246 
Proceedings of the Royal Society of Edinburgh. [Sess. 
D is the position of the lease rods, which determine the position of the 
threads in the warp relative to each other, and also the length of warp 
thread which shall be under increased strain during shedding. A is the 
fell of the cloth. 
The dotted line AD shows the position of the threads when the “ shed ” 
is closed. In order to form an opening or “ shed ” through which to pass 
Fig. 2. 
the shuttle carrying the weft, part of the threads are raised into position 
ABD, while the remainder are depressed into position ACD. 
AB + BD> AD . 
Therefore a length of thread AD must be able to stretch AB+BD— AD 
without the stress reaching the limit of elasticity, or breakage will occur 
during the continued repetitions of stress in shedding. The length AD 
is never much less than 27 inches, and in the broad looms of the Scotch 
woollen trade will be more. Therefore the length tested should be about 
© 
27 inches. 
Now, in all threads, except those of thrown silk, the fibres are much 
shorter than this : e.g. in crossbred worsted, 4-inch fibres ; in Botany 
worsted, 2 J -inch fibres ; in carded merino threads, 1-inch or even shorter 
fibres, are very common. 
Professor Hartig’s formula is only applicable when x is less than X ; 
but we have just seen that testing is only of value to the manufacturer 
when x is about ten times greater than X. 
Let us now consider the limiting case when x — 0, i.e. when the length 
of the thread under test is infinitesimal. 
The formula becomes 
y = nk , 
i.e. the strength of the thread is equal to the sum of the strengths of its 
component fibres. 
Practically, it would not be possible to test infinitesimal lengths of 
thread. Probably 1 millimetre would be the minimum length which 
could be tested on the best-designed machines. Experimental results show 
that the breaking strength of 1 millimetre of thread is never anything 
near equal to the sum of the breaking strengths of its fibres. There are 
several reasons why this should be so. 
