Numbers before 1850 involve increasing amounts of guesswork, and are pretty unreliable before 1800. Anyhow, the periods of inflation there correspond to gold strikes.

I don't think the graph supports the notion that inflation was more stable after the 1800-1914 period.

(Inflation during the Revolutionary War and Civil War was high due to the government printing money like mad. It would be fair to not count those periods. In fact, the Constitutional prohibition on printing money came about as a reaction to the Revolutionary War inflation.)