In Chapter 19, how well does Mr. Gilmer prove Tom's guilt in the eyes of the reader and the just, and can you suggest why these might be different?

(I believe you are discussing Horace Gilmer's cross-examination of Tom Robinson in Chapter 19.)

I believe Gilmer makes no impact upon the reader's decision about Tom's guilt during his cross-examination. Atticus' prior questioning of Tom firmly establishes Tom's innocence in the mind of most readers, and Gilmer does little to change that view. Gilmer's racist remarks only make it clearer that Tom is a second-class citizen in the eyes of the court (remember, Judge Taylor did nothing to stop Gilmer's use of the word "boy"). I believe there is no differentiation between the reader's viewpoint and "the just" nature of the testimony. Nearly all readers recognize that the Ewells are untruthful and that Tom is telling the real version of events. Obviously, Tom's treatment and final verdict are unjust.