Gnomonic Projection
The theory of this projection is to make a curved line appear and be a straight line on the chart, i.e., as though you were at the center of the earth and looking out toward the circumference. The Gnomonic Projection is of particular value in sailing long distance courses where following a curved line over the earth´s surface is the shortest distance between two points that are widely separated. This is called Great Circle Sailing and will be talked about in more detail later on. The point to remember here is that the Hydrographic Office prints Great Circle Sailing Charts covering all the navigable waters of the globe. Since all these charts are constructed on the Gnomonic Projection, it is only necessary to join any two points by a straight line to get the curved line or great circle track which your ship is to follow. The courses to sail and the distance between each course are easily ascertained from the information on the chart. This is the way it is done:
(Note to Instructor: Provide yourself with a chart and explain from the chart explanation just how these courses are laid down.)
Spend the rest of the time in having pupils lay down courses on the different kinds of charts. If these charts are not available assign for night work the following articles in Bowditch, part of which reading can be done immediately in the class room - so that as much time as possible can be given to the reading on Dead Reckoning: 167-168-169-172-173-174-175-176 - first two sentences 178-202-203-204-205-206-207-208.
Note to pupils: In reading articles 167-178, disregard the formulæ and the examples worked out by logarithms. Just try to get a clear idea of the different sailings mentioned and the theory of Dead Reckoning in Arts. 202-209.
WEDNESDAY LECTURE
Useful Tables—Plane And Traverse Sailing
The whole subject of Navigation is divided into two parts, i.e., finding your position by what is called Dead Reckoning and finding your position by observation of celestial bodies such as the sun, stars, planets, etc.
To find your position by dead reckoning, you go on the theory that small sections of the earth are flat. The whole affair then simply resolves itself into solving the length of right-angled triangles except, of course, when you are going due East and West or due North and South. For instance, any courses you sail like these will be the hypotenuses of a series of right-angled triangles. The problem you have to solve is, having left a point on land, the latitude and longitude of which you know, and sailed so many miles in a certain direction, in what latitude and longitude have you arrived?