MEMOIR OP THE LATE PROF. E. HODGKINSON^ F.R.S. 199 



beam is equal to the weight which would be necessary to 

 deflect the beam_, when placed on it at rest^ as much as the 

 travelling load deflects it. This position is purely hypo- 

 theticalj which may or may not give results approximating 

 to the truth, according to the dimension of the quantities 

 which constitute the fixed data of the problem. It is not 

 improbable that this reaction, the amount and direction of 

 which influence the motion of the moving weight over the 

 beam, is continually vibrating between a maximum amount 

 and zero, and that many times during the passage of the 

 weight over the beam the reaction may be nothing, and 

 therefore the moving load be abandoned to the influence of 

 its own gravity only. However this may be, it is certain 

 that its amount is never accurately measured by a formula 

 which produces an accelerating force of 



gd^ y 



S {2ax — x^Y 



as given by Prof. Willis. 



This subject has received considerable attention from 

 Mr. H. Cox, in a paper entitled " Dynamical Deflection 

 and Strain of Grirders,^' which is printed in the ' Civil 

 Engineer and Architect's JournaP for September 1848. 

 It appears that Mr. Cox has established, from the principle 

 of vis viva, that the moving body cannot in any case pro- 

 duce a deflection greater than double the central deflection, 

 the elasticity of the girders being supposed perfect. Prof. 

 Stokes, however, has shown that this conclusion of Mr. 

 Cox is not true — that, among the sources of labouring 

 force which can be employed in deflecting the girders, Mr. 

 Cox has omitted to consider the vis viva arising from the 

 horizontal motion of the body, and therefore has been led 

 to an inference which is not correct. The recorded ex- 

 perimental facts connected with the dynamical deflection 



