208 Mr. H. Carrington on Determination of Young' s Modulus 

 Hence 



a tan 6-{a-(b' + b) sin $} tan (6 + 24)) 



lJ= . , ie 



1 -f tan j ? 



g-$)tan(0 + 2$) 



or 



a{tan(9-tan (0 + 2<ft) | 4- {(&' + &) sin <fr|- tan (0 + 2<ft) 

 l4-tan(|-<£jtan(04-20) 



Neglecting the square and higher powers of the small 

 quantity (j> in the numerator and writing 



1 + tan ( ^ - <j)\ tan (0 4- 20) = 1 + tan - tan = sec 6, 



then y sec 6 = <t>{(b' 4- 6) tan 0-2a sec 2 <9}. 



.-. y = ${(&' + &)sin0-2asec0}. 



4a 

 Hence if sin 26 = y^y, tllen V = °- 



This relation is satisfied if, for instance, 6 = 1-5 in., 6' = 2*5 in.. 

 a = lin., and (9 = 45°. 



The above analysis and the diagram in fig. 1 will also 

 apply to the lateral curvature ; the axes of the pillars, axis 

 of the telescope, and the scale then being in the plane of the 

 central normal cross-section of the beam. 



When using the method, the beam was supported in a hori- 

 zontal position on knife-edges 12 in. apart, and symmetrical 

 with respect to the pillars and the central normal cross- 

 section. Two other knife-edges were placed on the beam at 

 points 8 in. apart, which were also symmetrical with respect to 

 the central cross-section, and the couples were applied by 

 weiohts suspended from the inner knife-edges. The weights 

 were increased by small amounts, and after every increase 

 both the scales were read. The readings were then plotted 

 against the weights, and the slopes of the resulting straight 

 lines were proportional to the principal curvatures. Thus, 

 if the values a and I in fig. 1 were the same for both pairs 

 of pillars and scales, then Poisson's Ratio was given by the 

 ratio of the slopes of the two lines. Also if M was the 

 bending moment and x the corresponding scale-reading for 



