1 S 1 3 .] Imperial Institute of France, S U ' 



grasses. But Dr. Smith conceives the^vitellus of Gsertner to be 

 the cotyledon. The object of Mr. Keith's paper is to show that 

 Gartner's opinion is correct, and that the viteiius does not pos- 

 sess the characters of a cotyledon. 



IMPERIAL INSTITUTE OF FRANCE. 



Accou7it of the Lahoiirs of the French Institute for 1812. 



(Continued from 111. 



Works Piuj^ted. 



Analytical Theory of ProLavilities. By M, le Comie 

 Laplace. 



In our history for 1811 we announced the speedy publication 

 of this work : the two parts of which appeared^ after an interval 

 of some months from each other, during the course of 1812. 

 Tlie first pnrt contains the preliminary researches, which were 

 indispensable for understanding the second, in which the author 

 has proposed problems so difficult as to require recourse to a 

 peculiar mode of analysis. After a short notice of the authors 

 who laid the first foundation cf the science of probabilities^ and 

 of*those who made some progress in constructing the edifice, M. 

 le ' Comte Laplace explains his theory of functions, which he 

 calls generafuig: one or two varialles. He explains tlie interpo- 

 lation oi it, the integration, and the transforinations. The 

 differentials of these problems contain factors raised to great 

 powers^ which require particular rules of integration. it is 

 impossible for us to give any idea of I Js method here ; we 

 cannot even make use of the arranged analysis vvhich occurs at 

 the end of the work. We shall only notice a general remark 

 which terminates the first part. Sometimes the series converge 

 rapidly in their first terms ; but this convergence often dimi- 

 nishes, or even changes into divergence. This ought not to 

 prevent us from making use of these series v/ith confidence^ 

 employing only the first terms, Vv^hen the rest of the series which 

 we neglect is the developement of an algebraic function or 

 integral, very small in comparison of that which precedes, 



" The second part commences with the general principlesj 

 with the definitions of the probaliility of simple or double events^ 

 of the probability of a future event drawn from an event observed^ 

 or of an event composed of several others, the respective possi- 

 bilities of which are given. Numerous applications serve to fix 

 the ideas in a matter so fugitive and so abstruse. We see, then^ 

 the laws of probability which result from the indefinite mulupli- 

 cation of events, the probability of errors from, the mean results 

 of a great number of observations^ and the mean results that are 



