moveable vernier, when the telescope is exactly in the meridian. Prior to the observation, therefore, the circle is adjusted so that the local sidereal time, or, in other words, the right ascension of the part of the celestial sphere in the meridian, is brought to the fixed vernier. The circle is then carried by the clockwork of the instrument, and when the cross wires of the telescope are adjusted on the object, the moveable vernier shows its right ascension on the same circle.

LESSON XLIII.—Corrections applied to Observed Places. Instrumental and Clock Errors. Corrections for Refraction and Aberration. Corrections for Parallax. Corrections for Luni-solar Precession. Change of Equatorial into Ecliptic Co-ordinates.

536. After the astronomer has made his observations of a heavenly body-and has freed them from instrumental and clock errors, if his telescope is not perfectly levelled or collimated, or his circle is not perfectly centred, or if the clock is either fast or slow-he has obtained what is termed the observed or apparent place. This, however, is worth very little he must, in order to obtain its true place, as seen from his place of observation, apply other corrections rendered necessary by certain properties of light. These properties have been before referred to in Arts. 450 and 451, and are termed the refraction and aberration of light. Refraction causes a heavenly body to appear proportionately higher the nearer it is to the horizon; in the zenith its action is nil; near the horizon it is very decided, so decided that at sunset, for instance, the sun appears above the horizon after it has actually sunk below it.

It will be seen, therefore, that refraction depends only upon the altitude of the body on the sphere of observation.

537. The correction for refraction is applied, therefore, by means of some such table as the following:

TABLE OF REFRACTIONS.

538. This table will give a rough idea of the correction applied; in practice, the corrections are in turn corrected according to the densities of the air at the time of observation. In the case of the transit circle, or altazimuth, the correction for refraction is applied by merely reducing

the observed zenith distance by the amount shown in the refraction table.

539. The aberration results from the fact that the observer's telescope carried by the Earth's annual motion round the Sun must always be pointed a little in advance of the star (Art. 451), in order, as it were, to catch the ray of light. Hence the star's aberration place will be different from its real place, and as the Earth travels round the Sun, and the telescope is carried round with it always

FIG. 64-Annual change of a Star's position, due to Aberration: abcd, the Earth, in different parts of its orbit; a'bc'd', the corresponding Aberration places of the Star, varying from the true place in the direction of the Earth's motion at the time.

pointed ahead of the star's place, the aberration place revolves round the real place exactly as the Earth (if its orbit be supposed circular) would be seen to revolve round the Sun, as seen from the star: the aberration places of all stars, in fact, describe circles parallel to the plane of the Earth's orbit—if the star lie at the pole of the ecliptic the circle will appear as one: the aberration place of a star in the ecliptic, since we are in the plane of the circle will oscillate backwards and forwards; that of one in a middle celestial latitude will appear to describe an ellipse. The diameter of the circle, the major axis of the ellipse, and the amount of oscillation, will in all cases be equal; but the minor axes of the ellipses described by the stars in middle latitudes will increase from the equator to the pole. The invariable quantity is 20′′492, and is termed the constant of aberration. It expresses, as we have seen, the relative velocities of light and of the Earth in her orbit. It is determined by the following proportion, bearing in mind

T

that the 360° of the Earth's orbit are passed over in 365 days, and that light takes 8m. 195. to come from the Sun:

Days.

365

m. s.

8 19: 360: 20.492

The mode in which the correction for aberration is applied may be gathered from Fig. 67.

FIG. 65.-s, the Star's true place; s', the Aberration place.

540. The direction of the Earth's motion in its orbit, called the Earth's Way, is always 90° behind the Sun's position in the ecliptic at the time; therefore the aberration place of the star will lie on the great circle passing through the star and the spot in the ecliptic lying 90° behind the Sun.

541. Observations of the celestial bodies near the Earth, such as the Moon and some of the planets, when made at different places on the Earth's surface, and corrected as we have indicated, do not give the same result, as their position on the celestial sphere appears different to observers on different points of the Earth's surface. This effect will be readily understood by changing our

position with regard to any near object, and observing it projected on different backgrounds in the landscape; the nearer we are to the object the more will its position appear to change.

542. To get rid of these discordances, the observations are further reduced and corrected to what they would have been had they been made at the centre of the Earth. This is called applying the correction for parallax.

Parallax is the angle under which a line drawn from the observer to the centre of the Earth would appear at the body of which observations are being made. When the body is in the zenith of an observer, therefore, its paraliax is nil; it is greatest when the body is on the horizon. This is termed the horizontal parallax. The line is always equal to the radius of the Earth, but being seen more or less obliquely, the parallax varies accordingly.