LAPLACE. 491 



924. In the Connaissance des Terns for 1815, which is dated 

 November 1812, there is an article on pages 215 — 221 relating to 

 Laplace's Theo7ne...des Proh. The article begins with an extract 

 from the work itself, containing Laplace's account of its object 

 and contents. After this follow some remarks on what is known 

 as Laplace's nebular hypothesis respecting the formation of the 

 solar system. Reference is made to the inference drawn by Michell 

 from the group of the Pleiades ; see Art. 619. 



925. In the Connaissance des Terns for 1816, which is dated 

 November 1813, there is an article by Laplace, on pages 213 — 220, 

 entitled, Sur les Cometes. 



Out of a hundred comets which had been observed not one had 

 been ascertained to move in an hyperbola; Laplace proposes to 

 shew by the Theory of Probability that this result might have 

 been expected, for the probability is very great that a comet would 

 move either in an ellipse or parabola or in an hyperbola of so 

 great a transverse axis that it would be undistinguishable from a 

 parabola. 



The solution of the problem proposed is very difficult, from 

 the deficiency of verbal explanation. We will indicate the steps. 



Laplace supposes that ?• denotes the radius of the sphere of 

 the sun's activity, so that r represents a very great length, which 

 may be a hundred thousand times as large as the radius of the 

 earth's orbit. Let V denote the velocity of the comet at the 

 instant wdien it enters the sphere of the sun's activity, so that r 

 is the comet's radius vector at that instant. Let a be the semi- 

 axis major of the orbit which the comet proceeds to describe, e 

 its excentricity, D its perihelion distance, ■sr the angle which the 

 direction of V makes with the radius r. Take the mass of the 

 sun for the unit of mass, and the mean distance of the sun from 

 the earth as the unit of distance; then we have the well-known 

 formulse ; 



a r 



r V sin OT = Va (1 — e ), 

 I) = a{l-e). 



