276 



SUPPLEMENT TO CHAP. XTV. 



[CHAP. i. 



experiment shows that within narrow limits, i.e., within the elastic limits, 

 the elongation or compression is directly as the force of extension or com- 

 pression. Supposing that this held true always for all values of A i, then, 



since a force produces a displacement A t, the force necessary to produce 



A 



a displacement t, will be times as great. Calling this force E, we have 

 A s 



AA 



The force E, then, is the force which would "be necessary to produce a dis- 

 placement s equal to the original length, if the law of proportionality of the 

 displacement to the force always held good for all values of A . Thig 



value 



(3) 



AA 



we call the coefficient of elasticity. 



From (8) we easily obtain for the force in the direction of the tangent 

 to the axis 



and lor the relative displacement 



(b) Fibre strain P, and moment M. 



As seen in eq. (1), the longitudinal strain upon an element of cross-sec- 

 tion d a is called P. In a curved piece conceive two cross-sections, aa 



