The colored American., 1899-12-09

q fixed quantity oil plastlc materlal lHs
clay, or putty) the change from each
TO the next could proceed by imper-
eeptible degrees. Our solid blocks af-
ford a study in arithmetic, for here
the numbers are distinctly shown.
Here, also, is a geometrlcal figure with
Commensurate parts. But the plastic
prism, undergoing similar transforma'
tions by varying the pressure on the
several faces, is not go easily dissecteo;
the edges may be incommensuraoie.
We thus pass from the domain OF
arithmetic to that of algebra. The sym
boil NxNxL still expresses the volume
of the prism, but the symbols nave
new meaning; no longer are they num-
bers, but the lengths Of the several
edges. new take ball, suspended by
a wire, and swinging as pendulum.
The length represents the height OF our
SO blocks, in one vertical row. Another
pendulum represents the height OF our
square prism where two BLOCKS are
seen one 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 3 swings
in the ssme time; and if the length OF
the pendulum equals the height OF a
sngle block, II 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 q very lmpor-
tant law of mechanics, which may be
expressed with the aid Of our formula,
thus: NxNxL equal constant; but here's
N expresses number aud L length;
N is the number of vibrations made by
the pendulum in a 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 slgebralc
sense, for incommensurable values; the
geometric conception may serve as
emblem of the physical law. At this
point, the second law of motion was IL
Iustrated by experiments with pulley
running down an inclined wire, with
increasing velocity.
Pure mathematics deals with ab-
stract conceptions, which cannot be
fully realized in practice. The walls OF
a room are nearly plumb; the angles
are nearly right angles, the height OF
the ceiling is about 80 many feet and
Inches. Absolute precision in time,
size or measur ament is unknown; Tor
as the mechanic increases his skill IN
fashloning the matelia's, the mathema
ticlan also increases his skill In ina
precision Of his measurements. The
idealist, soaring amid infinltesimals OF
this Nth dimension. may forget the
amenities of polite society, ana even
the duties OF home life. The professor
of applied mechanics may come tc
grief if he thinks he can manage better
, than a well trained horse in conduct
ing a wagon down steep hill. To
large extent, the mathematician lives il
different world of thought, and speaks
, language all mis- own. The function
, of higher ma .hematics on the ont
hand, is to cultivate the ideal in pure
thought; that which is absolutely true
{ snd 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 you
building lot, the capacity Of all you
| closets, the fitting Of the carpet, tn
figure on the wall paper, the tuning O
, YOUR piano, the coIors of the rainbow
( and tie problems of socialism. Tn
g study of mathematics demands scrupu
I lous attention to details. A misplaced
/, decimal point may change sense t
d nonsense; and a reversed sign, 1t
Il said, plunged that traia of passenge
v cars trough the rail road bridge a
< Ashtabula
c In the development Of mind, as
body, mixed diet Is needed. If othe
branches OF study were out Of reach
y however. mathematics in conjunction
with the varied applications to time
place, matter, force and energy, as de
> termined by OBSERVATION-DISCLOSURES
, and in1uctive reasoning combined
= would embrace sufficient variety for
y liberal education.
TProf Fosters paper on Science
will appear in our neXt.-ED
t Thanksgiving in "The Park"
Among the many ThanKsgivin