JAIME FERRER, 1495 AND JEAN FERNEL, 1528 PROBLEMATIC SURVEYS AT SEA AND ON LANDINTRODUCTION
This text is divided into three sections explaining the works by Jaime Ferrer and Jean Fernel separately before an evaluation of the spurious surveying and measurements employed by many travellers on the high seas. The first is predicated upon the rivalry between Portugal and Spain in their searches for new land and riches. In an endeavour to regularise the situation Their Majesties of Castile appealed to Pope Alexander VI to set down a line of demarcation between the Portuguese and Spanish spheres of discovery. In the end after three Papal Bulls were issued neither Portugal nor Spain were satisfied and decided to enter into a bilateral treaty agreed in 1494. The treaty had but four clauses;
1) a stripe or straight line from pole to pole 370 leagues west of the Cape Verde Isles. All to the east, north and south would belong to Portugal and everything west to Spain.
2) Neither are to explore in each other’s zones
3) 10 months to establish the meridian between the zones
4) permission for Castilian subjects to cross the Portuguese zone on the way west.
There was an exception that if Columbus before 20th June 1494 should discover any lands beyond the first 250 leagues, they would belong to Spain, and any other east of that point would be reserved for Portugal.
By then, Columbus had sailed to the Indies in 1492/93 and again in September 1493/94 returning in February 1495, hence this was a catch-all addition.
The 370 leagues though caused problems; where was the zero point in the Cape Verde Isles. At first it was from Boa Vista, the central and easternmost isle (at c16N/23W), but was then argued as being from the western most isle, Santo Antao (c17N/25W). Those differences geographically being important on the future coast of Brazil, but were later to be more important on the opposite side if the world when the Spice Islands were being apportioned. But, at no time in any text is the length of the League confirmed with reference to a known measurement taken on land. It can of course be deduced, and is not what is generally known.
THE SECOND LETTER OF JAIME FERRER
Correspondence between Jaime Ferrer and Their Majesties actually comprises three letters; two by Jaime Ferrer and a single response between them which prompted the second which will now be evaluated. They are included as an appendix to this research text.
The basic facts contained in the paragraphs of the response letter by Jaime Ferrer, 1495, with some comments contained within (brackets) included for information only.
1) 370 leagues start from the Islands of Cape Verde (league length not stated)
2) Cape Verde and Isles 15N; 370 leagues = 18 degrees; 1 degree = 20 5/8ths leagues at 15N
(Thus it is possible to evaluate the league, but what league is it?)
3) Sail along a parallel and the Pole Star is always at the same elevation (altura sailing)
4) Sail from Cape Verde Isles on a course 11.25 degrees north of west until the Pole Star elevation reads 18.333 degrees. Then turn south and sail until the Pole Star elevation lowers to 15 degrees and you are precisely 370 leagues west of Cape Verde Isles. (Tan 11.25=20%)
5) —– (problem of marking a line on the ocean)
6) Cape Verde, a quarter wind by 370 leagues at 20% = 74 leagues which is 3.333 degrees latitude. (Nominal ratio is taken from the Tavola de Marteloio, and 15 + 3.333 = 18.333).
7) Each degree has 700 stadia, although Ptolemy says 500 stadia (sleight of hand involved)
8) and 9) are just a methodology which is fraught with the difficulty of involving sailors.
10) Ptolemy, 500 stades/degree; 8 stades/mile = 22500 miles or 5625 leagues for circle
each degree = 15 and 225/360 leagues. i.e. 15 5/8ths leagues
Tropics; 164672 stades, 20584 miles, 5146 leagues
each degree = 14 and 106/360 leagues (14.2944)
Eratosthenes, 252000 stades, 31500 miles, 7875 leagues
tropics = 7204 2/5ths leagues
Rule of Three; 22500 Equator = 7875 (i.e. 7875/22500 = 0.35)
20584 = 7204.4 (i.e. 20584 x 0.35)
therefore, the tropics = 670.5 leagues or 2682 miles less than the Equator.
