The great work of Laplace (first edition 1812, third 1820) had in great part appeared at various previous times In the ' Memoirs' of the Academy of Sciences. It is remarkable, first by the extension of methods which it furnishes ; secondly, by its giving at one view the whole state of the science and its applications ; thirdly, by the particular attention given to the application of the theory to the results of obser vation. [Mess; LEAST SQUARES.] The next atop in the history is I'obsson'a 'Recherches cur lea I'robabilit6,8 des Jugemens ' 1837, which gives the grand results of Laplace by a somewhat different analysis, and applies them particularly to the decisions of courts of law. This species of application had been before considered by Condoreet, in his ' Easai cur l'Application de ]'Analyse h la Probabilit6 dee Decisions; Paris, 1785. It may also be worth while to mention the' Tmit6 do Calcul Conjectural, of Pariset, Paris, 1810, a work which deals largely in the theory of simple combinations. The elementary work of longest standing, which exhibits seine view of the higher mathematical appli cations, is the ' Tmit6 El6mentaire du Caleul des I'robabilit6a; by 31. Lacroix (second edition, 1822). The' F.ssai Philosophique' of Laplace, which is an introduction to the third edition of his theory, contains no mathematics, and may be usefully read with any elementary treatise. The ' Instructions Populeires slur le Calcul des Probabilit6e' by 31. Qectelet, Bruseele, 1828, contains the moat elementary view of the t nIaject, and uses only simple arithmetic.
In EngLand, since the publication of Simpson's Laws of Chance,' 1740, and the Laws of Chance,' by Samuel Clark, 1758, little was written on the mathematical theory except so far as it had reference to life annuities and assurance, until a very recent period. About 1S30 Messrs. Lubbock and Drinkwater (Bethune) published a tract ' On Probability,' in the' Library of Useful Knowledge; giving more general methods of applying modern algebraical' investigation than had before appeared in this country : by a binder's mistake this work Is often attri buted to Mr. De Morgan. In 1837, the article' Theory of Probe' pities; in the Encyclopaedia Metropolitan,' written by Mr. De Morgan, gave the results and methods of Laplace on most of the great questions of the theory. The Essay on Probabilities, and on their Application to Life Contingencies and Insurance Offices,' published by the same writer in the '1,..binet Cyclepaedial 1838, exhibits the principles with out mathematical investigation, and the results arranged in rules for use. The article on ' Probability' in the new edition of the' Ency clopaedia Motropolitana; by Mr. Galloway, gives the mathematical investigation of the higher parts of the theory, following the methods of Poisson. This treatise is published separately.
On subjects connected with this artiele,eee Ammo ; RISK; wA0En; MEAN; LEAST SQUARES; OBSERVATION AND EXPERIIIENT ; WEIGIIT ow OBSERVATIONS; ANNUITT ; MORTALITY; REVERSION, &C.