The compass used by the down-timers is "dry," the card pivots on a vertical pin, inside an empty bowl (Gurney 25). The epitome of the dry compass is, perhaps, the Admiralty Standard Compass, introduced in 1840 and still in use a century later (Gurney 208-10). It, together with the temperamental 1876 Thomson patent compass (240-64), are discussed in 1911EB.
In the wet form, the compass card is still attached to the needle, but they are floating on some kind of liquid, preferably a viscous one. The dry compass was favored during the sailing ship era, but steamship engine vibrations forced the eventual adoption of the wet version (Williams 136-7; Gurney 264-72), like the Ritchie model described by 1911EB .
Down-time, you had to be careful where you bought your compass. For example, in northern Europe, compasses frequently had hidden offsets (needle at angle away from north on card) of 6-11d*, to compensate for magnetic variation. On the other hand, Italian-made compasses lacked these offsets. (Gurney 63). An unsuspecting soul who bought a northern compass and then tried to use it in the Mediterranean could get an unpleasant surprise.
Curiously, compasses weren't routinely tested until the nineteenth century. After the 1707 Scillies disaster, the Navy inspected its compass inventory, and found that only three out of 145 were working properly (Wakefield 45).
The magnetic compass is subject to a number of inherent errors (earth's variation and ship's deviation), so mariners speak of three different kinds of directions: compass, magnetic (compass direction adjusted for deviation), and true (magnetic direction adjusted for variation). A surveyor, such as Grantville's Mason Chaffin, should be quite familiar with the phenomena of magnetic deviation and variation.
Magnetic Variation . The magnetic compass works, ultimately, because 1) the earth has a liquid iron outer core, 2) the molten iron is in constant motion, and 3) at least some of that motion is attributable to the rotation of the earth. The result is that a magnetic field is generated which, very loosely speaking, has one pole (place where a "dip" compass would point straight down) near the earth's true North Pole, and the other near the true South Pole. However, the earth's magnetic field is not a simple field, with two geometrically opposite poles, like the one generated by a bar magnet. Hence, the compass needles don't necessarily point exactly toward the true poles.
The difference, expressed as so many degrees to the east or west of true north (or south), is called variation (or declination), and differs depending on where on the earth the compass is situated. Variation is unaffected by heading, and compensation with counter-magnets is not possible. But it varies with location (and time). It is thus essential, especially when sailing great distances, to keep track of the magnetic variation so that the correct course can be steered.
The down-timers are well aware of the existence of magnetic variation. According to Williams (26), magnetic variation was first indicated on a European chart in about 1504. Cape of Good Hope is called Cape Aguilhas ("Needles") by Portuguese because of the way the compass misbehaves in its vicinity (Walker 1).Mercator tried to explain variation by postulating first one (1546) and then two (1569) north magnetic poles (NRC).
Nonetheless, one of the reasons for the loss of the English fleet off the Scillies in 1707 was that their navigators didn't make allowance for the magnetic variation in the region (7.5d*W at the time)(Gurney 95-6).
Determining a compass' variation requires taking the compass bearing of an object whose true bearing is known:
* Celestial object—The most commonly used celestial objects are Polaris, and the rising or setting Sun. While Polaris is always very close to true North, the Sun moves about, so you need to compute or look up its azimuth for a particular day and time.
* Landmark—If you have an accurate chart, and your ship's position is known, take the bearing of a landmark shown on the chart.
* Place Line—If your position is not known, sail so that two landmarks shown on the chart line up. Preferably, the landmarks are far apart.
An example of calculating magnetic variation was given by Hariot in 1595. The azimuth of sunrise was measured with the meridian compass, the simultaneous solar declination was estimated from successive noon values in the Book of the Sun's Regiment, and that was used as an entry, together with the ship's latitude, into Hariot's "Table of Amplitudes," arriving at the true azimuth of the sun. The variation was the difference between the true and observed azimuths. (Taylor 221).
