210 Young's Modulus and Poissons Ratio. 



different metals. The values of E in the first row were 

 deduced by the method of flexures, and those in the second 

 row from tensile experiments on the strips, using Marten's 

 Extensometer. The values of a in the fourth row were 

 obtained by the method of flexures, and those in the fifth 



F 



row were calculated from the equation <r= ^y. — 1, where il/ 



is the modulus of rigidity — the values of M being deduced 

 from torsion experiments on the strips. It should be noted 



E 



that an error of 1 per cent, in the ratio — j-, will result in an 



error of 4 per cent, or 5 per cent, in the calculated value 

 of a. 



The largest difference in the values of a by the two- 

 methods occurs for wrought iron. Since this material is 

 fibrous, it is quite possible that the difference may be caused 

 by the assumption of isotropy, which was made when 

 calculating a from values of E and M. 



It is important to notice that, according to the theory of 

 flexures, certain conditions must be fulfilled in order that the 

 method should yield accurate results. These are : — " That 

 the greatest diameter of the cross-section, and the third 

 proportional to the diameters in and perpendicular to the 

 plane of flexure, should not be great compared with the 

 radius of curvature of the flexure " *. Since the strips of 

 metal were 0'750 in. wide and 0*130 in. thick the third pro- 

 portional to the thickness and breadth was about 4*3 in. 



The flexure experiments were continued until the radius 

 of curvature of flexure was about 40 in. y and no indications of 

 failure of the method were then noted. In the case of some 

 of the timber specimens, the experiments were continued 

 until the ratio of the radius of curvahire of flexure to the 

 third proportional was as low as 6, but even in these cases 

 the method was found quite satisfactory. 



The dimensions of the cross-sections of the beams used by 

 Mullock f were 1 in. wide and \ in. thick, so that the third 

 proportional to the thickness and breadth was 4 in. The 

 minimum radius of flexure was usually about 200 in., but he 

 notes that the method gave accurate results when the radius- 

 of curvature of flexure was much less than this. 



* Thomson and Tait's { Natural Philosophy/ art. 718. 

 t Mallock, loc. cit. 



