( -^^5 ) 



''some time as a brillaiil disc. Also that the minute dark spot seen 

 "at ll^'49f" was produced by the portion of the shadow of II., then 

 "projected on I. Also that the small size of the following shadow 

 "spot at 'Jl''59^ was due to a part only of the shadow of II. being 

 "projected on the disc of Jupiter, the other part of this shadow 

 "having been intercepted by satellite I. 3) 



"But combining Mv. Comas' observation with my own, 



"there can be no doubt but that satellite I. was actually partially 

 "eclipsed by the shadow of II. on the night of August 14, 1891. 

 "So far as I am aware, this is the only indubitable instance of one 

 "satellite being eclipsed by the shadow of another." 



"P.S. The above times are Greenwich mean times. The Xautical 

 "Almanac time for the trïinsit ingress of satellite I. is llhSS""." 4). 



Before proceeding to the computation of epochs of such heliocentric 

 conjunctions we have investigated to what extent generally eclipses 

 of one satellite by the shadow of another are possible. That they 

 may occur is proved by the shadows of the satellites on Jupiter 

 itself. The question however is: l^t whether the shadows of the 

 foremost satellite reaches that of the more distant one in even/ helio- 

 centric conjunction and 2"^ whether tlie occurrence of total eclipses 

 is possible in any ca-e. In order to find an answer to these questions 

 we assume that the orbits all lie in a single plane which, being 

 prolonged, passes through the centre of the sun. We further imagine 

 a line in the plane of the orbits starting from the sun and passing 

 Jupiter at a distance equal to its radius, the distance from the centre 

 thus being equal to its diameter (see Plate I). This line cuts the 

 orbits of the four satellites each in two points. Beginning with the 

 point nearest the sun we shall call these points <j, e, c, a, h, d, f 

 and //. For clearness, sake the figure is given below (Plate I). 



Now suppose that I is placed either at a or at h. In both cases 

 the other satellites will be in\'ohed in its shadow cone as soon as 

 they come: 11/- at d, III /-at _/' and IV;- at It. 



The points of intersection with the orbit of II are c and d If 

 II„ is at c then I,j may be eclipsed in a but also If in b; III,- at f 

 and Wf at h. 



But if Wf is in d then only IIL and IV,- can be eclipsed, the former 

 at ƒ and the latter at h. 



The points of intersection with the orbit of III are e an<l f- If 

 III is at e there is the possibility of an eclipse for II„ at c, I„ at o, 

 \f at h, Wf at d and IV,- at It. If on the other hand it is in ƒ there 

 is siu'h a possibility oidy for IV, at li. 



It is evident ihat IV can only cause tiie eclipse of another satel- 



29* 



