tch, intensity, and timbre of each instrument.

When a molecule is acted on by various forces, a resultant motion is
unquestionably produced, but this would only tend to send the molecule
forward and back in _one_ direction, and, in fact, a direction it might
have taken in the first place if hit properly.

How any resultant can be established as regards the time necessary for
the molecule to take so as to complete a full vibration for the note
C_{11}, which requires 1/16 of a second, and for other notes up to
C''''', which only requires 1/4176 of a second, as when an orchestra is
playing, is certainly beyond human comprehension, if it is not beyond the
"transcendental mathematics" of the present day.

Unquestionably, the able mathematicians Lord Rayleigh, Stokes, or
Maxwell, if the problem was submitted to them, would start directly to
work, and deduce by so called "higher mathematics" the required motions
the molecules would have to undergo to accomplish this marvelous
task--the same as they have established the diameter of the _supposed_
molecules, their velocity, distance apart, and number of bombardments,
without any shadow of _positive_ proof that any such things as molecules
exist.

As S. Caunizzana has said: "Some of the followers of the modern school
push their faith to the borders of fanaticism; they often speak on
molecular subjects with as much dogmatic assurance as though they had
actually realized the ingenious fiction of Laplace, and had constructed a
microscope by which they could detect the molecule and count the number
of its constituent atoms."

Speaking of the "modern manufacturers of mathematical hypotheses,"
Mattieu Williams says: "It matters not to them how 'wild and visionary,'
how utterly gratuitous, any assumption may be, it is not unscientific
provided it can be vested in formulae and worked out mathematically.

"These transcendental mathematicians are struggling to carry philosophy
back to the era of Duns Scotus, when the greatest triumph of learning was
to sophisticate so profoundly an obvious absurdity that no ordinary
intellect could refute it.... The close study of _pure_ mathematics, by
directing the mind to processes of calculation rather than to phenomena,
induces that sublime indifference to facts which has characterized the
purely mathematical intellect of all ages."

Tyndall, however, states in all frankness, and without the aid of
mathematical considerations, that "when we tr