VOL. LXIII.] PHILOSOPHICAL TRANSACTIONS. 4'25 



the 4th. These tables are contained in a long paper of mine, which will be 

 published in the volume of our academy for 1771 ; but, if you please, I will send 

 them to you. These segments being known, it is clear that, besides their varia- 

 tions occasioned by the distance of the satellite from the edge of Jupiter, they 

 will be liable to others. First, in consequence of the change of Jupiter's 

 distances, both from the sun and from the earth. On this account, the magni- 

 tudes of these segments being known, for a particular epoch,* those known 



r>>«> 



magnitudes must be multiplied by -7-,, to determine the magnitude of the seg- 

 ment at any other time. In which expression, p and q denote the distances of 

 Jupiter from the sun and from the earth respectively, at the given epoch, and m 

 and n the distances, at the other time, for which the value of the invisible seg- 

 ment is required. 2dly. There will be other variations, depending on Jupiter's 

 height above the horizon. The segments which I have observed, have all been 

 reduced to the constant height of 15°. Mr. Bouguer, in his optics, hag given a 

 table of the degrees of light of the planets, at their different elevations above 

 the horizon, which, from my own observations, I have found to be very exact, 

 and useful for the present purpose. Now, as the segments are in the inverse 

 ratio of the numbers of this table, putting g for the number corresponding to 

 the elevation of 1 5°, and h for the number corresponding to any other elevation, 



the segments must be multiplied by ~. 3dly. These segments will yet be sub- 

 ject to another variation, depending on the aperture of the telescope. It is 

 certain that a larger aperture giving more light, the insensible part of the disc 

 must be smaller; and it seems demonstrable by theory, that this insensible part, 

 or the invisible segments, must be inversely as the squares of the apertures. 

 I resolved however to assure myself of this by experiment. For this purpose, 

 I carried my telescope to Mr. Messier's observatory, who has one of Dollond's 

 telescopes, of 34- feet length, and 40 lines aperture. On the 20th of August 

 1771, he saw the 2d satellite disappear in his telescope, through an aperture of 3 

 lines. The same satellite disappeared in mine, when the aperture was reduced to 

 the same quantity of 3 lines, and not before. We changed instruments, and, 

 repeating the experiment, found the same effect. Now, the insensible part was -j-bVo- 

 of the disc, in Mr. Messier's instrument, and -5^ in mine. These portions there- 

 fore, in these telescopes, were in the inverse ratio of the squares of the apertures. 

 Consequently, in order to determine the segments for an aperture of any num- 

 ber of lines k, the segments of my table, which are all calculated for an aperture 



of 24 lines, must be multiplied by -rj-- Hence, to compute the invisible seg-. 



• Known, by the author's tables, for any distance of the satellite from the edge of Jupiter, at the 

 particular epoch to which the tables are adapted. — Orig. 



VOL. XIII. 3 I 



