Tasman’s navigation: Part 1

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Gerritsz world map

Gerritsz world map, 1616 (click to enlarge)

Abel Tasman was travelling at a time when the Earth was properly understood to be a globe, and there was a standard method used to represent any position on the globe.

latitude and longitude

Lines of latitude and longitude

‘Longitude’, or how far east or west around the globe you were, was measured in degrees around a circle located on the equator. Lines of equal longitude continued directly north-south, to the poles. At the time Abel Tasman was voyaging, the Dutch convention was that all longitude was measured as East or West of the Peak of Tenerife. The Greenwich ‘meridian’, the line of 0° Longitude, wouldn’t be universally adopted until 1884.

Similarly, how far north or south you were, ‘Latitude’, was measured in degrees north or south of the equator, relative to the centre of the Earth.

This measurement system allowed any position on the globe to be represented unambiguously by the pair of numbers describing its latitude and longitude.

However, being able to accurately represent a location on the globe is quite different to working out the latitude and longitude of your current position… and Abel Tasman had only rudimentary methods for deriving this.

Tasman’s journal records his latitude and longitude, as well as his course directions, and bearings to visible features. In order to successfully interpret Tasman’s journal and charts it is important to understand just what he is measuring and recording.

COMPASS DIRECTIONS

Tasman reports course directions, and directions to land features using a 32 point compass. Most people are familiar with 16 point compass notation, but Tasman’s compass has a subdivision between each of those divisions with the additional direction indication ‘by’. The pattern of the compass used by Tasman is shown below.

lat and lon

Abel Tasman’s compass

His compass was a large and crude looking instrument suspended in a shape rather like a hanging flower basket. Inside that housing, the ‘card’ carrying the magnetic needle, was balanced on a needle. The top was sealed over with glass to keep it watertight.

Mounted around the top was a cross bar with sights on each end. These sights were used for lining up land features and also for getting accurate bearings of the sunrise and sunset positions.

All readings from a compass contain a discrepancy known as ‘variation’ which must be corrected. The ‘north seeking pole’ of the compass does not actually point quite to the true north.

The Earth’s magnetism is caused by the spinning ball of molten iron in the Earth’s core. The axis of that magnetic field is not perfectly in line with the axis that the Earth rotates around. The angular difference between the ‘true north’ position, and ‘magnetic north’ is called the ‘variation’. To compound matters, variation differs as you move around the globe, and different rock conditions cause local changes in the variation angle, as Tasman noted on Nov 22nd 1642;

‘we found that our compasses were not so steady as they should be, and supposed that possibly there might be mines of loadstone about here, our compasses sometimes varying 8 points from one moment to another’

To determine precisely where ‘true north’ was in comparison to his compass, Tasman used the sun. He measured the bearing of the rising sun, and that of the setting sun. True north lies directly between these positions (in the Southern hemisphere the sun still rises in the east and sets in the west, but it progresses there via the north). His variation on that day was the difference between what his sunrise/sunset bearings reported as north, and what his compass showed.

Tasman’s journal records all bearings as ‘true’ not ‘magnetic’; he had already made the correction for variation as he wrote his journal. On days that he was able to see the sunrise and sunset he also recorded the variation.

LATITUDE

How far north or south you are can be worked out from the knowing maximum height of the midday sun.

At the equator the midday sun is overhead, but at the poles it is only on the horizon. The further you move from the equator, the lower the angle of the midday sun. The angle it deviates from straight overhead is the angle you are away from the equator.

This is almost the correct answer, but like variation there’s another little twist. The Earth’s axis of spin isn’t quite upright in relation to its orbit around the sun. This is what causes summer and winter, and at any location on the globe, the midday sun is higher in summer than it is in winter.

There is a special correction chart for this, and Tasman carried one. It is a table showing the height angle, or ‘inclination’ of the midday sun at the equator for each day of the year. By comparing your measured midday inclination to the inclination at the equator for that day, you can derive your latitude.

As long as Tasman knew what day it was, and could measure the inclination of the midday sun, then he could work out his latitude.

Cross staff

Cross staff

In the fourteenth century Astronomers developed an instrument that did exactly this, and it quickly became an essential mariner’s tool. It was called a ‘cross staff’ among other names, and was a simple but remarkably effective device.

The cross staff had a long straight shaft, with another sliding bar mounted perpendicular to it in a way that allowed it to move up and down, like a trombone.

To use it you rested the end of the shaft on your cheek under your eye. You the slid the crossbar up and down, and raised the long bar until one tip of the crossbar was on the horizon, and the other tip on the sun.

The long bar of the cross staff was graduated with measurement marks. The position of the crossbar along the long shaft indicated the height of the sun in degrees above the horizon. Starting just before noon you measured the height of the sun, and kept measuring the inclination until it passed its peak. The highest angle recorded was the noon inclination.

