296 
astronomy. Treated directly, the diffi- 
culty of it is equivalent. to a species of 
impossibility ; but, by the methods of 
approximation, which have been in- 
vented, it may now be reduced to a cal- 
culation of some hours. Amongst these 
methods, that of M. Laplace appears 
hitherto, if’not altogether the shortest, 
at-least one of the most convenient, and, 
perhaps, the surest of- all: that of M. 
Leveudre, much more novel,-has, as yet, 
but rarely been put to the test, and, in 
anairect mnethods, experience alone. can 
decide. But the manner in which M. 
Legendre corrects his first approxinia- 
ticns, may have interesting and multi-? 
plied advantages ; the author is applying 
it to the are measured petiyeen Dun- 
kirk and Barcelona. He infers from it 
Inequalities in the density of the earth, 
which, indeed, account very naturally 
for the small irregularities discovered by 
observations in the latitudes and the azi- 
muths. 
The comet of 1770 has | long anid 
astronomers; it has been impossible to 
represent the observations, otherwise 
than by an ellipse, which. would bring 
back the comet twice in eleven YEarS.m—e 
Within the Jast thirty years it should 
have appeared six times, but it has ne- 
ver since been seen ; it had never been 
observed before 1770. This singular 
problem was proposed as the subject of 
a prize, obtained by M. Burckhardt, 
wlio has done all that could be expected 
from ‘an astronomer, as learned as he 
is laborious. After immense. calcula- 
tions, he concluded, that the comet 
should perform its "revolution in five 
years and a half; and of its having never 
ye-appeared, ie mast probable. cause 
must be, the perturbations of Jupiter, 
which may have changed the form of its 
orbit. The problem then became a ques- 
tion of analysis; MI. Laplace gave the 
canons of it; M. Burckhardt performed 
the calculations ; the result is, gn fact, 
that the comet, passing near Jupiter, had 
its orbit so altered, that hereafter it may 
always be too far from the sun eyer to 
be perceived from the earth, unless it 
should experience, ina contrary direc- 
tion, variations equally considerable. 
We have said nothing of the curious 
observations, and interesting discoveries, 
which have ‘sigualized the last eighteen. 
‘years. Since the ist of January, 1801, 
four new planets have been discuyered. 
RBI, Gauss and Burckhardt have calcu. 
lated their orbits, These planets are SO 
small, that it is not surprising that they 
Progress of the Sciences. 
_of the same magmtude, which cover ale 
~utility 10 themselves; but they may af 
Pons, Olbers, and Miss Herschel. 
_their orbits. have been calculated by 
[Oct Is 
should have escaped the eyes ue astroe 
nomers, accustomed to consider as uses 
less to the science the millions of stars. © 
As 
possibly are not of more 
most every point of the firmament. 
planets, they 
3 —_ 
ee 
ford. us more information, or, at least, 
occasion some new remarks, They have 
already extended our ideas. The known — 
plancts were all at very unequal distances 
fromthe sun; the four last are equally 
distant from it. This is.a new fact, ¥ 
which atiers no. calculation, deranges HO 
theory; one of these planets is~eccen=- 
tric, as much at least as Mercury; anos, 
ther, as much as Mars; the inclination 
of the second is alone greater than-the 
uiited inclinations of all the other pias: 
nets. The Zodiac must be enlarged; but 
the Zodiac is only a name;. astronomers. 
make no use of it, and -it has been long | 
known, that comets have sone.. This 
Ye: ee 
- great inclination, and the great eccens, 
tricity, will render mere dificult the cal- — 
culations of the perturbations; they will, 
perbaps, afford peombbreians an oppor, 
tunity of extending the limits of analysis, — 
and what may have appeared an incon~ 
venietice, may become an advantage. 
The first of these planets was deco veeet 
by M. Piazzi; the third, by M. Harding» 
and the other two, by M.Olbers. This diss 
tinguished astronemer, to whom the class 
of sciences bas just decreed, for the second 
time, the prize-medal founded byLalande, 
thought that these very smail planets . 
may. very probably be.the fragments of 
a more considerable planet, which some 
unknown cause has split into. several 
pieces. Tle concludes from it, that all 
their orbits must inteisect each other in 
two opposite points, that they must all - 
pass by one of these points, at each half 
revoluvion, and that in order to know 
them all, it is necessary to observe see 
veral times in the year these two regiong 
of the heavens. Accordingly, the four 
planets were found towards these points; 
and the two last since M. Olbers has 
suggested this idea, which is at least a 
very happy one. M. Olbers has, besides, 
discovered several comets, and has given 
a very simple and very ingenious method: 
for calculating their orbits, 
Seventeen comets have been discoe. 
vered since the year 1789. We are ins ; 
debted for them to the vigilance and care 
of MM. Messier, Bouvard, Mechain, 
Alt, 
Zach, Bode, 
MM, Mechain, Saron, 
, ; Englefield, 
