Navigation Distances
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In which is shown how to know the distance of any land to you in knowing the distance between any two places, whether you run alongside the land or directly towards the shore or otherwise, with other necessary things.
As I know that it is necessary and profitable for Seafarers to know how near or far they are from the land, I will provide several diverse rules for your consideration. First, because in running alongside the land there may be dangers that are a certain distance into the sea, that they may sail either inside or outside them. And likewise, as when at one distance for the land, it may rise up in such a shape or fashion, while if you are nearer, the land may rise in another form, for being far off, you shall see the inland hills, and when nearer, the hills or cliffs at the sea coast may take away this sight. Furthermore, it is very necessary to know in what fashion the land rises at diverse points of the compass, as often as the land alters, and to note it in some book in this manner: first the points of the compass, then the shape, and last the distance.
Landmarks to One Side
You may know how far you are from the land if there are two places on the sea coast that you know the distance between, and which are visible. While travelling parallel to the coast, wait until one place is athwart or beside you, and take a bearing on the other landmark. From the number of points between the bearings, you shall be a certain multiple of the distance between them from the shore, as shown in the table below. And in all cases one of the places must be directly beside you, to make it exact and true. And if the landmarks are not on the coast, but you know how one bears from the other, then if you can sail in that direction and have one of the places abeam of your vessel, then the same method shall also work.
- One Landmark Athwart
| Angle between Landmarks | Distance to Shore |
|---|---|
| 1 point | x 5 |
| 2 points | x 8/3 |
| 3 points | x 3/2 |
| 4 points | x 1 |
| 5 points | x 2/3 |
| 6 points | x 2/5 |
- An Example
Let us suppose that the two places are East and West from each other, and are 3 leagues asunder. Then when I have brought one of the places due South (or North) of me, I take a bearing on the other and find it bears 3 points of difference. Then the distance to the nearer landmark is 1 ½ times their mutual distance, or 4 ½ leagues.
Landmarks to Either Side
And if you come directly into land, having no cause to be athwart any of these known places, then to know how far you are from the land, you must find two landmarks one on each side of the bow, and take bearings on them as above. And the number of points between these bearings and your course can be used in the following table to determine how much further you are from shore than the landmarks are apart, which also having their mutual distance, provides the distance of your vessel from the shore.
- Landmarks either side of Bow
| Starboard | ||||||
|---|---|---|---|---|---|---|
| 1 point | 2 points | 3 points | 4 points | 5 points | ||
| Port | 1 point | x 5/2 | x 8/5 | x 7/6 | x 5/6 | x 3/5 |
| 2 points | x 8/5 | x 6/5 | x 11/12 | x 5/7 | x 1/2 | |
| 3 points | x 7/6 | x 11/12 | x 3/4 | x 3/5 | x 4/9 | |
| 4 points | x 5/6 | x 5/7 | x 3/5 | x 1/2 | x 2/5 | |
| 5 points | x 3/5 | x 1/2 | x 4/9 | x 2/5 | x 1/3 | |
- An Example
Let us suppose that we know the two places are 3 leagues asunder. Then at one time with my bow due North, the first landmark bears Northeast by North, and the other North Northwest, being 5 points of difference. Then the distance to the shore is nine-tenths their mutual distance, or just over 8 miles.
Bearings between Headlands
If you do not know how one headland bears from another, then in running along the coast, when you see one headland just starting to appear from behind the other, take a bearing with your compass, and how they both bear from you is how one bears from the other. And by this, you can correct your charts by doing this as often as you see two notable places together, whether they be islands, rocks, headlands, mouths of havens, sandbanks, or whatever else may be worthy of noting.
Distances between Uncharted Headlands
You may also know the distance between them if you know your ship's way. Having run along the coast and taken your bearing as above, as you will not want to come near to them, you will hove off from the land until you have brought your ship far enough out to sea at your discretion, and then when you are athwart of the first headland, take a bearing on the second headland. Then you shall set a course parallel to the two headlands by the first bearing you took, and take your ship's speed. At the time that you are athwart of the second headland, note the time that has past from the first headland, and then reckon the distance between them, and using the second bearing, you may also know how far you are from them.
Distances to an Uncharted Shore
In similar manner you may know how far it is to shore as you directly approach it, although you do not know the distance between any two places. First take the bearing between any two places on the shore with your cross-staff, and then move the Transitory or cross-piece exactly halfway along the remainder of the long staff. By running the ship in towards shore until the ends of the transitory agree again with the two marks, you shall be halfway to shore; then look how far the ship has gone, by its way and the time taken to run in, and the same distance remains between the ship and the land. And if you move the Transitory only a quarter of the distance, then at the place where the two marks line up, you shall be a quarter of the distance between the shore and your first observation, and it shall be three times the distance travelled to reach the shore.
The Ship's Way
The best manner in which to know the ship's way or speed, is to have a piece of wood to throw out overboard, tied to a small line of great length which you make fast at one end, and along that line at fixed intervals of 50 foot and 8 inches are pieces of line made fast with a small thread so they stand like a crow's foot. And for those that travel upon rivers and thus use land miles the pieces of line should be only 44 foot apart, but the passing of landmarks will be a better guide due to the flow of river currents. And so that the piece of wood should drive astern as fast as the ship moves away from it, you should always have the line coiled so that it goes out as fast as the ship travels. And also you should have a half-minute glass, or else a known phrase that takes that length to speak, or some other way of keeping time, so that the line being thrown out is made fast again just as the glass empties, or the phrase is complete. At this point, the line is hauled in again, and the number of marks is counted, and this is the number of nautical miles that you are travelling each hour. And the ship's way should be taken on every heading, and every change of wind strength, so that a reckoning of the ship's position can be made from knowledge of the speed and course alone. And all this to be recorded in the Ship's Log, first named from this very piece of wood.
