98 
Proceedings of the Koyal Scciety of Edinburgh. [Sess. 
The results of Table III. are shown graphically in fig. 1, while the 
graphical interpretation of Table IV. appears in fig. 2. Percentage con- 
tractions are plotted as ordinates, and yarn number reciprocals as abscissae : 
The reciprocal of 12 = ’0833 
„ „ 16 = *0625 
„ „ 24= 0417 
Fig. 1. 
11C denotes the graph for 11 turns of crossband twist, while 60 denotes 
the graph for 6 turns of openband twist. 
The graph which lies most evenly among the plotted points is a straight 
line in each case. Further, the openband lines all converge to a point in 
the second quadrant, while the crossband lines converge to a point in the 
fourth quadrant. That the graph may be a straight line is dependent on 
the degree of twist in the singles being a linear function of the yarn 
number. 
Equations (7 ) y — x(5x + 2n) -4- 4C 
and (8) y = x(5x— 3re)-r- 6C 
are empirical formulae which give results of practically the same value 
as the fundamental formulae (5) and (6), and also approximate closely to 
