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On account of this distortion of the Mercatorial chart, areas and spaces in the higher latitudes appear on such a chart much larger in comparison with those of the equatorial parts than they really are.

73. Wright's Graphic Explanation. - Mercator did not demonstrate, mathematically, the principles of his system. Toward the close of the 16th century, however, Edward Wright, an English scientist, gave a mathematical

E

Equator

(b)

(a)

FIG. 26

demonstration of the law on which Mercator constructed his chart. He assumed that a cylinder contained a spherical globe representing the earth, Fig. 26 (a), which was to swell, like a bladder, equally in latitude and longitude, until it coincided with the concave surface of the cylinder. At the same time the meridians widen out until they are everywhere the same distance from one another, as on the equator. In this way the spherical surface is made to coincide with the cylindrical concave surface. Cutting the cylinder down a meridian, and opening it out into a flat surface, Fig. 26 (6), we find on it a representation of a Mercator's chart.

74. For this reason all the meridians on a Mercatorial chart are parallel straight lines and the degrees of longitude are all equidistant; the latitude parallels are everywhere at right angles to the meridians, and hence the rhumb line, or track of a ship that steers a straight continuous course, or the relative direction, or bearing, between two places, can be represented as a straight line. For navigational purposes, therefore, the Mercatorial chart has a decided advantage over the polyconic chart.

75. Meridional Parts. – Further examining a Mercator's chart, we find that the degrees of latitude are all unequal, being increased in length from the equator to the pole in the same proportion as the degrees of longitude decrease on the globe. The lengths of the small portions of the meridians thus increased, expressed in minutes of the .equator, are called meridional parts, and the meridional part for any latitude is the line expressed in minutes of the equator into which the latitude is thus expanded.

The length of the line on a Mercator's chart, or the difference for any two latitudes between the meridional parts, which represents the difference of latitude, is known as the meridional difference of latitude.

76. Tables known as Tables of Meridional Parts have been constructed, which show the length in nautical miles into which the true latitudes must be expanded when a chart is being constructed on Mercator's projection. These tables are given in the collection of Nautical Tables accompanying this Course. They contain the meridional parts for every minute of latitude covering the regions of the Great Lakes. It will be shown later how, by the aid of these tables, the student may be able to construct a Mercatorial chart of any part of the Great Lakes or any part of a sea or coast line in general.

77. Charts in Use on the Great Lakes. - As stated before, the charts of the Great Lakes published by the U. S. Engineer Office (U. S. Engineer charts) are constructed on the polyconic projection, while those published by the Hydrographic Office (H. O. charts) are constructed according to Mercator's system. A comparison between the two charts, from the view point of a navigator, brings out the following characteristic features:

The Hydrographic Office chart contains more useful information relative to the navigation of the Lakes.

On the Hydrographic Office chart, distances can be measured in statute as well as in nautical miles, while on the U. S. Engineer chart only the statute mile is used.

The compass diagrams on the Hydrographic Office chart are both true and magnetic, and are divided into degrees as well as points and quarter points. On the U. S. Engineer chart the compass diagrams are true and expressed in points and subdivision of points only (except on the very latest, where the same compass diagram is used as on the Hydrographic Office chart).

The most important advantage of the Hydrographic Office chart is, however, to be found in the projection used in its construction, by means of which the course between any two places is represented by a straight line connecting them. On the U. S. Engineer chart the course from one principal place to another is indicated by means of dotted lines. This information is undoubtedly useful, but in certain cases these dotted lines are unreliable, for they do not always run in the direction they are supposed to indicate. If a navigator starts from one point to another, he sees by these dotted lines the true course to be run; if he can keep this course unerringly, it is all very well, but if he meets with any accident, or is blown off to one side of his course, he cannot find his new course on the U. S. Enginer chart as conveniently and correctly as he would on a Hydrographic Office chart, because, as before stated, the course between any two points on a polyconic chart must necessarily be a curved line. Hydrographic Office chart he has but to use his parallel

On a

ruler, and with the edge passing over his present position and the port-of destination, move it to the nearest compass diagram, when he obtains his new course at once, either true or magnetic, as he desires.

HOW TO USE CHARTS

If for any

Fig. 27

78. When a chart is properly spread out the top of it is toward the north, the bottom toward the south, the side to the right is east, and the side to the left is west.

reason it is otherwise, north will be indicated by the direction of the north point of the compass dia

grams situated somewhere on the chart. The latitude scale is found on the right and left sides of the chart, and the longitude scale at the upper and lower margins of the chart.

79. The instruments used in connection with charts are the parallel ruler, the dividers, and the course protractor.

80. The parallel ruler, Fig. 27, is usually made of ebony or gutta percha. The two parts are connected by cross-pieces of brass working on pivots in such a manner

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that they may be spread apart or pushed together and still remain parallel to each other. They are used for the purpose of transferring the direction of a bearing, or course, to the nearest compass diagram or vice versa. For instance, in Fig. 28, if it be required to find the bearing between a and b, the edge of a closed parallel ruler is laid between

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