AND LONG-CONTINUED CHANGES OE LOAD ON WROUGHT-IRON GIRDERS. 323 
I have assumed, for the sake of illustration, that every description of material, as re- 
gards its cohesive properties, follows the same law as that which we have experimented 
upon, or, in other words, in the ratio of its physical powers of resistance, that is to say, 
any beam will follow the same law in regard to its ultimate powers of resistance, when 
operated upon by a corresponding load due to that power. If this be true, we have 
only to follow the same rule as observed in the experiments, by loading cast-iron or 
wooden beams in the ratio of their cohesive powers of resistance, and their breaking- 
weights respectively. This has not been proved experimentally, but I hope at some 
future time to have an opportunity of extending the experiments, in order to determine 
to what extent these views are correct. 
The Lords Commissioners of Trade, in the exercise of their functions as conservators 
of the public safety, have adopted the rule that no railway bridge composed of wrought 
iron shall exceed with its heaviest rolling-load a strain of five tons per square inch of 
section upon any part of the bridge. The formula for this maximum of strain upon 
the material has been deduced from my own experiments on the model tube at 
Millwall. 
Assuming the top of the girder to be sufficiently rigid to prevent buckling by com- 
pression, the formula for the strength of the bottom section derived from these experi- 
ments is 
adc 
w=—> 
where the constant c= 8 Q. 
Applying this formula to the beam experimented upon, we have 
a , the area of the bottom=2-4 inches, 
d, the depth of' the beam=16 inches, 
c, the constant deduced from the model tube=80, 
Z, the span or distance between the supports =240 inches. 
Hence W= ^-,- 7 : — —=12-8 tons, 
240 
the ultimate strength of the beam. 
In order to determine the strain per square inch in these experiments, we find 
where S represents the strain per square inch upon the section a, produced by the 
greatest load w, laid upon the middle of the girder. 
It is necessary to observe that in a girder properly proportioned, the greatest strain 
per square inch will take place upon the bottom section ; so that if the strain upon the 
bottom section of such a girder be within the Government Commissioner’s condition of 
safety, the strain upon the top section will necessarily be within that limit also. In a 
girder having the cellular structure at its top section, the area of the top section should 
be very nearly once and a quarter that of the bottom section, or the areas of their 
