ASTRONOMY. 1?1 



the base EE' are given, and therefore the sides 

 EN, E'N, are also given. Hence, from either of 

 the triangles ESN, E'SN, SN is found, and also 

 the angle ESN, or the heliocentric place of the 

 node. GREGORY'S Astronomy, Book in. prop. 19. 

 WOLFII, Elem. Astron. 777. Thus the periodic 

 time of the planet is determined, and also its 

 mean motion. 



b. When observations of this kind are made at a con- 

 siderable distance of time from one another, it is 

 fo^nd that the nodes of every planet have a slow 

 motion retrograde, or in a direction contrary to 

 the order of the signs. 



169. The distance of a planet from the Sun, 

 and its heliocentric place, or its longitude as 

 seen from the Sun, may be determined by ob- 

 servations made at the time of its opposition to 

 the Sun. 



If E (fig. 20.) be the Earth, S the Sun, P a planet, 

 O its place reduced to the ecliptic, SN the line of 

 the nodes ; the points S, E, and O are in the same 

 straight line, because of the planet's opposition to 

 the Sun, and the angle ESN, that is, OSN, is 

 known from the last problem ; therefore the an- 

 gle PSO or PSE, the heliocentric latitude, is also 

 given. But the angle PEO, the geocentric latitude, 

 is given by observation, and the base ES, from 

 the theory of the Earth's motion ; therefore SP, 



or 



