THE TELESCOPE.-Telescopes are of two kinds, namely, refracting and reflecting telescopes. The refracting telescope consists of an object-glass which forms an image of the object, and an eye-glass by which the image is viewed. The reflecting telescope consists of a concave mirror which receives light from the distant object, and reflects it so that the rays converge to a focus and form an image, the image being viewed by an eye-glass. The terrestrial telescope consists of two telescopes like the preceding-which are called astronomical telescopes, and give an inverted image the second inverting the inverted image of the first, and so giving an upright image. Eye-pieces generally have two lenses, and have names according to the position of the focus. Ramsden's eye-piece has two lenses, the focus being just beyond the field lens. It is called a positive eye-piece, and it can be used as a magnifying glass. Huyghens' eye-piece also has two lenses, the focus being between the two. It is called a negative eye-piece, and cannot be used as a magnifying glass. These compound eyepieces enable us to get rid of spherical and chromatic aberration. The achromatic object-glass is made by joining together two lenses, one of flint glass and the other of crown glass. The dispersion is made equal and opposite, but the bending powers are unequal. A lens is equivalent to a number of prisms placed base to base, the outer prisms having a greater angle to cause the rays to bend more, so that all the rays may come to one point, called the focus. The magnifying power of a telescope is found by dividing the focal length of the object-glass by the focal length of the eye-piece.

THE EQUATORIAL TELESCOPE.-The equatorial is an ordinary telescope, mounted in such a way that it can easily be directed to any part of the heavens. The polar axis is parallel to the earth's axis, that is to say, it is inclined at an angle equal to the latitude of the place, at Washington about 39°, at London about 514°. The telescope can be moved round the polar axis in a plane which is parallel to the earth's equator, and this motion is said to be motion in right ascension. The telescope can also be moved up and down in a plane at right angles to the earth's equator, and this motion is called motion in declination. Whatever part of the skies an object is in, the equatorial can be directed to it, and the object can be kept constantly in view, because there is a kind of clock which drives the instrument round at the same speed at which the earth is turning round.

THE TRANSIT INSTRUMENT. The transit instrument is a telescope mounted on a horizontal axis, so as to be capable of moving in the meridian only. It is used to determine the exact moment at which celestial bodies cross the meridian, that is, when they are in a true north or south position. It is also used for determining the declination of celestial objects, that is, how far in angular measures these bodies are from the celestial equator.

sidereal

THE SIDEREAL CLOCK.-The clock is similar to an ordinary clock, but it is regulated to keep accurate time with the apparent diurnal movements of the stars, instead of with the mean sun. It shows the same time as clocks and watches only once in a year, namely, at the Vernal Equinox, about the 21st of March. It gains about four minutes each day on the ordinary clock, and in a year it gains a whole day, so that there are 366 sidereal days and only 365 solar days in one year. The sidereal noon occurs when the first point of Aries passes the meridian, and the hours are reckoned from 0 to 24. The time by the sidereal clock at which a celestial body crosses the meridian is equal to the right ascension of that particular object. Conversely, if the exact right ascension of a star be known, the error of the clock can be determined by observing a transit of the star.

THE CHRONOGRAPH.-The chronograph consists of a cylinder covered with paper, and made to rotate uniformly by clockwork. It is connected electrically with the sidereal clock, which, as it ticks, makes dots on the paper at equal distances by means of a recording pen, and these dots represent seconds. Fractions of a second are recorded by the observer touching a key, which causes a second pen to make a dot on the cylinder as it turns round. This dot would come between two second dots, and the distance is measured from these. In this manner the 180 or 100 of a second can be estimated. The small fractions of a second obtained by the chronograph are necessary in fixing the right ascension and declination by the transit instrument.

