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ELEMENTS AND CONSTRUCTION OF

SOLAR TABLES.

THAT you may have some idea of the manner by which astronomers have arrived at the knowledge of the dimensions of the solar system, and the positions and motions of the planets, we shall give you a few examples relative to the earth; from whence you may learn, that by similar observations and methods they have determined the same of the other planets. As the latitude of the place of observation is a principal element in all astronomical observations, we shall begin with the method of finding it.

TO FIND THE LATITUDE OF A PLACE.

Observe the greatest and least meridional altitudes of any star near the pole. If both the altitudes be on the same side of the zenith with the pole, half their sum is the latitude; but if the observations be on dif ferent sides of the zenith, half their difference is the co-latitude. There will be a necessity of correcting the observed altitudes for refraction. The pole star itself may do very well for this purpose. There will be about twelve hours between the observations; and therefore they must be made when the night is more than twelve hours long.*

TO FIND THE OBLIQUITY OF THE ECLIPTIC
TO THE EQUATOR.

Let the meridian altitude of the sun's center, which is always in the ecliptic, be observed on the days of the summer and winter solstice; the difference of these

*See Plate 15. Fig. 2.

altitudes is the distance of the tropics from each other, and half this quantity will be the obliquity of the ecliptic. Or the meridian altitude lessened by the co-latitude at the summer solstice, or the co-latitude lessened by the altitude at the winter solstice, will give the. obliquity sought. From the mean of a number of good observations made in the year 1772, the obliquity of the ecliptic to the equator was found to be 23°, 28'. And distant observations when compared together prove that it decreases at the rate of about half a second per

annum.

In this last way, the declinations of the planets or fixed stars are found; observing that their declination is of the same or a contrary name, viz. north or south, with the latitude of the place, according as its complement is less or greater than the altitude.

TO FIND THE TIME OF AN EQUINOX.

In a place whose latitude is known, observe the meridian altitudes of the sun's center on the day of the equinox, and also on the days preceding and following it; then the difference between these altitudes and the co-latitude will be the sun's declinations on these days, and at the times of the observations.

If either of these altitudes should prove to be equal to the co-latitude, that observation was made at the time of the equinox; but if not, the time of it may be thus found.

Let DG* represent the equator, AC the ecliptic, E the equinoctial point, and AD, BF, CG, the declinations of the sun at the times of the observations. Now the angle AED being the known obliquity

* See Plate 15. Fig. 3.

ELEMENTS AND CONSTRUCTION OF

SOLAR TABLES.

THAT you may have some idea of the manner by which astronomers have arrived at the knowledge of the dimensions of the solar system, and the positions and motions of the planets, we shall give you a few examples relative to the earth; from whence you may learn, that by similar observations and methods they have determined the same of the other planets. As the latitude of the place of observation is a principal element in all astronomical observations, we shall begin with the method of finding it.

TO FIND THE LATITUDE OF A PLACE.

Observe the greatest and least meridional altitudes of any star near the pole. If both the altitudes be on the same side of the zenith with the pole, half their sum is the latitude; but if the observations be on dif ferent sides of the zenith, half their difference is the co-latitude. There will be a necessity of correcting the observed altitudes for refraction. The pole star itself may do very well for this purpose. There will be about twelve hours between the observations; and therefore they must be made when the night is more than twelve hours long.*

TO FIND THE OBLIQUITY OF THE ECLIPTIC
TO THE EQUATOR.

Let the meridian altitude of the sun's center, which is always in the ecliptic, be observed on the days of the summer and winter solstice; the difference of these

* See Plate 15. Fig. 2.

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of the ecliptic, we have it and the declinations in the triangles CEG, BEF, from which we may find the arcs CE, BE, from the two last observations. Then say, as BC: BE:: 24 hours: the time from the second observation to the equinox. Thus may the quantity of the tropical year be determined by comparing dis tant observations together. But the tropical year may be more accurately determined by a calculation of the moments of the solstices; for the invention of which method we are indebted to Dr. Halley. The observation is exceedingly easy, and the calculation not difficult. It is as follows:

TO FIND THE TIME OF THE SOLSTICE

FROM OBSERVATION.

LET AVO* represent a small portion of the tropic near the solstice, and KVN a part of the ecliptic. Suppose the sun's places on three several days near the solstice to be K,L,M, then on the meridian he will be in H,F,G, the relation of which may be determined by the shadow of a stile, ab, projected on a board, cd, perpendicular to his rays at noon. From any given point as c, measure ch, cf, and cg, on the noons of the three days, then ch―cf=fh, and cg-cf=fg. By these means we have the proportion of distance of FH, FG; for fh: fg :: FH: FG.

It is known by geometry, that the distances AV, TV, are to each other as the squares of the subtenses AK, TL, so that the curve will have the property of a parabola, of which the solstitial colure VH will be the axis; in which having the three points H,F,G, we can find TV, the time from the second observation to the

* See Plate 16. Fig. 1.

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