When the cone is cut along a meridian and flattened out, the meridians and parallels will appear as shown in figure 9-21. In this case, the Northern Hemisphere was projected onto a cone placed tangent to the parallel at 45N, and the cone was cut along the 180th meridian.

To grasp the concept of gnomonic projection, again imagine the lighted spherethis time with a flat-plane paper placed tangent to the North Pole (fig. 9-22). The North Pole will project as a point from which the meridians will radiate outward as straight lines; and the parallels will appear as concentric circles, growing progressively smaller as latitude increases. The difference between this and conic

projection of the polar region is the fact that in the conic projection, the cone is cut and flattened out to form the map or chart, whereas the gnomonic projection will appear as is. On the conic projection, points lying close together on either side of the meridian along which the cone is cut will be widely separated on the map. The gnomonic projection, on the other hand, will give a continuous and contiguous view of the areas. Figure 9-23 shows the appearance of meridians and parallels on a polar gnomonic projection.

According to some authorities, to be conformal, a projection must possess both of the following characteristics:

1. It must be a projection on which direction is the same in all parts of the map. Obviously, for this directional conformality, the meridians (which indicate the direction of true north) must be parallel, and the parallels (which indicate true east-west direction) must be parallel to each other and perpendicular to the meridians.

2. It must be a projection on which the distance scale north and south is the same as the distance scale east and west.

Obviously, none of the projections that we have described have both of these characteristics. The only one that has the first characteristic is the Mercator. On this projection the meridians are parallel, and the parallels are parallel to each other and perpendicular to the meridians; therefore, the direction of north or east is the same anywhere on the map. With regard to the second characteristic, however, a distance of 15 degrees (for example) is longer in any part of the map north-south than a distance of 15 degrees east-west (even in the same part).

Figure 9-23.-Meridians and parallels on a polar gnomonic projection.

As for the transverse Mercator, the conic, and the gnomonic projections, a glance at the appearance of meridians and parallels on any one of these indicates not only that direction is different in different parts of the map, but that the direction of North (for example) in one part of the map may be precisely opposite to that of north in another. Lets call the two types of conformality we have mentioned directional conformality and distance conformality. Some authorities hold that directional conformality is all that is required for a conformal projection. A Mercator projection has this type of conformality, and this fact makes that type of projection highly advantageous for navigational charts. A navigator is primarily interested in determining geographical location of his ship; and the principal disadvantage of Mercator projectionthe north-south compared to east-west distance distortion (which increases with latitude)is negligible in navigational practice. This statement applies only to navigation in customary latitudes, however, since Mercator projection of the polar regions (above about 80-degrees latitude) is impossible.

For surveying and other purposes in which distance measurements must be consistent in every direction, Mercator projection presents disadvantages. To understand these, you have only to reflect on the fact that no distance scale could be consistently applied to all parts of a Mercator projection, which means that no square grid system could be superimposed on a Mercator projection; however, the transverse Mercator projection, as it is used in conjunction with the UTM military grid, provides relatively small-area maps that are virtually conformal, both direction-wise and distance-wise.