CHAP. XH.] METHODS COMBINED. 185 



R--T3 10 9^ 2 2n 8 -2rc + 5K, 2 2n#l 



B ~ H L J 



pf 2 "I 



~ H L J 



pf 1 



R D =g|^-n<J 



These reactions add up, as they should, equal to P. 



In practical cases of pivot spans, we have only to consider the 

 the outer spans ; as a load in the middle span B C = I rests 

 directly upon the turn-table. The above formulae are then all 

 we need. For a load in the right end span the same formulae 

 hold good, only remembering to put now R D in place of R^ 

 R c in place of R B , R B in place of R c , and R A in place of R D . 



If, however, neglecting the particular case of pivot spans, we 

 suppose the middle span B C = I loaded, we have a being 



now the distance of P from B, and k being now -j instead 



of 9, as above, H remaining the same. 

 nu 



%d. Load in B C. 



p r i 



R A =-^T| (S+4ri) /&+6 (n+1) %?(3 + 2n) #* I 

 ntl_ J 



I nK+tf+tei-Grf-fri*) JMS + lSra+Bn^JP+H Tf I 

 I (2n+6n*+4n?) k+(3+9n+6n*) #-H # I 

 J -2n T&-Z ^+(3 + 27i) I 



These reactions should also add up to P, as is the case. The 

 number n may be taken at pleasure, so that the end spans may 

 be as much larger or less than the centre spans as is desired. 



H, P and the quantities in the parentheses, it will be observed, 

 are for any given case, constants which may be determined and 

 inserted once for all. 



We have, then, only to insert the values of k for different 

 positions of the load P. Thus the equations for any particular 

 case are very simple and easy of application. 



