In Denmark, for instance, the system of education for the higher grades of the merchant service was particularly strict and effective. No Danish subject was allowed to act as master of a merchant vessel unless he had previously made two voyages in the capacity of mate, while the mates themselves had, and still have, to submit to a general examination, embracing (1st) a knowledge of dead-reckoning, the nature and use of logarithms, and the first rudiments of geometry; (2nd) the nature and use of the compass and log; and (3rd) the form and motions of the earth, and the geographical lines projected on its surface, so as to be able to determine the position of different places. It was also expected that he should understand the nature of Mercator’s charts, and the mode of laying down the ship’s course on them, together with such calculations as may be necessary for this purpose. Expertness in keeping a journal, in the use of the quadrant, and in making the necessary allowances for currents, lee-way, and the variations of the compass, were all required, together with some idea of the daily motion of the celestial bodies, of the sun’s proper motion, and the meaning of the words “horizon,” “refraction,” “semi-diameter,” “radius,” and “parallax.” He was also required to know how to use the instruments for calculating the elevation of the sun and stars, and the distance between objects on shore! Nor, indeed, was his examination limited to the more ordinary details of a navigator’s duty. He was expected to be expert in ascertaining what star enters the meridian at a given time at the highest and the lowest elevations, as well as in finding the latitude, both by means of the meridian height of the sun or of a star, and in determining the time for high and low water. He was further expected to understand the mode of calculating the time of sunrise and sunset, and of ascertaining the variations of the compass by means of one or more bearings in the horizon, and by the azimuth. [Sidenote: In Norway and Sweden.] In Norway and Sweden, mates of ships had to undergo a similar examination before being allowed to act in that capacity, and a still more rigid examination both as regards seamanship, navigation, and the general knowledge of business relating to shipping affairs, before they could command a vessel, together with a knowledge of the Customs and Navigation Laws, and of the usual averages and exchange. They had likewise to know something of the elements of shipbuilding, and of the mode of measuring a ship’s capacity. [Sidenote: Russia and Prussia.] In Russia and Prussia the mates and masters of merchant vessels, besides the qualifications above referred to, were required not merely to read and write their own language with accuracy, but to have some knowledge also of English and French.