(352.) 
Data of re- resistance of solids. 
sistance. 
Tredgold, 
Barlow,and 
Hodgkin- 
son. 
(353.) 
Geometry 
of the 
catenary. 
(354.) 
M. Navier. 
876 
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. 
Telford never made extenswe experiments on the 
Some special ones were indeed 
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 
two persons who first in recent times vigorously 
applied themselves to the practical determination 
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.) 
To Mr Hodgkinson we are also indebted for a 
useful investigation (in the Manchester Transac- 
tions) into the figure assumed by the chains of sus- 
pension 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,’ 
with particular application to curves of equilibration 
for bridges of masonry after the ingenious manner 
of Robison mentioned in Art. (334). 
In connection with suspension bridges, and also 
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 
MATHEMATICAL AND PHYSICAL SCIENCE. 
(Diss. VI. 
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.’ British mathematicians have 
lately paid much attention to these enquiries, with 
the prospect of a solid improvement in engineering 
theories.® 
The art of bridging over great spaces has been 
pushed, by the requirements of the railway system, to 
an astonishing extent, and under circumstances of 
peculiar difficulty. I shall connect these improve- 
ments with the name of Mr Roperr SrepHEnson, 
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 
time unequalled as skilful works of carpentry. During es eet 
the last century the Rhine at Schaffhausen was crossed 
by two spans of 171 and 193 feet. At Trenton, in 
America, the river Delaware is crossed by a wooden 4™¢r ica 
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 
degree the principle of the Tusutar Brinez, the Thetubular 
greatest discovery in construction of our day. But 
in reality the idea of it arose from a different con- 
sideration, 
During the first ten or fifteen years of railway ex- 
(355.) 
Mr Robert 
Stephen- 
son, 
(356.) 
en 
Switzer- 
land and 
(357.) 
bridge. 
(358.) 
Railway 
perience, engineers had gradually acquired a correct (+144 
perception of the manner in which cast and wrought 
iron may most effectually and economically be formed 
1 Edinburgh Tramsactions, vol. xiv. 
* About twenty years ago, the present writer showed that India rubber, which possesses to snch a remarkable extent the 
quality which may be termed cubical flewibility, 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. 
8 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. 
bridges. 
ee 
a 
