Every modern deep-sea navigator is familiar with what is known as Great Circle Sailing. For the landsman it may be sufficient to explain that this principle seems to contradict Euclid’s assertion that the shortest distance between any two points is a straight line. In the case of a globe this statement of Euclid does not apply. Every steamer between Liverpool and New York to-day sails on a great circle for the most part of her passage. “Great circles” are those whose plane passes through the centre of the earth: for example, the Equator is a “great circle.” Now as far back as the year 1497 Pedro Nunez made the startling but true announcement that in sailing from one port to another the shortest course was along an arc of a great circle of the terrestrial sphere. And this fact was appreciated by such Elizabethan navigators as John Davis in his voyaging across the North Atlantic. [Illustration: AN OLD NOCTURNAL. In the S. Kensington Museum.] The training of a navigator such as went on in Seville was very thorough, so that it formed an excellent precedent for all who had at heart the education of the complete navigator. The training in the year 1636 was a three-year course, and the following curriculum is given for that year by Sir Clements Markham in his “Sea Fathers”:-- First Year: (1) The sphere of Sacrobosco. (2) The four rules of Arithmetic: Rule of three, extraction of square root, cube root, and fractions. (3) The theory of Purbach, or planets and eclipses. (4) The spherical trigonometry of Regiomontanus. (5) The Almagest of Ptolemy. Second Year: (1) The first six books of Euclid. (2) Arcs and chords, right sines, tangents and secants. (3) To complete Regiomontanus and Ptolemy. Third Year: (1) Cosmography and navigation. (2) Use of astrolabe. (3) The methods of observing the movements of heavenly bodies. (4) The use of the globe and of mathematical instruments. (5) The construction of a watch. It must not be forgotten that the life on board a Tudor ship was, even for rough, rude, untutored seamen, full of hardships, even if full of adventure. Anyone who cares to look through the records of the voyages can see this for himself. We are accustomed to regard that as a romantic age; but the romance is only visible through the avenue of distance which now separates us from those times. The victualling was disgracefully mismanaged at the beginning of the sixteenth century. The crews of ships were actually allowed to fight in the English Channel for their country in a condition that was almost sheer starvation. Actually the commissariat department was so bad that ships had to return home from the region of battle to fetch supplies. There was nothing very romantic, either, in having to serve on ships which exuded a terrible stench from their holds. A horrible mixture of bilge-water and decayed food, coupled with the heat of the galley, helped to make the health of the Tudor sailorman anything but good.