IN BEAMS SUBJECTED TO TRANSVERSE STRAIN. 
233 
First, that in every case the resistance, or the value of F, is greater than that due 
to the tensile resistance of the metal. 
Secondly, that with the same depth of metal in the beam, and the same distance of 
bearing, the resistance is greater when the deflection is greater. 
Thirdly, that with the same deflection and the same length of bearing, the resist- 
ance is greater when the depth of metal in the beam is greater. 
And it follows from these results, that there is an element of strength depending 
on the amount of deflection in connexion with the depth of metal in the beam, or in 
other words, dependent upon the degree of flexure to which the metal forming the 
beam is subjected. 
The existence of an element of strength in addition to the resistances to direct ten- 
sion and compression being clearly proved by these experiments, it becomes inter- 
esting to ascertain the law under which it varies, in the form of beams experimented 
upon. 
Now if from the value of F, the tensile strength of the metal is deducted, it will 
be found that the remainder maintains nearly a constant ratio in each case to the 
depth of the metal in the beam multiplied by its deflection. It would appear, there- 
fore, that the total resistance, or the value of F, is composed of two quantities ; 
one being constant and limited by the resistance to direct tension, and the other 
varying directly as the degree of flexure to which the metal forming the beam is 
subjected. 
The applicability of this simple law may be tested by the results of the experiments, 
as follows : — 
Let ^=the resistance to flexure in the solid beam at the time of rupture ; 
and let D=the depth, 
^=the deflection, 
/= tensile resistance, 
and F= total resistance. 
Then in the solid beam 
f-\-(p-=.Y ; 
and let F', D' and represent the total resistance, depth of metal, and deflection of 
any other of the beams ; then, the lengths being equal, if the resistance arising from 
the lateral action varies as the depth of metal into the deflection. 
F'=/+9 
D'§' 
DS" 
The value of (p may be determined from this equation, applied to each of the experi- 
ments, in two ways ; first, by supposing/’to be a constant quantity; and secondly, 
by supposing /and <p to have a constant ratio. 
By the first mode, the whole of the errors of observation and irregularities of the 
strength of the metal would be accumulated in <p. By the second method, these 
irregularities will be divided between the values of f and (p. 
