Manchester Memoirs, Vol. hi. (191 2), No. 10. il 



the solution. The simplifications will not appear until 

 a particular application is attempted, when the terms will 

 fall into groups. The terms of the second order in the 

 solution can be written down, and the other terms can be 

 deduced by substitution in the stress equations. The 

 result is as follows (12) : 



Sec Table A for equations (12). 



These lead at once to the expressions connecting the 

 strains corresponding with (6). 



This paper has only dealt with the preparation of an 

 instrument for use on simple examples, but I feel sure 

 that it is well to have these cases treated in full. No 

 doubt, for completion, the case of curvilinear coordinates 

 should have been included, but this offers no considerable 

 difficulty, and may well be deferred till the question of 

 its use in Geostatics arises. 



Although the paper contains no illustrative applica- 

 tions, I may perhaps be allowed to state that I have taken 

 some steps to satisfy myself that the method proposed 

 appears to be of practicable application to the theory of 

 the cylindrical test-piece in Mechanical Engineering and 

 to the theory of arches and domes in Civil Engineering. 



Although I shall not consider any precise problem, 

 each of which will require its special method of final 

 treatment for surface-tractions, etc., I wish to show some 

 grounds for the belief which I have expressed that the 

 method of this paper lends itself to the treatment of 

 particular cases. 



For this purpose 1 have selected the case of a body 

 symmetrical about an axis, and subject to surface- 

 tractions only, also symmetrical about that axis. That is. 