THE MICROMETER.-The micrometer is used for measuring small arcs. It consists of two wires, which can be brought together or separated at pleasure by means of a screw. An equatorial star appears to move through about 15° in one hour, 1° in four minutes, 15' in one minute, or 15" of arc in one second of time. The distance that the wire moves for one turn of the screw is found by allowing a star to pass from one wire to

the other, and then allowing 15" of arc for every second of time taken in so doing. The diameter of the moon, the sun, or a planet can be estimated in angular measure by the micrometer, and then, knowing the distance of these objects, their size can be calculated from a knowledge of the relation that exists between the radius of a circle and its circumference.

THE THEODOLITE.-The theodolite is used for measuring horizontal and vertical angles, that is, altitude and azimuth. It consists of a small telescope, which can be moved up and down, and the inclination is shown by a graduated circle, called the altitude circle. The telescope can also be twisted around a vertical axis, and the angular distances of objects from the north point of the horizon measured, that is, azimuth.

THE SEXTANT.-The sextant is chiefly employed on board ship for observing the altitude of the sun, lunar distances, etc., in the determination of latitude and longitude. It consists of a telescope, through which the observer looks. Opposite to the telescope is a mirror, half silvered and half plain, so that he can see directly through the plain part to an object, and he can bring a second object to coincide with the first by means of a second mirror attached to the movable arm, which reflects its light on to the silvered part of the first mirror, and from thence through the telescope. The reading on the sextant then gives the angular distance between the two objects.

VERNIERS.-Verniers are divided scales, with their divisions a little smaller than those on the main scale to which they are attached. If a length equal to nine divisions of the main scale be divided into ten parts, then each of these latter will be less than the former. In general, n divisions of the vernier are equal to n 1 divisions of the scale, which enables us to read to the nth part of a division, whatever that may be. If the divisions on the main scale were tenths of an inch we could get hundredths by dividing a length equal to nine of them into ten parts, then the difference between the lengths of these would be of of an inch, that is, 10.

ANGULAR MEASUREMENT.-The measurement of the distances of the sun, moon, and planets depends upon our knowledge of the properties of triangles. Our knowledge of the size of the earth and other bodies in space depends upon angular measurement. Our knowledge of the mass, volume, and density of the sun, moon, and planets, and even the masses and distances of some of the stars, depends upon our ability to measure angles.

MEASUREMENT OF TIME. An ancient method of measuring time was by the gnomon, an upright stick in the ground which cast a shadow of the sun, the length and position of which varied according to the time of day, hence the sun-dial. Other methods consisted in chanting psalms, burning candles, and dropping water or sand from one vessel to another, hence clepsydra and hour-glass, etc. Clocks came into use in England in the fourteenth century; but instead of a pendulum a vibrating horizontal bar was employed-DeWyck's clock.

Galileo discovered the pendulum, which suggested itself to him by observing a swinging

lamp in the Cathedral of Pisa. Huyghens found that the vibrations of a pendulum were not equal for any length of swing; hence the introduction of the cycloidal pendulum. Hooke's anchor escapement was the next advance, which allowed of a smaller arc of swing and eliminated a certain amount of friction, but it is not used in the best clocks because of the recoil. Graham overcame the recoil just mentioned by using pallets whose surfaces were arcs of circles, hence dead-beat escapement. The chronometer escapement has a balance-wheel in place of a pendulum, which thus admits of a more compact arrangement than is possible in a clock with a pendulum; moreover, it will work in any position.

ALTITUDE AND AZIMUTH. -The altitude of a celestial object, as a star, is its angular height above the horizon, and its complement or that which is required to make it equal to a right angle is called the zenith distance. The azimuth of a celestial object is its angular distance from the north point of the horizon. It is found by drawing an imaginary arc from the zenith point through the object till it cuts the horizon, and then measuring the angular distance between this point and the north point.

