I at Jnjruvient far exhibiting Jupiter and his Maons. 



candlfdick ; ntjd in this fituatiou the rcprefentitlves .of the Sun, Earth, and JupUer, %% 

 alfo of t!ie fatellites, will all be in tlieir relative fituations for exhibiting the, general phenor 

 jnena of the Jovian as a detached fyftem. 



:.'fiut before I give a particular defcription of thefe phenomena as they will be exhibited 

 by the fatellitian, the reader will perhaps form a more accurate conception of the extent 

 of its application, if a fummary account be firft given of thofe minute irregularities in thcs 

 motioHS of the fatellites, which no Cmple machinery can be fuppofed to reprefent. 



The fatellites of Jupiter were difcovered by Galileo in January 1610, and called Medi- 

 ceanjlarsy in honour of Cofmo Medici great duke of Tufcany. This aftronomer conti- 

 nued his obfervations upon them for 27 years, till unfortunately the lofs of fight fruftrated 

 the fruit of his continued labours. In 1663 Borelli publiflied a theory of the Medicean 

 Stars, but had not acquired data fufficient for afcertaining the exadl quantities and qualities 



of their motions After him Caffini, in the year 1668, favoured the world with " Tables 



of the Motions of Jupiter's Satellites," which were improved and edited by him again in 

 1693. Thefe Tables have fince that time been rendered ftill more accurate by Meflrs. 

 Hadley, Pound, Bradley, &c. as alfo by the French aftronomers, and laflly by Wargentin 

 the Swedifh aflronomer, whofe beil Tables are now ufed in calculating the immerfions 

 and emerfions given in the nautical almanac. — ^The times of the mean periodical revolu- 

 tions have been already mentioned ; but they are fubje6l to fuch inequalities of motion a6 

 require the following equations for afcertaining their apparent places : viz. 



X. For the Ijght which depends upon Jupiter's eccentricity : %. For the light which de- 

 pends upon his change of place in his orbit : 3. For his anomaly : 4. For the mutual gravita- 

 tion of tlie three firfl, the period of which is upwards of 437 days : 5. For a period of 12 

 years for the third, accruing from an unknown caufe : 6. For a fimilar period for the 

 fourth, accruing from its eccentricity : 7. For the variable inclination of the orbit of the 

 fpcond ; and, 8. for apparent time. — ^The greateft; or grand equation, which depends upon 

 Jupiter's agomaly, has been {hewn to be different in different years : with the firft fatellite 

 it is pOflible for it to amount to i h. 18 min. 16 fee. ; with the fecond, to 2 h. 37 min. 

 12 fee. ; with the third, to 5 h. 16 min. 32 fee. ; .and with the fourth, to 12 h. 20'min. 

 '34 fee. at a certain time in fome particular years sbove fpecified, though in others it may 

 be nothing. 



From meafurements of the greateft elongations of thefe fateUites, taken by a microme- 

 ter, it does not appear xxrtairi that their orbits are elliptical, except that of the fourth : the 

 others, however, are by analogy fuppofed to be fuch, though the ellipfes are fo like circles 

 that they may be confidered as fuch, even in calculations, without any apparent error. 

 The diameters of thefe orbits, when viewed from the earth, fubtend but very fmall angles ; 

 viz. the firft fubtends 3'5S''» the fecond, 6' 14"; the third, 9' 58''; and the fourth, 

 17' 3<j"' — The diameters of each of the fatellites themfelves, compared to that of Jupiter, 

 fecm not to be accurately known. Mr. Herfchell's obfervations make that of the firft to be 

 not quite -j'^- of a fecond ; whereas, before his notice, they were each confidered to fubtend 

 an angle more than double this quantity ; for their diameters were eftimated at.j^ or -^goi 

 Jupiter. Future obfervations muft determine this point. 



7 In 



