1885.] theory of viscous solids. 279 



probably insensible deformation of the " solid " framework con- 

 sidered as an elastic solid. This will go on until the system of 

 molecular stresses corresponding to the system of strains is in 

 equilibrium with the external forces. 



So far the case is parallel to what happens when external 

 forces act upon a piece of jelly; but in the case of the jelly the 

 position of equilibrium is permanent, the strained framework 

 remains strained. In the case of the viscous body an interchange 

 of molecules is constantly going on between the " solid " and the 

 "liquid" portions of the mass; "attached" molecules are becoming 

 "unattached" and "unattached" molecules are becoming "at- 

 tached." This involves the replacement of strained " solid" ele- 

 ments by unstrained ones. 



But with the complete or partial breaking up of a strained 

 element a corresponding stress disappears simultaneously ; there 

 is no longer equilibrium between the external forces and the 

 system of stresses ; a further deformation of the mass will take 

 place till equilibrium is restored ; and so on continually. The 

 successive deformations are cumulative while the stresses are not. 

 The final change of form is the sum of the partial changes, but 

 the sum of the molecular strains has a constant average value. 



The rapidity with which the viscous body changes its form 

 under the influence of given external forces will depend (1) upon 

 the proportion of " liquid " to " solid " elements, which will affect 

 the strength of the " framework " and therefore the amount of 

 strain necessary to produce equilibrium, and (2) upon the rapidity 

 with which the interchange of molecules between the "solid" 

 and "liquid" portions of the mass takes place; and this again 

 will depend partly upon the proportion of "unattached" to "at- 

 tached " molecules and partly upon the mean average velocity of 

 the molecules. On both these grounds the rapidity of the change 

 of form will increase with the temperature. 



(3) Some applications of generalized space coordinates to 

 differential analysis. By Prof. J. Larmoe, M.A. 



This paper is being printed in full in the Transactions of the 

 Society. 



