My question refers to Gottfried Leibniz's "instrumentum longuitidimum" mentioned in some sites — a device that could record the course of a ship in sea and display its recent position directly on a map. I ask this because this statement inspired me to invent a mechanical device that is able to do so, and i'm very curius if this device was known to Leibniz.

The device which came to my mind is based on naval odometer with two gears as its output. One gear is attached to and rotates a cylinder which represents a map of earth, and the other is connected through a complicated mechanism to a compass and a screw. The compass is attached to a kind of leibniz cylinder which is itself attached to a kind of screw which rotates and moved verticaly as a result of its rotation. The detailed structure of the device is hard to tell, but it functions as a kind of "seismograph" — when the compass needle is perpendicular to the ship body (i.e its lattitude remains unchanged), only the map cylinder rotates, otherwise both the map cylinder and the screw rotate. In this way when the ship moves north or south the route recorded on the cylinder map goes up and down, correspondly.

So the point here wasn't only to get compliment for the device - but to know if it's already known. So is there already such mechanical device? was this device known to Leibniz?

  • $\begingroup$ Could you please name the sites, or other sources, that mention this device. $\endgroup$
    – Conifold
    Jan 13, 2017 at 23:23
  • $\begingroup$ This book mentions Leibniz's "instrumentum longuitidimum" - books.google.co.il/…. $\endgroup$
    – user2554
    Jan 14, 2017 at 13:56
  • $\begingroup$ The book you refer to gives a reference to the Complete works of Leibniz. If someone who is interested can read German... $\endgroup$ Jan 15, 2017 at 8:30

2 Answers 2


Leibniz bragged as early as 1671 about solving the problem of longitude, among a long list of other major problems, with the help of his "combinatory art" At the time he was euphoric about the sweeping capabilities of his "characteristica universalis" to solve any intellectual problems. Unfortunately, his letter does not give many details:

"I will demonstrate how to find longitudes completely, and provide a way for a person on a ship to know what his location is without the help of the sun, moon and stars which can not always be observed (yet Huygens's famous invention depends on them alone)". [quoted from Leibniz and the Kabbalah by Coudert, p. 154]

He published one solution in the Journal des Scavans in 1675, it was based on a clockwork with a new escapement mechanism. It is described, and pictured, in Matthews's Time for Science Education, p.170:

"He proposed using two balances and two spiral springs. Each spring was wound in tum by the train and then allowed to run down freely, controlled only by the inertia of the balance, the other spring being meanwhile wound. When the first spring had run down, it unlocked the second and so the cycle was to be repeated. He was oblivious to the fact, well known to Hooke, that as the spring unwound its motive power decreased."

The clockwork idea for the measurement of longitude was of course suggested already by Huygens. Leibniz's own comments show that he was a big idea man, and not a good fit for the problem of longitude which was largely practical.

"all these defects, that proceed from the imperfection of the matter, may be surmounted by a general remedy, without examining them here in particular. And that is, that for executing it in great, we may make use of massy springs, as are those of cross-bows, we being the masters of them, not wanting force or place in a ship to govern a great weight that may serve to bend them continually again... And it is easy to demonstrate, that by augmenting the size of the engine, and the force of the massy springs, we may make the error as small as we please..."

"It is easy to demonstrate" will have a long life in mathematical literature, and as Hooke put it on another occasion "as a clockmaker, Leibniz made a great mathematician."

Later Leibniz did get involved with something more perhaps in the spirit of the OP, but as usual with practical matters he did not pursue it too far. It was longitude measurement based on measuring magnetic inclination. In 1676 a British instrument maker and teacher of mathematics Henry Bond had claimed that magnetic inclinators can be used for measuring longitude. The Royal Society got interested, and Oldenbourg, its secretary, sent a copy of Bond’s book to Leibniz:

"As Leibniz explained, magnets were also “inclined toward the horizon,” and since these inclinations were also inconsistent when measured in a single location over time, it made sense to study this phenomenon too. Yet this required the use of a different kind of instrument, an “Instrumentum inclinatorium,” Leibniz wrote, “so that Inclinati Magnetis, which is different from declination, could be observed.”" [from Halle Orphanage as Scientific Community by Whitmer]

But it is possible that "instrumentum longitudinum" mentioned in Kempe's book, that "could record the course of a ship and automatically transmit these records to the map", was yet another of Leibniz's big ideas from 1700s. Indeed it sounds like an automated version of the oldest method in history, the dead reckoning, still in use until Harrison finally solved the problem of longitude with his marine chronometer in 1730s.


It is an interesting question what Leibniz proposed, but I suppose his proposal was not practical: it is not mentioned in the histories of navigation, which probably means that it was never implemented.

Your proposal is also not practical for many reasons. Determination of ship's position by tracking the speed and direction was a principal method of navigation even when astronomical methods became available. It has a strange name in English: "dead reckoning". It is very simply done by hand; you just plot the course and distance traveled on a map and obtain your position. The speed was measured with a log, as frequently as necessary, or in Leibniz times, it was just estimated by eye. The time was measured by hourglass and the course by magnetic compass corrected for deviation.

This method is not very accurate because it does not take into account currents, and drift, and because the usual ship logs do not measure the speed very accurately. (There is no such thing as "ship odometer". Odometer is used on wheeled vehicles). Mechanization of the procedure which you propose requires a complicated mechanical device which will only introduce additional errors and have no real advantages. A person has to stand on watch all the time anyway, and it is not difficult for this person to record the speed and course. Computation and plotting is a trivial procedure.

  • $\begingroup$ The problem of sea currents really renders it impractical to measure distance by naval odometer (who works well only in a static sea), but i still think that in a static sea the device i described can work well. I'm curius if Leibniz thought of it since it employs a kind of "Leibnz's wheel" with teeth that vary in length according to a sinusoidal pattern. Such a wheel can create the effect of multiplying the odometer speed output with the sinus of angle between ship body and compass needle direction. $\endgroup$
    – user2554
    Jan 14, 2017 at 14:04
  • $\begingroup$ Since a kind of Leibniz's wheel is neccesary for such a device, it's no wonder Leibniz might have invented such a device (himself the originator of "Leibniz's wheel"). My only question is whether or not he invented this? and where is it in his writings? i'm aware that this device has no practical uses, but it's interesting as an intellectual exercise. And by the way, it can be used to record the course of a carriage in land and display it's recent position directly on a map. $\endgroup$
    – user2554
    Jan 14, 2017 at 14:09
  • $\begingroup$ @user2554: I totally agree that it is curious to know what Leibniz proposed, and I hope someone will find out and answer. Myself, I do not know, so consider my "answer" as an extended comment. $\endgroup$ Jan 14, 2017 at 19:51

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