708 REPORT — 1891. 



Reo^iomontanus, for the years 1474 to 1506, which Columhus carried with him on 

 his voyages, nor those of Peter Apianus, for 15;21-70, were sufficiently accurate to 

 admit of satisfactory results, even though the actual observation left nothing to be 

 desired. Errors of 30 degrees in longitude were by no means rare, and it was only 

 when Kepler had published his ' Eudolphine Tables ' (1626), which according to 

 Lalande formed the basis of all astronomical calculations during a century, that 

 more exact results were obtained. The suggestion to determine longitude by 

 means of lunar distances or occultations of stars bore no fruit at that time, as the 

 knowledge of the complicated motion of the moon was still very imperfect. Still 

 less was known about the movements of the satellites of Jupiter which Galileo 

 had first espied in IGIO when looking at that planet through his telescope. They 

 became available only after tables of their revolutions and eclipses had been 

 published by Cassini in 1668. 



Another suggestion for the determination of longitude was made by Gemma 

 Frisius in 1530, namely, that a clock or timekeeper should be employed for the 

 purpose. One of Huygens's pendulum clocks was actuallj' carried by Holmes to 

 the Gulf of Guinea, but the results obtained were far from encouraging. 



The difficulties which still attended the determination of longitude in the six- 

 teenth centui-y are conspicuously illustrated by the abortive attempts of a Congress 

 of Spanish and Portuguese navigators who met at Badajoz and Yelves in 1524 

 for the purpose of laying down the boundary line, which Pope Alexander VI. had 

 drawn at a distance of 370 Spanish leagues to the west of Cape Verde Islands, 

 to separate the dominions of Spain from those of Portugal. Not being able to 

 agree either as to the length of a degree, nor even as to that of a league, they sepa- 

 rated without settling the question placed before them. 



So uncertain were the results of observations for longitude made during the 

 sixteenth and seventeenth centuries, that it was thought advisable to trust to the 

 results of dead-reckoning rather than to those of celestial observations. But the 

 method of dead-reckoning is available only when we have a knowledge of the size 

 of the earth, and this knowledge was still very imperfect, notwithstanding the 

 renewed measurement of an arc of the meridian by Snellius, the Dutch mathema- 

 tician (1615). This measurement, however, is remarkable on account of its having 

 for the first time applied the exact method of triangulation to a survey. 



The problem of measuring the ship's way had been attempted by the Romans, 

 who dragged paddle-wheels behind their ships, the revolutions of which enabled 

 them to estimate the distance which the ship had travelled. But time, the 

 strength of the wind, and the pilot's knowledge of the qualities of his ship, stiU 

 constituted the principal elements for calculations of this kind, for the * catena a 

 poppa ' which Magellan attached to the stern of his ship was merely intended to 

 indicate the ship's leeway and not the distance which it had travelled. The log, 

 which for the first time enabled the mariner to carry out his dead-reckoning with 

 confidence, is first described in Bourne's ' Regiment for the Sea,' which was pub- 

 lished in 1577. 



The eminent position wiiich Italian cartographers occupied during the fourteenth 

 and fifteenth centuries had to be surrendered by them, in the beginning of the 

 sixteenth, to their pupils, the Portuguese and Spaniards, upon whom extensive 

 voyages and discoveries had coaierred exceptional advantages. These, in turn, had 

 to yield to the Germans, and later on to the Dutch, who were specifically qualified to 

 become the reformers of cartography by their study of mathematics and of the 

 ancient geographers, as also by the high degree of perfection which the arts of 

 engraving on wood and copper had attained among them. German mathematicians 

 first ventured to introduce the long-neglected geographical projections of Hip- 

 parchus and Ptolemy, and devised others of their own. Werner of Niirnberg 

 (1514) invented an equivalent heart-shaped projection, whilst both Apianus and 

 Staben (1620 and 1522) suggested equivalent projections. StiU greater were the 

 services of Gerhard Cremer, or Mercator (1512-94), the Ptolemy of the sixteenth 

 century, who not only introduced the secant conical projection, but also invented 

 that still known by his name, which was calculated to render such great service to 



