aggerate the difference of summer and winter in the southern hemisphere, and to moderate it in the northern. But no such effect is produced. For heat diminishes in intensity according to the inverse proportion of the surface of the sphere over which it is spread; that is, in the inverse proportion of the square of the distance. (Plate I. Fig. 4.) SA2 S M2:: motion at M: motion at A. This is also the proportion in which the angular velocity of the earth about the sun varies. SA2: S M2 :: heat received at M: heat received at A. Therefore equal amounts of heat are received from the sun in passing over equal angles round it, in whatever part of the ellipse those angles may be situated. This is true however the ellipse may be divided by the straight line ASP. The two segments, A M P and A I P, will however be described in unequal times; but the greater proximity of the sun compensates for the more rapid description of the smaller segment, and thus an equilibrium of heat in the two hemispheres is maintained.

§ 295. These two great causes which we have spoken of as causing the variety of seasons, are, in some parts of the world, counteracted, and in all variously modified.

In the torrid zone the vertical sun raises such vapors and causes such rains, that the season which should be the hottest, is in some places the coldest of the year. And the intermediate months, which correspond to the spring and autumn of temperate climates, are the hottest of the year. Between the tropics then we find no regular summer and winter, but rainy and dry seasons.

In polar and circumpolar regions, the days lengthen and shorten so very rapidly, that spring and autumn are unknown; vegetation advances with the utmost rapidity, and harvests ripen in the short summer, which can never be brought to maturity under warmer suns.

In the temperate zones, the change from summer to winter lasts as long as each of these seasons, and we accordingly reckon four seasons. These do not however correspond with the astronomical seasons, for causes before given.

The lengths of the astronomical seasons differ considerably, as the following table shows.

the summer solstice,—

Days. Hours. Minutes.

Spring lasts from the vernal equinox to

92 21

50

Summer lasts from the summer solstice to the autumnal equinox,

Autumn lasts from the autumnal equinox to the winter solstice,

Winter lasts from the winter solstice to the vernal equinox,—

89 1 33

The autumn and winter of the northern hemisphere are shorter than the corresponding seasons in the southern, because the perihelion is passed through in the northern winter. If the earth were in its perihelion precisely at the time of the winter solstice, the northern autumn and winter would be of equal length, and the rest of the year would be equally divided between its spring and summer. As the perihelion is 10° in advance of the winter solstice, the winter season is most shortened by the rapidity of the earth in its orbit, and the summer season includes that portion of its orbit which is performed most slowly.

§ 296. All animals and plants have periods of repose. Some a long arctic sleep, others a slight cessation of their energies. All have periods of awakening to which their powers and habits are adapted.

While great causes bring us daily variety, a multiplicity of minor and apparently changeful causes bring us some of the most stable arrangements in nature. The climate of a place is made up of general, innumerable and local causes, which blending together, and sometimes counteracting one another, give year by year, and even for each month, almost unvarying results. Thus while we repose on the stability of this our home, we find daily something new to enjoy in its unexpected beauties.

CHAPTER XIII.

POSITION OF PLACES ON THE EARTH AND OF STARS IN THE HEAVENS.

Modes of defining position on the Earth's Surface. Methods of finding Latitude. Longitude. Its determination by the Moon's motion. The Sextant. Eclipses of Jupiter's Satellites. Determination of Local Time. Lunar Distances. The Theodolite. Celestial Globes and Maps. Apparent Motions of the Planets. The Fixed Stars. The Zodiac. The Constellations. The Milky Way. Proposed Revision of the Constellations.

§ 297. Having ascertained the shape and dimensions of our globe, we wish to find our position on it. This may be done in two ways, by referring our position to the natural features of land and water, or by giving our latitude and longitude. Both modes of description are employed, and each has its advantages. Our latitude and longitude remain unchanged, and they furnish the shortest and most exact mode of describing our position. Latitude gives us some notion of the climate of a place. But if we knew places on earth only by their latitude and longitude, we should find it as difficult to fix them in our mind as to remember the positions of the stars. The natural features of the earth are more easily remembered, but their dimensions, and the latitude and longitude of these, must be accurately fixed before we can refer smaller places to them.

