The fine tune is to raise or lower the weight swinging on the pendulum to adjust the duration of the swing. These clocks are quite special and were among the first to use the alloy "Invar" - an alloy containing a lot of nickel. This alloy undergoes a phase change to a lattice that is slightly more dense near room temperature. As the material expands from being heated, it simultaneously contracts as the phase changes to yield a near-zero thermal expansion. That way, the rod that holds the weight is always the same length and the clock is much more accurate for rooms with varying temperatures throughout the day or year - a feature that was much more important pre-air conditioning. This alloy (and slight variations) is commonly used in optical systems like telescopes and Lidar modules..