CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 175 
system of shears is, however, self-equilihrating. The shear is zero at the centre and 
at the circumference, and its greatest value does not exceed about 1/4 of the laterally 
applied shear. Its effects, at some distance inside the cylinder, will therefore he 
small compared witli the effects of the large and unljalanced lateral distribution 
of shear. 
We notice that, for so short a bar, the lateral contraction is very much less than 
the contraction we should expect according to the “ uniform tension ” theory. In 
fact it never amounts to GO per cent, of that contraction. For points deeper in the 
material, the contraction is much smaller than tliis. Thus, for /■ = (’2) o, the lateral 
contraction is 22 per cent, and for r = (‘4) a it is 9 per cent, of what it should be on 
the “ uniform tension ” hypothesis. This seems due to the fact, in itself extremely 
remarkaljle, that there are considerable radial and cross-radial tensions inside the 
material. Indeed, referring to Diagram 3, we see that the radial tension amounts to 
l)iagrani 3.—Showing Stress rr for the Cylinder under a Shearing Pull. 
about l/5th of the mean tension Q which would give the same total pull, and wJiich has 
been consistently taken as the unit of comparison. These tensions are changed to 
pressures after passing the ring of shear, whicli is in accordance with the general 
compressive effect mentioned aljove. 
It may be noticed that the shape of the successive curves on Diagram 3 suggests 
that, as we approach the outer skin, the two humps on either side of 2 = '5c would 
