Parallex or Parallel Error is a geometrical error that near-by heavenly objects, namely the Moon.
Instead of a spotlight of parallel light, a near-by object casts more of a conical floodlight. The reason why parallax matters to us is because in the nautical almanac, the center-to-center line direction from the Earth to the heavenly object is what is tabulated.
The particular cone angle is not tabulated, and needs to be calculated and added to the observed altitude to make an apples-to-apples comparison to the information in the almanac.
The Moon’s parallax can be almost 1 degree, and needs to be accounted for. The parallax can be calculated easily, if we know how far away the heavenly object is (which we do).
From the illustration, it should be apparent that the parallax is a function of the altitude measurement. It is a constant number for anyone on particular circle of constant altitude. The particular parallax angle correction corresponding to the particular altitude is known as parallax-in-altitude PA.
The maximum parallax possible is when the altitude is equal to zero (moonrise,moonset) and is designated as the horizontal parallax HP.