Mr. J. M. Heppel on the Theory of Continuous Beams. 59 



general case is to a certain extent discussed, the method of M. Navier 

 being perhaps rather indicated than fully developed. 



Prof. Moseley's work was altogether a most valuable contribution to 

 engineering science, and, as far as the present subject is concerned, no 

 doubt furnished the groundwork of the method applied by Mr. Pole to 

 the solution of other particular but more complex and difficult cases. 



The first case which engaged the attention of Mr. Pole appears to have 

 been that of the bridge over the Trent at Torksey, consisting of two spans 

 of continuous tubular beams, resting on abutments and a central pier. 

 For special reasons it had become necessary that the real conditions of 

 equilibrium of this bridge should be investigated with more than ordinary 

 precision ; and this Mr. Pole did by a method virtually identical with that 

 of M. Navier, though it does not appear that he had any previous know- 

 ledge of that method, except through the medium of Moseley's work. 

 Throughout Moseley's cases, however, the load on the beam is considered 

 as distributed uniformly over its entire length, whereas Mr. Pole had to 

 deal with the case of different loads on the two spans, and no doubt had to 

 devise the method of analysis necessary for its treatment. Mr. Pole's 

 paper on this subject is published in vol. ix. of the c Minutes of Proceed- 

 ings Inst. Civ. En.' 1849-50. 



As far as this went, however, it could hardly be considered to have 

 advanced the theory of the subject, as M. Navier's method included this 

 case, and much more; but about the same time Mr. Pole had to investigate 

 the case of a much larger work, the Britannia Bridge, where he had to 

 deal with some new conditions, which, as far as the writer is aware, were 

 then for the first time successfully treated. 



These were that, besides variation of load on the different spans, their 

 cross sections also varied, and there was imperfect continuity over the 

 centre pier, that is to say, that the points of support being supposed to 

 range in a straight line, the beam if relieved from all weight would cease 

 to remain in contact with them all, and would consist of two equal straight 

 portions, forming an angle pointing upwards. The process, which for 

 distinction may be called that of M. Navier, was skilfully extended by 

 Mr. Pole so as to include these new circumstances, and by its means 

 results were obtained certainly true within a very small limit, and as near 

 the absolute truth as any existing means of treating the subject would 

 produce. 



Mr. Pole's researches on this subject are published in Mr. Edwin Clark's 

 work on the Britannia and Conway Bridges, 1850. Both from the clear 

 and accurate treatment of the case and the record of the numerous and 

 delicate observations by which the theoretical conclusions were continually 

 verified and kept in check, they are most strongly to be recommended to 

 the attention of engineers having to deal with works of this character. 



The sequence of events now compels the writer to advert to some studies 

 of his own. In 1858-59, being then Chief Engineer of the Madras Rail- 



