Unstiffened Roadway in a Suspension Bridge. 455 



part depressed, then, taking the curve to be part of a circle, 



radius of curvature = —7- ; and - = 1 + — -5— A ; 



7, 



1_ ^ 



2^ 2 



The value of Jc varies as n 2 , as already stated, and equals 0- 7 foot 

 when W = 200 feet : also # = 32 feet, and v = 88 feet for a velocity 

 of 60 miles an hour ; hence the denominator of h 



= 1-0-0021 



(-Y 



and the increase of h above k is therefore evanescent even for a 

 velocity of 60 miles an hour. 



If any part of the rail, from accident or bad structure, is more 

 curved than I have supposed it to be, the radius of curvature of 

 that part will be smaller, and the effect of centrifugal force pro- 

 portionately greater. 



(2) Next suppose that there is at some point of the rail a 

 sudden change in the curvature, and that the tangents to the 

 two parts of the curve at that point make a small angle with 

 each other. The effect of this will be, that every time the wheels 

 of the train come to that point an impulse or blow will be given 

 to the roadway. The tendency of this blow will be suddenly to 

 separate the roadway curve (which is the same as the curve in 

 which the lowest points of the suspending rods lie) from the 

 suspended girder, since the girder is not attached to the sus- 

 pending rods. Thus the blow will bring into sudden action 

 the downward pressure of the girder, which will consequently 

 stifle the effect of the blow, and not suffer the roadway to be 

 thrown into a greater undulation than the girder itself can 

 assume under its own weight, as already described. No doubt 

 a molecular tremor will run along the roadway, girder, and 

 chain occasioned by the blow, but nothing more. 



I will, however, consider what the effect would be if the girder, 

 instead of lying unattached in the loops of the suspending rods, 

 were attached to the roadway. 



I must premise that if M be the mass of the girder, and a 

 vertical blow be given to it at any point between its two ends on 

 which it is supported, so as to cause that point to descend with a 

 velocity w, then § Mw is the whole momentum communicated to 

 the beam. For let V and b n be the distances of the point of im- 

 pulse from the left-hand and right-hand piers, b l + b ,t =2b; 

 then the velocity communicated to a point at a horizontal di- 



