lO Wilson and Weston, Torpedo-Boat Destroyers. 



A particular solution is 



z^ZTsin— (^c + t//) (6) 



A. 



where 



H= . when \ = L 



One form of complementary function for (5) which is 

 well-known, may be expressed as follows : — 



2 = cos— T-(/I/iSin;/.T + M.,Q.o%nx + N,sinh;^v + N„cosh;/.T) 

 + sin — ^(il/j'sin;/.v + A/'cosfi v + iV/sinhwa- + JV^^coshnx) (7) 



where M^, M„, &c., are constants to be determined by the 

 necessary conditions, viz. : — 



(a) Stress is zero at the ends ; 



(/3) Shearing force is zero at the ends ; 

 These require 



-— , = o for A- = + - , :i-3 = o for x = ± -, 

 dx^ — 2' dx 2 



from which 



MXo% - yv2 cosh - = H-rz-^. 

 2 2 2 Drr^ 



J/, sin— = N. sinh— , 

 » 2 ' 2 



,, . nl .J. . ,nl 

 J/,sm— = iv.sinh— , 



'2*2 



nl ^^ ,nl 



w nl ^r x.'^l ^-8^" 



yJ/,cos Tv.cosh— = — Tj^-, 



1 2 2 n 1^ 



i/jsin— = - A^^sinh— , 

 2 " 2 



vJ/, cos- =vV, cosh—, 



i/jSin— = -7V/sinh-. 

 2 2 



