How to handle unused wire in cable
In your particular example, the extra wire should be connected to the chassis ground of the meter and unconnected at the sensor. Since the wire is acting as an antenna, this gives any noise that is picked up a place to go that will not interfere with your signals.

In general, it depends on the design of the system. What is the extra conductor? Single wire, multiple wires, a wire and a shield, multiple shields? Are there power supplies at both ends? Are they isolated? Are the other conductors signals from a sensor (as in your example) or communication over a network?

This answer by Kortuk and the comments that follow make some really good points.

And this short article describes the advantages and disadvantages of various connection schemes:


  For cable shield connections there are four options, with advantages
  and disadvantages:
  
  
  Shield grounded at both ends: Good r.f. shielding but susceptible to ground loop currents that can be VERY large - up to at least 100 A
  in bad cases.
  Shield grounded at both end, with large-area parallel bonding wire: Good at r.f. and now the ground current flows mainly through the
  bonding wire, but the intense magnetic field that may result is not
  good news. The bonding wire size needs to be, for example, 10 mm^2.
  Shield grounded at one end only: No ground current but not good at radio frequencies for which the cable is more than 1/8 wavelength
  long. R.F. interference may actually be worse than for an unshielded
  cable.
  Shield grounded at the sending end and grounded through a capacitor (may be two in parallel, for effectiveness from about 100 kHz up to 1
  GHz and beyond) at the receiving end: Good at r.f. if the capacitor
  type and positioning are correctly-designed, and no low-frequency
  ground current. One capacitor needs to be of the type with an integral
  spark- gap so that it is not damaged by transient high-voltage spikes
  that may be induced on to the shield.