﻿in a Rectangular Bar by means of Polarized Light. 5 



The optical arrangements consisted in a source of light L 

 (a portable electric lamp with a ground-glass globe was 

 used), a polarizing nicol M, which was placed close behind 

 the glass bar, and an analysing nicol N, which was placed 

 on a small stand some distance away, and into which looked 

 a telescope T. The latter was focussed upon a network S 

 of squares o£ 5 mm. side, which was engraved upon a glass 

 plate and placed in contact with one of the vertical side faces 

 of the bar. 



The method of observing was as follows : — the nicols M 

 and N had their axes crossed and inclined to the vertical at 

 the required angle. A sufficient load was then applied, and 

 the corresponding isoclinic line traced by observing the 

 position of the black band with regard to the squares of the 

 network S and transferring it to squared paper. 



The band had always a certain breadth, but, except on a 

 few occasions, it was never so inconveniently broad as to 

 prevent its centre from being located with fair accuracy. 



In this way, by varying the inclination of the nicols to 

 the vertical, charts of the isoclinic lines were obtained. 

 From such charts the measurements were made of which 

 the results are recorded. 



§ 3. Theoretical Results taken as the Basis of Comparison. 



If we consider the flexure of a rectangular bar of span 2a, 

 height 2b, and breadth 2c in a vertical plane, the axis of x 

 being the axis of the bar, the axis of?/ vertically upwards, 

 and the axis of z perpendicular to the plane of bending, we 

 notice first of all that in strictness the system of stresses 

 P, S, Q acting in the planes parallel to sry (P being the 

 normal tension across a face perpendicular to x, $ the vertical 

 shear across the same face, and Q the normal tension across 

 a face perpendicular to y) is not independent of z, but varies 

 as we move transversely across the bar. 



If, however, this variation (at all events in so far as it 

 affects the principal axes of stress) were at all serious, it 

 would cause a variation in the axes of polarization of the 

 transmitted light as it travelled through the beam. Such a 

 variation would destroy all possibility of quenching the light 

 between crossed nicols, and the mere fact of sharply defined 

 black isoclinic lines being visible is evidence that the axes 

 of polarization inside the glass remain fairly constant as we 

 move across it transversely. 



We may, therefore, assume without serious error that the 

 stress system is approximately independent of :. In this 



