Contributions to Astro-Meteorology. 41 



a distance that its annual parallax is but a few seconds. Its 

 orbit about the sun will then be a conic section. Suppose now 

 the sun to be at rest, and regard the relative velocity of the 

 comet as the real velocity. Let fall a perpendicular from the 

 sun upon the direction of the comet's motion. The area 

 described about the sun in a unit of time will be equal to one- 

 half the product of this perpendicular into the comet's velocity. 



As, however, the velocity is in general comparable in magni- 

 tude to the planetary velocities, and the perpendicular is in ge- 

 neral enormously greater than the distances of the planets from 

 the sun, it follows that the areas described in a unit of time are 

 in general very much larger than corresponding planetary areas. 

 But these areas are as the parameters of their corresponding or- 

 bits. Hence in general the orbits of such comets would have 

 enormous dimensions in every direction, and the bodies them- 

 selves would remain invisible to us because of their great distance 

 from the earth. 



In two cases only would they come within our field of vision. 

 When the perpendicular is very small, a hyperbolic orbit would 

 result, differing in general not much from a right line. As the 

 radius of the sphere of our vision is only about four times the 

 distance from the earth to the sun, this case would rarely happen. 



The second case is when the relative motion of the comet is 

 very small, that is, when the comet and sun are moving in nearly 

 parallel paths with nearly equal velocities. An orbit very nearly 

 a parabola would result. This case would likewise be very rare, 

 since of all possible velocities of the bodies in the stellar spaces, 

 very few would be nearly equal and parallel to that of the sun. 



The parabolic form of the cometary orbits should not, then, 

 surprise us : this is not the only possible form ; on the con- 

 trary, it is one that is very rare ; but owing to the nature of 

 comets, and to our feeble powers of vision, we can see only those 

 which describe just these orbits. Nor is there reason for wonder 

 that the planes of their orbits have no relation to the plane of 

 the ecliptic. 



The characteristics peculiar to planets can be accounted for 

 by their formation in the solar system ; those peculiar to the 

 orbits of comets depend on the manner in which the sun attracts 

 them to itself from the depths of space. The latter, then, should 

 have an origin foreign to our system. To which of these two 

 classes belong the shooting- stars ? Are they planets, or are they 

 comets ? 



The planetary hypothesis has hitherto been favoured by astro- 

 nomers. The ring theory, however, as M. Schiaparelli believes, 

 leads to serious difficulties respecting the origin of the shooting- 

 stars, whether the rings be regarded as integral parts of the 



