114 
Proceedings of the Royal Society of Edinburgh. [Sess. 
The last five columns of Table IV. are headed by the letter which 
distinguishes the corresponding graph in fig. 5. A ± is obtained by calculat- 
ing from equation (1), A 2 from equation (2), B x from equation (3), B 2 from 
equation (4); C is a mean of the analytical equations, obtained in the 
conclusion of the mathematical analysis. The value of s, the distance 
from the axis of the thick thread of that centre of revolution which 
makes y 1 = y 2 > is calculated and substituted in either equation. 
The values of d 2 , f, n ± and n 2 are taken from Table III., and substituted 
in the equations. The latter thus reduce to the following simpler forms 
for the particular case under consideration. 
Fig. 5. 
Corresponding to 
Equation 1 , ft = 6 |g ( 1 1 *78* + 324) Graph 
»> 2? ft = 65*8^ 9’26# + 28 ) ,, A 2 
j) 3, ft = 65 -g ( 5*2 # + 324) „ B x 
” 4 ’ ^ = 6^ (2M * + 28 ) „ B 2 
Mean equation, y 1 or ft = gipg (10‘57# + 30*5) , C 
Fig. 5 shows graphically the results of Table IV. The ordinates 
represent percentage contraction ‘ the abscissae, turns per inch of twist. 