Determining the variation at a particular location is a bit tricky. Both daily and annual fluctuations occur. At Cheltenham, West Virginia, the westernmost declination is at 2 p.m., and the easternmost at 8 or 9 a.m. If time of year is considered, the range is from 6d*E on a summer morning, to 4.8d*W on an equinoctial afternoon (Sipe 77).
The Chief Pilot of the Portuguese India Fleet, De Castro, made numerous measurements of variation around 1540 and asserted that it could be measured with an accuracy of 0.5d* on smooth water and 2d* when the ship was rolling (Taylor 183).
The first map of magnetic declinations was made by Edmund Halley in 1699. I don't think a copy of that map made it through the RoF, but the 1911EB has a world map showing the magnetic variation (declination) as of 1907. The contour lines connect points at which the variation is the same, that is, so many degrees to the east or west of north.
Unfortunately, the 1907 map is virtually useless in the 1630s (and the same would be true of Halley's), because the magnetic variation changes dramatically over time.
The conventional wisdom in 1600 was that the variation was fixed (as taught by Gilbert in De Magnete). But by the time of the RoF, the down-timers already had collected evidence that Gilbert was mistaken. For example, Borough found that the declination at London in 1580 was 11d*4'E, while in 1622, Gunter said that it was only 6d*13'E. The discrepancy was at first ascribed to experimental errors. Sometime in OTL 1633, Henry Gillebrand began to suspect, based on new observations, that the declination had continued to trend westward, and he became sure of this in midsummer 1634 (and published his findings in 1635). This is explained at length in 1911EB "Magnetism", which offers numerous tables showing the change in declination in different parts of the world.
This "secular change" is just as geographically diverse as magnetic variation itself. Even outside the polar regions, it can be as fast as a 20d* shift in one year.
One silver lining is that, for a specific location, the change is fairly close to constant (Bloxham). Hence, local maps (like the USGS quadrangle maps) can be published which state both the current variation, and the annual rate of change, and they are then useable for a few decades for local compass correction.
The other is that, if archaeomagnetic data is fitted to a standard geomagnetic model (Van Gent; Pickering), it appears that the early seventeenth century might have been a relatively good time to rely on a magnetic compass. Van Gent's 1600 map suggests that for Atlantic voyages between 60d*N and 30d*N, the declination was usually not more than 10d* (the exceptions were between Newfoundland and Greenland, and in the SW Atlantic). Declinations were also less than 10d* in the waters lying in the Australia-SE Asia-Japan triangle.
If you are writing a story and you need to know the magnetic variation in a particular part of the world in the seventeenth century, I suggest taking a look at the tenth order CALS3K model (Pickering) and its successors.
Magnetic Deviation . The errors in magnetic compass bearings which are attributable to the ship and its contents are called deviations. They can vary depending on where the compass is located, and the direction of the ship's heading.
The earth's magnetic field induces transient magnetism in soft iron, and the resulting deviation is greatest when the ship is on an easterly or westerly course. Even in a wooden ship, there are iron items. João de Castro's 1538 observation of variation were "troubled by the proximity of artillery pieces, anchors and other iron." (Gurney 139)
These "soft iron" deviations change as the ship moves north or south (changes magnetic latitude). The force induced in "horizontal iron" (suc
h as a beam) is greatest at the equator, least at the poles. The reverse is true for vertical iron, and its direction reverses when the ship crosses the magnetic equator. Vertical soft iron in early 19C sailing ships included "hanging knees, nails, and bolts in the deck, the capstan spindle, anchor flukes, stanchions, chain plates, belaying pins, rudder stock." (180).
In wooden ships, the deviation is greatest when the ship is on an easterly or westerly course (Walker 67); this is the result of asymmetrical vertical soft iron, forward or aft of the compass (NGIA 13). Bear in mind that the compass is by the helmsman, at the rear of the ship.
