Alexani>i;u — Maxiimim Bending -moments on Short Girders. 29 



Also the horizontal distance of the black spot from the middle of the span 

 measures 2-52, which increased in the ratio 50 to 42 brings it to 3 feet. 



In this way the shortest span to accommodate any group of wheels may be 

 interpolated. It will require in general two trials, for at the first trial we 

 may find when the deviation of the point of max. bending from the middle 

 point of the span is measured, that placing the ruling-wheel there sets an end 

 wheel off the span altogether. We have then to slightly increase the span 

 and proceed again. 



Span. Moment. Displacement. Rate of Load. 



Feet. Foot -tons. Feet. Tons per foot. 



20 74-4 -734 1-495 



50 343-56 3 1-115 



Second Graphical Method with Circulak Arcs only. 



We have defined a parabolic right segment of modulus unity as having 

 the height at any point numerically equal to the product of the two segments 



into which the point divides the base. And we have also pointed out that it 

 represents the maximum bending-moments for the transit of a single rolling- 

 load, the height of the segment being made to scale in foot-tons an amount 

 equal to one-fourth the product of the load and the span. Now, by 

 Euclid II, 14, a semicircle will serve as a diagram of the square roots of 

 the maximum bending-moments in the same case to a vertical scale upon 

 which the height of the crown of the semicircle shall measure the square root 

 of the above product. 



If we suppose every vertical height on fig. 2 to be replaced by a height 

 equal numerically to its square root, we will have the diagram fig. 6, all the 

 parabolas becoming circular ares with centres at the points Si, S^, &e., as shown 

 on fig. 6, each arc beginning on the vertical line through the junction of the 



