226 MEMOIR OF EATON HODGKINSON. 



Mr. Brunei's impression was that where the rails are perfect the deflection is, 

 as it ought to be, less with a weight passing rapidlj^ over it than when it rests 

 upon it; '4iut the experiment is so diflicult to make, from the number of inter- 

 fering causes, that perhaps my impression is still only prejudice rather than 

 positive information." 



Mr, Cubitt, engineer of the Great Northem railway, could perceive no differ- 

 ence in the deflection of a large girder between the weight being stationary upon 

 it and passing over it at a great speed. The experiment was made upon a girder 

 47 feet span, and a heavy locomotive engine, the deflection being a tenth of 

 an inch 



The opinion of Mr. Charles Fox, engineer, is very decided on this point. He 

 states positively that, if the rails have been carefully laid over the portion of the 

 line resting upon the bridge, less deflection is caused in the girder by a load 

 passing at a high speed than at a low one, and that there is less deflection with 

 any rate of speed than when the weight is stationary. " I imagine this arises, 

 in a great measure, from the short time there is to overcome the inertia of the 

 mass ; of course the higher the velocity the less time is expended in the train 

 passing over the bridge." 



My. Glynn, of Butterly Iron Works, Derbyshire, thinks that, if the strength 

 of the beam were not great in proportion to the stress it had to sustain, the 

 weight, being stationary upon it, would tend to deflect it permanently more than 

 a weight passing rapidly over it. " This opinion is not formed from experience; 

 experiments on the subject would be very desirable." 



This is the testimony, conflicting as it is, of the highest authorities in the 

 .engineering profession respecting a most important part of their practice, viz : 

 the permanent stability of structures over which thousands of people are being 

 continually conve3'ed with rapid velocities. 



Perhaps ths simplest method to gain the conviction that the dynamical deflection 

 of a structure is different from its statical deflection is to place a weight, capable 

 of motion, and producing a sensible deflection, on the middle of a horizontal 

 ' flexible beam, between fixed supports. Let us now inquire what effect is pro- 

 duced by moving the weight to a point very near to its original position. It is 

 evident that the weight, being at the lowest point of the beam, cannot move 

 from this position without the application of a force. The effect of this force upon 

 the moving weight and flexible beam will, of course, depend upon its magnitude 

 and direction. If the direction of the force be vertical, whatever may be its 

 magnitude, it will not produce any horizontal motion in the moving weight. 

 If the direction of the force, however, is not vertical, the case is very different. 



The movable weight, abandoned to the influence of gravity and the reaction 

 of the beam, will have a complex, vertical, and horizontal motion, while the 

 flexible beam will be, from the same cause, put into a state of periodical oscilla- 

 tions, the number and amplitude of which will depend upon the moving forces 



and inertia of the beam. Let A B be the fixed supports of the beam, A D Bits 

 position after the weight has been placed upon it. If the point E in the beam 

 is sufficiently near to D, then the line D E may be considered straight ; produce 

 D E to meet the horizontal line A B in F, and put the angle D F B = ^. Let 

 the force H, applied to move the weight from D to E upon the inclined plane 

 D E, be in the direction of D E. It is evident that the force H can be decomposed 

 into two, viz., II sin acting vertically ;ap\\"ards, and H cos acting horizontally 



