16

Logic II 16

classes weights are small, and were therefore used for weighing costly
or even precious matter, our knowledge of ancient the practive of weighing
among the ancients allows us to guess with some confidence gives us ground for thinking it likely that about half
the weights would depart from their virtual standards by more,
and about half by less, than, say, 4 or 5 tenths or one per cent,
which, upon a ket, would be a little more than half from half to two thirds of a grain.
Now the whole interval here is 14 1/2 grains; and between 136.8
grains to 151.3 grains, there is no case of an interval of
more than a third of a grain not represented by any
weight of among the 144. To a person thoroughly familiar with
the theory of errors this shows that there must be four or
five different standards to which different ones aim to conform.
In order that every reader may see that this is
the case, I give a diagram upon which the abscissas
are grains and while the ordinates are represent the numbers of weights
among the 144 which are either exactly of the weight represented
by their abscissas of the points plotted or exceed that