262 Proceedings of the Royal Society of Edinburgh. [Sess. 
TABLE y. 
X. 
o ‘185 
2/12’s Worsted. 
l’9x 2 
v — 
6’s Worsted. 
J '02a; 2 + -325' 
J cc 2 + 14 - 4 ' 
0 
1-43 
1-43 
0 
•04 
1 
1*46 
1-44 
T2 
•06 
2 
1-54 
1-54 
•40 
•26 
3 
1-63 
1*64 
•73 
•60 
4 
1-71 
1*71 
1-00 
•99 
5 
1-78 
1-77 
1-20 
1-21 
6 
1-82 
1-82 
1-36 
1-36 
7 
1-86 
1*86 
1-46 
1-46 
8 
1*89 
1-89 
1*55 
1-51 
9 
1 *91 
1-92 
1-61 
1*54 
10 
1-92 
1-94 
1-66 
1-62 
11 
1-93 
1-96 
1-70 
1*65 
12 
1-94 
1-97 
1*73 
1-69 
13 
1-95 
1-97 
1-75 
1-72 
14 
1-96 
1'98 
1-77 
1-75 
The asymptote to which the latter graph approaches as x increases is 
y = 2. This asymptotic strength is much less than the breaking strength 
of 1 millimetre of thread, which, as shown in Table IV., is 2’66 lbs. There- 
fore it would appear not to be possible to construct a thread stronger than 
about 75 per cent, of the strength of 1 millimetre of thread. The graph 
of the experimental results practically coincides with the graph of the 
assumed “ witch ” curve. 
Fig. 8 shows similarly the relation between the curve for the 6’s single 
thread and the graph to y = — — — — ; the asymptote to which the latter 
x ~ f- X4 4 
approximates when x is large is y — T9. This maximum strength is 82 per 
cent, of the strength of 1 millimetre of the 6’s worsted thread. The 
