448 Royal Society : — 



subject, it appears also to have engaged that of M. Belanger, who in 

 his work entitled ' Theorie de la Resistance et de la Flexion Plane 

 des Solides &c.,' Paris, 1862, gives a very complete demonstration — 

 resulting in an equation which in one point of view is slightly more 

 general than that of M. Bresse, as it takes in variation of the moment 

 of inertia of the section from one span to another. In another point 

 of view its generality is slightly less, as it deals only with loads 

 distributed over each separate span uniformly, whereas M. Bresse 

 replaces the simple algebraical terms expressing these by definite 

 integrals expressing the load as a function of the distance from one 

 of the points of support. 



As far as the writer is informed, little has been done in France 

 to advance this theory beyond the point to which it was brought 

 by the writers last mentioned, and especially by M. Bresse ; but 

 valuable contributions to its development in reference to application 

 to practice are to be found in the work of MM. Molinos and Pronnier 

 above referred to, as well as in various papers by MM. Renaudot, 

 Albaret, Colignon, Piarron de Mondesir, &c. 



In England little or no attention appears to have been paid to this 

 subject by writers on mechanics till 1843, when the Rev. Henry 

 Moseley, Professor of Natural Philosophy and Astronomy at King's 

 College, London, published his work on the Mechanical Principles 

 of Engineering and Architecture. In part 5 of this work, which 

 treats of the strength of materials, four cases of continuous beams 

 are fully investigated, and the 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 con- 

 cerned, 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 in- 

 vestigated 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 knowledge of that method, 

 except through the medium of Moseley' s work. Throughout Mose- 

 ley' 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 ' Minutes 

 of Proceedings of 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. 