(Calculating at 700 stades / degree, but 7875 leagues = 20 7/8ths per degree and thus 87.5 Millara per degree. J F has used 20 5/8ths but it could be one of many miscopies. But the league now becomes apparent as Millara not Roman or Italian Miles)
11) Equator = 21 .625 leagues (but 360 x 21.625 = 86. 5 x 360 = 31140 and 87.5 x 360 = 31500)
Tropics = 20 4/360 = 80.044 leagues
(80. 044 x 360 = 2885.84 divided by 4 = 7203.96 i.e. 7204.)
12) Cape Verde, 370 leagues = 18 degrees at 15N therefore a degree at the Equator = 20.625. (But, 370 divided by 18 = 20.555 or 20 5/9ths not 20 5/8ths.)
13) Note. This paragraph is probably the most important of the whole letter and thus it is worth inserting it here-in;
From Cape Verde to the Grand Canary Island are 232 leagues of four miles per league, and it lies from the said Canary on a meridian almost at a third of lebeix or south western quarter, and is distant 15 degrees from the Equator, and the middle island of those which lie in front of Cape Verde lies in the quarter of the west towards northwest 177 leagues (away), which are equal to 5 2/3rds degrees; and from this middle island commences the terminus of the 370 leagues towards the West which terminus is 18 degrees towards the West from the said middle island, and on that parallel each degree is 20.625 leagues, counting 700 stades to a degree, according to the above cited learned men, although Ptolemy uses a different calculation.
Discussion; firstly and unfortunately, a third of Lebeix can be read as meaning 15 degrees west of south or 15 degrees south of South West (Lebeix). But the quarter of West is only 11.25 degrees north of west. Thus the two parts of the diagram illustrate the possibilities and also how the middle island’s position is determined; thus we can indicate that from Cape Verde to Gran Canary it is probably 12.37 degrees and this places Gran Canary at 27.37N which is acceptable for the latitude.
ChWAFD26
However, it is evident that the Leagues are Millara based as can easily be demonstrated.
Thus we have; 75RM = 90 Millara = 720 stades at 8 per millara
Therefore 700 stades = 87.5 millara and 1 League = 21.875 or 21 7/8ths millara
But 117 leagues = 468 millara = 577.044Km or 5.382 degrees at 15N (5.667 by JF)
And, 370 leagues = 1480 millara = 1824.84Km or 17.02 degrees at 15N (18 by JF)
Return to the diagrams and Cape Verde is 62.164 leagues west of Gran Canary which is 248.656 millara or by JF figures 247.5 millara/305.17Km/206.32RM, which is the equivalent of 1.924 degrees at 15N and in fact the two are 2 degrees apart longitudinally.
The alternative when set out from Gran Canary at 30 degrees it actually indicates Boa Vista the central island would be the correct locator for the measurements. It is a Mercator projection plot of the Canary to Verde route on the diagram which geographically confirms the text above.
14) Ptolemy Equator = 15.667 leagues and the Tropics = 14.33 leagues per degree.
(Therefore 370 leagues at 15N = 25.227 degrees {nearly 25.33}).
15.667L = 62.668M = 501.344 stades i.e. 62.5 miles
500 x Cos 23.75 = 457.656 = 14.302
500 x Cos 15 = 482.963 = 15.093 (15.667 x cos15 = 15.133)
Therefore 370 divided by 15.133 = 24.45 degrees.
15) Cape Verde 9.25 degrees north (according to Columbus).
The 180,000 equals 252,000 stades of differing lengths.
It is worth noting that EGR Taylor, page 177 of “The Haven Finding Art”, [3] wrote;
“Such a north/south line appeared, too, on some charts to show how the Pope was considered to have partitioned the world’s discoveries, although a commission summoned to Badajoz in 1524 to plot it precisely had broken up in confusion, for there was no way of fixing it over the ocean. One of the delegates had indeed put forward the idea that it could be done by the Rule of Marteloio. Sail out from the Canaries along a certain quarter of the wind, he said, and by the table you can calculate when you are 370 leagues west, and so find where the line is to run. “And supposing you found it, how could you mark it on the sea?” they replied.”
