CHAPTER XVI.

INSTRUMENTS OF PRECISION.

THE MERIDIAN CIRCLE.—The accurate registration of the positions of the heavenly bodies is one of the most important functions of an astronomical observatory. When the apparent places of an object at a sufficient number of different times have been duly recorded, it becomes possible to investigate the laws upon which its changes of position depend, and to predict its positions at subsequent times for the benefit of navigators and others to whom such predictions are of practical utility. For this purpose various instruments have been devised, but in all cases where it can be employed, the _transit circle_, or _meridian circle_, as it is indifferently called, is generally conceded to give the most trustworthy results.

With this instrument the observations are made when the celestial body under observation is crossing the meridian of the place where the instrument is set up, that is, when it “transits,” or “souths.” At this time the accuracy of the observations is least impaired by the ever-varying effects of atmospheric refraction.

The meridian circle consists of a refracting telescope—seldom exceeding 6 inches in aperture—which is fixed to a hollow axis at right angles to itself, and this axis is supported horizontally in an east and west direction, so that the telescope is only free to move in the plane of the meridian. A large graduated circle—or frequently two such circles—attached perpendicularly to the hollow axis, and read by microscopes fixed to the walls or iron pillars which support the axis, completes the essential parts of the instrument.

As the field of view of the telescope covers a considerable area, it becomes necessary to provide some means of marking the exact point within it which represents the meridional axis of the instrument. This is accomplished by placing at the common focus of the object-glass and the positive eye-piece a system of “cross wires,” consisting of tightly-stretched spider threads, two of which are fixed horizontally and nearly in contact, and five or seven vertically at equal distances apart. What the observer has actually to do is to incline the telescope at such an angle that the star is seen to traverse the space between the two horizontal threads, and then to record the exact times, by means of a chronograph and sidereal clock, at which the star appears to cross each of the equidistant vertical threads. By thus making five or seven observations and taking the average, greater accuracy is attained.

The time observations, as we have already seen, determine the right ascension of the star under observation, while the declination is indicated by the readings of the graduated circle, if the latter is so placed as to read 90° when the telescope is directed to the Pole.

The ideal meridian circle is thus simplicity itself, but the mechanical difficulties encountered in making such an instrument are insuperable. Perfect right angles and perfect circles exist only in our minds, so that after all the undoubted skill and care bestowed on its construction, the actual meridian circle is only an approximation to the ideal. Still, when the instrument is provided with levels and other means for estimating its deviation from the meridian plane in which it ought to move, the actual observations are capable of correction by mathematical processes, so that the final statements of positions sensibly represent those which would follow from the use of a perfect instrument.

The greatest possible care is taken to secure rigidity in all parts of the meridian circle. The hollow horizontal axis is supported on bearings which rest either on heavy piers of iron or walls of masonry, and the axis and telescope tube are firmly joined together at their intersection. The bearings for the axis are turned with extreme precision, and, to reduce the friction upon them, the pressure of the instrument is counterpoised by an arrangement of balancing weights.

Adjustments are provided for every needful purpose. The cross wires are fitted in a small frame which can by suitable fittings be given a small movement in the field of view until the right place for them is found, while the horizontality of the axis and its correct direction can be secured by other adjusting screws.

Since most of the observations have to be made at night, the field of view will generally be dark, and the exceedingly delicate spider lines will be invisible unless some means of illuminating them be provided. Usually a very tiny mirror is fixed diagonally at the intersection of the axis and the telescope, where it is held in position by a stiff wire. A light shining through the hollow axis is thus reflected into the field of view, and the threads are rendered visible. The intensity of this illumination of the field can be regulated in accordance with the brightness of the star under observation.

The instrument having been erected, one of the first tests applied to it is to see that it is correctly _collimated_, or, in other words, that the optical axis of the telescope is perpendicular to the axis of movement. For this purpose the telescope is directed to some distant object, such as a building, and some mark which falls on the intersection of the central spider threads is noted. The axis is then reversed end for end by a mechanical arrangement, and the telescope again pointed at the same object. If the mark again falls on the intersection of the cross wires, the collimation is correct; if not, the wires are moved with the frame containing them until the error is corrected.

To test the horizontality of the axis, a spirit-level long enough to stretch across the bearings, and called the “striding level,” is provided.