It was a crude device, but it worked surprisingly well. Christopher Columbus used one of these to cross the Atlantic and return to the same Island in the Caribbean three times.

Tasman however, probably did not use one of these.

The cross staff was simple but using it had two major difficulties. You had to look at two places simultaneously; the horizon and the sun, and any movement of the long shaft as you did this introduced an error. The other issue was a practical one… you had to look directly at the sun.

Tasman’s journal records latitude to the minute. You can’t reliably make a measurement to the nearest minute of a degree with a cross staff, it’s simply too crude.

Hoekboog

Hoekboog, or back-staff

Willem Jansz Blaeu was a famous map maker. He prepared maps for the VOC as a contractor and was a close friend of Hessel Gerritsz. In 1625 he published this illustration of a ‘Hoekboog’, or ‘angle bow’. This was a more accurate instrument that overcame the issues of the cross staff. It had been in use by the Dutch since at least 1623.

With the Hoekboog you stood looking at the horizon with your back to the sun (hence the English name for this type of instrument, the ‘back-staff’).

The eyepiece ‘F’ slides up and down, on a graduated bar ‘D’. You look through the eyepiece at the flat plate ‘A’. This has a notch cut in it, which you look through and line up with the horizon. The piece ‘G’ has a sharp edge on it and casts a shadow from the sun behind onto plate ‘A’. By adjusting the eyepiece up and down the suns shadow is made to line up with the horizon. Then the ‘inclination’ angle is read off the graduated bar ‘D’.

In his journal Tasman recorded his daily latitude and this was remarkably accurate. The latitude he recorded for Cape Foulwind is only wrong by 8km. From his deck, an observer could see a 100m high cliff from 40km away.

The cross staff and the Hoekboog were both accurate enough to have the error in measured latitude smaller than the distance that you could see. They were accurate to get you within sight of your objective.

There was no similar instrument for measuring Longitude. Whilst mariners could reliably know how far north or south they were, they could not confidently asses their position east-west.

It was because of this that the common practice for travelling long distances across the open ocean (where there are no physical features to tell you where you are) was to sail ‘lines of latitude’.

On a long journey on the featureless ocean, mariners would manoeuvre themselves to the same latitude as their destination, and then hold their course on that latitude until their objective came into sight. Tasman’s journal shows that this is precisely what he did on his journey to the Mauritius.

Aug 17th.

‘it was resolved that from Sunda Strait we shall sail 200 miles to the south-west by west, as far as 14° South Latitude; from there to the west-south-west as far as 20° South Latitude, and from there due west as far as the island of Mauritius.’

Mauritius lies in the latitude 20°S, and Tasman could measure his latitude accurately enough to be within sight of features at a given latitude. So he moved to the latitude of the Mauritius, and continued on until his destination came into view.

He was able to confirm that he had reached his destination by consulting his collection of coastal surveyings. These were drawings showing what the coast looked like at specific places. If you were trying to find a given place, and were in the correct latitude, then when you saw land you compared it to what you saw in the drawing. If it was the same, then you had arrived.

COASTAL SURVEYS
On Tasman’s voyage they were expected to meet new lands, and in order to enable other mariners to find these places in the future they drew outlines of the coasts that they saw.

All VOC vessels had a ‘Merchant’ on board; the person in charge of buying goods to trade. On Tasman’s voyage, the Merchant was carefully chosen for his additional skills. They appointed… ‘Jsaack Gilsemans, who is sufficiently versed in navigation and the drawing-up of land-surveyings’.

The illustrations in Abel Tasman’s journal were drawn by Isaac Gilsemans, from the deck of the Zeehaen… and these illustrations included coastal surveyings.

When they discovered new land in the Southern Ocean they named it ‘Anytony van Diemens Landt’ after the Governor of Batavia. Gilsemans recorded the outline of this land so that subsequent mariners could correctly identify the location.

When you have reached the West Coast of Tasmania, at the Latitude of 42° 30′ you will see this.

Tasmania coastal survey

Tasmanian coastal drawing by Isaac Gilsemans

The captions read:
A view of the coast when you are 5 myles from it.
A view of the coast when you are 2 myles from it.
A view of Anthonij van Diemens Landt, when you come from the west, and are in 42½ S. Latitude.

Without knowledge of longitude, coastal surveys were an essential part of navigation. When a mariner had located land at the specified latitude he could verify his position by comparing what he could see, with the coastal survey. If he saw the same in the drawing that he saw from the deck, then he knew precisely where he was… and he could then correct his longitude accordingly.

As Abel Tasman approached Mauritius his reported longitude was in error by 670 km, but it was nearly correct when he left. The Dutch navigators used the coastal surveyings to re-set their longitude.

Tasman had no instrument for measuring longitude, yet for his noon position he reported both latitude AND longitude. So how was this done?

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