No. 6.| INTRODUCTION. CHRONOMETERS. XXVII 
D‘ Supiter’s distance from the Earth at the time of observation (known from 
the ephemerides). 
the ellipticity of the section of the shadow traversed by the Satellite (a 
little different for the different Satellites). 
the semi major axis of the same section, corresponding to the mean dis- 
2 
R 
tances of Satellite and Planet. 
6 the jovicentric angular value of a. 
the Satellite’s jovicentric latitude above the plane of Jupiter’s orbit at the 
va) 
moment of heliocentric conjunction. In the case of the shadow Laplace 
neglects the angle between Jupiter’s equator and the plane of his orbit, 
because its effect would be of the same order as the square of the ellip- 
ticity, which is also neglected. 
y the angle between the Satellite’s relative motion at conjunction and the 
circle of latitude (towards the north). Owing to the small inclinations 
is never much different from 90°. 
w the Satellite’s jovicentric motion in one second of time, expressed in some 
convenient unit. 
The quantities s and y may be calculated by means of Damoiseau’s 
Tables in the following manner. According to Laplace 
s =," _(M_K) 
Ve 
where M is the number so designated by Damoiseau and taken out of his 
Tables by means of the arguments given in Adams’ continuation; K is the 
sum of constants added in order to make all tabular numbers positive’. 
M—K is the quantity called ¢ by Laplace. 
The angle y is given by the equation 
ds 
cos y an at 
where dy is the Satellite’s jovicentric motion in its orbit. This can be found 
by means of the quantity called “reduction” in Damoiseau’s Tables, but more 
readily and in some cases more accurately by the following consideration. 
M—K is of the form 
1 Tn the case of Sat. II, K is given by Damoiseau as 0.6400, but has been here applied 
as 0.6415, because the numbers of his Table XXIV are 0,0015 too great, 
