SECT. VIII. ASTRONOMICAL TABLES. 57 



the effects of each upon a pendulum ; the nearness of 

 the smaller mass making it produce a sensible effect as 

 compared with that of the larger : for by the laws of 

 attraction the whole earth must be considered as col- 

 lected in its center. By this method it has been found 

 that the mean density -of the earth is 5-675 times greater 

 than that of water at the temperature of 62 of Fahren- 

 heit's thermometer. The late Mr. Baily, whose accu- 

 racy as an experimental philosopher is acknowledged, 

 was unremittingly occupied nearly four years in accom- 

 plishing this very important object. All the planets and 

 satellites appear to be of less density fhan the earth. 

 The motion of Jupiter's satellites show that his density 

 increases toward his center. Were his mass homogene- 

 ous, his equatorial and polar axis would be in the ratio 

 of 41 to 36, whereas they are observed to be only as 41 

 to 38. The singular irregularities in the form of Sat- 

 urn, and the great compression of Mars, prove the in- 

 ternal structure of these two planets to be very far from 

 uniform. 



Before entering on the theory of rotation, it may not 

 be foreign to the subject to give some idea of the meth- 

 ods of computing the places of the planets, and of form- 

 ing astronomical tables. Astronomy is now divided into 

 the three distinct departments of theory, observation, 

 and computation. Since the problem of the three bod- 

 ies can only be solved by approximation, the analytical 

 astronomer determines the position of a planet in space 

 by a series of corrections. Its place in its circular orbit 

 is first found, then the addition or subtraction of the 

 equation of the center (N. 48) to or from its mean place, 

 gives its position in the ellipse. This again is corrected 

 by the application of the principal periodic inequalities. 

 But as these are determined for some particular position 

 of the three bodies, they require to be corrected to suit 

 other relative positions. This process is continued till 

 the corrections become less than the errors of observa- 

 tion, when it is obviously unnecessary to carry the ap- 

 proximation further. The true latitude and distance of 

 the planet from the sun are obtained by methods similar 

 to those employed for the longitude. 



As the earth revolves equably about its axis in 24 



