1904-5.] Mr T. Oliver on Diameters of Twisted Threads. 491 
projection width varies with the square of the eccentricity of the 
elliptical section. 
These curves are shown in fig. 7. 
The comparison of these results with that obtained by con- 
sidering the thread in its unstrained condition is beset with 
difficulties. The volume of the thread must necessarily be less 
Fig. 7. 
in the strained than in the unstrained condition, because (1) the 
yarn will stretch and thus decrease its sectional area; (2) each 
single thread is subjected to lateral compression. The latter cause, 
however, will not greatly affect the volume unless the twist is 
hard, as the fibres are free to a considerable extent to move 
away from the surface of compression. The amount of this com- 
pression cannot be arrived at by a priori reasoning, but must be 