No map or chart is of much value as a representation of the earth's surface. Particular portions of it may be faithfully represented on a plane surface, but a globe gives the only correct idea of it as a whole. There are two modes by which a correct representation of the earth's surface may be obtained; by finding the latitude and longitude of a great number of points, and filling in the intermediate spaces by local surveys; or by finding the latitude and longitude of a few points, two perhaps in each country, and then dividing the whole country into a number of triangles. In

both of these ways we must refer to the heavens for the position of our starting point.

§ 298. The latitude of a place is easily found. It is equal to the altitude of the elevated pole. Equal differences of latitude should not however be represented by exactly equal intervals of surface, if great exactness is required. The ellipticity of the earth causes degrees of latitude to be a little longer as we approach the poles. Latitude is reckoned from the equator, and is called north or south according as the place lies north or south of the equator.

The altitude of the elevated pole above the horizon might be directly observed on the limb of the mural circle, if any bright star stood directly therein. This not being the case, a bright star near the pole, (called the polar star,) is selected, and observed in its upper and lower culminationsthat is, when it passes the meridian above and below the pole. One half the sum of the star's greatest and least altitudes corrected for refraction gives the altitude of the pole, and therefore the latitude of the place.

It may be found by the observed altitude or the observed zenith distance of a star or other heavenly body when in the meridian. In observations at sea, the sun or moon is observed instead of a star, it being difficult, from the motion of the vessel, to obtain a correct observation of the meridian altitude of so small a body as a star appears. On land the inequalities of the surface make it difficult to obtain a true horizontal boundary, the zenith distance is therefore employed. The declination of the observed star being previously known, it must be added to the observed zenith distance (corrected), if both bodies are on the same side of the equator. But if the place is in north latitude, and the star has a southern declination, the declination subtracted from the zenith distance gives the latitude.

The zenith distance of a star may be obtained more accurately by making several observations on it at different altitudes, before and after culminating, when it is near the meridian. The latitude may thus be obtained within a few seconds.

If the latitude of one place is known, that of another may be found by observations on a star which passes near the zenith of both places. The calculation is more simple when both places are on the same meridian, and when both observations are made on the same day.

$299. These operations are so easy in practice, and opportunities are so continually offering themselves, that the latitude of a place may generally be determined even under the most unfavorable circumstances, and its determination, by means of celestial phenomena, is the most important application of astronomy to the purposes of civil life.

But the longitude cannot be so readily found. France, Holland and England for a long time offered in vain great rewards to any one who should discover a mode of ascertaining longitude at sea. In the latter part of the seventeenth century, Flamstead gave his opinion that if we had tables of the places of the fixed stars, and of the moon's motions, the longitude might be found. Upon this Mr. Flamstead was appointed astronomer royal, and an observatory was built at Greenwich for him; and the instructions to him and his successors were that they should apply themselves with the utmost care and diligence to rectify the tables of the motions of the heavens, and the places of the fixed stars, in order to find out the so much desired longitude at sea, for the perfecting of the art of navigation. It was not however till after Mr. Flamstead's death that the tables of the moon's motions were corrected, and an instrument invented by which altitudes could be taken at

sea.

The principle of this instrument is that property of reflected rays by which the angle between the first and last directions of a ray which has suffered two reflections in one plane, is equal to twice the inclination of the reflecting surfaces to one another. The instrument is called a sextant if one sixth part of a graduated circle is used, a quadrant if one fourth part. Sometimes a whole circle is

used.

§ 300. Let A B (Fig. 7, Plate I.) be the limb, or graduated are, of a portion of a circle 60° in extent, but divided into 120 equal parts. On the radius C B let a silvered plane glass D be fixed, at right angles to the plane