1904-5.] Mr T. Oliver on Diameters of Twisted Threads. 485 
while the other series, which interlaces the warp transversely 
according to some definite scheme or weave, is called the “weft.” 
Therefore the number of threads which can be crowded into a 
given distance in a horizontal plane, i.e. into cloth, must be 
dependent upon the horizontal dimensions of the threads. If a 
single thread is stretched horizontally, it is evident that its 
Fig. 1. — Horizontal Plan of Thread. 
horizontal projection is a rectangle if perfectly even spun, but in 
the case of a twofold twist the outline of the projection consists 
of two overlapping curves, each of which will be readily recog- 
nised as a curve of sines. 
At section A of fig. 1 the maximum width = two diameters 
of the single thread ; at section B, the minimum width = one 
diameter only ; while between A and B the projection width 
assumes every value from two diameters to one diameter as we 
pass from A to B. 
Fig. 2. — Section A. 
Fig. 3. — Section B. 
In passing beyond B on to D it is evident that the same values 
will be reached, but in the reverse order, until at D the projection 
width is again 2 d, where d = the diameter of the single thread. 
The next part of the problem is to find the average horizontal 
projection, because if we warp a large number of threads or weave 
a large number of picks (as the weft threads are technically 
termed) side by side, the probability is that the broad parts of 
