Astronomy

There is thus a double tidal wave produced by a spheroid of water which, in the simple case we have considered, has its axis directed towards the moon, as in Fig. 45. The earth, rotating within this liquid shell, successively brings different parts of the solid earth to the points of high and low water. If the moon were fixed, we should then experience two high and two low waters every day, but as it revolves in the same direction that the earth rotates, the average interval between two successive meridian passages is 24 hours 51 minutes. This, then, is the period in which alternate high waters or alternate low waters are experienced.

A similar train of reasoning applies to the attraction of the sun upon different parts of our planet, so that there are solar as well as lunar tides. Nevertheless, the moon is the dominating cause, for although the total attraction of the sun upon the earth is about 200 times that of the moon, its differential attraction upon the opposite sides of the earth, which is alone effective in producing tides, is only about ⅖ths that of the moon.

A simple mathematical investigation shows that the tide-raising force of a body is proportional to its mass, and approximately in inverse proportion to the cube of its distance from the affected body. Thus, it appears that if the moon were removed to 1·36 times its present distance, solar and lunar tides would be equal.

At the times of new and full moon, the sun and moon will produce two tidal spheroids of water upon our imaginary earth, having their axes coincident, and an exceptionally high tide will occur. This is a spring tide. When the moon is at its quarters the two ellipsoids tend to neutralise each other, and an exceptionally low or neap tide results. Two spring tides and two neap tides thus occur in each synodic month of 29½ days.

The height of the tide will also be affected by the variations in the distance of the moon. If the moon be at perigee the tide will be greater because of the smaller distance, and if this occur at new or full moon there will be a very high spring tide, while a less notable spring tide will occur when the new or full moon is at apogee.

The combination of the solar and lunar tides gives rise to what is called the priming and lagging of the tides. At new and full moons the combined tides will produce a spheroid of water with its axis directed towards the moon. When the moon is a few days old however, the crest will take up a position intermediate between the direction of the moon and that of the sun, and high water will therefore be accelerated. The same thing will happen during three or four days after full moon. Three days before full or new moon the combination of the two tides will displace the crest towards the sun, and therefore in advance of the moon, so that high water will be retarded. The retardation and acceleration correspond to lagging and priming respectively.

At the quadratures the combined tides simply reduce the height of the crest, since there is no reason why the deviation should be to one side any more than to the other. On account of priming and lagging, the tides on successive days are accelerated or retarded by as much as 13 minutes when the effects are greatest.

Sufficient has been said to indicate that tidal phenomena are very complex even when we suppose the earth to be very simply constituted. When we take into account the actual configuration of the land and the consequent restrictions in the movements of the water, these complications are increased tenfold. Yet, by continued observations, the recurrence of tides at any port can be predicted with tolerable accuracy. It is observed that there is a certain pretty regular interval of time between the moon’s meridian passage and the time of next high water; this is different at different ports, but is so nearly constant at a given place as to be called the establishment of the port. Observations being made at a great many places, the peculiar movements of the tidal wave can be investigated. For this purpose, it is convenient to draw on a map what are called co-tidal lines that is, lines passing through places at which high water occurs at the same moment. It then appears that it is only in the Southern Pacific where the water is of sufficient extent to permit the formation of the tide crest. The effect of this wave, which commences twice a day, is gradually spread over different parts of the world, but before it reaches most places other waves have commenced a similar journey. The tide at London, for example, coming round the north of Scotland and down the North Sea, really started in the Southern Pacific 66 hours before, and in the same way the tide at New York is a little over 40 hours old.

The height of a tide is thus regulated by the conditions of the sun and moon with regard to the earth when the primary tide was formed, and not by their relation when a tide is actually observed.

In the Pacific Ocean the tides are very feeble, but near the coast they vary enormously, and sometimes reach great heights. At Bristol the difference between high and low water sometimes amounts to fifty feet, and in the Bay of Fundy, Nova Scotia, it has been as much as a hundred feet.

The peculiarities of the tides at many places are due to interference. The primary tidal wave striking the British Islands travels partly up the English Channel, and partly round to the North Sea by the north of Scotland. At some places on the east coast the two waves almost neutralise each other, while at others there are even four high tides in a day.

The circumstances under which tides occur at a given place can only be determined by actual observations, as theory is at present utterly inadequate to deal with the manifold complications brought about by the configuration of the land, and the varying depth of the water.

Tidal Friction.—The regular influx of the tide supplies us with a source of mechanical energy, which in the future will no doubt become of immense importance to mankind. A great mass of water is raised to a higher level, and by suitable contrivances it can be made to do useful work during its subsequent flow to the ocean from which it came. Ordinarily, however, the water simply rushes back without its energy being utilised, and the potential power is merely transferred to another locality. It is manifest, however, that a certain amount of tidal energy is lost by friction as the water rolls to and from the rocky shores. This energy is converted into heat, and finally radiated into space, or dissipated. Now, the principle of the conservation of energy tells us that energy can neither be created nor destroyed, although its form may change from a useful to a useless one. It follows, therefore, that the energy lost through the tides must be abstracted from one source or another, and it has been shown that this energy is really derived from the earth’s rotation. As the earth steadily ploughs its way through its liquid envelope, the tides act as a break, and its rotational velocity is reduced; it is part of this lost energy of rotation which is dissipated by the tides.

One tendency of tidal friction is accordingly to lengthen the period of the earths rotation, and, therefore, to increase the length of the day. There are, however, counteracting causes, so that there is no certain direct evidence that the day has actually lengthened in historical times.

All the energy of rotation which is lost by the earth is not, however, dissipated by the tides. Some of it is transferred to the moon, with the result that the velocity of our satellite, and consequently the size of its orbit, must be increasing. From this it is inferred that the moon was formerly very much closer than at present, and an elaborate investigation of the conditions of its retreat has led Professor G. H. Darwin to his interesting theory of “tidal evolution.” (See p. 236.)

Professor Darwin has shown that if the term “tide” be extended to include distortions of the earth and moon at an earlier stage of their history, when both were fluid or viscous, a similar grinding down of the energies of rotation of both bodies must have taken place. The axial rotation of the moon, under these circumstances, would be retarded by the attraction of the earth on the tides raised in the moon, while that of the earth would also be slowed down, but in a less degree because of the moon’s smaller mass.

