In state 2 of Doppelmayr's map there are four additional entries: Leodium (Liege) in Belgium. Cadiz. Petropolis (now Leningrad) and Tornio in Finland. The name of Joseph Delisle appears against the entry for Petropolis. and name Maupertuis'  against that for Tornio where in 1736-37 he led an expedition to determine the exact length of a degree of arc on the polar circle, and hence to resolve the long-standing controversy as to whether the earth was flattened or stretched at the poles.[4]




As can be seen from Table I, the errors in the calculations for latitude are generally very small. but with one exception. This is for the island of Guadeloupe which was visited by the French scientists Varin and Des Hayes in 1682 as part of a most thoroughly planned expedition. The latitude of Guadeloupe is recorded by Doppelmayr as 14° 00' 00", compared to the actual position of its capital. Pointe a Pitre, of 16° 14' 00"; an error of over two degrees. This is such an exceptional difference compared to the next largest error in the table (Olinda. Brazil) of only 21' 30" that raises the question whether perhaps there was some confusion with SI. Lucia (Castries) which has almost exactly the same latitude as that recorded on Doppelmayr's map for Guadeloupe. 

To translate Doppelmayr's records of longitude into modeni terms two straight-forward adjustments need to be made.  First, because Doppelmayr was using as his zero meridian the classical base of the Isle of Fero (now the Isla de Hierro) in the Canaries, all his 10ngitudes need to be related to those which are today measured from the Greenwich zero meridian. Fortunately, Greenwich is included in his tables, with a longitude of 20° 12' 30" as measured by Flamsteed, so this figure must be subtracted from all eastern observations and added to all its western ones. The second adjustment arises because Doppel­mayer uses a 360° equatorial circumference rather than the 180°E/180°W which has been adopted since 1884. All his western measurements have therefore to be subtracted from 3600 to give their modern equivalents. These two adjustments have been made to the figures in column 3 of Table I to give their modern equivalent longitudes shown in column 4. These can then be compared with the true longitudes according to present-day reckoning listed in column 5. The differences are shown in column 6.
In the textual cartouche on the eastern hemisphere Doppel­mayr explains that there is a difference of 221/, degrees between the Isle of Fero meridian and a meridian based on Paris. His advice to the reader is scarcely a model of clarity but can be translated (with some paraphrasing) as follows:

'Since, as all modern astronomers and geographers agree, measurements of the distances between all the principal places in the earth calculated by means of celestial observa­tions. at least in respect of latitude and longitude, provide the most sure foundation for Geography, then such methods must be preferred to observations derived from the accounts of travellers. Just as Experiment is the mistress of everything taught, so we here hand down for the benefit of Geography a true record of all the places whose positions have so far been determined. Working from the ancient Ptolemaic prime meridian running through the Isle of Fero, the renowned astronomer J. D. Cassini has calculated, consistently and scientifically, the distance to the Paris Observatory to be one sixteenth part of a circle or 22 '/2 degrees. Also we have presented measures of latitude as a result of the most recent astronomical observations, taken from the accounts of scholars and other learned men. If then the longitudinal measures of these men are to be related to another meridian the Parisian longitude of 22½ degrees must be subtracted from the given longitudes; thus other longitudes can likewise be determined.'

A further complication, which was probably brought to Doppelmayr's notice after the map was published, was the awkward fact that there had been a miscalculation in establishing the longitudinal distance between Paris and the Isle of Fero. How this occurred is not clear, but instead of the 22'/2 degrees reported by Cassini, the longitudinal difference was found at the time to be 19° 51' 30"; slightly less than the true distance of 20° 00' 00". A further explanation in a second cartouche added to the western hemisphere in the second state of his map may be translated as follows:

'Since the latest celestial observations relating to the Isle of Fero show a distance between the Parisian meridian and this island's meridian of 19° 51' 30"; there is clearly a divergence between this figure and the 22'/2 degrees recorded by the most celebrated J. D. Cassini, amounting to 2° 38' 30". If this figure is subtracted from each individual observation of longitude in our tables the figure which remains will correspond to the longitude based on the Isle of Fero.'

 Reverting to Table I, it can be seen that the English observations are gratifyingly correct to within a few minutes of arc but further afield (for instance, Halley's early measurements made on 51. Helena) the errors widen. In the New World, the readings for Mexico City and Port de Paix (Haiti) must be questionable, corresponding to distance displacements of over 250 miles. On the other hand, those taken by the Jesuits at Goa, Malacca and in Peking are remarkably exact. The two latest measurements at Petropolis (Leningrad) by Joseph Delisle and at Tornio by Maupertuis added in state 2 of the map are also noticeably more accurate than many of the earlier ones. It could be an interesting exercise to load all the 142 observations given by Doppelmayr on to a mini-computer and correlate variations by date, by observational technique, by nationality of the astronomer, by distance from London, etc.  Another more complex scientific investigation could be to delve into the original records of the various expeditions to try and uncover the reasons for the margins of error which now appear.

Doppelmayr's map, constructed around this series of observa­tions, is an altogether more accurate representation of the world than predecessor maps. However, by showing California as a large island, he fails to recognise its true peninsular form: an acknowledgement that had been current since the maps of Nolin and Guillaume Delisle in the early 1700s. Instead of the actual latitude of the peninsula which lies between 23° and 32° N, the island on Doppelmayr's map extends as far north as 4SO; a misplacement of nearly a thousand miles. In the east, he has marked in outline the position of Japan as erroneously recorded on Sanson's maps; placed some twenty-five degrees east of its correct position. Doppelmayr's own rendering of Japan is somewhat more exact (in spite of no astronomical data being recorded) but is still approximately three degrees too westerly. Further southwards, the western most part of the coast of Australia is drawn at about 107°E in adjusted terms, compared to the modern longitude of Dirk Hartog's island of 113° E. It is not surprising that shipwrecks on this barren shore were a perpetual hazard in the seventeenth and eighteenth centuries for fleets making for the East Indies