536 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1762. 



the alteration of the style in England), and to the meridian of the Royal Obser- 

 vatory at Greenwich, are as follow: 



Number c is the period of 437 days, in which the 3 innermost satellites return 

 very nearly to the same situation in respect of one another, and of Jupiter's 

 shadow, in millesimals of a circle; and must be corrected by the equation of 

 number b, under a contrary title. The second satellite has a synodical equa- 

 tion of 16' or 17' in time, whose revolution is, in this period, to be sub- 

 tracted, if number c be less than 500; added, if greater. The first and third 

 satellites have also small synodical equations, returning in the same period, 

 that of the first satellite being about 3', of the third about 2' in time; 

 both to be added, if number c be less than 500; subtracted, if greater. 

 The orbit of the third satellite is manifestly eccentric, as well as that of the 4th. 

 Its apojovium in 1728 was about 10*^ of T, and moves forward 35° in 20 

 years: its greatest equation is about 15' in the satellite's orbit, or 7' in time. 

 The apojovium of the fourth satellite in 1728, was in 12^ 30' of ^, and moves 

 forward about 12*^ in 20 years : its greatest equation is 53' in the satellite's 

 orbit, or 59' in time. 



I found no reason to make any alteration in the semi-durations of the eclip- 

 ses of the first satellite from Mr. Pound's tables. 



The greatest semi-durations of the eclipses of the 2d, 3d, and 4th satellites in the 

 nodes, are I*' 27™, 1^ 47"", and 2^ 24"^* respectively. The nodes of the 2d sa- 

 tellite seem to be at rest in about 50*^ of xsr and ^ ; but the inclination of its 

 orbit varies from 2° 50' to 3° 52': it was least in 1668, greatest in 1715, and 

 seems to have been at its greatest and least once in the intermediate years. I 

 suppose it at the least in 1730. The nodes of the 3d satellite in 1/27, vvere in 

 164-° of ^ and ^, and move forward about 2-^° in 20 years: the inclination of 

 its orbit in 1 695 was 3", and has been increasing ever since: it seems as if it 

 would get to its maximum about 1765, and would then be about 3° 24'. Tlie 

 nodes of the 4th satellite in 1730 were in 13^** of jxc and ^, and move forward 

 2° in 12 years: the inclination of its orbit is about 2° 40', and does not seem to 

 vary above one or two minutes either way. From these elements it will be easy 



• The semi-durations of the eclipses of the 4th satellite will be about 2' more at the ascending, and 

 2' less at the descending node, on account of the eccentricity of its orbit. — Orig. 



