3S PHILOSOPHICAL TRANSACTIONS. [aNNO J 756. 



be due to the actions of the other planets Mars and Venus, which, since the 

 ascending nodes of both are within the first six signs, conspire also to diminish 

 the obliquity of the ecliptic. For which reason, if at any time by observations 

 there can be accurately known both this variation and the progress of the earth's 

 aphelion, then we may also come to know the forces of the planets Mars and 

 Venus, and to weigh their masses. 



Prop. 4. To determine the Motion of the Equinoxes due to the preceding 

 Causes. 



Here the motion of the equinoctial point is not investigated, so far as to the 

 earth's equator, because of the redundant matter there, may change its situation 

 in respect of the ecliptic by the force of Jupiter and Saturn, like as it can be 

 done by the forces of the sun and moon ; for this kind of mutation arising from 

 the actions of Jupiter and Saturn must be insensible : but we inquire after that 

 motion of the equinox, arising from the variation, which we have- showed 

 above can be made in the situation of the plane of the ecliptic. 

 '^\;The same things remaining therefore as in the preceding proposition, from the 

 point OT, where the equator cuts the circle ^e, demit mn perpendicular on de ; 

 then because J>g'. mn :: 1 : cos. dl or ck, and Dd: Dg:: l : s, it will be Dd: mm: 

 I : CK X «; or drawing the radius cs perpendicular to cl, and on cs the perpen- 

 diculars DR, er, HG, it will be i>d : mn :: Be : Rr X s; therefore the sum of all 

 the mn, while by the difference of the motions of the equinox and node the arc 

 DH is described, will be to the sum of all the dc/, as the sum of all the Rr X s, 

 is to the sum of as many arcs ne, that is, as rg X * to the arc dh. Therefore 

 the sum of all the mn, that is, the latitude of the equinoctial point, or its dis 



tance from the plane dce considered as immovable, is = ^^-i ^--, the let- 

 ter n denoting the motion of the node while the arc dh is described. Now, as 

 KG is equal to the difference or sum of the sines of the arcs dl, hl, according 

 as the points r, g lie on the same or on contrary sides of the centre c, the circle 

 ID representing the orbit of either Jupiter or Saturn, hence will result the fol- 

 lowing theorem : " Radius is to the sine of the inclination of the orbit of Ju- 

 piter or Saturn to the ecliptic, as the difference or sum of the sines of the dis- 

 tances of the node from the equinox at the beginning and end of a given time, to 

 a certain sine : then, as the difference of the motions of the node and equinox, 

 is to the motion of the node, so is the sine just found, to the sine of the varia- 

 tion in the latitude of the equinoctial point." Or again, since the variation in 



the obliquity of the ecliptic is, from the preceding prop. = ^ , and 



Ro xji_x_* -g ^^^ variation in the latitude of the equinoctial point, we thence 



DH ' 



have this other theorem: " The variation in the latitude of the equinox, is to 