THE SPHERE OF OBSERVATION.-The appearance of the starry sphere presents different aspects, depending upon the locality of the observer. At Washington the north pole is elevated about 39° above the horizon, at London about 514° above the horizon; this elevation of the pole always being equal to the latitude of the place of observation. The celestial equator being 90° distant from the pole, will cut the horizon of London at an angle of 384°, and that of Washington at about 51°, the northern side in each case being depressed below, and the southern side elevated above, the horizon.

when

PARALLAX.-The moon's place, looked at through a telescope from London and some distant place, as Cape Town, seems to change that is, the telescopes contain an angle. This contained angle is less when the sun is viewed in the same way, but when. stars are looked at similarly the angle disappears altogether-that is, stars have no parallax, while the sun, moon, and planets have parallax, or angular displacement caused by change of position.

ROTUNDITY OF THE EARTH.-The concave heavens; the disappearance of a ship at sea; the extension of the horizon as we ascend high elevations; the frequent circumnavigation of the globe; the earth's shadow cast by the sun upon the moon during an eclipse; the spherical form of the sun, moon, and planets-all confirm our belief that the earth is globular in form.

MAGNITUDE OF THE EARTH.-The size of the earth is found by observing a star in the exact zenith of any place, then traveling along a direct north line, till the star has declined 1° from the zenith, and measuring the distance traversed. This distance would be the length of 1° in miles, and 360 times that length would give the circumference of the earth.

DEMONSTRATION OF EARTH'S ROTATION.A heavy body set in motion tends to retain its original plane of motion. Foucault's pendulum consists of a heavy ball at the

end of a long wire, supported by a steel pivot on an agate plane. The ball, when set swinging, seems to change its direction of swing across a graduated circle on a table beneath it, but, as we know that the pendulum tends to keep to the same plane of motion, and that there is so little to prevent it from doing so, we conclude it is the earth which is turning on its axis and carrying the table with it. The gyroscope is essentially the same as the pendulum, a heavy rotating disk taking the place of the swinging bob of the pendulum. The rotating disk is supported inside a horizontal ring, this ring being in its turn supported by knife edges resting on steel plates in the circumference of a vertical ring, and this vertical ring is supported by a torsionless thread, so that all the parts are nicely counterpoised and are free to move. A pointer attached to the vertical ring is found to move over a graduated scale at the same rate as the pendulum changed its plane of motion; hence, we conIclude that it is the earth which moves, because we know that the rotating disc holds to its initial plane of motion. The rotation of the earth on its axis furnishes us with an invaluable unit of time.

REVOLUTION OF THE EARTH IN ITS ORBIT. -The stars which are seen nearest to the sun after sunset at different times of the year are not the same, but belong to different signs of the zodiac. This change of position of the sun with respect to the stars takes place at the rate of about 1° a day, so that the whole heavens appear to revolve once in a year independent of their diurnal revolution. This is due to the real revolution of the earth in its orbit. The stars appear to describe little ellipses in the course of a year, but, as a matter of fact, it is the light coming from the stars that is displaced by the motion of the earth in its orbit, the form of this orbit being elliptical, so that the star's position is changed in such a way as to project an ellipse similar to that which the earth traces out. This phenomenon is known as the aberration of light, and was discovered by Bradley.

VELOCITY OF LIGHT.-Fizeau determined the velocity of light by reflecting a spot of light from a mirror at one station to a second mirror at a distant station. The light was brought to a focus at the required points by means of lenses. A toothed wheel whose revolutions could be registered was so placed that its teeth revolved in the focus, and the spot of light could be seen between two teeth. It was possible to turn the wheel so quickly that the spot of light was stopped by a tooth coming up before it could pass through. The distance between the stations being known, and the rate at which the wheel turned, the velocity of light could be found. Foucault's method consisted of a rapidly rotating mirror, on which a beam of light was admitted through a slit. It was then reflected on to a lens, after which it was brought to a focus on a concave mirror at some distance. It was found possible to turn the mirror so quickly that it moved through a small angle before the spot of light returned. The distance between the mirrors, the rate of rotation of the mirror, and the amount of displacement being known, the velocity of light could be esti

mated. The velocity of light and the aberration angle being known the sun's distance can be found.

