CHAPTER XXIV.

THE ORDINARY WORK OF THE EQUATORIAL.

The equatorial enables us to make not only physical observations, but differential observations of the most absolute accuracy.

First we may touch upon the physical observations made with the eyepiece alone—star-gazing, in fact. The Sun first claims our attention: our dependence on him for the light of day, for heat, and for in fact almost everything we enjoy, urges us to inquire into the physics of this magnificent object. Precautions must however be taken; more than one observer has already been blinded by the intense light and heat, and some solar eyepiece must be used. For small telescopes up to two inches, a dark glass placed between the eye and the eyepiece is sufficiently safe; for larger apertures, the diagonal reflector, or Dawes’ solar eyepiece, already described, comes into requisition. Another method of viewing the sun is to focus the sun’s image with the ordinary eyepiece on a sheet of paper or card, or, better still, on a surface of plaster of Paris carefully smoothed. The bright ridges or streaks, usually seen in spotted regions near the edge, called the faculæ, and the mottled surface, appearing, according to Nasmyth, like a number of interlacing willow-leaves—the minute “granules” of Dawes, are best seen with a blue glass; but for observing the delicately-tinted veils in the umbræ of the spots a glass of neutral tint should be used.

The Moon is a fine object even in small telescopes. The best observing time is near the quarters, as near full moon the sun shines on the surface so nearly in the same direction as that in which we look, that there is no light and shade to throw objects into view. Hours may be spent in examining the craters, rilles, and valleys on the surface, accompanied with a good descriptive map or such a book as that which Mr. Neison has recently published.

The planets also come in for their share of examination. Mercury is so near the sun as seldom to be seen. Venus in small telescopes is only interesting with reference to her changes, like the moon, but in larger ones with great care the spots are visible. Mars is interesting as being so near a counterpart of our own planet. On it we see the polar snows, continents and seas, partially obscured by clouds, and these appearances are brought under our view in succession by the rotation of the planet. With a good six-inch glass and a power of 200 when the air is pure and the opposition is favourable, there is no difficulty in making out the coast-lines, and the various tones of shade on the water surface may be observed, showing that here the sea is tranquil, and there it is driven by storms. Up to very lately it was the only planet of considerable size further off the sun than Venus that was supposed to have no satellite; two of these bodies have however been lately discovered by Hall with the large Washington refractor of twenty-six inches diameter, and they appear to be the tiniest celestial bodies known, one of them in all probability not exceeding 10 miles in diameter. Jupiter and Saturn are very conspicuous objects, and the eclipses, transits, and occultations of the moons, and the belts of the former and rings of the latter, are among the most interesting phenomena revealed to us by our telescopes, while the delicate markings on the third satellite of Jupiter furnish us with one of the most difficult tests of definition. Uranus and Neptune are only just seen in small telescopes, and even in spite of the use of larger ones, we are in ignorance of much relating to these planets. The amateur will do well to attack all these with that charming book, the Rev. T. W. Webb’s _Celestial Objects for Common Telescopes_, in his hand.

To observe the fainter satellites of the brighter planets, or, indeed, faint objects generally, near very bright ones, the bright object may be screened by a metallic bar, or red or blue glass placed in the common focus.

So much with regard to our own system. When we leave it we are confounded with the wealth of nebulæ, star-clusters, and single or multiple systems of stars, which await our scrutiny. With the stars, not much can be done without further assistance than the eyepiece alone. The colours of stars may however be observed, and for this purpose a chromatic scale has been proposed, and a memoir thereon written, by Admiral Smyth, for comparison with the stars. The colour of a star must not be confused with the colours—often very vivid—produced by scintillations, these rapid changes of brightness and colour depending on atmospheric causes. Of the large stars, Sirius, Vega and Regulus are white, while Aldebaran and Betelgueux are red. In many double and multiple stars however the contrast of colours shows up beautifully; in β Cygni for instance we have a yellow and blue star, in γ Leonis, a yellow and a green star; and of such there are numerous examples.

Interesting as all these observations are, a new life and utility are thrown into them when instead of using a simple eyepiece the wire micrometer is introduced. This, as we have before stated, generally consists of one wire, or two parallel wires, fixed, and one or two other wires at right angles to these, movable across the field. This micrometer is used in connection with a part of the eyepiece end of the telescope, which has now to be described. This is a circle, the fineness of the graduation of which increases with the size of the telescope, read by two or four verniers. The circle is fixed to the telescope, while the verniers are attached to the eyepiece, carrying the micrometer, which is rotated by a rack and pinion.

