18

Logic II 18

how many weights of each class there would be, upon
this theory, in every half grain. There is also a brown
curve which whose ordinates are the sums of those of the
blue ones and which would not pass through every red dot
if it were to represent the observations with mechanical
accuracy. I repeat that this theory has not been the subject
of any but the simplest calculations. It is obvious that some
such theory must be true, but to decide how near my theory
probably comes to the true theory or how it ought to be able modified,
it would be a very intricate problem for the solution of which
the data are probably insufficient. It does not concern
us here; our objects being merely to make it clear that
truly natural classes may, and undoubtedly often do
merge into one another inextricably.

It is, I think, pretty certain that there were as many active
standards. Before the adoption of the metric system, every
city throughout the greater part, if not all, the continent of Europe