THE QUADRANT—TRANSIT INSTRUMENT—CLOCKS—STELLAR TIME—SOLAR TIME—“MEAN” TIME.

We must say a few words respecting the various instruments and aids to astronomical observation before proceeding, for astronomy requires very accurate calculations; and though we do not propose to be very scientific in our descriptions, some little idea of the manner in which observations may be made is necessary. The first thing to see about is the Angle.

Suppose we draw four lines on a piece of paper, ab and cd. These intersect at a point, m. We have then four spaces marked out, and called angles. The four angles are in the diagram all the same size, and are termed right angles, and the lines containing them are perpendicular to each other.

But by altering the position of the lines (see fig. 504), we have two pairs of angles quite different from right angles; one angle, a´ m´ c´, is smaller, while a´ m´ d´ is much larger than the right angle. The former kind are called acute, the latter obtuse angles. We can therefore obtain a great number of acute angles, but only three obtuse, and four right angles around a given point, m.

The length of the sides of an angle have no effect on its magnitude, which is determined by the inclination of the lines towards each other. We now may consider the magnitude of angles, and the way to determine them. For this purpose we must describe a circle, which is figured in the diagram. But what is a circle?—A circle is a curved line which always is at the same distance from a certain fixed point, and the ends of this line meet at the point from which the line started.

If we fasten a nail or hold a pencil on the table, and tie a thread to it, and to the other end of the thread another pencil, we can describe a line around the first pencil by keeping the thread tightly stretched. This line is at all points at equal distance from the centre point. Any line from the centre to the circumference is called a radius, and a line through the centre to each side of the circumference is the diameter, or double the radius. The circumference is three (3·14) times the diameter. Any portion, say k i l, is an arc, and the line, k l, is the chord of that arc. A line like m n is a secant, and o p is a tangent, or a line touching at one point only.

We may now resume our consideration of the angles by means of the circle. Let us recur to our previous figure of the right angles, around which we will describe a circle. We see that the portion of the circumference contained between the sides of the right angle is exactly one-fourth of the whole. This is termed a quadrant, and is divided into 90°—the fourth of 360 equal parts or degrees into which the whole circumference is divided. The angle of 45° so often quoted as an angle of inclination is half a right angle. To measure angles an instrument called a Protractor is used.

The Protractor, as will be seen from the accompanying illustration (fig. 507), is a semi-circle containing 180°. The lower portion is a diagonal scale, the use of which will be explained presently. The Protractor measures any actual angle with accuracy. If we put the vertical point of the angle and the centre point of the circle together, we can arrive at the dimensions of the angle by producing the lines containing it to the circumference. An angle instrument, figured herewith, may be assumed as the basis of most apparatus for measuring angles. An index hand, R R, moves round a dial like the hand of a clock, and the instrument is used by gazing first at one of the two objects, between which the angle we wish to determine is made—like the church steeples (fig. 508) for instance. The centre of the instrument is placed upon the spot where lines, if drawn from the eye to each of the objects, would intersect. The index hand is then put at 0°, and in a line between the observer and the object, A. Then the index is moved into a similar position towards B, and when in line with it the numbers of degrees passed over (in this imaginary case 20), shows the magnitude of the angle.

The simple quadrant is shown in the cut (fig. 510). This was so arranged that when any object in the horizon was being looked at through the telescope attached, a plummet line is at 0°. But if the telescope be raised to C S, the quadrant will move, and the line will mark a certain number of degrees of the angle which a line if drawn from the star makes with the line of the horizon. The “Astronomical Quadrants” are as shown in fig. 516, and consist of a quadrant of wood strengthened and fitted with a telescope. The circle is graduated on the outer edge, and a “vernier” is attached. The time is determined by the observation of the altitude of a star, and then by calculation finding out at what time the star would have the observed altitude. The quadrant is now superseded by circular instruments.

