COMETS. 



The angular motions at the mean and extreme distances from 

 the sun have been computed by the formulae 



1,296000 a 2 a- 



' 



In which a represents ^:he mean angular velocity, a the greatest, 

 and a", the least ; d' the perihelion, and d" the aphelion distances. 

 P is the periodic time of the comet, and a the mean distance. 

 The same numbers which express these angular motions, also 

 express in all cases the intensities of solar light and heat in the 

 several positions of the comet ; and also the apparent motion of 

 the sun, as seen from the comet ; and a comparison of these with 

 the corresponding numbers related to any of the planets, will 

 illustrate in a striking manner how different are the physical 

 conditions by which these two classes of bodies are affected ; and 

 this will be more and more striking, when the other groups of 

 comets have been noticed. 



Taking the comet of Encke as an example, it appears that 

 while its mean daily motion is 1076" or 18', its motion in aphe- 

 lion is only 5', and in perihelion nearly 13. Its motion in 

 perihelion, the light and heat it receives from the sun, and 

 the apparent motion of the sun as seen from it, are therefore 

 severally more than 150 times greater in perihelion than in. 

 aphelion. 



III. ELLIPTIC COMETS, WHOSE 3IEA!S T DISTANCES ARE NEARLY 

 EQUAL TO THAT OF URANUS. 



51. It might be expected, that comets moving in elliptic orbits 

 of small dimensions, and consequently having short periods, would 

 have been the first in which the character of periodicity would be 

 discovered. The comparative frequency of their returns to those- 

 positions near perihelion, where alone bodies of this class are 

 visible from the earth, and the consequent possibility of verifying 

 the fact of periodicity, by ascertaining the equality of the intervals 

 between their successive returns to the same heliocentric position, 

 to say nothing of the more distinctly elliptic form of the arcs of 

 their orbits in which they can be immediately observed, would 

 afford strong ground for such an expectation ; nevertheless in this 

 case, as has happened in so many others in the progress of phy- 

 sical knowledge, the actual results of observation and research 

 have been directly contrary to such an anticipation ; the most 

 remarkable case of a comet of large orbit, : long period, and 

 rare returns, being the first, and those of small orbits, short 

 174 