Various methods are employed for adjusting the instrument so that the telescope moves as truly as possible in the plane of the meridian. Collimation and level being correct, the telescope will move in a vertical plane, whatever may be the error in the direction of the horizontal axis, and therefore any star passing through the zenith will cross the centre of the instrument at the same moment that it crosses the meridian. A star away from the zenith, however, will not be seen on the cross wires when it crosses the meridian, unless the axis be truly east and west. Hence, by taking the difference of time between the observed transits of a star near the zenith and one a long way from the zenith, and turning the whole instrument in azimuth until this difference is equal to the difference of right ascensions of the two stars, the instrument is readily placed in the meridian.

Another useful method of adjustment is to observe the upper and lower transits of a circumpolar star. If the instrument moves truly in the meridian, the interval between the two transits will evidently be twelve sidereal hours.

Next, the declination circle has to be adjusted so that it reads 90° when the telescope is directed to the celestial pole, or zero when an equatorial star is under observation. An obvious way of doing this is to take the readings when Polaris, or other circumpolar star, is at upper and lower transits; the celestial pole lying midway between these positions, the average of the two readings, when corrected for refraction, should be 90°, and the circle would be shifted round in its fittings until this was the case.

Such, in mere outline, are the processes by which the meridian circle is set up. In actual practice, the greatest possible refinement is brought to bear on the adjustments, and every precaution taken to estimate the various errors so that due allowance may be made for them in the reduction of the observations. It has even been shown that the heat of the observer’s body, by affecting the lower side of the telescope tube more than the upper, introduces sensible errors in the measures of declination. Hence it is important to use metals of high conductivity in the construction of meridian instruments, so that errors due to the varying temperatures of different parts may be reduced to a minimum.

As an illustration of a modern meridian circle, we select that of the Lick Observatory. (Fig. 53.) This instrument has an aperture of six inches, and embodies all the improvements which have been introduced by the Berlin firm of Repsöld & Co.

The observatory containing a meridian circle is usually a very simple structure, as it is only necessary to provide an opening to the sky along a north and south line. This is sufficiently provided for by a series of narrow shutters in a building of ordinary construction.

To prevent confusion it may be pointed out that the term “transit instrument” is frequently restricted to a meridian instrument which is not supplied with large circles for the accurate measurement of declinations, although it may have a small circle to assist in directing the telescope. The use of such an instrument is evidently limited to the determination of time and right ascension.

[Illustration:

FIG. 53.—_The Meridian Circle of the Paris Observatory._ ]

THE ALTAZIMUTH.—Although the meridian circle furnishes us with the most accurate method of determining celestial positions, its use is somewhat restricted by the fact that it can only be employed for the observation of objects on the meridian. It sometimes happens, however, that bodies cannot conveniently be so observed, and other methods become necessary. This is especially the case with the moon during the first and fourth quarters, when it crosses the meridian in daylight, and it is then that an instrument called the _altazimuth_ is of special value. This is something like a transit circle in which the base supporting the piers is made to turn on a vertical axis, so that the telescope can be directed to any part of the heavens whatsoever. A fixed horizontal graduated circle, read by verniers or microscopes attached to the revolving part, gives the azimuth of the telescope when an observation is made, and the altitude is furnished by the vertical circles. The azimuth circle is adjusted to read zero when the telescope is pointed due north, and the altitude circle to zero when the telescope is horizontal. To secure the first adjustment, after correcting level and collimation, a star may be observed before it crosses the meridian, and again when it has exactly the same altitude after passing to the west; midway between the two positions would be due south, and the circle should read 180°. In adjusting the vertical circle, the telescope is made to point downwards to a trough of mercury, and it is known that the telescope is truly vertical when the reflected image of the cross wires is coincident with the wires themselves; the circle should then read 90°.

From a knowledge of the sidereal time at which a celestial body has an observed altitude and azimuth, the more useful co-ordinates of right ascension and declination can be calculated by spherical trigonometry.

One of the largest instruments of this class has recently been erected at Greenwich Observatory. The aperture of the telescope is 6 inches, and the rigidity of the various parts may be gathered from the fact that the instrument weighs something like six tons.

A _theodolite_ is a small portable form of altazimuth specially adapted for the needs of surveyors, but occasionally employed in astronomical work.

