40 
Proceedings of the Royal Society of Edinburgh. [Sess. 
that the original stress distribution is much altered. The stress system 
constructed from such data would be left very incomplete, and might be 
far from exact. 
For some time the writer had suspected that the determination of 
a system of stress was closely connected with that of hydrodynamic 
flow under corresponding conditions. The similarity in the mathematical 
investigation of the problems afforded by elastic solids and by viscous 
fluids supported this view. The practical value of demonstrating such 
a connection would be very great. The following comparison of certain 
systems of “ laminar ” fluid motion with the corresponding “ laminar ” 
stress systems is a first step in this direction. 
A stream line is defined to be a line drawn in a fluid so that its 
direction at any point is the direction of fluid motion at that point. 
Similarly, a stress line may be defined as a line drawn in a solid so that 
its direction at any point is the direction of one (the same) of the principal 
stresses at that point. It is desired to examine whether or not, under similar 
boundary conditions, the stream line system for a fluid is identical with 
one of the stress line systems for a solid. 
Attention is confined for the present to systems of stress due to the 
application of simple tensile loads to bars of various shapes. The treat- 
ment throughout is necessarily experimental. Test-bars of soft mild 
steel, 2 J inches wide and J inch thick, were employed ; these were shaped 
to various forms as regards their wider dimension, some of which are 
shown in figs. 2a to 6a. In all cases the thickness of the bar was left 
uniform. The tensile load was applied in the ordinary way by gripping 
the ends of each bar with serrated wedges in a testing machine. The 
arrows on the figures show the direction of the pull. The loading 
was carried to a point somewhat above the elastic limit of the piece, 
so as to obtain well-defined deformations, without at the same time 
allowing these to progress so far as to cause very great distortion. 
The bars had a smooth coating of mill scale, the removal of which from 
the deformed regions allows of good photographic reproduction of the 
specimens. 
The stream line diagrams were obtained by means of the well-known 
apparatus devised by Professor Hele-Shaw (1). In this apparatus the 
flow takes place between two pieces of plate-glass, which are kept a small 
distance apart by a thin template of the required shape. The fluid used 
is glycerine, of which there are two supplies, one clear and one coloured. 
The coloured supply is fed through a number of carefully spaced holes 
in a brass piece inserted in the upper glass plate, and the clear glycerine 
