MEMOIR OF EATON IIODGKINSON. 225 



tliey liacl been subject. From these unexpected results there is no appeal, how- 

 ever mucli they may be at variance with the impressions of the most cfifted 

 engineers. It now remains to connect these results with well-established 

 mechanical laws, a problem of great difficulty, the solution of which has been 

 accomplished by the labors of Professor Willis and Professor Stokes. (See 

 " Preliminary Essav on the Effects produced bv causing Weights to travel over 

 Elastic Bars/' by the Rev. Robert Willis, F. R. S., &c.) 



I\v neglecting the inertia of the bar, as being small in relation to the moving 

 weight. Professor Stokes has shown that — 



D=s-i-i/vsy 



D=centval dynamical deflection of the bar, produced by the weight moving 

 at the velocity V. 



S=central statical deflection produced by the same weight. 

 Z:=the length of the bar in feet. 

 Hence the dynamical deflection is double of the statical, when the velocity of 

 the moving weight is -/^ times the length of the bar between the supports. 



These results were not readily accepted by practical men, as they had been 

 accustomed to connect high velocities of the train with small deflections of the 

 bridge over which it passed. 



The late Robert Stephenson, in his evidence before the commissioners, states 

 that ho had seen the deflections less as the train passed over than when it was 

 lYi repose. From the observations which he had made he felt quite satisfled upon 

 the point, that no revision of the practical rules respecting the deflection of the 

 bridges was necessary. ''You will sometimes find," he adds, ''an exceptional 

 case occurs, if the engine happen to jump on the springs, which may, of course, 

 accidentally occur : but if it be a mere question of velocity I do not think it 

 increases the strain upon the girder. There ma}^ be a lateral strain backwards 

 and forwards when the whole train comes into pla}' and causes a jerk." 



^Ir. Locke, after making many experiments with locomotives passing over 

 bridges, arrives at the conclusion that there is but little diflerence in the deflec- 

 tion between high velocities and low. '' If there be," he remarks, " three or 

 four bad rails or joints upon the top of a bridge there is far more effect produced 

 upon the bridge. A bad joint is more serious than 10 or 12 miles' increase or 

 diminution of velocity." 



Mr. Ilawkshaw's opinion is, that there would l)e a greater deflection in a bridge 

 by running a weight over it than by allowing the same weight to rest upon it, 

 because there is always an iiTegnlarity in the surface of the rails, and the force 

 of impact is thereby brought into activity. W. H. Barlow stood under a wooden 

 viaduct while a heavy goods train passed over it. There was a slight deflection 

 produced by the heavy train, but the express, with a much lighter engine, and 

 moving at a greater speed, ])roduced a much worse effect. It seemed to pro- 

 duce a wave through the bridge, as it ought to do from the ordinary principles 

 of dynamics. This load was passing over the bridge in a very few second^:, and 

 therefore the total deflection is jierformed by the Aveight in a few seconds; and 

 it therefore becomes a kind of blow — the descent of a heavy weight — and the 

 bridge has not time to accommodate itself to the deflections required of it. These 

 deflections are propagated throughout the structure, and may prove wicecdingly 

 dangerous and disagreeable. 



]\ir. Rastrick always considered that when a weight passed rapidly over a 

 structure, tliere would be less deflection than if it were stationary. lie takes the 

 exanij)le, for comparison, of a man skating upon ice, and states that if he remain 

 stationary for a length of time he would soon go through the ice ; but he may 

 Bkate over it without any danger of going through, because the ice has no timo 

 to break. 



15 s 



