1870.] 



Theory of Continuous Beams. 



177 



in practice), was so exceedingly intricate when the numher of openings he- 

 came at all large, that in such instances it was of little practical use. 



In 1849 M. Clapeyron, a distinguished engineer and savant, devised a 

 much more direct and easy means of treating such cases, though he did 

 not at first succeed in giving to his own method all the simplicity and ele- 

 gance of which it was capahle. 



This was first done in 1856 by M. Bertot, civil engineer, who, by effect- 

 ing an elimination which had escaped Clapeyron, arrived at a remarkable 

 equation which has been the key to all subsequent treatment of the sub- 

 ject. This equation involves the bending moments over any three conse- 

 cutive points of support, and is well known in France by the name of the 

 " Theorem of the three Moments." 



In 1857 M. Clapeyron himself and M. Bresse, Professeur de Mecanique 

 applique'e a l'Ecole Imperiale des Ponts et Chaussees, appear to have dis- 

 covered this theorem independently of M. Bertot, and M. Bresse shortly 

 afterwards extended it to a much greater degree of generality. 



M. Bresse's researches on this subject are published in the third volume 

 of his ' Cours de Mecanique appliquee, 5 Paris, 1865 ; but they had been 

 communicated by him to the Academy of Sciences in 1862, and fully com- 

 pleted in the previous year. M. Bresse not only contributed to the ad- 

 vancement of the theory, but entered largely into the best methods of its 

 application to practice, and framed rules which have since, under an Im- 

 perial Commission, acquired the character of legislative enactments. 



M. Be'langer, Professeur de Mecanique applique'e a l'Ecole centrale, ap- 

 pears, about the same time as M. Bresse, to have made an independent in- 

 vestigation of this subject, and to have brought the theory of it to about 

 the same stage of advancement. 



Little has been since added to this theory in France, but valuable con- 

 tributions to its development in reference to practice are to be found in 

 the works of MM. Renaudot, Albaret, Molinos et Pronnier, ColignoD, 

 and Piarron de Mondesir. 



In England Professor Moseley is the first writer on mechanics who ap- 

 pears to have occupied himself with this subject. In his work on ( The 

 Mechanical Principles of Engineering and Architecture,' he gives several 

 examples of the application of M. Navier's method to important practical 

 cases. This work was published in 1843, and no doubt furnished the 

 groundwork for Mr. Pole's more extended investigations. 



In 1852 Mr. Pole had to examine the case of the bridge over the Trent 

 at Torksey, involving some new conditions not treated by Moseley, but 

 which he found the means of treating with perfect success. About the 

 same time Mr. Pole had to deal with the much more complex and im- 

 portant case of the Britannia bridge, in which, besides variation of load 

 from one span to another, variation of section also had to be considered, 

 and imperfect continuity over the middle pier. These conditions were 

 successfully imported into this method of Navier, which was, however, 



