J\T(Vic/iestei' Mevioirs, V^ol. Iviii. (19 14), No. 5. 13 



of the first differential coefficients of the displacement, 



we find 



'civ f I cv'^ 



(vu CU 

 ' \c,o rx 



fvv rii 



(20), 



as the only possible relation, and it is subject to the tests 

 which may be made as to the magnitude or existence 

 of /'. 



The previous paragraphs have given the general 

 outlines of the treatment of the question now proposed, 

 and I shall only indicate the lines of adaptation. 



In (17) write 8^ = F+^„ etc., and 



o^„ M',, ?/(/ 

 dy cz rx ' 



so that S / , , '\ , lo^\ 



;«<(=-((/) + /(, f /I, ), etc., . . . . (,2i;. 



The specifications of stresses previously given will then 

 apply to (19) if we replace F+ij.^ by F+fL^ + fx^ as far as 

 the terms in which space-differentiation is concerned, and 

 if we retain /^+/x, in the terms in which time-differentia- 

 tion is to be performed. The relations between ,ui, /U,, //j 

 and /x', //'., lix., are contained in (18) and (20), and it follows 

 that 



P^. = /^ft^-^) (^2)- 



\ <y cz/ 



Hence »i/ -^ ''' / ^ ' •\ ^\r 



7/ cy< z ■■ - ■ - 



and therefore that 



If k were a constant of about the magnitude of ;/, the 



