602 RICE ART. L 



+ [[[(v" - V') + ^(ci + C2)] hN + gV Sz^ 



r da da 1} ^ 



|_daJi 00)2 J) 



+ fadTDl = 0. 



Now we introduce the usual conditions, viz., 



f8Dr,y + fdDrjs = , 



fSDmi'y + f8Dmi"y + /5Dwi^ = , 



fbDrrii'^ + fWm2"y + fWm^s = Q , 



and in addition to these the further conditions that 



Sx', by', 8z', 8x", 8y", 8z" 



are arbitrary, and that 



8z^ = 8N cos 6 + ai5coi + a25w2 , 



where aiScoi + a25co2 is the tangential part of the displacement of 

 a point on the surface, ai and a2 being functions of coi and wj 

 and the angles between the vertical and the directions in the 

 surface defined by 6coi and 80)2. 



It follows from the conditions of equilibrium and these addi- 

 tional conditions that 



t = a, constant throughout the system, 



Ml' + 9^1 = Ml" + gzi" = Mi^ + gzi^, 

 M2' + gz2 = M2" + 9Z2" = M2^ + gzi^K 



^' _ ^' = n 

 dx' dx" "' 



^ _ ^' = n 

 dy' dy" "' 



dp' 



[605] 

 [617] 



dz' 

 dz" 



= - gy 



= — gy 



ft 



[612] 



