e of any real use.

That, he said, is a work infinitely beyond our present astronomers.

Yes, I said; and there are many other things which must also have a
similar extension given to them, if our legislation is to be of any
value. But can you tell me of any other suitable study?

No, he said, not without thinking.

Motion, I said, has many forms, and not one only; two of them are
obvious enough even to wits no better than ours; and there are others,
as I imagine, which may be left to wiser persons.

But where are the two?

There is a second, I said, which is the counterpart of the one already
named.

And what may that be?

The second, I said, would seem relatively to the ears to be what the
first is to the eyes; for I conceive that as the eyes are designed to
look up at the stars, so are the ears to hear harmonious motions; and
these are sister sciences--as the Pythagoreans say, and we, Glaucon,
agree with them?

Yes, he replied.

But this, I said, is a laborious study, and therefore we had better go
and learn of them; and they will tell us whether there are any other
applications of these sciences. At the same time, we must not lose
sight of our own higher object.

What is that?

There is a perfection which all knowledge ought to reach, and which our
pupils ought also to attain, and not to fall short of, as I was saying
that they did in astronomy. For in the science of harmony, as you
probably know, the same thing happens. The teachers of harmony compare
the sounds and consonances which are heard only, and their labour, like
that of the astronomers, is in vain.

Yes, by heaven! he said; and 'tis as good as a play to hear them
talking about their condensed notes, as they call them; they put their
ears close alongside of the strings like persons catching a sound from
their neighbour's wall--one set of them declaring that they distinguish
an intermediate note and have found the least interval which should be
the unit of measurement; the others insisting that the two sounds have
passed into the same--either party setting their ears before their
understanding.

You mean, I said, those gentlemen who tease and torture the strings and
rack them on the pegs of the instrument: might carry on the metaphor
and speak after their manner of the blows which the plectrum gives, and
make accusations against the strings, both of backwardness and
forwardness to sound; but this would be tedious, and therefore I wil