608 SPECIAL METHODS OF DISCOVERY. 



liquids, and gases, including astronomy, hydrostatics, 

 hydraulics, pneumatics, and acoustics, in the sciences of 

 light and radiant heat, and to a less extent in those of 

 electricity, magnetism, chemistry, and vital and mental 

 action. 



Many astronomical discoveries in particular have re- 

 sulted from its use. It was by means of calculations, based 

 upon known truths, that the effects of precession of the 

 equinoxes were discovered by Hipparchus, 128 B.C., by com- 

 parison of his own observations with those of Timocharis, 

 made 155 years previously. By calculation also, Newton 

 6 appears to have discovered the method of demonstrating 

 that a body might describe an ellipse, when acted upon by 

 a force residing in the focus, and varying inversely as the 

 square of the distance.' 1 By similar means he discovered 

 the specific gravity of the planets, and that the density of 

 Saturn is almost nine times less than that of our earth ; 

 also that our earth could not be a perfect globe, and 

 ascertained almost exactly how much it was flattened at 

 the poles. He also found, by similar means, that the pre- 

 cession of the equinoxes was due to the earth not being a 

 perfect sphere, and that the cause of it was, the greater 

 attraction of the sun and moon upon the extra mass of 

 matter existing around it at the equator. About the year 

 1770, Lagrange, by means of mathematical calculation, 

 discovered why it was that the moon always presents 

 nearly the same surface towards the earth, and that what 

 Newton had suggested was really the cause, viz., the 

 attraction of the earth upon the swelling or extra quan- 

 tity of matter at the lunar equator. In making this dis- 

 covery, he also arrived at another, viz., the cause of the 

 libration of the moon, i.e., why she always has a little 



1 Whewell, History of the Inductive Sciences, 3rd. edit. vol. ii. p. 452 t 



