  Cold samples of calcium atoms are prepared in the metastable $^{3}$P$_{1}$
state inside an optical cavity resonant with the narrow band (375 Hz)
$^{1}$S$_{0} \rightarrow ^{3}$P$_{1}$ intercombination line at 657 nm. We
observe superradiant emission of hyperbolic secant shaped pulses into the
cavity with an intensity proportional to the square of the atom number, a
duration much shorter than the natural lifetime of the $^{3}$P$_{1}$ state, and
a delay time fluctuating from shot to shot in excellent agreement with
theoretical predictions. Our incoherent pumping scheme to produce inversion on
the $^{1}$S$_{0} \rightarrow ^{3}$P$_{1}$ transition should be extendable to
allow for continuous wave laser operation.
