nd again as before, half of the time the message has taken to cross
and recross the Atlantic is added to the Greenwich record of noon at
Washington. The number of hours, minutes, seconds, and fractions of
a second between these two corrected records represents the
difference in solar time between the two places, and incidentally
the same moment of time has been established for both--at least, so
it would appear.
But is it established? That each message took an equal time to
travel each way is pure assumption, and happens to be a false one.
The accuracy of the result is vitiated by a condition of things to
which the Relativists have called attention. Our determination might
be defended if Washington and Greenwich could be assumed to remain
at rest during the experiments, and some argument might even be made
in its favor if we could secure any cosmic assurance that the
resultant motion of the earth should be the same when Greenwich
signalled its noon to Washington and Washington its noon to Greenwich.
Our present discussion is merely illustrative, or diagrammatic; so
we will neglect the velocity of the earth in its orbit round the sun,
some forty times greater than that of a cannon ball, and the more
uncertain and more vertiginous speed of the whole solar system
towards its unknown goal. Let us consider only the rotation of the
earth on its axis, the tide-speed of day and night. To fix our idea,
this may be taken, in our latitudes, at eighteen thousand miles per
day, or perhaps half the speed of a Mauser rifle bullet.
So fast, then, will Washington have been moving to meet the message
from Greenwich. So fast will Greenwich have been retreating from
Washington's message.
Now the ultimate effect of motion on the time-determination cannot
be calculated along any such simple lines as these. Indeed, it
cannot be exactly calculated at all, for we have not all the data.
But there is certainly _some_ effect. Suppose one rows four miles up
a river against a current of two miles per hour, at a rowing speed
of four miles per hour. This will take two hours, plainly. The
return trip with the river's gift of two miles per hour will
evidently require but forty minutes. _Two hours and forty minutes_
for the round trip, then, of eight miles.
Now then, to row eight miles in still water, according to our
supposition, would have required but _two hours_. But, some one
objects, the current must help the return trip as much as it
h
|