Stargazing: Past and Present

by Sir Norman Lockyer

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.

Fig. 159.—How the Length of a Shadow thrown by a Lunar Hill is measured.

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.

Fig. 160.—The Determination of the Angle of Position of the axis of Saturn’s Ring.