For this reason it is not possible to obtain a reasonable
definition of time with the aid of clocks which are arranged at rest
with respect to the body of reference. A similar difficulty presents
itself when we attempt to apply our earlier definition of simultaneity
in such a case, but I do not wish to go any farther into this
question.
Moreover, at this stage the definition of the space co-ordinates also
presents insurmountable difficulties. If the observer applies his
standard measuring-rod (a rod which is short as compared with the
radius of the disc) tangentially to the edge of the disc, then, as
judged from the Galileian system, the length of this rod will be less
than I, since, according to Section 12, moving bodies suffer a
shortening in the direction of the motion. On the other hand, the
measaring-rod will not experience a shortening in length, as judged
from K, if it is applied to the disc in the direction of the radius.
If, then, the observer first measures the circumference of the disc
with his measuring-rod and then the diameter of the disc, on dividing
the one by the other, he will not obtain as quotient the familiar
number p = 3.14 . . ., but a larger number,[4]** whereas of course,
for a disc which is at rest with respect to K, this operation would
yield p exactly.
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