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crepancy and variation will be found to arise from the received 

 theory not taking into account the resistance consequent on the 

 molecular disturbance accompanying curvature. 



In his former paper the author gave a formula by which the dif- 

 ference between the tensile strength and the apparent resistance at 

 the outer fibre could be computed, approximatively, in solid rectan- 

 gular beams and open girders ; and he now proposes to trace the 

 operation of the resistance of flexure, considered as a separate ele- 

 ment of strength, and to show its effect, in each of the forms of 

 section above indicated. Observing that the usual supposition of only 

 two resistances in a beam, tension and compression, fails to account 

 either for the strength, or for the visible changes of figure which 

 take place under transverse strain, he proceeds to discuss the effects 

 involved in such change of figure, and thence arrives at the follow- 

 ing conclusions applicable to the resistance of flexure : 



1 . That it is a resistance acting in addition to the direct exten- 

 sion and to compression. 



2. That it is evenly distributed over the sarface, and consequently 

 (within the limits of its operation) its points of action will be at the 

 centres of gravity of the half-section. 



3. That this uniform resistance is due to the lateral cohesion of 

 the adjacent surfaces of the fibres or particles, and to the elastic 

 reaction which thus ensues between the portions of a beam unequally 

 strained. 



4. That it is proportional to and varies with the inequality of 

 strain, as between the fibres or particles nearest the neutral axis and 

 those most remote. 



Formulae are then given, according to these principles, exhibiting 

 the relation between the straining and resisting forces in the several 

 forms of section experimented on, as resulting from the joint effect 

 of the resistances of tension, compression and flexure. The appli- 

 cation of these formulae to the actual experiments yields a series of 

 equations with numerical coefficients, in which, were the metal of 

 uniform strength, the tensile strength f, and the resistance of flexure 

 (j), would be constant quantities, and their value might be obtained 

 from any two of the equations ; but as the strength varies even in 

 castings of the same dimensions, and as a reduction of strength per 

 unit of section takes place when the thickness is increased, the values 