THE WIRE MICROMETER.—Notwithstanding that an equatorial telescope is usually furnished with circles for estimating the positions of objects observed, or to serve as a guide in directing the telescope to objects of known position, it is not entitled to be called an instrument of precision in the sense we are now considering. The provision for driving by clock-work and other causes are antagonistic to constancy of adjustment, and hence determinations of positions by the circles alone might be many seconds in error. Most large telescopes, however, are provided with some form of micrometer which not only serves for the measurement of planets, lunar craters, and the like, but may also be used to measure the angular separation of adjacent stars. In this way, by making a “triangulation” of stars visible in the field of view, and including at least two which have had their precise positions determined by the meridian circle, the positions of objects can be measured with great accuracy.

This method is especially valuable in the case of comets, which may cross the meridian in daylight, and are often too dim to be seen with the altazimuth.

Several forms of micrometers are in use, but the so-called _wire_ or _filar micrometer_ is most commonly seen in our observatories. The essential parts are very similar to those of the reading microscope (p. 172). Two parallel spider threads are so arranged on sliding frames that they may be brought into coincidence, or separated, by means of very finely-cut screws. Perpendicular to these are two fixed threads almost close together. The system of “wires” is viewed by a positive eye-piece, and the whole is attached to a draw tube so that it may be placed in position at the eye end of the telescope. In order that the wires and telescopic images may be sharply defined at the same time, the plane of the wires must be at the principal focus of the object-glass. The screws are provided with large heads which are graduated so as to show the hundredth of a revolution, and counting wheels register the numbers of complete turns.

Matters are so arranged that when both counting wheels indicate zero, the spider threads are coincident. Then, supposing one of the screws be turned through a revolution, the threads will be separated by a definite amount; an equal and opposite movement of the other screw will double the separation, and in all cases the distance between the threads will be registered in turns, and fractions of turns of the screws.

The next proceeding is to ascertain what is called the “value,” in angular measure, of the micrometer screw. This value will evidently depend upon the pitch of the screw and the focal length of the telescope to which the micrometer is applied, so that measurements merely stated in terms of revolutions of the screw would serve no useful purpose. It can easily be calculated that the images of two stars which are 28′ 39″ apart will be separated by an inch at the focus of a telescope of 10 feet focal length; then, if the screws have 100 threads to the inch, the angular separation of the wires corresponding to a single revolution will be one-hundredth part of 28′ 39″, that is, 17″·15, and the latter would be the value of that particular micrometer when used with the telescope in question. If the focal length of the telescopic object-glass were 20 feet, the linear separation of the images of two such stars as we have considered would be 2 inches, and the value would therefore be halved, so that measures of twice the accuracy would be possible. Since the stellar images and the cross wires are equally magnified by the eye-piece, the value of the screw is in no way affected by using eye-pieces of different powers.

In practice it is necessary to determine the value of the micrometer screw by actual measurement. For this purpose, the wires are separated by a known number of revolutions, say twenty, and the micrometer is adjusted so that a star of known declination travels exactly between the two fixed wires when the telescope remains at rest. With the telescope still fixed, the number of seconds required by the image of the star to traverse the distance between the separated wires is noted, and knowing the angle through which the star must have moved in that interval, the angular value of one turn of the screw is at once deduced. For work of extreme precision each individual turn of the screw must be separately evaluated, and allowances must also be made for changes of temperature.

When measuring the apparent diameter of a planet, the two threads are separated until the image just lies between them, and the sum of the readings of the two screws multiplied by the angular value of one turn gives the diameter in seconds of arc. The distance having been formed by other observations, the diameter of the planet in miles can be determined in the manner to which reference has already been made (p. 142).

[Illustration:

FIG. 54.—_The Micrometer applied to a Binary Star: a b, Fixed Threads; c d, e f, Movable Threads; s s, Components of Binary Star._ ]

One of the most important applications of the micrometer is in the measurement of double and binary stars. In this case the fixed threads are made to enclose the two stars, and the movable threads are made to bisect the star-images. (Fig. 54.)

