100 THIRD REPORT — 1833. 



itself, and consequently its specific gravity, enters. These va- 

 rieties of expressions, however, are not to be understood as 

 arising from any difference of opinion amongst the authors from 

 whom they proceed, but merely as different modes of expressing 

 the same principles : indeed, in reply to that inquiry of the 

 Committee with reference to this point, I may, I think, venture 

 to say there is not at present any difference of opinion on any 

 of the leading principles connected with the strength of mate- 

 rials, with the excejDtion of such as are dependent entirely upon 

 the imperfect nature of the materials themselves, and which, as 

 we have seen, will give rise to different results in the hands of 

 the same experimenter and under circumstances in every re- 

 spect similar. 



As I distinguish the doctrine of the absolute resistance or 

 strength of materials, which is founded on experiment, from 

 that which relates to the amount and resolution of the forces or 

 strains to which they are exposed, which is geometrical ; and 

 as I confine myself to the former subject only in this Essay, it 

 is not, I conceive, necessary to extend the preceding remarks 

 to any greater length. I shall therefore conclude by giving 

 a table of the absolute and relative values of the ultimate 

 strength and elasticity of various species of timber and other 

 materials, selected from those results in which I conceive the 

 greatest reliance may be placed. 



Formula; relating to the ultimate Strength of Materials in 

 cases of Transverse Strain. — Let I, b, d, denote the length, 

 breadth and depth in inches in any beam, w the experimental 



w 



breaking weight in pounds, then will j— r-^ = S be a constant 



quantity for the same material, and for the same manner of ap- 

 plying the straining force ; but this constant is different in dif- 

 ferent modes of application. Or, making S constant in all cases 

 for the same material, the above expression must be prefixed 

 by a coefficient, according to the mode of fixing and straining. 



1. When the beam is fixed at one end, and loaded at the 

 other, , 



bcT^-^' 



2. When fixed the same, but uniformly loaded, 



1 lie _ ^ 



3. When supported at both ends, and loaded in the middle, 



1 Itv _ ^ 

 4 ^ ZTrf^^ ~ ^' 



