891 



remember that the numerical coefficient of the integral in the for- 

 mula for i2, also depends on q. 



7. From the value of Xt of section N* 5 we shall derive a 

 value of the mass of Titan. Taking account of the equation Xj ^=^ 0, 

 for the motion of Hyperion's pericentre, neglecting terms of the 



©■■ 



order ( — ) , we get : 



m' 



— 9.3675 n'. — . (45) 



M 



From observation H. Struve ') for the mean motion of Hyperion's 

 pericentre gets the value: 



— 18."663; 

 correcting for precession, we get: 



— 18.»677; 



here the Julian year is the unit of time. 



Before comparing the theoretical value according to formula (45) 



with the observed motion, we ought to correct the latter on 



account of the secular variations caused by the sun, Saturn's ellip- 



ticity and the other satellites. According to H. Samter ') the values 



of these variations are respectively -f- O.'Oll, -|- 0."234 and 



-|- 0.°009 a year. Subtracting the sum of these numbers from the 



observed motion, the equation for the determination of Titan's mass 



becomes : 



m' 

 — 9.3675 n', — = — I8.*931 . (46) 



M 



m' 

 As 7i\ differs from n' only in the terms of order — and higher, 



I put n\ = 7i' and thus : 



n', = 365.25 X 22. '5770. 



Then from (46) we get : 



M 



— = 4080 . 

 m' 



This value agrees quite well with the value from the mean motion 



M Beobachtungen der Saturnstrabanten. Publications de I'Observatoire Central 

 Nicolas. Série II. Vol. XL 1898. p. 290. 



>) Die Masse des Saturnstrabanten Titan. Sitz. Ber. der Kön. Pr. Akad. der 

 Wissenschaften. 19J2. 



