1879.] On Most General Problems in Continuous Beams. 505 



found it advisable to use six thicknesses of plates in the booms at the 

 middle of the centre span, and they therefore made I there equal to 6. 



It is unnecessary to enter fully into the details of the complete 

 drawings exhibited. On each curve was written the scale to which it 

 was drawn. Employing the methods previously described, a few 

 hours will be sufficient for making all the necessary calculations. 



The results obtained for the new distribution of J were as follows : — 



In 1st and 3rd span. 



With rolling load Without rolling load 



m Y = 63999 ton feet, m x = 24000 ton feet, 



^=21,030,000, ^=8,462,223, 

 F^l^OOO^OO F 1= 488,910,000. 



^=1486, 

 ^=185040, 

 ^=107540, 

 £=9,191,200. 



In middle span. 



Without rolling load 



7^=85500 ton feet, 

 0!= 61,975,000, 

 F 1 =3,938,100,000. 



With rolling load 



7^=175500 ton feet, 

 ^=122,817,000, 

 1*!= 7,672,800,000, 



^=1988, 

 ny= 299310, 

 ^=310180, • 

 2l =24,048,500. 



Just in the same way the necessary summations may be made for 

 the most general cases, the moment of inertia and the load varying in 

 .any way whatever from point to point in a span. 



2 m 2 