Cause of Precession.—On account of the spheroidal form of the earth, we may regard it as a sphere which is surrounded by a ring of protuberant matter at the Equator. Now the attraction of the sun upon the spherical part will be quite independent of the position of its axis of rotation, and will, therefore, not affect the position of the Equator. It is different, however, with the ring; at the solstices the ring is inclined to the line joining its centre with the sun, and the near side is subject to a greater attraction than the side more remote from the sun. On account of this difference of pull, there is a tendency for the ring to move into the plane of the ecliptic, and this is what would happen if the ring were not in rotation. The practical outcome of this tendency, combined with the rotation, is to produce the twisting of the plane of the ring, and, therefore, of the plane of the Equator. At the equinoxes the plane of the ring passes through the sun, and although there is still a difference of attraction on opposite sides of the ring, the differential force is entirely directed to the sun, and therefore cannot produce any precessional effect.

The ultimate tendency to turn into the plane of the ecliptic thus depends upon the difference of the attractions on opposite sides of the ring, or rather that part of the difference which acts in a direction perpendicular to the Equator.

The terrestrial ring cannot change the position of its plane without taking the whole earth with it, and the rate of precession is thus very slow. The effect of solar precession alone would cause the equatorial plane to twist round with but little change of inclination; or the earth’s axis would travel with a conical movement round a perpendicular to the ecliptic passing through the earth’s centre.

It will be remarked that as the force-producing precession is identical with that which is effective in producing the tides, the moon must have a greater precessional effect than the sun. This is quite true, and on the average the precession-producing force of the moon is 2½ times that of the sun. When the moon is on the celestial equator, as it is twice a month, the differential force acts in the plane of the ring, and no precessional effect results. On the other hand, the greatest effect is produced by the moon when the earth’s Equator is most inclined to the line joining the earth and moon. The amount of this greatest inclination is different in different months according to the position of the moon’s nodes. In consequence of the revolution of the moon’s nodes, the moon’s orbit is inclined to the Equator at all angles from 18° to 28°, and back again to 18° in a period of 19 years. The precessional effect of the moon thus has a principal period of 19 years, while that of the sun has a period of a year during which it has two maxima and two minima. The summation of the effects of the sun and moon gives us the luni-solar precession, which is very variable in its actual rate, but averages about 50″·2 per annum.

Nutation.—If the precession-producing force were of constant amount, there would be no change in the inclination of the earth’s axis to the ecliptic. When the force is increasing, the equatorial ring is slightly tilted towards the ecliptic, and when it is decreasing the converse takes place. As the moon has the preponderating effect, these changes in the inclination will evidently depend mainly upon the changing value of the moon’s precessional force; that is, they will have a period of 19 years. Thus, if P, Fig. 46, represents the pole of the ecliptic, the north celestial pole would travel in a circle of 23½° radius about P if precession were uniform. Suppose, then, the celestial pole to be at a when the moon’s node is on the Equator—that is, when the inclination of the moons orbit to the Equator is greatest—from this time the integrated effects of the moon’s precessional force will be decreasing, and the inclination of the Equator to the ecliptic will be increased; the celestial pole will consequently recede a little more than the average from the pole of the ecliptic, so that after 9½ years it will be at b instead of c. During the next 9½ years the inclination of the moon’s orbit to the ecliptic will be gradually getting smaller, the precessional force will be proportionately reduced, and the obliquity of the ecliptic will be increased, so that the north celestial pole will have arrived at d after the lapse of 19 years. The prolongation of the earth’s axis thus describes a wavy curve, each wave extending over 19 years, so that there are about 1,400 waves during the great precessional cycle. This approach and recession of the two poles is called nutation, or nodding of the earth’s axis. The most recent investigation of its maximum amount, by Dr. Chandler, gives it as 9″·202. Besides the principal nutation there are others of very much smaller amount, due to the monthly changes of the moon’s declination and to the annual change of the sun’s declination.

The most obvious effect of nutation is that upon the inclination of the earth’s axis to the ecliptic—the “nutation in obliquity.” There is, however, a displacement of the equinoctial point, and corresponding nutations in longitude and right ascension.

As pointed out by Sir John Herschel, we have in nutation a splendid example of a periodical movement in one part of a system giving rise to a motion having the same precise period in another.

Effects of Precession.—The effects of precession may be conveniently summarised here, although some of them have necessarily been mentioned elsewhere:

(1) The first point of Aries revolves completely round the ecliptic, so that it passes through all the constellations of the zodiac in a period of 25,800 years. The “signs” of the zodiac, accordingly, no longer correspond with the constellations after which they are named.

(2) The Pole Star is constantly changing, since the north celestial pole travels round the pole of the ecliptic at a distance of about 23½° in a period of 25,800 years. About 14,000 years ago the bright star Alpha Lyræ was the Pole Star.

(3) The position of the north celestial pole is in time changed by 47°, and there may accordingly be this change in the north polar distances or declinations of all stars whatsoever. As the position of the ecliptic is almost constant, the celestial latitudes of stars will be but little affected by precession.

(4) The right ascensions and longitudes of stars, being reckoned from the shifting first point of Aries, are themselves changeable, passing through all possible values in the precessional period.

(5) The tropical year is shorter than the sidereal year by the time taken for the earth to travel through 50″·2—that is, 20 minutes 23 seconds.

(6) Celestial globes and maps, as well as star catalogues, can only represent the right ascensions and declinations of stars at a specified epoch.

CHAPTER XIV.
INSTRUMENTAL MEASUREMENT OF ANGLES AND TIME.

Graduated Circles.—Astronomy is essentially a science of precision, and the progress of our knowledge has to a large extent been dependent upon the increasing power of accurately measuring angles and time.

Let us see, first of all, how to measure angles.

A circle is divided into 360 degrees, each degree again into 60 minutes, and each minute into 60 seconds of arc; and yet, a second of arc is not a small enough quantity for many astronomical purposes. Now, unless a very large circle be employed, it is mechanically impossible to even mark the minutes of arc directly upon it, and if a very large circle were constructed, the distortion of its shape produced by its own weight would be sufficient to mar its accuracy.

