Weekly national intelligencer. [volume] (Washington [D.C.]) 1841-1869, 1853-11-19
COMMUNICATION.
TO THE EDITORS.

ne;eny full clear aud precise to enable adopts who are
familiar with the subject to grasp his idea; STILL as i
appears be intended for others also, he be wiling
make such further explanations will prevent mistake
by who desires investigate fairly and q appreciate
Justly the merit Of his discovery
Yhe object of this is to discuss the truth OF MS
physical theory and formulas the accuracy Of hs de-
examinations but to ascertain what is his theory and how
he deduces aud establishes his formulas From the &C
acknowledgement already made il will not be surprising
meaning should be attached to Mr.. CoUEss language
which il was intended convey, and if 50, ne IS
assured that it will be altogether unintenonal and from
,sconcepton ana it will afford pleasure to be put
right.
The distinction between an empirical formula and one
derived BY regular philosophic deduction is recognised
and appreciated. But formula that is susceptible of
demonstration may be emprcay used and is used by
who does not understand the Of the process
and in the adduced in illustration unless the
fer Introducing tho ratio of the circumference a
meteor, and for taking the time OF ra through definite
portion OF the pendulum rod is understood the principle
differs but slightly, if at all, from the method Of cacua-
ton by the clock maker far the person using
concerned
The time of vibration Of pendulum in cycloidal arc
IS equal TO the time of bodys fall through half the
length Of the pendulum multiplied by the ratio of the cir
unference to the diameter Admitting the received laws
Of motion, the proposition may be demonstrated. Il is
not rigdly true for circular generally although
the he small the will be so small as to be in
appreciabe and therefore for small may be safely
used IN practice In very large circular is sup
posed that experiment would show that the vibrations
will not conform to the rule demonstrated for cycoidal
1t s doubted whether the rule for cycoidal arcs upon
the data stated, be demonstrated rgdy BY what are
usually considered the principles of elementary geometry
Its demonstration depends upon the truth Of certain pro-
pertes OF the cycold for establishing which elementary
geometry Is not sufficient and Mr. CoUEs is understood
(not however, from the article in the Integencer but
from previous publications. not to attach much mpor
lance 10 the methods by which the properties Of the
cycioid demonstrated person may attain sufficient
evidence but short of demonstration to convince him of
the truth OF the properties of the cycod by other con-
Hderations, and even by mechanical methods Assuming
these properties part Of the data the proposition NAV
be demonstrated geometricaly 1t would give great sa
sfaction to see rigid demonstration Of the properties
N question upon what usually considered the prnc
pies of elementary geometry As intellect per-
haps as ever mortal man gifted with that of Pacha
has been exercised upon this without accomplishing
It by that method The absurdity is also recognised of
attempting to express numerical ratio between two he
terogeneous quantities, except by first referring even 10
conventional unit of its kind respectively and then
forming ratio between the resulting abstract numbers
This will not be quesonedb by any one and therefore the
reason Is plain for taking the time Of fall through ia de-
finite portion of the pendulum obtain the relation be-
tween the length and time Of vibration 1t may be Oh
served, however, that in considering two penduunrs
there is no absurdity in comparing the ratio Of their
lengths with the ratio Of their times and whatever may
De dimensions OF conventional the
viii be the same. So also with regard to solar dis
lance used by Mr. CoUEs The measure he gives of the
distance of the earth from the sun is the ratio Of the
radius yecor Of the earth to the suns diameter and it
perfectly indifferent Tin prncple1 whether his measure
Of length feet inches, miles, the ratio Will DE the
One, however, may be preferable 10 another Tor
cUnSehsSnce OF computation but the results viii be the
game
The formula which expresses Keplers third av-tbat
of the relation between the periods and the distances
pi3nets-notwithstandlng It's acknowledged utility and
conformity TO observed phenomena is il is believed
universally considered in the light in which il is viewed
by Mr. CcUEs, as being purely empirical and it viii be
no Light merit 70 establish IT. or any other that viii
form in its results with observation on the kind Of
basis II. which the first two laws Of Kepler rest
The subject Of the pendulum is introduced in the way
Of illustrations but the language afterwards used
amply that the planets pendulums ia another than
fgurative Even advocate Of the theory repu
dated BY Nr. CoUEs recognises analogy between the
phsnomena; that their distances increase SO
Their perodsand times Of vibration respectively increase
tnat IN one sense their motions alike regular and lie
Th 80" sc % reier them both to the principle
G.e appears to intend than this and that II
rs possible TO comprehend both motions h. tbe eo, ca
naua or that formulas for rotation and rtoption ~
tne planets may be deduced from that for the penG.nm
III Mr.. CoUEs does succeed land trnlv and baortI-
desire That he may succeed in deducing by legitimate
processes ana logical consequences from the eonstra,
ca laws OK the pendulum, formula for the rotation sa
revolution OF the planets which viii couforn in ~ ree
with observation he will achieve distinguished M
ana Will mud no difficulty securing the attention Of men
discovery. = = - F
abe relative times Of vibrations OF pendulums NAV he
expressed IN functions Of their lengths that
may DC the case as to revolutions Of planets il Il difficult
conceive how the relative times of rotation can lie en-
oraced IN or derived from the same formula whether
regard ther radn or their rad vectores as the pendu
lehgh ior' Notwithstanding the very great dif.
erehces Doth IN distance and SIZE Of all the panets
IRON Mercury to Mars their axia rotation i performed
- Deary the same time near twenty-four hours and
1eT exceeding them all in size and distance rotates
- css tan half their time Are not the
astronomers Of the time be relied on as correct or
near approximations
NI. CoCEs says: "Kepler's formula biased on the
square 81 the time and the cube Of ba d;.,a,oo go
80. nae sad, geometrcal expression OF an existing
-, snVWn % be correct by measurement The fore
1870 ia''on, based on the ratio between diameter
s ~ isulerehce, representing distance and orbit i
~ seyme ulcay demonstrated to be correct ~ thai
9 Vo.aihed stand as the truth on stronger
surement." ~
The logical correctness Of the methods both ueope,r
cal and analytical and the accuracy OF the result itb
which the ratio Of the circumference 10 tho dia,rt n
obtained will be admitted by every one who will aLe tho
pains 10 understand them. The use Of the ratio sons
only give validity to formula where the question i
from the diameter given to determine the circumference
the converse Now, the only difference pointed ont
an the passage quoted between his and Kepers Formula
is the Of this ratio instead Of squares and outs
Mr. Coues knows very well that the relation between tho
of two orbits may be well determined from the
squares Of their diameer and the relations between the
dimensions Of two globes from the cubes Of their diane
ters and the relations between two circumference by
the comparison Of the diameters themselves II we in
troduced the ratio between the diameter and crcumfer
and determined the values Of the orbits
soidity will not do Mr. Coues the wrong to saw that
he argues that because this ratio any function Of il
an element Of his formula therefore il Is geometrcaly