The first great circle intersects the meridian of 600 at 44° 24' 25", of 550 at 46° 5' 28" of N. latitude. The second great circle intersects the meridian of 450 at 48° 55' 47.5, of 40° at 49° 58' 27'', of 350 at 50° 46' 6'', of 300 at 51° 19' 44", of 250 at 51° 40' 3", of 200 at 51° 47' 28'', and of 150 at 51° 42' 7"'.* The following, from Mr. Coit's work, to which the student is referred for a variety of useful problems, and interesting information, will furnish a number of exercises. TRACK OF THE ARC OF A GREAT CIRCLE FROM CHESAPEAKE BAY TO BORDEAUX. Table showing the longitude of the intersections of the latitudes crossed by the arc of a great circle from Cape Henry's light-house, mouth of Chesapeake Bay, to the Corduan light, near Bordeaux; also showing the courses from the points of intersections of the latitudes crossed, and from intersection to intersection. On this track the difference or saving is 110. *The great circle courses and distances are as follows: From George's Shoal to the meridian of 600, 57° 14' and 407 miles. From 60° to 550 N., 62° 40′ E., and 234 miles. From 550 to Cape Race N. 66° 13' E., and 87 miles. From Cape Race to the meridian of 45 N. 61° 19' E., and 353 miles. From 45° to 40°, N. 700 18' E., and 205 miles. From 40° to 350, N. 74° 6' E., and 197 miles. From 350 to 300, N. 77° 57' E., and 191 miles. From 300 to 250, N. 80° 50' E., and 188 miles. From 25 to 200, N. 85° 45' E., and 186 miles. From 200 to 150 N. 89° 42' E., and 186 miles. From 150 to Cape Clear S. 86° 23', and 202 miles. For further information on Great Circle Sailing, see "The Practice of Navigation and Nautical Astronomy, by Lieut. Raper, of the Royal Navy," Art. 336, in which work will also be found a convenient table (tab. 5) called the Spherical Traverse table, for solving problems in this kind of sailing. See also a small collection of " Tables to facilitate Great Circle Sailing," by John Thomas Towson, published by order of the Lords Commissioners of the Admiralty. SUMNER'S METHOD. This is a method discovered recently by accident, and consists in calculating the ship's longitude by chronometer for two assumed latitudes, the one of which is the next even degree less, the other the next even degree greater (without odd minutes) than the latitude by dead reckoning. The two positions of the ship thus determined from the longitudes found and the assumed latitudes, being projected on a Mercator's chart, the line joining them passes through the true position of the ship, and any land it may happen to pass through in the vicinity, will have the same bearing from the ship that this line makes with the meridian. The theory is, that this line is a small portion of what the author terms a parallel of equal altitude, that is, a small circle of the terrestrial sphere, the pole of which is the point of the earth's surface, at which the sun is vertical or in the zenith at the instant of observation. To all places situated on this circle the sun will have the same altitude at the instant. Now since in the two computations in the above problem the latitude only is different, the altitude and declination, which are the other data, remaining the same, the altitude of the sun is therefore the same at the two positions determined, and they are in the same parallel of equal altitude, and as the observed altitude of the ship is also the same, the ship, too, is upon the same parallel of equal altitude, a small are of which may be regarded as a straight line. A perpendicular to the line determined as above will be in the direction of the sun's bearing, and the angle it makes with the meridian will be the sun's azimuth. For the perpendicular to an arc will pass through the pole of the arc. If two altitudes of the sun be taken, and two lines projected as above, passing each through the place of the ship, its actual position is determined by their intersection. For the method of allowing for the change of place of the ship between two observations for altitude, and for a variety of problems based upon the principle above explained, see Sumner's work. PART IV. SURVEYING 102. Has for its object to make upon paper an exact delineation called a map, plot, or draft, and sometimes to find the contents of ground. The most common mode of proceeding is to measure a base line upon the ground, as at Art. 10, and take the angles at each extremity with some instrument suitable for the purpose, thus determining the position of a distinct point. This is transferred to paper, by means of a scale of equal parts, and a semicircular protractor, as described in the same article. As many points upon the ground as may be desirable can thus be transferred to the map. If two points thus determined be the extremities of some straight boundary, as a wall, fence, or side of a building, the boundary itself is drawn by uniting the two points by a straight line. If the boundary be curved or irregular, as the bank of a stream, a coast, the border of a wood, &c., the prominent points should be determined on the map, as above described, and the boundary then traced through them with the hand, by the eye. The positions of points on a map may also be determined by taking their direction and distance from some point used as a basis or base point for the whole survey. Or, when more convenient, some one of the points determined from the first base point may itself become a base point for the determination of others more in advance. The direction of one point from another is expressed by the angle which the line of direction makes with some known line. A very convenient line for this purpose is a meridian or north and south line, for the direction of this latter may always be known by means of a magnetic needle, and the direction of any line from a north and south line by a compass. Allowance must of course be made for what is called the variation of the needle, which is determined by astronomical observations, in a manner to be hereafter explained. Distances are measured upon the ground with a tape or chain. The measuring tape is covered with wax, to prevent the effects of varying degrees of moisture, in contracting and expanding it. It is divided usually |