Google has a great site for free books. The Montessori Manual by Dorothy Canfield
Fisher has a nice overview about walking the line.
Why does the Montessori classroom use the line exercises? According to Fisher,
A child who can do that will be able, unconsciously,
to walk straight across a room to a chair, without
tripping or falling over the furniture.
Check out Exercise Eighteen about the baby ball, it sounds like an old fashioned tetherball.