PRESIDENTIAL ADDRESS. 475 



tion; (6) in which the perpendicular to the straight line parallel to the wave-surface 

 through the point of contact is the line of the resultant of the water- pressures acting 

 on the vessel. 



(3) The resistance to rolling is obtained by (a) electro-magnets, the current to 

 which is generated by the motion of the model, (6) secondary electro- magnet, the current 

 for which is in the first magnet, (a) represents the resistance due to the angular 

 velocity, (6) represents the square of that velocity. 



The variations in the lengths of the cranks and the speed of revolution give the 

 variation in the wave-form assumed. The variation in the electric current by resist- 

 ances in the circuit gives the variation in the resistances to rolling of the ship. For 

 instance, the current necessary to represent the resistance of a ship with bilge-keels 

 is very different from that for one without. 



It is hoped that sufficient has been said to call attention to the possibility of 

 extended study of the rolling of ships at sea, so that some valuable work may be 

 done in this important subject. 



The following Papers were then read : — 



1. The Origin and Production of Corrugation of Tramway Rails. 1 

 By W. Wobby Beaumont, M.Inst.C.E. 



The explanation of the presentation of this paper on a subject previously dis- 

 cussed in a brief paper by the author before the Association in 1907 is the fact 

 that, although the serious increase of corrugation since that date has caused much 

 trouble, expense, and public annoyance, the real cause of corrugation has not been 

 recognised. One and the chief reason for this is the fact that corrugation can only. 

 be prevented by calling halt in the direction in which tram-car design has 

 increasingly tended in recent times. Great weight on small wheels at high 

 speeds means a combination which is destructive to any permanent-way which, 

 as a tramway or street railway, can be made with any known materials and used 

 on the common highway. As an abstract of the paper which the author now 

 presents, he repeats and supplements the salient points appealed to in his 

 explanation of the causes and production of corrugation as previously outlined, 

 and this he does with a full knowledge of the numerous writings and experi- 

 ments on the subject by the authors of papers on the subject and of inquiries 

 by home and Continental bodies troubled by this engineering ailment. 



Although the physical and mechanical conditions involved in the origin of cor- 

 rugation are complex, the mode of operation of the causes is simple, and for an 

 explanation simple phenomena of known recurrence and adaptation in engineer- 

 ing works may be appealed to for this purpose. When a piece of cold iron 

 or steel is subjected to pressure exceeding the limit of elastic compression by a 

 rolling or hammering action, or by these combined, the result is spreading of the 

 material and change of the dimensions. The hammering or rolling work done 

 upon a surface tends to compress the material beneath it; but being nearly 

 incompressible and unchangeable in density, the material flows, und change of 

 form results. 



Generally the material thus changed in form suffers permanently no greater 

 stresses than those within its elastic limit of compression or extension. When, 

 however, the material is not free to flow or change its form in the direction in 

 which the stresses set up would act, the effect of continued work done on the 

 surface is the growth of compressive stress exceeding elastic resistance. 



In railway rails the freedom for the flow of the material is limited. Harden- 

 ing of the surface takes place, and destructive compression of the surface material 

 is set up. If the material be cast iron the destructive compression causes crum- 

 bling of the superficies, and the consequent relief of the material immediately 

 below from stress beyond that of elastic compression; but when the material is 

 that of steel rails crumbling is delayed by its greater elastic extensibility and 

 tcughnes6, the upper part near the surface being under intense compression, 

 differentiating from a maximum at the surface. 



1 Published in full in Engineering, The Electrician, and The Electrical 

 Review, September 8, 1911. 



