Weekly national intelligencer. [volume] (Washington [D.C.]) 1841-1869, 1853-11-19
TO TIE EDITORS.
OcroDga 90, 1856;


GENTLEMEN; In your paper of October 18th, over the
signature s. E. c., some examples of curious properties
Of numbers given Such publications, if they lead
greater attention to the theory Of numbers than it
has been usual to bestow upon it, may prove beneficial
The subject has been too much neglected by teachers
and there exists amongst them generally gross gnor-
ance of it, unless there has been recently great i'm
proyement. From the high attainments and deserved
reputation of several gentlemen who have within few
years past prepared treatses upon arithmetic for our
schools it is possible that there has been such improve
ment Formerly, with exceptions, arithmetic was
taught in this country only as an art and the books
upon it then in possessed little or no claim TO
scientific character and few teachers competent to
supply their defects
With regard to the examples alluded TO, would it not
be more to say that the properties they illus
rate are absolute properties Of numbers but are re-
ative to the system of notation to which they ap
piled Ten being the base Of the system Of notation and
enumeration which prevails, has led to the adoption OF
erroneous ideas of peculiar properties of that number
The only for the system, with that base, having
been almost uniformly adopted and which few
will question: is that is furnished with ten fingers,
which served him for his primitive instruments for calcu
ation.* Another number might have been selected for
the base which would be more convenient and present
advantages than the decimal The properties which
given, and in others of like character which
might be adduced would shift to another number if APP
piled different system of notation constructed upon
like principle to the decimal local of the
digit, but to different base and then the number nine
would fail to exhibit those properties This may easily
verified by trial. and is the for considering such
properties relative to the system Of notation and
absolute properties of the number.
1t is true that it has been stated by high authority
/ p
practical utility in the applications of mathematics and
ais little studied by large class of mathematician
deeply versed in the higher analysis" and sis in fact
isolated part of mathematics Such expressions are
likely give idea of the unimportance and nsgnif-
of this branch of science which they could hardly
have been intended to convey, and which it does
merit.
We have treatses upon the theory by many of the
ablet mahematcians by La Grange, LGgendre, Barlow
Cauchy Gauss the last of whom has furnished and
elegant formulas, and has devised the construction of
tables NEW in principle) which abridge labor in
astronomical computations, and in others Of like char
Perhapsit is presumptuous in not acquainted
with his works. and possibly possessing the capacity
justly appreciate hem suggest that his nvestga-
tons in this theory have led him to these improvements
1t may be equally to suggest that similar invest-
cations bore much part in the invention and construction
of that wonder ofart and SCIENCE the engine of Babbage
Although this theory presents questions of very
absruse character requiring for their management great
penetration and ingenuity, and familiarity with the
higher analysis still moderate acquaintance with the
elementary branches of mathematics will suffice to attain
knowledge of many of its methods, processes and
results Est euoddam prodire tenus, datur ultra "
for such knowledge will not only crafty rational curl
osty but will give clearer and more comprehensive views
of arithmetical operations and increased ability for
hand md
The object, however, Of this note is to solicit you to
prevail s. E. C. to apply his arithmetic the elucida
ton of statement made in very extraordinary work,
which appeared something than two years ago,
titled "a System of Mechanical Philosophy, being Re-
search inte the Laws of Force The statement will be
found on page 3l2, where, speaking of falling bodies it
says: If divide the space Of the perpendicular fall
into equal parts the velocity of the first part will be rs
l. of the second g. of the third s. and ON At school
used to be taught differently and, in simplicity
thought that really demonstrated that the
suit would be derenti and also that what taught
was confirmed by all experiments those of Calico
at the tower Of Pisa to the performances of Atwoods
machine should be gratifcd to learn what the more
recent experiments from which deduced this new
law promulgated this system Of mechanical philosophy
Very respectfully your obedient servant, E.
In the nomenclature of our Auglo-Saxon ancestors
80 was hundneon-g, l0Obundeon-tig, Ito hund endlu
fontg You any Of your correspondents who live in
region where cxicons and vocabulares accessible
will confer favor by informing whether the hund
imports hand and tg time 1t is stated that in one of
the earlier Gothic languages taium or tqiupd was the
name of 10. If so, the A. s. tyn 10y probably from
that source instead of being from the Greek deka as
Webster suggests The import Of tahund is two hands
May not then, the terms above given signify all on The
hands nine times, ten tines eerea times &c.? The nume-
ration of the AngoSaxon gives evidence that at one
time their system was not upon single base like our
decimal system but double Traces of the same charac
ter may be found in vernacular and in the French
and various other languages.
Leaving out Of view the difference Of velocity due to
different distances from the Of the earth and also
the effect Of the resistance Of the air and taking the We
octy Of tho first part for the unit then under the case
as stated the mean velocity Of the successive equal parts
or spaces will be:
" Tug