Comets in the Solar System. 21 



ments in the direct ratio of the volumes of the spheres which 

 contain their perihelions ; and he has finally substituted, in the 

 previous proportions, the surfaces of these same spheres, instead 

 of their volumes.* This proportion then becomes (l) 2 : (49) 2 : 

 30 : to the number sought ; or, as 1 : 2401 : : 30 : 62,030. 



According to this hypothesis, the sphere whose centre corres- 

 ponds with the sun, and its circumference with the distance of 

 Uranus, would include only from 60,000 to 80,000 comets. 



2. On the Light of Comets ; and on the means of deciding whether 

 this light emanates from these bodies tJiemselves, or is borrowed 

 from the Sun. 



It has often been matter of astonishment, and not^ perhaps, 

 without reason, that such questions as these should still be can- 

 vassed in that science which is regarded as of all others the most 

 advanced. Many individuals have found a difficulty in com- 

 prehending how those methods, and those instruments which 

 have led to the determination of the weight of the planets, should 

 be ineffectual in determining points apparently so much more 

 simple. To this it may be answered, that at first it was neces- 

 sary to bestow an exclusive attention to the observation of the 

 phases of these bodies, inasmuch as this was the most direct me- 

 thod of ascertaining the point, and because it had succeeded 

 when tried upon Mercury, Venus, and Mars ; and also that, in 

 default of this plan, it is true, that so soon as a comet, favour- 

 ably placed, shall present itself, the phenomena of polarization 

 will decide, at least for an appreciable part of its light, whether 

 it has been derived from the sun or not. But these more sim- 

 ple and direct methods having hitherto failed, I proceed now to 

 state that there is another mode by which the question may be 



* Halley's Table of Comets, which was the only one which Lambert could 

 employ at the time of the publication of his Lettres Cosmologiques, contained 

 only twenty-one of these stars, viz. six within the sphere of Mercury, and 

 eleven between his sphere and that of Venus. But 6 + 1 1 : 6 ; : 3 : I nearly. 

 _The surfaces of the spheres of Mercury and Venus being also nearly as 1 to 

 3, it was possible for Lambert to demonstrate that the laws of surfaces was 

 conformable to observation. Now-a-days, when the Table includes 137 co- 

 mets, it will be evident that the law can be no longer so verified, for 30 + 44 

 is not equal to 3 times 30, i. e. 90. 



