238 



Certainly it will be possible, — under favourable conditions — 

 to find in this way teclinical sufficient accordance between the 

 supposed curve and the one, derivated from it; but generally the 

 convergency of the described process is uncertain. 



In the following paper a convergent process will be given. 



2. The equation 



Ely"" + ky = q 

 is transformed in 



Putting y""z=<f(x) it becomes: 



X 



(f {x) + k' i If {x) dx* = 5' + Ax' -f Bx^ ^ Cx ^ 

 

 or, using the well-known relation 



I '/ (*•) dx' = \ — ^y— (f' (') ds 



D 







z 



ff (x) + k' 1 -!: <f (s) ds = q ^ Ax* + Bx^ + Cx + D. 





 A, B, C and D are constants of integration, which enable us to 

 satisfy the following conditions: 

 V. f = 0, y"' = at ,(; = 0. 

 2'. y" — 0, y'" = at .v — I. 

 The former conditions imply, as is seen from the relation 



Ax' + Bx' + Cx + D 

 y 



= I (p («) dx* 



k' 

 



that the coefficients A and B are zero. The coefficients C and D 

 are determinated by the latter conditions. 



3. According to Volterra the solution of the integralequation 



X 



<p {x) + ^' P^^ (P {')d' = q' + Cx + D 