(1) The ratio of the velocity of light and the earth in its orbit as determined by observation is as 10,089: 1.

(2) The earth completes its orbit in 365 days.

(3) Light would do the same journey in 3651 10,089

days.

(4) Knowing the time it would take to complete the revolution we can find how long it would take to cross the diameter, and therefore the radius.

(5) We multiply the number of seconds taken by light to cross the radius of the earth's orbit by the velocity of light, and it gives us 92,628,000 miles as the sun's distance.

THE SUN NOT ALWAYS AT THE SAME DISTANCE FROM THE EARTH.-In the Nautical Almanac the sun's apparent diameter is given for every day in the year. The apparent diameter was 32'35.2" on January 3rd, 1904, and on July 4th of the same year it was only 31'30.7". This proves the sun is farther away from us in summer than in winter.

PERIHELION AND APHELION.-When the earth is nearest to the sun it is said to be in Perihelion, and when farthest from the sun it is said to be in Aphelion.

THE EARTH MOVES WITH VARYING VELOCITY IN ITS ORBIT.-This is ascertained by measuring the sun's longitude for two successive days at different times of the year. by which means it is found in December to move over 61'10.0" within a period of twenty-four hours, while in June it only moves over 57'10.8" in the same time.

KEPLER'S LAW OF EQUAL AREAS.-Kepler found that the line joining the center of the sun with the center of the earth moved over equal areas in equal times, that is, the greater distance of the earth from the sun in June compensated for the smaller arc of motion in longitude, so that lines drawn from the sun to the extremities of the arcs moved over make equal triangles.

HOW THE INCLINATION OF THE ECLIPTIC TO THE PLANE OF THE EARTH'S EQUATOR IS DETERMINED.-The elevation of the sun above the horizon is measured by the shadow cast by the gnomon, or the north polar distance is ascertained by the transit instrument for each day in the year. In either case the sun will be found to oscillate backwards and forwards over an arc of about 47°, half of which arc is the inclination of the ecliptic to the equator.

NODES.-The two points where the plane of the ecliptic crosses the plane of the celestial equator or equinoctial are called nodes, that point at which the sun appears to come up from below the equator being called the ascending node, and that at which the sun appears to descend from above the same plane being called the descending node.

THE FIRST POINT OF ARIES.-The ascending node above referred to is the first point of Aries. It is universally used by astronomers for fixing the longitudinal and right ascension of celestial bodies.

THE SIDEREAL, SOLAR, AND MEAN SOLAR DAY. The sidereal day is the interval which elapses between two successive appearances of the same star on the meridian. The solar

day is the interval which elapses between two successive appearances of the sun on the meridian, but these are not of the same length. The mean solar day is the interval of time obtained by adding all the solar days in a year together, and then dividing by the number of days in a year.

EQUATION OF TIME.-The inequality of the solar days arises from two causes, namely, the obliquity of the ecliptic to the equator, and the unequal velocity of the earth in its orbit. The equation of time is the algebraic sum of these two variables- -that is to say, sometimes they both cause the sun to come too soon to the meridian; at other times one causes the sun to come up too soon and the other too late. In the former case the sum of the two corrections, and in the latter case the difference of the two corrections, is the equation of time, and so on.

THE SEASONS.-The seasons are the result of the revolution of the earth in its orbit and the inclination of the ecliptic to the equator. The sun on this account attains different heights above the horizon, giving different lengths of day and night. By reason of its giving to the earth more heat in the day than it loses by radiation in the night, and vice versa, we have summer or winter as the case may be.

THE YEAR. The ordinary or tropical year is the period which elapses between two successive appearances of the sun at the vernal equinox. The anomalistic year is the period which elapses between two successive returns of the sun to his perigean point. The sidereal year is the time which elapses between two successive appearances of the same star on the meridian at the same time of day.

