272 REPORT— 1867. 



Abstract of the Results of Tables I., II., and III. 



Transverse Strain. — Table I. 



The results of these experiments show that, within the elastic limits, the 

 deflections are in proportion to the pressures ; for example, in Experiment 1, 

 the deflections are almost exactly expressed by the formida 2 = -001361 lu, 

 where the constant -001361 is the mean, D^, of all the deflections for a 

 unity of weight derived from formula (3). By aid of this principle the value 

 of the weight, w, with its equivalent deflection, corresponding to the elastic 

 limit, was determined. 



The mean value of Dj, given in col. 4, the deflection corresponding to unity 

 of pressure and section, may be taken as the measure of the Jlexibiliti/ of the 

 different bars. In general, the least flexible bars give the highest values of 

 E and C, and, other things being the same, or nearly the same, the most 

 flexible bars give the highest values of u, the work of deflection correspond- 

 ing to unity of section. 



The bars of some of the experiments, 10, 18, 28, &c., with more than 

 an average flexibility, gave very high values for C, the working unit 

 of resistance to transverse strain, showing their great value when applied to 

 the springs of carriages and other constructions, where flexibility and 

 strength should be combined. Such bars as those of experiments 1, 12, 21, 

 &c., with less than an average flexibility, gave at least an average value for 

 C, showing their apphcability to all constructions where rigidity and strength 

 are requu-ed ; and so on to other cases. 



The mean value of E, the modulus of elasticity, given in col. 5, taken for 

 thirty of the best specimens, is 31,000,000 nearly, whilst the mean taken 

 for a like number, in col, 4, is about 32,000,000. This modulus exceeds 

 that of wrought iron by more than the 30th part. Steel having a much 

 greater flexibility than wrought iron, accounts for the approximation of their 

 values for the modulus of elasticity. The bars that have the greatest flexi- 

 bility, or the great value of Dj, other tilings being the same, have the least 

 value for the modulus of elasticity. 



The values of w, or the work of deflection for the unity of section up to 

 the elastic Hmit, may be taken as measures of the qualities of bars where 

 flexibility and strength are required. 



The bars generally exhibit very high powers of resistance to transverse 

 strain. The mean value of the unit of working strength, C, given in col. 9, 

 taken for one-half the number of experiments, is 6-83 tons, and for the 

 remaining half (omitting the last two experiments) this constant is 5-23 

 tons, giving a general mean of 6 tons. In the model tube of the Britannia 

 and Conway bridges, the value of the constant for hreahing weight is 

 6-7 tons. 



Taking 11 tons per square inch as the mean value of the compressive and 

 tensile resistances of wrought iron at the elastic limit, the value of C in 

 this case will be less than 2 tons ; hence it follows that the transverse 

 strength of these steel bars will be about 3| times the strength of wrought- 

 iron bars of the same dimensions. 



In order to determine the relative value of the two kinds of material 

 undergoing transverse strain, let us suppose two bars of the same length, 

 one steel and the other iron, having the same strength, to be similar in their 

 transverse sections ; then, as the strength of bars of similar section are as the 

 cubes of their depths, 



J 



