98 
The N.Z. Journal of Science and Technology. 
[Mar. 
The equation connecting s and x for a parabola is as follows : 
® u + 
x z 
6c : 
x- 
40c' 
-j- &c. 
from which it will be seen that provided the third and succeeding terms 
are negligible the two equations yield identical results. 
The distance c is known as the modulus of the catenary, and is twice 
the focal distance of the corresponding parabola. 
From the above equations it will be seen how closely the two curves 
resemble one another. And seeing that the properties of the catenary, as 
represented by its formulae, usually contain the curvilinear dimension s, 
the formulae for the parabola, being all straight-line dimensions, are more 
convenient. 
In considering the properties of a suspended wire with reference to 
transmission-lines it will be sufficient if we consider all cases which provide 
extreme conditions. Considering that a wire is subject to changing 
temperatures with the consequent changes in length, and to wind- 
pressures, it will be seen that we have four cases to consider : (1) Mini¬ 
mum temperature with high wind ; (2) maximum temperature with high 
wind ; (3) minimum temperature in still air ; (4) maximum temperature in 
still air. 
Case 1 gives the limit of tensile stress. Case 2 gives the greatest deflec¬ 
tion ; but since with increasing wind the angle of deflection becomes more 
nearly horizontal, the vertical deflection will always be less than in case 4. 
Case 3 is the limiting condition for stability, and will be considered later. 
Case 4 is, as we have seen, the condition of greatest vertical deflection, and 
is the subject of our first inquiry. 
Dealing with very high voltages, which unless properly safeguarded 
would become a grave menace to life and property, it is of the utmost 
importance that the wires should be carried at a sufficient height to render 
any chance contact impossible. For this purpose poles or supports must 
be provided of sufficient height, and spaced in such a way that at no point 
shall the wire approach nearer than the regulation safe distance from the 
ground. The diagram fig. 3 has been prepared to show the maximum 
sag-deflection between supports for different values of span and variation 
of temperature. 
Before we can determine this we must first determine the tension in 
the wire. Fig. 2 shows how this can be done graphically. 
An approximation is made throughout the following pages in taking 
T as the maximum tension in the wire instead of only the horizontal com¬ 
ponent. In certain extreme cases it is necessary to consider the vertical 
component also. In general, however, the assumption may pass. At the 
outset we have assumed a value, q, representing the ratio of load under 
wind-pressure to load in still air. The precise value that should be given 
to q is indefinite, depending on factors which are partly calculable and 
partly accidental. A value sufficiently wide must be given to cover all 
contingencies, with a little to spare. Taking a liberal value for q, we may 
in general ignore the vertical component of tension. 
In order to reduce sag-deflection to a minimum, the wire in case 1, 
the most extreme condition of loading, is taken as stressed to the yield- 
point, which for copper is 25,000 lb. per square inch. We can now obtain 
the tension in still air from the following formula, the derivation of which 