An ellipse is a flattened circle, or oval, and will be understood from the diagrams. Let us fix two pegs upon a sheet of paper, and take a thread longer than the distance between the pegs; draw with the pencil controlled by the thread a figure, keeping the thread tight. We shall thus describe an oval, or ellipse. The orbit of nearly all the heavenly bodies is an ellipse. The parabola is another curved line, but its ends never meet; they become more and more distant as they are continued. The comets move in parabolic curves, and consequently do not again come within our vision unless their direction be altered.

This figure has a long axis, ab (fig. 512); and perpendicular to this a short axis, de, passing through the centre, c. The two points, S S', are called the foci of the ellipse; also, as is evident from the construction of the figure, any two lines drawn from the two foci, to any point of the circumference, for instance, S and S'm, or Sm' and S'm', etc., which represent the thread when the pencil is at m or m', are together equal to the larger axis of the ellipse. These lines, and we may imagine an infinite number of such, are called radii vectores. The distance of the foci, S or S', from the centre, c, is called the eccentricity of the ellipse. It is evident that the smaller the eccentricity is, the nearer the figure approaches to that of the circle. The superficies of the ellipse is found by multiplying the two half axes, ac and dc, by each other, and this product by the number 3·14.

The Diagonal Scale is shown in the margin. It is used to make diagrams so as to bring the relative distances before the eye. The larger divisions represent, it may be, miles, or any given distance; the figures on the left side tenths, and the upper range hundredths of a mile. So a measurement from Z to Z´ will represent two miles, we may say, with so many tenths and hundredths.

The Transit instrument is due to Roemer, a Danish astronomer. It consists of a telescope so constructed as always to point to the meridian, and rotates upon a hollow axis, directed east and west. At one end is a graduated circle. The optical axis of the telescope must be at exactly right angles to the axis of the instrument; it will then move on the meridian. There is an eye-piece filled with two horizontal and five vertical wires, very fine, the latter at equal distances apart. The star appears, and the time it takes to cross is noted as it passes between each wire, and the mean of all the transits will be the transit on the meridian. For if we add the times of all the transits across the wires, and divide by five the number of them we shall get at a true result.

A good clock is also a necessary adjunct for astronomical observations, and the astronomical clocks and chronometers now in use record the time with almost perfect accuracy. The improvement in telescopes, the use of micrometers, etc., have greatly facilitated observations. In the transit clock we have a most useful timekeeper, for the ordinary clocks are not sufficiently accurate for very close observations. The sidereal time differs from solar time, and the twenty-four hours’ period is calculated from the moment a star passes the meridian until it passes it again. The sidereal day is nearly four minutes shorter than the solar day, and the sidereal clock marks twenty-four hours instead of twelve, like the old dial at Hampton Court Palace over the inner gate. The Chronograph has also been useful to astronomers, for by “pricking off” the seconds on a roller by itself, the observer can mark on the same cylinder the actual moment of transit across each wire of the instrument, and on inspection the exact moment of transit may be noted.

The Equitorial is another useful instrument, and by its means the whole progress of a star can be traced. The Equitorial consists of a telescope fixed so that when it has been pointed at a certain star a clock-work movement can be set in motion, which exactly corresponds with the motion of the star across the heavens, and so while the star moves from its rising to setting it is under observation. Thus continuous observations maybe made of that particular star or comet without any jerking or irregular movement.

We can thus see the uniform motion of the stars which go on in greater or lesser circles as they are nearer to or farther from the pole; and with the exception of the polar star, which, so far as we are concerned, may be considered stationary, every star moves round from east to west—that is, from the east of the polar star to the west of it, in an oblique direction. Therefore, as Professor Airy remarks, “Either the heavens are solid, and go all of a piece, or the heavens may be assumed to be fixed or immovable, and that we and the earth are turning instead of them.”

