20 M. Arago on the Number oj 



without the slightest trace of it being perceived during this long 

 period. It would require that the brilliancy of a comet should 

 greatly exceed that of any of the class which have been ob- 

 served for a century and a half, before we could hope to disco- 

 ver it, even with the strongest glasses, whenever its distance 

 from the sun shall have become equal to a radius of Saturn"'s 

 orbit. 



After having thus disposed of the objections which appear to 

 result from the numerical data which are supplied in the table 

 just alluded to, it will be found more natural that, in endea- 

 vouring to determine the number of comets which compose a 

 part of our solar system, we should start with the supposition 

 that the perihelions of their orbits are uniformly distributed in 

 space, unless some physical reason can be alleged to estabhsh 

 that it is not so. 



The number of comets really known whose perihelion dis- 

 tance is less than the radius of the orbit of Mercury, amounts 

 to 30. This radius, and that of the orbit of Uranus, are in the 

 ratio of 1 to 49. And the volumes of two spheres are to each 

 other as the cubes of their radii. If, therefore, we adopt the 

 hypothesis of the equal distribution of comets in all the regions 

 of our system, and calculate the number of those luminaries 

 whose perihelions are included in a sphere whose radius is the 

 distance of Uranus from the sun, the following proposition 

 would be supplied to us : — As the cube of 3 to the cube of 49, 

 so 30 to the number of comets sought ; or thus, (1)^ : (49)^ : : 



30 : . Or, in working out these numbers, as 1 : 117,649 : : 



30 : 3,529,470. 



Thus, within the orbit of Uranus, the solar system should be 

 ploughed by more than three million and a half of comets ; or, 

 we should rather find the double of that the true numbc, when 

 we consider that in this calculation the term which represents 

 the number of comets contained within the sphere of Mercury 

 is certainly much too small, and that it ought to be conceded 

 that the light of the day, and our cloudy skies, and a too south- 

 erly declination, remo\es from our sight not fewer than every 

 alternate one of these bodies. 



But Lambert, from considerations borrowed from final causes, 

 has rejected the supposition, that the number of comets aug- 



