6G 



Mr Greenhill, On height consistent with stability. [Feb. 7, 



Take the origin at the top of the pole in its vertical position 

 and the axis Ox directed vertically downwards: 



-y 



then if APB be the central line of the pole, supposed to be slightly 



1 dp . du 



£ where p = -^, 



curved under its own weight, we may put 



p CLOG 



and therefore the bending moment at P 



dp 



= EAtf 



dx 



This must be equated to the moment of the weight of PB about P, 

 which 



-wAj {y-y)dx, 

 Jo 



x, y' denoting the co-ordinates of any point Q between B and P, 

 and w the density of the substance in pounds to the cubic inch. 



Therefore the differential equation of the central line APB is 

 EAk^ x = wA\ X {y'-y)dx, 



or, differentiating with respect to x, 



\ pdx 



Jo 



= — io A xp, 



EAJc 2 ^ = -u 



or 





.(i). 



