VOL. XLIX.] PHILOSOPHICAL TRANSACTIONS. 33 



orce of Saturn. And the sum of these two, or the whole progressive motion of 

 the earth's aphelion, in 100 years, becomes 22' 58"-^, and its annual motion 

 13^' 47"'. And this agrees with the more celebrated astronomical tables, which 

 commonly show the annual progress of the earth's aphelion plus minus l' 3'^, 

 that is, deducting the 50'' regressive motion of the equinoxes, 13''. a. e. i. 



Corol. 1 . The linear errors of the planets inferior to Jupiter are, in each of 

 their revolutions, nearly as the forces of Jupiter exerted on these, and as the 

 squares of the times of revolution conjointly : and because the planes of these 

 orbits diverge but little from one another, and from the plane of Jupiter's orbit ; 

 the force of Jupiter for disturbing the motion of each, is as the distance of any 

 planet from the sun ; hence their angular errors in each of their revolutions, are 

 as the squares of the periodic times, and therefore in a given time as the periodic 

 time itself, or in the sesquiplicate ratio of their distances from the sun. There- 

 fore, putting the motion of the earth's nodes, in 100 years, 10' 22"4 in antece- 

 dentia, from Jupiter's force, and 3 5 "4- from that of Saturn, as above stated ; and 

 the periodic times being, for Mars 686.9785 days ; for Venus 224.701, and for 

 Mercury 87 .9692 ; hence results the following table : 



Motion of the nodes in From Jupiter's From Saturn's Whole regressive 



100 years, of force. force. motion. 



Mars 19' 30'/ l' 7'^ 20' 37^' 



Venus 6 23 O 22 6 45 



Mercury 2 294. 84. 2 38 



In like manner, if the earth's aphelion in 1 00 years, by Jupiter's force, move 



21 ' 44" in consequentia, and by Saturn's 1' 14"4^ ; for the rest of the planets there 



will be 



Motion of the aphel. From Jupiter's From Saturn's Whole progressive 



in 100 years, of force. force. motion. 



Mars 40' 52'/4- . » 2' 20'i 43' 13^' 



Venus . 13 22 46 14 8 



Mercury 5 14 18 5 32 



Corol. 2. Let iDd (fig. 8) represent the orbit of Jupiter, de the ecliptic, which 

 after 100 years has the situation dE, changing the node from d to d: draw the 

 arc Dg perpendicular to dE ; then will Dd be to d^^, as radius to the sine of the 

 inclination of Jupiter's orbit to the ecliptic, that is, as radium to sine of l'^ 19' 10 ; 

 therefore, orf being = lO' 58", as before mentioned, d^ will be = 15'' 9"; or 

 rather a star placed in the common section of the ecliptic and orbit of Jupiter, 

 will appear to recede gradually from the ecliptic, so as after 100 years its distance 

 from it will be 15' 9' ; and so through many ages the star's latitude will be al- 

 most equally increased ; and in like manner will all the stars, having the same 



VOL. XI. F 



