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II. THE SYSTEM OF CO-ORDINATES

On the basis of the physical interpretation of distance which has

been indicated, we are also in a position to establish the

distance between two points on a rigid body by means of

measurements. For this purpose we require a "distance" (rod S)

which is to be used once and for all, and which we employ as a

standard measure. If, now, A and B are two points on a rigid

body, we can construct the line joining them according to the

rules of geometry; then, starting from A, we can mark off the

distance S time after time until we reach B. The number of these

operations required is the numerical measure of the distance AB.

This is the basis of all measurement of length.[2]

[2] Here we have assumed that there is nothing left over i.e.

that the measurement gives a whole number. This difficulty is got

over by the use of divided measuring-rods, the introduction of

which does not demand any fundamentally new method.