364 ABSTRACTS OF SCIENTIFIC PAPERS 



on the assumption that no horizontal force is applied at the abutments 

 except what results from the load on the bridge. The calculations 

 referring to a practical example are detailed in full in an appendix 

 to the paper. They show that, for a uniform load, the chain of a 

 braced suspension bridge, the figure of which is described in the paper, 

 should be tapered at the middle to nearly one-tenth of its cross 

 section at the piers ; and the bottom member, which like the chain is 

 in tension throughout, should have its section increased in the ratio of 

 8 to 1 from the piers to the centre, where its section should be nearly 

 equal to that of the chain at the piers. A similar design applies to 

 the braced arch : and this distribution of material, slightly modified 

 to suit practical requirements, was patented by the author. A com- 

 parison is made between the weight of a braced arch or suspension 

 bridge built on this plan and the weights of bridges of other types, 

 to illustrate the advantage of the proposed design : and it is pointed 

 out that the braced arch has the further merit that none of its parts 

 are exposed to any considerable tension, a point of special importance 

 when the material is cast-iron or timber. 



The calculations proved the possibility of constructing a suspen- 

 sion bridge which should be as stiff as a girder without any com- 

 pressive members except some light diagonals, and showed that a 

 braced arch might be made stable under unsymmetrical loads, both 

 arch and suspension bridge being much lighter than the equivalent 

 girders. 



For an abstract of the theory of braced arches, identical in sub- 

 stance with that given in the above paper, reference may be made 

 to 56 of the article BRIDGES in the ' Encyclopaedia Britannica.' 



XXVIII. On the Application of Graphic Methods to the Determina- 

 tion of the Efficiency of Machinery. ' Transactions of the Royal 

 Society of Edinburgh,' 1877, vol. xxviii. p. 1. Ditto, Part II., 

 ' The Horizontal Steam- Engine,' 'Transactions of the Royal 

 Society of Edinburgh,' 1878, vol. xxviii. p. 703. 



This very important paper, the scope of which is much wider than 

 the title indicates, has been reprinted in full (pp. 271-341). It 

 describes a novel process of performing what may be termed a dyna- 

 mical analysis of machines, which allows the method of Reciprocal 

 Figures (explained in an earlier paper) to be applied in determining 

 the forces that act throughout the mechanism. The investigation of 

 fractional efficiency is one use to which this analysis may readily be 

 applied. The Keith Gold Medal for the period 1877-9 was awarded to 

 Professor Jenkin for this paper by the Royal Soc'Vty of Edinburgh. 



