Chap. 3. PHILOSOPHICAL DISCOVERIES. 257

the earth’s mean distance be represented by 100000, and thedistances of those several planets shall be represented by thenumbers 38710, 72333, 152369, 520096, 954006, re-spectively.

The distances of Mercury and Venus are determined by theirgreatest elongations from the fun. Let s (Fig. 54.) represent thefun, t the earth, and supposing avb the orbit of Venus to beperfectly circular, draw t v a tangent; then shall v representthe place of Venus where her elongation from the fun is greatest,and the triangle svt being right angled at v, it follows thatst, the distance of the earth from the fun, is to sv, the dis-tance os Venus from the sun, as the radius to the sine of theangle stv the greatest elongation of Venus from the fun. Inthis manner, the distances of the inferior planets are comparedwith the distance of the earth from the sum The distances ofthe superior planets are determined from their retrogradations,and, in such as have satellites, by the eclipses of those satellites.For example, let 1 (Fig. 55.) represent the planet Jupiter , andif the right line s 1, joining the centres of the fun and Jupiter ,be produced to m, then shall 1 m be the axis of his lhadow,the position of which is determined by the eclipses of the satel-lites, and shews the heliocentric place of Jupiter , /. e. his placeviewed from the fun. Produce the line t i, which joins thecentres of the Earth and Jupiter , to n, and n shall representthe geocentric place of Jupiter, i. e. his place when viewed,from the earth. The difference of those places gives the anglen 1 m or us ; the angle 1 t s, the elongation of Jupiterfrom the fun as seen from the earth at t, is easily found byobservation ; consequently all the angles of the triangle t i sare known, with the proportion of its sides, which is the semeas of the sines of those angles ; and thus the proportion of s 1,the distance of Jupiter from the fun, to s t, the distance of

L 1 the