261 
1906-7.] The Strength of Twisted Threads. 
where y is the ordinate of any point on the curve. 
x „ abscissa of the same point on the curve. 
a „ height of the point where the curve cuts the y-axis. 
b „ „ „ asymptote to which the curve approaches. 
k is a constant number. 
In the graphs for single threads a practically = 0. The general equation 
then simplifies for such to the following form : — 
y=b- 
v 3 
kx 2 + b 2 
Jcbx 2 
kx 2 + b 2 
bx 2 
Fig. 6. 
*185 
Table V. shows the values of y = 2— - 9 — — — compared with the 
"02a -{- *o25 
experimental values obtained for 2/12’s crossbred worsted. This equation 
is obtained by substituting b = 2\ a— 1’43, k = m 02 in the general equation. 
Table V. also shows the values of 
_ l*9fl3 2 
^ x 2 + 14-4 
compared with the 
experimental values obtained for 6’s single crossbred worsted. This latter 
equation is obtained by substituting 6 = 1*9, k = ‘ 25 in the second equation, 
i.e. the one deduced for single threads from the general equation, 
y = 
bx 2 
Fig. 7 shows graphically the relation between the curve for the two-ply 
*185 
thread 2/12’s worsted and the graph to y = 2 — 
02a 2 + -325 
