522 



-1891. 



minimum ellipse lias a semi-axis major 52'36 (Table II.), wliile below ae 

 the three curves are present. 



In figs. 6 and 7 are contrasted in like manner the isergonal curves 

 for the angles to ^ 30° and co = the supplement of 30°. In fig. 6 the 

 curve @ =: — 5 is wanting, and in fig. 7 the two curves @ = 5 and 

 @ = 20 are both wanting. 



In like manner are to be explained figs. 8-18. The numbers 

 needed for drawing the figures are furnished by equation (13). The 

 curves that in each figure separate the shaded area from the non- shaded 



Fig. 8.— 01 = 40°. 



Fig. 9.-0) = 140°. 



area are the ellipses for @ = 20 and @ = — 20. The shading is intro- 

 duced in order to compare more readily the corresponding curves in the 

 figures. 



25. The dotted curve in the several figures represents those values of 

 d and h for which the total change of direction in the relative orbit is 

 10° ; that is, a = 85°. It is that curve whose equation is A tan 85° ^ B, 

 or d^ + h^ sin^ 6 ^= A? tan^ 85°. It is therefore an ellipse whose centre 

 is the origin of coordinates, and it is similar in each figure to the isergonal 

 ellipses. 



26. Hypotheses about the parabolic cometary orbits. — It will be convenient 

 to make two assumptions about the distribution of the parabolic comets 

 and the distribution of the goals of their motions. There seems to be no 

 very well-marked relation between the ecliptic, or to speak more strictly 



