( 326 ) 



occurs a contact on the other side. In this case the duration will, 

 very nearly indeed, have to be multiplied by y/2. It thus becomes 

 for I and II, I and III, I and IV, II and III, II and IV, III and IV 



3^-574, 311-402, 3''057, Q^-2m,. 5i>006, 10ii-43, 

 or: 



3i>34'^, 31^24'^, 31» 3'", GHS'^i, 5'' 0"\ 10^126'^. 



These numbers hold only for those very rare occasions in which 1^^ 

 the occultation is central and 2"*^. the rate of change of the elongation 

 is equal or nearly so for the two satellites. As soon as there is 

 some difference of latitude the time during which the two satellites 

 are seen as a single body is of course smaller. 



2"^. Appendix. Investigation of the uncertainty, existing in the 

 determination of the synodic jjeriods of the satellites. 



In his introduction to the Tables Ecliptiques, p. XIX, Delambre says : 

 "Nous n'avons aucune observation d'éclipse antérieure èt 1660". Now let 

 us assume that the difference in time between the first eclipse observed 

 in 1660 and the last observed in 1816, two years before the publica- 

 tion of these tables, (taking into account also the next ones in 1660 

 and the preceding ones in 1816) leaves an uncertainty, in the case 

 of the four satellites, of 20, 30, 40 and 60 seconds, which will be 

 too favourable rather than too unfavourable. If we divide this un- 

 certainty by the number of synodic periods in 156 years, to wit 

 32193, 16032, 7951 and 3401, we get for the uncertainty of a 

 single period 



for I for II for III for IV 



0^00062, 0s00188, 0^-0050, 0^0176. 



Therefore, if we find that Delambre gives these periods to 9 places 

 of decimals of the second, we cannot attach much importance to 

 the fact. 



When Damoiseau, 20 years after Delambre, published new eclipse- 

 tables^) for the satellites of Jupiter, he adopted the period of I un- 



1) The tables of Delambre and Damoiseau were destined mainly to serve for the 

 prediction, in the astronomical ephemerides, of the eclipses of the satellites caused 

 by the shadow of Jupiter. It is for this reason that both he and Delamrre, united 

 all those terms of the perturbations in longitude which have the same argument 

 at the time of the opposition of the satellites, even though these arguments might 

 be different for all other points in the orbit. Therefore it becomes necessary once 

 more to separate these terms as soon as tables have to be computed from which 

 may be derived the longitude and the radii vectores of the four satellites for any 

 point of their orbits, tables such as have been given by Bessel in his Astrono- 

 mische Untersuchiingen and by Marth in the Monthly Notices of the Royal 

 Astronomical Society, Vol. LI, (1891). 



