66S 



Mr. J. Rice on tlie Form assumed 



Apply the conditions for a minimum value once more to 

 this and we obtain by conditions (6) and (1) 



Cy ' * + <^ ^ = Js ( CXy+ ^ T ' *} 



=cxy + cxy+ -j-ixT.d) y, 



and ex x + ^ (xT) = ^ (>T£), 



J 



t. *. ^ (*T) = oc$ + 2 . xT + * 2 A (>T) + x y ^ (xT) ' 

 and ~(xT)=-cxx + ijxT + xi,~^T) + f^(xT)^ 



These become 



(using the relation |=^1+,; A)- 



•T-*=#[*|;(«T)-*^(«T)-»] 

 and «T.j f - = _i[^( it T)_ rf ^(.T)-«r2 



(10) 



Now let i/r be the angle between the tangent to the curve 

 at P and OX, and Jet p be radius of curvature at P 



estimated as positive in the direction indicated. 



Then 



cc = cos ^r, 

 y = sin yjr, 



sin -dr 



x = j- i 



P 



