  We construct, for a second-order homogeneous Lagrangian in two independent
variables, a differential 2-form with the property that it is closed precisely
when the Lagrangian is null. This is similar to the property of the
'fundamental Lepage equivalent' associated with first-order Lagrangians defined
on jets of sections of a fibred manifold. We show that this form may be defined
on a fourth-order frame bundle but is not, in general, projectable to a bundle
of contact elements
