1669 - Measurement of the Earth and of the Distances at Sea

Jean Picard, a priest, an astronomer and a geodesist, aged 49, has measured an arc of meridian between Paris and Amiens, hence the radius and the circumference of the earth by extrapolation.

He is a pupil of Astronomer Pierre Gassendi (†1655), who was also a priest and a philosopher, and as of 1623 a promoter of heliocentricism, ten years before the sentence against Galileo Galilei (†1642). Picard is also one of the 21 first members of the Académie Royale des Sciences founded in 1666.

Colbert Presenting in 1667 the Members of the Académie Royale des Sciences to King Louis XIV

¤ Jean Picard is the humble 6th person from the left while famous Astronomer Jean-Dominique Cassini is the pompous bewigged 8th who dares to show a little boredom. It nevertheless seems that Cassini has just come in France to join the Académie this year, that is two years after the depicted ceremony. Christiaan Huygens, scientific director of the Académie, is the 9th from the left, just beside Cassini. In contrast with most of the attendants in awe, he weirdly stares at Cassini. Those two are the most eminent members of the Académie today. Jean-Baptiste Colbert, who is a member of the Académie as well as its practical patron, stands in the middle in an austere black suit. He introduces the scholars to the king. Testelin seems to have detected and portrayed a human comedy in this scenery under the disguise of a formal ceremony and in the guise of a vivid capture.

The mariners of the high seas should be especially interested in this measure as they roam over the immensity of our planet without knowing the distance they sail over. Yet they need a measure of the distance they have sailed to determine their longitude. At sea, there is no equivalent of a two-week walk or of a four-day ride, even in cabotage. A travel lasts what wind, current, swell and waves permit. There is no direct apprehension of distance once coast recedes and disappears.

Each minute out of the 21,600 ones (360° x 60’) which are swept by a whole meridian has been considered by geographers as a ‘mile’ after Nicolaus Germanus (†1490) who updated the works of Claudius Ptolemy (†168). But what sort of mile ? Germanus’ mile was a short one, as he dwarfed the earth by a third. That view was shared by contemporary Cartographer Paolo Toscanelli (†1482) so, relying on the latter, by Christopher Columbus (†1506). We know the consequence: heading West for India, supposed to be closer by a third of the circumference of the Earth, the navigator had to call for fresh water at an island of an unexpected New World which blocked his route to the west.

¤ It was an island of the Bahama archipelago that he named San Salvador, and Indios its inhabitants. From Toscanelli, he expected to reach Cipango – Japan by now – or Cathay – China by now – which were then seen as the Eastern outposts of mythic Indies.

Anyway, the Renaissance’s mariners ignored this scholar mile and carried on using their good old forefathers’ leagues, each one different from one another. This is William Bourne (†1582), author of the famous navigation manual A Regiment for the Sea (1574), who reconciled the old land 5,000-foot English mile with the geographers’ mile by equalling it at a minute of latitude. It was false but so appealing to common sense by its marvellous coincidence that this fictional geographical mile was popular with the British mariners and has even survived until today in coasting trade.

¤ For his Regiment for the Sea, Bourne copied and updated Arte de Navigar (1551), masterpiece of Martín Cortés de Albacar (†1582).

Truly unselfish, a complete scientist, Picard gave a decisive hand to Philippe de La Hire’s revised cartography of France. La Hire was 29 then. The scope of their correction is amazing : Brittany and Gascony move Eastward by several tens of leagues. We may guess that a few seafarers in Brest, La Rochelle or Bordeaux had beforehand noticed that something did not match between charts and real shorelines.

On purpose, Picard has invented a new instrument by combining a telescope and a micrometer, with which he carried out his measurement within a pattern of thirteen triangles along the meridian of Paris which passes by Amiens. He has assessed the minute of a meridian arc at 6,072 British feet, as measured by this method of triangulation by 49° of latitude over a distance of 70,000 toises.

¤ The toise is six-foot long and corresponds to the English fathom which is equally six-foot long but the French foot is larger than the English one by a 15th.

Willebrord Snel van Royen (†1626), better known as Snellius, was the first to use triangulation to measure a meridian arc. It was between Alkmaar and Berg-op-Zoom, some thirty leagues away without any relief between the towns. Triangulation consists of defining landmarks visible from one another all along the meridian, so as to enmesh it within a collection of triangles measurable by a side and angles. Afterwards, one has to work out, through trigonometry, segments of meridian from the triangles. It seems that mathematician Edmund Gunter (†1626), famous amongst other inventions for his primitive sliderule for the purpose of navigation, inferred from that Snellius’ measurement that the minute of arc, or geographical mile, would equal 5,887 feet.

