Can you please explain this chart to me?
Why does the R-1830 have less horsepower at 8,000 feet that 10,000 feet? In both cases the blower is on low, and at 8,000 feet the atmosphere is denser.
Exactly because the atmosphere is denser.
When the auxiliary S/C is in 'low' gear on the R-1830-86, the rated altitude (a.k.a. critical altitude) is at about 12000 ft. Rated altitude is the altitude above where the throttle can be fully opened; under that rated altitude the throttle is partially closed in order for the boost to be kept constant, or the engine might suffer detonation due to over-boosting. Lower we go under the rated altitude, the more throttling is needed to keep the boost in check; more throttling = more losses = less power. Obviously, if we go at even lower altitude, the supercharger need to start using a lower gear (if present - there was a lot of engines that have had just one S/C speed) so the throttle can be fully opened now (= less losses = more power) and the S/C will be drawing less power (= again more power). When in 'neutral' gear (as found on P&W 2-stage supercharged engines), the auxiliary S/C stage is de-clutched, or disengaged, meaning it draws no power from engine, meaning again there is more power left to turn the prop; the aux-stage is bypassed by the 'plumbing' and all supercharging is done by engine-stage supercharger.
Note that less dense atmosphere at 12000 ft than it is on, say, 8000 ft, will also mean that the exhaust backpressure is lower, and the air entering the cylinders is cooler a bit - those two things might add slightly to the engine power.
Please note that the graph is not very accurate when it is about lines under the rated altitudes, the power loss due to throttling is/was a lot less severe. Graph was not made by engine companies, but it was done by F. Dean by using the known power vs. altitude values. I'll attach the manufacturer's graph for the engine of FM-2.
The engines with swirl throttle managed to avoid a lot of throttling losses (Mikulin AM-35A and later, Jumo 213 series), so did the engines with hydraulically-driven supercharger (DB 601 and later engines, the V-1710 versions with hydraulically-driven auxiliary stage, as installed on P-63 and P-82 - they still have had throttle plates). The turboed engines were also not suffering much due to throttling losses, if at all, they used waste gates as means of avoiding not-certified over-boosting.