MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 197 



a dynamical deflection greater than the statical. The com- 

 putation of the effects of these component forces is attended 

 with great difficulty^ as they bring into full activity the 

 elastic forces of the beam and its inertia. The solution, 

 however, of this intricate problem, under certain restric- 

 tions, viz. when the weight of the beam is small com- 

 pared with the moving weight, and the deflection small 

 compared with the length of the beam, has been given by 

 Prof. Stokes. See ^ Transactions of the Cambridge Philo- 

 sophical Society,^ vol. viii. p. 707. 



The same distinguished analyst has given another solu- 

 tion to this problem when the mass of the moving weight 

 is neglected, or the eflPect of the weight reduced to a 

 travelling pressure. The exact solution of the problem 

 lies between these extreme cases, and is therefore circum- 

 scribed, by the labours of Prof. Stokes, in such a manner 

 that it can be approached to any degree of proximity re- 

 quired. The general dynamical equations from which the 

 dynamical deflection is computed, are so complex that a 

 complete solution of the problem, as exhibited in practice 

 by the moving weight being sustained by the beam in two 

 points, is not likely soon to be famished. Still, what has 

 been accomplished by Professors Willis and Stokes is suffi- 

 cient to show to practical engineers, that the startling 

 results of Sir Henry James and Capt. Galton, as obtained 

 at Portsmouth, and confirmed on the Ewell and Godstone 

 Bridges, are indicated by dynamical laws, the truth of 

 which cannot be controverted. If this be true — and there 

 can be little doubt of it — no engineer will be justified 

 in neglecting a just estimate of its efifects on the stability 

 of structures on the safety of which human life depends. 

 The Commissioners appointed to inquire into the applica- 

 tion of iron to railway structures, have rendered essential 

 service to the public by the discovery and experimental 

 development of the difierence between statical and dyna- 



