26G EECENT RESEARCHES ON THE 



connection between geological phenomena and terrestrial temperatures, 

 in so far as the latter is modified by the variable eccentricity for her 

 orbit. The amount of light and heat received from the sun in the course 

 of a year depends to an important extent on the eccentricity of the 

 earth's orbit ; but the distribution of the same over the surface of the 

 earth depends on the relative position of the perihelion of the orbit 

 with respect to the equinoxes, and on the obliquity of the ecliptic to the 

 equator. These elements are subject to great and irregular variations; 

 but their laws can now be determined with as much precision as the 

 exigencies of science may require. We will now more carefully examine 

 these elements, and the consequences' to which their variations give rise. 



As we have already computed the eccentricity of the earth's orbit at 

 intervals of 10,000 years, during a period of 2,000,000 years, by employ- 

 ing the constants which correspond to the assumed mass of the earth 

 increased hy its twentieth part, we here give the elements correspond- 

 ing to this increased mass. We therefore find that the eccentricity of 

 the earth's orbit will always be included within tlie limits of and 

 0.0693888 5 ^^^ i^ consequently follows that the ^>?c«m motion of the peri- 

 helion is indeterminate, although the actual motion and position at any 

 time during a period of 2,000,000 years can be readily found by means 

 of the tabular value of that element. The eccentricity of the orbit at 

 any time can also be found by means of the same table. 



The inclination of the apparent ecliptic to the fixed ecliptic of 1850, 

 is always less that -iP 41' ; while its inclination to the invariable plane 

 of the planetary system always oscillates within the limits 0° 0' and 

 3° 6'. It is also evident that the mean motion of the node of the 

 apparent ecliptic on the fixed ecliptic of 1850, and also on the invariable 

 plane, is wholly indeterminate. 



The mean value of the precession of the equinoxes on the fixed eclip. 

 tic, and also on the apparent ecliptic, in a Julian year, is equal to 

 50".438239 ; Avhence it follows, that the equinoxes perform a complete 

 revolution in the heavens in the average interval of 25,091.8 years; but 

 on account of the secular inequalities in their motion, the time of revo- 

 lution is not always the same, but may diHer from the mean time of 

 revolution by 281.2 years. We also find that if the place of the equinox 

 be computed for any time whatever, by using the mean value of preces- 

 sion, its place when thus determined can never differ from its true place 

 to a greater extent than 3° 50' 20". The maximum and minimum values 

 of precession in a Julian year are 52".G01080 and 48".212398, respect- 

 ively, and since the length of the tropical year depends on the annual 

 l^recessiou, it follows that the maximum variation of the tropical year 

 is equal to the mean time required for the earth to describe an arc which 

 is equal to the maximum variation of precession. Now this latter quan- 

 tity being 4".451G82, and the sidereal motion of the earth in a second of 

 time being 0".041067, it follows that the maximum variation of the tropi- 

 cal year is equal to 108.40 seconds of time. Ii>like manner, if we take 



