160 



Mr. A. Mallock on 



[June 19, 



a spherical head fitting into a spherical cavity in bb' at C, and C is 

 exactly half-way between A and A', and B and B'. When the bar is 

 bent in this frame by tnrning the screw D, the bending is accom- 

 plished by pure, equal, and opposite conples ; for since A A f BB' are 

 rollers and free to turn, there can be no tractions along the face of 

 the bar, and therefore the pressures are normal to the surf ace, and the 

 couples are equal in virtue of the equality of the distances AC A'C 

 and BC B'C. Thus for that part of the bar between B and B' the 

 radii of curvature R x and R 3 are constant, except in so far as they may 

 be affected by the surface distribution of pressure at B and B' which 

 as may readily be seen by the transverse section fig. 3, would tend 



Fig. 3. 



to make B 3 too large in the neighbourhood of the rollers ; but the 

 effect produced by this cause must be quite insignificant towards the 

 middle of the bar. The whole frame aa is mounted on a platform 

 with screw motions parallel and perpendicular to the length of the 

 bar, and the free ends of the wires are focussed in a fixed microscope, 



Fig. 4. 



Let hy, h 2 , \, & 2 , fig. 4, be the ends of the wires. The distances 

 Qh! l *t) (^1^2) resolved parallel and perpendicular to the length of the 

 bar respectively, are measured by the screw motions, first, when the 

 bar is unstrained, and again when it is bent by turning the screw 

 Let h, Jc, Ji, be these distances, then if 

 e= length of the wires, 

 r= radius of circle drawn on bar, 

 0= angle made by the wire with the normal to bar, 

 the increment of the distance between \ and h. 2 when the bar is bent, 



2er cos 6 



or h' — h is 