The Mural Circle is another very useful instrument, and is used by calling to aid the powers of reflection of quicksilver, in which a bright star will appear below the horizon at the same angle as the real star above the horizon, and thus the angular distance from the pole or the horizon of any star can be calculated when we know the inclination of the telescope. The Transit Circle is also used for this purpose, and is a combination of the transit instrument with the circle. In all calculations allowance must be made for refraction, for which a “Table of Refractions” has been compiled. From the zenith to the horizon refraction increases. The effect of refraction can be imagined, for when we see the sun apparently touching the horizon the orb is really below it, for the refraction of the rays by the air apparently raises the disc.

The clock and chronometer are both very useful as well as very common objects, but a brief description of the pendulum and the clock may fitly close our remarks upon astronomical apparatus and instruments. The telescope has been already described in a previous portion of this work, so no more than a passing reference to it has been considered necessary. We therefore pass on to a consideration of the measurement of time, so important to all astronomers and to the public generally.

Time was measured by the ancients by dividing the day and night into twelve hours each, then by sun-dials and water-clocks, or clepsydra, and sand-clocks. The stars were the timekeepers for night before any mechanical means of measurement were invented.

Sun-dials were in use in Elijah’s time, and the reference to the miracle of the sun’s shadow going back on the dial as a guarantee to Hezekiah, will be recalled at once by our readers. These dials were universal, and till sunset answered the purpose. But the hours must have been very varying, and on cloudy days the sun-dials were practically useless.

The water-clocks measured time by the dripping or flow of water, and they were used to determine the duration of speeches, for orators were each allotted a certain time if a number of debaters were present. This method might perhaps be adapted to the House of Commons, and speaking by the clock might supersede clÔture. We find allusions to these practices in the orations of Demosthenes. Even this system was open to objection, for the vases were frequently tampered with, and an illiberal or objectionable person was mulcted of a portion of the water, while a generous or popular adversary had his clepsydra brimming full. Some of these water-clocks were of elegant design, and a Cupid marked the time with arrows on the column of the clock of Ctesibius, while another weeping kept up the supply of water. The motive power was the water, which filled a wheel-trough in a certain time, and when full this trough turned over, and another was filled. The wheel revolved once in six days; and by a series of pinions and wheels the movements were communicated more slowly to the pillar on which the time was marked for 360 days, or with other arrangements for twenty-four hours.

The repeating of psalms by monks also marked the time, for by practice a monk could tell pretty accurately how many paternosters or other prayer he could repeat in sixty seconds. At the appointed hour he then awoke the monastery to matins.

Nature also marks time for us—as, for example, the age of trees by means of rings—one for each year; and horses’ teeth will guide the initiated to a guess at the ages of the animals, while the horns of deer or cattle serve a like purpose. But man required accuracy and minute divisions of time. He had recourse therefore, to machinery and toothed wheels. Till the mechanical measurement of time was adopted, the sunrise and sunset only marked the day, and the Italians as well as Jews counted twenty-four hours from sunset to sunset. This was a manifestly irregular method. To this day we have marked differences of time in various places, and at Geneva we have Swiss and French clocks keeping different hours according to Paris or Berne “time.” This, of course, is easily accounted for, and will be referred to subsequently.

We have read that the first clock in England was put up in Old Palace yard in 1288, and the first application of the toothed-wheel clock to astronomical purposes was in 1484, by Waltherus, of Nuremberg. Tycho BrahÉ had a clock which marked the minutes and seconds. If we had had any force independent of gravitation which would act with perfect uniformity, so that it would measure an equal distance in equal spaces of time, all the various appliances for chronometers would have been rendered useless. In the supposed case the simple mechanism, as shown in the margin (fig. 517), would have sufficed. The same effect would be produced by the spring, were it possible that the spring by itself would always uncoil with the same force. But it will not do so: we therefore have to check the unwinding of the cord and weight, for left to itself it would rapidly increase in velocity; and if we likewise make an arrangement of wheels whereby the spring shall uncoil with even pressure all the time, we shall have the principle of the watch.

