Although the coastal charts from the first quarter of the 19th century were an important step forward, there was still a long way to go before the target was reached, a satisfactory map of the whole country, both inhabited and uninhabited. The coastal charts were probably enough for sailors, given the conditions and standards of the time, but they were of less use to the Icelanders themselves, either as regards general knowledge of the country or for other purposes. By a fortunate coincidence, it happened that a man was to be found in Iceland who had taken a degree in mathematics and worked for a time as a surveyor abroad. This man was Björn Gunnlaugsson, a teacher at the grammar school at Bessastadir.
In a letter which he sent to the prefect on the 12th of August 1829, Björn urges that the Danish government should hand over to the Icelanders the instruments that had been used for the coastal survey. This request was not attended to at the time. The Icelandic Literary Society (Hid íslenska bókmenntafélag) then intervened and after a certain amount of hesitation undertook early in 1831 to advance a certain sum towards initiating a survey of the whole country. The prefect was asked to provide the instruments, and was quick to comply. The grant from the Literary Society was limited to one year, however, and was on condition that the survey began in Gullbringu- and Kjósarsýsla. The task was naturally entrusted to Björn Gunnlaugsson, and he had at least three months' holiday from teaching. During the summer of 1831 he surveyed the appointed area and made a map, which was at once sent to Copenhagen with a view to publication.
Björn Gunnlaugsson worked on the survey during the years 1831-1843. The Literary Society made Björn an annual grant and the financial position was eased when the Danish government made him a grant in 1836 which he continued to receive until 1846.
The original idea was to survey each county individually and make separate maps, but in the event it was felt impractical to undertake such a large task on account of the cost. O. N. Olsen was appointed to attend to the publication of the maps in Copenhagen. Olsen, who later became director of the surveying department of the Danish army, proposed that the map should be printed on four sheets. It was his task to take maps of the separate counties and regions as they arrived from Björn Gunnlaugsson, and join them together and reduce them. He probably also decided the scale and projection, though perhaps in conjuction with Björn.
Although Björn Gunnlaugsson's map is usually dated from 1844, no part of it probably was completed until four years later (1848). The Icelandic Literary Society was the publisher, as it says on the map itself, but the cost was paid by the Danish treasury. It is estimated to have cost six times as much as the survey.
Olsen made a second, smaller map of Iceland which is dated from 1849 although it probably didn't appear until a year later. It is simply a smaller version of the larger map on a scale of 1:960.000.
Björn Gunnlaugsson used the coastal charts as a starting point, as far as they went. He himself measured no base-lines, but simply extended the coastal surveyors' triangulation.
In the course of his survey Björn covered virtually the entire inhabited area and a good part of the uninhabited. Because of the cost, however, these journeys were not as extensive as he wished or considered necessary. But his principal concern was to map the inhabited regions, leaving a complete map of the rest of the country until a better opportunity. In some places he was forced to rely on accounts from local people, who were not all equally trustworthy, or make do with sketches. The central highlands, therefore, were still rather left out, although it was a great advance on previous maps. For the first time it was possible to get a reasonable picture of the lava-fields and glaciers and the course of the rivers in the highlands. There are of course more inaccuracies here than one would wish, but if he had attempted a more precise survey, he would never have been able to finish the task. It was better to relax demands where exactness was of less importance. It might be a long time before another survey would be undertaken with a view to map of the whole country. In spite of some errors, Björn Gunnlaugsson's survey and map are a great scientific achievement, unique of its kind, carried out with extremely limited resources both in finances and equipment.
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