[182] H. COX, ESQ., ON THE DEFLECTION OF IMPERFECTLY ELASTIC BEAMS, & c . 



thing as saying that as the experiment progresses, w increases in comparison with e too fast 

 at first, and afterwards not fast enough. At points of the curve from O towards A the 

 vertex of the parabola, the tangent to the curve becomes rapidly more and more nearly perpen- 

 dicular to the axis. In the hyperbola, on the contrary, the direction of the curve does not 

 change so rapidly and is not perpendicular till it meets the asymptote at an infinite distance 



w 

 from the origin. In cases of tranverse pressure, as we shall see, — is actually reduced not 



much less than one-half, and in all cases the greater this reduction, the greater will be the 

 errors of the parabolic formula. 



In the following tables the Parabolic and Hyperbolic formulae are compared with experi- 

 ments upon extension and deflection. The first table contains the mean results on four 

 different sorts of cast iron, shewing the corresponding extensions and weights for a bar 1 inch 

 square in section and 10 feet long, together with the weight computed from the extensions 

 by the parabolic formula 



w = Il6ll7e-201905e* 

 and the hyperbolic formula 



W = 118156.424 



+£+■4 



The second table contains the deflections and corresponding deflecting pressures applied 

 horizontally at the centre of a bar of Blaenavon iron 1.522 inches deep in the direction 

 of the pressure, and 3.066 inches broad, supported at points 13^ feet apart, with the 

 weights computed by the parabolic formula 



w = 149.9d - 7.204 d? 

 and the hyperbolic formula 



W = 155.64-r-(- + .081]. 



The results of the parabolic formulae are copied from the Report of the Iron Commission, 

 pages 59 and 70. It will be observed that in each case the mean error of the parabolic 

 formula is between 3 and 4 times as great as that of the hyperbolic formula. 