What is actually done then is to get a circle of convenient size, and to graduate it, as well as the highest mechanical skill is capable of, into such parts as may leave distinct and equal spaces between the separate divisions. A competent instrument maker would, for instance, put 4,320 divisions on the limb of a circle 16 inches in diameter, two consecutive divisions thus being 5′ apart. For work of the highest precision it is necessary to strictly investigate the errors of the divisions and to correct for them in all observations.

For the further subdivision of these graduations, verniers or reading microscopes are introduced.

The Vernier.—A graduated circle being attached to an instrument, what one has to do is to take a reading with reference to some fixed mark. If the fixed mark is seen to fall precisely on one of the divisions of the circle when observed with a magnifying-glass, the reading can be written down exactly. If there be no such coincidence, some means are required for accurately reckoning the fraction of a division. One method in general use on small instruments, and where extreme precision is unnecessary, is to employ a subsidiary scale which is called a Vernier, in honour of the Frenchman who invented it. This can be applied indifferently to a scale of degrees and parts of degrees on a graduated circle, or to a straight scale. With the aid of this device it becomes possible to measure angles with no greater probable error than a few seconds of arc.

The Reading Microscope.—If a greater degree of accuracy than 10″ be required, the vernier is superseded by a reading microscope. This is a compound microscope (Fig. 48) by which the scale can be observed, and at the focus of its eye-piece is a pair of spider threads which can be moved by a fine screw S. Looking into such a microscope, one sees a magnified picture of a very small part of the scale running through the field of view, as in Fig. 47. Running across the field, in the same direction as the marks on the scale, are the spider threads a b, which can be given a right and left movement by means of the screw. At the top of the field is the part called the “comb,” having its edge cut with saw-like teeth; like the threads, this is at the focus of the eye-piece. The scale is divided so that the smallest part is 5′, and in that case the teeth of the comb are arranged so that five of them equal a scale division. The reading microscope is a fixture, and the circle is brought into the position in which its reading is required by moving the instrument with which it is connected. The zero of the microscope is a point at the middle of the comb, and one has to determine what part of the scale corresponds with it. In order to do this, the threads or “wires” are moved until the next division lies between them, and the amount which the screw has been turned from the position of zero is read off on the graduated head of the screw. The dimensions of the parts, and the magnifying power of the microscope, are adjusted so that the screw must be turned five times to carry the wires through a space equal to a division on the scale. One division, therefore, will move the wires through 1′, and as the screw head is divided into 60 parts, a movement of ¹⁄₆₀th of a revolution will shift the wires through a second of arc. Even fractions of a second can be thus measured.

The introduction of this method of measuring minute angles is due to Ramsden, who first applied it at the end of the last century. The microscopes themselves are used for measuring fractional parts of the graduations of the circles, and usually four to six of them are applied to different parts of the same circle. In this way, errors arising from flexure of the circle, fluctuations of temperature, want of exact circularity, etc., are eliminated, so that finally, after taking every conceivable precaution, the astronomer can measure angles with the accuracy which is absolutely necessary in many branches of research.

Astronomical Clocks.—Means for the exact estimation of time are of no less importance in an observatory than arrangements for the accurate measurement of angles. Astronomical clocks are constructed with extreme care, but in principle they do not differ from ordinary time-keepers. As sidereal time is of the greatest use in an observatory, the hour hand only makes one revolution a day, and the face is provided with a seconds hand, which is plainly visible. The pendulum is of such a length that it performs its swing in a second. One of the most important improvements in clocks was the introduction of the “compensation” principle, whereby the equivalent length of a pendulum remains constant in spite of fluctuations of temperature. The mercurial pendulum which one very frequently sees in a watchmaker’s establishment has a glass or steel cylinder near the bottom partly filled with mercury; as the rod lengthens by increased temperature, the centre of gravity is raised by a corresponding amount, on account of the upward expansion of the mercury, and the rate of swing remains constant when the quantity of mercury is properly adjusted. The chief defect of this plan is that the mercury and the steel rod do not respond equally well to a change of temperature.

In the most approved clocks the pendulum rod is a compound one, consisting of rods, or concentric tubes, of zinc and steel. The pendulum bob is hung on a steel rod suspended from the top of a zinc tube, which in turn is fixed at the bottom end to a larger tube of steel; a rod attached directly to the latter is suspended by a flat spring in the usual manner. By this arrangement the unequal expansions or contractions of the different parts due to changes of temperature neutralise each other, so that a constant rate is the result. The tubes are pierced with numerous holes so that the inner and outer ones acquire the same temperature almost at the same time.

The rate of a clock is disturbed slightly by changes in the pressure of the atmosphere. When the air is densest there is a greater resistance to the swinging of the pendulum, and the clock will go more slowly. Although this only amounts to a small fraction of a second a day, it must necessarily be taken into account in such an establishment as that at Greenwich, to which all the country looks for the precise control of time-keepers. In the standard clock at Greenwich a magnet is raised or lowered by the changing height of a barometer, and its varying attraction upon a certain piece of iron attached to the pendulum compensates for the differences produced by change of pressure.

Pendulum clocks are obviously unsuitable for use at sea, so that chronometers are usually employed on ships. These are like large watches, very carefully constructed, with “compensation” balance wheels, and can generally be relied upon as good time-keepers.

After all precautions, however, no astronomer would put his faith in any clock for any length of time, as the best of them is liable to change its rate rather irregularly. The “error” of the clock is therefore very frequently determined by the observation of certain standard stars with the transit instrument. The stars can be relied upon to come to the meridian at the proper time, and any apparent departure from this time must be set down to the account of the clock.

The Chronograph.—A good clock, however, is not the only requirement of an observatory. It is necessary further to be able to record very precisely the moment at which an observation is made. If the clock be in the immediate vicinity of the observer, the time can be noted by counting the beats of the pendulum, and a practised observer will, by this “eye and ear” method, record times to the nearest tenth of a second. Mere estimation, however, is not very reliable, so that a mechanical method, which also permits greater subdivision of the second, is very generally adopted. The instrument is called a chronograph, and, although constructed in various forms, its function is to record on a sheet or strip of paper the regular beats of the clock, as well as the signals made by the observer. In one form of the instrument the recording sheet is fixed on a cylindrical drum which is made to revolve once a minute by a small clock. Beneath the drum is a pair of prickers worked by the armatures of electromagnets. One of these magnets is in connection with the clock, and a simple arrangement sends an electric current through it every second, with the result that the seconds are marked by small punctures on the paper. As the cylinder revolves, the marker travels slowly lengthwise, so that the clock record runs spirally from one end to the other. To facilitate the identification of the punctures, one is omitted at the end of every minute. When an observation is made, the observer presses a button, and a current is sent through the second magnet, with the result that a puncture is made alongside those made by the clock. In this way the exact moment at which an observation is made can be easily registered, and read off at any convenient time.

