the sun is actually seen above the horizon H'H, at S', when the orb is really below it at S.

EFFECT OF REFRACTION UPON THE SUN WHEN ON THE HORIZON.

88. All the other heavenly bodies are similarly affected, the time of their rising being accelerated, and that of their setting retarded. The period of the visibility of the stars above the horizon, is therefore increased by refraction.

89. REFRACTION INFLUENCED BY THE TEMPERATURE AND PRESSURE OF THE ATMOSPHERE. It has been found that the varying pressure and temperature of the atmosphere at the place of observation, produce a change upon the refraction for any given altitude. Astronomers for this reason in preparing tables of refractions for use, give due weight to the indications of the thermometer and barometer, in order to insure correctness in the results. Thus in the tables given in Art. 82. the estimates are made upon the supposition that the height of barometer' is thirty inches, and that the temperature is 47° Fah.

90. OF PARALLAX. The apparent angular displacement of a body caused by being seen from different points of observation is its parallax.

Thus, if two persons A and C, placed at two adjacent corners of a room were to look at a ball situated in the centre of the room, A would see it in a line with the opposite corner nearest to C, and C in the direction of the corner nearest to A; and the angle made by the two lines

1. The barometer is an instrument that measures the pressure of the atmosphere.

What effect has refraction on the rising and setting of all heavenly bodies? Does it lengthen or shorten the period of their visibility? Do the temperature and pressure of the atmosphere influence refraction? What is said respecting the construction of the tables in Art. 82? What is parallax.

of visible direction, would in a general sense be the parallax of the ball. Thus in Fig. 23, where the lines 1, 2; 2, 4; 2, 7; &c., represent the outline of the room, let B be the ball, A the place of the eye of one spectator, and C

the position of that of the other. The ball would be seen by the first in the direction ABX, and by the second, in the direction CBY, and the angle ABC would be the parallax of the ball, or the angular displacement that it suffers by being viewed from the two stations A and C.

91. Now if two astronomers, one at St. Petersburg, and the other at the Cape of Good Hope, were to observe the moon at the same absolute moment of time, and fix her position in the heavens, making allowance for refraction only, it is evident that their results would not be exactly alike; because the two observers behold the moon from different points in space, and would see her in different places on the celestial sphere; and such would be the case with any observers who were not making their observations from the same spot.

Explain from figure. Relate what is said respecting the observations upon the moon taken from different stations? Why must allowance be made for parallax in astronomical observations?

Allowance must therefore be made for this angular displacement or parallax in order to prevent confusion in astronomical calculations: and as in the case of longitude we must have some standard meridian whence to reckon the degrees of longitude, so in parallax we must have some standard station, from which all celestial objects are supposed to be viewed. This imaginary station is the centre of the earth, and the true position in the sky of any heavenly body, is determined by an imaginary line drawn from the centre of the earth to the centre of the body, and prolonged to meet the starry vault.

92. PARALLAX. HOW MEASURED. The angle contained between two lines, drawn from the centre of the body, one to the eye of the observer, and the other to the

centre of the earth, is the measure of the parallax of the body.

Thus, in Figure 24, where the curve PRZC represents

Where is the standard station from which all celestial objects are supposed to be seen? How is the true position in the heavens of a planet or planetary body determined? How is parallax measured? Explain from figure.

HORIZONTAL PARALLAX.

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a fourth part of a celestial circle extending from the horizon P to the zenith Z, MM', M2, M3 the moon at dif ferent altitudes, C, the centre of the earth, and A the place of the observer; AMC is the angle of parallax when the moon is in the horizon, AM'C, the same when she is fifty-five degrees above the horizon, and AM2C when she is near the zenith.

93. VARIATIONS IN PARALLAX-EFFECT OF ALTITUDE. It is evident from the inspection of the figure where the arc M, M', M2, M3, M2 represents a part of the moon's orbit that the parallax is greatest when the moon is on the horizon, and gradually diminishes until it becomes nothing at the zenith. At the zenith there can be no parallax, because the lines drawn from the centre of the moon at M3 to the place of the observer at A, and to the centre of the earth C, make no angle with each other but form one line; the moon must therefore be seen at the same place in the starry heavens; viz. Z, whether viewed from A or C.

What has been just stated in respect to the moon is true also of every other heavenly body, whose parallax can be measured; viz., that the parallax is greatest when the body is at the horizon, and gradually diminishes with the altitude, becoming nothing at the zenith.

94. HORIZONTAL PARALLAX. The horizontal parallax of a body is its parallax when seen upon the horizon. Thus, in Fig. 24, the observer being at A, the horizontal parallax of the moon is the angle AMC; an angle formed by drawing from the centre of the body whose parallax is sought two lines, one to the place of the spectator touching the earth, and the other to the centre of the earth.

95. EFFECT OF DISTANCE. The amount of parallax is influenced by distance; the greater the distance the less the parallax, and the smaller the distance the greater the parallax1. This is clear from a glance at Fig. 24, where

1. When this relation exists between two quantities they are said to be inversely proportional to each other.

When is the parallax greatest? When does it become nothing? Why does it? What is horizontal parallax? Explain from figure. Are the statements just made applicable to every other heavenly body having a parallax that can be measured? Is the amount of parallax influenced by the distance of a body? Give the rule.

S represents a planet more distant from the earth then the moon at M', but having the same altitude; and SS1 the path of the planet. Now the parallax of the planet S is the angle ASC which is evidently smaller than the angle AM'C, which is the parallax of the moon at M1.

96. Since the parallax decreases with the increase of distance, it results that when a body as a fixed star is situated very far from the earth the parallax becomes so small that it is impossible to measure it; a fixed star will therefore appear to occupy the same place in the heavens, whether viewed from the centre or the surface of the earth; indeed the same will be true if it is even observed from opposite sides of the earth's orbit around the sun.

97. EFFECT OF PARALLAX UPON THE TRUE POSITION OF A HEAVENLY BODY. The true position of a heavenly body, being that which it would have if seen from the centre of the earth, it is evident that the effect of parallax is to depress a body below its true position. In Figure 24, the true position of M, in the celestial vault is P, since it would appear at P if the eye was at C; but the spectator at A, sees the moon at the place L in the celestial vault, the luminary being depressed, the extent of the arc of parallax PL. The amount of depression at M' is P'L', and at M2 it is P'L'.

We thus see that parallax decreases the altitude of a heavenly body, and must therefore be added to the apparent altitude, in order to obtain the true altitude.

98. ON DECLINATION AND RIGHT ASCENSION. At the poles of the earth the effect of parallax, to its whole extent, would be to lessen the declination of a heavenly body, since it would cause it to appear nearer the celestial equator (which here coincides with the horizon) than its true position. At the equator of the earth the entire influence of parallax, if the body was in the east would be to increase its right ascension, and if in the west to diminish it. If it was on the meridian the declination

Explain from figure. What is said of the parallax of the fixed stars? What is the ef fect of parallax upon the true position of a heavenly body? Explain from figure. What effect has parallax upon the altitude, and how must the correction for altitude be employed? What is the effect of parallax upon declination and right ascension? At the poles?