mental distinction
between the metrical properties of point-tracks and rects. But in the
fourth assumption this fundamental distinction vanishes.

Neither the third nor the fourth assumption can agree with experience
unless we assume that the velocity c of the third assumption, and the
velocity h of the fourth assumption, are extremely large compared to
the velocities of ordinary experience. If this be the case the formulae
of both assumptions will obviously reduce to a close approximation to
the formulae of the second assumption which are the ordinary formulae of
dynamical textbooks. For the sake of a name, I will call these textbook
formulae the 'orthodox' formulae.

There can be no question as to the general approximate correctness of
the orthodox formulae. It would be merely silly to raise doubts on this
point. But the determination of the status of these formulae is by no
means settled by this admission. The independence of time and space is
an unquestioned presupposition of the orthodox thought which has
produced the orthodox formulae. With this presupposition and given the
absolute points of one absolute space, the orthodox formulae are
immediate deductions. Accordingly, these formulae are presented to our
imaginations as facts which cannot be otherwise, time and space being
what they are. The orthodox formulae have therefore attained to the
status of necessities which cannot be questioned in science. Any attempt
to replace these formulae by others was to abandon the _role_ of
physical explanation and to have recourse to mere mathematical formulae.

But even in physical science difficulties have accumulated round the
orthodox formulae. In the first place Maxwell's equations of the
electromagnetic field are not invariant for the transformations of the
orthodox formulae; whereas they are invariant for the transformations of
the formulae arising from the third of the four cases mentioned above,
provided that the velocity c is identified with a famous
electromagnetic constant quantity.

Again the null results of the delicate experiments to detect the earth's
variations of motion through the ether in its orbital path are explained
immediately by the formulae of the third case. But if we assume the
orthodox formulae we have to make a special and arbitrary assumption as
to the contraction of matter during motion. I mean the Fitzgerald-Lorentz
assumption.

Lastly Fresnel's coefficient of drag which represents the va