[190] H. COX, ESQ., ON THE DEFLECTION OP IMPERFECTLY ELASTIC BEAMS, &c. 



Here /x = 3.066, d = .761, and a = 81 inches: effecting the computation and substituting the 

 values of a and /3 above given, we find from (l) y = 120 x 144892, and from (2) $ = 4.2. 

 Hence for a bar 10 feet long and 1 inch square the hyperbolic formula for the compression 

 (d)is 



w = 144892 



*{i + **)- 



For another bar of the same iron 3.1 inches by 3.05 inches in section supported on points 

 13^ feet asunder, of which the experimental results are given in the Report, p. 75, we find that 



f=w-i- (1206.24 - .1933w). 



Hence by the same method of computation, as in the preceding case, the corresponding 

 formula for direct compression of a bar 10 feet long by 1 inch square, will be found to be 



w = 118927 



+ G+4 



For a bar of the same iron 1.05 inches in the direction of pressure by 2.05 inches broad, 

 on supports 9 feet asunder, of which the experimental results are given in the Report, p. 72, 

 it is found that 



f=W -7- (120.481 - 08875 w). 



Hence the corresponding formula for compression of a bar 10 feet long by one inch square 

 is found to be 



w = 157069 



■* {*♦")■ 



The several formula? for compression agree quite as closely as can be expected, when it is 

 considered that the size of the bar influences the hardness of the metal. The last of the pre- 

 ceding formulae indicates that the metal is hardest in the smallest casting, a result confirmed by 

 practical experience. To obtain complete accuracy a and /3 should have had different values 

 assigned to them in each of the above computations, but there are at present no data for ascer- 

 taining how far the tensile strength of a cast iron bar depends on its bulk. 



The great desideratum for perfecting the Hyperbolic or any other hypothetical law of 

 elasticity, is the want of knowledge of these variations of the strength and elasticity of the 

 material, which depend on the magnitude of the castings. It is greatly to be desired that this 

 defect of experimental data may not long continue unsupplied*. 



* The data of the numerical results of this paper are the valuable and careful experiments of Eaton Hodgkinson, Esq., 

 tabulated in Appendix (A) to the Report above referred to. 



July, 1851. 



