THE INSTABILITY OF THE HOMOGENEOUS. 413 



ously subsisting ; and bring about a totally different arrange- 

 ment. Thus, a stick poised on its lower end is in unstable 

 equilibrium : however exactly it may be placed in a perpen- 

 dicular position, as soon as it is left to itself it begins, at first 

 imperceptibly, to lean on one side, and with increasing rapid- 

 ity falls into another attitude. Conversely, a stick suspended 

 from its upper end is in stable equilibrium: however much 

 disturbed, it will return to the same position. The proposi- 

 tion is, then, that the state of homogeneity, like the state of 

 the stick poised on its lower end, is one that cannot be main- 

 tained. Let us take a few illustrations. 



Of mechanical ones the most familiar is that of the 

 scales. If they be accurately made, and not clogged by dirt 

 or rust, it is impossible to keep a pair of scales perfectly bal- 

 anced: eventually one scale will descend and the other as- 

 cend they will assume a heterogeneous relation. Again, if 

 we sprinkle over the surface of a fluid a number of equal- 

 sized particles, having an attraction for each other, they 

 will, no matter how uniformly distributed, by and by con- 

 centrate irregularly into one or more groups. Were it pos- 

 sible to bring a mass of water into a state of perfect homoge- 

 neity a state of complete quiescence, and exactly equal 

 density throughout yet the radiation of heat from neigh- 

 bouring bodies, by affecting differently its different parts, 

 would inevitably produce inequalities of density and conse- 

 quent currents; and would so render it to that extent hetero- 

 geneous. Take a piece of red-hot matter, and however 

 evenly heated it may at first be, it will quickly cease to be so : 

 the exterior, cooling faster than the interior, will become 

 different in temperature from it. And the lapse into hetero- 

 geneity of temperature, so obvious in this extreme case, 

 takes place more or less in all cases. The action 



of chemical forces supplies other illustrations. Expose a 

 fragment of metal to air or water, and in course of time it 

 will be coated with a film of oxide, carbonate, or other com- 

 pound : that is its outer parts will become unlike its inner 