It is to Huygens that the employment of the pendulum in clocks is due, and the escapement action subsequently rendered the pendulum available in simple clocks, while the manner of making pendulums self-regulating by using different metals, has rendered timepieces very exact. Of course the length of a pendulum determines the movement, fast or slow; a long pendulum will cause the hands of the clock to go slower, for the swing will be a fraction longer. A common pendulum with the escapement is shown (fig. 518). Each movement liberates a tooth of the escapement. The arrangement of wheels sets the clock going. The forms of pendulum are now very varied.

But in watches the pendulum cannot be used. The watch was invented by Peter Hele, and his watches were called “Nuremburg eggs” from their shape. The weight cannot be introduced into a watch, and so the spring and fusee are used. The latter is so arranged that immediately the watch is wound and the spring at its greatest tension, the chain is upon the smallest diameter of the fusee, and the most difficult to move. But as the spring is relaxed the lever arm becomes longer, and the necessary compensating power is retained. Watches without a “fusee” have a toothed arrangement beneath the spring.

The Pendulum. A “simple” pendulum is impossible to make, for we cannot put the connecting line between the “bob” and the clock-work out of consideration, so “simple pendulums” are looked upon as “mathematical abstractions.” The most modern clocks have what is called a “deadbeat” escapement, and a compensating pendulum. Clocks are liable to alter by reason of the state of the air and varying temperature, and until all our clocks are placed in vacuo we must be content to have them lose or gain a little. There is a magnet arrangement by which the Greenwich Observatory clocks keep time by compensation, corresponding with the fall or rise of the syphon barometer attached to it. The description need not be added. We may here state that detailed descriptions of all the instruments used in the Observatory, together with full information as to their use, will be found in a very interesting work by Mr. Lockyer, entitled “Stargazing,” to which we are indebted for some corrections in our summary.

We have spoken of solar time and sidereal time, and no doubt someone will inquire what is meant by mean time—an expression so constantly applied to the Greenwich clock time. Stellar time, we have seen, corresponds to the daily revolution of a star or stars. Solar time is regulated by the sun, and this is the astronomical time generally observed, except for sidereal investigations. But the sun is not always regular; the orbit of the earth causes this irregularity partly. The earth moves faster in winter than in summer, so the sun is sometimes a little fast and sometimes a little slow. Astronomers therefore strike an average, and calculate upon a Mean Sun, or uniform timekeeper. Mean time and true (apparent) time are at some periods the same—viz., on the 15th of April, on the 14th of June, on the 31st of August, and on the 24th of December. Twice it is after, and twice before it. The time occupied by this “mean” sun passing from the meridian and its return to it, is a mean solar day, and clocks and chronometers are adjusted by it.

Twenty-four hours represents a complete revolution of the heavenly bodies. The mean solar time is 23^h 56´ 4·091, while twenty-four hours of mean time are equal to 24^h 3´ 56·55 of sidereal time. The difference between the times is given by Dr. Newcomb as follows, and is called the Equation of Time:—

Measurement of Distances.

Before passing to consider the planetary system we must say a few words respecting the manner of ascertaining the distances of inaccessible objects, and by so doing, we shall arrive at an idea how the immense distances between the sun (and the planets) and the earth have been so accurately arrived at. To do this we must speak of parallax, a very unmeaning word to the general reader.

Parallax is simply the difference between the directions of an object when seen from two different positions. Now we can illustrate this by a very simple method, which we have often tried as a “trick,” but which has been very happily used by Professor Airy to illustrate the doctrine of parallax. We give the extract in his own words:—

“If you place your head in a corner of a room, or on a high-backed chair, and if you close one eye and allow another person to put a lighted candle upon a table, and if you then try to snuff the candle with one eye shut, you will find you cannot do it.... You will hold the snuffers too near or too distant—you cannot form any idea of the distance. But if you open the other eye, or if you move your head sensibly you are enabled to judge of the distance.” The difference of direction between the eyes, which is so well known to all, is ready a parallax. It can also be illustrated by the diagram herewith.

