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Figure of the Earth.

THE determination of the dimensions of the earth is a problem of great practical difficulty and has required centuries for its solution.

An exhaustive discussion of all the arcs measured has recently been made by Captain Clark, of England, and his results, now universally accepted, are as follows: Equatorial radius, 20,926,202 feet; polar radius, 20,854,895 feet; difference of the equatorial and polar radii is therefore 13.5051 miles, hence the polar compression is 27.0102 miles. The general figure of the earth (neglecting the comparatively slight inequalities of the land) is not an exact oblate spheroid of revolution for two reasons: First, the density of the earth is not uniform, but, so far as we know, increases as we approach the centre, and second, there are great irregularities in the density of the superficial portions which are composed of materials differing very widely in their specific gravity.

By virtue of the spheroidal figure of the earth, and of its axial rotation, a given body will be lightest at the equator and heaviest at the poles, for the following reasons: First, the centrifugal force is evidently greatest at the equator, and least at the poles; at the former it is 1-289 of the force of gravity, and at the latter it is evidently zero; and second, the equator is 13.5051 miles further from the centre than the poles are. Now, by actual observation at the equator, the acceleration due to gravity or the velocity imparted to a body falling freely from rest during one second of time is 32.09022 feet per second, while the centrifugal force due to the earth's axial rotation would, under the same circumstances, produce an acceleration of .11126 feet per second, but in the opposite direction; hence, if the earth did not rotate, and other things remain as at present, the acceleration would be the sum of these, or 32.20148 feet per second, and if we compute the acceleration at the poles by the well-known law of gravitation, remembering that the poles are 13 5051 miles nearer the centre than the equator, and that the acceleration there from the centrifugal force is zero, we find it to be 32.25498 feet per second, with of course intermediate values for other latitudes. These intermediate values have been well established by actual observation in all accessible latitudes. It is for these reasons that a clock regulated to keep correct time at any place, say at New York, will lose time if carried toward the equator and gain time if taken toward the poles; so also a pound of iron, for example, at Boston, would weigh less than a pound at Key West, and more than a pound in Greenland. These differences in weight could not, of course, be detected by the ordinary scales for weighing in general use, because the weights themselves would be similarly affected, but by the use of a spring balance the difference is easily and satisfactorily determined.

The discussion of the figure and motions of the earth opens up a vast field of inquiry and speculation in astronomy, physics, and geology.

Without entering deeply into the subject, we may remark that for many centuries the earth has been so situated in its orbit that the perihelion, or nearest point to the sun, has nearly coincided with the Wintersolstice-December 21-of the northern and the Summer solstice of the southern hemisphere. They actually did coincide about the year A. D. 1250, and since this date they have been slowly separating, being now about 110 apart. This separation is increasing at the rate of 61.75 annually, so that in about 10, 450 years the perihelion will occur at the southern Winter solstice. In the present condition of things we notice, as a matter of fact, that the Winter of the southern hemisphere is about seven days longer than in the northern; that the south pole has about 170 more hours of night than of day, while the north pole has about 170 more hours of day than of night, and that the Winter of the northern hemisphere occurs when the earth is at its least distance from the sun and in the southern when it is at its greatest.

For these reasons it would appear that the amount of heat received annually by the two hemispheres must be unequal, the northern receiving the most and the southern the least. Again it is seen that fully three-fourths of the land is in the northern hemisphere, while water covers nearly all the southern, and that the south pole is surrounded by ice to a much greater extent than the north pole. The mean annual temperature of the southern hemisphere during so many centuries may have been reduced so much lower than that of the northern as to cause there a vast accumulation of snow and ice, whose attraction may be sufficient to draw the water toward it, thus giving the earth an eggshaped form, submerging the southern lands by the ocean and leaving the northern high and dry. But when the present condition of things shall become reversed, as it will be in 9,820 years hence, the northern hemisphere will receive less heat than the southern, and if this take place to such a degree that ice will accumulate around the north pole to the extent it now does around the south the water will gradually flow back from the south to the north and the land of the northern hemisphere will become more or less submerged, while vast continents may be left high and dry in the southern. Such are the changes which are almost if not absolutely certain to occur in the distant future. North America is probably destined to experience another glacial period and our northern and Atlantic States-the nursery and home of American civilization and freedom-may again be submerged beneath the briny waves.

