Navigation using Declination

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Which shows how to handle the declination of the Sun, to know the altitude of the Celestial Pole above the Horizon, whether you are in normal climes, near the Equator, in the southern ocean, or near the Poles of the World.

Preliminaries

First, the altitude of the Celestial Pole where you are is the same as your Latitude, for your Latitude is the number of degrees you are from the equinoctial, and when you are under the equinoctial, which is when you are at the equator, the Celestial Pole lies on your Horizon, with no altitude, and the North Star is barely visible. And as you travel north, for every degree or 60 miles that you travel north, the Celestial Pole rises one degree into the sky, so while Latitude is the width that you are from the Equinoctial and Altitude is the height of the Celestial Pole, so they are one and the same. Likewise, the distance between the Equinoctial and your Zenith is the distance of the Celestial Pole from the Horizon, and so the height of the Celestial Pole is the distance of the Zenith from the horizon less the altitude of the Equinoctial which is the height of the Sun without any declination; that your Latitude is 90 degrees less the height of the Sun adjusted for seasonal declination.

Therefore you must know the seasonal declination of the Sun, to whit, you much also know what season you are in, and what part of the month to within a day, as each day the Sun moves along the Ecliptic and so its declination changes. So, if you do not know the declination of the Sun, then refer to the notes on Seasonal Declination until you know the current declination of the Sun.

Finally it is good to know roughly what part of the globe you are in, for there are different ways of finding your Latitude depending on while circle you lie within. But if for some reason you do not know, each method will give the same result or no result at all, some being easier or harder depending on where you are, but none shall give a wrong result.

Knowing all this, now take the height of the Sun at noon with your Cross-staff or Astrolabe, or however you choose to do it. And if you do not know how this is done, you need to refer to the preceding chapter, where I have explained it all in sufficient detail.

Finding your Latitude between the Ecliptic and the Arctic Circle

Given you have the height of the Sun at noon, and the declination of the Sun for the current day of the Season, if the Sun has North declination (it being summer or above the Equinox), then subtract the declination from the height of the Sun, and the remainder shall be the true height of the Equinoctial. Removing this value from 90, in degrees and minutes, that which remains shall be the true height of the North Pole above the Horizon, which is your Latitude. But if the Sun has South declination (it being wintry and below the Equinox), then add the declination from the height of the Sun, and the remainder shall be the true height of the Equinoctial, and that sum being removed from 90, the remainder shall be the true height of the North Pole above the Horizon, or your Latitude.

An Example

The Sun when measured due South with a Cross-staff is 48°30' above the Horizon, and has a North declination of 15°35' and that makes 42°55', which I take away from 90° leaving 37°05', so you may affirm that the North Pole is 37°05' above the Horizon; thus your Latitude is that of Seagate.

Finding your Latitude between the Equinoctial and the Sun

Furthermore, if you are under the Ecliptic being in the Tropics, that is near the equinoctial, and the Sun has some declination either to the South or North, and you find yourself between the Sun and the Equinoctial, when you have taken the true height of the Sun with your Astrolabe, to know the height of either of the two Poles of the World, first seek the declination of the Sun for that day, then add the declination of the Sun to its height, and it will exceed 90 degrees. If it does not, then you are not between the Ecliptic and the Equinoctial and may find your Latitude as above. Now look how many degrees it exceeds 90 and that shall be the true height of the Celestial Pole, that is whichever of the North and South Pole that is towards the side that the Sun is on, because your Equinoctial is the number of degrees above 90 (which is your Zenith) to the contrary from Sunwards.

And to find whether you are under the Equinoctial that being on the Equator, take the height of the Sun, and add the declination, and if the number is 90, then you are under the Equinoctial, and if it is less the Equinoctial lacks that amount of the Zenith, and the Celestial Pole is that much above the Horizon to the Sunwards. But if it is more than 90 degrees, then it signifies that you are between the Sun and the Equator, under the Ecliptic on the side that the Sun is on.

An Example

The Sun when measured at your South Meridian with an Astrolabe is 81°15' above the Horizon, and has South declination of 22°35' and that makes103°50', from which I take away 90° leaving 13°50', so you may conclude that the Equinoctial is 13°50' to the North of your Zenith, and the South Pole is 13°50' above the Horizon.

Finding your Latitude beyond the Equinoctial

And if you are to the South beyond the Equinoctial and between the Ecliptic and the South Pole, then to use the declination of the Sun to know the height of the South Pole, it being your Celestial Pole, then the above method suffices, but whereas we in the North add the South declination to the height of the Sun and subtract the North declination, so in contrary manner the Antipodeans must rebate the South declination for the height of the Sun, and add the North declination.

