Manchester Memoirs, Vol. Ivi. (19 12), No. 10. 5 



The solution is 



P. = ^eo_ ^fl'-^, ^9, 



^'- ~ dydz dz- 



^ _ d-Q.i _ d-^., de, 



^'~ Zv^ ^dxdz ^^^' 



^/a- «a'( y dy- 



^^ _ d'^x ^'4^, ^^3 _ ^-9i 



</a'- ^/at/)' dxdz dydz 



"T" ;_ ^ ^ r ~ -f- L 



^,:v^y </av/,': dydz dz' 



The complete solution finally is 



F=F, + F^ + F., etc., 



.S = ,Si + <5'o, etc., from (3) and (5). 



We have now obtained an explicit statement for the 

 elements of stress, applicable to all substances for which 

 these elements are continuous functions of the coordinates. 

 They may be taken to apply to most materials for 

 construction, and to apply fairly well to earth pressures 

 on a retaining wall, and less definitely to the pressures in 

 a corn bin or bunker or in a quicksand, but for different 

 reasons. 



Avoiding such special cases, we have to consider 

 (i) cases where Hooke's Law of connection between stress 

 and strain holds good, (2) cases where the elastic limit is 

 exceeded, (3) cases where a viscous flow of the material 

 is set up, and (4) the conditions for rupture. 



* In a paper by Sir G. B. Airy, published as a Report by the British 

 Association (1862, patje 82), the value of a general solution is minimised. 

 But giving the fullest value to that investigation, the solution there proposed 

 is covered if the ©-functions alone in (5) are retained, and the ^-functions 

 ignored. 



