58 ASTRONOMICAL TABLES. SECT. VIII. 



mean density of the earth is 6'565, which is greater than that 

 obtained by Mr. Baily by '89. While employed on the trigono- 

 metrical survey of Scotland, Colonel James determined the mean 

 density of the earth to be 5'316, from a deviation of the 

 plumb-line amounting to 2", caused by the attraction of Arthur's 

 Seat and the heights east of Edinburgh : it agrees more nearly with 

 the density found by Mr. Baily than with that deduced from Mr. 

 Airy's experiments. All 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 homogeneous, 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 astronomical tables. 

 Astronomy is now divided into the three distinct departments of 

 theory, observation, and computation. Since the problem of the 

 three bodies 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 centre 

 (N. 48) to or from its mean place gives its position in the 

 ellipse. This again is corrected by the application of the prin- 

 cipal 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 con- 

 tinued till the correetions become less than the errors of observa- 

 tion, 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. 

 Xow, the longitude, latitude, and distance of a planet from the 



