Chart schemes. Before commencing the preparation of a chart it is necessary to arrange a definite scheme for it, and the usefulness of the chart will depend materially on this preliminary plan, in which must be outlined its scale, size, limits, and features to be represented. New charts have sometimes been prepared simply to fit the surveys as they progressed or to fill immediate or local requirements. It is, however, desirable that general plans for series or groups of charts be made, and with changing needs, information, and conditions it is sometimes necessary that existing schemes be modified.

Compilation of information. Considerable work must usually be done to get the field records in shape for the published chart. The soundings must be plotted and the characteristic depths selected. Only a part of the soundings that are made can be shown on the original sheet and only a small part of these are used on the final chart. A selection is made showing the least soundings on shoals and bars, the channel depths, and the characteristic soundings in anchorages and other areas. The original surveys are generally made on a considerably larger scale than that on which the chart is published, in order that the soundings may be more thoroughly plotted. The sheets must then be reduced to the scale of publication, and this can conveniently be done by means of photography or with a pantograph.

The best judgment is required in selecting the important features to be shown on the chart and omitting the less important and not essential features which might tend to obscure the others. In charts of new regions where complete surveys are lacking, care must be exercised in weighing, combining, and adjusting information from various sources and which is, perhaps, more or less conflicting.

Projections. The surface of the earth being curved, there is no possible system of projection by which it can be represented on a flat sheet of paper in an ideally satisfactory way. Numerous methods of projecting the earth's surface upon a plane have been proposed and many of them are actually used for various purposes. In general each projection has qualities which are valuable for certain uses, and deficiencies which make it less valuable in other ways. Only four of the different projections need be mentioned here as of special interest in chart construction.

Mercator projection. This is a rectangular projection in which the meridians are straight lines spaced at equal intervals and the parallels are straight lines so spaced as to satisfy the condition that a rhumb line, or line on the earth cutting successive meridians at the same angle, shall appear on the developed projection as a straight line preserving the same angle with respect to the meridians.

This projection may be considered as the unrolling upon a plane of the surface of a cylinder tangent to the earth along the equator, and upon which the various features of the earth's surface have been projected in such manner as to satisfy the above requirement.

On this projection there is a constant distance between the meridians, whereas on the earth they actually converge toward the poles. The distance between the parallels increases in passing toward the poles, approximately in the proportion of the secant of the latitude. For each small portion of the map the relative proportions are maintained as on the earth.

Some characteristics of the mercator projection are these: The meridians and parallels are all straight lines and perpendicular to each other; there is no convergence of the meridians; the minute of longitude is a constant distance on the map; the minute of latitude increases in length from the equator toward the poles but locally retains its true proportion to the minute of longitude; areas and distances increase in scale with the latitude so that a given scale is strictly correct only for one latitude; great circles and consequently lines of sight are curved lines excepting the meridians and the equator; rhumb lines or lines having a constant angle with the meridians are straight, and for the same angle are parallel in all parts of the chart. These qualities are all rigid and the projection can therefore be used for all areas, small or large, up to the extent of the earth's surface, except that it cannot be extended to the poles, as there the length of the minute of latitude would become infinite.

An interesting fact regarding a rhumb line oblique to the meridians is that it is a spiral continually approaching but never reaching the pole; this spiral makes an infinite number of revolutions around the pole, and yet it has a finite length for the reason that the length of each revolution diminishes as the number of revolutions increases.

The mercator projection has been extensively used for nautical charts, for which it presents important mechanical advantages, in that adjacent charts can be joined on all their edges while still oriented with the meridian; all charts are similar; the border may be conveniently subdivided, giving a longitude scale applicable to any part of the chart, but a latitude scale that may be used in the same latitude only; courses are laid down as straight lines and can be transferred with parallel rulers from one part of the chart to another without error. On a mercator chart an island in latitude 60° would appear four times as large as an island of the same actual area at the equator, but this distortion of areas, while it gives erroneous impressions on charts of great extent in latitude, does not seriously affect the use of the chart for nautical purposes. Areas may also be correctly measured on a mercator map by taking each projection quadrilateral separately, subdividing it if necessary, and using the published tables of areas of quadrilaterals in different latitudes. Although distance scales vary with the latitude, distances can be taken from this chart with fair correctness by the use of the latitude border scale for the middle latitude, subdividing the total distance if there is much range of latitude. The inability to take off the great circle or shortest course directly from the mercator chart is from a navigational point of view a defect, but the most convenient solution for this appears to be the supplementary use of a gnomonic chart as will be described. The fact that lines of sight are not straight lines on this projection is another defect, as by the plotting of bearings and angles on approaching the land the positions of vessels are located on the chart; fortunately, however, the error due to this cause usually falls within the other uncertainties involved in locating a ship; if need be it would be practicable to allow for this curvature. In the polar regions, however, the faults of the mercator projection become so much exaggerated that it is not used for navigational purposes, but because of the absence of commercial navigation there this is a minor matter in the general question of chart projection. For the plotting of original surveys the mercator projection is not suited and is not used, for the reasons above mentioned.

