f/l Calculation of the Orbit qf the Comet. 109 



.sis be as 100 to 1, an addition of one fifty thousandth 

 part of its velocity would produce the same effect.* It 

 is evident, therefore, that the returns of comets to the 

 sun, are not only liable to great variations in respect to 

 time, in consequence of the actions of the planets, but 

 that these actions may be so considerable, especially on 

 comets of very eccentric orbits, as to cause them never 

 to return. 



Some astronomers have ventured to predict the re- 

 turns of comets on the principle of their uniformity, as 

 to the times of their revolutions, with as much certainty, 

 and attention to minute accuracy, as are due to deduc- 

 tions founded on the strictest principles of the mathe- 

 matics : But the only instance of such predictions being 

 verified in any degree by events, is that of Dr. H alley, 

 in respect to the comet of 75 years. This comet having 

 appeared, several times, at nearly equal intervals, indu- 

 ced this astronomer to hazard a conjecture, that it would 

 again return in the year 1758. The comet did indeed 

 appear, at a time not differing more than 12 or 14 months 

 from that predicted ; but this variation of time, in re- 

 spect to different revolutions of this comet, whose orbit 

 has so little eccentricity, is a fact corroborating the state- 

 ment I have made, of the effects which might be pro- 

 duced by the attractions of the planets on comets whose 

 orbits are very eccentric, such as those of 1680, 1769, 

 and many others, which have been observed during the 

 two last centuries. 



The identity of the comets of 1532, 1661, has been 

 considered as certain ; and its return in 1789 or 1790, 

 at an interval of 129 years, w"as predicted to the minute- 

 ness of hours and minutes, by a celebrated astronomer, 

 now living. The comet, however, did not at that time 

 appear, nor has it been observed since. I am far from 

 thinking that this, or any of the comets, have beeii 

 known to make more than one revolution about the sun, 



* See Prop. 16, and Corollaries, of Book T. of Newton's Principia, 

 where it is demonstrated, that the velocities requisite for bodies 

 moving in different conic sections, the focal distance of the vertex 

 being the same, is in the sub-duplicate ratio of their principal para- 

 meters. 



