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 part of the star's apparent Speed displacement, which is due to the solar motion, is gener the Solar ally called the parallactic motion; the rest of its 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.
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 stars have on this theory random peculiar motions in addition to the motion of the drift to which they belong, just as on the older theory the stars have peculiar motions in addition to the solar or parallactic motion shared by all of them.
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.
Doubt was first thrown on the accuracy of this number by an announcement from Hansen in 1862 that the observed parallactic inequality of the moon was irreconcilable with the accepted value of the solar parallax, and indicated the much larger value 8.97".
The fourth method is through the parallactic inequality in the moon's motion.
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.
The theoretical element is the ratio of the parallactic inequality to the solar parallax.
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.
The speed is very nearly four radii of the earth's orbit per year; thus the annual parallactic motion is equal to four times the parallax, for a star lying in a direction 90° from the solar apex; for stars nearer the apex or antapex it is foreshortened.
As has been explained the mean distance of a group of stars can be readily determined from the parallactic motion, which, when not foreshortened, is approximately four times the parallax; but to obtain a complete knowledge of the distribution of stars it is necessary to know, not merely the mean parallax of the group, but also the frequency law, i.e.
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.
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.
Cassini, moreover, set up an altazimuth in 1678, and employed from about 1682 a " parallactic machine," provided with clockwork to enable it to follow the diurnal motion.
Leverrier, in 1858, calculated a value of 8.95" for the solar parallax (equivalent to a distance of 91,000,000 m.) from the " parallactic inequality " of the moon; Professor Newcomb, using other forms of the gravitational method, derived in 1895 a parallax of 8.76".
The assured general fact as regards the direction of stellar movements was that they included a common parallactic element due to the sun's translation.