The upper end of a hanging chain is fixed whereas the lower end is attached to a mass M. The (massless) links of the chain are ellipses with major axes and minor axes l+a and l-a can place themselves only with either the major axis or the minor axis vertical. A four-link chain in which the major axes of the first and fourth links and the minor axes of the second and third links are vertical.  Presume that the chain has N links and is in thermal equilibrium at temperature ??.

a) Compute the partition function.

b) Calculate the average length of the chain.