450 THE PRINCIPLES OF SCIENCE. [CHAP. 



scientific prophecy were founded upon this knowledge, 

 and if at present we cannot help wondering at the precise 

 anticipations of the nautical almanack, we may imagine, 

 the wonder excited by such predictions in early times. 



Combined Periodic Changes. 



We shall seldom find a body subject to a single periodic 

 variation, and free from other disturbances. We may ex- 

 pect the periodic variation itself to undergo variation, 

 which may possibly be secular, but is more likely to 

 prove periodic ; nor is there any limit to the complication 

 of periods beyond periods, or periods within periods, which 

 may ultimately be disclosed. In studying a phenomenon 

 of rhythmical character we have a succession of questions 

 to ask. Is the periodic variation uniform ? If not, is the 

 change uniform ? If not, is the change itself periodic ? 

 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 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. The tides of 

 the ocean consist of a series of superimposed undulations. 

 Not only are there the ordinary semi-diurnal tides caused 

 by sun and moon, but a series of minor tides, such as the 

 lunar diurnal, the solar diurnal, the lunar monthly, the 

 lunar fortnightly, <the solar annual and solar semi-annual 

 are gradually being disentangled by the labours of Sir W. 

 Thomson, Professor Haughton and others. 



Variable stars present interesting periodic phenomena ; 

 while some stars, 8 Cephei for instance, are subject to very 

 regular variations, others, like Mira Ceti, are less constant 

 in the degrees of brilliancy which they attain or the 

 rapidity of the changes, possibly on account of some longer 

 periodic variation. 1 The star /3 Lyrae presents a double 

 maximum and minimum in each of its periods of nearly 1 3 

 days, and since the discovery of this variation the period 



1 Herschel's Outlines of Astronomy, 4th edit. pp. 555 557. 



