eory gives a complete
explanation. It is well known that the laws of motion are not valid for
any axes of reference which you may choose to take fixed in any rigid
body. You must choose a body which is not rotating and has no
acceleration. For example they do not really apply to axes fixed in the
earth because of the diurnal rotation of that body. The law which fails
when you assume the wrong axes as at rest is the third law, that action
and reaction are equal and opposite. With the wrong axes uncompensated
centrifugal forces and uncompensated composite centrifugal forces
appear, due to rotation. The influence of these forces can be
demonstrated by many facts on the earth's surface, Foucault's pendulum,
the shape of the earth, the fixed directions of the rotations of
cyclones and anticyclones. It is difficult to take seriously the
suggestion that these domestic phenomena on the earth are due to the
influence of the fixed stars. I cannot persuade myself to believe that a
little star in its twinkling turned round Foucault's pendulum in the
Paris Exhibition of 1861. Of course anything is believable when a
definite physical connexion has been demonstrated, for example the
influence of sunspots. Here all demonstration is lacking in the form of
any coherent theory. According to the theory of these lectures the axes
to which motion is to be referred are axes at rest in the space of some
time-system. For example, consider the space of a time-system {alpha}.
There are sets of axes at rest in the space of {alpha}. These are
suitable dynamical axes. Also a set of axes in this space which is
moving with uniform velocity without rotation is another suitable set.
All the moving points fixed in these moving axes are really tracing out
parallel lines with one uniform velocity. In other words they are the
reflections in the space of {alpha} of a set of fixed axes in the space
of some other time-system {beta}. Accordingly the group of dynamical
axes required for Newton's Laws of Motion is the outcome of the
necessity of referring motion to a body at rest in the space of some one
time-system in order to obtain a coherent account of physical
properties. If we do not do so the meaning of the motion of one portion
of our physical configuration is different from the meaning of the
motion of another portion of the same configuration. Thus the meaning of
motion being what it is, in order to describe the motion of any system
of objects without ch