544) LAPLACE. 



approclie tellement de la certitude, que le resultat observe devient 

 invraisemblable dans cette liypothese ; ce resultat indique done avec 

 une tres-grande probabilite, I'existence d'une cause primitive qui a deter- 

 mine les mouvemens des planetes a se rapprocber du plan de I'ecliptique, 

 ou plus naturellement, du plan de I'equateur solaire, et a se mouvoir 

 dans le sens de la rotation du soleil... 



Laplace then mentions other circumstances which strengthen 

 his conclusion, such as the fact that the motion of the satellites is 

 also in the same direction as that of the planets. 



A similar investigation applied to the observed comets does 

 not give any ground for suspecting the existence of a primitive 

 cause which has affected the inclination of their planes of motion 

 to the plane of the ecliptic. See however Cournot's Exposition de 

 la Theorie des Chances . . . page 270. 



Laplace's conclusion with respect to the motions of the planets 

 has been accepted by very eminent writers on the subject ; for 



example by Poisson : see his Recherches sur la Proh page 802. 



But on the other hand two most distinguished philosophers have 

 recorded their dissatisfaction ; see Professor Boole's Laws of 

 Thought, page 864, and a note by K. L. Ellis in The Works of 

 Francis Bacon ... Vol L 1857, page 848. 



988. Laplace devotes his pages 262 — 274 to a very remark- 

 able process and examples of it ; see Art. 892. The following is 

 his enunciation of the problem which he solves : 



Soient i quantites variables et positives t, t^,...ti_^ dont la somme soit 

 s, et dont la loi de possibilite soit connue ; on propose de trouver la 

 somme des produits de cliaque valeur que pent recevoir une fonction 

 donnee i(/(t, t^, t^, (fee.) de ces variables, multipliee par la probabilite 

 correspondante a cette valeur. 



The problem is treated in a very general way; the laws of 

 possibility are not assumed to be continuous, nor to be the same 

 for the different variables. The whole investigation is a charac- 

 teristic specimen of the great powers of Laplace, and of the brevity 

 and consequent difficulty of his expositions of his methods. 



Laplace applies his result to determine the probability that 

 the sum of the errors of a given number of observations shall lie 

 between assigned limits, supposing the law of the facility of error in 



