### Dead Reckoning In dead reckoning the navigator finds his posit...
There still isn’t a consensus on whether the term "dead reckoning” ...
For most ships in the 16th century, the only available means of kee...
The log line is a mechanism to measure the speed of a ship. The mos...
*Landlubber* - a person unfamiliar with the sea or sailing
The poop (or stern) is the back or aft-most part of a ship. ![ship...
**Portulan charts** are ancient nautical charts (originally from th...
A **rhumb line** is an arc crossing the meridians of longitude at t...
**Bianco’s Table** (or toleta de marteloeo) was essentially a trigo...
This is the diagram the author mentions: ![tondo e quadro](https:/...
Origin of knot as a unit of speed. The knot is equal to one nauti...
Five Centuries of Dead Reckoning
E. G. R. Taylor
term 'dead reckoning', so the
Admiralty Navigation Manual
is a corruption of the old 'cfecf-uced reckoning' or 'position by
account', and is used to cover all positions that are obtained from 'the
course the ship steers and her speed through the water,, and from no
factors.' (The last italics are ours.) Had Master William Borough, Chief
Pilot of the Muscovy Company, and presently to be appointed to Queen
Elizabeth's Navy Board, come across this definition, he would have
picked a two-fold quarrel with their present Lordships at Whitehall. For
his use and explanation of the term is the earliest of which we have
knowledge, although it does not appear even then to have been new.
'And in keeping your dead reckoning', he wrote in 1^80 (having cer-
tainly never heard any nonsense about ded-uced reckoning) 'it is very
necessary that you do note at the end of every four glasses' (i.e. every
half-watch) 'what way the ship has made, by your best proofs to be used,
and how her way hath been through the water considering the sagge of
the sea to leewards, according as you shall find it growen: and also to
note . . . the wind, upon what point you find it then, and of what force
and strength it be, and what sailes you bear'. Borough was addressing
two experienced ship-masters, and for the old-time pilot there was cer-
tainly no quite separate 'estimated position' to be arrived at (according
to the Manual) when the D.R. position is adjusted for the estimated
effects of winds, currents and tidal streams. And the reason for this was
a very good one, namely that the speed of the ship through the water was
itself still a matter of estimate and not of measurement. The log line had
indeed very recently been invented but, as we shall presently see, it was
known only to a few, and even when known was (like all novelties)
viewed by sailors with suspicion. Most English seamen, and all foreign
still determined the ship's way by 'pondering withall what space
she was able to make with such a winde and such direction' as a young
English Jesuit named Stevens put it, when trying to explain to his father
how the Portuguese ship in which he was travelling to Goa in 1579 was
navigated. Landlubbers aboard ship are, of course, a useful source of
information about sea-practice, because they describe all those things
that sailors themselves take for granted, although very likely they mis-
interpret what they see.
Such an observer was the German monk, Felix Faber, who in 1483
went on a pilgrimage to the Holy Land, as a passenger in a three-masted
Mediterranean galley. The pilot was a man skilled in the paths of the sea,
he says, but he had with him other experienced men, astrologers and
augurs (or so Felix imagined them to be) who considered the signs of the
stars and the sky, formed a judgment as to the winds, and so directed the
pilot. All alike were expert in the art of judging from the look of the sky
whether it would be stormy or fair weather, taking into account also the
colour of the sea, the behaviour and movements of dolphins and flying
fish, the way that smoke rose, the lights that played on the masthead at
night, and the scintillations from the oars as they were dipped into the
water. At night, too, they could tell the hour simply by inspection of
the stars. They kept a mariner's compass set always against the mast,
besides another on the poop by which a lantern burned at night; and when
at sea they never took their eyes off the latter; there was always someone
watching it, and from time to time he sang out sweetly and melodiously,
an indication that the voyage was going prosperously, while by this
same song the man at the helm was directed how to steer. Nor did the
helmsman ever move the rudder unless by his order who, up above, was
watching the compass; for it was he who discerned whether the ship
was proceeding in a straight line, on a curve or sideways. This last is not
a very seaman-like way of stating what went on, but we understand what
Brother Felix meant. And he continues with the information that besides
the 'Stella Maris' as they called the mariner's needle, naming it from
the star toward which it turned, they had other aids or instruments by
which to judge the courses of the stars and the blowing of the wind,
whereby they picked out those narrow paths of the sea
timae) which must be followed. These aids, no doubt, were a useful
supplement to the astrologers and soothsayers (if such they were, and
not just the master's mate and the bo's'un), for they included a chart
carrying a scale and criss-crossed with
thousands and thousands' of lines
(as it seemed to the landsman)—in fact a Mediterranean plain chart or
portulan, on which were painted sixteen or more wind-roses, with the
rhumb lines ruled out in different colours. Every day (says the Brother)
the pilot and his assistants hung over this chart, conferring together, for
from it they could tell where they were, even when no land was
visible, and clouds hid the stars, and from it, too, they learned what course
to follow, from point to point along the 'lines'. Such in short was
navigation by dead reckoning in 1483 as observed by a tyro awed and
mystified, as all plain men then were, by the pilot's boast that he could
set course for an unseen destination, and avoid hidden dangers 'without
sight of sun, moon, or stars', helped only by a compass no broader than
the palm of his hand and a piece of painted parchment.
