to Transverse Strain in Beams. 419 



mine with certainty the modulus of elasticity of the metal 

 employed ; but as in the first experiment four measurements, 

 and in the second three, are given for loads not exceeding 

 712 lb., the average result of these may probably be taken as 

 nearly correct ; and the modulus has been calculated from the 

 mean deflexion for every pound of load up to 712 pounds, up 

 to which amount it may fairly be assumed that stress and 



strain are directly proportionate, by the formula E = ^ g . 



In the other two experiments no observations are recorded 

 for loads between 40 and 712 lb., and those given for these 

 loads do not appear sufficiently reliable to found any satis- 

 factory conclusions upon them. 



Wl 



The moment of transverse stress in column 2 is — — 



4 



The normal deflexion in column 4 is that which would 



exist under each load if the limits of elasticity were not 



WP 

 exceeded, and is calculated by the formula & = . ... , ■; or if 



B 2 be the deflexion already ascertained for any given load W 2 , 



W 



S 1= = ™^&2- The amounts so calculated vary little from the 



observed deflexions until the amount of tensile stress ap- 

 proaches that which would cause rupture by direct strain, 

 after which the latter become considerably in excess. 



The tensile stress per inch on the lower fibres is 2 so 



long as the stress varies directly with the strain, but can never 

 exceed the breaking stress. Mr. Barlow's experiments on the 

 direct tensile strength of cast iron, made, as may be presumed, 

 upon samples of iron similar in quality to those employed in 

 his experiments on transverse strain, give 18,876 lb. as the 

 mean breaking stress in eight trials. It must, however, be 

 observed that these experiments give various values from 

 15,747 to 22,035 lb.; and that while the strength of a bar 

 longitudinally strained is that of its weakest part, the tensile 

 strength of the part of a bar transversely strained is precisely 

 that at the centre of its length, and may generally be sup- 

 posed to be more than the amount which, for the above 

 reason, is obtained by experiments on direct longitudinal 

 strain. If those experiments are rejected in which a distinct 

 flaw was found to exist in the metal at the point of rupture, 

 it will be found that the average stress actually supported 

 without rupture in three of the experiments was 21,400 lb.; 

 and it may fairly be assumed that the tensile strength at the 



