Young s Modulus and Poisson's Ratio. 



207 



fig. 1, which refers to the measurement of the longitudinal 

 curvature. A pair of pillars with small mirrors, m, m, 

 pivoted to their upper ends, were fixed to the beam. The 

 lower ends of the pillars were bent in order to make point- 

 contact in the plane of the couples on the upper and lower 

 surfaces of the beam. For a beam 1 in. wide and £ in. thick the 

 distance a in tig. 1 was about lin. and was symmetrical with 



Fig. 1, 



respect to the central normal cross-section. The mirrors 

 were adjusted so that the scale was reflected by them along 

 the telescope shown, and the adjustment was made so that 

 the axis of the telescope, axes of the pillars, and the scale 

 were all in the plane of the couples. 



The full lines show diagrammatically the position of the 

 line of sight before the beam was bent. The chain and 

 dotted lines show their positions when the beam was bent 

 concave upwards. 



The correct scale-reading from which the curvature should 

 be calculated is x±y = z, and it was found that by suitably 

 choosing the lengths a, b, and //, the value of y could be 

 made sensibly to vanish, for 



y = c sin 6 — c sin (0 + 20), 



a — b' sin <f> — b sin </>+//( tan ., — ) 

 "costf' 6 " cos (0 + 20) 



