424 Mr. R. C. Nichols on the Resistances 



(d-h) 2 (d-h-d,) 2 



2d l 



9 9 



J, 

 d — h=g+ ^ = ^0 + m) 



d\ _ d 



J~ 2 



and h^d^-^p), (19) 



the moment of tensile stress 



and the moment of compressive stress 



b |(i^i! - ^ A -*r)- s y ( w + g) ' 



Therefore the total moment of stress is 



B^(6(»-m») + g) (20) 



If we can find the value of cr the above equation will de- 

 termine the breaking weight for a beam of this description, 



the moment of stress being — — . 



° 4 



Now what appears to determine rupture is the maximum 

 tensile strain. The amount of elongation with the maximum 

 load supported was found in the examination of Mr. Barlow's 

 first two experiments with solid beams to be respectively 

 •003777 and "004078. For his third and fourth experiments 

 the modulus of elasticity could not be satisfactorily determined, 

 but assuming it to have been the mean of those found in the 

 other two, or 20,236,000, the maximum elongation in these 

 cases was '004185 and -004228. Remarking how nearly all 

 these values approximate to each other, we may take the 

 amount of elongation which will cause rupture at about *004. 



In the case we are now considering the maximum elonga- 

 tion is 



2eh S 2 — a-— m /ni . 



e i=-r = w — > .... (21) 



E 

 whence 



2-m 





(22) 



With the value of a so obtained the moment of stress will be 



