Distance by vertical sextant angle.

Using a sextant, a distance may be obtained of a vertical object of known height, by measuring the angle subtended by the object at the eye of the observer. The determination of the distance is then merely a problem of solving a right angled triangle. One can either do this by calculation of by looking up the solution in “Distance by vertical sextant angle” tables in Nories. For accuracy the angle obtained from the sextant must be corrected to allow for index error.
Calculation. To calculate the distance from the object the following formula is used:

If the object is between the observer and the horizon then the observed angle must be corrected for index error and the height must be corrected for the height of tide.

• Index error is the observed error of the sextant.
• Dip is the correction for the observer’s height of eye and is obtained from page 453 in
  Nories Tables. It can also be obtained from the nautical almanac which includes a correction for refraction as well. The correction must be subtracted from the observed angle.