to the Academy on Nov. 11, 1872, concerning the four 

 great planets, Jupiter, Saturn, Uranus, and Neptune. 



The theory of Mercury, presented in 1843, since com- 

 pletely revised, was only definitely completed in 1859. 



The theory of Venus was given in 1S61. 



That of the Sun (the Earth) in 1853 and 1858. 



That of Mars in 1861. 



The theory of Jupiter in 1872 and 1873. 



That of Saturn in 1S72 and 1S73. 



The theory of Uranus, given in 1846, and connected 

 with the discovery of Neptune, was the subject of a new 

 work presented on Nov. 15 last. 



Finally, the last theory, that of Neptune, is offered by 

 us to the Academy to-day. 



The theories of Jupiter, Saturn, Uranus, and Neptune 

 have the peculiarity that they are developed in functions 

 of indeterminates, so that their use may be prolonged 

 during an unlimited time. 



The theories once established, it will be necessary to 

 compare them with the long and valuable series of 

 meridian observations devised by Rosmer, instituted for 

 the first time at Greenwich, in September 1750, by the 

 famous observer Bradley, and continued since then to our 

 own days in the great observatories. But as the posi- 

 tions of the moving stars are connected with the fixed 

 stars, it is evident that it will be necessary also to be 

 assured of the relations of the stars among themselves, 

 with respect to the equinox and the ecliptic. This 

 necessity is particularly imposed in respect to right 

 ascensions, on whicli specially depends a knowledge of 

 the motions of the planets. The work was effected in the 

 memoir of April 5, 1854, for the series of observations of 

 Bradley. This was a dehcate subject, for it necessitated 

 the revision of the labours of Bessel, given in his work 

 entitled " Fundamenta Astronomia;." We have had to 

 propose various corrections in the positions of the funda- 

 mental stars, and the verification of the accuracy of these 

 corrections was put to the test ((7// contours) in Germany. 

 The result confirmed all our determinations. Conse- 

 quently they have served us in establishing v/ith certainty 

 the positions of the stars of comparison during the 120 

 years of observations which we have had to consider. 



The comparison of the motions of Mercury with the 

 theory given by us in 1843 did not present from the first 

 a satisfactory result. The transits of Mercury across the 

 Sun furnish data of very great precisioti, but which it 

 was not possible completely to satisfy. 



This first result fills us with uneasiness, it is known. 

 May not some error in the theory have escaped our 

 notice ? New researches, in which everything was tested 

 in various ways, only tend to convince us that the theory 

 was accurate, but that it did not agree with the observa- 

 tions. Years passed, and it was only in 1859 that we 

 managed to discover the cause of the established anoma- 

 hes. We discovered that they are all connected with a 

 very simple law, and that it is sufficient to increase the 

 motion of the perihelion by 30); seconds per century to 

 reduce everything to order. 



Tlie displacement of the perihelion acquires thus in the 

 planetary theories an exceptional importance. It is the 

 surest indication, when it must be increased, of the exist- 

 ence of a cosmical matter yet unknown, and circulating 

 like other bodies around the Sun. It matters not whether 

 this matter may be agglomerated into a single mass, or 

 disseminated in a multitude of meteorites independent of 

 each other. Provided that its parts all circulate "in the 

 same direction, these effects combine to impress upon the 

 perihelion a direct motion. 



The consequence is clear. There exists in the neigh- 

 bourhood of Mercury, between the planet and the Sun, 

 without doubt, a matter, a material hitherto unknown. 

 Does it consist of one or more small planets, or of 

 meteorites, or even of cosmical dust ? The theory does 

 not pronounce on this point. On many occasions, trust- 

 worthy observers have declared that they observed signs 

 of the passage of a small planet across the Sun ; but 

 nothing definite has been reached on this subject. 



We should not, however, doubt the accuracy of the 

 conclusion. We shall see, in fact, the same analysis 

 applied to the discussion of the observations of Mars lead 

 to an analogous result, and this result found fully verified. 



Bessel has said of the theory of the sun that it has not 

 made the progress we should have expected from the 

 great number and the value of the observations. This 

 estimate has for long troubled our mind, too trustful of 

 this supposed accuracy of the observations. After 