The problem of Badajoz was amplified by the ideas of other Seamen who specified another distance from Santo Antao, the most westerly of the Cape Verde Isles, as being 22 degrees plus 9 miles. However this led to the Treaty of Saragossa and a further division.
COMMENT
Thus it can be clearly shown that Jaime Ferrer knew of the Portolan Chart measurement of 90 Millara per degree but being typical of his age accepted previous supposedly “great authorities’” statements, in this case Eratosthenes and his 700 stades, but was sorely misled therefore. However as I can indicate later, Columbus used this measurement as part of his League distance at four millara per league.
THE COSMOTHEORIA OF JEAN FRANCOIS FERNEL, 1528
Written by a Frenchman in Medieval Latin, it is not the easiest of translations to make and suffers from expressions that are no doubt colloquial to Paris in the age of Jean Fernel. It is therefore firstly given as written (and also inserted here-in as an appendix), then explained in modern parlance to indicate the measurement of the degree of latitude it purports to establish. I am using a facsimile copy obtained from, Facsimile Publisher, Delhi-110052, India, for the sum of 7 Euros including postage! The original was published as follows;
Excudebat Simon Colinaeus Parisiis Anno Christi, caelorum & siderum conditoris M.D.XXXVII, ad Calendas Februarii.
Thus, published in Paris, 1528, and is headed; Joannis Fernelii ambianatis cosmotheoria, libro duos complexa. Its dedication is as follows; Praepotenti Ac Serenissimo Lusitaniae Regi Joanni Tertio, Joannes Fernelius Ambianas, Saluten.
The first pages are a discussion of the work of Aristotle before the text on page six where we read; Non mediocre sane inter eruditiores viros hac in resubortam novimus discordiam. Eratosthemi siquide philosopho (cuius placita apud Strabonem videre licet) visum est gradui cuique circuli maioris 700 stadia deberi, quae Italica miliaria 87 cum semille essiciunt.
Thus we can immediately understand that Jean Fernel knew of the spurious calculation for a degree of latitude derived from the mixture of the Roman Mile, the Millara and the reduction from a mathematical 720 stades to 700 stades and thus it is nonsense.
Further on that page we read; Ptolemy vero (ut ad minors quantitates seriatim deducar) 500 stadiorum, seu 62 Italicorum milliariorum cum semille, partem unamquanquae stabiliuit.
Calculations indicate that 87.5 millara of 700 stades is 62.5 millara for 500stades.
And lastly; Ob id ergo causae, idipsum experiment comprobans, deprehendi accurate supputatione, cuiquae gradui circuli maioris tam in terrae quam in maris convexo 68 Italica miliaria, passus 95 cum una quarta respondere.Haec autem stadia Romana 544, passus 45 cum una quarta vel exactius cum septemdecim septuagesim issecundis essidiunt. Hanc tandem experientiam (diligent collation peracta) opinionibus Campani, Almaeonis & aliorum proxine accedere dignovi. Cuiuis enim gradui 56 milliaria cum duabus tertiis tribuentes, aiunt milliariu quodquae 4000 cubitis, seu passibus 1200 constare. Milliarioru itaquae 56 cum duabus tertiss quos aiut unico gradui respondere, passus erut 68000, qui per 1000 distrbuti, plane declarat cuilibet gradui 68 milliaria Italica ad amussim deberi: eritquae differentia passuum prope 95.
The data for his 68 Italica + 95 passus follows, and the 544 +45 passus is no more than a reduction of the 700. However the reference to the Arab measurement given by Alfraganus as 56 2/3rds miliaria of 4000 cubits is the measurement carried out under the auspices of Caliph al-Ma’mun. My text ChMEA/1 covers this data and indicates again that the medieval mindset was to accept the “great scholar’s” texts unquestionably, when in fact the actual measurement is 56.25 Arab Miles as I have conclusively proven and was provided by another of the four surveyors of the period.
