384 Mr. A. Mullock. &.. M '*ure of [Mai. 1'.-. 



The reading was then taken on D. W being then moved forwards 

 until another scale division had been reached, the position of W . .u 

 D was again read, and so on. The process was afterwards reversed 

 and mill ings of the same kind taken when the load was being 

 diminished step by step. 



All these results were then plotted, and the curve drawn through 

 the observations gave a measure of the angle between the ends of the 

 beam in terms of the force applied to its middle point. In nearly all 

 cases the lines drawn through the plotted observations were straight 

 lines, within the limits of errors of observation, but, in general, tin- 

 lines for each substance differed appreciably, according to whether 

 the strains were increasing or decreasing. Some of the plotted 

 diagrams are appended to show the kind of accuracy attained. 



The actual linear motion of the central knife-edge was always verjfr 

 small, not in any case exceeding 0'00016 inch. 



I pass now to the treatment applied to the experimental results, in 

 order to deduce from them the values of Young's modulus. 



If I, b, t are the length, breadth, and thickness of a beam (originally 



straight), 



q = Young's modulus, 



F = Normal force applied at its mid-length, 

 = Angle made by the tangent at each end with the tangent at its 



mid-length, 



, FP 3FZ* 



= and = 



If, now, B be the distance between the divisions of the scale S, 



n, the number of divisions through which the images of the scales 



are relatively displaced, and 

 / the focal length of the collimator, 

 the angle observed, = nljf. 



Now = 40, because 20 is the actual alteration of angle between 

 MI and M 2 , and this is multiplied by two by the reflection. 



Also, if B be the reading of the position of W on the arm D, and r 

 the distance between K 4 and K s , the downward force acting on K 3 is 



F = W ~ ; 

 r 



3WR/P 

 hence q = 



In this expression^ for the value of q, the factor /r/cr is a con- 

 depending only on the apparatus, since I is the distance between K! 

 and K.. 



