The wet weather has had such a worrying effect on the tournament that playing on Sunday is not so much the issue as which Sunday?
After the second worst start in the history of the championships - only 1991 has been worse, so far - and not much respite in the conditions in prospect, Alan Mills, the referee, wonders when the tournament will end.
"As far as we can see into it, it's five days of not too hopeful weather," Mills said last night, after the first complete washout of a day's play since 1992. "There are sort of spells and windows amongst it, but there isn't one day when it says we're going to have a fine, clear, warm, sunny day, even in the middle of flaming June.''
The wettest June, in fact, since 1987.
"Playing on Sunday is obviously an option we are seriously considering at the moment," Mills confirmed, "but it is not just in the Club's hands as to whether we can do it. We've got to get permission from the council and the police before we can even contemplate doing it.''
The police do not appear keen on a repetition of People's Sunday '91. Inspector Philip Coates, who is in charge of security, said: "The Club have previously said they wouldn't want to play on the middle Sunday. When it happened in 1991, it caused so many problems the general view was we didn't want to do it again.''
Mills, while acknowledging logistical difficulties, has fond memories of a unique occasion. "I personally thought the middle Sunday in '91 was probably the most inspiring day that I have spent at Wimbledon," he said. "The people and the atmosphere was just electric, and I thought it was an absolutely great success.''
He added, "But also, weatherwise, we did have a forecast for the Sunday in 1991 that said it was going to be a good day. It would be, let us say, a bit silly of us if we, knowing the weather forecast, open up everything and we spend a day like today. So that's another consideration that has to be taken into account.''
So what next? "We keep soldiering on and playing as many matches as we can," Mills said. "We have a certain number of rest days built into the second week from the singles players' point of view. The longer it goes on like this, the more chance they keep losing their rest days and they will have to play matches back-to-back.
"We've already cut the doubles down to three sets. We have still got 28 ladies who haven't finished their first round singles. We've got six men who are unfinished in their first round singles. So we've got 34 matches that are an absolute priority to play.''
Might the situation call for reducing the men's singles to the best of three sets? "It hasn't been done, as far as I can remember, but again that's another option.''
And would there be a time limit if the championships go into the third week? "I think Tuesday would probably be a deadline, because players have other commitments.
Having invested some pounds 100m in a new No 1 Court complex, had the Club made a mistake in not having a retractable roof.?
Tim Phillips, chairman of Wimbledon's order of play sub-committee, said: "This is an old chestnut."
So will there never be a roof? "I don't think anybody would say `never', but we have considered it from every single angle, not least from the players' angle, and the view of the moment is where we are.
"On the question of rain, in terms of putting a giant umbrella over the championships, it would be lovely to do it. We haven't found the practical solution that answers all the issues. One of the main considerations is the fact that this is an outdoor tournament. It's a grass court tournament, and what about the players who don't play on a covered court?''
So why not floodlights and night play? "Because then the grass gets dewy and slippery."
Mills added, "This is another answer to the lights question. The BBC did a trial, and all the moths arrive on the court.''
How about taking up the grass, then?
Mills interjected, "I don't think that needs an answer."
Meantime, as a sage once said, they wait who ought to stand and serve. And so too do the sodden spectators.