  When a static cylindrical system is subjected to equal and opposite torques
top and bottom it transports angular momentum along its axis. The external
metric of this static system can be transformed to Levi-Civita's form by using
helical coordinates. This gives the external metric of a static cylinder three
dimensionless parameters corresponding to the mass per unit length, the total
stress along the cylinder, and the total torque.
  The external vacuum metric of a spherical system is characterised by its mass
alone. How many parameters characterise the external metric of a general
stationary cylindrical system? Leaving aside the radius of the cylinder which
defines the scale we find that there are five parameters, the three above
mentioned, to which should be added the momentum along the cylinder per unit
length and the angular momentum per unit length. We show how to transform
Levi-Civita's one parameter metric to include all five.
