1916] on Polarized Light and its Applications to Engineering 585 



diagram may be constructed which shows the centre hnes of a 

 number of these curves, with the directions of the axes of stress 

 marked on them. If lines of stress at some distance away from the 

 notches are now considered, they will clearly be parallel and perpen- 

 dicular to the sides of the plate, but as they approach the discon- 

 tinuity they must bend towards the centre line in order to pass 

 through the narrow neck, since they cannot maintain their continuity 

 in any other way. From these observations one can see how they are 

 actually guided, and that they come close together at the extremities 

 of the notches and produce an intense stress at these points. Other 

 lines of principal stress at right angles to the first set are also in- 

 dicated by the measurements, and the two systems give a kind of 

 framework diagram which shows the direction of the principal 

 stresses at any point, and therefore completes the experimental solu- 

 tion of the problem. The stress distribution in a plate cut to a 

 required form, and stressed in an arbitrary manner by forces in its own 

 plane, is therefore capable of solution experimentally. 



Complete Solution. 



The complete experimental solution of the stress distribution in a 

 plate stressed by forces in its own plane, may be illustrated by an 

 investigation by Mr. Scoble and myself of the case of the action of a 

 rivet near the edge of a riveted joint, since we can determine the 

 sum (p + q) of the principal stresses, their difference (;? — 2), and 

 their directions. In this problem we can no longer neglect either 

 principal stress, and it is in general necessary to determine both 

 their directions and magnitudes. If the uniform tension stress in 

 the full section of a plate is represented by equally spaced lines in the 

 direction of stress, we may expect to find alterations in their direc- 

 tions and distances apart as they draw near to the discontinuity 

 produced by the rivet, and an optical examination shows that the 

 lines of stress approach one another very closely as they pass around 

 the rivet, and afterwards diverge again if the overlap of the plate is 

 sufficient to permit this. It is not difficult to explore the whole of a 

 plate stressed in this way, by determining both the sum and difference 

 of the stresses at a sufficient number of points on the lines of stress 

 so found, and some of the measurements for the cross section passing 

 through the centre of a rivet in a plate are shown in Table III., for 

 the case of a plate in which both the overlap and the widths of metal 

 on each side of the rivet are equal to the diameter of the rivet. 



In these determinations the distance r of the point examined is 

 measured from the centre of the rivet in terms of its radius a, while 

 the stress pr across the section and the stress pt in the section are 

 given in terms of the mean stress. 



The experimental values of the sums and differences are plotted 



