  The one-dimensional fall of a folded chain with one end suspended from a
rigid support and a chain falling from a resting heap on a table is studied.
Because their Lagrangians contain no explicit time dependence, the falling
chains are conservative systems. Their equations of motion are shown to contain
a term that enforces energy conservation when masses are transferred between
subchains. We show that Cayley's 1857 energy nonconserving solution for a chain
falling from a resting heap is incorrect because it neglects the energy gained
when a transferred link leaves a subchain. The maximum chain tension measured
by Calkin and March for the falling folded chain is given a simple if rough
interpretation. Other aspects of this falling folded chain are briefly
discussed.
