In chapter seventeen of To Kill a Mockingbird, what does Atticus attempt to establish through Bob Ewell's testimony?
Bob Ewell beat up his daughter and claimed that Tom Robinson raped her in an effort to cover up the fact that Mayella threw herself at a black man. Since Bob Ewell is one of the lowest of men in the county, he doesn't have the sense to create a proper case built on lies. Add that to the fact that the Ewells depend on racism to win the case, they must have felt like they didn't have to do much to convict Tom. Plus, neither side has any evidence to show one side is lying and the other is not. Therefore, Atticus must show the court what isn't there in the case in order to prove his client is innocent.
First, Atticus shows the court that there is no medical evidence to prove that Mayella was raped. There isn't even a doctor (an expert) for either side to call upon to witness one way or the other that a rape had occurred. If Atticus can show that no doctor was called, then it either means no rape happened at all and the Ewells are lying, or Bob Ewell doesn't care enough about his daughter to call one. Either way Bob Ewell looks bad. Bad enough to beat up his own daughter to convict a black man? But Ewell claims that he didn't have five dollars to spend on a doctor to tell him what he had already witnessed. Because Ewell knows how the South works, he didn't think he needed any other proof than his own testimony to convict a black man. Atticus does a perfect job establishing Ewell's lack of fatherly love, but the lack of medical evidence isn't enough to dissuade a jury of hundreds of years of prejudice.
Next, based on the testimony of Sheriff Tate, Mayella Ewell was beat up mostly on the right side of her body. This evidence shows that whoever punched her led mostly with his left arm; that is to say, a left-handed man most likely inflicted the wounds found on Mayella's body. To prove this further, Atticus has Mr. Ewell sign his name without telling him why. Ewell falls for it and proves that he is left-handed. This is significant because Tom Robinson's left arm and hand are crippled, even a whole foot shorter than his right arm, because it got caught in a cotton gin when he was a boy. There is no way that Tom could have beaten up Mayella Ewell with his left hand or arm. Therefore, the purpose of chapter seventeen is to establish the lack of medical evidence available to support Ewell's claim, and that someone who is left-handed beat up Mayella Ewell.
Atticus' main purpose with Bob Ewell's testimony is actually two-fold.
First of all, Atticus works to prove that Bob Ewell didn't care enough about his daughter's health to seek the help of a doctor. This is an odd behavior for a parent, especially if he is so excited to get Mayella to testify in court against her supposed attacker. You would think Bob Ewell would want as much evidence as possible.
Secondly, Atticus tries to prove that Bob is left-handed. Bob clearly shows he doesn't understand what it means to have strength in both hands or one more than the other because on the last page of the chapter, he confused the question while proving himself to be left-handed.