504 



Profs. John Perry and W. E. Ayrton. [Dec. 11, 



At any point in the first span 



M=l-6aj 2 -194135aj. 

 At any point in the second span 



M=25173 + r95a3 2 -585a?, 

 and the diagram for half the bridge is OBB f B"B"\ 



3. The Boiling Load covering only the Middle Span. 

 We find that M 1 =M 2 =22096 ton feet. 



M =M 3 =0. 



At any point of the first span 



At any point of the second span 



M=22096 + l'95a3 2 -585a?, 

 and the diagram for half the bridge is OCC C" O" . 



4. The Rolling Load covering the ends Spans only. 

 We find that M!=M 2 =14788 ton feet, 



Mo=M s =0. 

 At any point in the first span 



M=l-6aj 2 -- 246-06*. 

 At any point in the second span 



M=14788- 0'95» 8 -285aj. 



and the diagram for half the bridge^is shown in ODD'D"D'" '. 



5. OFF'F"F"' is the diagram for half the bridge when only the 

 first span is covered with the rolling load. 



6. OGG'G"G"' is the diagram for half the bridge when only the 

 first two spans are covered with the rolling load. 



As the depth is supposed to be constant, the moment of inertia of 

 each section is now supposed to be nearly proportional to the greatest 

 bending moment which is ever found at that section during any of the 

 above distributions of load, and the ordinafces of the diagram AEE, 

 &c, show the values which have been assumed for the moment of 

 inertia of each section, these values being either 1, 2, 3, 4, 5, 6, or 7. 

 If the girders had not been of constant depth, so that the moment of 

 inertia might have been changed by altering the height of the girder, 

 as well as the areas of the booms, we should have proceeded in a 

 slightly different way to get the diagram of I. As it was, our students 



