10 Sir G. Greenhill 



on 



The area displaced between the water-line and profile of 

 the ice is then 



£^fc-j (l-^oo.,.), .... (6) 



and this area up to infinity is -. 



The ice is deflected into two cylindrical surfaces, symme- 

 trical on each side of ; and if the line-load over is W 



per unit length, it is buoyed up by the displacement — of 

 water; and 



q 2 p /I. .V 2pe\kJ 



»(M 



The bending moment (B.M.) of the ice is a maximum 

 under 0, and is 



EI S - "*iW - s *V* - J f - J ({ ufw. (8) 



The maximum skin stress of the ice has then a tension or 

 pressure length h } such that 



^phe 2 = max. B.M. =-^pke z aq\ .... (9) 



The shearing force F at a distance # is then given by 

 2F = W-^(l-<r^cos ^) = ^V^cos^ 



as a verification. 



11. A central line-load W at the middle of a plank or 

 beam, of limited length 21, floating on water, will give a 

 downward deflexion tj such that, from x to /, 



Eig+,Jjy-*y<te'=o (i) 



Elg-pJW =0, .... (2) 



Elg+W =0, . . . . (3) 



