CONSTITUTION OF BODIES. 623 



in which the present state is not regarded as influenced by any state which 

 has ceased to exist. For if we expand 6 t _ u by Taylor's theorem, 



,, a dd w 2 d-0 



^**^* ITS *"*** 



and if we also write 



f f 30 f* 2 



A = $ ( w ) dca ' B =\ 4 () dot, C= -2- 1/, () dw, &c. 



Jo Jo J o 1 . 2 



then equation (l) becomes 



where no symbols of time are subscribed, because all the quantities refer to 

 the present tune. 



This expression of Boltzmann's, however, is not in any sense a physical 

 theory of the phenomena ; it is merely a mathematical formula which, though 

 it represents some of the observed phenomena, fails to express the phenomenon 

 of permanent deformation. Now we know that several substances, such as 

 gutta-percha, India-rubber, &c., may be permanently stretched when cold, and 

 yet when afterwards heated to a certain temperature they recover their original 

 form. Gelatine also may be dried when in a state of strain, and may recover 

 its form by absorbing water. 



We know that the molecules of all bodies are in motion. In gases and 

 liquids the motion is such that there is nothing to prevent any molecule from 

 passing from any part of the mass to any other part ; but in solids we must 

 suppose that some, at least, of the molecules merely oscillate about a certain 

 mean position, so that, if we consider a certain group of molecules, its con- 

 figuration is never very different from a certain stable configuration, about which 

 it oscillates. 



This will be the case even when the solid is in a state of strain, pro- 

 vided the amplitude of the oscillations does not exceed a certain limit, but if 

 it exceeds this limit the group does not tend to return to its former configu- 

 ration, but begins to oscillate about a new configuration of stability, the strain 

 in which is either zero, or at least less than in the original configuration. 



The condition of this breaking up of a configuration must depend partly 

 on the amplitude of the oscillations, and partly on the amount of strain in 

 the original configuration ; and we may suppose that different groups of mole- 



