PARALLAX (7rap6,XXats) is the difference in direction of a body caused by a change in the position of the observer. For members of the solar system the word is more specifically used to mean the difference in direction as seen from the observer and from the earth's centre. It is used in this sense by Ptolemy. In fig. 1, let 0 be the observer, E the centre of the earth, and M the position of the moon, planet or sun, then the angle OME is the parallax. This varies with the altitude and is greatest when the body is on the horizon. At zenith distance z sin
sin z. When z=90°, sin p =
and this value of p is called the hori zontal parallax or briefly the parallax. For all bodies but the moon, p is so small that it does not differ appreciably from sin p, and is usually expressed in sexa gesimal measure. A further re finement is required owing to the spheroidal figure of the earth and the numerical values generally given are those of the Equatorial horizontal parallax.
The moon being by far the nearest of the celestial bodies was the first to have its parallax determined. Hip parchus showed that the sum of the parallaxes of the sun and moon was equal to the sum of the angular radii of the sun and of the shadow of the earth thrown on the moon in a lunar eclipse. If the parallax of the sun be considered as inappreciable compared with that of the moon, the moon's parallax is found to be 58'.
Parallax of the moon is directly determined from observations of declination made at two places like Greenwich and the Cape which are nearly on the same meridian. The theory of the observa tions will be readily grasped from fig. 2.
The angles z, and
are observed and other data are obtained from the latitude of the observatories and the known size and shape of the earth. In practice, stars are observed in positions near the moon in order to eliminate uncertainties of ref faction and instrumental errors. In this way Henderson obtained a value of 57'2".3 for the moon's equatorial horizontal parallax in 1837. From a series of observations of a small lunar crater in the years 1905-10 the value 57'2".5 was found.
A second method rests on a comparison of the force of gravity at the earth's surface with its value at the moon. If M and in be the masses of the earth and moon, r the mean distance, and P the sidereal period of revolution of the moon about the earth M-1---m
where 7=3.14. Also, g, the value of gravity at the
earth's surface, • determined accurately from pendulum observa tions=
HenceCY -470 M . . As the quantities
on the right hand side are known with great accuracy, d is accurately determined as 57'2".7.
In accordance with the law of gravitation the relative distances of the planets are known, and tables of their positions and movements take the distance of the sun from the earth as unit of length. To deter mine the value of this unit, it is only necessary to obtain the distance or parallax of one of the planets at a time when it is nearest the earth. The first accurate determination of the sun's parallax was obtained in 1672 from a series of observations of Mars when in opposition made in South America and Paris, from which a value of 9".5 was obtained. The utilization of the tran sit of Venus for this purpose was advocated by Halley, and at the transit of 1769, the times of ingress and egress of the planet on the sun's disk were observed by astronomers dispatched to various parts of the globe, including Capt. Cook in Otaheite. From these observations a value of 8".6 was obtained. The transits of 1874 and 1882 were widely observed for the same purpose, but the re sults were disappointing owing to the impossibility of precise de termination of the times of ingress and egress. In 1877 Gill made an expedition to the island of Ascension and observed the opposi tion of Mars, using a heliometer to measure the distance of the planet from neighbouring stars. He made his observations after sunset and before sunrise, the parallactic displacement of the planet from its calculated position as seen from the centre of the earth being in opposite senses and of largest amount at these times. A value of 8".78 was deduced. The successful result of this series of observations led Gill to make a very elaborate series of heli ometer observations of the small planets Victoria, Iris and Sappho, in 1888 and 1889, when they were in opposition. The resulting value of the solar parallax was 8".80.