190] Tides and Comets 237 



problem at all manageable, but which were certainly not 

 true, and consequently, as he was well aware, important 

 modifications would necessarily have to be made, in order 

 to bring his results into agreement with actual facts. The 

 mere presence of land not covered by water is, for example, 

 sufficient by itself to produce important alterations in tidal 

 effects at different places. Thus Newton's theory was by* 

 no means equal to such a task as that of predicting the 

 times of high tide at any required place, or the height of 

 any required tide, though it gave a satisfactory explanation 

 of many of the general characteristics of tides. 



190. As we have seen (chapter v., 103 ; chapter vn., 

 146), comets until quite recently had been commonly 

 regarded as terrestrial objects produced in the higher 

 regions of our atmosphere, and even the more enlightened 

 astronomers who, like Tycho, Kepler, and Galilei, recog- 

 nised them as belonging to the celestial bodies, were un- 

 able to give an explanation of their motions and of their 

 apparently quite irregular appearances and disappearances. 

 Newton was led to consider whether a comet's motion 

 could not be explained, like that of a planet, by gravitation 

 towards the sun. If so then, as he had proved near the 

 beginning of the Prindpia, its path must be either an ellipse 

 or one of two other allied curves, the parabola and 

 hyperbola. If a comet moved in an ellipse which only 

 differed slightly from a circle, then it would never recede 

 to any very great distance from the centre of the solar 

 system, and would therefore be regularly visible, a result 

 which was contrary to observation. If, however, the ellipse 

 was very elongated, as shewn in fig. 73, then the period 

 of revolution might easily be very great, and, during the 

 greater part of it, the comet would be so far from the sun 

 and consequently also from the earth as to be invisible. 

 If so the comet would be seen for a short time and become 

 invisible, only to reappear after a very long time, when 

 it would naturally be regarded as a new comet. If again 

 the path of the comet were a parabola (which may be 

 regarded as an ellipse indefinitely elongated), the comet 

 would not return at all, but would merely be seen once 

 when in that part of its path which is near the sun. But 

 if a comet moved in a parabola, with the sun in a focus, 



