POL 



inclination to the Ecliptic, the line of the apsides, the eccentricity, and 

 consequently the greatest equation of the centre all vary. In Mars the 

 eccentricity, the lines of the apsides and nodes, vary by the action of 

 Venus, the Earth, and Jupiter; as also his place in his orbit, which is 

 not the case with Mercury and Venus, in consequence of their nearness 

 to the Sun. In Jupiter and Saturn, the place in their orbit, the -motion 

 of the apsides, and the change of eccentricity, are chiefly produced by 

 their action on each other ; but in the disturbance of the inclination the 

 other planets have a sensible effect. Uranus, from his great distance, 

 Buffers no disturbance in his motion but from Jupiter and Saturn. 



Two interesting results are obtained from the investigation of the 

 planetary disturbances. 1. That both in the system of primary and se- 

 condary planets, two elements of every orbit remain secure against all 

 disturbances, the mean distance, and the mean motion, i. e. the trans- 

 verse axis of the orbit, and the periodic time. 2. That all the inequali- 

 ties in the planetary motions are periodical, and after a certain time run 

 through the same series of changes. This accurate compensation of the 

 planetary inequalities arises from three conditions ; 1st. that the eccen- 

 tricities of the orbits are small j 2d. that the planets all move in the same 

 direction, ?'. e. from west to east ', 3d. that the planes of their orbits are 

 but little inclined to one another. 



PLANET, time of its passing over the meridian. See Time. 

 POLAR Sean.Sce S^aa, Polar. 



POLYGONS regular, to find tlie area of. 



Let ^ represent the length of one of the equal sides, n the number of 

 them j then 



'n . / 90 H 1900 N 



Area = s 2 x -r * an - f ) 



4V n J 



.Hence the following Tablo : 



Trigon - .v2 X 0.4330127 



Tetragon = ** X 1.0000000 



Pentagon sv X 1.7204774 



Hexagon r= ** X 2.5980762 



Heptagon = ** X 3.6339124 



Octagon = **, X 4.8284271 



Nonagon = g X 6.1818242 



Decagon = ** X 7.6942088 



Undecagon = s* X 9.3656399 

 Dodecagon * 2 X/ 

 2GB 



