(1) 



522 Dr. J. Prescott on the Torsion of 



displacements parallel to the axes o£ x and y of the particle 

 originally at (x, y, z), 



u = — Tzy | 



V = TZX ) 



Fig. 1. 



> 5 2 



The displacement w is unknown but is assumed to be a 

 function of x and y only. This assumption means only that 

 each similar element of rod has the same strains. 

 If n is the modulus of rigidity the shear strains are 



= *% +n ) w 



= n \W e - T V ( 3 ) 



It is next shown that there is a function yjr of x and y 

 such that 



'by 3*' ••••••• W 



d* By' W 



whence S x = — n (^^ — tx ), (6) 



