SYDNEY

THE fastest way to lance a country’s anxieties about women and power is to appoint a female leader. For the three years and three days that Julia Gillard was prime minister of Australia, we debated the fit of her jackets, the size of her bottom, the exposure of her cleavage, the cut of her hair, the tone of her voice, the legitimacy of her rule and whether she had chosen, as one member of Parliament from the opposition Liberal Party put it, to be “deliberately barren.”

The sexism was visceral and often grotesque.

There were placards crying “Ditch the Witch,” toys designed for dogs that encouraged them to chew on the fleshier parts of her anatomy, and, most recently, a menu offering “Julia Gillard Kentucky Fried Quail — small breasts, huge thighs and a big red box.” By the end of her term, on June 27, the prime minister struggled to be heard above the sexist ridicule. When she addressed this, she was accused of igniting “gender wars.”

To point this out is not to imply that Ms. Gillard was flawless: far from it.

Her biggest problem may have been the way she became Australia’s first female prime minister. Under the Westminster system, voters elect parties, who are able to change leaders at will. In June 2010, Ms. Gillard, then deputy prime minister, deposed Kevin Rudd, with support from other members of their governing Labor Party, ostensibly because of poor polling. “The government,” she said, “had lost its way.” It was the first time that a sitting prime minister in Australia had been overthrown by his own party during his first term. Meanwhile, Mr. Rudd never left the picture. He stayed in government, and last month — almost exactly three years after Ms. Gillard had pushed him out — he returned the favor, after polls suggested that the party would be annihilated at the coming election.

Uneasiness over the way Ms. Gillard came to power fed deep currents of misogyny throughout her time in power. (She remains a member of Parliament but will retire at the election.)

She was pragmatic and effective, presided over solid economic growth, reduced Australia’s carbon emissions and enacted historic reforms in the areas of education and disability. History will be kind to her.

But she made many mistakes: abandoning a promise not to introduce a carbon tax, being slow to condemn corruption in her party, and negotiating a limp tax that failed to reap significant revenue from Australia’s mining boom.

She lacked canny political instincts and was unable to project her natural warmth, humor and empathy or convince the public of her sincerity.

Women across Australia had clinked glasses at her ascension: at last, the mold was smashed. She was an unmarried red-haired atheist with no children, living with a hairdresser boyfriend who often rose early to tend to her tresses. Yet Ms. Gillard was determined not to let her sex be a distraction. She fought the 2010 election hard, playing politics like the boys, with wit, pragmatism and tough debating skills. She ignored the sneers, the contempt and the catcalls.

Then, last year, her father died. While she was still grieving, a radio shock jock named Alan Jones declared that Ms. Gillard’s father must have died of shame. Shortly afterward, in Parliament, the leader of the Liberal opposition, Tony Abbott, said that Ms. Gillard’s government should “die of shame.” Ms. Gillard delivered a blistering response. She would not be lectured to, she said, by a man who had stood next to placards calling her “bitch,” and who had suggested that men had a better temperament for leadership. “My father did not die of shame,” she said coolly. “What the leader of the opposition should be ashamed of is his performance in this Parliament and the sexism he brings with it.”

“If he wants to know what misogyny looks like in modern Australia, he doesn’t need a motion in the House of Representatives. He needs a mirror.”

As her popularity dropped — especially among men — Ms. Gillard’s failings were unfairly pegged to the fact that she had dared to talk about the perils of female leadership. With gender dominating front pages for months, the media described her daily as a failed experiment. Even her fiercest critics conceded, in the final weeks, that no other prime minister was ever treated with such vitriol.

At her last news conference, Ms. Gillard said being the first woman “does not explain everything about my time in the prime ministership, nor does it explain nothing.” Her voice quavered when she said, “What I am absolutely confident of is that it will be easier for the next woman and for the woman after that and the woman after that, and I’m proud of that.”

The woman who had been known for playing politics like a man had suffered the most extraordinary, foul attacks on a woman we have seen in this country. Both her success and her failure acted like pipe songs, luring the snakes of contempt and woman-hating from their baskets. School students threw sandwiches at her.

Now the demons have settled, if wakefully. Mr. Rudd has revived his party’s chances at the next election, and commentators have turned from misogyny to taxes, carbon, refugees and investment; there is a discomfiting sense of relief that the woman has gone.

But we have all changed for having a female prime minister. Ms. Gillard was unable to control her party or her political narrative; unlike Margaret Thatcher, who silenced critics by staring them down, she seemed to only spur them on. But her steel and stoicism were remarkable.

And the robust discussion we had about archaic attitudes about women has mattered.

A 4-year-old girl from Canberra, when told that Australia had a new prime minister, said: “Really? What’s her name?” This, too, matters.