Constand, a former Temple University employee, claims Cosby sexually assaulted her in early 2004 after she was given three blue pills and wine.
Constand said Cosby called the pills "your friends" and told her they would "help take the edge off".
The Associated Press doesn't typically identify people who say they're victims of sexual assault unless they grant permission, which Constand has done.
Constand is one of about 50 women who have accused him of assault dating back decades. O'Neill said jurors should know it's the defense's turn.
Cosby's testimony was hidden from public view until The Associated Press petitioned to have it unsealed in 2005. The famed comedian paid her almost $3.4 million in 2006.
The trial might even end sooner if not for the defense team.
The deposition also was included at Cosby's first trial, which ended with a hung jury past year.
Bill Cosby's lawyers have lost another bid to cut his sex assault retrial short.
Judge Steven O'Neill ruled that prosecutors could have the Cosby Show star's deposition testimony read into the record, handing the prosecution a key victory in its effort to portray the comedian as a serial predator.
Cosby's lawyers say prosecutors haven't proved charges he drugged and molested a woman at his suburban Philadelphia mansion more than a dozen years ago.
The model previously claimed Cosby drugged and assaulted her in Lake Tahoe, Nevada in 1982.
"Any of these things that she says happened would not have happened within 10 to 15 minutes, as she said", Milman told jurors during his testimony, saying the effects she recounted would have taken almost three hours to set in.
Five of Cosby's other accusers have testified in this trial.
After the prosecution formally rested its case today, Cosby's team motioned for acquittal, citing the non-paralyzing effects of Benadryl the prosecution's expert testified to and the expiration of the statute of limitations, suggesting the alleged 2004 sexual assault Cosby is on trial for against Constand could have happened at an earlier date.
"The symptoms that she described after taking a therapeutic dose would not have occurred within 10 to 15 minutes", Dr. Milman said, under direct examination from Becky James, an attorney for Mr. Cosby.
He said he gave quaaludes to women he wanted to have sex with, using them "the same as a person would say, 'Have a drink'".
Alcohol would only enhance each pill's sedative effects, Rohrig said, leading to impaired vision, "mental clouding", dulled senses, short-term memory impact, and would engineer muscle weakness and clumsiness.
Rohrig also testified that studies showed Quaaludes, also known as Methqualome, didn't often leave users feeling foggy the next morning.
Cosby's lawyers argued on Thursday that prosecutors were out of line for implying they were wrong to help star defense witness Marguerite Jackson write a statement outlining how she says Cosby's chief accuser mused about framing a celebrity. Prosecutor Stewart Ryan irked Cosby's lawyers during Jackson's cross-examination on Wednesday by repeatedly saying they "created" her affidavit.
O'Neill was upset that Cosby's lawyers had just one witness ready to testify on Thursday - a drug expert who will take the witness stand after prosecutors call their own drug expert.
Book publisher Judith Regan has confirmed model Janice Dickinson told her that Bill Cosby allegedly drugged and raped her in the 1980s. He says it was consensual. Spokesperson Andrew Wyatt for actor and comedian Bill Cosby, holds his fist held high as he and Bill Cosby leave for the day from Cosby's sexual assault trial at the Montgomery County Courthouse, Wednesday, April 18, 201.
Harry Milman, the defense pharmacology and toxicology expert, said Cosby could not have given Constand Quaaludes, because they only ever came in the form of a white pill.
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