As the earth revolves round the sun in about 365 days, at a distance of 95,000,000 miles (96), it may be found, by a simple computation, that its annual motion must be at the rate of about 19 miles in a second.

DEFINITIONS.

108. The Ecliptic is that great circle of the celestial sphere, which the sun appears to describe in his apparent annual motion.

The plane of this circle, which necessarily passes through the centres of the earth and sun, is called the plane of the ecliptic, or sometimes simply the ecliptic.

109. The Zodiac is a zone of the celestial sphere, extending 8° or 9° on each side of the ecliptic.

The sun and moon, and all the principal planets, have their motions within the limits of the zodiac.

110. The Obliquity of the Ecliptic is the angle which the ecliptic makes with the equator. Thus, the angle QEC, Fig. 18, is the obliquity of the ecliptic. It is evidently measured by CQ or BD, the greatest north or south declination of the sun. The obliquity of the ecliptic is about 23° 28'.

111. The Equinoctial Points or Equinoxes are the two points in which the ecliptic and equator intersect each other. The point at which the sun passes from the south to the north side of the equator is called the vernal equinox, and the other, the autumnal. Thus E is the vernal equinox, and F the autumnal equinox. The straight line, joining the equinoctial points E and F, is called the line of the equinoxes.

The Solstitial Points or Solstices are the two points in the ecliptic at which the sun's declination is the greatest, north and south. They are therefore 90° from the equinoxes. That to the north of the equator is called the summer solstice, and the other, the winter. Thus C is the summer and D the winter solstice.

The terms equinox and solstice are also used to denote the times at which the sun is at those points.'

* Formerly they were used only to refer to the times. At present they are applied to both the times and points: the context always indicating the sense in which they are used.

112. The Signs of the Ecliptic are twelve equal parts, into which the ecliptic is conceived to be divided, beginning at the vernal equinox and proceeding eastward. Each sign therefore contains 30°. They are designated by names or characters as in the following table.

The vernal equinox is sometimes termed the First point of Aries. A body or a point is said to have a direct motion, when its motion is from west to east, according to the order of the signs of the ecliptic, and a retrograde motion when the motion is in a contrary direction, or from east to west.

113. The Equinoctial and Solstitial Colures are two declination circles passing through the equinoxes and solstices. Thus, EPFP' is the equinoctial colure, and PCP'D is the solstitial colure.

It is evident that the solstitial colure passes through the poles p and p' of the ecliptic, as well as through those of the equator, and that the equinoctial points E and F are its poles.

114. The Tropics are two small circles parallel to the equator and passing through the solstices. That to the north of the equator is called the tropic of Cancer, and that to the south, the tropic of Capricorn. Thus CC' is the tropic of Cancer, and DD' the tropic of Capricorn. The distance of the tropics from the equator is evidently equal to the obliquity of the ecliptic.

The Polar Circles are two small circles parallel to the equator, and at a distance from its poles equal to the obliquity of the ecliptic. That about the north pole is called the arctic circle, and that about the south pole, the antarctic. Thus pq is the arctic, and p'q' the antarctic, circle.

Circles corresponding to the tropics and polar circles, and bearing the same names, are conceived to be drawn on the earth's surface, dividing it into five portions called zones. The zone be

tween the tropics is called the torrid zone; the two between the tropics and polar circles are called the temperate zones; and the two within the polar circles are called the frigid zones.

115. The Right Ascension of a body is the arc of the equator intercepted, to the east, between the vernal equinox and a declination circle passing through the body. Thus EG is the right ascension of the star S.

The right ascension and declination (27) of a body, designate its situation in reference to the equinoctial colure and the equator.

116. A Circle of Latitude is any great circle passing through the poles of the ecliptic. The arc pSH is part of a circle of latitude.

117. The Longitude of a body is the arc of the ecliptic intercepted, to the east, between the vernal equinox and a circle of latitude passing through the body.

The Latitude of a body is the arc of a circle of latitude intercepted between the body and the ecliptic. The latitude is north or south, according as the body is on the north or south side of the ecliptic. Thus, EH is the longitude, and HS the latitude, of the star S, north.

The longitude and latitude of a body designate its place in reference to the circle of latitude passing through the vernal equinox and the ecliptic.

PROBLEMS.

118. To find the obliquity of the ecliptic. The obliquity of the ecliptic may be found from the equation, tang dd' = tang E sin Ed' (106), in which dd' and Ed' are known from observation, and the angle E is the obliquity of the ecliptic. This gives,

It may however be more accurately obtained from the sun's declination, found for several days at noon (102), about the time of either solstice. From these declinations, the value of CQ, the greatest declination, may be deduced by interpolation; and this expresses the obliquity of the ecliptic (110).

The obliquity is subject to some slight changes that will be noticed in the next chapter.

119. To change the right ascension and declination of a body into longitude and latitude, or the contrary.

Let S be the body, and let E and S be joined by an arc of a

great circle. Put angle QEC

which is supposed to be known, A

obliquity of the ecliptic,

EG, the right ascension,

HS, the

D GS, the declination, L EH, the longitude, a = latitude, N = the angle GES, and N' the angle HES. Then, for the change from right ascension and declination to longitude and latitude, we have, from the triangles EGS and EHS (App. 48 and 49),

For the change from longitude and latitude to right ascension and declination, we have, in like manner,

When the declination or latitude is south it must be taken negative. The subsidiary arc N or N' may always be taken affirmative and less than 180°. When one of the quantities L and A is in either the fourth or first quadrant, it is evident the other must be in one of these two; and when one of them is in either the second or third quadrant, the other must be in one of these. With attention to these remarks and to the trigonometrical rules for the signs of the quantities, the preceding formulæ are applicable, whatever be the situation of the body.

For the sun, or any point in the ecliptic, as S', we evidently have tang A; tang A = cos & tang L;

tang L tang D

COS &

F

FIXED STARS.

120. Positions of the fixed stars. When EG, the right ascension of one star S, has been obtained (106), the right ascension of any other body may be found from the observed interval in sidereal time, between its passage over the meridian and that of the star. This interval added to the right ascension of the star, expressed in time, or subtracted from it, according as the passage of the body is later or earlier than that of the star, will evidently give its right ascension in time. The method of finding the polar distance or declination has been already given (102).

When the right ascensions and declinations of the stars have been found from observations, their longitudes and latitudes may, if required, be computed by the last article.

121. Constellations. The ancients, in order to distinguish the various groups of stars, imagined figures of men, animals, and other objects, to be drawn around them in the concave surface of the celestial sphere. The group of stars contained within the contour of any one of these imaginary figures is called a Constellation. Each constellation bears the name of the figure which limits it.

The number of constellations formed by the ancients is 48. To these about 40 have since been added; some of them being small constellations, formed of stars not included in the ancient constellations, but most of them are in that part of the southern hemisphere not visible to the ancient observers. Twelve of the constellations follow one another along the ecliptic, and bear the same names as its signs. These are called zodiacal constellations.

122. Stars of a constellation. The stars of a constellation are distinguished from one another by the letters of the Greek alphabet, which are applied to them according to their apparent relative size or brightness. The principal star in the constellation is usually named a, the second 8, the third y, and thus on. When the number of stars in a constellation exceeds the number of letters in the Greek alphabet, as it generally does, the remainder are designated by the letters of the Roman alphabet or by numbers. The expres