  We demonstrate operation of a constant-pressure flowmeter capable of
generating and accurately measuring flows as low as $2\times10^{-13}$ mol/s.
Generation of such small flows is accomplished by using a small conductance
element with $C\approx 50$ nL/s. Accurate measurement then requires both low
outgassing materials ($<10^{-15}$ mol/s) and small volume changes ($\approx 70$
$\mu$L). We outline the present flowmeter's construction, detail its operation,
and quantify its uncertainty. The type-B uncertainty is $<0.2$ % ($k=1$) over
the entire operating range. In particular, we present an analysis of its
hydraulic system, and quantify the shift and uncertainty due to the slightly
compressible oil. Finally, we compare our flowmeter against a NIST standard
flowmeter, and find agreement to within 0.5 % ($k=2$).
