204 
Proceedings of Royal Society of Edinburgh. [sess. 
Let us now compare the analytical and experimental results, 
more closely by plotting on squared paper the figures obtained 
for one of the yarns, — e.g. 2/1 2s worsted, as shown in 
fig. 14. 
The equation y or y + a = 5 k (x + g^ 2 is the relation when 
the fibres are perfectly free to rotate. 
The equation y = kx 2 is the relation when the fibres have no 
relative motion. 
Fig. 14. 
Curve O c is symmetrical with the open-hand limb of the yarn 
curve about a vertical line through C. 
M is the point of maximum length for the condition of free 
fibre rotation. 
C is the point of maximum length for the actual yarn. 
It will now he instructive to summarise the main conclusions 
which may he inferred from a study of the analytical and 
experimental data set forth in the foregoing tables and 
diagrams. 
The following relations have been discovered to hold : 
