ACCORDANCE OF QUANTITATIVE THEORIES, c. 215 



conducted observatories to compare the position of the 

 principal heavenly bodies as actually observed with what 

 might have been expected theoretically. This practice 

 was introduced by Halley when Astronomer Royal, and 

 his reduction of the lunar observations gave a series of 

 residual errors from 1722 to 1739, by the examination 

 of which the lunar theory was improved. Most of the 

 greater astronomical variations arising from nutation, 

 aberration, planetary perturbation were in like manner 

 disclosed. The precession of the equinox was perhaps 

 the earliest residual difference observed ; the systematic 

 divergence of Uranus from its calculated places was one 

 of the latest, and was the foundation of the remarkable 

 discovery of Neptune by anticipation. We may also class 

 under residual phenomena all the so-called proper motions 

 of the stars. A complete star catalogue, such as that 

 of the British Association, gives a greater or less amount 

 of proper motion for almost every star, consisting in the 

 apparent difference of position of the star as derived from 

 the earliest and latest good observations. But these 

 apparent motions are often due, as is expressly explained 

 by Baily 1 , the author of the catalogue, to errors of obser- 

 vation and reduction. In many cases the best astronomi- 

 cal authorities have differed as to the very direction of 

 the supposed proper motion of stars, and as regards the 

 amount of the motion, for instance of a Polaris, the most 

 different estimates have been formed. Residual quantities 

 will of necessity be often so small that their very existence 

 will be doubtful. Only the gradual progress both of theory 

 and of accurate measurement will clearly show whether a 

 discrepancy is to be referred to previous errors of obser- 

 vation and theory or to some new phenomenon. But 

 nothing is more requisite for the progress of science than 



1 ' British Association Catalogue of Stars,' p. 49. 



