1919.] Anderson.—Long-distance Electric Transmission-lines. 105 
If z is less than x the apex lies within the span, and the pull of the wire 
is always downward. If 2 is greater than x the apex lies without the span. 
If z = x the apex is at the end of span, and when z — 0, at mid-span. 
Example : The span is 800 links and the slope 5° 00'. Then x = 400, 
and c, by fig. 2, = = 5370. 
z — x c tan 0 — x 
= 5370 tan 5° - 400 
= 69. 
Therefore the apex is 69 links outside the span, and we have an upward 
pull, the amount being the weight of 69 links of wire. 
In order to ascertain whether the line is stable we have to consider the 
adjoining span also and ascertain the resultant vertical pull. Owing to the 
property of the parabola established in equation (6) that the curvature with 
respect to the x axis is independent of slope, we may regard the slopes as 
purely relative. Consider the two terminal points in adjoining spans as on 
the same level, and regard only the change in slope at the middle point. 
Thus if we have two spans, one of 800 links sloping down 4° 00' and one of 
600 links sloping up 3° 00', the change of slope is 7° 00'. From the 
diagram fig. 5 the limiting angle for 8 chains is 4° 16' and for 6 chains 
2° 43'. Their sum is 6° 59'. We therefore miss stability by 1', or we may 
say that stability is practically neutral. 
As in connection with fig. 3, if the spans are of unequal length the 
tension, and therefore c, will not always correspond with that shown for any 
particular span. The error will, as a rule, be inconsiderable. In a special 
case we may refer directly to equation (7), giving the proper value to c. 
It is interesting to note in connection with fig. 5, where the curves 
are plotted for a parabola and are tangent curves which are very nearly 
straight lines, that the corresponding lines for the catenary lie about mid¬ 
way between the curve and the tangent at the line of zero slope. 
We have thoroughly examined what happens under various conditions 
m still air, and it only remains to form some idea what happens under 
wind load. 
When wind load comes on, the tension in the wire increases, the wire 
stretches, and therefore sag-deflection increases. 
