II

The System of Co-ordinates

Einstein continues to explain how to measure the distance between two points on a rigid body. He assumes we have no standard for measuring distance and thus uses an undefined rod as a standard. This rod can be placed end-to-end, giving a distance in a standard called "rods." Should the distance not be an even number of rods, the rod can be divided into smaller divisions, allowing measurement in fractions of rods, such as 9 rods plus 45 percent of a rod or 9.45 rods. This system can now be the basis for all measurements of length.

Every position of an object or event can be specified in reference to a point on a rigid body. The Earth is a rigid body with well-known locations that can be used as reference points. Einstein uses Trafalgar Square as his reference point in the English translation of his book.

Now, what about objects that are not on the Earth? Let's say there is a cloud above Trafalgar Square. The cloud's height can be measured by extending a pole to the cloud and then measuring the length of the pole. The location of the cloud can be specified by the location of the foot of this pole and the length of the pole.

We can eliminate the need for named points of reference by applying the Cartesian system of coordinates, which uses three intersecting planes (x, y, and z). An object can be located by its x, y, and z coordinates. Using indirect means (such as triangulation), we can free ourselves from physical rods and poles to make measurements.