1905-6.] Mr T. Oliver on Take-up in Twisted Threads. 195 
variance with experimental evidence. I give the opening sen- 
tences of his analysis, because it is in these I judge he goes wrong : 
“ Supposons, en effet, un cylindre de diametre d et longueur L et 
tachons de determiner le raccourcissement de ce fil par l’effet de 
la torsion. 
La ligne ab prendra la position bed quand L aura re 9 U un tour 
de torsion et nous aurons : 
ab = deb = ab' = L . 
De meme, l’on aura, pour deux tours de torsion, 
ab — a'eb — a"b' = L' . 
II s’ensuit que 
A' = L-L' = L± JL 2 - 7r 2 d 2 
Translation : — “ Let us suppose a cylinder of diameter d and 
length L, and let us try to determine the contraction of this thread 
by the effect of twist. 
The line ab will take the position bed when L will have 
received one turn of twist, and we shall have 
ab = deb = ab' = L . 
Similarly, one w r ill have for two turns of twist 
db = a'eb — a"b' = L' . 
It follows that 
A' = L - iMl ± ^\F^d 2 
Obviously, the positive sign to the radical gives an inadmissible 
solution, and, from the same principles as before, Professor Amat 
easily deduces that the contraction due to n turns of twist 
A n — L — JL? - mr 2 d 2 , 
which we may reduce to 
A n — 17 ^ n approximately. 
2L 
Differentiating this result, we find that 
dA n 7r 2 d 2 
dn 2L 
^if the ratio be taken as a constant^ , 