The Planet Mars.

THERE has been a great deal of speculation of late years as to the habitability of the planet Mars. No observations will ever establish this point; all that can be said is that the astronomical conditions are not unfavorable to organic life.

The orbit of this planet is very elliptical; its mean distance from the sun is about 141,500,000 miles and the difference between its aphelion and perihelion distances is not less than 13,000,000 miles, and as it receives from the sun less than half the amount of heat and light that the earth does, this great variation in its distance from the sun must very seriously affect the climate, especially of its temperate and polar zones.

The length of its year is 687 of our days, and it rotates once on its axis in 24 hours 37.4 minutes. Its average distance from the earth at opposition is about 48,500,000 miles, but under the most favorable circumstances this distance is reduced to about 35,500,000, which is the nearest approach the planet can make to us. These favorable approaches occur when the planet is in or near its perilion, which happens in the month of August at intervals of fifteen years.

The inclination of the planet's equator to the plane of its orbit is 240 50', differing very little from our own, and therefore it has its torrid, temperate, and frigid zones, and a succession of seasons substantially the same as we have.

Mars has two moons, Phobos and Deimos, discovered by Professor Hall, of the Naval Observatory, Washington, D. C., during the favorable opposition of 1877. The outer one, Deimos, revolves around

THE PLANET MARS-Continued.

the planet in 30 hours 18 minutes, at a distance of 14,600 miles, and the inner one, Phobos, in 7 hours 39 minutes, less than one-third of Mars' day, at a distance of 5, 800 miles. The orbits of both moons are circular, and in the plane of the planet's equator.

By reason of the short periodic time of Phobos compared with the axial rotation of Mars, this satellite rises in the west and sets in the east, but Deimos conducts himself like our own moon-that is, rises in the east and sets in the west.

Solar and lunar eclipses are very frequent phenomena on Mars, Phobos being eclipsed at every full moon, and crossing the sun's disk at every new moon. As regards the amount of moonlight they furnish to the planet, they fall far short of our moon, their combined light being about 1-60 of that given by our satellite.

The apparent angular diameter of Mars during a favorable opposition is 24"; its actual diameter is then very nearly 4 200 miles. And its surface is therefore a trifle more than one-fourth, and its volume one-seventh that of the earth.

The control which the planet exercises over its satellites furnishes us with a very accurate means of determining its mass, which is a little less than one-ninth of the earth's mass. And therefore it follows that its density is only seven-tenths of that of the earth, and its superficial gravity such that a body which weighs 100 pounds here would weigh only 38 pounds on the surface of Mars.

When the planet is viewed through a powerful telescope, the surface presents a reddish appearance, with certain markings, some of which are permanent, while others recur at regular intervals, with the same general outline. Around the poles brilliant white patches of a circular form are seen. Their regular recurrence leads to the belief that they are extensive snow-clad regions or zones varying in size according to the season of the planet's year. Mars has an atmosphere somewhat rarer than ours, and the spectroscope reveals the presence of aqueous vapor in it.

The surface presents some striking peculiarities as regards the distribution of land and water. There are no great oceans and continents such as we have, but both are arranged in long narrow belts like the Mediterranean and Red Seas. Until quite recently the dark portions were generally believed to be water and the bright parts land, but it is far more probable that the opposite is true and that the long narrow and nearly parallel lines, formerly called canals, are in reality parallel mountain ridges. In confirmation of this we may take the following illustration from terrestrial phenomena. Suppose we station ourselves on the summit of some lofty mountain such as Pike's Peak, from which we can survey an extensive tract of country, the creeks and rivers would appear like bright silver threads on a dark background and the ponds and lakes as brilliant patches with the same environment, since water reflects more light than the land; therefore it follows that if the earth were viewed from a great distance, the dark portions would be land and the bright ones water. Such also would be the appearance of the surface of Mars, and, therefore, the formerly so-called canals which the Martians were supposed to have excavated for commercial and other purposes are really mountain ridges in the sea.

