448 THE PRINCIPLES OF SCIENCE. [CHAP. 



time after time to the same value. If we strike a pendu- 

 lum it presently returns to the point from which we 

 disturbed it, and while time, the variable, progresses 

 uniformly, it goes on making excursions and returning, 

 until stopped by the dissipation of its energy. If one body 

 in space approaches by gravity towards another, they will 

 revolve round each other in elliptic orbits, and return for 

 an indefinite number of times to the same relative positions. 

 On the other hand a single body projected into empty 

 space, free from the action of any extraneous force, would 

 go on moving for ever in a straight line, according to the 

 first law of motion. In the latter case the variation is 

 called secular, because it proceeds during ages in a similar 

 manner, and suffers no Trep'oSo? or going round. It may 

 be doubted whether there really is any motion in the 

 universe which is not periodic. Mr. Herbert Spencer long 

 since adopted the doctrine that all motion is ultimately 

 rhythmical, 1 and abundance of evidence may be adduced 

 in favour of his view. 



The so-called secular acceleration of the moon's motion 

 is certainly periodic, and as, so far as we can tell, no body 

 is beyond the attractive power of other bodies, rectilinear 

 motion becomes purely hypothetical, or at least infinitely 

 improbable. All the motions of all the stars must tend to 

 become periodic. Though certain disturbances in the pla- 

 netary system seem to be uniformly progressive, Laplace 

 is considered to have proved that they really have their 

 limits, so that after an immense time, all the planetary 

 bodies might return to the same places, and the stability of 

 the system be established. Such a theory of periodic sta- 

 bility is really hypothetical, and does not take into account 

 phenomena resulting in the dissipation of energy, which 

 may be a really secular process. For our present purposes 

 we need not attempt to form an opinion on such questions. 

 Any change which does not present the appearance of a 

 periodic character will be empirically regarded as a secular 

 change, so that there will be plenty of non-periodic varia- 

 tions. 



The variations which we produce experimentally will 

 often be non-periodic. When we communicate heat to a 



1 First Principles, yd edit. chap. x.-p. 253. 



