66 ASTRONOMICAL TABLES. [SECT. vm. 



the planets and satellites appear to be of less density than 

 the earth. The motions of Jupiter's satellites show that his 

 density increases towards his centre. Were his mass homo- 

 geneous, his equatorial and polar axes 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 Saturn, and 

 the great compression of Mars, prove the internal 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 methods of 

 computing the places of the planets, and of forming astro- 

 nomical tables. Astronomy is now divided into the three 

 distinct departments of theory, observation, and compu- 

 tation. Since the problem of the three bodies can only be 

 solved by approximation, the analytical astronomer deter- 

 mines the position of a planet in space by a series of correc- 

 tions. Its place in its circular orbit is first found, then the 

 addition or subtraction of the equation of the centre (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 

 observation, when it is obviously unnecessary to carry the 

 approximation 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 hours, 

 at the rate of 15 in an hour, time becomes a measure of 

 angular motion, and the principal element in astronomy 

 where the object is to determine the exact state of the heavens 

 and the successive changes it undergoes in all ages, past? 

 present, and to come. Now, the longitude, latitude, and dis- 

 tance of a planet from the sun are given in terms of the 

 time, by general analytical formulae. These formulae will 



