18 M. Arago on the Number of 



sion on this subject at present would be premature ; because it 

 is clear that 137 orbits cannot supply general results, free from 

 accidental influences. 



Distances of Perihelions. — Between the sun and the orbit of 

 Mercury, 80 ; between the orbits of Mercury and that of Ve- 

 nus, 44 ; Venus and the Earth, 34 ; the Earth and Mars, 23 ; 

 Mars and Jupiter, 6 ; beyond the orbit of Jupiter, 0. 



It seems difficult, after perusing this table, not to consider it 

 as demonstrated, that the perihelion distances are not all equally 

 possible. Nevertheless, when we devote a little more attention 

 to the several conditions of the problem, we shall probably be 

 led to modify the deductions derived from the first glance. And 

 here it will be expedient, in the first place, clearly to recognise 

 the difficulty. 



If the perihelions were uniformly distributed throughout the 

 celestial spaces, the number of those which would exist in those 

 concentric spheres, which are nearest to the sun, and having for 

 radii the radii of the orbits of Mercury, of Venus, and of the 

 Earth, would stand to each other in the ratio of the volumes of 

 their spheres ; or, to express it in numbers, as the cubes of 3.9, 

 7.2, and 10, (3.9)^ (7.2)3, ^^^ f^^Qy . t^gj jg ^^ g^y^ as 59, 

 373, and 1000. 



Let us now write, under these last cyphers, the number of 

 comets which are known to be included within the spheres of 

 Mercury, Venus, and the Earth, and we shall find that they are 

 29, 74, and 110. 



The first, 29, is very nearly the half of 59, whilst 74 is not 

 quite a fifth of 373 ; and 110 is not more than between the 

 ninth and tenth part of 1000. The number of observed comets, 

 therefore, does not augment at all proportionably to the volumes 

 of the spaces which include their perihelions. 



But before altogether renouncing this law, it will be right to 

 inquire if, for all the regions, more or less distant from the sun, 

 the number of comets which are perceived may not be the same 

 aliquot part of the total number of those stars, the perihelions 

 of which are placed in these same regions. And all that is re- 

 quired to enable us to answer that it is not, is only to put the 

 question in the precise terms which we have employed above. 

 The comets whose perihelions are placed between the orbits 



