Page:Eddington A. Space Time and Gravitation. 1920.djvu/93



any surface it requires two independent numbers or "coordinates" to specify the position of a point. For this reason a surface, whether flat or curved, is called a two-dimensional space. Points in three-dimensional space require three, and in four-dimensional space-time four numbers or coordinates.

To locate a point on a surface by two numbers, we divide the surface into meshes by any two systems of lines which cross one another. Attaching consecutive numbers to the lines, or better to the channels between them, one number from each system will identify a particular mesh; and if the subdivision is sufficiently fine any point can be specified in this way with all the accuracy needed. This method is used, for example, in the Post Office Directory of London for giving the location of streets on the map. The point (4, 2) will be a point in the mesh where channel No. 4 of the first system crosses channel No. 2 of the second. If this indication is not sufficiently accurate, we must divide channel No. 4 into ten parts numbered 4.0, 4.1, etc. The subdivision must be continued until the meshes are so small that all points in one mesh can be considered identical within the limits of experimental detection.

The diagrams, Figs. 10, 11, 12, illustrate three of the many kinds of mesh-systems commonly used on a flat surface.

If we speak of the properties of the triangle formed by the points (1, 2), (3, 0), (4, 4), we shall be at once asked, What mesh-