After the find of a certain projection in Cartometric Analysis I of the 1367 Pizigani chart the next step in cartometric analysis is to look for an optimized projection, the one the portolans probably originally had. A new software was used to find a better fit equirectangular projection and compare it to a Mercator fit. For that purpose a different approach was used than before. In the previous analysis the portolan was zoomed over a modern map and the average difference of the best fit was given in km. Now the outline of a modern map was placed over the portolan and the difference given in mm. That way a subtle error was removed.[1] A new length base for the portolan was chosen and adjusted to allow direct comparison with the results of the previous analysis.[2]
The best result was an equirectangular projection on 34.5° N with 8.393 mm error. That is very close to the 8.404 mm for the 35°[3] previously used. The suspected original 36° projection[4] was by 8.452 mm close too. The error by the medieval compilers was certainly larger than 0.2 mm. So all these projections are in the same error range. Just the Mercator with 9.497 mm looks less likely. The Mediterranean graphic results of Analysis II look much like before in Analysis I.
Besides Cape Sim both projections show an unusually high error near southern France. The suspicion came up that this isolated anomaly was caused by a medieval compilation error. For a check the map was cut at the 50 gon N (45° N) parallel.
The "Main Atlantic" part south of 50 gon N was now a projection on 37.2° with a 4.38 mm error. That is close enough to 36° (which had a 4.40 mm error) to suspect here the same projection on 36° as for the Mediterranean. But even with the same projection the scale is only 83 % of what the Mediterranean had.
A projection of the "Caerte" and "Carta" on c. 50° N did not make sense.[6] It was previously concluded that some (pre 1500) cartographer made a mistake in the projection base or the maps originated from a larger map that went further south. Now this Analysis II of the Pizigani chart proved that speculation to be right. The Pizigani north had the suspected south part of these two northern maps. This find supports the rumors that a Jan Jansz alias de Paep in 1532 published a now lost map collection covering Europe from France (Bretagne) to the Baltic (Gdansk).
It seems the Pizigani was at one stage of transmission created by joining two maps. One was an equirectangular projection on 36° and the other one on 50°. A connection between the Mediterranean centered normal portolans and the 1500s north portolans was already suspected. But to find part of the north portolan in the normal portolan is a surprise. It proves that both portolan traditions go back to two maps. A northern one on 50° N and a southern one on 36° N. These two maps with gon grid need a special chapter below.
Now the cartometric analysis gave evidence for two maps in different projections and scales. These two source maps for the cipher maps had to have a gon grid and were a stage in transmission after the world map and before the cipher map.
The scale accuracy is mainly influenced by medieval compilation errors. An analysis of the 21 Mediterranean 5 by 5 gon sections gave 13 sections with an average scale 6.5 % too large and 7 sections in average 3.9 % too small. One (128.6 %) was excluded. Overall that is a +- 5.6 % average scale error.
Larger parts like the Atlantic are more accurate than the small 5 by 5 gon sections. The 83 % has an estimated error below +-2 %. It probably was originally 83.33 %, because 1/5 or 20 % of 83.33 % added to 83.33 % results in 100 % which was preset for the Mediterranean. The scale of the Mediterranean is therefore 20 % larger than the Atlantic. But the Atlantic scale is not 20 % smaller than the Mediterranean. That would be 80 %, not the 83 % we have.
From this number relation we can fairly conclude the Mediterranean scale is an enlargement of the Atlantic scale - the opposite of what the historians thought for over 100 years. So in hindsight it would have been more useful to set the Atlantic scale to 100 % and the Mediterranean to 120 %. But too late now.
By similar reasoning the 70 % found for the Channel section part, with the 50° projection may be originally rather 66.9 %. This map part is small and therefore may have an error of +- 5 % - almost like the gon sections. By a scale of 66.9 % it had the same scale at 49.5° (55 gon) N as the other Atlantic part had at 36° (40 gon) N.[7]
The southern gon map must at least have covered all that the Pizigani in its accurate parts here had. The northern limit was just south of Ireland.[8] The southern limit are the Canary Islands to 30 gon N. The eastern limit includes the Caspian Sea. The outline of this sea at the Pizigani has close similarities with that of the Atlas Catalan by Cresques (1375) and the more detailed Caspian maps of Atlas Egerton 73 and 2803 of c. 1510.[9] This relation suggests the Caspian was always part of the portolan transmission, and that most portolans without it may just reflect a lack of need - it was not directly reachable by Mediterranean ships.[10]
The western limit probably included the Azores islands. We know their "discovery" was ordered after a map from Italy reached Portugal in 1428. The Pizigani had an island in the Atlantic just at the latitude of the main island. With its distance less than 10 gon from the Canaries it would be unthinkable to leave out this important islands group.
The map we got that way has an unusually wide proportion totally unfit for any parchment sizes or codices. The lack of Ireland strongly points to a limitation in map height. So probably there was another map on the same skin side.
The crucial feature of this map is the projection on 50° N. The scale analysis above suggested the scale at this latitude was probably the same as at the Main Atlantic section of the southern map. That would ease the combined use of the two maps and further explains where the odd 50° section in the southern map came from - it was just copied from the northern map.
If the northern map had the same width on the parchment as the southern, it would reach Hudson Bay in the west. If available there was a rationale to present the whole Hudson Bay.[13]
The map went at least down to 50 gon N, but we have no way to conclude the southern end of the map. But it would be convenient for a navigator to find the northern Azores at 43 gon N there, the others he could find on the more detailed southern map.
That raises the question, why a southern map at all? The northern extended south would offer a greater area of Africa and America than the two map solution offers. But it has to be remembered that the primary purpose of a sea chart is not to offer geographic knowledge but to point the way to ports of trade. In classical and medieval times the main ports of trade were in the Mediterranean. The southern map had two times the area and enough space for the most important port names here. So it seems possible that the names on the portolans date back to the early medieval gon maps.[14]
Close together the maps now cover an area with a 1 : 1.420 side ratio. That is central in the value range of early portolan chart parchments what had a mean value of 1.402.[15]In the west the map would cover the later Norse settlements at Iceland, Greenland, Newfoundland and Vinland. It would extend to the western coast of Hudson Bay and covers 142 gon in longitude. It may be interesting to note that three such maps would cover the whole northern globe with an overlap of 6 % or just over one 5 gon rectangle column each. This suggests the scale size issue could have another reason besides the extension of the southern map.
This northern map - suggested by the cartometric analysis above - gives a hint regarding its maker and to a legendary medieval book cited in a partly burned letter by the great Mercator. See "The Maps of King Arthur?"
