The equation of light, the constant of aberration, and the parallactic inequality of the moon; the value of the velocity of propagation of light enters in the reduction of the two first, but as this is better known than the sun's parallax, no disadvantage results.
If three plates (or three sets of exposures on one plate) are taken at intervals of six months, when the stars in the region have their maximum parallactic displacements, the first and third plates serve to eliminate the proper motion of the star, and the detection of a parallax is easy.
The chief term in the lunar longitude which introduces the ratio of the distances of the sun and moon from the earth explicitly is known as the parallactic inequality; by analysis of the observations P. H.
As early as 1573, Thomas Digges had suggested that this theory should necessitate a parallactic shifting of the stars, and, consequently, if such stellar parallaxes existed, then the Copernican theory would receive additional confirmation.
It was used by him in his earliest observations of double stars (1779-1783); but, even in his hands, the measurements were comparatively crude, because of the difficulties he had to encounter from the want of a parallactic mounting.
If a sufficient number of stars are considered, their peculiar motions will mutually cancel and the parallactic or solar motion can then be derived.
The fourth method is through the parallactic inequality in the moon's motion.
Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.
The theoretical element is the ratio of the parallactic inequality to the solar parallax.
The determination of the solar parallax through the parallactic inequality of the moon's motion also involves two elements - one of observation, the other of purely mathematical theory.