A sextant is a mechanical device for measuring the angle between two objects. Most commonly associated with navigation at sea, a sextant can also be used to help calculate the height of trees, buildings, flagpoles or any other vertical object.
The Arabs knew all about this technique. In early days, they used one or two fingers width, a thumb and little finger on an outstretched arm or an arrow held at arms length to sight the horizon at the lower end and Polaris at the upper.
The critical development was made independently and almost simultaneously by John Hadley in England and by Thomas Godfrey, a Philadelphia glazier, about 1731. The fundamental idea is to use of two mirrors to make a doubly reflecting instrument—the forerunner of the modern sextant.
Choose an observation point from which you can clearly see both the top and the bottom of the object you wish to measure. Determine the exact distance between the observation point and the base of the object.
Set the sextant to zero and look at the object through the eyepiece, adjusting your view until it is in the center of the frame.
Adjust the sextant arm to split the screen in two halves. Continue moving the arm until the top half of the object on one side of the image is aligned with the bottom half of the object on the other side of the image.
Read the angle from the arc of the sextant.
Use a scientific calculator to find the height of the object by multiplying its distance from the observation point by the tan of the angle that you measured. For example, if you were 150 feet from the base of the object, and the recorded angle was 75 degrees, the height of the object would be 150 x tan 75 = 560 feet.
Remember to add the height you are holding the sextant above the ground to the total height of the object.
This video will help you:
Errors and Adjustments
The sextant is subject to a number of errors and adjustments. To find the true altitude of a celestial body from the observed these must be allowed and adjusted for.
Briefly these are:
- Index Error
Index error is an instrumental error. When looking through a sextant at the horizon the exact level horizon will seldom be seen to be at 0°.
Sextant set at 0° – horizon split.Before every sextant session the Index error should be determined.
Index error corrected for – horizon level.
If the error is less than 0° it should be added to whatever reading is obtained – if more subtracted. Hint: remember Noah, if off the Ark – add, if on the Ark – take off.
Dip is an adjustment made for the height of the eye above sea level. In practice this is usually taken as 0.98 times the square root of the height of the eye in metres above sea level multiplied by 3.28.
Refraction is extracted from the Nautical Almanac. It allows for the “bending” of light rays as they travel through successive layers of varying density air.
Parallax corrections are needed if the observed body is a planet, the sun or the moon. From the Almanac.
Semi-diameter correction is needed if the observed body is the sun or the moon. In this case either the top or bottom of the celestial object (known as upper or lower limb) is made to touch the horizon. To obtain the centre of the body this correction is applied – from the Almanac.
Once all the corrections are applied we have the true altitude. And this subtracted from 90 gives us the zenithal distance to the sub-stellar point. Which means we know exactly how far we are from that elusive point on the earth which is at right angles to our observed celestial body!
Read here about the various uses of sextant