406 Mr. R. C. Nichols on the Resistances 



be, in comparison with their elongation or contraction, some- 

 thing extremely small, and the resistances thereby occasioned 

 comparatively insignificant. 



Mr. Barlow says " there are in fact two distinct changes of 

 figure. There is the change produced by the tension and 

 compression, which if acting alone would result in the figure 

 efg h (a rectangle), and there is the change produced by the 

 curvature, which if acting alone would result in the figure 

 I p norm (a similar rectangle with the upper and lower sides 

 curved), the combination of these effects is necessary to pro- 

 duce the figure which a beam assumes under transverse strain"*. 



But this is to take into account twice over the greater part 

 of the displacements by which the resistance is occasioned. If 

 the area of the first figure represent the resistances caused by 

 direct strain, it is clear that the addition caused by the second 

 displacement cannot exceed that represented by the space not 

 included in both areas. 



What the experiments show us is a loss of resisting power 

 with the increase of deflexion, manifested, as already pointed 

 out, by an increasing ratio of deflexion to load, and therefore 

 something absolutely the reverse of a resistance to flexure. 



In addition to the conclusion already quoted as to the 

 position of the neutral axis, which has been shown not to be 

 confirmed by the experiments, Mr. Barlow makes this further 

 comment upon them : — 



" In the first beam a strain (load) of 5786 lb. caused an 

 extension ... at the outer fibres ... =30 divisions . . . therefore 



an extension of . „.. » , of the length. The beam was 7 ft. 

 1792-4 ° 



4 in. long, 6 in. deep, and 2 in. thick, so that with a strain 

 .(stress) off — -x — ^ — — = j 10,608 lb. at the outer fibres, the 



extension produced was ., _ t . . of the length. But in referring 

 r 1/92*4 s s 



to the experiments made by Mr. Hodgkinson, it will be seen 



that a force of 10,538 lb. applied by direct tensile strain extends 



cast iron -— ^ of its length, being nearly double that exhibited 



by the beam." 



Now an extension of this amount with such a stress, 

 unless the limit of elasticity were exceeded, implies a modulus 

 of elasticity E = 10538 x 1056 = 11,127,028 only; whereas 

 the values of E deduced by Mr. Hodgkinson from his 

 experiments on various samples of cast iron vary from 

 13,730,500 to 22,907,700, that for Carron C B being 17,270,000, 



* Phil. Trans. 1857, p. 471. 



