268 Mr. G-. Wilson. On a Method of determining the 



VIII. " On the Occlusion of Hydrogen and Oxygen by Palladium." 



By Ltjdwig Mond, Ph.D., F.R.S., William Ramsay, Ph.D., 

 LL.D., Sc.D., F.B.S., and Johx Shields, D.Sc, Ph.D. 



The Society adjourned over the Christmas Recess to Thursday, 

 January 20, 1898. 



64 On a Method of determining the Reactions at the Points of 

 Support of Continuous Beams." By George Wilson, 

 M.Sc. Demonstrator in Engineering in the Whitworth 

 Laboratory of the Owens College, Manchester. Communi- 

 cated by Professor Osborne Reynolds, F.R.S. Received 

 November 20, — Read December 16, 1897. 



The theory of continuous beams has been the subject of so much 

 research in the past that further investigation would seem almost 

 superfluous. In certain cases which occur in practice, however, the 

 computations arising out of the existing methods become com- 

 plicated and laborious, if not impossible to reduce, so that any 

 solution which avoids these difficulties may be of sufficient value to 

 warrant its publication. 



Mr. Heppel, in a paper read before this Society,* has traced the 

 developments in the theory, culminating in the discovery of the 

 ' Theorem of Three Moments,' by M. Bertot, in 1856, and independ- 

 ently by M.M. Clapeyron and Bresse, in 1857. Previously to 

 Clapeyron, Javier and other authors had sought the solution of the 

 problem by obtaining the reactions at the various points of support 

 of the beam ; Clapeyron, however, first introduced the innovation of 

 considering the bending moments at the points of support as the 

 unknown quantities to be determined. 



M. Bresse, in his ' Cours de Mecanique Appliquee,' has discussed 

 very fully the solutions of the various problems by this method, on 

 the supposition of a constant moment of inflexibility of the sections 

 of the beam both for the case of spans of arbitrary lengths and also 

 for cases where the end spars are equal but of different length to 

 the intermediate spans whose lengths are all supposed to be equal. 



Mr. Heppel, in the above mentioned paper, published solutions in 

 which the spans were divided into two, three, four, or five equal 

 parts throughout each of which the load and the cross section of the 

 beam were supposed to remain constant, although varying from one 

 division to another. 



Professors Perry and Ayrtonf have dealt with the question of a 



* c Eoy. Soc. Proc.,' toI. 18, p. 176. 

 f Ibid., toI. 29, p. 493. 