At Greenwich a room is set apart for a number of chronographs, each in communication with an instrument in the various observatories.

CHAPTER XV.
TELESCOPES.

The Refracting Telescope.—The function of a telescope is two-fold. First, to magnify the heavenly bodies, or, what comes to the same thing, to make them look as if they were nearer to us, so that we can see them better. Second, to collect a much greater number of rays of light than the unassisted eye alone can grasp, so that objects too dim to be otherwise perceptible are brought within our range of vision.

There are two forms of telescope, distinguished as Refractors and Reflectors. The simplest form of refracting telescope is exemplified by the common opera-glass, and large refractors are not essentially different. Such instruments depend for their action upon the formation of an image by a lens. One can easily illustrate this by producing upon the wall of a room an inverted image of a candle or gas flame with a spectacle lens (one adapted for a long-sighted person), or with one of the larger lenses from an opera-glass. Having such an image, it may be magnified by means of another lens, just as one may magnify a photograph with an ordinary reading glass. Technically, the lens which forms the primary image is called the object-glass of the telescope, and that which is used to magnify this image is called the eye-piece. The object-glass is usually a large lens, which is placed at one end of a tube, while the eye-piece is a much smaller lens, placed at the other end. Means are provided for adjusting the distance between the two lenses so as to admit of distinct vision.

Matters are, however, not quite so simple as has been stated. There is a very great difficulty introduced by the fact that a lens made out of a single piece of glass gives an image which is surrounded by fringes of colour, so that some device has to be adopted in order to destroy, as far as possible, this enemy of good definition. In the early history of the telescope, this so-called chromatic aberration was considerably reduced by making small object-glasses of very great focal length.^[4]

Lenses of 100-feet focus, however, are not easy to employ as object-glasses, and astronomy was, therefore, greatly benefited by Dollond’s invention of the achromatic lens in 1760. This is a compound lens, usually consisting of a double convex crown-glass lens and a concavo-convex, or double concave, lens of flint glass. The curvatures of the lenses, and the optical properties of the two kinds of glass composing them, are such that the colour due to one of them is practically neutralised by that due to the other acting in opposition. A section of such an object-glass, with the “cell” in which it rests, is shown in Fig. 49.

In this way the focal length of the lens, and, therefore, the length of the telescope tube, can be kept within reasonable dimensions, while the definition is improved. There is, however, usually a little outstanding colour, due to the imperfect matching of the two lenses, and if one looks through a large refractor, even of a good quality, a purple fringe will be noticed round all very bright objects. This only affects a few of the brighter objects, while millions of others which are dimmer may be seen free from spurious colour.

It may be remarked that the curved surfaces of the lenses forming telescopic object-glasses must not be parts of spheres. If they are, the images will be rendered indistinct by spherical aberration, and the optician has to design his curves to get rid of this defect at the same time as chromatic aberration.

A new form of telescopic objective, consisting of three lenses, which has many important advantages, has recently been invented by Mr. Dennis Taylor, of the well-known firm of T. Cooke & Sons, York.

Such a lens as this illustrates the perfection which the optician’s art has now attained. Six surfaces of glass have to be so accurately figured that every ray of light falling upon the surface of the lens shall pass through the finest pinhole at a distance of eighteen times the diameter of the lens.

The Reflector.—In a reflecting telescope, the object-glass of the refractor is replaced by a concave mirror. In order that such a mirror may reflect all the rays from a star to a single point, its concave surface must be part of a paraboloid of revolution, that is, a surface produced by the revolution of a parabola on its axis. If a spherical surface be employed, all the rays will not be reflected to a single point, and the images which it gives will be ill-defined. Yet it is astonishing to find that the difference between a parabolic and spherical surface, even in the case of a large mirror, is exceedingly small. Sir John Herschel states that in the case of a mirror four feet in diameter, and forming an image at a distance of forty feet, the parabolic only departs from the spherical form at the edges by less than a twenty-one thousandth part of an inch.

An image being formed by a mirror, it is next to be viewed with an eye-piece just as in the case of a refracting telescope. Here there is a little difficulty, for if the eye-piece be applied in the direct line of the mirror, the interposition of the observer’s head will block out the light. Several ways of overcoming this have been devised, but the plan most generally followed is that which Newton adopted in the first reflecting telescope which was ever constructed. With his own hands Newton made a small reflector, 6¼ inches long and having an aperture of 1⅓ inches, with which he was able to study the phases of Venus, and the phenomena of Jupiter’s satellites. This precious little instrument is now one of the greatest treasures in the collection of the Royal Society of London. The general design of this telescope is shown in Fig. 50. The concave mirror is at the bottom of the telescope tube, and normally it would form an image of a star near the end of the tube. A plane mirror, however, of small size intercepts the rays and reflects them to the side, where they converge to a focus. This image is observed and magnified by an eye-piece, as in the refractor. It is true that in this arrangement the plane mirror, or flat, renders the central part of the principal mirror ineffective, but the loss of light is very much less than would be the case if the eye-piece were placed in position to view the image centrally.

In the hands of Sir William Herschel the reflecting telescope was greatly developed. The great telescope with which he enriched astronomical science had a mirror four feet in diameter, and its tube was 40 feet in length. With the view of utilising the whole surface of the mirror and dispensing with a second reflecting surface, the four foot mirror was placed at a small angle to the bottom of the tube, so that its principal focal point was no longer at the centre, but at the side of the tube.

In practice, however, it is found that the Herschellian form of reflector does not give the best definition, and it is now very seldom seen.

Among other forms, the “Cassegrain” is perhaps the most important. During the last year or two this form has received a great deal of attention, more especially in regard to its special adaptability for photographic purposes.

