Weekly national intelligencer. [volume] (Washington [D.C.]) 1841-1869, 1853-10-22
COMMUNICATION.
FORMULA OF MR.. CoUEs FOR OBTAINING THE
DIAMETER OF THE SUN

| of circle bears to its diameter.
! We did not publish this method with any hope
| that it would at once commend Itself to those who
are exclusively the observers and calculators in
astronomy They obtain, Of course, the ratio Of
! planetary period to planetary distance by Keplers
law, and naturally prefer the established method in
which they have been educated 1t is sufficient fer them
to arrive at facts and they need not trouble themselves
with principles Mathematical astronomy does not
qure sound theories of planetary notion The hypothe
sis of Poemy would the mathematical inquiry the
present day as well as the theory of Newton say
WELL for DIR. Whewell Ellis. Induc. Sc considers the
Ptoemaic system the best basis for computation and
IN fact the epicyces of Ptolemy used in
order to simplify in certain cases. the process of asro
| nomcal calculation.
Our formula, believe, is valuable, it throws
new light upon the principles of planetary motion. KEEP
ler law that the squares Of the times to each other
as the cubes of the distances is only expression
of existing fact established by instrumental
ment His formula is emnenty useful in computation,
but it reveals principle of planetary motion.
In order to compare the two formula, win suppose
that sought to know the proportion between the time
OF the oscillation or beat) Of the pendulum from the
length Of its rod and this is strictly analogous to the
calculation OF planetary periods from planetary distances
An arthmecal statement is obtained which expresses
the proportion sought Experiments prove the correct
ness of the rule, and cockmaker with this rule,
always find the length Of rod in feet and nches which
will give desired oscillation. He hos method of cal
culaton But there is nothing in the method which leads
to knowledge of the principle which governs the motion
of pendulum.
For the purposes of philosophical inquiry principle
well method Of calculation is required. In the
first place. them the beat expressed in time the
other term-the length of the rod-should be also ex
in and fba
this what is the time of the beat the time takes for
body to fall perpendcuarly through the length of the
pendulum rod? Having thus the distance from the
tire of oscillation n the time of the vibration in the
arc found by the ratio which the diameter Of circle
bears to its circumference The inquiry has result
ed not only in method Of calculation, but also in know
ledge of the principle of the pendulum oscillation
The planets the pondula of eternity, which beat
the years, the centuries, and the ages of time Their
orbits bear to their distances proportion be phioso
phicaly expressed only by the ratio which the circum
ference of circle bears its dameter and both terms
must be expressed in time, in what is equivalent to
time
In illustration of these views will calculate by
formula the period of the earths revolution from its
distance assuming this distance be 109 6 Of the suns
diameter which is nearly correct
1895 = 9S697 (Which is the square of the ratio be-
tween diameter and circumference - ILL., the square
root of Ill - 1882 1882 x l09.Gl = 365 % days.
The Kepler formula founded the square of the
time and the cube of the dstance) is only, we have
said geomctrcal expression of an existing ratio shown
to be correct by The foregoing calcula
on based on the ratio between diameter and circumfer
ence, representing distance and orbt) be geomc
cdI demonstrated to be correct; that periods thus
obtained stand the truth stronger evidence than
results obtained from instrumental measurement.
We have been asked-and surely the question ask
cd without philosophical consideration Of the subject
IT the diameter of the could be exactly ascerained-
why use this as the unit of the of distance "
We reply that the diameter of the sun be accurately
ascertaned, we shall show in this paper and by
using the suns diameter, express both period and DIS
lance a time is shown by the result of the computa-
tion, the being in solar days. We DO think
it would be difficult for philosophc mind to solve the
problem how distance, expressed in suns diameter, yields
an answer in solar days. 1t is not accidental but the
suit BY law Of the solar system It's incumbent on
however to demonstrate that the suns diameter is
exactly S7O l07 mesa mile being 7920th of the earths
mean diameter which is very nearly, if not exactly
English mile
The diameter Of the sum- as settled by the instrument
tai of its disc, is about $4,000 English
miles. Our ascertained diameter and the measured d-
differ less than 10 900 miles, 1t is admitted on
all sides that this diameter be obtained by nsru
mental measurement within 10, 900 miles, for the follow
ing reasons;
In the first place. the of the suns Disc
at tn. earth aphelon running through many years. and
by the most skilfu observers, vary from 81 33 to 30
29" (Ency Britt In the second place. tho calculated
result from the Of the disc depends the rs
sumed distance Of the sum- which cannot be known by
measurement within 800 900 miles (IIinds's Solar Sys-
tenn
II supposed by many astronomers that the in the
value given the suns diameter f there is an error is
in making il too large and the for this opinion
given The measured disc has decreased from time to
time regularly aud constantly that it has created the
suspicion that the bulk Of the is actually becoming
less and less from its continual emission Of the rays Of
light and heat This dminuton is however, more pro-
perry ascbed to the gradual improvement Of the iusru
ments used and Of the skin in the Of them As the
instruments not yet beyond improvement and the
observers skill has not attained its zenith future
may reduce the diameter Of the sun to So l67
mesthe value which, we believe we have asceriaaed
Even now in calculations for eclpses it is found neces
sary to decrease the Of the disc 81 or 6u rs
an allowance for irradation-this rradation being
apparent enlargement Of the suns disc by its efu-
gence There is them nothing in the instrumental mea-
surement to prove that its diameter not $40 G7 miles
II truly comforting thought that not left to
the uncertainty Of the Of the suns diane
We have the symmetrical relations Of the spheres of
the solar system. II we know the period Of revolution
Of planet-for instance Of Mars-we once cacu-
late its distance far accurately than by any nsru
mental measurement of the distance So If We know the