of the service rendered to Navigation by Mr. John Thomas Towson's "Tables to facilitate the Practice of Great Circle Sailing." By means of a diagram and a table of easy entry, the whole operation of finding several courses in succession is reduced almost to a matter of inspection.

If the reader have a terrestrial globe before him, it would afford a means of reference and illustration more useful than anything else, in respect to the principles of Great Circle Sailing; but a map would to a certain degree be useful for the same end. It is one of the most familiar propositions in Spherical Geometry, that the shortest line which can be drawn between any two places on the surface of the globe is an arc of the great circle that passes through them both; while, on tho other hand, the smallest study of the nature of a rhumb-line, the course followed in ordinary sailing, will show that the rhumb from one place to another can never coincide with a great circle, unless both of those places lie either on the equator or on a common meridian. Maps and charts, being flat representations of curved surfaces, are of necessity distorted, and are only correct near the equator; the distortion increasing as the poles are approached. One consequence of this is, that the relative advantages of Mercator and Great Circle Sailing are not readily seen on a common map or chart; for the course which on the globe is the shortest, is on the chart made to appear very much the longest, and vice versa. In a perfect great circle (neither on a meridian nor on the equator), the course is perpetually changing; it does not remain the same at two places even a degree asunder. But in practice it is necessary to break up the course into a number of stages, each having a definite direction for a short distance. It is this breaking up of the great circle

into a large number of practical sailing courses that Mr. Towson has so conveniently effected in his Tables.

The Tables give the Latitudes, Courses, and Distances on the great circles of the globe, corresponding to each degree of longitude. Supposing a voyage to be determined on, and the latitudes and longitudes of the port of departure and the port of destination given, then the Tables would show what course between the two ports would coincide with an arc of a great circle, and would consequently be the shortest. The voyage is to be performed, as it were, in a series of stages, each stage being marked by a particular course, and then another course for the next following stage. The stages vary in length in a ratio depending on the number of miles contained in a degree of longitude, which number decreases as we approach the poles from the equator; and at each successive stage the compass course or bearing is changed.

It follows from the nature of great circles (of which the equator is one), that the northern and southern halves of a great circle must each have a point of greatest separation from the equator, and equally distant from it; and these points give rise to many designations and quantities in Mr. Towson's Tables. Thus, either of these points is called the vertex of the great circle to which it belongs; the arc intercepted between the vertex and the equator is the latitude of vertex; the meridian that passes through the vertex is the meridian of vertex; and the arc of the equator contained between the meridian of vertex and the meridian of any place on the great circle is the longitude from vertex. The meridian of the vertex always intersects the great circle at right angles, and, with the equator, divides a great circle into quadrants; and in each of ose quadrants the elements are the same; that is,

the latitudes, courses, and distances corresponding to each degree of longitude from the vertex in one quadrant, truly represent those for the corresponding degree in each quadrant belonging to tho same great circle; so that in practice the calculations for 90° arc available for 360°, with a little attention as to east and west, and north and south.

Full instructions on the use of the Tables and the Linear Index which accompanies them are given in the work itself, to which the reader is referred.

A variation of this system is known by the name of Windward Great Circle Sailing. When a ship is unable, on account of adverse winds, to sail directly to her port, she is put on that tack by which she nears her port by the greatest proportion of the distance. sailed. For example, if her proper course be due N.E., but if unfavourable winds compel her to take a course a little N. or S. of that direction, that deviation or tack ought to be adopted which will in the end least lengthen the voyage. But this nearest distance can only be determined by great circle sailing, since it is only this system which gives the true course, and which consequently can show which is the best tack. The rule for windward sailing, as laid down by Mr. Towson, is this: Ascertain the great circle course by the index, scale, and tables, and put the ship on that tack which is the least removed from it.

Another variety of the system is Composite Great Circle Sailing. Theoretically, great circle sailing is complete it gives absolutely the shortest course between two ports; but practically, there may be reasons against its full adoption. The vertex of the course may be in such a high latitude, that ice, or polar lands, or other obstructions, may lie in the way. Hence the mariner may be induced to make a compromise between

parallel sailing and great circle sailing, by using a portion of each. The method of proceeding in such a case is as follows: the mariner determines what shall be the highest latitude which he is willing to reach; this he will call the "maximum latitude." He takes this latitude as the latitude of vertex, and marks out a great circle course corresponding thereto. When the ship has reached the vertex, which will necessarily be as soon as she has attained the maximum latitude, the voyage is conducted along the parallel east or west, until the difference of longitude of the ship and destination shows that the ship has reached the vertex of the arc which passes through the destination. After this, the ship follows the arc of a great circle to her destination. In this system there is a saving of distance, as compared with Mercator Sailing, beginning and the end of the voyage; while the middle portion is lengthened for the sake of keeping within a practicable latitude.

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When a vessel gets off the Great Circle course, it will not be necessary, in practice, to calculate the course anew, since a moderate deviation will not sensibly alter the bearing of the port to which bound.

A ready way of finding the Great Circle route when elaborate rules and linear tables are not available, is Sir G. B. Airy's (Astronomer Royal) "Method for Sweeping Arc of a Circle" an on Mercator's chart; it approaches very near to the correct projection of a great circle, on one side of the equator.

1. Join the two places by a straight line. Find its middle. Draw thence a perpendicular to that line on the side next the equator, and, if necessary, continue it beyond the equator.

2. With the middle latitude (between the two places) enter the following table, and take out the corresponding parallel.

3. The centre of the required sweep will be the intersection of this parallel with the perpendicular.

The distance between Tairoa Head (Otago) and Panama is 6823 miles by Mercator, and 6608 miles by Great Circle Sailing.

From the Cape of Good Hope to Cape Horn the distance by Mercator is 3792 miles, by Great Circle 3590 miles.

From Cape Clear to St. John (Newfoundland) the distance by Mercator is 1751 miles, by Great Circle 1676 miles.