Let us suppose iurther that a spectator who saw the Ingress at r, and therefore as early as posaible. should by the rotation of the earth be carried to c, where be would son the egress as late as possible, while the spectator of the late ingress at e is in like manner carried to c, where be sees the earliest egre.a.• In the first came the time of the transit is increased as much as possible by the effect of parallax, and in the latter case it is equally dinnmshed. Now suppose the parallax of the sun to have a certain value, the parallax of Venus and the effect of these parallaxes in increasing or diminishing the duration of the transit for any specified places of observation can be computed. Hence when the durations are really observed, the differences between the observed duration and that which would have been observed if the spectator had been placed at the centre of the earth will fix the actual amount of the parallax. The especial excellence of this method consists in the with which a particular phenomenon can be observed, namely, the first streak of light which is seen after the interior contact at Ingress and the last streak before the interior contact at egress. Two points on the earth are chosen where the beginning and end are both visible, in one of which the duration is shortened as much as possible, while it is increased in the other. Every observation of either ingress or egress can in fact be used for determining the parallax, provided the longitude of the place of observation and the time be sufficiently well known ; but where both the ingress and egress are observed, the duration alone requires care. Transits of Venus were observed in 1761 and 1769, and the parallax of the Inn deduced by various geometers. (Lagrange,' 3Idmoires de Berlin,' 1766; Der Venus Durch ang,' Gotha, 1824.) The next transits will take place in 1874 and 1882.
In the preceding part of this article the methods of determining the parallaxes, and consequently the distances of the bodies composing our system, have been described, and we will now point out the way in which this knowledge is applied. Every observation of the sun, moon, or planets is affected by parallax and must be corrected for this pre vious to further calculation. All celestial bodies are apparently elevated by the refraction of the atmosphere, and those of our system are depressed by the effect of parallax. In nautical works there are
tables for reducing the observed altitude of any heavenly body to its trite altitude. namely, to that which it would have if there were no atmosphere and the spectator were at the earth's centre. In most of the problems from which the longitude is determined astronomically, in solar eclipses, occultations, and lunar distances the great difficulty and trouble is in computing the effect produced by the moon's parallax. Astronomers have invented convenient formula3 for this purpose, according to the planes to which the bodies are referred. Thus in working out an occultation, the moon may be referred to the plane of the horizon, when the effects of parallax in altitude, and, if great accuracy be required, in azimuth, must be computed; or again, to the when the parallax in right ascension and declination is to be calculated ; or finally, to the ecliptic, when the parallaxes in longi tude and latitude must be found. The rules for these computations are given In treatises on Astronomy.
The mean equatorial horizontal parallax of the sun, according to Eneke, Its true value for every ten days is given in the ' Naut. Alraan.' at the end of the ephemeris of the sun and moon. The equatorial horizontal parallax of the moon for mean noon and midnight Is at page III. of each month, and the parallaxes of the planets are in the last column of the planetary meridian ephemeris.
One effect of parallax is, that the moon appears under a larger angle when near the zenith than when near the horizon. This is contrary to common opinion, but may be very proved experimentally, by any one who can handle a sextant with ordinary care. When the moon Is in the zenith, the horizontal diameter may be augmented from 30" to There is a table for this augmentation of the moon's semidiameter In most nautical works.
CUILealli of Parallax (la eosstante de le parullo.re) is the angle under which the earth's radius would be seen at the centre of the moon when she is at her mean distance. The radius chosen by La Place is that which belonp to a latitude of which the square of the sine se 1.