20G 
MR. L. N. G. FILON ON THP] ELASTIC EQUILIBRIUM OF 
The system of frictional shears required to prevent the ends expanding will be 
towards the centre ; tlie parts of the material round the centre will therefore be 
de})ressed, and the compressing |)lanes (supposed rigid) will have to compress 
the outei' portions more than the inner, if the cross-section is to retain its original 
plane form, i.e., remain in contact with the compressing planes throughout. It is 
thus not surprising that the greatest pressure should be at the perimeter, being in 
fact nearly 2d times the pressure at the centre. 
Diagram 9.—Showing Stress for Cylinder com¬ 
pressed between Rough Planes (second example). 
Lengths aLon^ Axis of cyLinder. 
Diagram 10.—Shomng Stress rz for Cylinder com¬ 
pressed l)etween Rough Planes (second example). 
We see also that, near the mid-sections, the cross-radial traction changes from a 
pressure to a tension as we go towards the circumference, so that the outer parts of 
the material are subject to two pressures, parallel to the axis and the radius respec¬ 
tively and to a tension, at right angles to these. It should be noticed here that, in 
the diagrams, the ordinates representing the stresses increase negatively upwards. 
This has been found convenient in this case, where, OAving to the general pre¬ 
dominance of ju'essures, the greater paid of the stresses haAm the negatiA-e sign. 
