42 
Proceedings of the Royal Society of Edinburgh. [Sess. 
If the bars be examined, it is seen that in each case there is an area in 
the region of the notch where the deformation has taken place in a manner 
different from that in the more remote parts of the bar. The explanation 
of this is readily apparent from the stream-line diagram, if it be admitted 
that it represents, even approximately, the system of maximum principal 
stress. For in the neighbourhood of the notch the stress lines (stream lines) 
are convex inwards, and there is, therefore, a tension normal to the system 
shown. Since the third principal stress — that in a direction perpendicular 
to the plane of the diagram— is zero, the surfaces of sliding cut the plane 
of the diagram, within the region considered, in lines which are every- 
where normal to the stress lines shown ; these surfaces are inclined at 50° 
to the plane of the diagram. In parts more remote from the notch the 
stress lines (stream lines) become convex outwards, so that the second 
principal stress of the face is one of compression. In this case the surfaces 
of sliding are normal to the plane of the diagram, and their traces on this 
plane are lines inclined at 50° to the stress system shown. If the bars are 
watched during the earlier stages of the deformation, it is seen that the 
first Liiders’ lines to appear are those in the region of least width ; upon 
the wide face these have a direction normal to the maximum principal 
tension, and upon the narrow faces they are inclined at 50°. The lines are 
very numerous on account of the relatively great intensity of stress here, 
and therefore most of the scale is removed eventually from this region. 
.The fact that many of the lines of Ltiders are normal to the direction of 
stress has been noticed by Hartmann, but he has considered them as 
forming a third system of deformations. So far as the writer’s observations 
go, these lines are always traces of surfaces which have the usual slope in 
another direction. 
When the stress lines (stream lines) have no curvature the second 
principal stress is zero — if the loading is simple — and in regions where this 
is the case the lines of Luders upon the wide face of the bar may be either 
normal to, or inclined at 50° to the stress lines. An attempt has been made 
to determine on the diagrams the points of inflexion of the curved stream 
lines, by laying a straight-edge along each in turn. In general, it appeared 
that there was a certain length sensibly straight between the convex and 
the concave parts — that is to say, the departure from straightness was so 
slight between two points on each stream line that it could not be detected 
by the eye. These two points were marked with as much care as possible, 
and two sets of curves were drawn through them, shown dotted in figs. 
2 b to 66. It should be understood clearly that no great accuracy is claimed 
for these dotted curves. The method of determination is rudimentary, 