The whole system of position circle (as it is called) and wire micrometer, is in adjustment when (1) the single or double fixed wires and the movable ones cross in the centre of the field, and (2) when with a star travelling along the single fixed or between the two fixed wires, the upper vernier reads 180 and the lower one reads zero.

This motion across the field gives the direction of a parallel of declination; that is to say, it gives a line parallel to the celestial equator, and, knowing that, one will be able at once, by allowing the object to pass through the field of view, to get this datum line. For instance, supposing the whole instrument is turned round on the end of the telescope, so that one of the two wires _x_ and _y_, Fig. 104, at right angles to the thin wires for measuring distance, shall lie on a star during all its motion across the field of view; then those two wires, being parallel to the star’s motion, will represent two parallels of declination; and we use the direction of the parallels of declination to determine the datum point at right angles to them, that is, the north point of the field. We have then a _position micrometer_, that is, one in which the field of view is divided into four quadrants, called north preceding, north following, south preceding, and south following, because if there be an object at the central point it will be preceded and followed by those in the various quadrants. The movable wires lie on meridians and the fixed ones on parallels when adjusted as above.

The position circle is often attached to, and forms part of, the micrometer instead of being fixed to the telescope, and in screwing it on from time to time, the adjustment of the zero changes, and the index error must be found each time the micrometer is put on the telescope.

In practice it is usual to take the north and south line as the datum line, and positions are always expressed in degrees from the north round by east 90°, south 180°, and west 270°, to north again in the direction contrary to that of the hands of a clock.

The angle from the east and west line being found by the micrometer, 90° is either added or subtracted, to give the angular measurement from north. But to make these measurements we want a clock; a clock which, when we have got one of these objects in the middle of the field of view, shall keep it there, and enable the telescope to keep any object that we may wish to observe fixed absolutely in the field of view. But in the case of faint objects this is not enough. We want not only to see the object, but also the wires we have referred to. Now then the illuminating-lamp and bright wires, if necessary, come into use.

The following, Fig. 159, will show how we proceed if we merely wish to measure a distance, the value of the divisions of the micrometer screw having been previously determined by allowing an equatorial star to transit. It represents the position of the central and the movable wire when the shadow thrown by the central hill of the the lunar crater Copernicus is being measured to determine the height of the hill above the floor of the crater. It has been necessary to let the fixed wire lie along the shadow; this has been done by turning the micrometer; but there is no occasion to read the vernier.

Except on the finest of nights the stars shake in the field of view or appear woolly, and even on good nights the readings made by a practised eye often differ, _inter se_, more than would be thought possible. In measuring distances we have supposed for simplicity that we find the distance that one wire has to be moved from coincidence with the fixed wire from one point to another, and theoretically speaking the pointer should point to O on the screw head when the wires are over each other, and then when the wires are on the points, the reading of the screw head divided by the number of divisions corresponding to 1˝ will give the distance of the points in seconds of arc. But in practice it is unnecessary to adjust the head to O when the wires coincide, and the unequal expansion of the metals of the instrument, due to changes of temperature, would soon disarrange it. It is also somewhat difficult to say when the wires exactly coincide, and an error in this will affect the distance between the points. It is therefore found best to only roughly adjust the screw head to O, and then open out the wires until they are on the points and take a reading, say twenty-two; the screw is then turned, in the opposite direction and the movable wire passed over to the other side of the fixed one, and another reading taken, say eighty-two; now the screw has to be moved in the direction which decreases the readings on its head from one hundred downwards, as the distance of the wires increases, so that we must subtract the reading eighty-two from a hundred to give the number of divisions from the O through which the screw is turned, and the reading in this direction we will call the indirect reading, in contradistinction to the direct reading taken at first. So far we have got a reading of twenty-two direct and eighteen indirect, which means that we have moved the screw from twenty-two on one side of O to eighteen on the other side, or through forty divisions, and in doing so the movable wire has been moved from the distance of the two points on one side of the fixed wire to the same distance on the other, or through double the distance required. Therefore forty divisions is the measure of twice the distance, and the half of forty, or twenty divisions, is the measure of the distance itself between the two points to which our attention has been directed, whether stars, craters in the moon, spots on the sun, and the like.

Let us consider what is gained by this method over a measure taken by coincidence of the wires as a starting-point, and opening out the wires until they cut the points. In the method we have just described there are two chances of error in taking the measurements—the direct and indirect; but the result obtained is divided by two, so that the error is also halved in the final result. Now by taking the coincidence of the wires as the zero, or starting-point, the measure is open to two errors, as in the last case—the error of measurement of the points, _plus_ the error of coincidence of wires, an error often of considerable amount, especially as the warmth of the face and breath causes considerable alteration in the parts of the instrument, making a new reading of coincidence necessary at each reading of distance. As the result is not divided by two, as in the first case, the two errors remain undivided, so we may say that there is the half of two errors in one case and two whole errors in the other.