Page 7 has the following tabulation, but prior to this is the comment that PI is 22/7.
| Cuiuis gradui ambitus terrae | 68 milliaria | 95 ¼ passus |
| Totus terrae & maris ambitus | 14514 milliaria | 285 3/7 passus |
| Terrae diameter | 7800 milliaria | |
| Eiusdem semidiameter, sequentiu balis | 3900 milliaria |
Quo facile lit cuiquae arithmetices officio, cunctas quantitates milliaris & passibus expressas, in cateras mensuras resoluere, tabella supposuimus mensurarum varietate refertam. Granum hordei mensurarum omnium minima;
Digitus grana habet, 4; Palmus digitus conflate, 4; Pes palmos habet, 4:
Cubitus sesquipes est palmus habens, 6; Passus simplex palmos habet, 10;
Passus geometricus pedes habet, 5; Pertica est pedum, 10;
Stadium Italicum passus habet, 125; Milliarium Italicum stadia habet, 8; seu passus, 1000; Milliarium Germanicum habet passus, 4000; Milliarium Sueuicum habet passus, 5000.
Thus armed with the data Jean Fernel has provided we can evaluate the measurement of a degree of latitude he has already noted as being, 68m + 95 ¼ passus.
The complete page discussing the evaluation is appendix 2, copied directly from the facsimile copy already mentioned. It is very legible and should therefore be capable of usage by any researcher interested enough in the whole subject. I caution the translation via a Latin programme as the Medieval Latin is quite different and subject to vagaries in spelling for the same word.
That page is number 9 in the text section of “Cosmotheoria”, and the lines there-in pertinent to this investigation are as follows; 3-11 discuss the diagram of a gallows frame to read off the sun altitude; 11-34 the solar readings for the degree change in latitude and lines 34-45 discuss the measurement method used.
Commencing with the diagram text, the “semidiametros” is 8 feet and thus the CD arm (the scale bar) is 8√2 or 11.314 feet. This is to be subdivided by 90 degree sections each having 60 minute sections for correct reading of the sun’s altitude on any given day. Thus each degree is c1.5 inches and each minute division c0.025 inches or 1/40th inch. Even manufactured to the greatest accuracy in modern terms that is a line every 0.635mm, and when we consider the Ligne of Paris the standard of the age is the 144th part of the Pied du Roi of 324.8mm it is 2.255mm per Ligne, thus requiring 3.5 divisions for the minute distance.
If we now look at the solar information contained in the text, I will freely translate it into common everyday parlance; please note g = gradus/degree and m = minute.
“On the 25th August the sun at the meridian was at g49 m13 elevation and as that day was the 11th day in Virgo the declination was g7 m51 which calculates for latitude g48 m38. On the 26th August at latitude g49 m38 the sun was elevated g47 m51. On the 27th August it was g47 m26; on the 28th August it was g47 m05 and on the 29th August it was g46 m41. He then goes on to say that he had ascertained from local inhabitants he was 25 leagues from Paris. The return journey was used to measure the distance by the revolutions of the carriage wheel which is 20 feet or 4 passuum circumference and it took 17024 revolutions to return to my start point of the 25th August. The total distance for the journey was therefore 68096 passus, equivalent to 68 Italian miles and 96 passus. I have reduced this to 68 Italian Miles and 95 ¼ passus for accuracy.”
If we now look at the details of the Sun’s declination we can determine the units of declination used and thus confirm the daily position of Jean Fernel, north of Paris. He states that on the 25th August, the 11th day of Virgo the declination is g7 m51 or 7.85 degrees. The sun is at 49.2167 and thus we have 90 – 49.2167 = 41.3667 to which we add the declination of 7.85 and the latitude is therefore 48.6333, that is, g48 m38. But we must note that on the following day, 26th August the latitude is given as g49 m38 and he has travelled 25 leagues north. The Roman Degree of latitude is 75RM, and thus it would appear there is a discrepancy of 6 Roman Miles + 904.75 passus, or 6904.75 passus from his 68 + 95 1/4.
But where was he from 27th August to 29th August; the only methodology we have available is to calculate his latitude from declination tables of the age. I am using those produced in 1543, being the nearest I could find in terms of date.
25th August; 49.2167 – 7.4167 = 41.8 and 90 – 41.8 = 48.2 latitude.
26th August; 47.85 – 7.05 = 40.8and 90 – 40.8 = 49.2 latitude.
