( 328 ) 



part, p.p. (Ill), (V), (VII) and (VIII) the letter i (the number of 

 synodic periods) is multiplied. 



These daily motions are so nearly equal for several of the equations 

 of II, III and IV that, in order to make them out, we must take 

 from the tables the motions for a long interval, e.g. for 10 years, 

 (duly taking into account the number of periods). These must then 

 be divided by the number of days (10 years = 3652 or 3653 

 days). Multiplying this quotient by the synodic period in days, we 

 get 360° -\- a fraction. The 360° are of no account ; the fraction 

 is the factor of /; we thus recognise which is the equation w^e have 

 to deal with. In the preface of the second part of Damoiseau we 

 look in vain for any information on the subject. 



I. For this satellite five terms have been taken into account. 

 W. 1 with an amplitude of 1°-16, is the equation of the velocity 



of light ; its argument is U — u^. 



N°. 2, (amplitude 0°'29), is the equation caused by the ellipticity 

 of Jupiter's orbit ; the argument is the mean anomaly of Jupiter z^^ — n^^. 



N°. 3 is 180° + the mean anomaly of the Earth, f7— rr'; by 

 its aid and that of W. 1 /. e. the difference in longitude between 

 the Sun and Jupiter, we find, in the table of double entry IX, one 

 term of the geocentric latitude of the satellite. 



W. 4 with an amplitude of 0^-45, shows the perturbation caused 

 by II in the motion of t. The argument is ui — uu. 



N°. 5, (amplitude 3°'07) gives the jovicentric latitude of I, neces- 

 sary to find the second term of the geocentric latitude. The argument 

 is ui — Ai. 



II. Seven terms. N". 1, 2 and 3 have the same arguments as the 

 analogous terms for I ; the amplitudes of N°. 1 and 2 are half those 

 of I. The term of the latitude to be taken from IX, by the aid of 

 1 and 3, is of course the same for all the satellites. 



N". 4, (amplitude l°-06), shows the perturbation caused by III in 

 the motion of II. The argument is uu — um. 



N". 5, 6 and 7 serve for the latitude. 



N"- 5, (amplitude 3°"05), has the argument uu — -tiv ; 



N». 6, ( „ -47), „ „ „ uii—Au ; 



N«. 7. ( „ -03), „ „ „ wii— ^m. 



III. Nine terms. Nos. 1, 2 and 3 are the same as for I and II; 

 the amplitudes of W. 1 and N". 2 are 0°-29 and 0°-07. 



