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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 1, since, according to Section XII,

moving bodies suffer a shortening in the direction of the motion.

On the other hand, the measuring-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 π = 3.14 . .

., but a larger number,[19] whereas of course, for a disc which

is at rest with respect to K, this operation would yield π

exactly.