482 Proceedings of Royal Society of Edinburgh. [sess. 
on the diameter of the thread, although he erroneously applied 
this term, not to the actual diameter, but to what was really the 
pitch of the threads in the warp, i.e. the diameter of the thread 
plus the space between the threads. We find another stepping- 
stone in the evolution of this subject in comparative setting or 
caaming tables included in Murphy’s classical Art of Weaving, 
published about the beginning of last century. It is, however, not 
too much to say that “rule of thumb” held practically undisputed 
sway in this field until thirty years ago. 
About 1875 the late Mr Robert Johnstone, of Galashiels, a 
shrewd Scotch designer, possessed of remarkable powers of obser- 
vation, put out a little work entitled Designer’s Handbook, in 
which he gave a rule to set webs in the reed. After stating the 
rule, he appends the following note:— “I have often been asked 
why the square root of the size weight of a yarn multiplied by the 
numbers stated in this rule gives the number of the reed which 
should be used. I answer the question in this way : of an inch 
divided by the square root of any weight of yarn is equal to the 
diameter of it. Now if that is so, the diameter of 1 cut yarn will 
be -J- of an inch, and that of 25 cut will be of an inch.” The 
yarns were numbered on the Galashiels system. The above state- 
ment, though rather loosely worded, is the first instance, so far as 
the present writer is aware, in which the diameter of a yarn was 
employed in its proper sense as a basis on which the “ set ” for 
a given yarn might be determined. The conclusions arrived at are 
all the more remarkable since Mr Johnstone must have deduced 
them by observation on cloths alone, as he had no means of 
making micro-measurements. Besides, neither he nor his fellow- 
workmen could have been burdened with much education, nor had 
he the advantage of consulting literature on the subject, since there 
was none. Johnstone’s rule is held in high repute amongst Scotch 
designers, and it is safe to say that it gives very good results for 
the average Scotch woollen cloths, for which the rule was intended. 
The great epoch in this subject, however, occurred in 1880, when 
the late Mr Thos. R. Ashenhurst, then head of the textile de- 
partment of Bradford Technical College, gave out the results of 
his experiments and deductions to the textile public. Mr 
Ashenhurst’s experiments consisted of measuring the diameters of 
