Only one hour and 42 minutes of action was possible on Centre Court and just 77 minutes on Court One as play was halted four times on a frustrating day for players and spectators.
Play started almost four hours late and the downpours meant that only two singles matches were completed.
Serena Williams brushed aside the challenge of Daniela Hantuchova, while Amelie Mauresmo beat Jennifer Capriati.
Capriati later claimed the inclement weather had played a key role in her defeat.
"I strained my left shoulder and I think it was because I didn't get a good warm-up," said the American.
"When the rain came down for the first time, I should have stopped because that's when I got broken. Then I had two double faults and I was serving right into the rain."
The weather also caused havoc with the men's quarter-final programme.
Tim Henman just had time to win the first set 6-3 against Andre Sa while top seed Lleyton Hewitt never set foot on court for his match with Dutchman Sjeng Schalken.
"We know that it is physically possible to build a roof as has happened elsewhere," said Tim Phillips, the chairman of the All England Club.
"We owe it to tennis fans to investigate all the possibilities for play to take place even if it is raining.
"At the same time, we must have positive answers to a number of vital questions and, above all else, it is essential that neither player safety nor the grass growth on any courts is affected by such a structure.
"We continue to carry out experiments that might give us solutions to these potential pitfalls."