185] 



UNIFORM FLEXURE. 



491 



cutting the XY- plane at a distance - below the origin. Such a 

 plane remains normal to the line of centers, and the flexure is circular 

 (Fig. 155). If the section is rectangular, the sides y = + become, 



snce v = 



while the sides x = + -= become, since 



or since g is constant, circles, so that the cross -section becomes like 

 Fig. 156. 



. Fig. 155. 



Pig. 156. 



In an experiment by Cornu a bar of glass was thus bent, and 

 points of equal vertical displacement were observed by Newton's 

 fringes produced by a parallel plate of glass placed over the strained 

 plate. The curves u = const, are 



# 2 ny^ = const. 



a set of hyperbolas whose asymptotes make an angle a with the 

 Z-axis given by ctn 2 = y. By photographing the fringes and 



measuring the angle Cornu obtained a value of ^ very near to > 

 the value given by Poisson. 



The case a 2 4= * s precisely like that just treated, except that 

 the roles of the X and F-axes are interchanged. We pass therefore to: 