THE POSITION CIRCLE.—It is frequently necessary to be able to specify a direction, as in the case of a planet’s equator, or the line joining the components of a double star. Such directions are expressed by “position angle,” which may be defined as the angle from the north point, reckoned from 0° to 360° through east, south, and west. For these observations, a _position circle_ is usually attached to the micrometer. This is a circle graduated from 0° to 360°, which can remain fixed in position as regards the telescope, while the part containing the wires and micrometer screws can be rotated by means of a rack and pinion. A vernier attached to the movable frame indicates the required angles.

To adjust the position circle the vernier is set to zero, and the telescope directed to a star; the circle and micrometer are then together turned round until the diurnal movement of the star, which is east and west, makes its image to traverse the space between the fixed wires. The movable threads will then lie in a north and south direction. The circle remains in this position during subsequent observations, while the micrometer is rotated until the movable threads are in the required direction, the position angle then being read off on the circle.

THE HELIOMETER.—Another means of measuring small angles for astronomical purposes is afforded by the instrument called the _heliometer_, which, as the name will at once suggest, was invented for measurements of the sun. This instrument is a telescope mounted equatorially, but differs from the ordinary telescope, inasmuch as the object-glass is cut across the centre, and means are provided for separating the two halves by moving one or both parts in the direction of the line of bisection, and also for measuring the amount of displacement. The cell containing this somewhat peculiar object-glass can be rotated so that the line of division of the lens may be placed in the same direction as the line representing the distance to be measured.

The action of the instrument depends upon the fact that any small part of a lens is competent to form a complete image of a celestial body, so that when an object-glass is bisected, and the two halves separated laterally, two distinct images will be produced, each differing only from the image formed by the complete lens in being less bright.

To measure the distance from a star to a planet, let us say, as in observations of the parallax of Mars, the lenses are separated to such an extent that the image of the star formed by one half, coincides with that of the planet formed by the other half, and the amount of separation noted. As a check, the measurement is repeated with the lenses separated in the opposite direction. The angular value corresponding to a known separation of the semi-lenses being determined, just as in the case of the micrometer screw, the angle between star and planet at once follows. Angles ranging from a few minutes to about two degrees can be measured in this way with great accuracy.

In the hands of Dr. Gill, of the Cape Observatory, the heliometer has yielded very valuable results in connection with the distances of the sun and stars.

OTHER INSTRUMENTS.—There are other instruments which may fairly be classed as instruments of precision, but space permits little more than a mention of their names.

The _zenith telescope_ is a telescope specially designed for the measurement of the angular distances of stars from the zenith, for precise determinations of latitude by Talcott’s method.

The _prime vertical instrument_ is nothing more than a transit instrument, so arranged that the observing telescope swings in a vertical plane which is perpendicular to the plane of the meridian. From the observed times at which a star passes the prime vertical on the eastern and western sides, the latitude of the place of observation can be ascertained with great accuracy.

It is perhaps at sea that the labours of astronomers are of most direct value in everyday affairs, and it is precisely here that the instruments of high precision cannot be employed, in consequence of the absence of firm supports. Nevertheless, there is one instrument—_the sextant_—which yields results that satisfy all requirements when carefully constructed and placed in good hands. A graduated arc extending over about 60° (from which the name is derived) is supported by a light framework, and pivoted truly on the centre of the arc is the radius bar, or index arm, which carries a vernier for reading off the angles to be measured. A plane mirror is fixed to the index arm, over the centre of movement, and another, of which only half is silvered, is fixed to the frame near its outer edge. A small telescope parallel to the surface of the frame is directed towards the fixed mirror, so that the continuation of its axis is in line with the boundary between the silvered and clear part of the glass. Thus, while one object may be seen by direct observation through the clear glass, another, in quite a different direction, may be seen after reflection from the surfaces of the two mirrors.

The sextant is chiefly used for measuring the altitude of the sun, about noon for the determination of latitude, and in the morning or evening for the correction of chronometers. In such observations, the sextant is held in the right hand, with its plane vertical, and the sea horizon is sighted directly with the telescope; the index arm is then moved until the reflected image of the sun is brought into coincidence with the horizon. The reading is then taken, and if the adjustment is such that zero is indicated when the reflected and direct images of the same object are observed, it will give the altitude. The actual angle recorded by the sextant is only half that between the objects observed, but by numbering half degrees as whole ones, the true angles are read off directly. For observations of the sun the instrument is provided with coloured glasses of different shades, attached so that they can readily be interposed to reduce the intensity of the light.