COMETS. 



book of Newton's Principia, which propositions form in substance 

 the ground -work of the entire theory of gravitation, that a body 

 which is under the influence of a central force, the intensity of 

 which decreases as the square of the distance increases, must move 

 in one or other of the curves known to geometers as the " CONIC 

 SECTIONS," being those w^ch are formed by the intersection of 

 the surface of a cone by a plane, and that the centre of attraction 

 must be in the FOCUS of the curve ; and in order to prove that 

 such curves are compatible with no other law of attraction, it is 

 further demonstrated that whenever a body is observed to move 

 round a centre of attraction in any one of these curves, that centre 

 being its focus, the law of the attraction will be that of gravitation ; 

 that is to say, its intensity will vary in the inverse proportion of 

 the square of the distance of the moving body from the centre of 

 force. 



Subject to these limitations, however, a body may move round 

 the sun in any orbit, at any distance, in any plane, and in any 

 direction whatever. It may describe an ellipse of any eccentricity, 

 from a perfect circle to the most elongated oval. This ellipse 

 may be in any plane, from that of the ecliptic to one at right 

 angles to it, and the body may move in such ellipses either in the 

 same direction as the earth or in the contrary direction. Or the 

 body thus subject to solar attraction may move in a parabola with 

 its point of perihelion at any distance whatever from the sun, 

 either grazing its very surface or sweeping beyond the orbit 

 of Neptune, or, in fine, it may sweep round the sun in an 

 hyperbola, entering and leaving the system in two divergent 

 directions. 



To render these explanations, which are of the greatest interest 

 and importance in relation to the subject of comets, more clearly 

 understood, we have represented, in fig. 1, the forms of a very 

 eccentric ellipse, aba' b', a parabola a p p\ and an hyperbola 

 a h h' y having s as their common focus, and it will be convenient 

 to explain in the first instance the relative magnitude of some 

 important lines and distances connected with these orbits. 



5. Ellipses or ovals vary without limit in their eccentricity. 

 A circle is regarded as an ellipse whose eccentricity is nothing. 

 The orbits of the planets generally are ellipses, but having 

 eccentricities so small that, if described on a large scale in 

 their proper proportions on paper, they would be distinguish- 

 able from circles only by measuring accurately the dimensions 

 taken in different directions, and thus ascertaining that they are 

 longer in a certain direction than in another at right angles to it. 

 A very eccentric and oblong ellipse is delineated in fig. 1, of which 

 a a' is the major axis. The focus being s, the perihelion distance 

 148 