In the Cassegrain telescope, the plane mirror of the Newtonian form is replaced by a small convex mirror which is part of a hyperboloid of revolution, its axis and focal point being coincident with those of the primary mirror. The rays are in this way reflected back to the mirror at the bottom of the tube, and in order that the image may be seen, it is necessary to cut out the middle part of the mirror to admit the eye-piece.

Although the small mirror must theoretically be hyperbolic, tolerable definition is obtained even if it be spherical or ellipsoidal, and its actual departure from these forms is so slight as to be beyond detection by measurement, so that the figuring of such mirrors can only be tested in the telescope. For photographic purposes this telescope has the very important advantage that a short telescope is equivalent to a very long one of the Newtonian form, or refracting telescope, so that the image of sun, moon, or planets formed at the focus is very large in comparison with the size of the telescope. A modification of this form of telescope, in which the small mirror is out of the path of the rays falling upon the larger one, and no longer obstructing the central part, has been recently revived by Dr. Common, and has become generally known as the “Skew Cassegrain.”

In reflecting telescopes the mirrors were formerly made of speculum metal (an alloy of copper and tin), and the word speculum is even now commonly employed to signify a telescopic mirror, although it is usual to make the mirror of glass, with the concave surface silvered and highly polished.

One is frequently asked for an opinion as to which is the better form of telescope, the reflector or refractor, and it is a question that one finds some little difficulty in answering. On one point, however, all are agreed, namely, that the reflector has the advantage in regard to its achromatism; it is indeed perfectly achromatic, while the so-called “achromatic” refractor is at best only a compromise. For the rest, one cannot do better than quote the evidence of Dr. Isaac Roberts before the International Astro-photographic Congress:—“The reflector requires the exercise of great care and patience, and a thorough personal interest on the part of the observer using it. In the hands of such a person it yields excellent results, but in other hands it might be a bad instrument. The reflector gives results at least equal, if not superior, to those obtained with the refractor, if the observer be careful of the centering, and of the polish of the mirror, and keeps the instrument in the highest state of efficiency; but when entrusted to an ordinary assistant the conditions necessary for its best performance cannot be so well fulfilled as the same could be in the case of the refractor.” One great practical advantage of the reflector is that there are fewer optical surfaces, so that a large reflector may be obtained for the price of a much smaller refractor.

Eye-Pieces.—So far we have regarded the eye-piece of a telescope as a simple lens, but it is evident that the spherical and chromatic aberration of such a lens will interfere with its performance. For occasional use, however, even a simple lens is very serviceable if the object observed is brought to the centre of the field of view.

Compound eye-pieces are of various forms, each having certain advantages, the desiderata being freedom from colour and “flatness of field”—that is, stars in different parts of the field are to be equally well in focus. Those most commonly employed are the Ramsden and Huyghenian eye-pieces. The former consists of two plano-convex lenses of equal focal lengths, having their curved faces towards each other, and being placed at a distance apart equal to two-thirds of the focal length of either lens. Such an eye-piece can be used as a magnifying-glass, and it is therefore placed outside the focal image formed by the telescope with which it is used; on this account it is called a positive eye-piece. This kind of eye-piece is not quite achromatic, but its flat field of view gives it a special value for many purposes.

In the Huyghenian eye-piece there are again two lenses, made of the same kind of glass. That which comes nearest to the eye has a focal length of only one-third that of the field lens, and the distance between the two lenses is half the sum of the focal lengths. This form of eye-piece cannot be used as a magnifying-glass in the ordinary sense, and as the field lens must be placed on the object-glass or mirror side of the focus, it is called a negative eye-piece. The Huyghenian eye-piece is more achromatic than the Ramsden, and is more widely used when it is only required to view the heavenly bodies. In instruments employed for purposes of measurement, a positive eye-piece is essential in order that the spider threads may be placed at the focus of the telescope. The images formed by an astronomical telescope are upside down, and neither of the eye-pieces described reinverts them.

A special form of eye-piece is therefore used when a telescope is employed for terrestrial sight-seeing. The desired result is obtained by the introduction of additional lenses, but there is a corresponding reduction of brightness.

For viewing the sun some device is necessary to reduce the quantity of light entering the eye. To look at the sun directly, even with a small instrument, is very dangerous. The arrangement usually adopted is a solar diagonal, in which the light is reflected from a piece of plane glass before entering the eye-piece; the piece of glass is wedge-shaped, so that the reflection from one surface only is effective; if the glass had parallel sides, the solar image would be double.

Magnifying Power.—The magnifying power of a telescope depends upon the focal length of the object-glass, or speculum, and that of the eye-piece. Optically, it is equal to the former divided by the latter, so that the greater the focal length of an object-glass, or the smaller the focal length of the eye-piece, the greater will be the magnifying power. In a given telescope, the object-glass, or speculum, is a constant factor, and the magnifying power can only be varied by changing the eye-piece. The focal length of the Lick telescope, for example, is about 600 inches; with an eye-piece which is equivalent to a lens of one-inch focus, the magnifying power would be 600; with a lens of half an inch focus, it would be 1,200, and so on.

The magnifying power which can be effectively employed, however, depends upon a great variety of circumstances. First, the clearness and steadiness of the air; then there is the quality of the object-glass, or speculum, to be considered; and also the brightness of the object to be observed, for when the object is very dim, its light will be spread out into invisibility if too high a power be used.

In practice, good refractors perform well with powers ranging up to 80 or 100 for each inch in the diameter of the object-glass. Thus, on sufficiently bright objects, a six-inch telescope will work well with a power of about 500, while a 30-inch may be effectively employed with powers between 2,000 and 3,000.

Illuminating Power.—It has already been pointed out that magnification is not the only function of a telescope. As a matter of fact, the most powerful telescopes in the world fail to produce the slightest increase in the apparent size of a star, for even if these objects be brought to apparently a 3,000th part of their real distances, they are still too far away to have any visible size. But although a star cannot be magnified, it can be rendered more visible by the telescope, for the reason that the object-glass collects a greater number of rays than the naked eye. The pupil of the eye may be taken to have a diameter of one-fifth of an inch; a lens one inch in diameter will have 25 times the area of the pupil, and will therefore collect 25 times the amount of light from a star; a two-inch lens will grasp 100 times, and a 36-inch 32,400 times as much light as the pupil alone. Practically all these rays collected by the object-glass, or speculum, of a telescope cannot be brought into the eye; some are lost through the imperfect transparency of the glass, or the imperfect reflecting power of the speculum. Still, allowing a considerable percentage for loss, there is an enormous concentration of light when a large telescope is employed.

