24 KANSAS CITY REVIEW OF SCIENCE. 



body not to vary as the distance diminished) will move in a parabolic orbit. If 

 the orbital velocity be less than this, the body will move in an ellipse. If it be 

 greater, the orbit will be an hyperbola, the sun in every instance being situated at 

 the focus. 



For that portion of this theorem relating to elliptical orbits Sir Isaac Newton 

 found immediate application in our planetary system, and his wonderful sagacity 

 had anticipated that its more general application would be found in the motions 

 of comets. The appearance of the great comet of 1680 afforded him a most 

 excellent opportunity. He found this comet to move in an orbit which, if an 

 ellipse, was so greatly elongated as to be undistinguishable from a parabola. The 

 period of this comet is estimated at 575 years, and it is supposed to be identical 

 with the comet of 1194 B. C; with that of 618 B. C; with that of 43 B. C, 

 which was supposed to be the soul of Caesar taking its place in heaven ; with that 

 of A. D. 575, which was seen at noonday close to the sun; and with the mag- 

 ficent comet of A. D. 1105. 



Applying the above theorem to the comet of 1682, Sir Edmund Halley was 

 led to predict its reappearance in 1759 — a prediction fully justified by the event. 

 This comet again appeared in 1835, and is again due at its perihelion in 1910. 



Since the year 1680 several comets have appeared which were found to move 

 in hyperbolic orbits, viz: those of 1723, 177 1, and the second comet of 181 8. 



Now, since the parabola and hyperbola are curves of infinite length, it is. 

 evident that comets moving in either of these could never before have visited 

 our system, nor is it possible that they should ever return. Again, it is found 

 that while all the planets revolve around the sun in the same direction and nearly 

 in the same plane, comets move in any direction and in planes greatly inclined to 

 each other, which shows that they cannot be regarded as permament members of 

 our system. 



It is interesting to speculate upon the career of a comet which moves in an 

 orbit of infinite length. We cannot but think, as it has visited us on one 

 branch of such a curve to retire on the other, that at some time in the past it 

 must have swept around some fixed star or sun, whose distance can be measured 

 by no means at our disposal, and that on its outward journey it will reach a point 

 at which the attraction of some other fixed star will predominate and cause the 

 comet to visit it, just as it did our sun. And as these comets may thus in time 

 traverse the utmost bounds of space in search of equilibrium, so may, and so 

 does, our ponderous sun himself obey the same law and traverse space about 

 some unknown center of force; and thus is it possible that he may now be 

 moving in a cometary orbit, from which he will ultimately be deflected into a 

 planetary by some sun mightier than he, and by the process of cooling and per- 

 turbation be reduced to the state of a planet, while the planets of his own system 

 will become his satellites. If such a speculation be admissible, it is easy to see 

 that in time all matter would be caused to revolve around a common center, and 

 all systems would be reduced to one. 



