In chapter thirty what situation do both Atticus and Scout recognize?To Kill a Mockingbird by Harper Lee

When Jem and Scout are brought back to the house in Harper
Lee's To Kill a Mockingbird, the doctor sees to Jem's broken arm.
(Jem will not regain consciousness until the next day.)

At
the end of chapter twenty-nine, Scout has realized that Boo Radley is in Jem's room, in
the shadows. At the beginning of chapter thirty, the doctor shoos everyone out, and
Atticus, seeming to know that the lights would be difficult for Boo, takes the group
onto the front porch where Boo can sit in the dark, rather than sitting in the living
room.

Heck Tate (the sheriff) and Atticus have a serious
argument. Atticus believes that Jem killed Bob Ewell when he attacked the children. Heck
Tate insists that Ewell fell on his own knife. Atticus argues that this is not the
truth, and refuses to lie to protect his son, knowing that if he does so, his children
will lose faith in him for lying. Atticus stresses to Heck Tate that Jem and Scout are
all he has in the world.

Heck Tate insists that this is the
story they will release, but then unexpectedly points out to Atticus that he is not
trying to save Jem: there was no way Jem could have killed Ewell,
with a broken arm. Heck Tate insists that a private citizen should not be punished for
stopping a crime. Without a fuss, Atticus finally understands that Heck Tate is speaking
of Boo Radley—who killed the man responsible for the needless death of another man (Tom
Robinson), and who tried to kill Atticus' kids. The sheriff goes on to say that should
the news get out, no one would leave Boo alone for the heroism he had displayed. Heck
knows that this would be an injustice for the gentle and solitary man who has been
locked away from the companionship of society for so many
years.

Heck Tate leaves, and Atticus repeats the "official
cause of death" to Scout: Bob Ewell fell on his knife. When Atticus asks Scout if she
understands, she puts it quite simply: to do otherwise would be like killing a
mockingbird—something that never hurts anyone else, never does any
harm.

Atticus and Scout realize that Boo Radley saved the
children's lives from the attack of Bob Ewell.