The Altazimuth Mounting.—Having got a telescope, we have next to see how it can be best supported, for unless it be a very small instrument indeed, it will be impossible to hold it in the hand like a spy-glass. However a telescope be mounted, provision must be made for turning it to any part of the sky whatsoever. Very frequently one of the axes on which the instrument turns is vertical, while the other is horizontal. Such a stand for a telescope is called an altazimuth mounting, for the reason that it permits the instrument to be moved in altitude and in azimuth.

As a rule, one finds only small telescopes mounted in this manner. The objection to it is that, as one continues to observe a heavenly body, two independent movements must be given to the telescope in order to follow the body in its diurnal movement across the heavens. If we commence observing a star newly risen, for example, the telescope must trace a stair-like path in order to follow it, as it ascends into the heavens.

The Equatorial Telescope.—A much more convenient method of setting up a telescope is to mount it as an equatorial. The essential feature of this instrument is that one of the axes of movement, instead of being vertical, is placed parallel to the axis of the earth. This is called the polar axis, and, when the telescope is turned around such an axis, it traces out curves in the sky which are identical with those described by the stars in their diurnal motions. If, then, the telescope be directed to a star or other heavenly body, it can be made to follow the object and keep it in view by a single movement. The axis at right angles to the polar axis is called the declination axis, and is necessary in order that the telescope may be moved towards and from the Poles so that all the heavenly bodies above the horizon may be included in its sweep.

One very important advantage of the equatorial is that as only one motion is required to keep a star in view, so long as it is above the horizon, the necessary movement may be furnished by clock-work. A good equatorial is accordingly provided with a driving clock, which is regulated so that it would drive the telescope through a whole revolution once a day. Unlike an ordinary clock, the driving clock of a telescope is regulated by a governor, in order that the instrument may have a continuous and not a jerky movement.

The telescope is also provided with clamps and fine adjustments, one each in R. A. and declination, in order that it may be under the control of the observer. It is evident that the telescope must be capable of moving independently of the driving gear, so that it may first be placed in the desired direction; when this is accomplished, the R. A. clamp is used to put the telescope in gear with the clock. The declination clamp is them made to fix the telescope firmly to the declination axis. Fine adjustments in both directions are necessary, because it is impossible to sight a large instrument with such precision as to bring an object exactly to the centre of the field of view.

Some of the driving clocks fitted to equatorials are very elaborate. As clocks regulated by governors are not such reliable time-keepers as those regulated by pendulums, arrangements are made by which the accuracy of a pendulum can be electrically communicated to a governor clock. One of the best forms of electrically-controlled clocks is that devised by Sir Howard Grubb.

Another important feature of an equatorial is that it can be provided with circles which enable the telescope to be pointed to any desired object of known right ascension and declination. One of these is the declination circle, attached to the declination axis and read by a vernier fixed to the sleeve in which the axis turns; this is adjusted so as to read 0° when the telescope points to any part of the celestial equator, and 90° when it is directed to the Pole. The other circle is attached to the polar axis, and determines the position of the telescope with regard to the meridian; this is called the hour circle, and is divided into 24 hours. When the telescope is on the meridian, the hour circle reads zero, so that its reading in any other position gives the hour angle of the telescope. Having given the right ascension and declination of a heavenly body which it is desired to observe, the telescope is turned until the declination circle reads the proper angle, and the hour circle indicates the hour angle which is calculated for the particular moment of pointing the telescope. [The hour angle is the difference between the right ascension of the object and the sidereal time of observation.] In this way it is easy to find objects of known position which are invisible to the naked eye, and one can even pick up the planets and brighter stars in full sunshine. Conversely one can determine from the circles the right ascension and declination of any object under observation, but for various reasons only approximate results can be obtained in this way. The chief use of the circles on an equatorial is therefore to provide a means of pointing the telescope.

Telescopes of 4 inches aperture and upwards are usually provided with a smaller companion called a finder. This has a larger field of view than the main telescope, so that objects which are of sufficient brightness can readily be picked up and brought to the centre of the finder, the adjustments being such that the object is then also at the centre of the field of the large telescope.

There are, of course, many practical details connected with the working of an equatorial with which space does not permit us to deal. It may be remarked, however, that the adjustment of the polar axis is very simply performed by first inclining it at an angle approximately equal to the latitude of the place where it is set up, and setting it as nearly as possible in the meridian by means of a compass or by observations of the sun at noon. The final adjustment is then made by a series of observations of stars of known position.

Some of the World’s Great Telescopes.—Thanks to the wide public interest taken in astronomical matters, a large number of powerful telescopes has been set up in various parts of the world. To the British Islands belongs the honour of possessing the largest telescope in the world. This is the giant reflector erected by Lord Rosse, in 1842, at Parsonstown, the mirror being 6 feet in diameter, and the focal length 60 feet. Many very valuable observations were made with this instrument in its early days, but of late years it seems to have fallen into disuse. One reason may be that the mounting is not of the most convenient form, and makes the telescope unsuitable for photographic work.

Coming next in point of size to the Rosse telescope is the reflector erected at Ealing, by Dr. A. A. Common. The glass mirror of this telescope is 5 feet in diameter, 5 inches thick, and weighs more than half a ton. Dr. Common aimed specially at constructing the largest possible telescope which could be equatorially mounted and provided with a driving clock, and he was only limited to an aperture of 5 feet by the impossibility of obtaining a glass disc of larger size. He has attained such great skill in this work that he was able to produce a perfect mirror 5 feet in diameter in three months time, although no less than 410,000 strokes of the polishing machine were required.

The telescope is of the Newtonian form, and the mounting is quite unique. The polar axis consists of an iron cylinder, made up of boiler plates, 7 feet 8 inches in diameter, and about 15 feet long. From the top of the cylinder, near its outer edge, two horns, each 6 feet long, project outwards, and the tube of the telescope swings on trunnions attached to the ends of the horns. The main part of the telescope tube is square, built up of steel angle iron, and carries the mirror at its lower end; the upper part of the tube, which carries the “flat” and eye-piece, is round, and of tinned steel strengthened by a skeleton framework.

