288 Astronomy. [Lecture 19. 



The third law of Kepler is, that the areas are 

 in proportion to the times : That is, that the 

 time occupied by a planet in passing the different 

 arcs AD, DE of its orbit are to one another, as 

 the areas of the trilineal spaces A S D, D S E ter- 

 minated by these areas, and by the right lines AS, 

 DS, and DS and ES ; these areas are, by the 

 same reasoning, to one another, as the time which 

 the planet employs in passing through the arcs 

 which terminate them. Hence we see that these 

 times are shorter in proportion as the planet is 

 nearer the sun, for then the area of the triangle 

 is so much smaller. Newton has proved that 

 these three laws are necessary consequences of 

 the projectile force combined with the centripetal 

 or attractive force, which retains the planets in 

 their orbits; and the demonstration, now much 

 simplified, finds a place in all our higher treatises 

 of mechanics and astronomy. 



Astronomers have divided the planets into two 

 classes ; the first class they call primary planets, 

 principals. They are eleven in number, viz. 

 Mercury, Venus, the Earth, Mars, Ceres, Pallas, 

 Juno, Vesta, Jupiter, Saturn, and the Georgium 

 Sidus or Uranus. Those of the second class 

 they call secondary planets or otherwise satellites 

 or moons. 



The primary planets are such as revolve round 

 the sun only. These are also divided into supe- 

 rior and inferior; those being called superior 

 planets whose distance from the sun is greater 



