888 Mr. R. P. Greg on Meteorolites or Aerolites, 



one-half of the heavens, a result doubtless not of chance, and 

 seeming to indicate that the matter whose mass we are investi- 

 gating is nearer the sun on the side of the summer solstice than of 

 the winter. This circumstance must be taken into consideration, 

 not for the purpose of introducing it as an essential condition 

 into the solution of the problem, but, on the contrary, of arriving 

 at a result which shall be independent of it. 



" This consideration will lead us not to make use of the mo- 

 tion of the earth's perihelion, although it is better known than 

 that of Mars. The earth's perihelion being in fact situated in 

 that very portion of the heavens occupied by the perihelia of 

 more than three-fourths of the asteroids, the second term which 

 enters into the expression of its motion may become appreciable 

 as compared with the first and of the contrary sign : inasmuch 

 as these terms are respectively proportional to the excentricities 

 of the terrestrial orbit and the orbits of the small planets, and as 

 the excentricities of these last are at the mean nine times greater 

 than that of the earth. 



" The perihelion of Mars is situated much more favourably in 

 relation to the mean direction of the perihelia of the asteroids ; 

 and besides the excentricity of its orbit is greater. As a result 

 of these two conditions united, the second term which enters 

 into the expression of the motion of the perihelion is only one- 

 fourth of the first. Now this superiority of the first term may 

 be expected to continue after the discovery of a great number of 

 new asteroids, whether this predominance of the perihelia in the 

 mean direction of the summer solstice shall be confirmed, as it pro- 

 bably will be, or whether we shall be obliged to return to the idea of 

 a uniform distribution of them through every part of the heavens. 



" In accordance with these remarks, I have found that if the 

 mass of the whole group of asteroids was equal to the mass of 

 the earth, it would produce in the heliocentric longitude of the 

 perihelion of Mars an inequality which in a century will amount 

 to eleven seconds. Such an inequality, supposing it to exist, 

 surely could not have escaped the notice of astronomers. If we 

 reflect that this inequality will become strikingly sensible at the 

 moment of the opposition of Mars, we must believe that at pre- 

 sent, and although the orbit of Mars has not been determined 

 with perfect accuracy, it cannot nevertheless admit of an error in 

 longitude greater than one-fourth of the inequality which we 

 have pointed out. Hence we conclude that the sum total of the 

 matter constituting the small planets situated between the mean 

 distances 2*20 and 3*16 cannot exceed about one-fourth of the 

 mass of the earth." 



In a second memoir {Compt, Rendus, t. xxxvii. p. 965) M. Le 

 Verrier establishes the following propositions : — 



