lO R. F. GWYTHER, Spccijicalion of ihe cUinents of stress. 



and therefore 



"'^4(^+/^:). ^tC, 



We may, from principles of continuity, determine that F 

 shall have such a value that 



?^+?>l + ?i^=0 (..), 



ex- dy- C7J 



so that the whole "condensation " is confined to F. We 

 may then re-write (9) in the form 



{m + «)v-^+ ?'V7<i = p{F+ pi) 



with two analogous equations (12). 



These equations may otherwise be written 



(jF- (ffi + fi)\/ -F+ ()^i - // V 7'i = 



and this form repeats itself for other coordinate systems. 

 They will be considered at length in the following Part. 



It has been part of the object of this investigation to 

 make stresses rather than displacements the chief object, 

 and to make use of displacements only as far as they 

 must necessarily be made use of 



6. Viscous forces. 



On the usual theory, the inclusion of viscous forces in 

 addition to elastic forces, only requires that in the equa- 

 tions throughout, ;/ should be replaced by 



{ !i-\- V— I and }n by ( ;// + ~v— ]• 

 \ dtj V 3 ctJ 



This alteration may be introduced in the final results, as 

 it will make no essential difference in the mode of pro- 

 cedure described. 



