Ptolemy had fixed his first meridian at the Fortunate Islands (Canaries), and in the new era the Spaniards, with the sanction of the Pope, had adopted the same point; though the Portuguese, as if in recognition of their own enterprise, had placed it at Madeira,—as is shown in the globes of Behaim and Schöner, and in the map of Ruysch. The difference was not great; the Ptolemean example prevailed, however, in the end.[378] In respect to latitude there was not in the rude instruments of the early navigators, and under favorable conditions, the means of closely approximate accuracy. In the study which the Rev. E. F. Slafter[379] has made on the average extent of the error which we find in the records of even a later century, it appears that while a range of sixty geographical miles will probably cover such errors in all cases, when observations were made with ordinary care the average deviation will probably be found to be at least fifteen miles. The fractions of degrees were scarcely ever of much value in the computation, and the minute gradation of the instruments in use were subject to great uncertainty of record in tremulous hands. It was not the custom, moreover, to make any allowance for the dip of the horizon, for refraction or for the parallax; and when, except at the time of the equinox, dependence had to be placed upon tables of the sun’s declination, the published ephemerides, made for a series of years, were the subjects of accumulated error.[380] [Illustration: REGIOMONTANUS’ ASTROLABE. This cut follows the engravings in Ruge’s _Geschichte des Zeitalters der Entdeckungen_, p. 106, and in Ghillany’s _Ritter Behaim_, p. 40. Cf. Von Murr, _Memorabilia bibliothecarum Norimbergensium_, i. 9.] With these impediments to accurate results, it is not surprising that even errors of considerable extent crept into the records of latitude, and long remained unchallenged.[381] Ptolemy, in A. D. 150, had placed Constantinople two degrees out of the way; and it remained so on maps for fourteen hundred years. In Columbus’ time Cuba was put seven or eight degrees too far north; and under this false impression the cartography of the Antilles began. The historic instrument for the taking of latitude was the astrolabe, which is known to have been in use by the Majorcan and Catalanian sailors in the latter part of the thirteenth century; and it is described by Raymond Lullius in his _Arte de navegar_ of that time.[382] Behaim, the contemporary of Columbus, one of the explorers of the African coast, and a pupil of Regiomontanus, had somewhat changed the old form of the astrolabe in adapting it for use on shipboard. This was in 1484 at Lisbon, and Behaim’s improvement was doubtless what Columbus used. Of the form in use before Behaim we have that (said to have belonged to Regiomontanus) in the cut on page 96; and in the following cut the remodelled shape which it took after Behaim. [Illustration: LATER ASTROLABE.