COMETS. ■ 25 



The motion of a comet as it recedes from the sun becomes slower and 

 slower, so that comets of parabolic or hyperbolic orbits may reach such a great 

 distance that their motion may be but a few feet per second. Now, such is the 

 immense distance of the fixed stars that such a velocity may obtain before any one 

 of them would exert a predominant influence upon the motion of the comet; and 

 this, it is reasonable to suppose, is generally the case. 



If, now, we remember that the form of orbit is determined by the velocity, 

 we are led to suspect that, generally, comets leaving our system on hyperbolic or 

 parabolic orbits will visit other systems on ellipses, and that comets leaving other 

 systems on these infinite curves would be most apt to visit us in ellipses. This 

 may explain why so few of the comets which approach the sun move in hyper- 

 bolic orbits. Since there can be but one velocity which gives a parabolic orbit, 

 while an increase or diminution of same would give either an hyperbola or an 

 ellipse, we may assume that few if any comets ever moved in strictly parabolic 

 orbits. And should a comet at any time move on a parabola, it would soon be 

 forced to abandon it for either an elhpse or hyperbola by the attractions of other 

 bodies. 



There is great difficulty in determining the exact orbits of comets: First, 

 because (as will be shown further on) comets are very light bodies, and therefore 

 their motions are subject to great derangements from the attractions of the 

 planets. Second, because in most cases they can be observed while traversing 

 only a small portion of their orbits. By lengthening out an ellipse it may be made 

 to approach more and more nearly to the form of a parabola, so that if the two be 

 placed with their vertices touching, they may be made to coincide for a greater 

 and greater distance. It will be seen, therefore, that if a comet can be ob- 

 served only while it is within the limits of this coincidence (which is always the 

 case with comets of so-called parabolic orbits), it is impossible to determine the 

 orbit beyond. A good illustration of this is afforded in the theory of projectiles. 

 We are taught that, neglecting the resistance of the air and the motion of the 

 earth, a body projected in any direction except vertically will describe a parabola. 

 Now, in order that a body so projected should describe this curve, it must be 

 given a velocity equal to that which it would acquire by falling to the center of 

 the earth, supposing all the matter in the earth collected at that point, and the 

 acceleration to be constantly equal to 32.2 feet per second. This would be about 

 seven miles per second; and since no such velocity can be given to a projectile, 

 it is evident that they all move in ellipses so very much elongated that there is no 

 objection to regarding them as parabolas. 



The difficulty, therefore, in calculating the orbits of comets is not caused by 

 any defect in theory, is not because these bodies refuse to obey the same laws 

 which control the motion of all matter; but simply because it is not always pos- 

 sible to obtain sufficient data. While science has thus reached the motions of 

 comets, and shown them to consist of inert matter, obeying the general laws of 

 motion, it has been able to postulate little with regard to their physical constitution. 



Situated in the head of a comet is a bright nucleus like a star; next this and 



