Installment twenty-two

At the end of our previous installment, Captain Mann was in the middle of
explaining the workings of the date line.
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Installment Twenty-two:

"You all see how ludicrous the matter appears when analyzed but a little.
The truth is, the whole question is one not of gaining or losing time, but
of computation.
"I carry with me," said the captain, "an extract from an article on the date
line which I found many years ago. I will read it with your permission. It
states the whole proposition more clearly than any word of mine could
possibly do. Here it is:
'The revolutions of the earth itself, as measured at fixed localities, are
what measure and number the days, not the revolutions that may be
indicated in the diary of a traveler. A person traveling east or west around
the world puts himself at variance with the numerical order of its
revolutions as computed at any fixed point; and the variance must be
corrected. That is the question involved in keeping a definite and identical
day on a round earth. Attending to this one point, a person need never
lose the definite day. To illustrate: Let us suppose a man to start from
point 'A' and travel eastward. Suppose he is able to fly around the world
and come back to his starting point in ten days. Every day, of course, he
is carried around by the revolution of the earth. But traveling, as he is,
with the earth, from west to east, each day he gains upon the earth one
tenth of its circumference. So in ten days, he would gain ten tenths, or a
whole circumference. So when he arrives at 'A' he finds that those who
have remained there have marked ten revolutions of the earth, and have
had ten days of time. But the earth has taken him around as many times
as it has them; and it addition to that, he has passed around once himself,
which is the same as another revolution for him, making eleven, and giving
him, according to his calendar, as he kept it from day to day, eleven days
instead of ten. What shall he do with that extra day? Drop it from the count.
Why? Because he knows that the earth itself has made only ten revolutions
as marked at point 'A' and the revolution of the earth itself is what marks
the day; not the times one individual goes around it. The individual must
make his count correspond to that of the earth wherever he is.
If the person goes around westward, this process is simply reversed. If he
travels at the same rate, his journey each day cancels one tenth of the
revolution of the earth as far as his count is concerned. In ten days he would
lose one whole revolution and would find, when coming to point 'A', that his
calendar shows only nine days instead of ten. What should he do? Add into
his account that lost day. Why? Because he knows that the earth has made
ten revolutions. Although he has been around the earth once, it has been
in such a direction as to apparently cancel one of its revolutions, and take
it out of the count. Instead of adding one, as in the other case, now he must
add to it to be in harmony with the real condition of things.
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To be continued...