: 
(1383.) 
M. Lever- 
rier’s inves- 
tigations ; 
Cuar. IL., § 5.] 
amounted to two minutes of longitude. M. Bouvard 
to his latest years, perhaps his latest hours,} che- 
rished the hope of extricating this theory from its 
difficulties. He also engaged his nephew M. Eugéne 
Bouvard in the same career, who appears to have 
followed it with much zeal and intelligence, and 
in 1845 constructed new tables of Uranus. But by 
this time two geometers had separately and inde- 
pendently undertaken the problem, with the deter- 
mination of finding, if possible, a physical solution 
of all this perplexity. The earliest in point of date 
was Mr Adams, a young graduate of Cambridge; the 
other was M. Leverrier of Paris, whose attention 
was directed to the subject by M. Arago. As the 
researches of M. Leverrier, though second in point of 
time, occasioned the actual recognition of the planet, 
and thus stamped the correctness of the solution with 
success, we shall consider them in the first instance. 
M. Levernrier is, we believe, a native of St Lo 
in Normandy, a province which has been singularly 
productive of eminent men (Laplace and Fresnel 
were of the number). With no advantages, but the 
reverse, he won a high position at entering the 
polytechnic school, which he constantly maintained. 
He at first, we believe, attached himself to chemis- 
try, but his taste for physical astronomy was soon 
developed, and was advanced entirely by his private 
efforts. It is a peculiarity of the mode of culti- 
vating the sciences in Paris, that such abstruse 
and difficult studies are not merely engaged in tem- 
porarily for purposes of academial distinction, but that 
they actually become a “ carriére” or calling, and are 
pursued in that methodical manner for which the 
French are distinguished. In 1845, when he com- 
menced the careful examination of the theory of 
Uranus, M. Leverrier was already favourably known 
by his researches on comets, and on the orbit of 
Mercury, but especially by immense calculations, con- 
nected with the secular inequalities of the planets, by 
which his ability and hardihood in computation had 
been thoroughly exercised. He began his new en- 
quiry with the method and intrepidity of calculation 
which distinguish him, He revised with the most 
minute care the observations of Uranus, and 
computed afresh every sensible perturbation which 
theory recognised as arising from known planets. 
This done, and having compared the most probable 
orbit with observations which he collected from 
authentic sources, and especially from the Greenwich 
observations which were communicated to him for 
this purpose, the result was, that even confining 
himself to observations since 1781, arranged in 
eleven convenient groups (each resulting from many 
observed places), and attributing to each group the 
PHYSICAL ASTRONOMY.—M. LEVERRIER—MR ADAMS. 
829 
largest error which could be in reason allowed, 
and even admitting that all these errors were in the 
direction most favourable to the assumption, it was 
still impossible to account for more than one-fourth 
part of the observed discordances. 
M. Leverrier then assumed that a perturbing 
planet existed beyond the orbit of Uranus, and at 
nearly double its distance from the sun, in conformity 
with the empirical law, (usually attributed to Bode 
the German astronomer,) which expresses with gene- 
ral accuracy,thus far, the arrangement of the planetary 
system. The law is, that the distances of the planetary 
orbits from Mercury are successively doubled. This 
assumption—(it was absolutely necessary to assume 
some distance to begin with)—was ingeniously con- 
firmed by other considerations. 
Leaving the perturbations in latitude out of ac- 
count, he now considered each error of Uranus in 
longitude as the expression of a perturbation due 
to the action of the unknown planet, and capable 
therefore of algebraic expression in terms of the ele- 
ments of that planet, namely its excentricity, longi- 
tude of perihelion, epoch in its orbit, and mass; but, 
as we have already remarked, the first three of these 
elements must be considered as incorrectly assumed 
for Uranus itself, as well as the mean distance of that 
planet, and, therefore, there are four unknown correc- 
tions for its elliptic elements, making in all eight quan- 
tities to be eliminated from the discordances of theory 
and observation. So complex an elimination cannot 
be directly effected ; and even if it could, the result 
could not be depended on, as the possible error of 
each observation involves a fresh and important 
source of doubt in the conclusion, M. Leverrier 
proceeded, by a series of gradually restricted assump- 
tions, to find within what limits the more important 
elements might be made to vary without producing 
effects incompatible with observation, and his atten- 
tion was at first confined to the approximate mean 
longitude of the planet. He obtained a result after 
a prodigious amount of tentative calculation. The 
excentricity and position of the perihelion were then 
inferred. On the lst June 1846 he announced to 
the Academy of Sciences that the true longitude of 
the expected planet for 1st January 1847 was 325°, 
with a probable error of 10°. This result was im- 
mediately published in the Comptes Rendus. 
Between the 1st June and 3lst August 1846, 
when his third memoir on the perturbations of 
Uranus appeared, M. Leverrier busied himself in ob- 
taining a farther approximation to the elements and 
place of the suspected planet. He now assumed the 
correction of the mean distance amongst the other 
quantities to be sought. By a fresh calculation he 
1M. Bouvard was born in 1767. He performed almost all of the numerical calculations required by Laplace in his great 
work, and was associated with that eminent man by the most friendly ties. He “ ceased to calculate and to live” 7th June 
1843. 
(134.) 
(135.) 
how con- 
ducted : 
Their re- 
sult, 
(136. 
M. Lever- 
rier’s final 
announce- 
ment ; 
