On the Formation of the Tails of Comets. 119 



city. Now gV of a mile would give in twenty days an apparent 

 displacement in the plane of the orbit of about half a minute of 

 an arc, which is more than the difference between the observa- 

 tions and the best ephemeris. From which it appears, that if 

 the force necessary to keep up the rotation were to be diminished 

 more than seventy thousand times, its effect upon the orbit ought 

 still to have been perceptible. 



If we were to suppose the tail to have been only 4,000,000 

 miles long, while the comet was nearest the sun, which is not 

 much more than half its length, as seen in the day time on the 

 28th of February, then the velocity found as above, would be 

 about one hundred and fifty times less ; which would still be 

 about four hundred and seventy times too great. To reduce it as 

 low as is necessary we must then suppose, farther, that there 

 was four hundred and seventy times more matter in the head of 

 the comet. 



If we imagine, as some astronomers have done, the only bond 

 of connection between the different parts of the comet to be that 

 of gravitation, the force will have to be the same, and it will 

 have the same effect upon the motion of the centre of gravity. 



There is another mode in which the supposed entire connected 

 mass of a comet may be conceived to be set in rotation, besides 

 that which we have been considering, viz. by the action of the 

 excess of the sun's attraction for the nearer over that for the more 

 remote parts of the comet. Let us attempt its investigation. It 

 will be observed that this force cannot alter the orbit, and that 

 the only inquiry will be whether it is of sufficient intensity to 

 produce the known rate of rotation. Now let G= resultant of 

 the differences between the sun's actions upon the various points 

 of the tail, and his action upon the extremity supposed distribu- 

 ted over the whole length ; Y= distance of point of application 

 of this force from the sun ; g— sun's force of attraction at the 

 unit of distance ; D= distance of nucleus from the sun; d= 

 distance of extremity of tail ; and x= distance of any point in 



Cs 



the tail : then, / — . xdx= sum of moments of forces soliciting 



the different particles ; and / jj. xdx= sum of moments of forces 



equal to force at the extremity of the tail. This being the case, 

 we may proceed with the investigation as follows ; GY = 



