Index Error.—From what has just been stated it follows that half the difference of the two readings is the index error, which can be at once corrected by the screws moving the vernier, giving correction No. 2.
To correct the error in altitude of the pole, the circle is then set to the declination of the star given by the almanac, corrected for refraction, and the telescope brought above or below the star as the error may be, and the polar axis carrying the telescope is moved by the setting screws, until the star is in the centre of the field.
3rd Adjustment.—A single observation of any known star, about 6 hours to the east or west will give the error of the polar axis east and west, the difference between the observed and true declination being this error, and it can be corrected in the same manner as the last. These observations should be repeated, and stars in different parts of the heavens observed, in order to eliminate errors of division of the circle until the necessary accuracy is obtained.
For example:
| Observed dec. of Capella | 43° | 50´ | 30˝ | Telescope west. | |||
| 47° | 0´ | 0˝ | Telescope east. | ||||
| ——— | ——— | ——— | |||||
| 2) | 90° | 50´ | 30˝ | ||||
| ——— | ——— | ——— | |||||
| 45° | 25´ | 15˝ | 47° | 0´ | 0˝ | ||
| Error due to refraction | 0° | 0´ | 7˝ | 43° | 50´ | 30˝ | |
| ——— | ——— | ——— | ——— | ——— | ——— | ||
| Instrumental declination | 45° | 25´ | 8˝ | 2) | 3° | 9´ | 30˝ |
| True declination | 45° | 52´ | 0˝ | ——— | ——— | ——— | |
| ——— | ——— | ——— | Index error | 1° | 34´ | 45˝ | |
| 26´ | 52˝ |
This indicates that the pole of the instrument is pointing below the true pole, and index error 1° 34´ 45˝.
| Observed declination of Pollux 6h. west | 28° | 19´ | 18˝ |
| Refraction | 0° | 0´ | 46˝ |
| ——— | ——— | ——— | |
| 28° | 18´ | 3˝ | |
| True declination | 28° | 20´ | 10˝ |
| ——— | ——— | ——— | |
| 0° | 1´ | 38˝ |
This shows the pole to be 1´ 38˝ east of true pole.
4th Adjustment.—For the estimation and correction of the third error, that of collimation, an equatorial star is brought to the centre of the field of the telescope, the time by a clock noted, and the hour circle read. The polar axis is then turned through half a circle, and the star observed with the telescope on the opposite side (say the west) of the pier, the time noted, and the hour circle read. Subtract the first reading from the second (plus twenty-four hours if necessary) and subtract the time elapsed between them, and the result should be exactly twelve hours, and half the difference between it and twelve hours is the error in question. If it is more than twelve hours the angle between the object end of the telescope and the declination axis is acute, and if less then it is obtuse. This error can then be corrected by the proper screws. A little consideration will show, that if the angle between the object end of the telescope and the declination axis be acute, and the telescope is on the east side of the pier, and pointing to a star, say on the meridian, the hour circle will not read so much as it would do if the line perpendicular to the declination axis were pointing to the meridian. When the telescope is on the wrest side of the pier, the circle will read higher for the same reason, and therefore the difference between the angle through which the hour circle is moved and 180° is equal to double the angle between the line perpendicular to the declination axis and the collimation axis of the telescope; allowance being made for the star’s motion.
For example γ Virginis, Dec. 0° 46´·5.