^54 Comets. 



their greatest length and development ; thus indicating 

 plainly the action of the sun's rays as the exciting cause of 

 that extraordinary emanation. As they continue to recede 

 from the sun, their motion diminishes, and the tail dies away, 

 or is absorbed into the head, which itself grows continually 

 feebler, and is at length altogether lost sight of, in by far 

 the greater number of cases never to be seen more. 



Without the clue furnished by the theory of gravitation, 

 the enigma of these seemingly irregular and capricious move- 

 ments might have remained for ever unresolved. But New- 

 ton, having demonstrated the possibility of any conic section 

 whatever being described about the sun, by a body revolving 

 under the dominion of that law, immediately perceived the ap- 

 plicability of the general proposition to the case of cometary 

 orbits ; and the great comet of 1680, one of the most remark- 

 able on record, both for the immense length of its tail and 

 for the excessive closeness of its approach to the sun (within 

 one-sixth of the diameter of that luminary), afforded him an 

 excellent opportunity for the trial of his theory. The success 

 of the attempt was complete. He ascertained that this comet 

 described about the sun as its focus an elliptic orbit of so great 

 an excentricity as to be undistinguishable from a parabola 

 (which is the extreme, or limiting form of the ellipse when 

 the axis becomes infinite), and that in this orbit the areas 

 described about the sun were, as in the planetary ellipses, 

 proportional to the times. The representation of the appa- 

 rent motions of this comet by such an orbit, throughout its 

 whole observed course, was found to be as satisfactory as 

 those of the motions of the planets in their nearly circular 

 paths. From that time it became a received truth, that 

 the motions of comets are regulated by the same general laws 

 as those of the planets, — the difference of the cases consist- 

 ing only in the extravagant elongation of their ellipses, and 

 in the absence of any limit to the inclinations of their 

 planes to that of the ecliptic, — or any general coincidence 

 in the direction of their motions from west to east, rather 

 than from east to west, like what is observed among the 

 planets. 



It is a problem of pure geometry, from the general laws of 



