then the
time-units of {alpha} and {gamma} are also congruent.

By means of these axioms formulae for the transformation of
measurements made in one time-system to measurements of the same facts
of nature made in another time-system can be deduced. These formulae
will be found to involve one arbitrary constant which I will call k.

It is of the dimensions of the square of a velocity. Accordingly four
cases arise. In the first case k is zero. This case produces
nonsensical results in opposition to the elementary deliverances of
experience. We put this case aside.

In the second case k is infinite. This case yields the ordinary
formulae for transformation in relative motion, namely those formulae
which are to be found in every elementary book on dynamics.

In the third case, k is negative. Let us call it -c squared, where c
will be of the dimensions of a velocity. This case yields the formulae
of transformation which Larmor discovered for the transformation of
Maxwell's equations of the electromagnetic field. These formulae were
extended by H. A. Lorentz, and used by Einstein and Minkowski as the
basis of their novel theory of relativity. I am not now speaking of
Einstein's more recent theory of general relativity by which he deduces
his modification of the law of gravitation. If this be the case which
applies to nature, then c must be a close approximation to the
velocity of light _in vacuo_. Perhaps it is this actual velocity. In
this connexion '_in vacuo_' must not mean an absence of events, namely
the absence of the all-pervading ether of events. It must mean the
absence of certain types of objects.

In the fourth case, k is positive. Let us call it h squared, where h
will be of the dimensions of a velocity. This gives a perfectly possible
type of transformation formulae, but not one which explains any facts
of experience. It has also another disadvantage. With the assumption of
this fourth case the distinction between space and time becomes unduly
blurred. The whole object of these lectures has been to enforce the
doctrine that space and time spring from a common root, and that the
ultimate fact of experience is a space-time fact. But after all mankind
does distinguish very sharply between space and time, and it is owing to
this sharpness of distinction that the doctrine of these lectures is
somewhat of a paradox. Now in the third assumption this sharpness of
distinction is adequately preserved. There is a funda