and which we employ as a standard measure. If, now, _A_ and _B_ are two
points on a rigid body, we can construct the line joining them
according to the rules of geometry; then, starting from _A_, we can
mark off the distance _S_ time after time until we reach _B_. The
number of these operations required is the numerical measure of the
distance _AB_. This is the basis of all measurement of length.[2]
[2] Here we have assumed that there is nothing left over _i.e._ that
the measurement gives a whole number. This difficulty is got over by
the use of divided measuring-rods, the introduction of which does not
demand any fundamentally new method.
Every description of the scene of an event or of the position of an
object in space is based on the specification of the point on a rigid
body (body of reference) with which that event or object coincides.
This applies not only to scientific description, but also to everyday
life. If I analyse the place specification Trafalgar Square,
London [3] I arrive at the following result. The earth is the rigid
body to which the specification of place refers; Trafalgar Square,
London is a well-defined point, to which a name has been assigned, and
with which the event coincides in space.[4]
[3]
I have chosen this as being more familiar to the English reader than
the Potzdammer Platz, Berlin, which is referred to in the original.
(R. W. L.)
[4] It is not necessary here to investigate further the significance
of the expression coincidence in space. This conception is
sufficiently obvious to ensure that differences of opinion are
scarcely likely to arise as to its applicability in practice.
This primitive method of place specification deals only with places on
the surface of rigid bodies, and is dependent on the existence of
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