“She always looks so extreme,” a fellow teacher observes of Maggie Smith’s trademark rigidity in “The Prime of Miss Jean Brodie” (1969), putting her finger on the straight-backed, nose-high hauteur audiences enjoyed for more than half a century.

A shrill and tragically short-sighted instructor at a school full of impressionable-aged girls, Jean Brodie proved to be the defining credit of the English stage legend’s screen career, to the extent that her strict-but-caring Harry Potter character, deputy headmistress Minerva McGonagall, could be the selfsame martinet, curdled by several more decades of disappointment. (Kids who grew up on the J.K. Rowling adaptations will surely appreciate “Prime” once they’re older.)

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That’s not to say she was never better. In fact, Smith, who died Friday, never gave a bad performance, and just as fine wines improve with age, that also goes for the legendary actor’s biting brand of vinegar, which became the most delicious ingredient in her run as the withering dowager of “Downton Abbey.”

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