Tables of "meridional parts" are published which give the distance in terms of minutes of longitude from the equator to the various parallels; with these tables a mercator projection may readily be constructed.

Airy proposed a graphical method of sweeping the arc of a great circle on to a mercator chart, and tables are published for this purpose. The method is only approximate and is limited in application, and the supplementary use of a gnomonic chart would appear to be preferable.

Polyconic projection. In plotting the original surveys it is essential that a projection be used which will for the area included on a survey sheet show the points in their correct relation both as to direction and distance. These conditions are substantially fulfilled by several projections, of which the polyconic is used in the United States. If a hollow cone were placed so that it would either be tangent to the earth's surface along one of the parallels of latitude or cut it along two parallels, and the points projected on to this cone, and the cone then unrolled and laid out flat, the result would be a conical projection, of which there are several variations. If successive tangent cones be used and each parallel of latitude be developed as the circumference of the base of a right cone tangent to the spheroid along that parallel, the result is the polyconic projection, which has been used for field sheets and for the large scale charts, as well as for the topographic maps of the United States. This projection has valuable qualities for moderate areas of the earth's surface, within which the scale is approximately uniform, areas retain nearly their true proportions, and great circles and consequently all bearings and directions are approximately straight lines. The parallels of latitude are arcs of circles with radiuses increasing as we recede from the pole; therefore they are not truly parallel and the length of the degree of latitude increases either side from the central meridian. The meridians converge toward the poles and become slightly curved as we recede from the central one; the longitude scale is everywhere correct, but the latitude scale is strictly correct only on the central meridian. The angles of intersection of parallels and meridians are right angles or nearly so. The polyconic projection is not used for very extensive areas of the earth's surface, as for instance a hemisphere.

Gnomonic projection. In this projection the eye is assumed to be at the center of the earth and the features are projected upon a plane tangent to some point on the earth's surface. It is practicable to use this projection for oceanic areas, and it has the very important quality that every straight line on it represents a great circle of the earth. To obtain the great circle or shortest course between two points it is therefore only necessary to draw a straight line between the points on a gnomonic chart. Because of the great distortion near the edges this projection is not otherwise adapted to navigational use, and it is employed only to mark out the general course, and sufficient points are then transferred to a mercator chart. The gnomonic chart is therefore useful in supplementing the mercator chart, supplying its deficiencies as to convenience in marking out great circle courses. The great circle course can be derived not only more easily and quickly from the gnomonic chart than by computation, but the chart is also to be preferred because the course marked out on it will show at once if any obstruction, as an island or danger, is met or too high a latitude is reached. A modified or composite course can readily be laid out on a gnomonic chart.

Arbitrary projection. The few charts published of the polar regions are sometimes on an arbitrary projection, in which the meridians are straight lines radiating from the pole and the parallels are equidistant circles with the pole as center. The latitude scale is uniform. At some distance from the pole the longitude scale becomes very much distorted, but the projection is a practicable and convenient one for the immediate polar regions. Gnomonic and conical projections are also used for the polar charts, differing little from the foregoing for moderate areas.

Scales. Charts are published on a variety of scales to suit different needs of navigation, and the usual classification depends on scale. In addition to the ocean charts covering a single ocean in either one or several sheets and intended for navigation on the high seas, there are for our Atlantic coast the following series:

Sailing charts, scale about 11200000, for general coastwise navigation.

General coast charts, scale 1400000, for local coastwise navigation.

Coast charts, scale 180000, for approaching the coast at any point and for inside passages.

Harbor and channel charts, of various large scales from 15000 to 160000, for entering harbors and rivers and passing through channels.

The expression of scales by miles to the inch or inches to the mile is the more familiar. The expression of scale in the manner used by the Coast Survey and by most of the European countries, by standard fractions as 180000, meaning that any distance on the chart is 180000 of the actual distance on the earth, has some advantages. For instance, the relation of these fractions gives at a glance the relation of the scales of the charts. Thus a 180000 chart is on a scale five times as large as a 1400000 chart.

For the more important harbors charts have been published on several different scales to meet various needs. Thus New York Harbor is shown on charts of scales of 110000, 140000, 180000, 1200000, 1400000 and 11200000, each of course including a different area.

The selection of suitable publication scales is of prime importance; a large scale permits of greater clearness and of showing more detail, but on the other hand restricts the area and the points that can be shown on a single sheet, or else makes a chart of excessive dimensions. In general in chart preparation the scale should be restricted to the minimum that can be used to fulfill the particular object and clearly represent what is desired. A chart of very large scale is not convenient for plotting, and a moving vessel may pass quickly beyond it or into range of objects beyond the limits of the chart.