In chapter seventeen what does atticus attempt to establish through heck tates's testimony.

In Chapter 17 of To Kill a Mockingbird,
Atticus Finch questions Mr. Heck Tate, Maycomb's law enforcement officer.  On the night of the
attack against Mayella Ewell, her father, Bob Ewell, went to Tate's office and "said get out to
his house quick, some nigger'd raped his girl."  Tate hurried to the scene of the supposed crime,
questioned the victim and her father, and observed details pertaining to the violent situation in
which Mayella seemed to have found herself. 

When Atticus requested
Heck Tate's testimony, he intended to prove two primary points, one of which was considerably
more significant than the other and should have resulted in the acquittal of Tom Robinson.  The
first, and least, of the two messages Atticus intended to send the jury was that Bob Ewell was,
in fact, not overly concerned with his daughter's health and well-being, since he did not attempt
to procure the services of a doctor for her.  This fact might suggest that Ewell was a poor
father figure and that he did not want to incriminate himself, which was a distinct
possibility.

The second point that Atticus attempted to make through
Heck Tate's questioning was that, considering his disability, Tom Robinson could not have harmed
Mayella Ewell in a way that would have resulted in her sustaining the injuries observed by Tate. 
Because Robinson's left arm had been injured when he was a child and, as a result, was useless,
Robinson could not have choked Mayella with both hand.  Furthermore, Robinson could not have
given Mayella a blackened right eye or bruised her "on her arms" or the right side of her face. 
Knowing this, the jury should have found it impossible to, in good conscience, convict Robinson
of the crimes of which he was accused.