The colored American., 1899-12-09


clay, or putty) the change from each
to the next could proceed by imper-
ceptible degrees. Our solid blocks sf-
ford a study in arithmetic, for here
the numbers are distinctly shown.
Here, also, is geometrIcal figure with
Commensurate parts. But the plastic
prism. undergoing similar transforma-
tions by varying the pressure on the
several faces, is not 30 easily dissected;
the edges may be incommensurabie
We thus pass from the domain OF
arithmetic to that of algebra. The sym
Dol NxNxL still expresses the volume
of the prism, but the symbols have
new meaning; no longer are they num-
beTs. but the lengths OF the several
edges, 1 new take ball, suspended by
a wire, and swinging as a pendulum.
The length represents the height OF our
36 blocks, in one vertical row. Another
pendulum represents the height of our
squers prism where two blocks are
seen a1e side of The base; and while
the first pendulum makes one swing,
the SECOND makes two. A third pendu'
Ium, whose length represents the
prism 4 blocks high, makes swings
IN the same time; aud if the length of
the pendulum equals the height OF a
sIngle block, it also is found to make
as many swings as the number OF
blocks in one horizontal row, OF the
corresponding prism. These simple
experiments illustrate a very impor-
tant law of mechanics, which may be
expressed with the aid OF our formula,
thus: NxNXL equal constant; but heres
n expresses a number aud L a length;
n is the number of vibrations made by
the pendulumin given time, while IL
is the length Of the pendulum; when
one increases, the other diminishes, but
the product of L by the square OF n ls
unchanged. What is here true in an
arithmetical sense, for values expressed
by numbers, is true also IN an algebTaic
sense, for incOmmensuTable values; the
geOmetric conception may serve as
emblem of the physical law. At this
point, the second law of motion was il
Illustrated by experiments with pulley
running down an inclined wire, with
increasing veloclty.l
Pure mathematics deals with ab-
strsct conceptions, which cannot be
fully realized in practice. The walls of
a room are nearly plumb; the angles
are nearly right snglts, the height OF
the ceiling is about SO many feet and
inches Absolute precision in time,
siza or measur ament is unknown; for
as the mechanic increases his skill in
fashiOning the mateIiRs, the mathema
t1clan also increases his skill In Ihe
precision of his measurements. The
idealist, soaring amid j1finltesimals OF
this Nth dimension. may forget the
| amenities Of polite society, and even
the duties of home life. The professor
of applied mechanics may come to
grief if he thinks he can manage better
|
ing a wagon down a steep hill. To a
large extent, the mathematician lives in
different world Of thought, and speaks
a language all MS own. The function
Of higher ma ,hematies on the one
| hand, is to cultivate the ideal in pure
| thought; that which Is absolutely true,
and can be true, only when the con-
ditiOns are ideal, impossible Of at
tainment; YET the realm OF mathe,
matics touches home life at thousand
points; as in the size and shape of your
building lot, the capacity OF all yOu'
closets, the fitting Of the carpet, the
figure ON the wall paper, the tuning OF
your piano, the oolOrs of the rainbow,
and the problems of socialism. The
study of mathematics demands scrupu-
lCGz attention to details. A misplaced
decimal point may change sense to
nonsense; and a reversed sign, 1t is
said, plunged that train of passenger
cars trough the rail road bridge al
Ashtabuls
In the development of mind, as OF
body, mixed diet Is needed. If other
branches OF study were out of reach,
however. mathematics in conjunction
with the varied applications to time,
place, matter, force and energy, as de-
termined by experiment-deducti
and inductive reasoning com b1ned-
would embrace sufficient variety for q
liberal education.
[PrOf. Fosters paper on Science"
will appear in our next.-ED
Thanksgiving in "The Park"