Downie, master in HMS Glory, 1790, wrote: "I am convinced that the quantity and vicinity of iron, in most ships, has an effect in attracting the needle . . . the needle will not always point in the same direction, when placed in different parts of a ship . . . [T]wo ships, steering the same course by their respective compasses, will not go exactly parallel to each other yet when their compasses are on board the same ship, they will agree exactly." (Walker 11)
A small amount of iron close to the compass can be as disturbing as a large mass further away. A belt buckle, moved closer than twelve inches, can cause a deviation. So can a ballpoint pen at five inches, or a wristwatch with a metal band a foot away, a knife at two feet, or a metal handle axe at four (Sipe 84-5). With some qualifications, the magnetic field strength is inversely proportional to the cube of the distance (83).
As you might expect, deviation became a greater concern in the nineteenth century when iron hulls were introduced. The deviations experienced on an iron ship can exceed 50d*! (Gurney 189, 200, 217). When the steel is hammered, bent, riveted or welded, the earth's magnetic field imprints it, converting it into a "subpermanent" magnet which records the direction the ship was "headed" when built. (Mixter 60-1).This "semicircular" deviation can be observed on any heading, as it is maximized when the subpermanent dipole is at right angles to the compass needle.
Deviation is measured by "swinging the ship"; placing the ship on each standard heading and comparing the compass bearing to the true one. The known variation (unaffected by heading) is taken into account, and the residual error is the deviation.
There are two basic approaches to dealing with deviation. The 19C British Navy method was to never assume that the compass was correct; rather, routinely swing the ship. The Merchant Marine approach was to judiciously place counter-magnets so as to counterbalance the deviation. This can be tricky, especially until the underlying theory is rediscovered. (Gurney, 255-6; Togholt, 24-5; Williams 131-6). Some correction, at least, is desirable on iron ships, since large deviations can cause the compass needle to become sluggish or erratic.
Magnetic Dip. The first compasses had a needle which could only pivot horizontally. In 1581, Robert Norman discovered that if the needle were permitted to move vertically, it would dip (Walker 9-10). This magnetic "inclination" of the needle varies across the world. The needle will point straight down at the magnetic poles, and is flat at the magnetic equator (a wavy line ranging perhaps 10d* north and south of the true equator). The unreliability of magnetic compasses in the polar regions is a consequence of dip; the magnetic force on the needle is then primarily vertical, and the needle may be more responsive to ship movement than to the tiny horizontal magnetic force.
In 1602, Gilbert and colleagues suggested that dip could be used to determine latitude when the sky was overcast (Taylor 247). This was a forlorn hope; points of equal dip are not uncommonly 20-30d* latitude apart.
Looking at the NOAA 2005 World Magnetic Model, it appears that the lines of equal inclination are fairly shallowly sloped between around 60d*N and 30d*S (except near the Cape of Good Hope), so that if dip were regularly measured along with latitude, it might be possible, in a pinch, to estimate the change in latitude based on the change of dip. However, this probably wouldn't be known to anyone in the 1632 Universe until there was a systematic study of magnetic dip.
Dipping needles are nonetheless useful in correcting the deviation observed when a ship heels over (tilts).
Gyrocompass . A gyroscope is a device designed so that it can spin rapidly, and mounted so that its axis can point in any direction. The axis will continue to point in the spin-up direction unless it is disturbed by an external force. The combinational of the earth's gravitational force, and the centrifugal force imparted by earth's rotation, causes it to precess so it points to true north (and south). Changes in the ship's heading don't change the forces acting on the gyroscope so it will continue to point that way. The principle of the gyroscope was enunciated by Foucault in 1852, and the first gyrocompass was installed by Sperry in 1910 (Mixter 73).
The gyrocompass has the advantage of pointing to True North; it is not subject to magnetic variation or deviation. And a properly adjusted gyrocompass is usually accurate to one degree or better. However, it requires constant electrical power (to keep the gyro spinning), and its accuracy decreases as the ship moves about 75 degrees latitude. (Dutton 171). Of course, the latter problem is also experienced with magnetic compasses, which tend to go haywire in polar regions. I don't know when gyrocompasses will become available.
