1909-10.] Method of investigating Certain Systems of Stress. 41 
occupies the space between the coloured streams. It has been shown 
by Stokes (2) that the stream lines of a viscous fluid, when in a very 
thin sheet, are sensibly the same as those of a perfect liquid, except for 
a distance from the boundaries equal to the thickness of the sheet. 
It is necessary, therefore, to keep the thickness of the inserted forms 
small ; they were actually cut from the thinnest Bristol board, and had 
a mean thickness of 0 0 15 inch. In order to obtain good photographic 
results the coloured supply of glycerine was tinted with chrysoidine. 
The method of investigation was as follows. The steel bars and the 
cardboard templates were cut, as nearly as possible, to the same dimensions. 
The bars were loaded, as already explained, until considered satisfactory, 
taken from the testing machine, and, after the removal of any loosely 
adhering scale, were photographed. Some of these photographs are repro- 
duced in figs. 2a to 6<x. Next, each cardboard template was inserted in turn 
in the flow apparatus, and as soon as steady conditions were established 
the system was photographed, with the results shown in figs. 2b to 65. A 
point — usually the middle point — of each deformation line was transferred 
from the print of the bar to the corresponding flow diagram, by means of 
tracing paper. Through this point on the flow diagram a curve was drawn 
so as to make a constant angle of 50° with all the stream lines which it 
/ crossed, and this curve was then transferred back, by the same means, to the 
photograph of the steel bar, as shown by the fine black lines in figs. 2c to 6c. 
The close agreement of most of these curves with the lines of deformation 
is very evident in the illustrations. 
The agreement, though close, is not perfect, for many reasons. There is 
first the fact, already mentioned, that the bar has been deformed somewhat 
by the load, and therefore the lines of Ltiders are not all due to the same 
stress distribution ; and the lines which appeared first are displaced 
slightly on account of subsequent deformations elsewhere. Further, the 
loading is seldom perfectly axial. Then, in spite of all the care taken, 
there are sure to be some errors in the geometrical construction, and 
others again in the double transference of the curves. Lastly, as has 
been pointed out by the writer on a previous occasion (3), the inclination 
of the lines of Ltiders is subject to some variation, and irregularities 
not infrequently occur, which may be due to an imperfectly axial loading, 
to an imperfectly homogeneous material, or to other causes unknown. 
The method of gripping the ends of the test piece (even if the load is 
perfectly axial), and the incorrect spacing of the apertures of the flow 
apparatus, give rise to slight errors which are probably negligible in 
comparison with the above. 
