MECHANICS AND USEFUL ARTS. 25 



. . 



We also made some experiments, by means of the large apparatus 

 before mentioned, on curved bars, and these bore much greater weights 

 at high velocities than straight bars ; but the deflections of these bars 

 were very great compared with their length. In drawing attention to 

 these experiments, we would remark that, in actual structures, where 

 the deflections are so very small, the effect of cambering the girders, 

 or of forming a curved pathway for the load, would, be of less compar- 

 ative importance, and might tend to introduce practical inconven- 



ience.' 



The general opinion of engineers being at variance with the above 

 results, the commissioners made experiments upon two bridges in ac- 

 tual use and arrived at similar conclusions. They continue : "In 

 addition to the above experiments, we have made many for the purpose 

 of supplying data for completing the mechanical theory of elastic 

 beams. If they be in any manner bent, the concave side will be com- 

 pressed, and the convex side extended. From experiments the follow- 

 ing formulas were deduced for expressing the relation between the 

 extension and compression of a bar of cast-iron, ten feet long and one 

 inch square, and the weights producing them respectively : 



Extension, . . . w= 116117e 201905e2 

 Compression, . . . 10 = 107763d 36318^2 



And the formulae deduced from these for a bar one inch square, and 

 of any length, are : 



For extension, w = 13934040 ]- 2907432000 ~ 



For compression, '=129315GOy 522979200 J 



Where / is the length of the bar in inches. 



These formulas were obtained from the mean results of four kinds 

 of cast-iron. 



The mean tensile strength of cast-iron, derived from these experi- 

 ments, is 15,711 pounds per square inch, and the ultimate extension 

 one 600th of the length, and this weight would compress a bar of iron 

 of the same section one 775th of its length. It must be observed, that 

 the usual law is very nearly true for wrought-iron. 



" Many denominations of cast-iron have got into common use, of 

 which the properties had not yet been ascertained with due precision. 

 Seventeen kinds of them have been selected, and their tensile and 

 crushing forces determined. Experiments have also been made upon 

 the transverse strength and resistance of bars of wrought and cast 

 iron acted upon by horizontal as well as vertical forces. These ex- 

 periments will be found to exhibit very fully the deflections and sets 

 of cast-iron, and the defect of its elasticity. The bars which were 

 experimented upon by transverse pressure were of sections varying 

 from one inch square to three inches square, and of various other sec- 

 tions, and the actual breaking weights show that the strength of a bar 

 one inch square should not be taken as the unit for calculating the 

 strength of a larger casting of similar metal, although the practice of 

 doing so has been a prevalent one, for it appears that the crystals in 

 the portion of the bar which cools first are small and close, whilst the 



3 



