102 
The N.Z. Journal of Science anb Technology. 
[Mar. 
It happens that the range of tension along the 90° isothermal is small, 
and for all practical purposes the tension may be taken as constant. Sag- 
deflection then becomes proportional to the square of the span. 
CO * 
For office use a template may be cut from the formula y = —, giving 
AC 
the proper value to c, using a distorted scale for convenience ; then on the 
longitudinal section slide the template along the tee square till the two 
points of support lie on the curve ; draw in the curve and measure the 
clearances vertically. 
So far only level spans have been considered. It is a well-known pro¬ 
perty of the parabola that the locus of middle points of all parallel chords 
is a diameter passing through the point of contact of the tangent parallel 
to those chords. 
It follows from this that the greatest sag is always at midspan. 
Now, in the parabola OADF (fig. 4) take any chord AF, C being its 
middle point. Let OB = z and the span — 2x. Then, since y = 
z 
AB = 2c 
DE = 
FG = 
CE = 
(z -\- x) 2 
2 c 
(z 2x) 2 
~2c 
AB +FG 
The maximum sag in the span AF 
= CD = CE — DE 
= AB + FG - DE 
z 2j r {z j r 2x) 2 (z A*) 2 
4c 
2 c 
x* 
2 o' 
x* 
2 c 
.(6). 
