METHOD OF VARIATIONS. 65 



bility was more rapid, then it became gradually slower ; 

 and this decrease in the length of time reached its limit 

 between the years 1840 and 1844. During that time its 

 period was nearly invariable ; at present it is again 

 decidedly on the decrease 1 ." It is evident that the 

 tracing out of such complicated variations presents an 

 almost unlimited field for interesting investigation. The 

 number of such variable stars already known is consider- 

 able, and there is no reason to suppose that any appreciable 

 fraction of the whole number has yet been detected. 



Principle of Forced Vibrations. 



All investigations of the connection of periodic causes 

 and effects rest upon a most important and general prin- 

 ciple, which has been demonstrated by Sir John Herschel 

 for some special cases, and clearly explained by him in 

 several of his works u . The principle may be formally 

 stated in the following manner : ' If one part of any 

 system connected together either by material ties, or by 

 the mutual attractions of its members, be continually 

 maintained by any cause, whether inherent in the consti- 

 tution of the system or external to it, in a state of regular 

 periodic motion, that motion will be propagated through- 

 out the whole systems, and will give rise, in every member 

 of it, and in every part of each member, to periodic move- 

 ments executed in equal period, with that to which they 

 owe their origin, though not necessarily synchronous with 

 them in their maxima and minima.' The meaning of the 

 proposition is that the effect of a periodic cause will be 

 periodic, and will recur at intervals equal to those of the 



* Humboldt's 'Cosmos' (Bohn), vol. iii. p. 229. 



u 'Encyclopaedia Metropolitana/ art. Sound, 323; 'Outlines of 

 Astronomy/ 4th edit. 650, pp. 410, 487-88 ; ' Meteorology/ Reprint, 



p- !37. 



VOL. II. F 



