This chapter is a half-way house, starting the process of generalising the idea of a jet to take account of derivatives higher than the first. There are several advantages to be gained by restricting attention at this stage to second order jets. The coordinate notation introduced in the previous chapter may still be used, and the difference between “holonomic” and “non-holonomic” jets may be seen quite clearly; the integrability condition for a jet field may be expressed in terms of second order jets; and the Euler–Lagrange equations for a variational problem may be expressed in the form of a “second order jet field”. It should be clear, however, that many of the constructions involving second order jets may be generalised further to jets of arbitrary order.