Fort Worth daily gazette. (Fort Worth, Tex.) 1882-1891, 1885-03-29
vs.. CONCRETE
A Discussion, the outgrowth Of the
Arlington Institute.

HASDLEY, TEN.. March %, 1885.
To the Editor OF the Gazette.
In recent number saw an article
from the pen Of Prof. Hogg, in reply
to certain structures In communities
ton from one "Rusticus." concerning
the institute held at Arlington.
The professor, in taking Rusticusp
to task. states That on entering, Prof
Handy WAS speaking on the subject Of
arithmetic, and seemed uncertain
whether the divisor was concrete or
abstract
AS failed TO make myself clear by
what said on that occasion, aud be-
levinR also that, what 10 written IL
mightier than what lie said" would
like space enough in your paper to ex-
plain my position 30 there may be no
uncertainty in the matter.
When Prof. Hogg and Col. Cham
beIs entered the house, was speaking
OF the terms in multiplication That
the multiplicand was concrete num-
Der, the mulliplier abstract. and the
product of the same denomination ss
the multiplicaud. L further stated
that when the multipiier W as very
much greater than the mul iplicand,
the multiplicand was often used 10
| mul iply without atit citing the product.
For example, what will 375 ards of
cloth cost ~ seven cents per yard?
Now. whatever can be said Of these
terms in multiplication can be said Of
them in division. In multiplication
We have the factors and seek the
product. In division we have the
product (dividend) and one factor and
seek the other But the point Ia as
TO which factor is the divisor. To
divide by either factor gives the other.
Divide Joy the multiplicand and your
divisor is u concrete number. This is
precisely true, AS laid down by Prof
Naye iu HIS reply to 'Rusticus. Line
o impaired with line. surface With sur
face, ,oiid,wilh lid, etc This is x4ctly
true whenever you divide the product
divide by the factor known In null
tipl cation AS the multiplIcsnd.
For example, this same problem In
multiplication can be utilized In divis'
ion. Given 1925 cents To buy cloth at
Z cents per yard, how many yards oil
cloth eau bu. +?
Here the product 10 divid ed by the
multiplicand. The product Is called
the dividend, the multiplicand the di-
| VltOTr fDul We ~ Abb W klNC Ahto RApp
lem under different conditions some
times. Given 1925 cents for 375 yards
of cloth, " hat IL the price OF one yard
do you divide by Undoubtedly by
the abstract multiplIer 375 yards ;
which gives Your quoIient cent?.
This 10 In exact harmony wiih the
mathematical truth thai, 10 DIVIDE the
product by one isotpr, gives the other.
Now, while this was my explanation
Of the relation OF thete terms 10 each
other, | further tried 10 explain that,
by an ''illegaotn disqui-ition and lit
tie phoelosophy, we could, logically
consider the multiplicaDd aud product
concrete, even when as stated, using
the multiplicand as the multiplier,
and by a parity OF reasoning, we can,
when dividing by the abstract (mui /
plier) conclude we have in effect divi.
ded by the quotient and found the real
divisor; ana, ss the product has be,
J come the dividend, the multiplieSbd
the divisOr, the muliiplier the quo
tient, we further adj 10 the complica'
I ton by declaring the quotient 10 the
divisor and the divisor Is the quotient
This Is as near as can rec llect the
substance OF what / said on the coca
sion referred 10, aud believe my posi-
tion Is CORE ct, and l believe all VINO
have carefully examined the mattel
, will ayr with me
/ feel great interest in the success
, of the institute work. May 10 be th'
means OF advancing the standard o
, education in both city and county Z
our very highest ideal;
j A. HAMBY.
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