1,,J RECIPROCAL DIAGRAMS IN SPACE. 



The com|>m>nt8 of stress as thus defined will be 



/' ~&F\ d'FJF '_ <fF 





(d'FJF '_ <fF A 

 ~ '/' '/:</*!/' 



\ 



/ 

 \ 



lf ' F d * F d ' F \ 

 jE2x1xdjl dJdydz)' Pa ~ \dxdy ,ly,lz dfdzdx)' 



y 



This is a more complete, though not a perfectly general, representation of 

 a state of stress ; but as the functions are not linear, it is difficult of application. 



If however we confine ourselves to problems in two dimensions, either 

 method leads to the expression of the three components of stress in terms of 

 the function inti-oduced by the Astronomer- Royal*. 



d>F 



dF //' 



Here * = dx' y= dy ' 



and if ab and a^8 be corresponding lines, the whole stress across the lin 

 is perpendicular to aft and equal to Paf3. 



* "On Strains in the Interior of Beams." Phil. Tram. 1863. 



