TRANSACTIONS OF THE SECTIONS. 
9 
itsnniihs and the images ceasing to overlap (from the moon’s limb gradually 
reeding from that of the sun), we shall then be able to calculate with considerable 
miracntwhat distance from the moon’s surface perceptible refraction ceases, and 
JBtliisitLichwe want to know. It is scarcely necessary to observe that the same 
ms fCTCTSed may also be used (and perhaps nmre advantageously) at the end of 
imiDiiim. _ 
On Spots in the Sun. By Henry Lawson, F.R.S. 
lie object of this paper was to point out the advantages of eraplonng, for obser%'a- 
■“3oa solar spots, telescopes with larg« aperture. In using these instruments the 
aw anploTS a pecoliar eye-piece (sec Brit. Ass. Report for 184(5), which permits 
fcvbole aperture to be effective; anti he has had several occasions of ascertaining 
to^aliar appearances and inequalities of illumination which the large apertures 
^it,areiiiviable with smaller apertures. 
On tfic Calculation of llte Perlur/jfJtions of Planets and Comets. 
By Sir J. W. Lubbock, Bart., F.R.S. 
Ihjactiincy of the tables which give for an indefinite time the places of the older 
is at present sufficient for the purposes of astronomy, and is commensurate 
*>4 ibp accuracy of observation } or if this statement appears to be exa^crated, it 
hilitleistbe admitted that the sensible errors which remain are owing rather to 
®d«rl«ice b the numerical comuutatioo than to the imperfection of the method 
Such a result is owing to iW uniuterrnpted latiours of the greatest mathe- 
wicians from the time of Newton, tuid is justly regarded as one of the greatest 
Hjapbs of human intelligence. But it mu-H he recollected that these methods, by 
perturbations of the older planets have been obtained, are applicable 
®'lie Ctei; of orbits nearly circular, and little inclined to each other! so that the 
PtfslMlutiguof the problem of the three bodies, as it is called, remains to the 
imperfect. The methods in use far tlie older planets are founded, as is 
JJdtwwa, upon the development of the disturbing function in terms of the mean 
yiiea. M. Binetbaa indeed carried this development to quantities of the seventh 
■>1 inclusive; but such a development is quite insufficient in the case of comets or 
“(Urooving in highly eccentric and Inclined orbits, which prublem presents tar 
“JJT difficulty 5 while the nature of the expression is such, that it U evidently im- 
to carry further such a made of dcvelopmenl, even if the expressions were 
’y'otly convergent when Uie eccentricity passes a certain limit, 
w only memoir vvith which I —-i 
-v-oy memoir with which I am acquainted which pro fosses to give » ge^rai 
lum ^ problem otherwise than by mechanical quadratures, is due to M. 
• lots important work is translated in the * Conn, ties Temps ’ for 1847. I nat 
^"atheinaticiun has considered the case when r-<r', that is, when the disturbed 
^laferior; and has illustrated the nuestion by the mmii-rical calculation of the 
the Af k». M llnnkpri ilcvoloDsthc disturbing 
the comet of Enckc by Saturn. M. Hansen develops the disturbing 
»according to multiple angles of the eccentric anomaly of the disturbed plane 
^wording to multiple angles of the true niuimaly of the ' 
Hanaeo next converts the cosines and sines of the multiple ang 
of the disturbing planet into sines and cosines of multiple angles 
i“ 2 ““onialy of that planet 5 so that finally the <li*wrbi^ function rn^hj- 
diTT- eccentric anomaly of the disturbed planet and the mean a ^ 
plMct; but thoMi siics which serve to give the sines and cosines 
^;‘«Bllipl«.ofthe true anomaly, in terms of sines and cosinea of the mean ano- 
and the process becomes "tremely laborio , 
f‘th M. Hansi'n has «.n«dmtl. in which, in consequrace ^ 
approxlwatinn docs not rcqnirc to be carried ntbers 
*^>4 tol l perturbations of the some comet by Jupiter, and m many others 
consideration. Morcuver, in this aa in every . 
fbc disturbing function literally, all qi^titie 
^though when Vy are of a different sign, m 
destroy each other; but such reductions cannot be foreseen. Ine nu 
