MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 195 



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 sta- 

 bility of structures over which thousands of people are being 

 continually conveyed with rapid velocities. 



Perhaps the simplest method to gain tbe 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 produced by moving tbe weight 

 to a point very near to its original position. It is evident 

 that the weight, being at the lowest point of the beam, can- 

 not 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 moveable 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 

 oscillations, the number and amplitude of which will de- 



pend upon the moving forces and inertia of the beam. Let 



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