Navigation by Cross-Staff

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In which we are shown how to take the height of the Sun with the Cross-staff or Astrolabe, and also how to find the true Meridian, with other necessary matters.

The Use of a Cross-Staff

To take the true height of the Sun at sea, the best way is to do it with the Cross-staff, as the sea is always in motion, and causes the ship to heave and yaw to varying amounts, and also as the degrees are marked more clearly and larger upon the Cross-staff than the Ring or Astrolabe; in addition, with a large instrument any error is seen sooner and better than it is with a small instrument.

Now to take the height of the Sun, that is to know the Altitude of the Pole above the Horizon, first take a bearing on the Sun with a compass, so as to know when the Sun approaches the Meridian. As soon as you see the sun has come to the South and by East, then begin to take the height of the Sun with the Cross-staff in the following manner. Put the Transitory or cross-piece on the long staff, then set the end of he long staff against the corner of your eye, closing the other eye, and moving the Transitory forwards or backwards until you see the lower end of it is at the Horizon and the upper end is in line with the middle of the Sun. Once both ends agree with the Sun and the Horizon at one time, you have the true height of the Sun; this done, continue to observe until you see the Sun at its highest and beginning to descend, and then you have finished. Notwithstanding the above comments, it is best to take the height of the Sun with the Cross-staff with the Sun is under 50 degrees above the Horizon, for two reasons. The first is that until the Sun is 50 degrees in height, the degrees are well spaced and clearly marked on the Cross-staff, but after this, the marks are closer together, and smaller. The other is that when the Sun is under 50 degrees in height, you may easily take the height, as you may easily see both the upper and nether end of the Cross-staff at one time; but if it exceeds 50 degrees, then due to casting your eye upwards and downwards so much, you may soon make an error. So that if the Sun passes 50 or 60 degrees in height, you must put down the Cross-staff and use the Mariner's Ring, or Astrolabe.

Customising a Cross-Staff

For readings when the Sun is bright, a smoked glass at the upper end of the Transitory will reduce the strength of the light on your eyes. If you do not have a smoked glass upon your staff, instead you can cover the Sun with the end of the Transitory, up to the very upper brink of the Sun (so that you need not behold its brightness), and with the other end of the Transitory, take a true reading of the Horizon. That being done, as the Sun is 30 minutes in diameter, you shall rebate 15 minutes or ¼ of a degree from the measurement of the altitude or height of the Sun, and what remains is the true height of the Sun as if read from the centre of the Sun.

And furthermore there is some error in taking a sighting of the Sun or a star with the Cross-staff, and that occurs by this means; that the true centre of the reading is based on the sight of the eye, and is thus within the middle of the eye and not in the outside of the eye or the end of the long staff. So the end of the long staff, when set into the corner of your eye stands somewhat further out that the sight of the eye, wherefore you much pare away a little of the end of the staff; for some men more, and others less, because some men's eyes be further into their head than others, and the bones of some men's face stand further out than some others do.

The Use of an Astrolabe

The Astrolabe is best used to take the height of the Sun if it is very high, at least 60 degrees, and this is because when the Sun comes near the Zenith, its light has great strength, and can pierce the sights of the Astrolabe, and then it is not good to use the Cross-staff, and so this way you may preserve your eyes.

Now to take the height of the Sun with the Common Ring or Astrolabe, follow these steps. Once the Sun is near the Meridian or South, observe it until it reaches its greatest height. Hold the Ring upon one of your fingers, and turn the Alhidada or sights up and down, until you see the show of the Sun pierce or pass through both the sights, being sure that the Astrolabe hangs upright. You may prove that it hangs true in this manner; look at the number of degrees and minutes the Alhidada marks on the Astrolabe, then turn the Alhidada to the same number of degrees and minutes on the other side of the Astrolabe, and the take the height of the Sun again, if the two agree, then the Astrolabe hangs upright, but if it does not, measure the height of the Sun on this side, and measure the diversity between the two readings. Subtract from the greater height half the difference, or add half the diversity to the lesser height, and that shall be the true height of the Sun, even though the Astrolabe does not hang upright.

There are many types of astrolabe, each with its own adherents. More information on them can be found [here], [here], and even [here].

Finding the True Meridian

It is moreover convenient to know the true Meridian, or South, which you must do either with a good Compass, or with a perfect dial or Needle, but if you are on land, you may do the following instead. On a piece of timber, or any other fixed surface, mark a circle with a pair of compasses, then in the middle or centre where the foot of the compass stood, set a wire upright as carefully as you can, and then you may take your measurements.

1. First, look in the morning as the Sun rises (ensure it is on plain ground so that you can see the Horizon circle, without any interference), for the shadow of the wire, and there set a mark; then at the setting of the Sun, set another mark, both at the circumference of the circle. Then divide that with your compasses evenly in two pieces, and draw a straight line from the wire or centre of the circle to the middle dividing mark, and that shall be true meridian.
2. Or else (still ensuring the wire stands upright), first look before noon for when the top of the wire shadow touches or crosses the edge of the circle, and there make a mark, and in the afternoon in like manner at the very point the shadow leaves the circle, make a mark; this done, as carefully as you can divide these two marks in the middle, as was said before, draw a line form the centre or wire to the middle mark, and that line shall be your true meridian.
3. Yet another approach is to look and watch when the wire gives the shortest shadow, and there make a mark, then draw a line from that mark to the wire, which shadow shall be true meridian; but this is least accurate of all the methods.