3. THE SEXTANT AND THE MEASUREMENT OF ALTITUDE
9 THE FUNCTION AND PRINCIPAL OF A SEXTANT
37. FUNCTION OF A SEXTANT
Although an instrument of precision, the sextant is merely a simple means of measuring angles. These angles can be in any plane – horizontal, vertical, or oblique, and because of this, the sextant is of considerable value to the navigator in each of the two main branches of navigation: coastal navigation and Astro-navigation.
The main type of marine sextant in use today is the micrometer sextant. The older ‘vernier’ sextant although potentially just as accurate, is much more difficult to read is no longer manufactured and has fallen out of favour with most navigators. The great advantage of the more modern micrometer sextant lies in the speed and ease with which it can be read without a microscope under poor light.
The traditional marine sextant is a precision instrument costing upwards of £500 new, and even a second-hand reconditioned model will cost over £80 from a reputable instrument dealer. Traditional sextants, when properly adjusted, are accurate and can be read to 10 seconds of arc (10″).
At less than a quarter of the price of a traditional sextant, there is an excellent micrometer sextant on the market made of specially stabilised plastic. Although less accurate than metal sextants, reading to about 1 minute (1′) of arc, this is quite accurate enough for small craft purposes since the limiting factor is the stability of the platform used for observations – the vessel’s deck – rather than the accuracy of the sextant. The principle disadvantage of these plastic sextants is their lightness; the average weight of a traditional metal sextant is about 2 kilos which gives greater steadiness when taking observations in a stiff breeze. All sextants, whatever their size, construction, and price, do fundamentally the same job. The main advantages of the more expensive instruments are that they are larger, more accurate, and easier to read and have finer telescopes and accessories all of which improvements are directed to one end – to make the instrument easier for the navigator to use. With the lower priced version one cannot expect the luxury of hermetically sealed mirrors, and the mirrors will, therefore, suffer unavoidably from exposure to salt spray and may well not last for more than a year or two if put to fairly rugged use. On the other hand, of course, the mirrors may well be replaceable and at the low initial cost, one may consider the instrument to be expendable and buy a new one every few years instead of a traditional sextant, which one can expect to last a lifetime. In any case, it is not unheard of for an expensive sextant to be lost overboard or damaged when its user is thrown around in bad weather, and to carry a plastic sextant on board as a spare may be sensible.
38. THE PRINCIPLE OF A SEXTANT
The sextant is called an instrument of double reflection because although it’s graduated arc (A in fig. 9-1) is about one-sixth of a circle (hence the name sextant), the graduations on that arc read up to about 120º. In fig. 9-1., the two mirrors of a sextant are marked I and H. A ray of light from an object is seen striking the first mirror I, from which it is reflected into the second mirror E which reflects it again through a telescope T to the observers eye.
The principle of the sextant in based on two simple laws of optics:
When a ray of light strikes a plane mirror, the angle of incidence is equal to the angle of reflection (see. fig. 9-2). The angle of incidence, the normal, and the angle of reflection, all lie in the same plane.
(The normal is an imaginary line drawn at right angles to the surface of the mirror)
It follows that if a ray of light is reflected twice by two plane mirrors, the angle between the first incident ray and the second reflected ray is twice the angle between the mirrors.
In fig. 9-3, XIHL is the path of a ray which is reflected from the two mirrors of a sextant, I and H. XI (when produced) meets HI at L.
The angle HLX is, therefore, the angle between the first and last directions of the ray.
The angle between the mirrors is HMI, and this is equal to the angle between the normal’s NI and KH. The angles between the ray and these two normal’s are and. Since an exterior angle of a triangle is equal to the sum of the internal and opposite angles, it follows that: –
∠HKI = θ – θ (in ∆HKI) and ∠HLI = 2θ- 2θ (in ∆HLI) but ∠HLI is the angle between the first and last directions of the ray, and is therefore twice the angle between the mirrors. In the sextant (fig. 9-3) the first mirror I is called the Index Mirror because it is attached to the Index Bar B. It can, therefore, be said that the angle through which the reflected ray rotates is equal to twice the angle through which the mirror rotates.
For this reason, the arc of the sextant (A) is graduated to indicate twice the angle through which the Index Bar B (and Index Mirror I) rotates from the zero mark on the scale. Although the sextant arc is only about 60º, the instrument may be used to measure angles up to about 120º.