﻿Character of Cometary Orbits. 51 



perihelion, to the other end, the above ratio may be taken to re- 

 present approximately the ratio of the changes produced in the 

 two orbits during one revolution. 



If a, a 1 be the semiaxes of the two orbits, and 8a, Ba ! the 

 changes which they undergo in one revolution, 



Sa'-\e) ' 



If P' 2 =«' 3 , so that P' is the periodic time in an orbit whose se- 

 miaxis is a', then 



Sa 2/e'Yf F.SF 



-Ml 



a 



3 ' qia>* 



if q is the common perihelion distance of the two orbits. If, 

 now, P ; , a', &c. belong to Encke's comet, 



e'=-153, «' = 2-216, P' = 3-296, 3P=^, £ = 0-340. 



obo 



Let us now take « = 200,000, so that the aphelion distance is 

 400,000, or about half the distance of a star whose parallax is 

 0"*25. On substitution and reduction we obtain 



^=•018. 



a 



Thus, on the assumption that, under the same circumstances as 

 to velocity and distance from the sun, the resisting medium would 

 offer the same amount of resistance to the comet of long period 

 as to Encke's comet, we arrive at the conclusion that its aphelion 

 distance will be diminished by about '018 of its original length. 

 A diminution to this amount would be sufficient to change a 

 comet's motion in some cases into a periodical revolution about 

 the sun. There are, however, reasons for believing that the 

 retardation which comets of long period have undergone on first 

 becoming attached to the solar system must have been greater 

 than the retardation which Encke's comet now experiences. The 

 first reason is, that a comet appears to lose at each approach 

 to the sun its rarest and most volatile parts, or those which 

 offer the greatest resistance to motion ; and the second is, that 



E2 