If two persons, A and C (fig. 523), from different stations, observe the same point, M, the visual lines naturally meet in the point, M, and form an angle, which is called the angle of parallax. If the eye were at M, this angle would be the angle of vision, or the angle under which the base line, A C, of the two observers appears to the eye. The angle at M also expresses the apparent magnitude of A C when viewed from M, and this apparent magnitude is called the parallax of M.

Let M represent the moon, C the centre of the earth represented by the circle, then A C is the parallax of the moon; that is, the apparent magnitude the semi-diameter of the earth would have if seen from the moon. If the moon be observed at the same time from A, being then on the horizon, and from the point B, being then in the zenith, and the visual line of which when extended passes through the centre of the earth, we obtain, by uniting the points, A C M, by lines, the triangle, A C M.

Therefore, as A M, the tangent of the circle stands at right angles to the radius, A C, the angle at A is a right angle, and the magnitude of the angle at C is found by means of the arc, A B, the distance of the two observers from each other. As soon, however, as we are acquainted with the magnitude of two angles of a triangle, we arrive at that of the third, because we know that all the angles of a triangle together equal two right angles (180°). The angle at M, generally called the moon’s parallax, is thus found to be fifty-six minutes and fifty-eight seconds. We know that in the right-angled triangle M C A, the measure of the angle, M = 56´ 58, and also that A C, the semi-diameter of the earth = 3,964 miles. This is sufficient, in order by trigonometry, to obtain the length of the side, M C; that is, to find the moon’s distance from the earth. A C is the sine of the angle, M, and by the table the sine of an angle of 56´ 58 is equal to 1652/100000; or, in other words, if we divide the constant, M C, the distance of the moon, into 100,000 equal parts, the sine, A C, the earth’s semi-diameter = 1,652 of these parts. And this last quantity being contained 60 times in 100,000, the distance of the moon from the earth is equal to 60 semi-diameters of the earth, or 60 × 3964 = 237,840 miles.

In a similar way the parallax of the sun has been found = 8·6, and the distance of the sun from the earth to be 91,000,000 miles.

Let us first see how we can obtain the distance of any inaccessible or distant object. We have already mentioned an experiment, but this method is by a calculation of angles. The three angles of a triangle, we know, are equal to two right angles; that is an axiom which cannot be explained away. We first establish a base line; that is, we plant a pole at one point, A, and take up our position at another point, B, at some distance in a straight line, and measure that distance very carefully. By means of the theodolite we can calculate the angles which our eye, or a supposed line drawn from our eye to the top of the object (C) we wish to find the distance of, makes with that object. We now have an imaginary triangle with the length of one side, A B, known, and all the angles known; for if all three angles are equal to 180°, and we have calculated the angles at the base, we can easily find the other. We can then complete our triangle on paper to scale, and find out the length of the side of the triangle by measurement; that is the distance between our first position, A, and the object, C. It is of course necessary that all measurements should be exact, and the line we adopt for a base should bear some relative proportion to the distance at which we may guess the object to be.

In celestial measurements two observers go to different points of the earth, and their distance in a straight line is known, and the difference of the latitudes. By calling the line between the observers a base line, a figure may be constructed and angles measured; then by some abstruse calculation the distance between the centre of the earth and the centre of the moon may be ascertained. The mean distance is sixty times the radius of the earth. The measurement of the sun’s distance is calculated by the observations of the transit of Venus across his disc, a phenomenon which will again occur on 6th December, 1882, and on 8th June, 2004, the next transit will take place; there will be no others for a long time after 2004.

All astronomical observations are referred to the centre of the earth, but of course can only be viewed from the surface, and correction is made. In the cut above, let E be the earth and B a point on the surface. From B the stars, a b c d, will be seen in the direction of the dotted lines, and be projected to e i k l respectively. But from the centre of the earth they would appear at e f g h correctly. The angles formed by the lines at b c d are the parallactic angles, f i g h and h l show the parallax. An object on the zenith thus has no parallax. (See fig. 524.)