246 



satisfies the equation EF y"" -\- ki/ = — ky„. Using the relation 

 — EI ny„"" = — ky„, we find the condition : 



kt/„ 



whence: 



V h kvy„ = — %„ 



ft 



— f* 



f' + 1 

 We therefore can obtain the deflexion 

 H 



adding 



1 + 



fi + 1 

 — ft 



O + rr.)- 



j/n to the sura of tiie curves y, 

 1 



y of the beam by 

 //, . . . yn, or by adding 



//„ to tlie sum y, + Vi + ■ ■ ■ + .V"- 



1 + nJ "'■ 1 + fi' 



Thus we can stop the drawing of curves, as soon as two conse- 

 cutive ones y„ and y„_|_i are found, the oidinates of which are 

 proportional. 



Tiiough — generally — the above mentioned proportionality only 



appears exactly after an infinite number of iterations, it nevertheless 



will be approximately observed tolerably soon. Neglecting in such 



a case that part of the last found loading diagram which troubles 



the proportionality between its ordinates and those of the foregoing 



diagram, we can use the preceding remark, provided that 1° the 



neglected load diagram be insignificant, and 2" it gives no rise to 



following load diagrams which grow larger and larger. 



kl* 

 The second condition is satisfied when -=-t.<^ 14600. 



El 



The justification of this latter statement can be given most 



naturally by the aid of the deductionfi, given by Mr. Droste. We 



therefore refer to his paper. 



