  We extend and develop our previous work on the evolution of a network of
cosmic strings. The new treatment is based on an analysis of the probability
distribution of the end-to-end distance of a randomly chosen segment of
left-moving string of given length. The description involves three distinct
length scales: $\xi$, related to the overall string density, $\bar\xi$, the
persistence length along the string, and $\zeta$, describing the small-scale
structure, which is an important feature of the numerical simulations that have
been done of this problem. An evolution equation is derived describing how the
distribution develops in time due to the combined effects of the universal
expansion, of intercommuting and loop formation, and of gravitational
radiation. With plausible assumptions about the unknown parameters in the
model, we confirm the conclusions of our previous study, that if gravitational
radiation and small-scale structure effects are neglected, the two dominant
length scales both scale in proportion to the horizon size. When the extra
effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$
initially does not. Eventually, however, it does appear to scale, at a much
lower level, due to the effects of gravitational back-reaction.
