﻿Character of Cometary Orbits. 45 



orbit per annum, and that between these values there are as 

 many comets with one velocity as with another. Let us consider 

 whether these assumptions require modification. 



First, with regard to the assumption as to the parallax of the 

 nearest stars, it is to be remarked that there are only two stars 

 known to have parallaxes as great as half a second. Hence in 

 only two directions from the sun are we certain that the distance 

 of the nearest stars is as small as that which corresponds to a 

 parallax of half a second. 



But the greater the distances of the nearest stars are assumed 

 to be, the less will be the percentage of comets with excentricities 

 greater than 1*02. It will be well, in order to avoid all possi- 

 bility of obtaining too high a percentage through assuming too 

 small a value for the distance of the nearest stars, to calculate 

 what the percentage would be on the extreme assumption that 

 their parallax is only -05". (As the sphere which would enclose 

 all the stars whose parallaxes are greater than '05" will be 1000 

 times as large as the sphere which encloses the two stars whose 

 parallaxes are greater than '5", it is extremely improbable that a 

 large number would not be met with within this sphere in all 

 directions from the sun.) The result of calculation on this as- 

 sumption is that, of the comets whose perihelion distances are 

 unity, the average percentage having excentricities greater than 

 1'02 lies between 19 and 23, the first of these values being the 

 percentage calculated when R is taken equal to 400,000, and the 

 second when R is taken equal to 4,000,000. 



Secondly, with regard to the velocities which comets have on 

 first coming into the sun's attraction, we remark that the smaller 

 these velocities are assumed to be, the smaller will be the per- 

 centage of comets with excentricities greater than 1'02. We 

 must then inquire whether we have assumed these velocities to 

 be greater than they really are. 



Now, as I have before remarked, the average velocity of comets 

 before coming under the predominant attraction of the sun must 

 be as great as the average velocity of the fixed stars. Let us con- 

 sider, then, what evidence we have regarding the velocities of 

 the stars. 



I. The velocities of the stars relatively to the sun arising from 

 the sun's motion in space is about 1*6 per annum. 



II. The sums of the squares of the proper motions of the stars 

 before and after correction for the sun's motion differ by only 

 a small fraction of the whole uncorrected sum. The explana- 

 tion of this fact appears to be that the average proper motion of 

 the stars is much greater than the sun's proper motion. 



III. When the parallax as well as the proper motion of a star 

 is known, the component of its velocity perpendicular to the line 



