452 Archdeacon Pratt on the Undulation of an 



In the same manner it may be shown that at this same point 



•7^7 in the first parabola = — -7^ in the second ; 



that is, they have a common tangent at that point. 



4. The formula) thus deduced are ready for application to any 

 particular example. In the Hooghly Bridge b — 200 feet, 

 H = 33 feet 4 inches, 



/3= 



200 + 350 + 400 tons _ 19^ 

 200 + 350 tons 711* 



and the foregoing formulae give the following numerical results 

 for different positions of the moving load on the bridge : — 



Distance the train has passed along on the 

 roadway, or t. 



40 



feet. 



80 120 

 feet. feet. 



160 



feet. 



200 

 feet 



240 



feet. 



280 

 feet. 



320 

 feet. 



360 



feet. 



400 

 feet, 



Greatest depression of road- "| 

 way under the train, in \ 

 feet J 



Horizontal distance of this 1 

 depression J 



Greatest elevation of road- \ 

 way beyond the train . . . J 



Horizontal distance of this 1 



elevation from the left pier. J 



0'64 



33 

 0-28 

 271 



1-57 



56 

 097 

 275 



2-15 



73 



1-73 



279 



2-24 



86 

 2-24 



1-99 



97 

 2-42 



287 297 



1-54 



105 

 2-25 

 309 



1-01 



113 

 1-78 

 324 



0-53 



120 

 I'll 

 342 



0-16 



127 

 0-39 

 367 



Hence the greatest depression occurs nearly about the time 

 when the greatest elevation occurs, a little before it, that is, 

 when the train is nearly halfway over the span; the distance 

 between the lowest point of the roadway and the highest point 

 at that time, measured along the roadway, is about 200 feet, 

 or half the length of the span; and the greatest depression is 

 somewhat behind the middle point of the train. 



On the effect of the Iron Girder in checking the undulation of the 



Roadway. 



5. Suppose it possible that the undulation described and calcu- 

 lated in the last paragraph can take place in the roadway and 

 heave up the girder, as represented in the following diagram (fig.3). 

 More than half of the weight of the girder will be brought to 

 bear upon the point P where the girder touches the roadway 

 curve (which is the same as the curve into which the lowest ends 

 of the suspending ro^ds are thrown), unless this curve is of no 

 greater curvature at P than that of the girder by its own weight. 

 The length of the girder to be used in the Hooghly Bridge is 



