$ 2 4 a] Periodic and Secular Inequalities 311 



the disturbed planet ; and the corresponding inequalities of 

 motion are the periodic inequalities, which for the most part 

 go through a complete cycle of changes in the course of a 

 few revolutions of the planets, or even more rapidly. The 

 other part of the disturbing force remains nearly unchanged 

 for a considerable period, and gives rise to changes in the 

 elements which, though in general very small, remain for a 

 long time without sensible alteration, and therefore continu- 

 ally accumulate, becoming considerable with the lapse of 

 time : these are the secular inequalities. 



Speaking generally, we may say that the periodical 

 inequalities are temporary and the secular inequalities 

 permanent in their effects, or as Sir John Herschel 

 expresses it : 



" The secular inequalities are, in fact, nothing but what remains 

 after the mutual destruction of a much larger amount (as it very 

 often is) of periodical. But these are in their nature transient and 

 temporary ; they disappear in short periods, and leave no trace. 

 The planet is temporarily withdrawn from its orbit (its slowly 

 varying orbit), but forthwith returns to it, to deviate presently as 

 much the other way, while the varied orbit accommodates and 

 adjusts itself to the average of these excursions on either side 

 of it." * 



" Temporary " and " short " are, however, relative terms. 

 Some periodical inequalities, notably in the case of the 

 moon, have periods of only a few days, and the majority 

 which are of importance extend only over a few years ; but 

 some are known which last for centuries or even thousands 

 of years, and can often be treated as secular when we only 

 want to consider an interval of a few years. On the other 

 hand, most of the known secular inequalities are not really 

 ] er nanent, but fluctuate like the periodical ones, though 

 only in the course of immense periods of time to be reckoned 

 usually by tens of thousands of years. 



One distinction between the lunar and planetary theories 

 is that in the former periodic inequalities are comparatively 

 large and, especially for practical purposes such as computing 

 the position of the moon a few months hence, of great 



* Outlines of Astronomy, 656. 



