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In the first place we entirely shun the vague word "space," of

which, we must honestly acknowledge, we cannot form the slightest

conception, and we replace it by "motion relative to a

practically rigid body of reference." The positions relative to

the body of reference (railway carriage or embankment) have

already been defined in detail in the preceding section. If

instead of "body of reference" we insert "system of

co-ordinates," which is a useful idea for mathematical

description, we are in a position to say: The stone traverses a

straight line relative to a system of co-ordinates rigidly

attached to the carriage, but relative to a system of

co-ordinates rigidly attached to the ground (embankment) it

describes a parabola. With the aid of this example it is clearly

seen that there is no such thing as an independently existing

trajectory (lit. "path-curve"[6], but only a trajectory relative

to a particular body of reference.

[6] That is, a curve along which the body moves.