Any new scholar mile, Snellius’ one in its days, or Picard’s now, has never be used by the mariners who nevertheless came to consider lately that an appropriate sea mile – this term does not exist but the notion has surfaced as high seas travels multiply – would differ from the land mile and extend to 6,000 feet or so, by comparing dead reckoning course and real one and bringing out a difference of a fifth on average.

log or loch

The mariners have adjusted the chip log – or loch – accordingly. As everybody knows, the log is meant to measuring ship speed. It consists of a wooden board attached to a line on which knots have been made at regular intervals. One does the measurement when the ship is steady on a course. One drops the board in the sea as a fixed point and lets the line run as the ship sails straight while a sand glass gives the timing. The length of the line cleared off board, that is the number of knots, indicates ship speed in miles per hour.

For Bourne, and for his followers until today, a chip log displays knots every seven fathoms, that is 42 feet, for a 30-second sand glass – which gives a mile of 5,040 feet an hour. Today, the mariners of high seas have come to a knot every eight fathoms, that is 48 feet, and a theoretical 28.8-second sand glass – which gives a mile of 6,000 feet an hour – but which is practically a 28-second one, which overestimates speed to 6,170 feet an hour.

This speed is necessary to work out the distance sailed by the ship and, from that distance, the longitude.

The mile and the knot are still fuzzy notions, depending on the instruments one has got, on the measures used at one’s birthplace, and on one’s feeling. The scholars envision to give it a universal value but we may bet that it will take some time.

¤ It is worth noticing that the newly appointed professor of mathematics at Cambridge, a position which encompasses geography teaching, Isaac Newton, 26 years old only but already noticed, has adopted Picard’s measure for the earth in his own reflections and lessons. }

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IN RETROSPECT FROM TODAY

NOTE A - On the chart of France revised by La Hire & Picard.

The differences are huge as we can see on this overlay of charts.

Chart of France before (light line) and after La Hire's work

NOTE B - About quality of Picard’s measurement.

He developed specific instruments for this purpose from telescopes and micrometers to improve shooting precision by a factor 25.

In 1669 nobody knows yet, of course, that Picard’s measurement is very accurate as a mean value: 6,072 feet for a today value at 6,076. Isaac Newton will be faithful to Picard’s measure as a reference for his own works.

NOTE C - About mile variations.

Also nobody knows for sure that a minute of arc has slightly different values depending on latitude but it was in the air for a very few enlightened minds. Cassini, for instance, came to the assumption that the earth could be no spheroid because he could observe in 1666 that Jupiter was an ellipsoid.  

In 1672, a Picard’s close colleague, a member of the Académie des Sciences too, Jean Richer, aged 42 then, will observe a variation of the beat of a pendulum when transported from Paris to Cayenne. He correctly infers that it results from a change in gravity due to latitude which indicates that the earth is flattened at the poles and inflated at the equator. He has to shorten the length of the pendulum to re-tune it accordingly. (As everyone knows after Huygens, the period of a pendulum is proportional to the square root of its length.)

NOTE D - On the aftermath of Picard’s measurement.

The measure of the arc of meridian will be expanded from Paris to Collioure and from Amiens to Dunkirk in the late 1670s. It happens that the data delivered to Cassini have a bias which makes him think that the earth is an ellipsoid but flattened at the equator, despite contradictory Richer’s observation.  It will become a mania by the Cassinis, Gian Domenico then his son Jacques, to argue this view against the entire world…

No doubt that Cassini was a great astronomer. Two examples out of tens: (1) he had the intuition of the trajectory of the comets, which he transmitted to Edmund Halley with the result that everybody knows about Halley’s comet prediction; (2) he worked out the distance from the Sun to the Earth. A mastermind, he also proved to be stubborn, alas.

In 1687 Newton will demonstrate by reasoning that the earth is an ellipsoid flattened at the poles and give it an order of magnitude at 1/230. It will be proved and precisely metered at 1/300 by an overall experience performed by three teams carrying out measures through three expeditions (1735-43) at the equator, at the north of Scandinavia and in France, which involves the fine flower of French scholars : Maupertuis, Clairaut, Camus, Le Monnier, La Caille, Godin, Bouguer, La Condamine, Jussieu. The quest for the proof empties the Académie des Sciences…

NOTE E - On the nautical mile.

It will progressively surface during the next century as a basic notion as the real dimension of the earth will emerge from mist. In 1669 Picard is already very close but the average human mindset, still extremely far. A nautical mile based on Picard will remain theoretical until it will have slowly and discreetly become commonplace.

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SUGGESTED BIBLIOGRAPHY

William Bourne – A Regiment for the Sea – London, 1574 - available on the Internet but not very digestible

Bill Bryson – A Short History of Nearly Everything – London, 2003

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CREDIT

Henri Testelin – Colbert présente au Roi les Membres de l’Académie Royale des Sciences – Oil on Carton © Musée des châteaux de Versailles et du Trianon