( 324 ) 



stances in question. Let the amplitudes be between and 3 signs, 

 so that both the satellites, as seen from the Earth, (the head being 

 turned to the North Pole), are to the left of and both receding from 

 the planet. Before the conjunction I is to the right of 11, but the 

 motion of I is quicker than that of II. I will overtake II as soon 

 as its amplitude is 44°39', that of II being then 26°14'. At the 

 same time, however, the apparent velocities are equal. Now as I 

 approaches its greatest elongation it retards its motion much more 

 considerably than II, the amplitude of which is so much smaller. 

 The consequence is that, after the conjunction, I is left behind, and 

 gets again to the right of II as before conjunction. 



This case represents a transition between two other cases. 1. If, 

 under the same circumstances I is somewhat more in advance (has 

 a greater amplitude), it will pass II, but after a while will be over- 

 taken by II, which then, as seen from the Earth, passes behind it. 

 2. If, however, I is somewhat less ahead, it will continue to be 

 seen to the right of II, the distance I — II going through a minimum 

 but not reaching zero. 



Now, in order to answer the question, how long will be the 

 duration of the occultation counted from the first external contact, 

 the apparent radii of the satellites must be known. Owing to the 

 irradiation they are greater at night than in daytime ^) as several 

 observers have actually found. The observations of the satellites of 

 Jupiter being made nearly exclusively at night time, we will adopt 

 the apparent radii holding for the night. I took the mean of the 

 values found by See at the giant telescope at Washington on the 

 one hand and that found by several observers on the other. (I have 

 taken the values as summarised by See himself). For the reduction 

 to the unit used throughout for these computations, viz the radius 

 of the equator of Jupiter, this radius is taken = 18"-37 in accordance 

 with Damoiseau. 



Diameter Radius 



I l"-07 =z 0' -058 0^029 



II -95 052 026 



III 1 -56 085 -0425 



IV 1 -41 076 038 



^) Vide e.g. T. J. J. See, Observations of the Diameters of the Satellites of 

 Jupiter, and of Titan, the principal Satellite of Saturn, made with the 26 inch 

 Refractor of the U. S. Naval Observatory, Washington; 19 Oct. 1901. Astr.Nach- 

 richten W. 3764, (21 Jan, 1902). 



