102 THIRD REPORT — 1833. 



elasticity, deduce it immediately from the formula . .^ ^ = E, 



o u ct 



substituting for w the height in inches of a column of the ma- 

 terial, having the section of the beam for its base, which is equal 

 to the weight w, and this is then denominated the modulus of 

 elasticity. It is useful in showing the relation between the 

 weight and elasticity of different materials, and is accordingly 

 introduced into the following Table. 



The above formulae embrace all those cases most commonly 

 employed in practice. There are, of course, other strains con- 

 nected with this inquiry, as in the case of torsion in the axles 

 and shafts of wheels, mills, &c., the tension of bars in suspen- 

 sion bridges, and those arising from internal pressure in cylin- 

 ders, as in guns, water-pipes, hydraulic presses, &c. ; but these 

 fall rather under the head of the resolution of forces than that 

 of direct strength. It may just be observed, that the equation 

 due to the latter strain is 



< (c — w) = w R, 



where t is the thickness of metal in inches, c the cohesive power 

 in pounds of a square inch rod of the given material, n the 

 pressure on a square inch of the fluid in pounds, and R the in- 

 terior radius of the cylinder in inches. Our column marked C 

 will apply to this case, but here again not more than one third 

 the tabular value can be depended upon in practice. 