PRECESSION AND NUTATION.-The sun and moon attract the protuberant portion of the earth's equator more on that side nearest to them than on that side farthest away, and in this way the differential attraction tends to tilt the axis a little, so that it describes a circle in about 25,800 years. The moon's differential attraction is greater than that of the sun. On account of the moon continually changing its relation to the earth's equator, it causes the axis of the earth to describe a circle with a wavy circumference, to which effect the term nutation, or nodding of the earth's axis, is applied.

ASTRONOMICAL SYMBOLS AND ABBREVIATIONS.

MEASUREMENT OF THE SIZE OF THE SUN AND PLANETS.-The ratio between the radius of a circle and its circumference is always the same, no matter how large or small the circle may be. Thus, an arc of 57.2958° on any circle is equal in length to the radius of that circle; and if this be reduced to seconds of arc, we get 206,265" as the number of seconds in a length of arc equal to radius. The mean angular diameter of the sun, as measured by the micrometer, is a little over 32' of arc. We may consider the sun to form part of the circumference of a circle, with its distance from the earth as radius. There are 1920'' in 206,265 32', and =108 nearly; hence the dis1920

tance of the earth from the sun is 108 times the diameter of the sun, whatever that may be. But we know the distance of the sun to be 92,885,000 miles; so that the diameter of 92,885,000 the sun must be =860,000 miles. 108 The same method applies to the planets and their satellites as well as to the sun. The angular diameter of the body being measured in seconds of arc, it bears the same ratio to 206,265 (the number of seconds in a length of arc equal to radius) that the diameter in miles bears to the distance in miles; or, calling the actual diameter d, and the real distance D, DX angular diameter. For exwe have d= ample the moon, in round numbers, is 240,000 miles distant, and its angular diameter is a little over 31'; hence, by the formula, its diameter is

d=

206,265

S

Seconds of Time.

LATITUDE, LONGITUDE, RIGHT ASCENSION, AND DECLINATION.-Terrestrial latitude is

Ditto, repeated..

Harton coal-pit. Probable value.

TO FIND THE PERIOD OF A PLANET.-The synodic period may be readily observed, and from it the actual time occupied by a planet in completing its revolution round the sun can be calculated. For example, the synodic period of Mercury is 115.9 days; this means that the earth and the planet being in a line with the sun at any time, the latter has progressed in its orbit so quickly as to complete an entire revolution and again overtake the earth during the period of 115.9 days. Now 360° the earth moves 0.9856° in a day, and 365.25 in the entire period 115.9 0.9856° 114.2°. But the planet has moved 360° +114.2°= 474.2° in the same time, hence the period of the planet is to that of the earth as 114.2° : 114.2°365.25

474.2°, that is,

88 days nearly.

474.2° SHOOTING STARS.-The names of the principal meteor swarms and the dates of their appearance are as follows:

Name.

Andromedes

Lyrids.

Leonids. Perseids.

Comet I. 1861

23 November Biela's 20 April.. 15 November Tempel's, 1866 11 August...Comet III. 1863 The number of stars in the northern hemisphere in Argelander's catalogue is 324,000. The number of known variables is 111, and the suspected variables 381. Roughly, then, there is one variable in every 660 of the known stars. According to Duner, about 1 in 7 of the third type stars is variable.

TO FIND THE TIME OF SUNRISE AND SUNSET BY MEANS OF THE TERRESTRIAL GLOBE.The time of sunrise or sunset may be found for any day by elevating the north or south pole equal to the sun's declination north or south for any given day. The place being under the brass meridian, the hour circle should be set at XII., and then the place should be rotated first to the eastern horizon and then to the western and the times on the hour circle noted, the former being the time of rising, and the latter that of setting of the sun. Twice the time of setting of the sun gives the length of the day, and twice the time of rising gives the length of the night. Example: 20th January, 1890, sun rose, 8.15; set, 3.45.

