105

ON MEASURES

pears to be this, that when we measure the
length of two objects by a third object, the
length of the latter, or the instrument employed,
must remain the same until it have been applied
 to both the objects which are to be measured
 ; or if it vary, it must vary in a known
degree. Suppose it is wished to ascertain the
relation of length between two trees lying
apart from each other on the ground. The
only requisite for doing this is a staff, or rod,
or any other instrument which shall continue
of the same length during the process of measuring.
 The process over, although the rod
might be instantly altered in length, it would
be as good a measure as before of the length
of these or any other objects: for suppose the
measurement to be repeated after this alteration
 in the instrument, the same relation of
length between the two trees would be obtained.
 But if the rod varied in its length in
an unknown degree, between applying it to the
first tree and the second, whether this interval
was a minute or an age, it is obvious that it