Weekly national intelligencer., 1854-01-07
COMMUNICATION.
To The Editors Of the National Ln,eRigencsr

+
To the Editors of the National MteHigencer:
GENTLEMEN: Mr. CoUEs's formulas seem not likely Il
engage the serious attention Of any who has estab
shed just title to consideration for ability and at
tainments in the mathematical, physical and mechanical
sciences Indeed he expresses expectation that for
awhile at least such will be the As Of your
readers to be altogether Indifferent the sub
ject propose to venture observations upon the
import and significance Of the formulas and upon some
Of the principles advanced in connexon with them.
Mons Louis Montalte has overlooked the design of
former communication. 1t intended to draw out n
clearer and precise enuncaon Of the principles
this system, of the grounds which they rest and
the manner in which the formulas connected with
and depend upon them. 1t also to learn how the
new system dsposes Of certain wellknown phenomena
which apparently in conflict with it, and to point out
where ssme links seemed to be wanting to render the
chain of argument advanced in its support connected and
conclusive
With Mons. Montalte, entertain profound respect
for mathematical demonstration, and when they are
comprehended, embrace, without the shadow OF doubt
or distrust, the truths established by them also be-
eve that knowledge Of the method and principles Of
demonstration, and of the truths estab
shed BY it. gives increased ability for comprehending
and investigating the principles Of mechanical philoso
phy and is indispensable for fully understanding some Of
its doctrines. hope, therefore, he will induce Mr.
Coues to hold that science in like estimation Perhaps
may be willing to embrace the system on some-
thing short of mathematical demonstration but certain
not on such as has yet been adduced in its support
which is entirely inadequate. :,
The hrst formula of Mr. Coues is for determining the
time of planets revolution from its distance and the
converse. .. .m
Now, if the product of planets distance lin miles)
into the square root Of the distance be multiplied by
certain constant quantity the result will be the time of
its revelation in days is not necessary that days
and miles should be taken the units of measure ANY
others will answer, but then the constant must be made
to conform This is Kepers law, expressed in different
terms from those in which it is enunciaed only for the
purpose of comparing it with Mr.. Couess formula. This
constant obtained by taking the square Of the
quotient of the square of the number of days in any
planet revolution by the cube of the number Of miles
in its radius vector
Mr. Couess formula the radius vecor in the same
way precisely but his constant quantity is obtained from
different elements. .
l was therefore somewhat astonshed at reading that
an eminent mathematical scholar had expressed the follow
ing opinion
have been the calculations and applied the formu
la of planets the solar system and have been
much grafed at the conviction which it leaves of its truth
seems to me Mr. Coues has got important principle
ceednsy interesting and probably destined to be of great
practical utility in science" ...
simple inspection Of the formula ought to have
shown him that the results given by the formula would
have fixed relation to the results given by Keplers
third law determined by the relation Of the constants in
and convictions at which this eminent scholar arrived
although my dferent-but that he should have
made the results of the application of the formula
most of the planets of the system the ground of his
cluson. This lessons somewhat the confidence of the
expectation of the great impulse which the progress of
the science Of astronomy is receive from this dscoye
ry, which his opinion might otherwise lead to en-
tertain
If person desired to determine the length of mea-
surng rod, from applying it to object of known
length suppose SO feet and found the rod contained in
the object exactly hundred times the length of the
rod would be determined be 99lO0 of foot lust as
certainly as if 1t had been applied to thousand The
only purpose to be served by repeated application
veral objects of known length would be to eli
inmate the errors of imperfect application Or, if he
knew the rod to be 99-100 of q foot he would also
know beforehand what would be the result of it's ap-
plicaton to kno Wn lengths So also simple inspection
of this formula suces to show that just the constant
in it less equal to- greater than that in Keplers
law, SO just exactly in the proportion will the
suit be less equal to- greater from its application
the different planets Of the system sis hoped this
scholars distinction is supported by some subsan
enviable. . s.... -.-.
1t is unjust however, to Mr. Coues to say that his
formula is identical with Keplers His constant is de-
rived from different elements. These may be so assum-
ed possibly within the limits within which they are con-
sdered to be accurately determined will render the
constants in the two and consequently the results very
nearly the same. .#.. .@
Kepers third law makes the quotient Of the cube Of
the number Of miles in any planets distance by the
square Of the number of days in its period of revolution
constant quantity all the planets give the same result
Mr. Coues has observed that the product of the square
Of the circumference Of the by the diameter gives
this constant quantity very nearly This relation SO far
as know, is original observation of his, and may be
worthy of consideration whether he is able determine
the diameter of the sun by independent methods not
The matter of Importance s will it enable
kepers third law or Mr. Couess if he prefers i with
the other llestablished laws Of motion / am unable
to do this, but will not undertake affirm that Of
ability in mathematical and physical science will not
Mr. Coues has done it, and until it is DONE even it
is admitted to be true it will rest better ground
than Keplers. The intimate and necessary connexon
of kepers first laws with the other established laws
of motion has heen demonstrated That of his third
law, which is confirmed by observation has been but
neither does it initiate against those laws So sso
admitting this formula to be true, there is
expect that it will disturb the received and well estab
shed doctrines Of mechanical philosophy 1t is alto
geher illusion to suppose that it will facilitate astro
nomical computations. 1t presents such advantages
knowledge Of the diameter of the sun necessary
for this formula. This is nearly equivalent to know
ledge Of its distance which, with the time Of the earths
revolution will furnish the constant in Keplers third
law and will enable to determine the distance Of
other planet when its period Of revolution is known and
the Mr. Coues thinks he has determined the
diameter Of the with great accuracy. If he can do
it, not within few hundred miles, but within thou
sand to the satisfaction of astronomers he will confer
great benefit and his services will be cheerfuly acknow
lodged.
Let US attempt IN examination Of the principles on
which he proceeds to accomplish this He says:
eff know the period of revolution of ARIanetNars
for nsancewe at calculate its distance far
accurately than by any instrumental Measurement Of the
distance"
If have the constant for Kepers law, this is grant