CliiCULAli CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 181 
Diagrams 3-G give curves showing the variations of the stresses, with r, for the 
values of r equal to 0, (’2) a, (‘4) a, ('6) «, a. I have omitted the intermediate value 
(•8) a, because the series used converge in this case inconveniently slowly, and no 
methods of approximation, such as were employed in the case r — a, are here avail¬ 
able. Observation of the curves for the smaller values of r will, however, in most 
cases suggest the process by which they are deformed continuously into the curve 
Diagram 6.—Showing Stress rz for the Cylinder under Shearing Pull. 
Len^bha c3,Lon^ Axis of cyUnder. 
corresponding to r = a. In Diagram 3, of course, this is not obvious, but here, as has 
been shown, discontinuous changes occur. In Diagram G it is also not quite clear 
how the curve for r— (■G)a becomes transformed into the rectangle corresponding 
to r = «. The curve for r = (’G) <i has, however, already developed a double humj>, 
and its righthandmost ordinate’s rate of increase is fast diminishing. This suggests 
that the two humps will rise and aj)proach each otlier, ultimately covering the 
rectangle, wliilst the two “ tails” will dwindle doAvn to zero. 
Hemarks of a similar character ujjply to Diagram 5. 
