Mr. W. H. Barlow on an Element of Strength in Beams. 475 
ingly from Major Wade’s experiments, it appears that with the same 
metal subjected to different modes of casting, an increase of trans- 
verse strength may accompany a decrease in the tensile resistance. 
Respecting the limit of action of the resistance of flexure, the 
author observes, that in all the simple solid sections, the points of 
action are eyidently the centres of gravity of the half-section ; while 
in the compound sections it is necessary to compute the centre rib and 
flanges as for two separate beams in which the resistance of flexure 
is different, and has its point of action at the centre of gravity of the 
separate portions. It would appear that the elastic reaction deve- 
lopes this resistance to the full extent when the section is such that 
a straight line may be drawn from every point at the outer portion 
to every point at the neutral axis within the section; but that if 
the form of section is such that straight lines drawn from the outer 
fibres or particles to the neutral axis fall without the section, then it 
must be treated as two separate beams, each having that amount of 
resistance of flexure due to the depth of the metal contained in it. 
The last section of the paper is devoted to the consideration of 
the resistance of flexure in wrought iron ; and experiments are first 
given to determine the position of the neutral axis, from which it is 
found to be at the centre of gravity of the section, as in cast iron ; 
so that the action is the same in both materials, except as to the 
amount of the extensions and compressions with a given strain; and 
the formulze given for cast iron will also apply to wrought iron. As 
wrought iron yields by bending and not by fracture, the relative value 
of f and ¢ are not so easily ascertained ; moreover the ultimate com- 
pressive strain which wrought iron can sustain is little more than 
half its ultimate tensile strength ; nevertheless the force required to 
overcome the elasticity of the material is nearly the same, whether 
applied as a compressive or tensile strain ; the difference being, that 
the force which overcomes elasticity when applied as a compressive 
strain leads to the destruction or distortion of the material, while, 
in the case of the tensile strain, the elasticity may be overcome long 
before the material yields by absolute rupture. 
A statement is given of the results of experiments made by Pro- 
fessor Barlow, in 1837, to show the weights which overcome the 
elasticity of the metal when applied transversely as compared with 
the weight necessary to produce the same result when applied by 
direct tension, and from these it is concluded that the resistance of 
flexure in wrought iron, considered as a force acting evenly over the 
surface, is nearly equal to one-half of the tensile resistance. 
In an Appendix to this paper, by Professor Barlow (read at the 
following meeting), the preceding principles are applied to beams 
and rafters of non-symmetrical section. 
With this view, the case of the double-flanged girder with un- 
equal flanges is selected and discussed, and formule deduced, which 
are then tested by comparison with the results of experiments by 
Prof. Hodgkinson, published in the ‘ Manchester Memoirs ;’ a selec- 
tion being made of those in which the girders differed most from 
each other in section, dimensions, and bearing-distance. The chief 