But to set a course was not to follow that course. The galley could not
sail close to the wind, but must tack to and fro, or 'traverse' as it was
then called, so that it was necessary to keep a traverse board or traverse
book in the steerage, and the course made good had to be worked out
from this each day and entered in the Journal. This meant that something
in the nature of
traverse table was required, and in fact a far-off ancestor
of Inman's tables, going back more than five hundred years, has survived
in the sailing directions which form part of Andrea Bianco's Atlas of
And the mention of a similar table in a Genoese inventory of
1390 carries the date back farther still. Nor need such a table have even
then been a novelty, for the properties of the right-angled triangle, and
in particular the fact that the ratios which we term the sine, cosine and
tangent of any angle were constant no matter what the dimensions of the
triangle, had been familiar since the propositions of Euclid were once
more studied in the twelfth century. Bianco's table or
Toleta de
as it was termed, is a graphically determined set of
for the northing
(southing) and easting (westing) corresponding to a run of fixed length
(100 miles) along each of the eight quarters, points, or rhumbs of the
wind, from n\°, 22^°, 33J
, &c, up to 90
, which makes up a quadrant
of the compass. As the charts of those days were ruled in rhumbs and
showed no latitudes (which were not then observed in navigation) the
term 'd. lat.' does not appear, the columns being headed
According to the Toleta a ship sailing 100 miles along the sixth point
from North (67J
), for example, would make 92 miles easting and 38
miles northing, and so for other distances in proportion, which could be
worked out by proportion, using the Rule of Three or Golden Rule.
Even simple arithmetic was however a stumbling block to the majority,
and Bianco's Atlas also contains a scheme or diagram, constructed on
the principle of the sinical quadrant, from which a graphical solution of
the traverse could be obtained. The basis of the diagram was a large
square accurately subdivided into eight rows of eight small squares. From
the top left-hand corner were drawn the sixteen half-points and points
(beginning at
in a quadrant. The whole was surrounded by a circle
showing the principal points of the compass. To indicate how the
diagram was to be used, a naked cherub runs along the top of the large
square, stepping off distances with a pair of dividers nearly as tall as
and opened to the width of a small square. Presumably the
diagram was intended to be drawn to the same scale as the chart and any
distance pricked off on the one could then be transferred to the other.
The northing and easting were, of course, measured directly from the
'scheme' and no arithmetic was required. With the Great Age of
Discovery, initiated by the Portuguese, long ocean voyages were begun
which required observations of latitude to check the D.R. position, and
latitudes began to be marked in the margin of the portulan chart.
Corresponding tables were eventually prepared by the Jewish mathe-
maticians responsible for working out new navigational methods, among
them the
which set out the distances to be sailed along
each rhumb in order to raise or depress the pole one degree, together
with the corresponding easting or westing (departure). The degree of
the meridian was taken as 17^ leagues of 4 miles, and as an example we
can extract the following figures from the table as set out in the oldest
surviving Portuguese navigating manual: 'Item per 6 quartas releva per
grao 46 legoas e mea, at afastaras da lynha direyta 42 legoas per grao et
* It is reproduced in Fontoura da Costa's A