The phase behaviour of long hard rods is independent of their length t
o breadth ratio in the limit that this ratio is very large. We form a
binary mixture of rods with different length to breadth ratios but the
same second virial coefficient. As the second virial coefficient is t
he same for both components, their phase behaviour in the pure state i
s identical. However, the difference in their shapes-one is longer and
thinner than the other-results in an increased interaction between a
pair of rods of different components. As the difference in shape of th
e two components is increased, first isotropic-isotropic coexistence i
s observed (with a critical point), then in addition nematic-nematic c
oexistence. At first there is a nematic-nematic critical point but thi
s point reaches the isotropic-nematic transition, creating a four phas
e region. Gibbs' phase rule, as usually stated, permits a maximum of t
hree phases to coexist simultaneously in a binary athermal mixture. He
re, the symmetry between the two components allows four to coexist. (C
) 1996 American Institute of Physics.