Manchestei Memoirs, J'o/. iviii. (1914), No.l 

 and 



— {«(t>.. + t^J} 



as identical with 



7/, 



~je., + ej, etc (/') 



we treat P' as identical with t\ etc {c) 



and in the integration of the resulting equations the 

 multipliers 111 and n are treated as constants. 



Since the relative variations of p and vi arid n may 

 reasonabl}' be considered as possibl)' greater than the ratio 



-r : r, the terms arising from these variations should be 



considered before the results of a further expansion of the 

 displacement should be considered in the mathematical 

 expressions. 



5. If we now equate P' and /'', Q' and Q, R' and R, 

 we readily obtain 



/ r- c- c^\ /?-e, c'e.2 c-0..\ 



\(l.v- dy- cz- J ' \ca- d)'- Cz^ / ' ' 



and two analogous equations (9). 



Before making any modifications in these equations, 

 it is well to review the analytical character of the assump- 

 tions that have been employed. 



Neither 



cB ?e, CO., 



dx <!j oz 



nor 



s=^s', r=r\ u=2", 



are relations which would preserve the same analytical 

 form on change of the directions of the co-ordinate axes. 

 In the resulting equations the outstanding characteristic 

 is that ,oB,, oG,, f>Q. have the character of normal stresses. 

 Having made these remarks, I return to (2) and put 



o =y'>^i,, o, = /'>/',, a. -/'"+//, , . ■ (10), 



