  The fraction of cosmic string loops which collapse to form black holes is
estimated using a set of realistic loops generated by loop fragmentation. The
smallest radius sphere into which each cosmic string loop may fit is obtained
by monitoring the loop through one period of oscillation. For a loop with
invariant length $L$ which contracts to within a sphere of radius $R$, the
minimum mass-per-unit length $\mu_{\rm min}$ necessary for the cosmic string
loop to form a black hole according to the hoop conjecture is $\mu_{\rm min} =
R /(2 G L)$. Analyzing $25,576$ loops, we obtain the empirical estimate $f_{\rm
BH} = 10^{4.9\pm 0.2} (G\mu)^{4.1 \pm 0.1}$ for the fraction of cosmic string
loops which collapse to form black holes as a function of the mass-per-unit
length $\mu$ in the range $10^{-3} \lesssim G\mu \lesssim 3 \times 10^{-2}$. We
use this power law to extrapolate to $G\mu \sim 10^{-6}$, obtaining the
fraction $f_{\rm BH}$ of physically interesting cosmic string loops which
collapse to form black holes within one oscillation period of formation.
Comparing this fraction with the observational bounds on a population of
evaporating black holes, we obtain the limit $G\mu \le 3.1 (\pm 0.7) \times
10^{-6}$ on the cosmic string mass-per-unit-length. This limit is consistent
with all other observational bounds.
