1909-10.] Method of investigating Certain Systems of Stress. 39 
the third principal stress is zero. Thus, when one face only is con- 
sidered, the deformations may be inclined at an acute angle to the 
longitudinal edges of the bar, as ab (fig. 1), or they may be normal to 
these edges, as de. Further examination shows that a normal line, cb 
or de , of one face becomes a sloping line, ba or ef, of an adjacent face, 
and that there are other lines which slope continuously across all four 
faces. 
When a well-developed network of Luders’ lines has been obtained upon 
a bar subjected to a “ laminar ” stress system, the general scheme of stress 
A 
Y 
Fig. 1. 
direction can be constructed by simple geometry. This method of investi- 
gation, due originally to Hartmann, can be applied usefully to problems 
with which pure mathematics is at present unable to cope ; but it suffers 
from a disadvantage which limits its employment. For some deformation 
must occur before any Luders’ lines appear, and hence there is some 
distortion of the original system of stress. This is not very serious 
if the stress is fairly uniform throughout the piece ; but the cases in 
which the stress variation is considerable are those which particularly 
require investigation, since they offer so many difficulties to mathematical 
solution. In these cases only the parts of the body where the stress is 
greatest will show any lines, unless the deformation is carried so far 
