adox in my doctrine of the nature of
space which is not in essence inherent in the theory of the relativity
of space. But this doctrine has never really been accepted in science,
whatever people say. What appears in our dynamical treatises is Newton's
doctrine of relative motion based on the doctrine of differential motion
in absolute space. When you once admit that the points are radically
different entities for differing assumptions of rest, then the orthodox
formulae lose all their obviousness. They were only obvious because you
were really thinking of something else. When discussing this topic you
can only avoid paradox by taking refuge from the flood of criticism in
the comfortable ark of no meaning.

The new theory provides a definition of the congruence of periods of
time. The prevalent view provides no such definition. Its position is
that if we take such time-measurements so that certain familiar
velocities which seem to us to be uniform are uniform, then the laws of
motion are true. Now in the first place no change could appear either as
uniform or non-uniform without involving a definite determination of the
congruence for time-periods. So in appealing to familiar phenomena it
allows that there is some factor in nature which we can intellectually
construct as a congruence theory. It does not however say anything about
it except that the laws of motion are then true. Suppose that with some
expositors we cut out the reference to familiar velocities such as the
rate of rotation of the earth. We are then driven to admit that there is
no meaning in temporal congruence except that certain assumptions make
the laws of motion true. Such a statement is historically false. King
Alfred the Great was ignorant of the laws of motion, but knew very well
what he meant by the measurement of time, and achieved his purpose by
means of burning candles. Also no one in past ages justified the use of
sand in hour-glasses by saying that some centuries later interesting
laws of motion would be discovered which would give a meaning to the
statement that the sand was emptied from the bulbs in equal times.
Uniformity in change is directly perceived, and it follows that mankind
perceives in nature factors from which a theory of temporal congruence
can be formed. The prevalent theory entirely fails to produce such
factors.

The mention of the laws of motion raises another point where the
prevalent theory has nothing to say and the new th