NO. 6.] INTRODUCTION. CHRONOMETERS. XXVII 



D' Jupiter'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). 

 a the semi major axis of the same section, corresponding to the mean dis- 



tances of Satellite and Planet. 

 ft the jovicentric angular value of a. 

 s the Satellite's jovicentric latitude above the plane of Jupiter's orbit at the 



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 y 



is never much different from 90. 

 tv 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 



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 1 . 

 M K is the quantity called by Laplace. 

 The angle y is given by the equation 



ds 

 cosy=^ 



where dv 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 In 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. 