Here then we use the micrometer to measure distances; but from a very short acquaintance with the work of an equatorial it will at once be seen that one wants to do something else besides measure distances. For instance, if we take the case of the planet Saturn, it would be an object of interest to us to determine how many turns, or parts of a turn, of the screw will give the exact diameter of the different rings; but we might want to know the exact angle made by the axis with the direction of the planet’s motion, across the field, or with, the north and south line.

If we have first got the reading when the wires are in a parallel of declination, and then bring Saturn back again to the middle of the field and alter the direction of the wires until they are parallel to the major axis of the ring, we can read off the position on the circle, and on subtracting the first reading from this, we get the angle through which we have moved the wires, made by the direction of the ring with the parallel of declination, which is the angle required. We are thus not only able to determine the various measurements of the diameter of the outer ring by one edge of the ring falling on one of the fine wires, and the other edge on the other wire, but, by the position circle outside the micrometer we can determine exactly how far we have moved that system, and thus the angle formed by the axis of the ring of the planet at that particular time.

The uses of the position micrometer as it is called are very various. In examination of the sun it is used to ascertain the position of spots on the surface, and the rate of their motion and change. The lunar craters require mapping, and their distances and bearing from certain fixed points measuring, for this then the position micrometer comes into use.

The varying diameters and the inclinations of the axes of the planets and the periods of revolution of the satellites are determined, and the position of their orbits fixed, in like manner. When a comet appears it is of importance to determine not only the direction of its motion among the stars, but the position of its axis of figure, and the angles of position and dimensions of its jets. The following diagram gives an example of the manner in which the position of its axis of figure is determined. First the nucleus is made to run along the fixed wire, so that it may be seen that the north vernier truly reads zero under this condition; if it does not its index error is noted. The system of wires is then rotated till one of the wires passes through the nucleus and fairly bisects the dark part behind the nucleus.

It need scarcely be said that these observations are also of importance with reference to the motion of the binary stars, those compound bodies, those suns revolving round each other, the discovery of which we owe to the elder Herschel. We may thus have two stars a small distance apart; at another time we may have them closer still; and at another we may have them gradually separating, with their relative position completely changed. By means of the wire micrometer and the arrangement for turning the system of wires into different positions with regard to the parallel of declination, we have a means of determining the positions occupied by the binary stars in all parts of their apparent orbit, as well as their distances in seconds of arc. It is found, however, by experience that the errors of observation made in estimating distances are so large, relatively to the very small quantities measured, that it is absolutely necessary to make the determination of the orbit depend chiefly on the positions. And this is done in the following way.

It is possible, by knowing the position angles at different dates, to find the angular velocity, and since the areas described by the radius vector are equal in equal times, the length of the radius vector must vary inversely as the square root of the angular velocity, and by taking a number of positions on the orbit of known angular velocity, we can set off radii vectores, and construct an ellipse, or part of one, by drawing a curve through the ends of the radii vectores; and from the part of the ellipse so constructed it is possible to make a good guess at the remainder. The angular size of this ellipse is obtained from the average of all the measures of distance of the stars. This ellipse is then the apparent ellipse described by the star, and the form and position of the true ellipse can be constructed from it from the consideration of the position of the larger star (which must _really_ be the focus), with reference to the focus of the _apparent_ ellipse; for if an ellipse be seen or projected on a plane other than its own, its real foci will no longer coincide with the foci of the projected ellipse.

The methods adopted in practice, for which we must refer the reader to other works on the subject, are, however, much more laborious and lengthy than the above outline, which is intended merely to show the possibility, or the faint outline of a method of constructing the real ellipse. When the real ellipse or orbit is known, it is then of course possible to predict the relative positions of the two components. Let us consider in some little detail the actual work of measuring a double star.

A useful form for entering observations upon, as taken, is the following, which is copied from one actually used.

TEMPLE OBSERVATORY.

No. 1. _April 12, 1875·276._

DOUBLE STARS.

STRUVE 1338.

R.A.—9h. 13m. 28s. DECL. 38° 41´ 20˝.

Magnitudes—6·7, 7·2.

POSITION.

Zero, 109·8.

DISTANCE.

