196 THE PRINCIPLES OF SCIENCE. 



in a succession of predictions grounded on the theory of 

 gravitation as to the inequalities of the planetary move- 

 ments caused by mutual perturbations. These inequalities 

 are so numerous, so small, and so complicated in character, 

 that it would be an almost hopeless task to attempt to 

 discover them empirically or tentatively by the compari- 

 son and classification of observations. But theory pretty 

 easily indicates the period and general nature of the 

 inequality to be detected, and by elaborate calculations 

 even the amount of the effect may be assigned. Thus 

 the inequality arising from the attraction of Venus and 

 the earth was estimated by Sir George Airy to amount to 

 no more than a few seconds at its maximum, while the 

 period is no less than 240 years. Nevertheless, the in- 

 direct effects of this inequality upon the moon's motion 

 are considerable, and are entirely verified in the lunar 

 theory. Although prediction by theory is the general 

 rule in physical astronomy, yet the empirical investiga- 

 tion of divergences from theory sometimes discloses effects 

 which had been overlooked, or points out residual effects 

 of unknown origin. 



Quantities determined ~by Theory and not verified. 



It will continually happen that we are able, from 

 certain measured phenomena and a correct theory, to 

 determine the amount of some other phenomenon which 

 we may either be unable to measure at all, or to measure 

 with an accuracy corresponding to that required to verify 

 the prediction. Thus Laplace having worked out an 

 almost complete theory of the motions of Jupiter's satel- 

 lites on the hypothesis of gravitation, found that these 

 motions were greatly affected by the spheroidal form of 

 Jupiter. Hence from the motions of the satellites, which 

 can be observed with great accuracy owing to the frequent 



