# Knot IX: A Serpent with Corners explained — A Tangled Tale > Chapter companion for A Tangled Tale by Lewis Carroll. ## What happens Hugh and Lambert are on the beach at Little Mendip, where Hugh experiments with buckets to test the principle of displacement. He is puzzled when the displaced water seems less than the bucket's bulk. At dinner, Hugh presents his difficulty to Balbus, who sets them a geometry problem about a flower-garden with a serpentine gravel-walk. Balbus then retreats to his room to ponder Hugh's mechanical paradox, writing a satirical essay on immersion and displacement before falling asleep. ## Themes in this chapter ### Education and Learning The chapter centers on a practical science puzzle and a geometry problem, illustrating the process of inquiry and problem-solving. ### Humor and Absurdity Balbus's essay humorously extends the displacement principle to absurd conclusions, such as a man being inevitably drowned by partial immersion. ### Logic and Paradox Hugh's bucket experiment and Balbus's essay both explore the logical paradoxes of displacement and infinite regress. ## Character check-ins ### Hugh Conducts bucket displacement experiment and later presents his puzzle to Balbus. ### Lambert Lies on the beach doing nothing and dismisses Hugh's concerns about displacement. ### Balbus Tutor who sets the garden geometry problem and later writes an essay on the displacement paradox. ## Key lines > Water, water, every where, Nor any drop to drink. Despite being surrounded by water, there is none available to drink. _Opening epigraph from Coleridge's 'The Rime of the Ancient Mariner', setting a tone of ironic abundance and scarcity._ > It'll just take one more pebble. Just one additional pebble will cause the bucket to sink. _Hugh's experiment with bucket displacement, illustrating the concept of buoyancy._ > If a body is immersed in liquid, it displaces as much liquid as is equal to its own bulk? An object submerged in liquid pushes aside a volume of liquid equal to its own volume. _Hugh recalls Balbus's lesson on Archimedes' principle, which he then tests with buckets._ > Like a serpent with corners? A path that winds back and forth in a rectangular pattern, resembling a snake with right-angle turns. _Lambert's description of the gravel-walk that runs around the garden in concentric laps._ > Shade of Newton! By the ghost of Isaac Newton! _Balbus's exclamation of surprise as he contemplates the infinite regress in the displacement problem._ ## Links - HTML: https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-ix-a-serpent-with-corners - Book: https://www.betterreads.online/discover/a_tangled_tale_se - All chapters: https://www.betterreads.online/discover/a_tangled_tale_se/chapters