492 Prof. C. A. Car us Wilson on the Influence of 



to show that at any point whatever the shear is inversely pro- 

 portional to its distance from the point of contact. 



Experiment 4. The beam was examined under circularly 

 polarized light, as in Clerk-Maxwell's experiments, in order 

 to obtain the variations in the amount of the strain uncom- 

 plicated by variations in the directions of the principal stress- 

 axes ; white light was used. 



The loci of points of equal shear were found to be circles, 

 as in the figure ; circles of equal shear were obtained up to 

 8 millim. diameter with this beam. 



Hence the shear at any point a equals the shear at b, if 

 o b a is a circle, and o b the normal at o ; i. e. shear at a 



p _ L pcos6 



= k 



ob 



o a 



k being some constant, but p cos 6 is the resolved part of the 

 pressure at o * along o a ; hence the shear at any point is 

 inversely proportional to its distance from the point of contact. 



Proposition III. 



The state of strain at the centre of the beam when doubly 

 supported may be found by superposing on the state of strain 



due to bending only, that due to surface-loading without 

 bending. 



* See Professor Boussinesq's results quoted already. 