An Example

The height of the Sun being 28° above the Horizon due North at noon, and the declination of the Sun being 21° to the North, I add the declination of the sun to its height which makes 49° being the height of the Equinoctial above the Horizon, and removing that sum from 90°, there remains 41°, which is the distance between the South Pole and the Horizon, or your southern Latitude.

A General Rule for Latitude

When handling declination, the true height of the Poles is known. Always consider which Pole is above the Horizon, and if the North Pole is above the Horizon, always add the South Declination to the height of the Sun, or subtract the North declination. Contrariwise, if the South Pole is above the Horizon, you must add the North declination or take away the South declination from the height of the Sun. Now to know which of the Poles is above the Horizon is a very easy matter, and is known in two ways. If the North Pole is above the Horizon you may know it by the Stars around the Pole, being the North Star and the Waines and Guards. Neither do I believe that you can pass so quickly beyond the Equinoctial that it is not known to you. Also you may know it by the arc or bearing of the Stars and lights around you.

Finding your Latitude beyond the Arctic Circle

For more accurate determination of the Sun's declination, if you have any occasion to travel to the North or South beyond the Arctic circles, or 67° of Altitude, and if the Sun has any great declination towards those parts that you are in, then the Sun shall not go down under the Horizon in a long time, and if you were right under either of the Poles of the World, then the Sun would not go under the Horizon in half a year, so there should continually be day. Moreover, it is easy to lost track of the Meridian in these parts, for the methods for finding the Meridian rely on sunrise and sunset, or on the height of the Sun changing significantly as she moves across the sky, or on the compass having a known or constant variation, but none of these hold at the extreme Latitudes. Despite this, it is possible to take the height of the Sun at or about noon, the height of the Sun changing little across any short period.

However, it is also possible to find your Latitude by the height of the sun at midnight, or when the Sun is at its lowest, so long as it cannot set that day. First with your Cross-staff observe the Sun at its lowest, taking the true distance between the Horizon and the Sun. Then take the declination for that day, or if the declination is changing rapidly each day, it being Spring or Autumn, then take half the difference between that day's declination and the next, for even though the sun is up, it is midnight, and halfway between the days. The Sun's true declination being known, subtract the height of the Sun from its declination and so you have the true amount in degrees and minutes that the Equinoctial is under the Horizon, and then removing that amount from 90, the remainder is the height of the Pole above the Horizon, or your Latitude. And if the Sun's declination is less than the height of the Sun at midnight, then you have made a grievous error and should check your instruments and tables.

An Example

Now suppose I were far to the North on the Summer Solstice, the Sun being at a Northern declination of 23°30' and I take the Sun due North it her lowest point, being just 6° above the Horizon. Then subtracting the height from the declination I am left with 17°30' for the depth of the Equinoctial beneath the Horizon, and subtracting this from 90° there remains 72°30' for the true height of the North Pole being my Latitude.

Observations on far Northern Climes

The above methods of determining Latitude is very necessary for those who occupy Swenway and Finmark, and also those that would attempt any voyages of discovery into the North, whether to the Northeast above Ruska, or the Northwest seeking a passage beyond Terranova, either way to the lands of the Far East. If either where attempted, there is no doubt that they should find it navigatable either to the East or West, and I am of the opinion that the thing most feared in journeying northwards does not deserve to be feared so greatly as it is, that being the reason why they are so loathe to go very far into the North, which is the frozen zone. But my opinion is that in summer time it is not to be feared, as the further into the north the more temperate or warm it is, by means of the long continuance of the Sun; and as we see by common experience that a thing made warm cannot suddenly be made cold, neither is there any doubt of any great cold until the Sun return south of the Equinoctial in mid Autumn. And I believe that if a ship should sail northwards beyond 80° they would find it very temperature and warm until the middle of Harvest, for there is a space of nine weeks from 14 Meadow to 16 Breeze when the Sun should come no closer to the Horizon than 10° to the North or 20° to the South, and shine without respite for 18 weeks between 12 Blossom to 18 Fruit. And yet is it possible that it may be cold there until the end of Meadow, for the Sun must have some time to make the air warm. For as a thing once being cold cannot be suddenly made warm, likewise a place being once warm cannot be suddenly made cold.

And furthermore, those in the Latitude of 80° have a short parallel, for the whole compass of the earth and sea going East and West and round about to that place again in the same parallel is but 3750 nautical miles rather than the 21,600 nautical miles at the Equator. So in sailing only 1500 miles East or West they may find a new route being far shorter and saver than those currently known, even if only navigable during the late summer months.