244 Dr Lelimann's Inquiries regarding 



pies, that no third case can exist. Now, it is easy to see, that a 

 comet which sliould turn round its axis, in the first of these 

 ways, could not have a tail ; for, if we suppose that some parts 

 of the atmosphere of the comet were upon the point of extend- 

 ing, over a larger space of the side opposite the sun, than of any 

 other side, they would be immediately displaced by the rotatory 

 motion, since they must possess this motion in common with the 

 nucleus. It may therefore be admitted, that, before a comet 

 can have a tail, it must necessarily ahvays present the same side 

 to the sun. Knowing that some comets shew no trace of a tail, 

 while others acquire one near their perihelion, we may consider 

 it as established, that the former turn in the manner of planets, 

 and the others in the manner of satellites. But if a comet ai- 

 w^ays present the same side to the sun, it can only be, because 

 it has a greater mass on the side which it thus presents, than 

 on the opposite side, as La Place has demonstrated with respect 

 to the moon. Its centre of gravity will therefore be found be- 

 tween the centre of iigure of the nucleus and the sun, and nothing 

 prevents us from supposing this centre of gravity near the sur- 

 face of the nucleus. 



The accelerating forces, to which each particle of the atmos- 

 phere of a comet will be subjected, are the following, 1*^, The 

 power of expansion ; 2^Z^, Tlie gravitation toward the sun ; 

 Sdli/, The gravitation toward the nucleus ; ^thly^ The attrac- 

 tion of all the other particles of the atpiosphere. 



The fourth of these powers is so feeble, that, in our inquiry, 

 it may be considered as an infinitely small quantity, on account 

 of the extreme rarity of such an atmosphere. The same might 

 almost be said of the gravitation toward the nucleus ; for this nu- 

 cleus has so little density, that even when it is in proximity to a 

 planet, it exercises no appreciable attraction upon it. This is a 

 circumstance which may be verified by the comet of 1770, 

 which approached the earth to a distance only seven times great- 

 er than that of the moon, without producing any sensible action 

 upon it. However, the parts of a cometary atmosphere, which 

 are near the nucleus, are so situated, that we cannot neglect the 

 attraction which this nucleus exercises upon them. There re- 

 main, therefore, three powers acting upon this atmosphere ; the 

 power of expansion, the gravitation toward the sun, and the gra- 

 vitation toward the nucleus. Let us decompose each of these 



