What persuades the lynching-party to give up on their attempt on Tom's life in To Kill a Mockingbird?

In chapter 15 of Harper Lee's To Kill a
Mockingbird we find the Finch children, Jem and Scout, facing a lynch mob
whose purpose is to attack Tom Robinson and, perhaps even, their own father, Atticus
Finch.

Ever since the moment that Atticus Finch takes
over the defense of Tom Robinson in court for his supposed rape of a white woman, the
lives of both Jem and Scout change considerably. One of the most salient features of
their new lives is that they have become more courageous than they have ever been; after
all, the entire town of Maycomb is against Atticus for defending a black man regardless
of the fact that Tom Robinson is, quite obviously, innocent of all
charges.

All this is important to understand what happens
next: After Atticus and his kids go to the jail to ensure the safety of Tom Robinson,
the mob shows up to lynch Tom. Scout and Jem actively confront the mob. As a result, the
mob threatens Jem, who is Atticus's only son, and give Atticus an ultimatum to get out.
Scout, however, comes forward and makes the clever move that dissuades the mob from
acting.

Scout sees that, among the mob members, is none
other than little Walter Cunningham's father, Mr. Cunningham. Scout has had run-ins with
the young Cunningham. In the beginning of the novel we find her attempting
to explain the extreme poverty of the Cunninghams to her teacher. Later in the story
we witness when she is made to eat lunch with the very hungry Cunningham boy and is told
by Calpurnia that it is Scout's duty to treat little Walter Cunningham, and anyone who
shares a plate with her at her table, as a welcomed
guest.  

It is imaginable that all these memories with the
junior Cunningham shock and confuse Scout: Therefore, she wonders how can a family man
in dire straits spend his energy trying to kill a man who should be presumed innocent.
The father of the same boy whom she has been taught to treat with uttermost respect!
This is the moment when she calls out Mr. Cunningham by name and last name, and reminds
him who he is and the worthlessness of what he is about to
do.

Facing Mr. Cunningham is the equivalent of taking away
one source of energy from the lynch mob. Calling and singling him out is a way to point
out that he has no business following a this group: He is his own person, and he does
not have to play by the ignorant rules of Maycomb. This action immediately breaks down
the gist of the mob and separates Cunningham from the rest of the men. And, like the
saying goes: Divide, and conquer.