202 Proceedings of Royal Society of Edinburgh. [sess. 
mically. In order to suit the scale of the logarithmic paper, the 
ordinates really represent logarithms of half the percentage 
-contractions. 
It is found in every case that a straight line can be drawn 
evenly amongst the plotted points for each thread, within reason- 
able limits of experimental error. The assumed law is therefore 
true, because if 
y + a — c(x ± b) m 
log {y + a) = log c + m log ( x ± b) 
Y = C +mX, 
which is an equation of the first degree, and therefore represents 
& straight line. Also Y and X are the ordinate and abscissae 
respectively of any point on the diagram in fig. 12, m is the slope 
of the line, C is the intercept which the line makes on the axis 
of Y, 
Y 
m — tan 0 = — — - (see fig. 13). 
The Y axis is not shown on the diagram, but C may be calculated 