27th August; 47.433 – 6.6667 = 40.7666 and 90 – 40.7666 = 49.23 latitude.
28th August; 47.083 – 6.30 = 40.7833 and 90 – 40.7833 = 49.2167 latitude.
29th August; 46.6833 – 5.933 = 40.75 and 90 – 40.75 = 49.25 latitude.
Thus it is a simple matter of stating the following scenario; on the 25th August Jean Fernel measured the latitude of his start point in Paris and then moved one degree north such that on the 26th August he was 25 leagues/75 RM north and confirmed the reading. He then sojourned there until 29th August checking his readings and calculating his latitude accurately. After the reading at noon on the 29th August he prepared to depart and probably on the 30th August he returned by carriage to Paris carefully counting the revolutions.
At this point it is necessary to indicate that J Fernel is using the Julian calendar and hence 25th August is his 11th day of Virgo, which in our terms and the Gregorian calendar it would be the 4th September. The rather fraught 11 days lost through the calendar changes brought about by the Papal Bull of 4th October 1582, which although readily accepted by Italy, Portugal and Spain was roundly rejected in many countries of Europe.
Thus we arrive at the distance measure given of 17024 wheel revolutions, which J Fernel equates to 68096 passus or 272384 pedes. There are arguments in the “London, Edinburgh and Dublin Philosophical Magazine and Journal of Science” [4] of 1841, 1842 and 1843 written by Professor De Morgan and Thomas Galloway. A.M., F.R.S, where they explain fully the measurements and arguments put forward by many illustrious persons of the age, including changing the actual measurements given to the Toise.
COMMENT
At this point it is necessary to state that J Fernel is living in the age of Francois 1st of France who reigned from 1515 to 1547 and the following information should have been to hand for all the persons who discussed this Cosmotheoria. I quote, “L.Aune est un mesure de longueur ancienne instauree par l’Edit royal de Francois 1er. Elle se devisa par seize. Mais l’Aune de Paris se voulait de quatres pieds romains exactement.”
Jean Fernel is quite correct therefore in his usage of the Roman Measurements and we can plainly state that unfortunately he was c7RM adrift in measurement on his return journey.
CALENDARS AND ALMANACS
Any evaluation of medieval texts prior to c1600 requires the Julian calendar to be used unless the text dates have been updated by an editor and it is clearly stated as such. We have the evidence for dates from the voyages of C Columbus and thus know that in fact we should revise them all by 11 days to meet the Gregorian calendar and be able to celebrate the actual day not the false date.
But that means when C Columbus gives sun elevations and calculations are made from them we also require using the correct declination tables. The “Manuel de Pilotage a l’usage des pilotes Bretons” par Guillaume Brouscon [5] actually contains three differing declination tables and the first is used here-in to determine the J Fernel latitudes.
| DATE | TABLE 1 | TABLE 2 | TABLE 3 |
| Aug 24th | g7 m51 | g7 m58 | g8 m00 |
| Aug 25th | g7 m28 | g7 m36 | g7 m38 |
| Aug 26th | g7 m06 | g7 m14 | g7 m17 |
| Aug 27th | g6 m43 | g6 m51 | g6 m55 |
| Aug 28th | g6 m19 | g6 m29 | g6 m32 |
| Aug 29th | g5 m57 | g6 m07 | g6 m08 |
| Aug 30th | g5 m34 | g5 m45 | g5 m45 |
There is another slightly different version by G Brouscon in his 1543 Nautical Almanac, now held by the Huntington Library, USA. Thus if declinations were measured on a personal basis at the solstitial dates they could be used as an accurate figure and by interpolation to the day length the others resolved. The problem is of course the observer, is he accurate and how wedded to personal observation, i.e. first principles, and as printed lists were probably not available it was the only methodology, but it is playing with numbers and accuracy is thus at risk.
COLUMBUS AND HIS LATITUDES AND DISTANCE MEASUREMENT
It is worth adding paragraphs here-in dealing with the figures given by Columbus as to latitudes, and his usage of the league based upon the millara. Thus we gain an understanding of his very limited navigational expertise and the measurements of the age.
