THIRD (and posthumous) Stfvetzsizatv (1827).-On the Development of the Distance of Two Planets, and of its Elliptic Co-ordinates; Ou the Tides of the Atmosphere.
We have spoken freely of the defects of Laplace's character, both political and scientific, and it is now our more pleasing task to say a few words on the 316canique Waste,' as a whole. We might dwell upon the great discoveries, such as those of the long inequality of Saturu and Jupiter, the cause of the acceleration of the inoon's moan motion, the explanation of the peculiarities in the motion of Jupiter's satellites, with a long train of similar achievements ; but this, though most common method of describing the character of a philosopher, is not the sort of description which should be given of the . 116eanique Celeste.' Its bulk is about 2000 quarto pages ; cud, owing to the emission of all the stepa which a good mathematician may be relied DU as able to supply, it would, If expanded to the extent in which Euler would have written the same matter, have probably reached 10,000 pages. If all this work had been collected by cue man, even from the writings of others, we should have called him the Delambre of the theory of gravitation, and should have prized his writings for their extent, their faithful representation of the state of the science at a particular time, and the diligence displayed in the undertaking. When to the preoediug, which is forgotten in the splendour of some of the results, we add that to Laplace is due the discovery of much, the development of more, and that by the employment of his own resources in a manner which takes all the originality cud power of the investigator, and the arrangement and combination of the whole, wo may begin to see how he has earned his fame.
There is moreover another consideration which applies to the author of the ' 316cauique C6leste' more thau to any other, except that of the Principle.' When an investigator produces one result after another, upon detached and uucoonected subjects, we may feel admiration of his skill and sagacity ; but we can never know whether he followed a route with the determluatioo of overcoming a specific difficulty or not.
He tells us where he succeeded, but not where he failed. It is other wise when an original writer attempts a complete system, at every part of which he must work, and must show the world either a result or a blank. It is seldom that Laplace leaves off at the same point with his predecessors, though obliged, as just stated, to strive fur pre-eminence on every single point. Had he consulted his own glory, he would have taken care always to note exactly that part of his own work in which he had a forerunner ; aud it is not until this shall have beau well and precisely done, that his labours will receive their proper appreciation. His mathematical style is utterly destitute of the sym metry of that of Lagrange and the simplicity of that of Euler, and he is frequently even clumsy. He pays little attention to extreme correctness of form. Upon fundamental priuciplea, whether of mechanics or analysis, he frequently needs a commentator, at least fur the student.
Laplace explained his discoveries in a work entitled ' Exposition du Syetame du Monde,' of which the fifth edition bears the date 1S21. The account here given is in style and clearuess of a superior kind, somewhat too egotistical, and partaking of the di-positiou to suppression already noticed. A similar companion to the ' Theory of Probabilities' appeared as a preface to the work itself, and was published separately (filth edition, 1825), under the title of ' Essai Philosophique sur les Probabilit6s.' A little treatise, published in 1821, called Pr6cia de Bilistoire de l'Astronomie,' afterwards was made the fifth book of the fifth edition of the Systanie du Monde.' His lectures on the elemeutary branches of mathematics are in the 'Lecons de Mole Normalo.' Of the Th6orio dee Probabilit6s' we must speak precisely as of the M6canique C6leste,' adding perhaps that there is no part of the latter in which more original power is displayed than in the former. The subject being somewhat isolated, its results are little known; they have however been extensively applied to astronomy, both by Laplace himself, and particularly by the German writers.