124 On the Formation of the Tails of Comets. 



new tail. The particles may be supposed to be detached from 

 the outer parts of the nebulosity by the sun's repulsive force, so 

 called ; in which case they would fly off in the directions of the 

 lines diverging from the sun, along which the force acts, but 

 would be made by the attraction of the nucleus to pursue paths 

 somewhat, though doubtless slightly deviating from these lines, 

 and concave towards the axis of the tail ; or, we may imagine them, 

 as Olbers and Bessel have done, to undergo some modification by 

 the action of the sun, by reason of which they are first repelled 

 outward from the nucleus, and then driven away from the sun 

 into the depths of space by his superior repulsion. According to 

 this view of the matter, they acquire an initial velocity in leaving 

 the nucleus, and subsequently, under the action of the sun's re- 

 pulsive force, supposed to vary according to the law of the in- 

 verse squares, they will move off in hyperbolas, having the sun 

 in their remote focus, and concave towards the axis of the tail. 

 This, or an equivalent fact, has been established by Olbers, and 

 I find may be easily shown by introducing into the investigation 

 of the ordinary case of central forces the modifications conse- 

 quent upon the supposition that the two components of the ac- 

 celerating force are positive instead of negative. These hyper- 

 bolic paths will be changed more or less by the continued repul- 

 sive action of the nucleus. Combined with these motions with 

 respect to the nucleus, there will be the orbitual motion which 

 each particle had at the instant of leaving the head, which will 

 be retained afterwards. The effect of both these motions will 

 be to make each particle describe a hyperbola having the sun in 

 its remote focus. For, the particle may be conceived to start 

 from a point of the orbit, or near the orbit, with an initial velo- 

 city equal and parallel to the velocity in the orbit, or equal to this 

 modified in amount and direction by the repulsion of the nucleus, 

 according as one or the other of the two views that have been 

 given of the mode of disengagement of the particles be taken, 

 and afterwards to be repelled by the sun. (I here regard the 

 repulsive action of the nucleus as having no other effect than to 

 impart a certain projectile velocity, in a moderate distance.) It 

 is to be observed, too, that the motion with respect to the nucleus 

 will be modified by the change in the direction and velocity of 

 the nucleus subsequent to the escape of the particles. Also, if 

 the two motions just mentioned be contemplated as subsisting 