Firstly his method for establishing the measure of a degree was to compare the ship distance travelled with the altitudes of the sun irrespective of any change of declination. In his Guinea voyage text he records that in the Isles of Los Idolos he found he was only 5 minutes latitude above the Equator (but he states different latitude in his notes as my text ChMEA/1). These isles are c9N and the 5 minutes is the sun’s northerly declination. At Elmina he therefore assumed he was on the Equator when in fact it is at 5.5N and the declination was 5.617 degrees, hence no reading. Off the coast of Cuba he thought he was at 42N when in fact declination was 17 degrees and thus 42-17 = 25N, and is correct.
Therefore it is fair to opine that cartographers using his data were sorely misled as they used his latitudes, but by using the millara the chart measurements would be correct.
But latitudes are generally given by sighting the Pole Star, and as they give a direct reading for latitude they are the normal mariner’s method. If readings are taken from the sun’s altitude then provided tables of declination are used and are accurate the latitude should be known. But if nowadays or it has been calculated by A N Other after 1582 it is likely to be up to 3 degrees adrift because of the calendar change. It could actually be worse than that; if some are using corrected dates and others not, and they did not bother to announce which basis was used on the assumption “That everybody knew”, it is the same as accepting data from 1000 years earlier; i.e. Eratosthenes 700 stadia degree. There is also the small matter of year numbers being mixed up between January 1st and Lady Day (21st March) and the day being from noon not midnight. But Columbus states days normally in his journal.
CAUTIONARY TALE
I have no doubt that many researchers have had reason to access the NOAA website for their device to determine the sun declination, altitude and many other facets of surveying data required to establish locations.
But please note that if you are researching any date prior to October 1582 the dates are given by the Gregorian calendar and must be adjusted to obtain correct declinations and thus latitudes for the Julian. Go to; https://www.esrl.noaa.gov/gmd/grad/solcalc/azel.html
A REASON FOR THE CHIOCE OF 370 LEAGUES
The 1448 Chart of Andrea Bianco [6] contains either an island 1500 miles long to the west or an island that is 1500 miles west of the position shown on the chart, which is approximately 2 degrees west of Cape Vert. (The text on the chart is far from clear.)
Cape Vert is at 17.5 west; then add 2 degrees to the drawn island and 18.25 degrees for the 375 Leagues (1500 miles) and we have a total longitude of 37.75 degrees west.
Jaime Ferrer states, from Cape Vert to the islands are 5.667 degrees; that + 18 degrees to the Line of Demarcation = 23.667 degrees west. Andrea Bianco shows the last land in the west at 20.25 degrees from Cape Vert. But as shown the Jaime Ferrer distances are short by a ratio of 35:36 or 87.5/90, not much really but it all adds to the impossibility of accuracy.
ChWAFD26
The minimum westing from the Treaty is 41W and this can be read as an attempt to ensure that the Ixola Antarticha was solely within the sphere of Portuguese influence and exploration ( should it be proven to exist). It also provides a landfall position on which to mark the Line of Demarcation, as it cannot be established on the ocean. Thus any other land could be determined by sailing either northwards or southerly from this “Island” and all lands to the east are Portuguese and that to the west Spanish. But as the Junta at Bajadoz does not appear to be aware of the possibility, then perhaps the Pope was the better informed.
That is just a thought on the possible reasons for 370 leagues as it does not appear to be a logical distance measure, but it was politics of course, but the distance cannot be marked on the ocean.
THE MILLARA; IT HAD TO BE CAPABLE OF GROUND MEASUREMENT
Since the late 19th century it has been thought that the Millara was 5/6ths of a Roman Mile, and this was determined by observations on Portolan Charts etc. But the sixth part of 5000 pedes is an awkward number and thus it has been deduced as possibly derived from the digitus level of measurement. My texts have always stated that this is not an acceptable basis for the Millara derivation as it is both a mariners and geographer’s measurement. The mariner had to be able to mark off on the ships rail or on a logline, subdivisions such that the distance and speed could be calculated with a degree of accuracy and thus certainty. The Geographer had to be able to measure the distance on land such that the charts being drawn were again as accurate as possible. This means it had to be a finite measurement on land and one capable of constant reproduction in a very simple manner.
