462 



NA TURE 



\Scpt. 27, 1877 



workers stopped, when the research will gradually die out 

 from want of support. On the other hand, if, as you, Sir, 

 admit, we are on a track of a discovery which will in time 

 enable us to foretell the cycle of droughts, public opinion 

 should demand that the investigation be prosecuted with 

 redoubled vigour and under better conditions. 



My object in writing th\s letter is to express a hope 

 thnt your powerful influence may not be wanting in 

 furtherance of a branch of inquiry from which I, as an 

 individual worker in it, am undoubtedly of opinion that 

 the greatest national benefit must in time arise. If fore- 

 warned be forearmed, then sucli a research will ultimately 

 conduce to the saving of life both at times of maximum 

 and minimum sun-spot frequency. 



Owens College, RIanchester, September 20 



PROF. ADAMS ON LEVERRIER'S PLANETARY 

 THEORIES 



'T~'HE following admirable statement concerning Le- 

 -*■ verrier's more recent work was made on the occasion 

 of the presentation of the gold n-.edal of the Astronomical 

 Society, in February, last year, to him by Prof. J. C. 

 Adams, the president. It will be read with a mournful 

 interest at the present time : — 



It is not many years since our medal was awarded to 

 M. Leverrier for his theories and tables of the four 

 planets nearest the sun, viz.. Mercury, Venus, the Earlh, 

 and Mars. Long before this he had been occupied with 

 the larger planets, but before proceeding further w th 

 their theories he found it necessary to establish on solid 

 foundations the theory of the motion of the earth, on 

 which all the rest depend, and this again naturally led 

 him to investigate the theories of the three nearer planets 

 which, with the earth, constitute the inferior portion of 

 the planetary system. 



By the comparison of these theories with obser- 

 vations, M Leverrier was led to two interesting results. 

 He found that in order to bring the theories of Mercury 

 and Mars into accordance with observation, it v?as neces- 

 sary and sufficient to increase the secular motion of the 

 perihelion of Mercury, and also the secular motion of the 

 perihelion of Mars. 



Hence M. Leverrier inferred that there existed on 

 the one hand, in the neighbourhood of Mercury, and on 

 the other, in the neighbourhood of Mars, sensible 

 quantities of matter the action of which had not been 

 taken into account. 



This conclusion has been verified with respect to 

 Mars. The matter which had not been considered, turns 

 out to belong to the earth itself, the mass of which had 

 been taken too small, having been derived from too small 

 a value of the solar parallax. A similar increase of the 

 mass of the earth is indicated by the theory of Venus, 

 and a cor^-esponding increase of the solar parallax is 

 likewise derived from the lunar equation in the motion of 

 the sun. 



With respect to Mercury, a similar verification has 

 not yet taken place, but the theory of the planet has 

 been established with so much care, and the transits of 

 the planet across the sun furnish such accurate obser- 

 vations, as to leave no doubt of the reality of the phe- 

 nomenon in question ; and the only way of accounting 

 for it appears to be to suppose, with M. Leverrier, the 

 existence of several minute planets, or of a certain quan- 

 tity of diffused matter circulating about the sun within 

 the orbit of Mercury. 



The results which M. Leverrier had thus obtained 

 from his researches on the motions of the inferior planets 

 added to the interest with which he now entered upon 

 similar researches on the system of the four great planets 

 which are the most distant from the sun. Such researches 

 might furnish information respecting matter hitherto un- 

 known existing in the neighbourhood of these planets. 



Possibly they might afford indications of the existence of 

 a planet beyond Neptune, and at any rate they would 

 provide materials which would facilitate future discoveries. 



As I shall have occasion to explain later on, the 

 theories of the mutual disturbances of the larger planets 

 are far longer and more complicated than those of the 

 smaller, so that all that M. Leverrier had yet done might 

 be almost regarded as merely a prelude to what still re- 

 mained to be done. Increased difficulties, however, far 

 from deterring, seemed rather to stimulate him to greater 

 exertions. 



On May 20, 1872, M. Leverrier presented to [the 

 Academy an elaborate memoir, containing the first part 

 of his researches on the theories of the four superior 

 planets, Jupiter, Saturn, Urmus, and Neptune. This 

 memoir contains an investigation of the disturbances 

 which each of these planets suffers from the action of the 

 remaining three. Throughout this investigation the de- 

 velopment of the disturbing function, as well as that of 

 the inequalities of the elements is given in an algebraical 

 form, in which everything which varies with the time is 

 represented by a general symbol, so that the expressions 

 obtained hold good for any time whatever. Thus the 

 eccentricities and inclinations, the longitudes of the peri- 

 helion and of the nodes are all left in the condition of 

 variables. The mean parts of the major axes, which 

 suffer no secular variations, are alone treated as given 

 numbers. 



At the end of the resumi of the contents of this 

 memoir, given in the Comptes Rendus, M. Leirerrier lays 

 down the fallowing almost appalling programme of the 

 work still remaining to be done. 



It would be necessary, he says, — 



1. To calculate the formulae, and to reduce them into 

 provisional tables. 



2. To collect all the exact observations of the four 

 planets, and to discuss them afresh, in order to refer their 

 positions to one and the same system of co ordinates. 



3. By means of the provisional tables, to calculate the 

 apparent positions of the planets for the epochs of the 

 observations. 



4. To compare the observed with the calculated 

 positions, to deduce the corrections of the elliptic ele- 

 ments of the four planets, and to examine whether the 

 agreement is then perfect. 



5- In the contrary case, to find the causes of the dis- 

 crepancy between theory and observation. 



Extensive as is this programme, it has already been 

 completely carried out as regards the planets Jupiter and 

 Saturn, and partly so as regards Uranus and Neptune. 



Having received from the Academy the most effectual 

 cncourat;ement to pursue his researches, M. Leverrier 

 lost no time in bringing them gradually to completion, so 

 that they might become available for practical use. 



Accordingly, on August 26, 1872, he presented to the 

 Academy a memoir containing a complete determination 

 of the mutual disturbances of Jupiter and Saturn, and 

 thus serving as a base for the theories of both these 

 planets, which are closely connected with each other. 



Again, on November 11, 1872, he presented his deter- 

 mination of the secular variations of the elements of the 

 orbits of the four planets, Jupiter, Saturn, Uranus, and 

 iNeptune. These variations are mutually dependent on 

 each other, and must be treated simultaneously. Their 

 determination consequently involves the solution of sixteen 

 differential equations, which are very complicated in form, 

 and can only be integrated by repeated approximation. 



This part of the work forms a necessary preliminary- 

 to the treatment of the theory of any one of these planets 

 in particular. 



On March 17, 1S73, M. Leverrier presented to the 

 Academy the complete theory of Jupiter ; and on July 14 

 in the same year he followed it up by the complete theory 

 of Saturn. 



