228 CONTINUOUS GIRDER. [CHAP. XIII. 



These numbers change signs by pairs alternately, and every 

 other one follows the law of the Clapeyronian numbers. In 

 fact those with the odd indices are those numbers, and the even 

 ones, commencing with 0, 1, 3, follow the same law. 



The above comprises all the formulae thus far given, in a 

 shape very convenient for reference. The reader who has fol- 

 lowed attentively our explanation of their use, needs nothing 

 more to solve the case of equal spans completely. The expres- 

 sions, however, for the reactions are unnecessary. As we have 

 seen from Art. 148, we need only the moments and shears at 

 any support in practical calculations. The practical formulae 

 necessary and sufficient for any case will be found in the next 

 Art. 



15O. Girder continuous over any Number of Level Sup- 

 ports ; Symmetrical with respect to tbe Centre, and with 

 two variable end Spans n I and p I on each side. 

 89.]* 



Moments at Supports : 



wheni<r+l, - A c '- r 



when m> r, M* = =* +*\ ' 



I p C B _I + 2 (n + p) 0, 



Shear at Supports loaded span, 



unloaded spans, 



_, M m 



D m == T~ 



For nniform load, 



7bur. Franklin Institute, March and April, 1876. 



