496 Prof. C. A. Cams Wilson on the Influence of 



The curve of ben ding-stresses is a tangent to the curve of 

 loading at a span of 73 rnillim., as measured from the figure, 

 whereas it is apparently 82 millim. when actually observed ; 

 it would appear more correct to determine this span by draw- 

 ing the curve through two points which can be observed with 

 accuracy, and then drawing the tangent and measuring the 

 intercept, since the experimental determination of the span 

 giving coincidence of the two dark bands is one liable to 

 considerable error. 



By drawing lines from the centre to the points along the 

 top surface corresponding to longer spans we see that the 

 deviation of the so-called " neutral axis " from the centre is 

 considerable : thus even at a span = 10 depths = 190 millim. 

 it should be 1 millim. above the centre. 



Proposition IV. 



The strain at every point along the normal due to loading- 

 varies directly as the load. 



Experiment 7. The beam is placed on two supports as 

 before, with a small central load, and the points of intersection 

 of the black bands with the normal are noted. The load is 

 now increased up to the safe limit when the points of inter- 

 section are observed to remain unaltered. 



We know that the strain at any point on the normal due to 

 bending is proportional to the load ; hence if the point of 

 intersection of the curves of bending and loading remains the 

 same when the load is increased, we know that the strain at 

 any point due to the loading must vary as the load. 



Proposition V. 



To determine the constant in the equation to the curve of 

 loading along the normal for any beam. 



Let X represent the vertical through the centre of a 

 beam centrally loaded, E the point of contact of the load with 

 the top of the beam EK; OY the axis of shear, E = 6 ; 

 KAM the hyperbola of loading for any given load, CAHD 

 the line of stresses due to bending along C E, for the same 

 load, the span being chosen so that CAH is a tangent to the 

 hyperbola at A ; i. e. so that the dark bands coincide at B. 

 Then Y and X are the asymptotes of the hyperbola. 



It has been proved that the equation is of the form 



y = &-, where y is the compressive stress at a point on the 

 normal E C at a distance X from 0. If W is the load and b 