2X3.45 74-length of day.
2X8.15-16= length of night.

The months and days of the months are all marked on the ecliptic, so that the sun's place for any day is determined by finding the day on the ecliptic and noting the part of the sign of the zodiac corresponding to that day, and if the globe be turned till this part of the ecliptic comes to the meridian, the latter will indicate the declination of the sun.

Note. The Analemma is a convenient projection of the ecliptic on which the sun's declination may be readily found, as it is noted for every day in the year.

NUMERICAL FACTS RELATING TO THE SUN. --Solar Parallax (equatorial horizontal), 8.80"0.02". Mean distance of the sun from the earth, 92,885,000 miles; 149,480,000 kilometers. Variation of the distance of the sun from the earth between January and June, 3,100,000 miles; 4,950,000 kilometers.

Linear value of 1" on the sun's surface, 450.3 miles; 724.7 kilometers. Mean angular semidiameter of the sun, 16' 02.0'. Sun's linear diameter, 866,400 miles; 1,394,300 kilometers. (This may, perhaps, be variable to the extent of several hundred miles.) Ratio of the sun's diameter to the earth's, 109.3. Surface of the sun compared with the earth, 11,940. Volume, or cubic contents, of the sun compared with the earth, 1,305,000. Mass, or quantity of matter, of the sun compared with the earth, 330,000+3000. Mean density of the sun compared with the earth, 0.253. Mean density of Force the sun compared with water, 1.406.

In

of gravity on the sun's surface compared with that on the earth, 27.6. Distance a body would fall in one second, 444.4 feet; 135.5 meters. Inclination of the sun's axis to the ecliptic, 7° 15'. Longitude of its ascending node, 74°. Date when the sun is at the node, June 4, 5. Mean time of the sun's rotation (Carrington), 25.38 days. Time of rotation of the sun's equator, 25 days. Time of rotation at latitude 20°, 25.75 days. Time of rotation at latitude 30°, 26.5 days. Time of rotation at latitude 45°, 27.5 days. (These last four numbers are somewhat doubtful, the formulæ of various authorities giving results differing by several hours in some cases.) Linear velocity of the sun's rotation at his equator, 1.261 miles per second; 2.028 kilometers per second. Total quantity of sunlight, 1,575,000,000,000,000,000,000,000,000 candles. tensity of the sunlight at the surface of the sun, 190,000 that of a candle flame; 5300 times that of metal in a Bessemer convertor; 146 times that of a calcium light; 3.4 times that of an electric arc. Brightness of a point on the sun's limb compared with that of a point near the center of the disk, 25 per cent. Heat received per minute from the sun upon a square meter, perpendicularly exposed to the solar radiation, at the upper surface of the earth's atmosphere (the solar constant), 25 calories. Heat radiation at the surface of the sun, per square meter per minute, 1,117,000 calories. Thickness of a shell of ice which would be melted from the surface of the sun per minute, 48 feet, or 14 meters. Mechanical equivalent of the solar radiation at the sun's surface, continuously acting, 109,000 horse power per square meter; or, 10,000 (nearly) per square foot. Effective temperature of the solar surface (according to Rossetti), about 10,000° C., or 18,000 F.

NEBULAR HYPOTHESIS.-According to this theory, all the members of our solar system once existed in a state of highly heated gaseous or nebulous matter, which extended far beyond the orbit of our most remote planet, Neptune. This matter was supposed to have received a motion of rotation, and, as it cooled, became more and more condensed, the central portion leaving a ring of protuberant matter in the equatorial region, which, after becoming detached, would continue to revolve in the same direction as the parent mass, something after the fashion of Saturn's ring. This detached ring, it was presumed, would break up, and collecting into a globular mass retain its motion of rotation, and take up an additional motion of revolution around its primary. The detached planets formed in this way would, by a similar process, throw off their satellites, which, after long ages of cooling, have assumed their present state.