Cuar. IL., § 2.] PHYSICAL ASTRONOMY—LAPLACE. 815 
been also slowly increasing. The result is that the In conclusion of this subject, I regret that space (64. 
moon’s motion has been continually accelerated. does not allow me to advert particularly to Laplace's 51°01) 2t 
Now, we have in the last section referred by anti- remarkable success in accounting for some singular satellites. 
cipation to this acceleration as having led to the 
belief that the moon must at last fall to the earth. 
Laplace’s discovery, however, shows that the acce- 
leration has a limit, depending on that of the ex- 
centricity of the earth’s orbit, which having reached 
its minimum, the lunar mean motion will begin to 
be retarded, and will continue so through a vast 
cycle of ages, and so on alternately. Theory enables 
us to assign, with considerable accuracy, the amount 
of the acceleration, which is now about 10” of lon- 
gitude in a century. 
peculiarities in the system of Jupiter’s satellites, 
arising from, and partly occasioning, an exact com- 
mensurability in the periods of some of them (which 
Sir John Herschel has lately observed to hold also 
in the Saturnian system in a somewhat different 
manner), a case which we have seen to be especially 
excluded in the instance of the planets, and which 
has been pronounced by a very competent judge (Mr 
Airy) to be “ the most curious and complicated sys- 
tem that has ever been reduced to calculation.’ It 
ought to be stated, however, that Laplace’s dis- 
£68.) Besides this very satisfactory discovery, Laplace covéries were based upon a previous and highl 
Earth's : pp naires a Rigas pred marae ape ge Oe sieht guy 
ellipticity investigated three of the lunar inequalities in a man- original investigation of Lagrange, 
and solar ner Jeading to curious and unexpected results. Two 
parallax 4 these depend on the spheroidal figure of the earth. II, In the second place, we shall briefly state the 
deduced ‘is P S eu 2 P ° y A ; 
from the The nutation of the earth’s axis, which is due to the nature of Laplace’s happy explanation of a great in- Hong ie 
8 attraction of the moon on the protuberant equatoreal equality of the solar system, to which, like the fact} Jupiter 
motion. 
parts of the earth, is exactly reproduced by the equi- 
valence of action and reaction in the movements of 
the lunar orbit, only less perceptible in degree on 
account of the length of the leverage at which they 
aré effected. The inequality of the moon’s motion 
in latitude may be used to determine the degree of 
compression of our globe at the poles. Laplace de- 
duced from the Greenwich observations of the moon 
the fraction zz, and, from a relative inequality in 
longitude, z+; @ coincidence really astonishing, not 
of the lunar acceleration, especial attention had been and Sa- 
turn, 
called by the sagacity of Halley, and which, like it, 
resisting all the efforts of geometers to interpret, 
threatened the credibility of the Newtonian theory of 
gravity. We are therefore to look upon this step as 
something more than a solution of a difficult problem; 
it was a new, peculiar, and unsuspected combination 
of circumstances on which it depended, and the solu- 
tion afforded a key in all time coming to difficulties 
depending upon a like cause. 
Halley had ascertained, that by comparing mo- 
only as between themselves, but also when compared Eeny 
dern with the most ancient observations of Jupiter and | 0." 
: . . . . ese ine- 
with the mean result of laborious investigations by 
Saturn, the mean motion of the former planet had been qualities ; 
- 
actual measurement of the earth’s surface. The other 
result we referred to was the determination from the 
lunar theory of the solar parallax,—in other words, 
the distance of the earth from the sun, which enters 
into the expression of a certain inequality of the 
moon’s motion in longitude. From the observed 
amount of this inequality, Laplace obtained a value 
of the solar parallax exactly coincident with that 
obtained with so much labour on occasion of the 
transit of Venus in 1769. Strange and admirable 
result (as Laplace himself remarks), that the astro- 
nomer, immured in his observatory, and watching our 
satellite through his telescopes, and reading the re- 
sult by the aid of mathematical analysis and the 
theory of gravitation, should be able to determine the 
figure of our earth, and its distancé from the sun, 
with perhaps quite as great accuracy as by any direct 
measurements. Truly the wonders of fact exceed 
those of fiction, and the divinations of true science 
may match the pretensions of her counterfeit, astro- 
‘logy. 
accelerated, and that of the latter retarded. Lambert 
remarked subsequently that, if we confine ourselves 
to modern observations alone, an opposite change 
would appear to be in progress. The amount of the 
error of the tables was so considerable (amounting to 
20’ or more in the middle of the eighteenth century, 
and capable, in fact, of becoming much larger), as to 
have been (along with the,apsidal motion of the lunar 
orbit) one of the first subjects of anxiety and specu- 
lation to geometers, when the Newtonian theory came 
fairly into discussion. For nearly forty years this 
stubborn inequality was vainly attempted to be ac- 
counted for by Euler, Clairaut, D’Alembert, Lagrange, 
and by Laplace himself, before the latter hit upon 
the true cause of the anomaly. It was long, and 
naturally, believed to be a properly secular inequa- 
lity, arising from the average mutual effects’ of the 
planets Jupiter and Saturn, though Lambert’s re- 
mark rendered this less probable. It was in the course 
of the consequent research that Laplace proved that 
the mutual action of the two planets could produce 
1 We here add that very recently Mr Adams has discovered that Laplace, and also his followers, in confining their at- 
tention to the radial effect of the sun’s interference with the lunar motions, as affected by the excentricity of the earth’s orbit, 
have unwarrantably assumed that the area described by the moon a unit of time is invariable, 
He finds, on the contrary, tan- 
gential perturbations depending on the same cause, and sensibly modifying the amount of secular mean motion deduced from 
theory.—(Philesophical Transactions, 1853.) 
