ON THE CAPXDBE OF COMETS BY PLANETS. 



521 



Jupiter witli an original angle of w = 10°, and having d and h such as to 

 be repi'esented by a point within the blank area of fig. 2, will leave the 

 vicinity of the planet in an elliptic orbit whose semi-axis major is less 

 than 20, and whose period therefore is less than ninety years. 



The larger curve that lies above ae in the shaded area is the isergonal 

 ellipse for @=50. As @ increases the lower part of the curve tends to 

 approach the radical axis ae, with which it coincides when @ ^ oc. For 

 points in the area below ae (distinguished by the oblique-line shading), 

 the planet increases the velocity of the comets, and the comet would be 

 thrown permanently out of the solar system. The smallest semi-transverse 

 axis, the one corresponding to the vanishing ellipse, is (Table II.) 36"90, 

 and the isergonal curve for @ = — 50 is drawn in the figure. 



23. Isergonal ellipses for w=:170°. — In fig. 3 are drawn the three 

 ellipses corresponding to the values of @, — 5, — 20, and — 60. The 

 ellipses above ae do not appear, inasmuch as the smallest possible elliptic 

 orbit has a semi-axis major of 206'3 (Table 11.) and a period of about 

 3,000 years. The radical axis ae is 'OSMG (or over eight divisions) above 

 OE. 



24. Figs. 4 and 5 are like diagrams for co = 20° and w = 160°. 

 With altered numbers the explanation of Arts. 22 and 23 apply with 

 slight change to these figures. The line ae in figs. 4 and 5 is nearer to 



Fig. 7.-0. = 150°. 



OE than is the same line in figs. 2 and 3. In fig. 4 the line for @ = — 20 

 appeal's below ae, while above ae are the three curves for + 5, + 20, and 

 + 50 respectively. In fig. 5 the ellipse for @ = 50 is wanting, since the 



