| 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˝.
| Divisions of micrometer. | 0 | ·1 | ·2 | ·3 | ·4 | ·5 | ·6 | ·7 | ·8 | ·9 |
| 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.