If the nebular hypothesis is true-and all the structural and dynamical features of the solar system appear to confirm it-Mars must be many millions of years older than the earth, and in consequence of its comparatively small volume, it may have long since cooled down to a temperature incompatible with animal and vegetable life such as we know; but as it now exists, all the conditions necessary for the support of organized beings are there, viz.: Land and water, an atmosphere, and a regular succession of the seasons, Spring, Summer, Autumn, and Winter.

The Galaxy or Milky Way.

DURING any clear night when the moon is absent a faint white band, somewhat irregular in breadth and intensity, can be seen extending obliquely across the sky. This girdling belt or band is commonly known as the Galaxy or Milky Way, from its whitish or milky appearance, and has been an object of study by astronomers from the remotest antiquity.

Disregarding slight deviations in its brightness, breadth, and direction, its course is that of a great circle inclined at an angle of about 630 to the celestial equator and cutting this circle in points whose right ascension are 6h. 47m. and 18h. 47m., and therefore its poles are situated in right ascension 12h. 47 m. and declination 270 N., and right ascension Oh. 47m. and declination 270 S. At the point of nearest approach to the south pole, and where it is brightest, there is seen a dark, vacant space about 80 long by 50 broad, so conspicuous as to attract the notice of the most superficial observer; it is called by navigators the "Coal Sack." In it only one solitary star is visible to the naked eye, but it is by no means devoid of telescopic stars. Its striking blackness is probably due in part to the effect of contrast with the brilliant star-ground by which it is surrounded."

The brightness of the Milky Way in this neighborhood is very striking compared with that in its most northern course, and conveys the idea of greater proximity. This circumstance has led astronomers to believe that the visible heavens is in the form of a flat ring like a discus or quoit, of immense and irregular breadth and thickness, within which we are eccentrically situated, nearer to the southern than to the northern portion.

It is absolutely impossible to give even a faint idea of the number of stars crowded together in this wonderful band.

More than 120,000 have passed across the field of view of a telescope in fifteen minutes. The total number is absolutely incalculable. Although composed of a vast assemblage of stars, there are about fifty vacant spaces absolutely devoid of stars so far as we are at present able to determine. One of the most remarkable of these is situated in the constellation Sagittarius, in right ascension 17h. 57m. and declination 270 51 S., and therefore visible in our latitude. This black hole' of the heavens is nearly circular, and has on the northwest side of it four orange-colored stars.

Another vacant space is found a little to the east of this hole, of a crescent shape, but not quite so black as the former.

Not even an approximate estimate can be made of the distance of the telescopic stars in the Milky Way. Their light has doubtless been many thousand, perhaps millions, of years travelling to us at the rate of 186,000 miles per second. Their distance is absolutely inconceivable. If the universe of visible stars, to which our solar system belongs, and of which the Milky Way forms the outer edge or boundary, is of such prodigious dimensions, what must be the size and distance of the gaseous nebula-those island universes-which our large telescopes have revealed far beyond the confines of the Milky Way? The question cannot be answered; it is beyond human comprehension.

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Astronomical Constants.

THE mean obliquity of the ecliptic for the year 1902 is 23° 27′ 7.2.

inution, 0.46.

Mean annual dim

The present accepted value of the solar parallax is 8". 81 at the earth's mean distance, which is 92, 790,000 miles, with a probable error of about 75,000 miles more or less.

The eccentricity of the earth's orbit is 0.016771; we are therefore 3, 112, 560 miles nearer to the sun at perihelion (January 1) than at aphelion (about July 1).

