572 THE PRINCIPLES OF SCIENCE. [CHAP. 



that this discrepancy really involves the doctrine of the 

 equivalence of heat and energy, and it was applied by 

 Mayer, at least by implication, to give an estimate of the 

 mechanical equivalent of heat. The estimate thus derived 

 agrees satisfactorily with direct determinations by Dr. 

 Joule and other physicists, so that the explanation of the 

 residual phenomenon which exercised Newton's ingenuity 

 is now complete, and forms an important part of the new 

 science of thermodynamics. 



As Herschel observed, almost all great astronomical dis- 

 coveries have been disclosed in the form of residual dif- 

 ferences. It is the practice at well-conducted observatories 

 to compare the positions of the heavenly bodies as actually 

 observed with what might have been expected theoretically. 

 This practice was introduced by Halley when Astronomer 

 Koyal, and his reduction of the lunar observations gave a 

 series of residual errors from 1722 to 1739, by the examina- 

 tion of which the lunar theory was improved. Most of 

 the greater astronomical variations arising from nutation, 

 aberration, planetary perturbation were discovered in the 

 same manner. 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 clue to the remarkable discovery 

 of Neptune. 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 obser- 

 vations. But these apparent motions are often due, as 

 explained by Baily, 1 the author of the catalogue, to errors 

 of observation and reduction. In many cases the best 

 astronomical authorities have differed as to the very direc- 

 tion 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 often be so small that their very existence 

 is doubtful. Only the gradual progress of theory and of 

 measurement will show clearly whether a discrepancy is to 



1 British Association Catalogue of Stars, p. 49. 



