ON RAILWAY SUSPENSION BRIDGES. 155 
structures by the percussive action of trains moving at different velocities. 
It must be admitted, iz limine, that we have not at present sufficient justi- 
fication to recommend that railway trains should be allowed to pass over 
the platforms of suspension bridges except at moderate speed; nor, as a 
matter of every-day practice, should the locomotive engine be allowed to act, 
except slowly, while passing over such a bridge. 
With these limitations of speed, and of action of the driving-wheels, of the 
locomotive, the resistance to weight which must be provided for in a railway 
suspension bridge, need not be more than to meet the maximum load above 
assumed, namely, one ton per lineal foot of the platform, in addition to the 
weight of the platform itself, of the chains and their accessories, and of the 
suspension-rods, all of which are matters of strict calculation dependent 
upon the span. 
3rd. Strength of the Chains—The mathematical theory of suspension 
bridges has been so fully entered into by the best foreign and English 
authors, more particularly by the French, amongst whom M. Navier is the 
most distinguished, that little need be said now, except to give the hest 
admitted formule for calculation. There is so little practical difference in 
the form of the curve which the chain of a suspension bridge assumes when 
freely suspended without a load, and when fully loaded, that is, the difference 
in form between a catenary and a parabola, that the most esteemed writers 
on this subject have, by common consent, agreed to consider the curve of 
the chain of such a bridge to be a parabola rather then a catenary, on 
account of the very much greater simplicity of the mathematical calculations. 
Perhaps it may not be irrelevant to enter very briefly into this. 
When a heavy chain, freely suspended from two fixed points, is acted on 
_ by the force of gravity only, the form of curve which it assumes is called 
the catenary. If, however, the chain be loaded with weights, distributed in 
such a manner that for each unit of length (ez. gr. for each foot), measured 
along the horizontal tangent at the lowest point of the curve, the weights 
should be equal to each other, the effect of such a distribution is to cause 
the curve of the chain to approach in form to another curve called the 
parabola. If the distributed weights become so great that the weight of 
the chain may be neglected in comparison with them, the form which the 
curve assumes in this case is accurately that of the parabola. 
In most, if not all ordinary cases, the weight of the chain is, however, 
never inconsiderable in relation to that of the platform and of the testing- 
load together; and consequently the form of the chain is never exactly 
that of the parabola, though it approaches more nearly to this curve than to 
the catenary; so near, that for all practical purposes it may be considered 
to have attained that form, viz. of the parabola. 
In the case where the curve of the principal openings has a chord, say 
for instance of 424 feet, and a versed sine of 293 feet, or the proportion 
between the chord and versed sine of between 14 and 15 to 1, the two 
curves (catenary and parabola) passing through the points determined by 
these conditions approach so near to each other in form, that their greatest 
distance, measured in a vertical line intersecting both of them, is only 0°6 
(3)5th) of an inch. 
4th. The Rigidity of the Platform—This is perhaps the most important 
point of the subject, and has probably hitherto been least considered, and, 
strictly speaking, the novelty of the inquiry is confined to this alone. In 
all the earlier examples of suspension bridges, the object of the engineer 
‘appears to have been to construct the platform as light as possible. In 
_-many instances this was carried to a most dangerous extent; even in the 
