yianchester Memoirs^ Vol. Ivii. (191 3), .V^. 5. 3 



In a foot note on page 5 of the paper referred to, I 

 stated that my solution differed to this extent from a 

 sohition previously given by Sir G. B. Airy, by the intro- 

 duction of the ^- functions. I must now withdraw the 

 implication that Airy's solution is not as general as that 

 which I then proposed. 



We may, however, proceed further with the alteration 

 in form of the solutions. We ma}'^ select any three of 

 the six functions to equate to three elements of strain, 

 provided that we are able to deduce values of the other 

 three functions from the three elements of strain selected, 

 and then we may omit as before the three selected 

 functions from the expressions for P, Q, R, S, T, U. 



It seems that the only components of strain to be 

 excluded are such combinations as 



du dv dv du 

 Jx' dy' dx'^d}' 



which do not introduce w, and will not serve for the 

 purpose required. 



The sets of functions therefore which may not be 

 omitted from the values of P,Q,R are 9i, 63, and ^, ; 

 9.., Oi, and ^., ; 9,, 93, and ^. ; conditions that are other- 

 wise seen to be necessary. 



The results arrived at apply also to the cases of 

 solution in cylindrical- and spherical-polar co-ordin- 

 ates, and as the expressions in these cases are longer, 

 the convenience of effecting a reduction in the number 

 of functions will be the greater. 



The question of the generality of the proposed solution 

 naturally arises, and is not without mathematical interest. 

 It appears that the solution is quite general although the 

 six arbitrary functions can, from the form in which they 

 appear, be so grouped as to be reduced to three. 



