268 RECENT RESEARCHES ON THE 



and we should be unable to estimate the interval between the epochs of 

 elements which differed by only a few thousand years, shice they would 

 manifestly be so nearly identical with our own that the value of legitimate 

 conclusions would be greatly impaii'ed by the unavoidable errors of the 

 observations on which they were based. 



The duration of the different seasons is also greatly modified by the 

 eccentricity of the earth's orbit. At i)resent the sun is north of the 

 equator scarcely ISOi days, and south of the same circle about 178f days ; 

 thus making a difference of 7f days between the length of the summer 

 and winter at present. But when the eccentricity of the orbit is nearly 

 at its maximum, and its transverse axis also passes through the solstices, 

 both of Avhich conditions have, in past ages, been fulfilled, the summer, 

 in one hemisphere, will have a period of 19S| days, and a winter of only 

 166Jdays, while, in the other hemisphere, these conditions will be re- 

 versed 5 the winter having a period of 198^ days, and a summer of only 

 166^ days. The variations of the sun's distance from the earth in the 

 course of a year, at such times, is also enormous, amounting to almost 

 one-seventh part of its mean distance — a quantity scarcely less than 

 13,000,000 of miles ! 



Passing now to the consideration of the elements of the planet Mars, 

 we find that the eccentricity of his orbit always oscillates within the 

 limits 0.018475 and 0.139G55 ; and the mean motion of his perihelion is 

 17".781156. The maximum incliuation of his orbit to the fixed ecliptic 

 of 1850, and to the invariable plane of the planetary system, is 7° 28' and 

 50 50' respectively. The minimum inclination to both planes being 

 nothing, the mean motion of the node is indeterminate. 



The secular variations of the orbits of Jupiter, Saturn, Uranus, and 

 Neptune, present some curious and interesting relations. These four 

 planets compose a system by themselves, v.hich is practically independ- 

 ent of the other planets of the system. 



The maximum and minimum limits of the eccentricity of the orbits of 

 these four planets are as follows : 



iMaxiumm eccentricity. Minimum eccentricity. 



Jupiter 0.0G08271 0.0251928 



Saturn 0.0813289 0.0123719 



Uranus 0.0779G52 0.011757G 



Xeptune 0.01150GG 0.0055729 



The maximum and minimum inclinations of their orbits to the invari- 

 able plane of the planetary system have the following values : 



Maximum iucliuation. Minimum incliuation. 



Jupiter 0^ 28' 5G{' 0° 1 1' 23" 



Saturn 1 39 17 IG 



Uranus 1 7 10 5125 



Keptune 17 21 33 13 



