1904-5.] Mr T. Oliver on Diameters of Twisted Threads. 481 
The Diameters of Twisted Threads, with an Account of 
the History of the Mathematical Setting of Cloths. 
By Thomas Oliver, B.Sc. (Lond. & Edin.). Communicated 
by Dr C. G. Knott. 
(MS. received January 27, 1905. Read March 20, 1905.) 
During the last generation the idea of reducing the “ setting ” 
of cloths to mathematical accuracy has been gradually taking hold 
of the minds of thinking men in the various textile trades. That 
this end is perfectly attainable is perhaps an open question, but 
there can be no doubt that the investigation of such problems 
must lead to a more satisfactory knowledge of the factors which 
determine the construction of fabrics. 
The base from which these “ setting ” theories begin is natur- 
ally the diameter of the thread, since the “set” of a cloth, i.e. 
the number of threads in some unit distance, usually the inch, 
made in any one weave or scheme of interlacing, is inversely 
proportional to the diameter of the thread employed in the 
construction of the cloth. Clearly, then, the first step in this 
investigation must be the determination of the diameters of the 
numerous “ counts ” or numbers of yarns in the various materials 
which are in use in the textile industries. But this is by no 
means such an easy task as it may seem at first sight. The 
diameter of a thread is neither easily measured at any one section, 
nor a constant quantity throughout its length. Especially is this 
the case with woollen yarns, in which the fibres projecting from 
the body of the thread in every conceivable direction renders the 
averaging up of the section a tedious and often unsatisfactory 
operation. 
The history of the mathematical setting of cloths is, however^ 
not confined to the last generation. The earliest record of a 
systematic attempt to attain this end is preserved in the British 
Museum in a copy of Mathematical Sleaing Tables , calculated 
by Mr Joseph Beaumont, a writer on the Irish linen trade in 
1712. He recognised that the setting of cloths should be based 
PROC. ROY. SOC. EDIN. — VOL. XXV. 31 
