What test does Danforth devise to determine why Abigail was put out of the Proctor house?
By way of evidence for his claim that Abigail wants to eliminate his wife, John Proctor tells the court that he "[has] known her," and, further, that "A man will not cast away his good name" by confessing to such a sin were it not totally true. John also tells the court that
In her life [...], [Elizabeth has] never lied. There are them that cannot sing, and them that cannot weep -- my wife cannot lie.
Danforth confirms with John that when Elizabeth dismissed Abigail from their service seven months prior, she did so with full knowledge of the affair between Abigail and John. He asks, directly, "[She] knew [Abigail] for a harlot?" and John affirms that this is true. Danforth sends for Elizabeth and he orders John and Abigail to turn their backs and keep silent as she enters and answers Danforth's questions. Elizabeth, in her misguided but generous desire to protect her husband's reputation denies that John is a lecher and calls her dismissal of Abigail the effect of "los[ing] [her] wits" one night after she "came to think [John] fancied [Abigail]." In this way, Danforth appears to confirm Abigail's innocence and John's guilt. If John is a liar, then Mary Warren is implicated by his dishonesty since she comes to court with him. It becomes very easy for Danforth to maintain his position that "the voice of Heaven is speaking through the children."
In Act III, Danforth finds himself in unfamiliar territory. He, and the court, believing they have doing God's work and saving the afflicted girls from the devilish witchcraft, are faced with Proctor's confession that he has had a relationship with Abigail. Knowing that the confession will soil his name, and embarrass his family, Proctor confesses that he has "known" Abigail. Abigail, enraged, vehemently denies the accusation. So what is Danforth to do? He summons Elizabeth (who has been in prison since Act II) to court. He warns Abigail and Proctor to turn their backs to Elizabeth and to make no motion or noise when she enters. Calmly he asks why Elizabeth fired young Abigail. Elizabeth is now faced with a dilemma. Does she lie (remember Proctor has just told us that Elizabeth would never lie) in order to protect her husband, or does she charge him with the crime of lechery in open court. Sadly, Elizabeth chooses to lie for her husband, and Danforth trick has worked. In his mind the evidence is clear- Abigail is innocent and Proctor has lied.