What They Saw
They grew cells in batch or continuous culture with sodium nitrate, ammonium acetate or chloride, or dinitrogen gas. Cultures were either carbon- or sulfate-limited. Dissolved oxygen was kept above zero. Nitrogenase activity was measured by acetylene reduction and hydrogenase by methylene blue (or by adding H-T with radioactive tritium and measuring radioactivity of resulting water when oxygen was the electron acceptor).
There was about twice as much hydrogenase activity when cells were fixing nitrogen in batch than when they had either ammonium or nitrate. They cite other results in A. chroococcum and A. vinelandii that showed higher activity with nitrate than ammonium though, but still less than when fixing nitrogen. This might be because cells have to adapt to use nitrate, and they'll be fixing nitrogen before that happens. But care is necessary because activity changes over the course of a batch culture, increasing throughout exponential phase even when standardized by protein concentration.
In continuous cultures, they started growing with ammonium, then switched to nitrogen-free, watched what happened with hydrogenase and nitrogenase, and then pulsed a limited amount of ammonium. As expected, nitrogenase activity started up and rose to a plateau, then immediately stopped when ammonium was added, and restarted when it was removed. Hydrogenase activity showed a similar pattern, though more delayed, and it never went all the way to zero.
In sulfate-limited culture, hydrogenase activity was lower even when fixing nitrogen, about the same as with ammonium in carbon limitation, and when going from fixing to non-fixing (with ammonium), the activity declined a bit but then went back up to about the same level. Results were similar going from non-fixing to fixing. So with sulfate limitation, nitrogen source doesn't matter much.
Also with nitrogen-fixing cells in sulfate limitation, when they increased the dilution rate, hydrogenase activity decreased but nitrogenase increased. The decrease wasn't linear, though; it leveled off.
They also tested whether adding hydrogen to the atmosphere of an ammonium-grown culture would influence hydrogenase activity, and it did! Hydrogenase activity doubled. This was not the case with sulfate limitation though, only carbon limitation. They didn't test nitrogen-fixing cells.
What This Means
The continuous culture experiments helped overcome the constantly changing activity in batch cultures.
That hydrogenase activity lags behind nitrogenase activity increase when ammonium runs out could be explained by the last observation: maybe nitrogenase starts producing hydrogen (as it does) and this stimulates hydrogenase activity.
They reasoned from the data that excess carbon might inhibit hydrogenase activity somehow (like catabolite repression). I'm not sure that makes sense, but it seems possible, and does fit with the data from batch cultures, sulfate limitations, and increasing dilution rates. Interesting.