lO Wilson, Failure of certain Cast Steel Dies. 



(4) p-t^rf^r^^o. 



dr dx 



dr dr 

 /A\ . X /'^''' " divx dil 



<" '=\;^:•^^.^^)+^'';■ 



/ox ^t^^^ ^' div\ dii 



(9) ^=K^>^J- 



Let 



2^(3X+2jLt) 2/,(3A + 2;u) 



then the following values satisfy the above equations : — 



10) / = - - A ^-^ + J Ax + ^.rlog- 



a r~ a- b a ^r^ 



« + ^ I , , , , 2(a + b), . 



2 ^'^^ 



(11) / = ^4 ^ + ^;t: + . Jx[ log- + I ) 



^ ^ « r- a-b a \ ^r, / 



« + ^ I , , T , 2(a + ^), , 



(12) '=^ \q = <^. 



and eive 



(13) // = ^^ '-^ 'A + Axr\og~ + {a + b)Axr 



a r 



(a + b)'^ I . , a--b~ , . 



' ^— ^,.(PA- + />2) + —^ 2A(y,.V + ya). 



