196 Proceedings of Royal Society of Edinburgh. [sess. 
i.e. the rate of increase of contraction relative to increase in the 
degree of twist is constant. This result at once appears suspicious. 
Anyone who has made even qualitative experiments would expect 
that the rate of increase in take-up will become much greater as 
the twist gets harder. 
The error which Professor Amat has dropped into is simply 
this : he asserts that ab = a"cb. 
Now ab is merely a geometrical contour of the cylinder which 
cuts across the fibres (see fig. 9), and is not a material line or 
\ \ 
\ 
\ 
-V 
Fig. 8. — Diagram illustrating Professor 
Amat’s Theory. 
fibre itself. The continuity of this line is not preserved as 
torsion proceeds. Therefore we cannot say that ab is equal to 
anything at a subsequent period of the torsion. 
It may be asserted, however, that since ab becomes ab for one 
turn, that it must be reduced to some shorter length a"b for two 
turns. 
That is true ; but if this procedure be adopted, acb will be 
equal to twice the hypothenuse of a right-angled triangle erected 
on half of ab, and not equal to the hypothenuse ab' of a right- 
angled triangle erected on ab, since a"cb is two turns of the 
