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With this and with a second difficulty prevailing here we shall

have to deal in detail later.

IV. THE GALILEIAN SYSTEM OF CO-ORDINATES

As is well known, the fundamental law of the mechanics of

Galilei-Newton, which is known as the law of inertia, can be

stated thus: A body removed sufficiently far from other bodies

continues in a state of rest or of uniform motion in a straight

line. This law not only says something about the motion of the

bodies, but it also indicates the reference-bodies or systems of

coordinates, permissible in mechanics, which can be used in

mechanical description. The visible fixed stars are bodies for

which the law of inertia certainly holds to a high degree of

approximation. Now if we use a system of co-ordinates which is

rigidly attached to the earth, then, relative to this system,

every fixed star describes a circle of immense radius in the

course of an astronomical day, a result which is opposed to the

statement of the law of inertia. So that if we adhere to this law

we must refer these motions only to systems of coordinates

relative to which the fixed stars do not move in a circle.