But at 5/6ths is it a quantifiable measurement, capable of easy use on board ship or even on land for that matter; I believe it is not one that would be used because of its complexity. The basic figures are as follows: 1 Roman Mile = 1000pm = 5000p = 1.47917662Km given that the Pes = 11.64706 statute inches (nominally 11.65 ins.) and 5/6ths of the Roman Mile is therefore at 1/6th = 833.333 pedes or 246.529m. Thus, 5 x 246.529 metres is 1.232647183Km per Millara, nominally accepted as 1.233KM.
But 5/6ths x 5000p = 4166.667p and if divided into the standard 8 stade subdivisions, each is 520.83p or 154.081 metres, and close to the Eratosthenes’ calculation that can be made. Thus the measurement of 520.833p on board ship by a log is practically impossible as its subdivision becomes a nonsense figure. But we must consider the vagaries of Medieval mathematics and consider if they would have chosen a close alternative to the actual figure, that of 525 pedes which subdivides in either, 21 x 25p; 35 x 15p; 70 x 7.5p; 105 x 5p, all of which are capable of calculation on board ship with no error determined. But none of that is from any information available to us today.
Thus I was convinced the precise 5/6ths division of a Roman Mile was not the actual Millara as known in the 14th century, it was a close figure and sufficed for our use as a check on the charts, but it was certainly not the actual measurement used by mariners/geographers.
LAND MEASUREMENT IN ROMAN TIMES; A POSSIBLE SOLUTION
The land surveying techniques of the Roman Agrimensores or Geometres is well known and documented. It has as its basis a square unit measuring 120 x 120 pedes entitled the Acti Quadrati. This was an important measurement as it could be set out by a simple right angle triangle of 120 x 120 x 170 pedes with no appreciable error. That is because the Pythagorean calculation gives 120 x 120 = 28800 and 170 x 170 = 28900, and hence the hypotenuse should be 169.7056p, or 0.2944p error which in our terms is 3.5 inches in 1980 inches hypotenuse. At the single level it is 288/289 for the calculation, and the spurious one!
If we now consider the handrail on a medieval ship and the fact that it in all probability had length marks carved thereon for the log, how easy it would be for a 6p, a fathom interval, a twentieth part of the AQ to be the norm to gauge the distance travelled or speed of the ship. But of course we now meet the usual problem of non-coordination of measurement as the Roman Mile of 5000p is actually 41.667AQ. This however is easily resolved as other rather awkward measures were by the medieval methodology of manipulation, sleight of hand and substitution of an approximate unit to resolve a difficult calculation. Hence the Roman Mile, originally 1.47911Km and having 5000p or 41.667AQ, morphed into a Roman Mile of 42AQ, 5040p or 1.491Km, a mere 11.81 metres expansion and probably not even noticed by the majority of the population as they were not really involved. Thus 5/6ths of the new unit is so easy to evaluate and use on board ship or land as 5/6ths of 42AQ is 35AQ or 4200p reflecting the original 42AQ Mile, and the Millara was thus born. Simply, 5/6 x 42AQ = 35AQ = 4200p = 1.24251Km and it is a mere 9.86 metres/millara difference which quite frankly is irrelevant in terms of mariners measures and geographers measurements on a chart.
But I think there is also a precedent for the use of the 42AQ or 5040P. In this period and the preceding eras the “Geography of Strabo” and thus “Eratosthenes” was available with its determination of the world size as 252000 stades calculated from the 1/50th part by measurement, which is 5040 stades. As we have seen in the preceding text the 700 stades per degree was considered correct and thus I can opine that the Millara is 5/6ths of 5040p and is thus 4200p or 1.24251Km. But of course that also means that the Millara is 700 fathoms of 6 pedes thus reflecting the 700 stades per degree of latitude given by Eratosthenes. But I now remind you that in Genoa the Miglio Italiano was thought of as 1000 passi or 7000 palmi and they developed the Genoese Marittimo Miglio of 10 stades of 185.2 metres approx. There is a complete logic within the metrological system developed in Genoa in the middle Ages.
