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REPORTS ON THE STATE Ot SCIENCE. — l9l9i 



gives the position of the unstretched fibre which is inside the spar in 

 fig. 9 (A) and outside it in fig. 9 (B). Owing to the existence of thrust, 

 this may be anywhere. OL'N' is the curve obtained by erecting, at each 

 point of AOB, an ordinate representing the stress at that point. OLN is 

 the tangent at 0, to this curve, i.e., it would, represent the stress, if Hooke's 

 law held throughout. L, L', N, N', are the intersections of this tangent 

 and the curve, respectively, with the top and bottom of the spar. M, M' 

 are the projections of the L, L' upon the opposite face of the spar. 



Then MN = greatest stress due to bending moment only, as calcu- 



lated from the curvature ; ^ M' N'= greatest stress due to bending moment 



only, obtained from direct observations of stress in the extreme fibres, 

 the usual law of stress across the section being assumed. It was in this 

 way that the stress due to bending moment plotted in figs. 6, 7, 8 was 

 obtained, viz. : — by taking the algebraic half difference of the stresses in 

 the extreme fibres. 



Now, owing to the well-known characteristics of the usual stress- 

 strain diagram, the slojje of the line 17 N' is always less (whether in the 

 case of fig. 9(B) or that of fig. 9(A)) than the slope of the line LN. It 

 follows that M'N' is always less than MN, that is, the stress calculated 

 from the curvature should always be greater than the stress obtained 

 directly from the optical observations. The exact opposite has ajjparently 



DEFLECTIONS OF NODES OF TOP SPAR. 



iM^th. of Spar 

 Fig. 11. 



been observed, except precisely for the least of the loads for which curves 

 are given. 



Another conceivable explanation would be that the Young's modulus 

 used in computing the stresses from the curvature was not correct. But 

 this supposition is also negatived by the fact that some curves show the 

 ' optical ' in excess of the ' curvature ' stress and others show it in defect. 



It is most important that further experiments should be undertaken 

 to resolve this discrepancy. Of course, it has to be borne in mind that the 

 determination of curvature from a number of observations of deflection is 

 necessarily very imperfect : at the same time, it is interesting to note that 

 in the determination of the points of inflexion, where the curvature vanishes, 

 the method of deflections and the optical method give results which agree 



