44 
Proceedings of the Royal Society of Edinburgh. [Sess. 
further, that the thickness of the bar does not remain uniform during 
this period, so that the third principal stress is no longer zero. But 
the resemblance of the fracture outline to the inner dotted curve is quite 
noticeable. 
In order to show more fully the form of the curves of deformation, a 
number of fine lines have been drawn upon the upper halves of figs. 2 b to 
6b. Passing upwards from the transverse centre line, the first series, 
which extend to the outer dotted curve, are everywhere normal to the 
stream lines ; these represent the traces of surfaces inclined at 50° to the 
paper. Above the inner dotted curve there are drawn two series of curves, 
sloping respectively to the right and to the left, which are inclined at the 
constant angle of 50° to the stream lines ; these represent the traces of 
deformation surfaces at right angles to the paper. The actual positions of 
the deformation lines found upon any bar must be considered as largely a 
matter of chance. 
If, as is most convenient, the stream lines are such that the flow is the 
same for each, then for each stress line the total tension (or compression) is 
constant. And, as with the stream lines the velocity of flow is inversely 
proportional to their width, so with the stress lines the intensity of tensile 
(or compressive) stress is inversely proportional to their width. Thus by 
careful measurements of the width of the stream lines it should be possible 
to determine closely the magnitude of the stress at any point of the bar, 
and to plot lines of constant stress. So far the writer has not attempted 
this rather tedious operation. For great accuracy, the holes in the brass 
plate for the coloured glycerine streams would require very careful spacing, 
in order that the stream system at this part of the template should be 
identical with the stress system at the corresponding place in the bar. The 
uniform spacing adopted is correct only for a template extending to infinity 
on that side of the notch. 
Summary. 
By experimental methods a close similarity has been shown to exist 
between certain simple stress systems and the corresponding systems of 
hydrodynamic flow. How nearly exact this similarity is, and how widely 
the application of the principle may be extended, are points which remain 
to be determined. 
In a simply loaded bar there are secondary stresses which vary with 
the shape of the bar; the existence of these secondary stresses explains 
some apparent anomalies in the character of the lines of deformation. 
