SEQUEL TO THE EPOCH OF NEWTON. 443 



tected, in the planetary theory such an inequality, hitherto unnoticed, 

 arising from the mutual attraction of Venus and the Earth. Its whole 

 effect on the earth's longitude, would be to increase or diminish it by 

 nearly three seconds of space, and its period is about 240 years. " This 

 term," he adds, " accounts completely for the difference of the secular 

 motions given by the comparison of the epochs of 1783 and 1821, and 

 by that of the epochs of 1801 and 1821." 



Many excellent Tables of the motions of the sun, moon, and planets, 

 were published in the latter part of the last century ; but the Bureau 

 des Longitudes which was established in France in 1795, endeavored 

 to give new or improved tables of most of these motions. Thus were 

 produced Delambre's Tables of the Sun, Burg's Tables of the Moon, 

 Bouvard's Tables of Jupiter, Saturn, and Uranus. The agreement be- 

 tween these and observation is, in general, truly marvellous. 



We may notice here a difference in the mode of referring to obser- 

 vation when a theory is first established, and when it is afterwards to 

 be confirmed and corrected. It was remarked as a merit in the method 

 of Hipparchus, and an evidence of the mathematical coherence of his 

 theory, that in order to determine the place of the sun's apogee, and 

 the eccentricity of his orbit, he required to know nothing besides the 

 lengths "of winter and spring. But if the fewness of the requisite data 

 is a beauty in the first fixation of a theory, the multitude of observa- 

 tions to which it applies is its excellence when it is established ; and 

 in correcting Tables, mathematicians take far more data than would be 

 requisite to determine the elements. For the theory ought to account 

 for all the facts : and since it will not do this with mathematical rigor 

 (for observation is not perfect), the elements are determined, not so as 

 to satisfy any selected observations, but so as to make the whole mass 

 of error as small as possible. And thus, in the adaptation of theory to 

 observation, even in its most advanced state, there is room for sagacity 

 and skill, prudence and judgment. 



In this manner, by selecting the best mean elements of the motions 

 of the heavenly bodies, the observed motions deviate from this mean 

 in the way the theory points out, and constantly return to it. To this 

 general rule, of the constant return to a mean, there are, however, some 

 apparent exceptions, of which we shall now speak. 