Altitude and Azimuth
For celestial navigation (see second article), we will need to be able to describe the positions of celestial objects. From the observer's standpoint, the easiest system is to measure the angle between the object and the horizon (altitude) and between the horizontal direction to the object and true north (azimuth). While both altitude and azimuth are needed to completely define the position of an object in the sky, many celestial navigation problems are solved just by use of multiple altitude readings. Azimuth is used mostly for correction of compasses.
Measuring Altitude
To measure altitude, you need a reference, either "down" (established by a plumb line) or "level" (the true horizon). Unfortunately, at sea, plumb lines sway, and horizons are obscured by mist, waves, and spindrift (Callaghan 154).
Down-time Instruments . The down-timers had several devices to use for measuring altitude. The first was the mariner's astrolabe. This had a circular scale, and a radially mounted, rotatable arm (alidade) holding a pointer and a sight at each end. The astrolabe was suspended from a cord so it would be vertical. You eyed the star through the two sights and then read off the altitude from where the pointer crossed the scale. For a sun sight, you let the sun shine through one hole and illuminate the other.
One person steadied it, a second took the sighting, and a third read off the altitude. The larger the astrolabe, the more accurate were its measurements. A seven inch diameter astrolabe might be read to thirty arc-minutes, and a two-footer to ten (Graham). However, large astrolabes were cumbersome to use. Sometimes, the navigator made a landing just so the astrolabe could be used more easily. (Miller)
Then there was the "sea ring." In one version, the sun shone, through a hole, onto a scale engraved on the inner surface. In another, the sun cast a shadow onto the scale. Like the astrolabe, the "sea ring" was a hung device which didn't need a horizon. (Swanick 87-88).
Another device was the simple quadrant, not to be confused with the later Davis quadrant. It was first used at sea in 1461. It was a quarter-circle arc, with sights along one straight edge. A plumb line hung from the vertex. One sailor sighted through the two holes while another read off where the plumb line cross the scale on the rim of the arc. (Williams 35)
According to John Davis (1595), the astrolabe and quadrant were difficult to use on shipboard, except when the sea was calm. (Phillips-Birt 139) You can imagine the astrolabe, or the plumb bob of the quadrant, careening wildly as the ship was buffeted by waves.
By the 1630s, these devices had been largely superseded by the cross-staff (forestaff), consisting of a staff and a sliding transom (the cross-piece).You put your eye at one end of the staff, and slid the transom toward or away from you along the staff, until the top of the transom was aligned with the star and the other end with the horizon. Since you looked somewhat like an a
rcher, this was called shooting the stars. The staff was graduated so you could read off the location of the cross-piece. While the cross-staff could be used by one person, it was awkward to keep both the horizon and the celestial object aligned, simultaneously.
The sixteenth century cross-staff came with three or four cross-pieces, of different lengths. Typically, the staff was about 2.5-3 feet, and the transoms were 15, 10 and 6 inches long. The largest would be used when the star was high in the sky, and the smallest when it was close to the horizon (which would be the case for the North Star when a ship was near the equator). For each, there was a table for converting the location of the transom to the observed angle.
The length of the staff and cross-pieces dictated its region of usefulness; Swanick (76) says that it could only be used to sight objects between twenty and sixty degrees altitude, which would be degrees of latitude in the case of the Polestar. The cross-staff was best used when the altitude was substantially less than sixty degrees, since for higher elevations, the corresponding graduations on the staff were small. (Phillips-Birt 128, 145)
Digges' Prognostications also warned the down-timers that there is a parallax problem with the cross-staff; it would yield the correct altitude only if the eye were at the center of the staff (Taylor 206). Since the staff wasn't transparent, that was impractical, so the user had to make a downward correction to the nominal altitude. Hariot actually calculated the necessary individual correction for Raleigh and certain other English explorers, but on average it was about 1.5d* (Taylor 220).