212 Dr. J. Prescott on the 



Finally, 



w 



m H2=s-l'167~, 



or Fl 2 W 

 — =4-012- 1-167^- 



W 



= 4-012 jl-O-291-jr-j 



{1-0-291^} 



Therefore p = 4-012 ^ EnCK ^ n^W" 



Z 2 

 W 



whence 



= P Jl- . 2 91p-} 



= P -0-291W, (138) 



4-012 



P + 0-291W = P =^p v'EnCK (139) 



The above is the equation that holds jnst when instability 

 occurs provided W is very small compared with P. 

 Now the buckling load when P is zero is, by Case 6, 



Therefore the equation 



P/ 2 W7 2 / ^ rw „ AM 



¥0T2 + 12*6 =VE,CK . . . (140) 



is true in two cases : 



(1) when P =0, 



(2) when W = 0. 

 Moreover, this last equation can be written 



P + 0-312 W = P , (141) 



which does not differ much .from (139). It seems very 

 probable then that equation (140) will be a good one for 

 all values of the ratio of W to P. 



If the ratio between W and P is fixed it is possible to find 

 the actual values of these loads when buckling occurs, but 

 the problem is very awkward unless one of the loads is 

 small compared with the other. It is worth while, however, 

 to work out the case where P is small compared with W, so 

 as to see if equation (140) remains approximately true in 

 one more case. This we will now do. 



