By changing amount of charge on the cathode and the anode (this means changing the voltage) you can control how much the electron is accelerated (because the cathode repulses the electron and the anode attracts it). The more acceleration and electron experiences the more energy it can impart to whatever it hits, and, of course, the only things to hit are the neon and mercury atoms spread throughout the tube.

Here comes the punch line. For certain energies the electron can carry it can excite an electron of either mercury or the neon to a higher energy level. The excited electron stays there for a few nanoseconds and than drops down to its lower energy level by emitting a photon of a certain color, a spectral line if enough atoms do this. In the meantime the electron that imparted the energy no longer has the initial impetus to reach the other side. This has the effect of creating a beautiful glow in the tube as the exited atoms emit light.

Our job in this lab is to identify at what voltages these spectral lines appear at and to see how many of the electrons get intercepted in route when the spectral lines do appear. In order to be absolutely sure that we know when the spectral lines show up it is necessary to use a spectrograph to look at the spectral lines and determine when they show up.

The picture below is a photograph of the Frank Hertz apparatus. You can see the spectroscope at the left for observing the tube and seeing when the spectral lines show up.