igis-] 



SEE— THE EULER-LAPLACE THEOREM. 



347 



it being understood that the final angle 4g/2,c is neglected as very 

 small. 



Euler next considers the effect of i whole revolutions : 



/ = 2iTr, 

 and finds for the radius vector : 



y 





Putting for the following aphehon, ^=(2i-|-i)7r — 6, there will 

 result 



I I - r , {2i+ qtt ^ 



whence the radius vector becomes 



y = 



i-r 



(2i+ i)7r(i -U)sg 



The successive distances of the planet from the sun are dimin- 

 ished in the following: manner : 



I. Perihelion 

 Aphelion 

 II. Perihelion 

 Aphelion 

 III. Perihelion 

 Aphelion 



g 7r(i - ^l)gg 



I - r c{i- lY ' 



_g_^ 27r(l + ^^)gg 



I + r <i + r)' ' 



g 37r(i - h^)gg 



I - r c{i - f)2 ' 



g 47r(i + U)gg 



I + r ^(i + r)=^ ' 



g 57r(i - U)gg 



I - r c(i - ly 



, etc. 



