Surface-Loading on the Flexure of Beams. 487 



inch. Two screws in the two sides of the frame enable 

 lateral pressure to be applied. The whole frame can be moved 

 in anj direction in its own plane, so that all parts of the beam 

 may be examined. The optical arrangements consist of two 

 nicols, of which the upper is provided with a graduated disk on 

 which the angle of rotation can be observed ; a microscope 

 with micrometer-eyepiece can be fitted when it is desired to 

 measure the fringes ; circularly polarized light can be used 

 when required. 



The beams used were marked on one side with 2 millim. 

 squares ; they were covered with paraffin and marked in a 

 dividing-engine and then etched ; the lines thus formed 

 enabled the position of dark bands to be determined with 

 accuracy. 



Proposition I. 



If a beam of glass be laid on a flat surface and loaded across 

 its upper surface, the shear at any point on the normal at the 

 point of contact of the load is inversely proportional to the 

 distance from the point of contact. 



Experiment 1. A beam of annealed glass 61 millim. x 6*5 

 millim. x 20 millim. deep was placed in the steel straining- 

 frame with its narrow side resting on a piece of thin paper. 



A steel roller 2 millim. in diameter, 10 millim. long, was 

 placed across the middle of the top surface and loaded by the 

 screw. 



The nicols were crossed and at 45° to the axis of the beam. 



A quarter- wave mica plate was placed between the beam 

 and the analyser, with the plane containing the optic axes at 

 right angles to the length of the beam. 



At that point a on the normal where the difference of phase 

 between the ordinary and extraordinary pencils traversing the 

 beam is equal and opposite to the difference of phase produced 

 by the mica plate — the effect will be as if there were no 

 strained glass between the two nicols, and there will therefore 

 be a black spot as the nicols are crossed. 



The position of this spot on the normal is plotted on a 

 sheet of squared paper, and an ordinate parallel to the axis 

 chosen to represent the shear. 



A second quarter-wave plate is now superposed on the first, 

 and the black spot consequently moves up the normal to where 

 the shear is twice what it was at a ; this point, b, is noted, the 

 second mica plate removed, and the load reduced until the 

 black spot with one mica plate is brought to b . In this way 

 a series of points a, b, c, d on the normal are found at any one 

 of which the shear is twice what it is at the point below. 



Now it is proved later on that the strain at any point 



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