Thus speed per hour becomes a simple exercise in fathoms per second. Thus if the logline was marked in 42p or 7 fathom sections, then 1 millara per hour is known after 36 seconds such that the simple calculation is; 3600 ÷ 36 = 100 x 42 = 4200p. Speed is therefore the number of 7 fathom sections travelled in 36 seconds and becomes Millara per Hour.
CONCLUSION
In this day and age we are so absorbed with accuracy that we forget the mindset of medieval persons at our peril. They were not too worried about adjusting measurements or numbers to obtain a simple answer, given the complexity of some calculations, particularly if the numerals are the old Roman system. Thus when we read that tables of declination were mostly calculated individually and had sufficient variation in their construction to alter a latitudinal reading considerably, we should be cautious and perhaps not accept any as read but produce a latitudinal spread within which the actual place being noted is to be found. The length of a degree is another critical measurement which can only be determined on the face of the earth. Thus we know that the oblate spheroid of our globe produces a variation of degree lengths between the Equator and the Pole. The degree of latitude at 0 to 1 degree north does not equal the degree of longitude measured on the Equator. But medieval mariners were convinced of that “truth”. Add to this the variation in the actual measurements purporting to be the same, at least in name, and the recipe for utter confusion is set down. The Roman Mile was a standard of the time, but it had regional variations and thus the small variation I have discussed above and therefore the Millara could be manipulated to suit. Columbus used the Portuguese Geometric League which is 5/6ths of the Portuguese Maritime League and measures c2.67 nautical miles; it is in fact 4 millara and 2.6615 Nautical Miles.
But why a very well educated person such as Jean Fernel should clearly state that the degree had 700 stadia and was 87.5 Italian Miles, yet prove to himself it was closer to 68 Roman Miles and continually interchange the measures is perhaps indicative of the mindset I am indicating. The fact that Jaime Ferrer used it in his letter to Their Majesties when the Millara was so well known is inexplicable. I therefore consider a cautious approach to the subject advisable in future.
REFERENCES
1) Ferrer Jaime, taken from Appendix D of S E Dawson, Society of Canada text on line.
2) Fernel, Jean Francois. Joannis Fernelii ambiantis Cosmotheoria, libros duos complexa.
Published, Parisiis, In aedibus Simonis Colinaei, 1528. Facsimile copy 2017, India.
3) Taylor, EGR. “The Haven Finding Art”, 1956. London, Hollis and Carter
4) Penny Cyclopaedia, available online at www.biodiversitylibrary.org
5) Brouscon, G. text available at, >http://gallica.bnf.fr
6) Bianco Andrea. Biblioteca Ambrosiana F 260 inf (1) & C46, in Cartes Portolanes.
The Woods Hole Oceanographic Institute published in February 1992 a text by Roger A Goldsmith and Philip L Richardson, entitled “Numerical Simulations of Columbus’ Atlantic Crossings”, online ref a260807.pdf and includes most of the details required for an analysis.
My texts, ChMEA/1, ChMES/1 and ChMIL/1 should be read in conjunction with this text to evaluate the whole subject of marine measurements for sailing and portolan charts, as well as the possible latitudinal measurements which could have been obtained by survey methods. They will be found on the Charts abstracts page.
FIRST APPENDIX CONTAINING THE THREE LETTERS OF 1495 TAKEN FROM THE TEXT BY SAMUEL E DAWSON, PUBLISHED IN 1899 AND AVAILABLE ON LINE AT; https://archive.org/details/linesofdemarcati00daws.pdf
SECOND APPENDIX CONTAINS THE ORIGINAL FACSIMILE COPY OF PAGE 9 FROM COSMOTHEORIA, LIBER PRIMUS. It is available online.
THE THIRD APPENDIX IS A DIAGRAM ILLUSTRATING THE TEXT OF JAIME FERRER AND THE DISTANCES DISCUSSED HERE-IN TAKEN FROM MY TEXT ChWAF/1, AS IN FACT IS FIGURE 1 USED HERE-IN.
ChWAFD27
ChWAFD28
ChWAFD29
ChWAFD30
fernel02
ChWAFD19