Direct. Indirect. ½ Diff. 17 97 10 16 97 9·5 ——————— 9·75 mean.

Readings. 170·1 170· 169·5 169·8 ————— 4) 679·4 ————— 169·8 109·8 90·0 ————— 19·8 169·8 Position = 150° 19·8 ————— Distance = 1˝·828. 150

* * * * *

No. 2. _Feb. 5th, 1875·09._

DOUBLE STARS.

STRUVE 577.

R. A.—4h. 34m. 9s. DECL. 37° 17´

Magnitudes—7, 8.

POSITION.

Zero, 88·9.

DISTANCE.

Direct. Indirect. ½ Diff. 12·5 99·5 6·5 12·6 99·2 6·7 ——————— 6·6 mean.

Readings.

79·5 81·5 81·2 ————— 3) 242·2 ————— 81·1 mean.

88·9 90·0 ————— -1·1 81·1 -1·1 ————— 82·2 Position = 262°·2. 180·0 ————— Distance = 1´·237. 262·2

The star having been found, the date and decimal of the year are entered at the top, and a position taken by bringing the thick wires parallel to the stars. A distance—say direct—is then taken, and the degrees of position 170°·1, and divisions of the micrometer screw seventeen, read off with the assistance of a lamp and entered in their proper columns. The micrometer is then disarranged and a new measure of position and an indirect distance taken, and so on. At the end of the readings, or at any convenient time, the zero for position is found by turning the micrometer until the wires are approximately horizontal, and then allowing a star to traverse the field by its own motion, or rather that of the earth, and bringing the thick wires parallel to its direction of motion; this may be more conveniently done by means of the slow-motion handle of the telescope in R. A., which gives one the power of apparently making the star traverse backwards and forwards in the field. The position of the wires is altered until the star runs along one of them. The position is then read off and entered as the zero. In describing the adjustments of the position circle we made the vernier read 0° when the star runs along the wire, for that is practically the only datum line attainable; since, however, the angles are reckoned from the north, it is convenient to set the circle to read 90° when the star runs along the wire, so that it reads 0° when the wires are north and south.

Now as positions are measured from north 0° in a direction contrary to that of the hands of a watch, and an astronomical telescope inverts, we repeat the bottom of the field is 0°, the right 90°, and so on; now the reading just taken for zero is the reading when the wires are E. and W., so that we must deduct 90° from this reading, giving 19°·8 as the reading of the circle when the wires were north and south, or in the position of the real zero of the field. Of course theoretically the micrometer ought to read 0° when the wires are north and south, but in screwing on the instrument from night to night it never comes exactly to the same place, so that it is found easier to make the requisite correction for index error rather than alter the eye end of the telescope to adjustment every night. The readings of position must therefore be corrected by the number of degrees noted when the wires are at the real zero, which in the case in point is 19°·8, which may be called the index error.

It is also obvious that the micrometer may be turned through 180° and still have its wires parallel to any particular line. The position of the stars also depends upon the star fixed on for the centre round which our degrees are counted; for in the case of two stars just one over the other in the field of view, if we take the upper one as centre, then the position of the system is 0°, but if the lower one, then it is 180°; in the case of two equal or nearly equal stars, it is difficult to say which shall be considered as centre, and so the position given by two different persons might differ by 180°. There are also generally two verniers on the position circle, one on each side, and these of course give readings 180° different from each other, so that 180° has often to be added or subtracted from the calculated result to give the true position. All that is really measured by the position micrometer is the relative position of the line joining the stars with the N. and S. line. In order, therefore, to find, whether 180° should be added or not, a circle is printed on the form, with two bars across for a guide to the eye, and the stars as seen are roughly dotted down in their apparent position—in the case in point about 150°. Our readings being now made, we first take a mean of those of position, which is 169°·8, nearly, and the zero is 109°·8; deduct 90° from this to give the reading of the N. and S. line 19°·8, then we deduct this from the mean of position, 169·8, giving us 150° as the position angle of the stars.

It often happens that the observed zero is less than 90°, and then we must add 360° to it before subtracting the 90°, or what is perhaps best, subtract the observed zero from 90°, and treat the result as a minus quantity, and therefore add it to the mean of position readings instead of subtracting as usual. The observations of the second star give a case in point: the zero is 88°·9, and subtracting this from 90°, we get 1°·1; we put this down as -1°·1 to distinguish it from a result when 90° is subtracted from the zero; it is then added to the mean of position readings 81°·1, giving 82°·2, but on reference to the dots showing the approximate position of the stars, it is seen that 180° must be added to their result, giving 262°·2 as the position of the stars.

