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. A system of co-ordinates of which the
state of motion is such that the law of inertia holds relative to it is
called a Galileian system of co-ordinates. The laws of the mechanics
of Galilei-Newton can be regarded as valid only for a Galileian system
of co-ordinates.
V.
THE PRINCIPLE OF RELATIVITY (IN THE RESTRICTED SENSE)
In order to attain the greatest possible clearness, let us return to
our example of the railway carriage supposed to be travelling
uniformly. We call its motion a uniform translation ( uniform because
it is of constant velocity and direction, translation because
although the carriage changes its position relative to the embankment
yet it does not rotate in so doing). Let us imagine a raven flying
through the air in such a manner that its motion, as observed from the
embankment, is uniform and in a straight line. If we were to observe
the flying raven from the moving railway carriage. we should find that
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