In a fifteenth-century manuscript incorporated in the collection of scientific treatises known as _Rímbegla_ the following passage is to be found (p. 482): ‘Between Bergen and Nidaros (Trondhjem) there are about four degrees, so one degree comes to about a nautical “tylft”.’ Pausing here, we may observe that the voyage from Bergen to Trondhjem was evidently recognized to be four nautical ‘tylfts’. The passage continues: ‘now a degree on land and a “tylft” at sea are equal, and there are two “tylfts” in a day’s (dægur) sailing.’ To the expression used for a day’s sailing attention will have to be directed later on, but for the present it may be allowed to stand in the non-controversial form into which it is translated above. Taken as an accurate statement of the case, this quotation from _Rímbegla_ has given us the following table: 1 vika = 5 nautical miles. 1 tylft = 1 degree (60 nautical miles). 2 tylfts = 1 day’s sail (120 nautical miles). Now if a day’s sail be taken here as equivalent to twenty-four hours, we have precisely the divisions of distance which, as I said at the outset, we ought to expect where the measurement is effected by time. A ‘vika’ represents an hour’s run, a ‘tylft’ twelve hours, and a day’s sail twenty-four hours. Whether, the geographical distances which they are alleged to represent have been correctly stated is another matter, into which we may now look a little more closely. It is evident that the assumed correspondence between a ‘tylft’ and a degree, which, having regard to the state of navigation in the saga period, must in any case have been accidental, rests upon the hypothesis that the length of a voyage from Bergen to Trondhjem is four degrees or 240 nautical miles. The difference of latitude between the two places is in fact little more than three degrees, and even the rhumb-line connecting Bergen and Trondhjem is not 240 nautical miles in length; this error, however, need not necessarily have any effect on the author’s calculation. But on working out the shortest distance covered by a ship sailing from the one place to the other, it is apparent that in calling this distance four degrees a serious under-statement is made which vitiates the conclusion arrived at. This distance as sailed at the present day is said to be 318 nautical miles, and calculation or inspection of a chart will show that it is impossible to bring it much below 300, so that if this represents four ‘tylfts’, calculated by time, as it probably did, our table must be revised as follows: 1 vika = 6·25 miles. 1 tylft = 75 miles. 1 day’s sail = 150 miles.