Now as to distance, take the case of the second star. Subtract the first indirect reading from 100°, giving 0·5, and add this to the direct reading, 12·5, making 13·0, which is the difference between the two readings taken on either side of the fixed wire; the half of this, 6·5, is placed in the next column, and the same process is repeated with the next two readings: a mean of these is then taken, which is 6·6 for the number of divisions corresponding to the distance of the stars. In the micrometer used in this case, 5·3 divisions go to 1˝, so that 6·6 is divided by 5·3, giving 1˝·237 as the distance. A table showing the value in seconds of the divisions from one to twenty or more, saves much time in making distance calculations; the following is the commencement of a table of this kind where 5·3 divisions correspond to 1˝.

┌──────┬─────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐ │Divi- │ 0 │ ·1 │ ·2 │ ·3 │ ·4 │ ·5 │ ·6 │ ·7 │ ·8 │ ·9 │ │sions │ │ │ │ │ │ │ │ │ │ │ │ of │ │ │ │ │ │ │ │ │ │ │ │micro-│ │ │ │ │ │ │ │ │ │ │ │meter.│ │ │ │ │ │ │ │ │ │ │ ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │ 0 │0·000│·018│·037│·056│·075│·093│·112│·131│·150│·168│ ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │ 1 │0·187│·205│·224│·243│·262│·280│·299│·318│·337│·356│ ├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │ 2 │0·375│·393│·412│·431│·450│·468│·487│·506│·525│·543│ └──────┴─────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘

In the first column are the divisions, and in the top horizontal line the parts of a division, and the number indicated by any two figures consulted is the corresponding number of seconds of arc. In the case of a half difference of 2·3 we look along the line commencing at 2 until we get under 3, when we get 0˝·431 as the seconds corresponding to 2·3 divisions.

It is necessary to adjust the quantity of light from the lamp in the field, so that the wires are sufficiently visible while the stars are not put out by too much illumination; for the majority of stars a red glass before the lamp is best. This gives a field of view which renders the wires visible without masking the stars, but a green or blue light is sometimes very serviceable. A shaded lamp should be used for reading the circles on the micrometer, so as not to injure the sensitiveness of the eye by diffused light in the observatory. A lamp fixed to the telescope, having its light reflected on the circles, but otherwise covered up, is a great advantage over the hand-lamp. In very faint stars, which are masked by a light in the field sufficient to see the wires, the wires can be illuminated in the same manner as in the transit, but there is this disadvantage—the fine wires appear much thickened by irradiation, so that distances, especially of close stars, become difficult to take.

* * * * *

We come now to the differential observations made with the equatorial. Let us explain what is meant. Suppose it is desired to determine with the utmost accuracy the position of a new comet in the sky. If we take an ordinary equatorial, or an extraordinary equatorial (excepting probably the fine equatorial at Greenwich), and try to determine its place by means of the circles, its distance from the meridian giving its right ascension and its distance from the equator giving its declination, we shall be several seconds out, on account of want of rigidity of its parts; but if we do it by means of such an instrument as the transit circle at Greenwich, we wait till the comet is exactly on the meridian, and determine its position in the way already described.

As a matter of fact, however, the transit circle is not the instrument usually used for this purpose, but the equatorial. We do not however just bring the comet or other object into the middle of the field and then read off the circles, but we differentiate from the positions of known stars; so that all that has to be done in order to get as perfect a place for the comet as can be got for it by waiting till it comes to the meridian—which perhaps it will do in the day-time, when it will not be visible at all—is to determine its distance in right ascension and declination from a known star, by means of a micrometer. Of course one will choose the brightest part of the comet and a well-known star, the place of which has been determined either by its appearance in one of the catalogues, or by special transit observations made in that behalf. We then by the position micrometer determine its angle of position and distance from the known star at a time carefully noted, or we measure the difference in right ascension and the difference in declination.

Continental astronomers have another way of doing this which we will attempt to explain. Suppose we wish to find the difference in declination of a star and Jupiter, we place the ring, A D, Fig. 163, in the eyepiece of the telescope and watch the passage of Jupiter and the star over this ring micrometer. It will be clear that, as the motion of the heavens is perfectly uniform, it will take very much less time for the star to travel over the ring from B to C than it will for Jupiter to travel over the ring from _b_ to _c_, because the star is further from the centre; and by taking the time of external and internal contact at each side of the ring, the details of which we need not enter upon here, the Continental astronomers are in the habit of making differential observations of the minutest accuracy by means of this ring micrometer, whilst we prefer to make them by the wire micrometer.