It is evident that such an enormous instrument as this cannot be made to travel by clock-work with the necessary uniformity without some very efficient arrangement for reducing friction. Dr. Common’s plan—and it is here that his instrument is unlike others—is to make the hollow polar axis water-tight, and to fix it in a tank of water. At the bottom of the polar axis is a ball and socket joint to keep it in position, and at the top is another bearing, which can be adjusted so that the polar axis lies truly in the meridian. It was found necessary to introduce 9 tons of iron into the bottom of the hollow polar axis in order to sink it to the proper angle, and to put sufficient weight on the bearings to give stability to the instrument. In this way the great mass is brought into the region of manageability, and the driving clock, which is driven by a weight of 1½ tons, is able to do its work efficiently. Such, in general outline, is this wonderful telescope, which, although not so large as Lord Rosse’s famous instrument, is undoubtedly its superior in light-grasping power and general utility, and more especially in its adaptability for photographing the heavens.

Among other large reflecting telescopes now in use are the four-foot reflectors at Melbourne and Paris, and the three-foot reflectors at South Kensington and the Lick Observatory, California.

The largest refracting telescope yet constructed is one of 40 inches aperture for the new Yerkes Observatory of the University of Chicago. It is interesting to note here that Professor Keeler, in his report as an expert upon the performance of the object-glass, considers that there is “evidence for the first time that we are approaching the limit of size in the construction of great objectives.” Unlike a mirror, a lens can be supported only upon its circumference, and it is the bending by its own weight that proves detrimental to its defining power. If the lens be made thicker with a view of overcoming this defect, the absorption of light by the glass increases, so that there is in the end no special gain by increasing the size.

The length of the Yerkes telescope is 62 feet, and it will be provided with all accessories pertaining to astrophysical research. The Yerkes telescope, however, is not yet in actual use, and meanwhile the world-renowned Lick telescope, of 36 inches aperture, keeps the lead among active big refractors. The story of the foundation of this monster instrument is not much less wonderful than the telescope itself. Brought up in poor circumstances, with few opportunities for intellectual development, James Lick, nevertheless, amassed a fortune in business, and having few relations, he was anxious to dispose of his wealth in such a way as to bring him that fame which he had failed to achieve in other directions. Although it is very probable that he had never looked through a telescope in his life, the idea of a large telescope had taken a very firm hold upon his mind, and, thanks to the influence of his advisers, it was definitely announced in 1873 that Mr. Lick’s bid for immortality was to take this form. Several sites were examined by experts, and finally Mount Hamilton, California, 4,200 feet above sea-level, was selected. An excellent road, 26 miles in length, made at the cost of the county authorities, connects the observatory with the nearest town, San José, 13 miles distant.

Owing to various delays, operations were not commenced until 1880, and five years were consumed in clearing away 72,000 tons of rocks and in erecting the buildings.

Mr. Lick had stipulated for the erection of “a telescope superior to and more powerful than any telescope yet made,” and Messrs. Alvan, Clark & Co. contracted to supply a lens of 36 inches aperture for the sum of 50,000 dollars. It turned out, however, that it was much easier to make such a contract than to fulfil it. To produce large discs of optically perfect glass, even in the rough, requires the greatest possible skill and patience, and this part of the work was undertaken by Feil & Co. of Paris. The flint glass disc was safely delivered in America in 1882, but the crown disc was cracked in packing. The elder Feil having retired from business, the duty of providing a new block of crown glass devolved upon his sons, who, after two years spent in vain attempts, ended in bankruptcy, and it was only through the elder Feil again resuming business that the much-required disc was finally completed in 1885. After the lapse of another year, the rough discs were fashioned, in the workshops of the Clarks, into the most marvellous of telescopic lenses.

The mounting of the object-glass is worthy of the occasion, as will be seen from our illustration (see page 40). The tube is no less than 57 feet long, and 4 feet in diameter in the middle part. An iron pier, 38 feet high, beneath which lie the remains of Mr. Lick, supports the equatorial head, and a winding staircase enables the observer to reach the setting circles. Inside the hollow pier is the powerful driving clock which turns the telescope to follow the heavenly bodies in their apparent movements. Finders of 6, 4, and 3 inches diameter, rods for the manipulation of the instrument, and all necessary accessories, complete what must long remain one of the most perfect instruments at the service of astronomical science. The 200,000 dollars expended upon it have already been amply justified by the work accomplished, while Mr. Lick’s dream of immortality has become a reality.

The following list indicates some of the large refractors now (Feb., 1897) doing active service:—

It is right to add, however, that opinion is still greatly divided as to whether these telescopes of large aperture really repay the expense and labour involved in their erection and use. On the very rare occasion when the “seeing” is practically perfect—which occurs perhaps only a few hours in a year—it is probable that the superiority of a large telescope is very marked, but under average conditions there seems to be little advantage over instruments of moderate size for many classes of observations.

Certain it is that a great deal of valuable work is done with comparatively small telescopes, ranging from six to fifteen inches aperture, and this in all departments of astronomical research. Hence, some of the most active observatories do not figure in the above list; among them may be mentioned the observatories of Harvard College (U.S.A.), Potsdam, Paris, Heidelberg, Cape of Good Hope, Edinburgh, South Kensington, Stonyhurst College, and the observatory of Dr. Isaac Roberts at Crowborough, Sussex.

Housing of Equatorials.—The building which accommodates an equatorial telescope must evidently be designed to admit of giving a clear opening to any part of the sky. Usually this is accomplished by making the roof, or dome, with a circular base, provided with wheels, which run on rails. It is then only necessary to open a narrow portion of the dome, extending from top to base, and to turn the dome until this aperture is in the required direction. One of the most elaborate domes now in existence is that built by M. Eiffel for the great refractor of the Nice Observatory. The lower part of the building is in the form of a square (see Frontispiece), having a side of about 87 feet, and a height of about 30 feet. The dome itself is 74 feet in diameter, and the moving parts alone weigh 95 tons.

