188 
SECOND REPORT — 1832 . 
and published; but, for the sake of uniformity of system, it 
would be desirable to re-compute them. 
5. I have mentioned that the perturbations of the small 
planets and of Encke’s comet give good reason to believe that 
the mass of Jupiter adopted by Laplace is too small. Laplace’s 
estimation is founded on Pound’s measures of the elongation of 
Jupiter’s satellites ; and I am not aware that any measures have 
been made since that time. It is extremely desirable that they 
should be measured, at least those of the fourth satellite. It 
would be sufficient, in observing the transit of Jupiter, to ob¬ 
serve also the transit of this satellite, one or two days before 
and one or two days after the time of its greatest elongation, as 
the theory of the satellites could be applied without difficulty 
to this measure. 
6. The dimensions of the orbit of Encke’s comet, as investi¬ 
gated by Encke, depend upon the assumed law of density of the 
resisting medium. In fact, by assuming a law, he has estab¬ 
lished a relation between the diminution of the aphelion distance 
and the diminution of the perihelion distance which would not 
hold with any other law. It will be interesting now or at some 
future time to investigate separately from observations the dimi¬ 
nution of these two elements, as a means of proving Encke’s 
law, or of suggesting a new one. 
7. The perturbations of Biela’s comet have not been calcu¬ 
lated, I believe, for the interval between 1772 and 1806, nor 
those of the node and inclination from 1806 to 1826. It is de¬ 
sirable that this should be done, both for ascertaining the iden¬ 
tity of the comet of 1772 (which is not perfectly established), 
and for examining whether this comet, like Encke’s, gives any 
indication of a resisting medium. 
8. The most laborious part of the expansions in physical 
Astronomy is completely dispensed with by the use of Burck- 
hardt’s formulae in the French Memoires for 1808. ButBurck- 
hardt expressed himself very doubtful as to their accuracy; 
and they do not comprehend any terms depending on inclina¬ 
tion. It is desirable that they should be verified, and extended 
to the terms depending on the inclination. 
9. The theory of the perturbations of Pallas has so often 
and so vainly been proposed, that it would seem useless to urge 
it again,® and still more so to propose the theory of the pertur¬ 
bations of Encke’s comet. Yet I conceive this to be the pro¬ 
blem which at present demands the efforts of Physical Astro¬ 
nomy. It is plain that there is no hope of solving it by any of 
the usual methods, as the series, which in other cases are con¬ 
vergent, here either diverge or converge so slowly as to be 
