Combining the Corrections

Starting with your measured angle, usually called Hs, which stands for Height Sextant, applying these corrections will give your observed or corrected altitude, usually called Height Observed or Ho.

Ho = Hs —dip —refraction +/-semi-diameter (if using the sun).

Meridian sights

A meridian sight has a lot going for it. First, as long as you can see it and know its declination you can use any celestial body. Secondly, although it helps to know the time, this is not absolutely essential. You can estimate when a body is at its zenith without a watch. Thirdly, you do not need complicated sight reduction tables or maths. Fourthly, it will always give you a position line, which is your latitude.

When you take the sun's altitude at noon you are measuring the angle between your horizon and the sun's zenith (see Figure 15.1). The angle between your horizon and your zenith is always 90°.

If you subtract the altitude of the sun, whatever it is, from 90° you get another angle, which is called the zenith distance. This is true of any celestial body and the zenith distance of any celestial body plus its altitude always comes to 90°. When a celestial body is at its zenith, the angle between a line from the centre of the earth to the body and the equator is its declination. Where this line passes through the surface of the earth it is on a parallel of latitude that has exactly the same value as the body's declination, as shown in Figure 15.2.

Your latitude, which is what you wish to discover, is your angular distance north or south of the equator (see Figure 15.3).

Put these three facts together and when you are in the northern hemisphere and a body has a northerly declination, then your latitude is your zenith distance plus declination and when the declination is southerly then your latitude is your zenith distance, minus declination (see Figure 15.4).

15.1 Zenith Distance

Declination = Latitude on earth

Equator

Equator

15.2

In the northern hemisphere ail latitudes are north of the equator and labelled NORTH.

Equator

In the southern hemisphere all latitudes are south of the equator and labelled SOUTH.

15.3

In the southern hemisphere it is all back to front so the general rule for both hemispheres is:

+ Declination when both it and your position have Latitude = Zenith Distance: the same name ie both NORTH or both SOUTH.

— Declination when it and your position have different names.

A star's declination is fixed but the sun's changes daily because the tilt in the earth's axis makes it look as if the sun travels between the northern and southern hemispheres according to the season of the year. It reaches its furthest north (23.5°N) on the summer solstice. Then changing its declination daily it travels south to 23.5°S in

In the northern hemisphere ail latitudes are north of the equator and labelled NORTH.

Equator

In the southern hemisphere all latitudes are south of the equator and labelled SOUTH.

DECLINATION AND POSITION BOTH NORTH LATITUDE Since AB and CD are parallel to each other then

Angle ABZ = CDZ = Zenith Distance. By Inspection Latitude = Zenith Distance + Declination.

The sun is so far from earth that its rays of light reaching the earth are parallel to each other and not like rays spreading out from a cone. This is also true of stars.

ZENITH DISTANCE

sextant altitude

DECUNA-nON

ZENITH DISTANCE

sextant altitude

Equator

DECLINATION SOUTH AND POSITION NORTH LATITUDE Since AB and CD are parallel to each other then

Angle ABZ = CDZ = Zenith Distance. By Inspection Latitude = Zenith Distance - Declination.

15.4 A Meridian Sight time for the winter solstice. To calculate your noon latitude you must know the sun's declination on the day you take your sextant reading.

Your observed altitude must also be corrected for dip, refraction, and if you are using the sun, semi-diameter. The final equation for your noon sight is:

Latitude = 90 — observed altitude — dip — refraction + / — declination +/ — semi-diameter.