A segment of the chain of length s starting
from x = 0 will have a tension T of s on it
at its upper end, at an angle of phi of s
to the horizontal. It will have a horizontal
tension T of zero at its other end, and its
weight, lambda s g, will act downwards. Since
the chain is hanging in equilibrium, we can
resolve forces. Resolving vertically T(s)
sin phi(s) equals lambda s g. Resolving horizontally,
T(s) cos phi(s) equals T(0). Dividing equation
1 by equation 2 will eliminate the T(s)
and will yield an equation for tan phi, in
the form s/a, where a will be some combination
of our constants.
