The Sextant is a precision instrument used at sea for measuring altitudes of celestial bodies and horizontal angles between terrestrial objects and also their vertical angles.
Principle of the Sextant
1. When a ray of light is reflected by a plane mirror, the angle of incidence is equal to the angle of reflection, with the incident ray, reflected ray and the normal lying in the same plane.
2. When a ray of light, suffers two succesive reflection in the same plane, by two plane mirrors, the angle between the incident ray and the final reflected ray is twice the angle between the mirrors.
The first principle is simple and requires two explantion. The proof of the second principle however is given below.
A ray of light from X is incident on the index glass at an angle @ with the normal PQ. It reflects making the same angle with the normal. The reflected ray meets the horizon glass at an angle of incidence B and is again reflected making the same angle with the normal R.
The angle between the incident ray and the final reflected ray then is angle S. The aangle T between the mirrors is equal to the angle between their normals i.e. angle.
To prove that angle,
S = twice angle
Q = @ – B
Multiplying by 2
2Q = 2@ – 2B ………………(i)
Again, 2@ = 2B + S
(ext. angle = sum of interior opposite angles)
Substituting in (i)
2Q = 2B + S – 2B = S
When the sextant reads zero, the index and horizon glasses are parallel to each other. When the Index bar and therefore the Index glass is rotated through any angle, the angle between the incident ray and the rotated through any angle, the angle between the incident rat and the final reflected ray is twice the angle through which the index bar was rotated. The arc of the sextant is only 60° in extent, but due to the principle of double reflection, we are able to mark the arc and measure angles upto 120°. Sixty degrees being a sixth of a circle, the instrument is known as a Sextant.
The present day sextants are provided with micrometres which enable easy and accurate reading of angles to an accuracy of 0.1′ of arc. The vernier sextant is now practically obsolete.
Errors and Adjustments
The error on a sextant may be classified as:
The Adjustable Errors are :-
(a) Error of Perpendicularity
It is produced by the index glass not being perpendicular to the plane of the instrument. To check for this error, clamp the index bar at about the middle of the arc, and holding the sextant horizontally, with the arc away from you, look obliquely into the index mirror till the arc of the sextant and it’s reflection in the index mirror, are seen simultaneously. If they appear in alignment, errors of perpendicularity is not present. If not, turn the first adjustment screw at the back of the Index glass, until they appear in alignment.
(b) Side Error
It is caused by the horizon glass not being perpendicular to the plane of the instrument.
To check for side error,by day, clamp index bar at zero, hold the sextant horizontally and observe the horizon through the telescope. If the true horizon and it’s reflection in the mirror half of the horizon glass, appear in alignment, side errors is not present.
If they do not, side error exists. It can be removed by turning the second adjustment screw (the top screw at tthe back of the horizon glass), until the true and reflected horizons appear in the same line.
To do this at night, clamp the index bar at zero and holding the sextant vertically, observe a star through the telescope. If the star and it’s reflection are not displaced horizontally, side error is absent. If they are displaced horizontally, the error exists and can be eliminated by adjusting the 2nd adjustment screw till there is no horizontal displacement between them.
(c) Index Error
It is caused by the index glass and the horizon glass not being parallel to each other, when the index bar is at zero. To find the index error, by day, using the horizon, clamp the index bar at zero and holding the sextant vertically, view the horizon through the telescope. If the true horizon and it’s reflection appear in the same line, Index error is not present. If they appear displaced vertically, turn the micrometer drum till they are in the same line. The micrometer reading then is the index error, which is on the arc if the micrometer reading is more than zero, and off ther arc if it is less than zero
To eliminate Index error, clamp the index bar at zero and looking through the telescope, turn the third adjustment scre, till the true horizon and it’s reflection appear in alignment. The third adjustment screw is located below the 2nd adjustment screw, and towards the side, at the back of the horizon glass.
The index error can also be found using the sun. With the idnyex bar clamped at zero, using the necessary shades, view the Sun through the telescope, holding the sextant vertically. Turn the micrometer, ‘on the arc’, till the upper limb of the reflected Sun touches the lower limb of the True Sun. Note the reading ‘off the arc’. If the two readings are the same, Index error is not present. If not, the amounts of the Index error is half the difference between the two readings and named ‘on the arc’ or ‘off the arc’ respectively according to whether the ‘on the arc’ reading or the ‘off the arc’ reading was larger.
To find the index error at night, clamp the Index bar at zero and holding the sextant vertically, view a star through the telescope. If the star and it’s reflection are not displaced vertically, index error is not present. If they are displaced vertically, adjust the micrometer till they appear with no vertical displacement. The micrometer reading then is the index error. To correct this, with the index bar clamped at zero, turn the third adjustment screw, till any vertical displacement between the star and it’s reflection is eliminated
The second and third adjustments being carried out on the horizon glass itself, one adjustment may affect the other. It is therefore advisable after adjusting one, to check for the other. When the Index error is not large, it is usually left uncorrected, as frequent adjustments may cause the adjusting screw to become slack. The error if left uncorrected should be allowed for when correctinf the measured angle.
(d) Error of collimation
It is due to the axis of the telescope not being parallel to the plane of the instrument.
Old sextant were provided with an adjustable telescope colalr so that this error if present, could be removed by adjusting the collimating screws on the telescope collar. In present-day sextants, the telescope is attached to the body of the Sextant in such a manner that it cannot tilt. These sextnats are therefore not provided with any collimating screws.
Non Adjustable error
(a) Graduation error
It is due to the inaccurate graduation of the main scale on the arc of the micrometer/vernier
(b) Shade error
It is due to the two surfaces of the coloured shades not being exactly parallel to each other.
(c) Centring error
It is caused due to the pivot of the index bar not being coincidnet with teh center of teh circle of which the arc is a part.
(d) Optical errors
It may be caused by prismatic error of the mirrors or aberrations in the telescope lenses.
(e) Wear on the rack and worm, which forms the micrometer movement would cause a black-lash, leading to inconsistent errors.
For video illustration of sextant checkout Casual Animation sextant tutorial.