The seeds of the women's competition have never found the turf of these courts quite so barren; but nor, equally, is there much in the way of fresh, green roots. For not even Zheng Jie, the wild card whose survival to the semi-finals testifies to the fate of the four women originally drawn to contest them, can quite vitiate a sense that the passage of the Williams sisters has been mapped out rather more inexorably.
On the hottest afternoon of the tournament, by far the most intimidating quarter-final performance came from Serena, who pulverised Agnieszka Radwanska 6-4, 6-0. Over the previous week her young opponent had seemed one of the few candidates to fill the new vacuum at the top of the women's game, caused first by the retirements of Justine Henin and Kim Clijsters, and expanded here by the brittle performances of Ana Ivanovic and Maria Sharapova. But the way the situation is being exploited so mercilessly by the Williams sisters suggests a stagnant interregnum rather than a changing of the guard.
Radwanska sporadically looked the part in the first set, trying to keep her opponent on the move, but in the second she was pinned back by a fusillade of heavy serves and returns. The set was all over in 19 minutes.
Venus was made to work rather harder by Tamarine Tanasugarn, but turned up the volume whenever necessary. In the dying embers of her resistance, Tanasugarn helplessly discarded her racket after a serve of 125mph blurred past her; Venus promptly fired the next one across at 127mph, matching the tournament record she set in the fourth round. Earlier, in the process of saving six break points in a single game, she had produced three serves of 125 or 126mph. Seeming as restless as her sister would later prove ruthless, she won 6-4, 6-3, without really finding her range.
Venus, of course, was a pivotal figure in the campaign for prize money parity with the men, and found her due reward last year, picking up the same cheque as Roger Federer. But whatever their relative standing in the eyes of the fans, the suspicion persists that the biggest problem for the women's game is no longer equality, but sameness. There is a lack of conviction in the next generation, and there must be a dread among the organisers that the Williams sisters will produce a final as arid as the two they have already contested here.
Even after all these years, they are admired here rather than adored. But surely their distaste for the treadmill of the tour merits greater sympathy, and likewise their ability to marry the insouciance of the dilettante to a competitive hunger as ravenous as any dour professional. They may not be sweet, but they have their own confectionery appeal: Serena being a gourd of power, and Venus the physical embodiment of hauteur.
Tanasugarn certainly played her part, at 31 determined to enjoy the biggest stage of her career. But feisty as she was, she could not match the dynamism of the other diminutive Asian who had entered uncharted territory. In defeating Nicole Vaidisova 6-2, 5-7, 6-1, Zheng became the first Chinese player, male or female, to make the last four of any grand slam. In the summer when American athletes go to Beijing to test the balance of sporting power, she proved far too combative for Vaidisova, who surrendered the first set with a tame double fault and – much like Ivanovic, when Zheng was snapping at her heels – never settled into her elegant stride.
Serena is likely to prove rather less pliant. "I think she's been doing a fabulous job," she said of Zheng. "And I don't think it's luck. I'm definitely not going to underestimate her." But nor would she overestimate her sister. Asked if Venus was a worthy favourite for the title, she said: "I would never say she's the favourite when I'm still in the draw. What are you on?" Pressed to name the one quality she might take from her sister, she relented. "Wow, I would have her legs. She has the sexiest legs."
Venus must first deal with Elena Dementieva, who eventually saw off Nadia Petrovna 6-1, 6-7, 6-3 in a schizophrenic encounter that disclosed irresolution in both players. As fifth seed, Dementieva should be favourite. But nobody is under any illusions.
"We want to deserve to be there," Venus said, when asked about the destiny that seems to beckon the siblings. "We have to play the best tennis to deserve it. I think it doesn't matter for us, how the next player's playing. We believe that we're the best on the court at the moment."
Out of court: What Serena and Venus do in their spare time
* Has just launched her own fashion label, Arenes (Serena backwards, like Oprah Winfrey's Harpo). Venus has modelled for her sister.
* Has appeared in Swimsuit edition of Sports Illustrated, and did a nude shoot for magazine Jane this year.
* Is currently setting up the Serena Williams Foundation. On her website she says: "The Serena Williams Foundation deals with education. I will be giving high school kids grants from all over the country. Aiding them and helping to send them to college and learn a trade or learn enough to start their own company. Learn more about the Serena Williams foundation in the coming months. There is so much we can and will do. I can't wait to send the first kid to college!"
* Serena's television appearances include playing Miss Wiggins in an episode of the comedy My Wife and Kids in 2002, appearing in cartoon form in The Simpsons in 2001, ER in 2005; Law & Order: Special Victims Unit in 2005 and the Disney cartoon Higglytown Heroes in 2007.
* Head of her own interior design company, V Starr Interiors, based in Palm Beach, Florida. Launched her own fashion design label, EleVen, in 2007. In 2001, Williams was named one of the 30 most powerful women in America by American Home Journal.