310
Molesworth’s pocket-book
•Telegraph Construction, by R. S. Brough__
continued
Equation to the Parabola:
x2 = 2 c (y - c).
. In the neighbourhood of its vertex, the catenary
differs but little from the parabola, whose focal
distance is equal to half the modulus of the
catenary.
Let p = strain at the vertex, flien c w = p.
‘ The strain at any point of the catenary is found
from the equation t = y w. Hence the strain at
the lowest point is least; and the strain at any
other point is equal to the strain at the lowest
point plus the weight of a piece of the wire, whose
length is equal to the height of the point in
question above the lowest point.
In telegraphy it is the maximum strain, or that
at the insulator, which is kept constant, and there-
fore the strain at the lowest point is variable.
Hence we have frequently to deal with catenaries
of different parameters.
Fibstly. When the points of support of the wire
are on the same level.
Let a = the length of the span.
d = the “ dip ” of the wire, or versed-sine
of the curve.
p = the strain at the lowest point of the
curve.
t = the strain at the insulator.
w = the weight of the wire per unit of
length.
s = the length of the wire in the span.