Length of the sidereal year, 365 days, 6 hours, 9 minutes, 9.6 seconds of mean time. Length of the tropical year (from equinox to equinox), 365 days, 5 hours, 48 minutes, 46.07 seconds of mean time.

Mean distance from earth to moon, 238, 850 miles.

The length of a second's pendulum, that is, one which vibrates once in a second, in vacuo,

ASTRONOMICAL CONSTANTS-Continued.

at any place whose latitude is 1, is 39. 01254 + 0.20827 sin2 / inches. At New York it is 39. 1013 inches.

The acceleration of gravity in one second of mean solar time is 32. 086528+ 0.171293 sin2/ feet. The half of this is the distance through which a body falls (in a vacuum) in one second. The velocity of light is 186, 330 miles per second.

Light requires 8 minutes and 18 seconds to pass from the sun to the earth when at its mean distance, as given above; therefore, when we look at the sun we see him not where he actually is, but where he was about 8 minutes and 18 seconds ago; his true place is then always in advance of his apparent place.

1902

Pole Star.

MEAN TIME OF TRANSIT (AT NEW YORK) AND POLAR DISTANCE OF POLE STAR.

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From June 16 to August 1 both the upper and lower transits take place during daylight. The azimuth at the time of greatest eastern or western elongation can be easily computed from

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sin p
COS I

where A denotes the azimuth, p the polar distance, and the latitude of the place.

DATE OF GREATEST ELONGATION.

To find the time of greatest eastern or western elongation, let H denote the hour angle, and / and p as before, then we shall have

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This quantity, H, added to or subtracted from the time of transit given above, according to the elongation required, will give the mean time of the greatest elongation at any place whose north latitude is 1.

NAME OF STAR.

Star Table.

FOR IDENTIFYING THE PRINCIPAL FIXED STARS.

Declination

a Andromeda..

N 28 31

y Pegasi (Algenib) aCassiopeiæ..

N 14 37

a A rietis

8 Persei (Algol)..

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1 18.0 +10 40.0 1 13.2 +10 44. 8 N 55 58 0 42.2 +11 15. 8 N 22 59 +0 40.0 +12 38. 0 N 40 341 39.9 +13 37.9 aCoronæ Borealis. N 16 18 3 8.2 15 6.2 aScorpii (Antares). N 45 543 47.1 +15 45. 1 aLyra (Vega). S8 193 47.6 +1 45.6 aAquila (Altair). aOrionis (Betelguese). N 7 234 27.6 +16 25.6 aCygni (Deneb) Canis Majoris (Sirius). S 16 35+5 18.4 +17 16. 4 aCephei aGeminorum (Castor).. N 32 76 5.7 +18 3.7 Aquarii BGeminorum (Pollux).. N 28 16+6 16.6 +18 14.6 a Piscis Aus. aCanis Minor.....

aTauri (Aldebaran) aAuriga (Capella). 8Orionis (Rigel)

N5 296 11.6 +18 9.6 a Pegasi (Markab).

Declination

On Meridian.
Upper. Lower.
O I
H. M. H. M.
N 12 28+ 8 40.1 +20 38.1
S 10 37+11 56.5 +23 54.5
N 19 43 +12 47.5 +0 45.5
N 74 35 +13 27.5 + 1 25.5
N 27 413 49.71 47.7
S 26 12 14 59.32 57.3
N 38 4117 9.35 7.3

8 36 +18 21.46 19.4 44 55+19 13.57 11.5 62 9+19 51.5 + 7 49.5 0 49 +20 35.8 +8 33.8 S 30 10 +21 27.1 + 9 25. 1 N 14 39 +21 34.7 + 9 32.7

To find the time of the star's transit add or substract, according to the sign, the numbers in the second column of figures to the date of the transit of the pole star given above. Thus, for a Andromeda February 1. Lower Transit of Polar Star is 4 h. 40.9 m. A M., to which add 10 h. 40 m. and we have 3 h. 20.9 m. P. M for December 1, we find 7 h. 27. 1 m. P. M., etc.

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