78 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



was a work quite unexampled at the time of its 

 erection (1826), and showed a sagacious confidence 

 in the employment of a material then comparatively 

 little trusted. 



(352 ) Telford never made extensive experiments on the 

 Data of re- resistance of solids. Some special ones were indeed 

 sistance. made under his direction on wrought iron in par- 

 ticular, but in general he seems to have relied upon 

 the old ones of Musschenbroek and Buffon. The 

 Barlow, and two persons who first in recent times vigorously 

 Hodgkin- applied themselves to the practical determination 

 son - of the data of resistance so long deficient, were Tred- 



gold, a private engineer, and Professor Barlow of 

 Woolwich. The data they obtained have since been 

 generally used, not only in this, but in other coun- 

 tries. Tredgold's works (on Carpentry, Strength of 

 Timber, &c.) show a very great aptitude in applying 

 the results of science to practice, and an acquaintance 

 with both which is rarely attained. Mr Eaton Hodg- 

 kinson has made many valuable additions to Tred- 

 gold's work, and has contributed an excellent paper 

 on the strength of pillars to the Philosophical Trans- 

 actions (1840.) 



(353 > ^ Hodgkinson we are also indebted for a 

 Geometry useful investigation (in the Manchester Transac- 

 of the , tions) into the figure assumed by the chains of sus- 

 catenary. p ens i on bridges. The elegant properties of the 

 simple or geometrical catenary were fully investi- 

 gated a century and a half since by the Bernouillis 

 and by David Gregory, but the application of sus- 

 pended structures of immense weight to purposes of 

 utility suggested new problems. Amongst these, 

 perhaps the most interesting was the catenary of 

 uniform strength, in which the section of the sus- 

 pending chains is made everywhere proportional to 

 the strain which they have to resist at that particu- 

 lar point. Its equation was investigated by Mr Da- 

 vies Gilbert in 1826. An elegant and valuable con- 

 tribution to the geometry of catenarian curves was 

 made by the late Professor Wallace of Edinburgh, 1 

 with particular application to curves of equilibration 

 for bridges of masonry after the ingenious manner 

 of Robison mentioned in Art. (334). 



(354.) I n connection with suspension bridges, and also 

 M. Navier. with researches on the yielding of elastic materials, 

 we must record the name of M. Navier, a very 

 eminent French engineer and writer on practical 

 and theoretical mechanics. His work on suspension 

 bridges (1823) is one of the earliest and best. He 

 is also well known for his physico-mathematical re- 

 searches on the yielding of elastic solids to pressure 



under given circumstances, in the course of which he 

 came into collision with Poisson, who gave a some- 

 what different theory. The subject is one of ex- 

 treme difficulty, owing to our ignorance of the 

 molecular constitution of bodies ; and it is believed 

 that all these investigations were so far erroneous 

 that they were based upon the assumption of a single 

 constant to represent the resistance of bodies to 

 change of form and dimension. These (form and 

 dimension) are two very different things, and require 

 distinct treatment. 2 British mathematicians have 

 lately paid much attention to these enquiries, with 

 the prospect of a solid improvement in engineering 

 theories. 3 



The art of bridging over great spaces has been (355.) 



pushed, by the requirements of the railway system, to Mr Robe 

 . i a 1 ,>Stephen- 



an astonishing extent, and under circumstances or son r 



peculiar difficulty. I shall connect these improve- 

 ments with the name of Mr ROBERT STEPHENSON, 

 the inventor of the Tubular Bridge, a work which, 

 in its very simplicity, is a triumph of art, and being 

 nothing more than a hollow beam of somewhat pecu- 

 liar construction, supported at the ends, it is an ad- 

 mirable instance of a structure of which the stability 

 may be easily reduced to calculation. 



The wooden bridges of Switzerland were for a long (356.) 

 time unequalled as skilful works of carpentry. During bri ( J > ee e g n i 

 the last century the Rhine at Schaffhausenwas crossed Switzer- 

 by two spans of 171 and 193 feet. At Trenton, in land and 

 America, the river Delaware is crossed by a wooden America ' 

 bridge, of which one arch is 200 feet in span. It is 

 on the bow principle, an elastic wooden arch, convex 

 upwards, being skilfully braced and united to a level 

 roadway passing through the spring of the arches. 

 The American lattice bridge, very simply and skil- 

 fully contrived, has great firmness, owing to the depth 

 of the framing, and exercises no horizontal thrust on 

 the piers. The widest spanned wooden bridge in the 

 world, 340 feet, across the Schuylkill, at Philadel- 

 phia, designed by Wernwag, combines the bow and 

 lattice principle. 



In these we might see foreshadowed in some faint (357.) 

 degree the principle of the TUBULAR BRIDGE, theThetubul 

 greatest discovery in construction of our day. But brid S e - 

 in reality the idea of it arose from a different con- 

 sideration. 



During the first ten or fifteen years of railway ex- (358.) 

 perience, engineers had gradually acquired a correct ^^ y 

 perception of the manner in which cast and wrought bridges. 

 iron may most effectually and economically be formed 



1 Edinburgh Transactions, vol. xiv. 



2 About twenty years ago, the present writer showed that India rubber, which possesses to such a remarkable extent the 

 quality which may be termed cubical flexibility, is yet scarcely at all compressible in fact, just as much as water, and no more. 

 Though not otherwise published, he has been in the habit of demonstrating this in his annual course of lectures. 



3 Professor Stokes in Cambridge Transactions, vol. viii. ; Mr Clerk Maxwell in Edinburgh Transactions, vol. xx. Mr M. 

 Rankine in Cambridge and Dublin Math. Journal for 1851 and 1852. Experimental data are still deficient ; but M. Wertheim 

 has lately published some valuable ones (which are still in progress) in the Annales de Chimie. 



