XXYIII 



THE GENESIS OF DOUBLE STAES 

 By Sir George Darwin, K.C.B., F.RS. 



Plumian Professor of Astronomy and Bxperimental Philosophy in the 



University of Camhridge. 



In ordinary speech a system of any sort is said to be stable when 

 it cannot be upset easily, but the meaning attached to the word is 

 usually somewhat vague. It is hardly surprising that this should be 

 the case, when it is only within the last thirty years, and principally 

 through the investigations of M. Poincar^ that the conception of 

 stability has, even for physicists, assumed a definiteness and clearness 

 in which it was previously lacking. The laws which govern stability 

 hold good in regions of the greatest diversity ; they apply to the 

 motion of planets round the sun, to the internal arrangement of those 

 minute corpuscles of which each chemical atom is constructed, and to 

 the forms of celestial bodies. In the present essay I shall attempt to 

 consider the laws of stability as relating to the last case, and shall 

 discuss the succession of shapes which may be assumed by celestial 

 bodies in the course of their evolution. I believe further that homo- 

 logous conceptions are applicable in the consideration of the trans- 

 mutations of the various forms of animal and of vegetable life and in 

 other regions of thought. Even if some of my readers should think that 

 what I shall say on this head is fanciful, yet at least the exposition will 

 serve to illustrate the meaning to be attached to the laws of stability 

 in the physical universe. 



I propose, therefore, to begin this essay by a sketch of the 

 principles of stability as they are now formulated by physicists. 



I. 



If a slight impulse be imparted to a system in equilibrium one of 

 two consequences must ensue ; either small oscillations of the system 

 will be started, or the disturbance will increase without limit and the 

 arrangement of the system will be completely changed. Thus a stick 

 may be in equilibrium either when it hangs from a peg or when it is 

 balanced on its point. If in the first case the stick is touched it Mill 

 swing to and fro, but in the second case it will topple over. The first 



