-Tx 



64 Mr. J. M. Iieppel on the Theory of Continuous Beams. 

 there were any number of particular values of x to be considered, as a . b 

 j, Jc, I, the corresponding values of ^ being e v e 2 , &c, t n . lt e n , it 

 might be written 



e i(Fi(«)+F/(*)(*-«)) 



+ «£(*!.(*) + Fi'(«X» - *)) ~ ( P,W + F 2 '(«)(*- «))] 



+ « 3 [(FaW + F 8 '(^-c)) - (F 8 (6) + F 3 (b)(x- b))~] 

 + &c. 



+ ew[F.W-<F il (A) + F.(*)(*-*))] ; 



Hn_(24), y = 0; 



" e^F^ + F^-a)] 



+ e 2 [(F 2 (5) + F,'(4XZ - h )) - (F 2 («) + F»(/-«))] 

 + , 3 [(F 3 (c) + F 3 '(c)(Z-c)) - (F 3 (6) + F' 3 (*)<7-6))] 

 + &c. 



_y 



If, now, the formation of the functions F^a), F/(a) &c. be examined, it is 

 evident that this equation may be written 



T=A<£ 1 + B<£ 2 + C, 



where A and B are known functions of a, b, c, &c, and e 1} e 2 , e 3 , &c, and C 

 is a known function of the same, and fx v ja 2 , [i 3 , &c. 



If the adjacent span to the left be now considered, it is evident that a 

 precisely similar equation may be obtained, which may be written 



T'sA'fc + B'^ + C; 



adding these, and writing t for T + T', which is known as it is the tangent 

 of the small angle which the neutral lines of the two spans would make at 

 the point 1 if relieved from all load, 



t= (A + A')fc + B^> 2 + B> + C + C, 

 which may be written 



%(<t»o> 0i»0 2 ) = O; 

 similarly for the other bearing points in succession, 



3 » 4 )=O, &c, 



where the number of equations is two less than that of the quantities 



