Private 
814 
the tranquillity of a philosopher. He was respected 
characterof and rewarded alike by kings and democrats—he was 
Lagrange. 
(60.) 
Laplace. 
(61.) 
Improve- 
ments in 
the Lunar 
Theory. 
honoured and promoted in three great states, Sar- 
dinia, France, and Prussia. Though patronized by 
the despotic Frederick, and lodged in her palace by 
the gentle queen of Louis XVI., he escaped the 
misfortunes of almost every one of his contempora- 
ries, including Laplace, Lavoisier, and Delambre ; he 
retained his scientific appointments throughout all 
the frenzy of the French Revolution. His mildness 
of disposition and disinterested devotion to science, 
more than the European celebrity of his name, con- 
tributed to this result. He was equally fortunate 
in his scientific relations. Euler, D’Alembert, and 
Laplace, whilst they were emphatically his rivals, 
were also his sincere friends. If he ever felt jealousy, 
MATHEMATICAL AND PHYSICAL SCIENCE. 
(Diss. VI. 
it was perhaps towards those who, he thought, at- 
tained too easily by circumstances to a high reputa- 
tion : Monge seems to have been of this number. It 
is remarkable that for a series of years Lagrange di- 
verted his mind altogether from mathematics, and 
studied chemistry, natural history, and even meta- 
physics. His reply is well known, when asked how 
he liked the first of these sciences ; “ Oh,” said he, 
“J find it on trial as easy as algebra.’ It may be 
doubted whether in our own day he would have 
given as favourable an opinion ! 
He was unassuming in conversation, and dis- 
liked speaking of himself. His commonest answer 
was “I don’t know.’ He was happy in his domestic 
relations, and died universally honoured and regret- 
ted, 10th April 1813. 
§ 2. Lapuace.—Lunar Theory Improved.—Great Inequality of Jupiter and Saturn.—Theory of 
the Tides.—Young; Dr Whewell; Mr Airy.— Theory of Probabilities —Character of 
Laplace as a Physicist and Author. 
Prerre Srwon Laprace has generally, and not 
without reason, been considered as a sort of exemplar 
or type of the highest class of mathematical natural 
philosophers of this, or rather the immediately preced- 
ing age. The causes of this, and the degree in which 
it is warranted, we shall endeavour to state towards 
the close of this section. In the meantime, finding it 
quite impossible within our prescribed limits to notice, 
ever so briefly, all his more material investigations, 
we shall select three or four marked by their ori- 
ginality and general interest. Such are, 1, His im- 
provements of the lunar theory. 2. His discovery 
of the cause of the great inequality of Jupiter and 
Saturn’s motions. 3. His theory of the tides. 4. 
His work on probabilities. 5. We shall consider 
his character as a general physicist, and as a writer. 
I. First, then, we are to speak of the improve- 
ments of the lunar theory effected by him, The ap- 
plication of Newton’s own principles to the perfecting 
of the theory of the moon’s motion has been related 
in Sir John Leslie’s Dissertation, and so far as the 
labours of Clairaut, D’Alembert, Euler, and Mayer, 
are concerned, belongs distinctly to the middle por- 
tion of the last century. The errors of Mayer's 
tables little exceeded one minute of space, which was 
twice more accurate than in Halley’s time. With 
one important exception, the main outstanding dif- 
ferences between theory and observation had disap- 
peared. The eclipses recorded in the Arabic and 
Chaldean annals could not (as Halley first observed) 
be correctly explained by the motion of the moon as 
given by recent tables. At length it became admit- 
ted that the mean motion of the moon has been 
accelerated from century to century by a minute 
quantity, which, in the lapse of thousands of years, 
has become recognisable. It amounts to this, that 
the moon comes to the meridian two hours sooner 
than she would have done had her present period 
remained invariable from the earliest astronomical 
records of eclipses. It is at once evident how delicate 
a test this must be of changes otherwise imperceptible. 
The effect on the dimension of the moon’s orbit may be 
thus expressed, that at each lunation she approaches 
nearer to the earth than during the last by one-four- 
teenth of an inch! thus describing a spiral of almost 
infinitely slow convergence. The minuteness of the 
effect maybe illustrated by the shortening of the 
pendulum of a clock by an amount absolutely in- 
sensible, which yet, after days and weeks, will alter 
by many seconds the time shown by the hands. 
(59.) 
(62.) 
% Secular 
After several unsuccessful speculations as to accelera- 
the cause of this anomaly, Laplace, in 1787, thus sa- tion of the 
tisfactorily accounts for it: —It is well known that the #0 
sun’s attraction on the earth and moon lessens, on 
the whole, the tendency of the latter to the former, 
and lengthens permanently the lunar period. But, 
so far as this effect is uniform, it does not directly 
appear. The effect is greater, however, when the 
earth is near the sun than when it is farther off. 
The lunations are therefore longer in winter (when 
the earth is in perihelion) than in summer. ‘This 
is called the annual equation, and the amount is 
very sensible for this reason, that (as may be easily 
seen) the perturbing force varies inversely as the 
cube of the sun’s distance. Now, though the earth’s 
mean distance from the sun has not varied in the 
lapse of ages, the excentricity of the earth’s orbit 
has been diminishing from the earliest historic times, 
and the average inverse cube of the distance has 