As will be seen from the illustration, there are two shutters, each a little wider than half the possible opening: these run on short rails, and are moved simultaneously by means of an endless rope. The whole of the dome is built up of steel angle iron, covered with very thin sheet steel. In order to facilitate the manipulation of the dome, its great weight is buoyed up by means of a float attached to its base and immersed in a circular tank of water of a little greater size than the base of the dome. If any mishap occurs with this gigantic tank, the dome rests on wheels which run on a circular rail, so that the work need not be interrupted. The whole arrangement is very easily turned with the aid of a winch by one man when the dome is floating, but when resting on the wheels several men are required at the winch.

This brief description will serve to illustrate some of the problems which confront the possessor of a very large telescope. For smaller instruments, the observatories follow pretty nearly the same plan, except that it is unnecessary to provide an arrangement for floating the dome.

The observatory which shelters a reflecting telescope need not differ very greatly from one which contains a refractor. If the instrument be a Newtonian, it is generally convenient to sink the polar axis below the level of the floor in order that the observer may not be at too great a height from the ground, and in that case, the dome, or its equivalent, is all that is necessary. For his five-foot reflector, Dr. Common designed an observatory which is not of the ordinary form, but gives the necessary opening partly by means of large shutters, and partly by a revolution of the whole house. It is not everyone who is able to lay out £8,000 on such a dome as that erected at Nice by M. Bischoffeim.

The varying position of the eye end of a telescope, when it is turned to different parts of the sky, makes it necessary to provide comfortable and safe seating accommodation for the observer, more especially when the telescope is a very large one. In the case of the Yerkes telescope, the eye-piece will be 30 feet higher when observing near the horizon than when observing near the zenith, and the observer must necessarily follow the telescope. The most convenient arrangement in such a case is to raise or lower the floor of the observatory as occasion demands. The floor of the Yerkes Observatory is 75 feet in diameter, and by means of electric motors it can be given a vertical motion of 22 feet. A similar arrangement was provided for the Lick telescope from the designs of Sir Howard Grubb. With smaller instruments, observing ladders and adjustable chairs of various forms are employed.

The Equatorial Coudé.—A form of equatorial telescope which has possibly a great future before it is one introduced at Paris under the name of the equatorial coudé, or elbowed telescope. Its practical advantage is that the observer remains in a constant and comfortable position, so that revolving domes and elevating floors, or other arrangements serving similar purposes, are no longer necessary. The telescope tube is of two parts of nearly equal length, and what is ordinarily the lower half of the tube forms part of the polar axis, while the other half is attached to it at right angles. At the point of intersection of the two halves of the tube is a plane mirror, and there is another mirror in front of the object-glass. If the latter mirror were removed, such a telescope would only enable the observer to see objects lying along the celestial equator, but by its means objects in all parts of the heavens can be brought within range to an observer gazing down the hollow polar axis. The largest instrument is that at the Paris Observatory, which has an object-glass 23½ inches in diameter for visual observations, and another of the same size for photographic purposes.

Fixed Telescopes.—There is still another method of using a telescope. The telescope itself may be fixed, and the light of the heavenly bodies may be reflected into it by means of a mirror which is made to revolve so as to keep pace with their movements. Foucault devised an instrument called the siderostat for this purpose, and although it is not largely employed for telescopic observations, it is very widely utilised for spectroscopic work, where the spectroscope is of a kind not readily attached to a telescope.

Another instrument used for the same purpose has recently been brought forward under the name of the coelostat. This is simply a mirror which is made to turn on a polar axis in its own plane, and since a reflected ray of light moves through twice the angle that the reflecting surface turns through, the mirror is made to revolve at the rate of one revolution in two days. As the name indicates, the whole heavens appear stationary in such an instrument, whereas in a siderostat, only one star at a time appears at rest, while its neighbours slowly revolve round it.

Photographic Telescopes.—The application of photography to the study of the heavenly bodies marks one of the greatest advances of the present century. The instruments which are employed for this purpose range from the ordinary tourist camera to the largest telescope. Unlike a person sitting for a portrait, the heavenly bodies cannot be made to stand still for the purpose, and as instantaneous photographs can only be obtained in the case of the sun and moon, it is usually necessary to make the camera follow the stars very exactly during the time of exposure, in order that the images may fall on precisely the same parts of the photographic plate.

Some guiding arrangement is, therefore, essential, and generally the photographic camera or telescope is attached to an ordinary equatorial which is driven by clock-work, or very carefully by hand if the camera be a small one. In the guiding telescope are two spider threads at right angles to each other, and it is by constantly keeping the image of a star at the intersection of these “wires” that the operator ensures the images remaining in a constant position upon the sensitive plate.

An ordinary portrait camera, in the hands of a skilled observer, yields very beautiful pictures, but they are naturally on a small scale. The field of view of such an instrument is so large that a whole constellation may be photographed with a single exposure.

Portrait lenses of 6 inches aperture in the hands of Dr. Max Wolf and Professor Barnard have given magnificent delineations of the Milky Way, and of the extremely faint nebulosities which are to be found in many parts of the heavens.

For many purposes, however, telescopes of greater power are required, and here it may be remarked that the distance between the images of any two adjacent stars will vary in direct proportion to the focal length of the telescope. In the same way the size of the image of a planet, the moon, or a comet, increases as the focal length of the objective is increased.

Refracting telescopes which are employed for photography require object-glasses which are specially “corrected” for the photographic rays. White light is compounded of light of all colours, but it is the blue and violet constituents which are effective in producing photographic action on an ordinary sensitive plate. Now, an object-glass which is intended for visual purposes is made to focus at the same point as many as possible of the rays which are most effective to the human eye, that is the green, yellow, and red, and usually there is a blue or purple halo round the images of the brighter objects, which is, however, too feeble as a rule to interfere with visual observations. This blue halo, will evidently result in defective definition if the lens be employed for photography. By putting the plate at the point where the blue rays are most nearly focused, a better image is obtained; but for really good work a photographic object-glass must be so designed that all the blue and violet rays are brought to one and the same focus. Such a lens will consequently be a very poor one for visual observations. At the present time, 18 photographic telescopes, each of 13 inches aperture, and corrected in this way, are at work in various parts of the world for the international star chart.