17 



The table given at the end of the paper has been formed 

 in the manner indicated above, and gives corresponding values 

 of 1/2 a and li/l. Values intermediate to those given may be 

 obtained quite correctly, to the given number of decimal places, 

 by interpolation. 



Case 2. — Pin-jointed Column with Eccenteic Loading. 



In this case, if A B (fig. 1) denotes 



the original axis of the column, the com- 



\fi pressive force P is assumed to act along 



a line parallel to A B at a distance / 



from it. 



Let the deflection at the centre 

 be h. 



Take the origin of co-ordinates at 

 0, the centre of the bent column. 

 Let e — f+h. 



Then the fundamental equation, with- 

 out any approximations, is 

 dip 

 E I p — 

 dy 

 3 = P fe — y J, where p 



(l+p 2 ) ^ 



dy 



denotes — 



dx 



EI 



Write — a 2 and integrate 



P 



-,=y 2 - 2ey + 2a 2 = (e-y) 2 -e 2 + 2a 2 



(l + p 2 ) 

 from which 



since p = o when y = o. 



4a 4 -^ 2 -2 ey + 2a 2 ) 2 



l r 



fy 2 -2ey + 2a 2 ) 2 

 Now write e — y~e cos <f> 



.'. d y — e sin <£ d <£ 



2 a 2 

 .'. x = 2 a 2 — e 2 sin 2 </> 



(i+p 8 ) 



