500 Prof. C. A. Carus Wilson on the Influence of 



deep x 5*5 niillim. thick, was placed in the steel straining- 

 frame on two steel rollers 2 millim. in diameter, and centrally 

 loaded over a similar steel roller. 



The span chosen was 60 millim., giving for p the value 3*15. 



The nicols were crossed and set at an observed angle, and 

 the black band plotted on squared paper corresponding to the 

 squares on the glass beam. This band of course represents 

 the locus of points where the axes of principal stress are 

 parallel to the directions of the planes of the nicol. 



The nicols were then turned through a small angle a, the 

 new position of the black bands plotted, and so on for several 

 different angles. These curves are shown in Plate II. The 

 lines of principal stress are easily deduced from these and are 

 shown in Plate II. fig. 4. 



Since communicating the above, Sir George Stokes has 

 gone very fully into this problem, and has kindly allowed me 

 to quote the following extracts from letters I have received 

 from him on the subject : — 



" Let A be the point in the upper surface where the pres- 

 sure (P) is applied ; B, C the points of support below, which I 

 suppose to be equidistant from A : D the middle point of BC. 

 Let y be measured downwards from A ; denote BD or DO 

 by a, and AB by b. You have the expressions for the stresses 



/ 2P 1\ 

 produced by P in an infinite solid [%= — * /-> an( ^ ^ ne 



question is, What system must we superpose on this to pass 

 to the actual case ? This, as 1 showed you, is the system of 

 stresses produced by a system of forces applied to the surface. 

 The forces consist — (1) of the two pressures JP at B and C; 

 (2) of a continuous oblique tension below, represented in 

 drawing by a fan of tensions directed at every point of the 

 lower surface from the point A. 



" Imagine now the beam cut into two by a plane along 

 A D. Consider one half only, say that on the B side. Every- 

 thing will remain the same as before, provided we supply to 

 the surface A D forces representing the pressures or tensions 

 which existed in the undivided beam. On account of the 

 symmetry, the direction of these must be normal. 



" At I) the vertical pressure on a horizontal plane in the 

 infinite solid is compounded with an equal vertical tension 

 due to the fan. Hence, of the vertical pressure in A D which 

 must be superposed on the vertical pressure in the infinite 

 solid, we know thus much without obtaining a complete solu- 

 sion of the problem, namely, that it must equal minus 2P/7T& 



