16 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



Private the tranquillity of a philosopher. He was respected 

 characterof an( j rewar ded alike by kings and democrats he was 

 Lagrange. poured an( j p rom oted 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, 



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, 

 " I 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- ( 59 

 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. LAPLACE. 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. 



(60.) PIERRE SIMON LAPLACE has generally, and not 

 jap ace. ^hout 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. 



Im e ' t ' ^en, we are * speak of the improve- 



ments in ments of the lunar theory effected by him. The ap- 

 the Lunar plication of Newton's own principles to the perfecting 

 Theory. o f ^ e 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 maybe 

 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 may be 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. 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 Moon ' 

 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 



