1074 CHAKLIER, ON PERIODIC ORBITS. 



Let these be ^^ and tj^, then we have from (25) 



da 





Take for brevity iq^ = 0, so that 



(29) i6«=»'-(/»; + .«D = (^= + 3's: 



It is hence in the case 1) 



''.+''= = 195.^0 ■ 



And in the case 2) 







^; + 



•^2 = 



49 .2 

 " 256^0 • 



The values of a and Z> 



are 



now: 



1) 



a- 



1 c^ 



" 12« -0 





h'^ 



_ ] i2 



2) 





— -^ 5" 



and 



And in all these fornmlae S,^ has the same designation, viz. 

 the coordinate of that point, where the curve cuts the '% axis. 



It is to be observed that for all curves of the same family 

 the excentricity is the same, namely for 1) yi — 3/.i and for 



Hence the minor axes in both curvus are both linite; the 

 major axis of 2) is so also; but the major axis of 1) increases 

 as 1: V^t. The former expressions for a and h were not so 

 conspicuous, owiug to the fact that ß' + ß'^ was infinite when 

 ^t becomes evanescent. 



It is interesting to classify the periodic curves with regard 

 to the values of the constant of Jacobi C. It is, namely, a 



