64 THE PRINCIPLES OF SCIENCE. 



periodic likewise ; nor is there any limit to the complica- 

 tion of periods beyond periods, or periods within periods, 

 which may ultimately be disclosed. In studying, then, a 

 phenomenon of rhythmical character we have a succession 

 of questions to ask. Is the periodic variation uniform "? 

 If not, is the change uniform 1 If not, is the change itself 

 periodic 1 Is that new period uniform, or subject to any 

 other change, or not \ and so on ad infinitum. 



In some cases there may be many distinct causes of 

 periodic variations, and according to the principle of the 

 superposition of small effects, to be afterwards more fully 

 considered, these periodic effects will be simply added 

 together, or at least approximately so, and the joint result 

 may present a very complicated subject of investigation. 

 Thus the tides of the ocean consist of a series of super- 

 imposed undulations, of which the number and characte 

 have by no means been determined as yet. Not only are 

 there the ordinary and very obvious semi-diurnal tides 

 caused by sun and moon, but a series of minor tides, 

 such as the lunar diurnal, the solar diurnal, the lun 

 monthly, the lunar fortnightly, the solar annual and sola 

 semi-annual are gradually being disentangled by th 

 labours of Sir W. Thomson and others r . 



Variable stars present very interesting periodic phen 

 mena ; while some stars, S Cephei for instance ar 

 subject to very regular and equal variations, others, lik 

 Mira Ceti, are less constant in the degrees of brilliane 

 which they attain or the rapidity of the changes, pos 

 sibly on account of some much longer periodic variation 8 . 

 The star /3 Lyree presents a double maximum and 

 minimum in each of its periods of nearly 13 days, and 

 since the discovery of this variation the period in a period 

 has probably been on the increase. 'At first the varia- 



1 'British Association Report,' 1870, p. 120. 



9 Herschel's ' Outlines of Astronomy/ 4th edit. pp. 555-557. 





