1904 - 5 .] Mr T. Oliver on Diameters of Twisted Threads. 483 
a large number of threads in different sizes and materials with a 
micrometer, and taking the average for each yarn number. These 
numbers are tabulated in his work on Textile Calculations , 
published in 1884. 
Subsequently he found that the following empirical formula 
gave results closely approaching to the number tabulated from 
his experiments. The diameter, expressed as a fraction of an 
inch, is equal to the reciprocal of the square root of the number of 
yards per lb., with a deduction of 10 per cent, from the square 
root for worsted, cotton, linen, and silk yarns, while for woollen 
yarns a deduction of 16 per cent, should be made. This deduction 
is sometimes spoken of as the allowance for surface fibre, which 
is, however, quite erroneous, as the surface fibre is far too variable 
a quantity to be reckoned as proportional to the diameter or any 
other attribute of the thread. It has really no physical meaning 
whatever. The reason that there should be a deduction is purely 
a mathematical one, i.e. to make one number correspond with 
another. Ashenhurst was helped towards the explanation of his 
diameter rule by Mr T. F. Bell, of Belfast, in 1889. The full 
correspondence on this matter will be found in the Textile 
Educator , February 1889, of which Mr Ashenhurst was the 
editor. There is little doubt that it is a very useful formula, 
and gives very good results when applied, in conjunction with his 
other setting formulae dealing with variations in weave (a subject, 
however, outside the scope of this paper), to the average run of 
cloths made in Yorkshire, where the practice is to set cloths 
much closer than is customary in the Scotch trade. There has 
been very little done in this field of research since the time of 
Mr Ashenhurst’s experiments. The statements enunciated by him 
have been repeated by lecturers, and have figured in text-books 
and examination papers for over twenty years, until textile 
students are beginning to consider these statements as absolute 
as the inverse square law of gravitation, while practical men 
rock over to the other extreme, treating the whole matter as 
theoretical humbug, and people generally do not trouble to in- 
vestigate the subject further. This course is clearly not in 
accordance with the scientific spirit of inquiry permeating other 
branches of industry at the present time. While all honour is 
