Elastic Solids to Metrology. 



597 



apart. From the symmetry the tangent at the middle point 

 is horizontal ; this is taken as axis o£ x, the axis of y being 

 drawn vertically downwards. In fig. 2 the support shown, A ? 

 is comparatively near the centre. In such a case is the 



Fig-. 2. 



Fisr. 3. 



Fig. 4. 



Fig. 5. 



Fig. 6. 



highest point of the bar bent under its own weight, and 

 the curvature is of one sign throughout. In ligs. 3 to 6 the 

 supports are at a greater distance from the centre, and the 

 curvature changes sign between and A ; this is the normal 

 condition in modern standards of length. The scale to which 

 the ordinates are drawn is the same in all the figures 2 to 6, 

 the bending being much exaggerated. 



The notation employed is as follows : — E is Young's 

 modulus, p the density, '21 the complete length of the bar, 

 ay the cross section, w (= gpco) the weight per unit length, 

 o)tc 2 the moment of inertia of the cross section about the 

 perpendicular through the C.G. to the plane of bending. 



In Ihe absence of gravity the bar would be strictly hori- 

 zontal ; y denotes the vertical displacement, when gravity 



Phil. Mag. S. 6. Vol. 2. No. 12. Dec. 1901. 2 R 



