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 ap-
plied to both the objects which are to be mea-
sured ; 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 mea-
suring. 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 altera-
tion in the instrument, the same relation of
length between the two trees would be ob-
tained. 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