VOL. LXni.] PHILOSOPHICAL TRANSACTIONS. i. 423 



two methods, of my invention, for perfeCjiting the theory of Jupiter's satellites. 

 The former of these methods serves to measure their diameters, and the latter is 

 intended to make the observations comparable with each other, though made in 

 different places, and with different instruments. You know, that the observations 

 of the eclipses of the 3d and 4th satellites, made by different observers, vary 

 from each other 3, 4, and 5 minutes, and sometimes more ; and that there is even 

 a pretty sensible difltrence in those of the 2d. In the 38th page of the preface 

 to my Essay on the Theory of the Satellites, which has been presented to the 

 R. s., I mentioned the inequality discovered by Mr. de Fouchy, and I suggested, 

 that the perfecting of this theory might perhaps depend on the quantity of this 

 inequality, which Mr. de Fouchy has not determined, not having been at leisure to 

 resume the subject, since the year 1732. The segment of the disc which is not 

 eclipsed, when the satellite disappears, must vary in the proportion of the squares 

 of the distances of Jupiter from the sun, and from the earth. This is what 

 a little reflection will make evident to every one, and this is the first cause of 

 the inequality. Since Mr. de Fouchy's observation, it has been discovered, that 

 the light of the satellite also decreases, in proportion to the proximity of Jupiter's 

 disc; the brightness of the planet weakens that of the satellite, and, for this 

 reason, the eclipses, which happen too near the opposition [of Jupiter to the 

 sun], are considered as defective. Besides, the light of Jupiter, as well as that 

 of his satellites, is different, in his different elevations above the horizon: when 

 the planet is low, more rays of light are lost, in their passage through a thicker 

 atmosphere; and whenever the light is less, the segment, which is not eclipsed 

 when the satellite disappears, and which I call the insensible segment, increases, 

 and occasions another inequality in the moment of the eclipses; lastly, the power 

 of the telescopes, or their aperture, which, according as it is greater or less, give 

 more or less light, contributes to the variation of this segment. Here then are 

 4 causes of inequality, which I reduce to one principle, and the following is the 

 scope of my researches. When the satellite disappears, there is certainly a 

 segment of its disc which remains uneclipsed; the magnitude of this varies, on 

 account of the 4 causes just mentioned; thence it follows, that if in one eclipse 

 the segment is abd, and in another Khd, when the satellite 

 disappears in the 2d eclipse, it will have got less into the 

 shade, by a part of its diameter Bi: which part hb, there- 

 fore, must be the value of the equation between the two 

 eclipses. Now, if we call xh, a; ab, b, the radius of the 

 disc of the satellite r, the semidiameter of the shadow, 

 taken from the tables, r, and the total duration of the eclipse 



d, the time taken up in going over Bi, or the equation ("), will be ^"'^^~ , which 



