24^ PHILOSOPHICAL TRANSACTIONS. [aNNO 1685. 



part of the moon still obscured, or its limb could not be seen at all. The times 

 of the principal phases were as follow. 



Correct times. 

 At 9** 32"" 25' the penumbra. 



9 50 10 ... . beginning of the eclipse. 

 JO 58 25 ... . the total immersion. 

 12 43 0.... beginning of the emersion. 



Description and Uses of an Instrument for Ending the Distances of Jupiter s 

 Satellites from his Axis. By Mr. J. Flamsteed, Math. Reg. and F. R. S. 

 N" 178, p. 1262. '/' ^!' 



In pi. 8, fig. 2, the small circle in the middle represents the planet Jupiter, 

 the 4 concentric circles the proper orbits of his 4 satellites, duly proportioned 

 to the breadth of his body ; the distances between the parallel lines intersecting 

 them, being each equal to one of his semidiameters. The 4 divided circles 

 next without these, are distinguished into as many parts as there are days and 

 hours in each satellite's revolution ; the innermost of them serving for the first 

 or innermost satellite, that next it for the 2d, that next without this for the 3d, 

 and the outermost for the 4th ; above which is a small divided arch of 15°. 



By this instrument to find the distances of the satellites from Jupiter's axis 

 to a proposed time. 1. Find the parallax of Jupiter's orbit to the time pro- 

 posed, and note whether it be to be added or subtracted. 2. Extend the thread 

 from the centre of the instrument over the parallax numbered in the small arch; 

 it cuts off in the 4 divided circles so many hours, as each satellite takes up in 

 passing from the axis of the shadow to the axis of Jupiter, viewed from the 

 earth ; these I call the simple parallactic intervals, which, if the parallax was to 

 be added, are also additional, if to be subtracted, they are to be subducted. 3. 

 To these parallactic intervals, add the times of half the duration of the eclipse 

 of each satellite; which, for the first, may be assumed ih. 10m. for the 2d 

 ih. 30m. greater exactness being needless ; but for the 3d and 4th, when 

 eclipsed, (their immersion into the shadow and emersion from it being com- 

 monly given in the tables) take half the difference of these times at the next 

 eclipse to the time proposed, for the half duration, and add them to the simple 

 parallactic intervals, so you have them augmented. But note that as often as 

 the 4th satellite is not eclipsed, (which is 2 years in every 6) its interval needs 

 no augmentation, the tables showing the very time when it passes the axis of 

 the shadow. 4. Find in the tables the times of the eclipses of each satellite 

 next preceding the time proposed, and when the 4th is not eclipsed, find the 

 time of its passing the axis of the shadow; to which, if the parallactic intervals 



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