244 Proceedings of the Royal Society of Edinburgh. [Sess. 
XXY. — The Influence of Twist on the Strength of a Thread. By 
Thomas Oliver, B.Sc. (Lond. and Edin.), Carnegie Research 
Fellow. Communicated by Dr C. G. Knott. 
(MS. received May 20, 1907. Read May 20, 1907.) 
On this very important subject I have not been able to discover much 
published work of a quantitative description. Professor Hartig, a writer 
in Dingier s Polytechnic Journal, 1879, appears to have made a special 
study on the strengths of threads, and was able to express the results of 
his investigation in the algebraic formula, 
ThfX 9 7ltC y 
y = —x A - —x + nk , 
A A 
where y = the resistance of the thread to rupture, i.e. the strength of the thread. 
x = the length of the thread under test. 
A = the length of each fibre composing the thread. 
(The fibres are evidently assumed of equal lengths.) 
n = the number of fibres contained in a cross section of the thread. 
k = the resistance of a fibre to rupture, i.e. the strength of the fibre. 
/x = the coefficient of resistance to slipping of the fibres on each other. 
Professor Hartig evidently used /x in a different sense from its general 
meaning as the coefficient of friction. In his formula fx is the absolute 
resistance to slipping per unit length of fibre, and not a ratio. He stated 
further that jx varied between the limits '00005 gram and 9015 grams 
per millimetre, the former limit applying to threads composed of silk 
filaments without twist, the latter limit to woollen threads with an 
abnormally “ hard ” twist. 
I have not the full details of Professor Hartigs analysis at my disposal. 
I am indebted to a French work, Essai des Matieres Textiles, by J. Persoz, 
Director of the Conditioning House at Paris, for the above information. 
However, it is not difficult to see how the formula has been arrived at. 
Suppose for simplicity that a thread is composed of parallel lines of 
fibres broken at intervals of A, as shown in fig. 1. The adhesion necessary 
to form a thread could be afforded by a size or glue. 
Let M and N represent the jaws of the testing machine, distant x units 
of length from each other. A and B represent lines of fibres which are 
continuous ; C and D, lines of fibres which are discontinuous between the 
