Provisional Theory of Leda. 



13 



With these numbers we obtain, according to the formulas in the se- 

 cond book of the Mecanique Celeste, the following values of the equations 

 of perturbation. 



SECULAR PERTURBATIONS. 



Annual Variations of the eccentricity and Perihelion s Longitude. 

 } e = — 0. 000 008 847 202 — . 000 000 542 488 . ^ 



— . 000 008 176 920./*" - 0.000 000 127 794./*'", 

 <$W=+ 56". 491 + 1". 491. /* v + 54". 938./*"+ 0".062 . /*"', 

 where ju,\ y u.' v and /*'" are, as in the Mecanique Celeste, the corrections due 

 to the received masses of Saturn, Jupiter and Mars respectively. 



Annual Variations of the Inclination and Nodes Longitude as referred 

 to the foot Ecliptic or Fixt Stars. 



<$^ = — 67". 363 — 2". 310 . ^ — 64". 998 . /*" — 0".055 . /*"'. 

 H=— 0", 387 — 0". 005 . /* v — 0". 380 . ^ — 0". 001 . /*"'. 



PERIODICAL PERTURBATIONS. 

 1°. Inequalities independent of the Eccentricities. 

 For the Longitude 



' + 233". 357 . sin (n'\t- n.t + e IV - e) 



- 436 . 997 . sin 2.(n' v . t - n . t + - f ) 



- 36. 469 .sin 3.(n ,v .« - n . t + e IV - e) 

 •j - 8 . 605 . sin 4.(n'\t -n.t + £ IV - f ) 



2 . 220 . sin 5.(« Iv .i - n A + e" - s) 

 . 679 . sin 6.(n'\t - n.t + e" - e) 

 0. 156 . sin 7.(n :v .i - n.« + s IV - e) 



}v = (l + f*") 



: (1 • /*•)■• 



+ 3 . 544 . sin (n v . t - n .t + « v - a) 



- 1 . 907 . sin 2 .(n v . t-n.t + t v - s) 



- . 163 . sin 3 .(n v . t-n.t + 6 V - e) 



- . 024 . sin 4 .(n v . t-n.t + * v - e) 



■ 7 . 116 . sin t-n.t + e" - e 



+ (1 4- /*"') . J - . 180 . sin 2 .(«"'. t-n.t + t" - e) 



| - . 040 . sin 3 .(»"'. t-n.t + e'" - 6) 



Nova Acta Reg. Soc. Sc. Ups. , III Ser. 



