220 



the interval t. Thus we learn that in one complete revo 

 lution the eccentricity is unchanged. 

 By a well known property of the ellipse 



&quot; (1 ~* 2) = 1 + e cos (0 - co) 



r . v * snr /a \ 



.*. = 1 + e cos (9 co) 



P 



putting sin a = 1 we get by differentiating 



2rvdv de , . dca 



p d t d t d t 9 



so that 



7 O SI V&amp;gt; 



= - sin n t 



2 x a 

 .*. coj co . cos n t) 



where co , coj are the values of co at the beginning and 

 end of the interval t. Thus we learn that the changes in 

 co are very much greater than those in e 9 but that by 

 the end of one revolution both have returned to their 

 original values. 



