, 1874-05-02
THE MOONS DISTANCE.
Why Different Values Have Boon la.
signed by Astronomers.
Tho Important Problem Solved,

suo ltupo1tds1I FFCDlem SolyeQ.
Astronomy iB often npoken Of ~ an oxao1
sctonco. 1tis entitled to tho namo, by virtuo os
tho rigorous oxactnoss Of ia roasonipCB
but scarcely 80 with regard to all its con.
olusions. The facts Of apparent position
at any assigned timo and place can be- stated
with worry close approximation to tho truth. and
q great many ratlos Of distance have boen O..
tablta}Iod. But there Ia yet room for great I'm.
provemcnt in the important itoms Of actual dl.
monslon and distance. Astronomers aro not vol
entirely agreed in their opinions a. to the exaot
form and bizo Of the earth. They diro,
to tho extent Of fully one part In
1000 OF tho whole In thoir eatin1atcs Of tho dis.
taoce Of tho moon by oue part In 200 In tho
distance Of the sun !; and by = htill creator por.
centago In the actual distances Of those few Of
the fixed atars which present gulf botwoon III
And them that appears to bo susceptible Of moa
suroment. Thoso differences involve oquallyRroat
psrcontagos Of error in liuoal dimension, and
much creator In the oatimntos Of volume and
mass. And this Btatoment docs not rotor to
comparisons Of recent estimates with those Of
hundred years ago, but to those Of tho present
day.
It may be thought that tho science Of ns.
tude that wo ought to DO sgreed a. to tho dis.
lance OF our no1t-door neighbor--tho moon. Yet
the statements Of distance do not agree to within
moro than 100 mileR. Leaving cut Of t1o ao.
count tho round number, 2A0. 900 miles, giyon III
many Of tho text books, the latest statements Of
moan distance vary from 238,799 to 239,0OO
miles. ~
If wc take the onrth's moan equatorial radius,
Of 8,9C2o miloH, AZ the unit. thon tha
moons diatance II the oosocant Of tla
parallax. or OF tho anglo which that radua sub.
tends. when two straight lines, drawn from ita
o1tromities, meet at tho contra OF the moon. Tho
value OF tha anglo Ia found by making nearly
Simultaneous observations Of tho moons poel-
ton from different points on tho oarth's surface.
By comparison Of humorous observations,
chiefly those made at Greenwich and tho Caps
Of Good Hope, tho following values OF the moan
Hanson, tho compntor OF tho celebrated Tables
do Ia luuo, 9,419.57; Airy, the preBont British
Astronomer Royal, 3,424.94 Burg (witl Berlin
observations addod), 8, AT; Henderson, s.421.s;
and subsequently, s,422.7. Tho distance do.
creasoa about.70 miles for an increase Of one
aocond in the parallax.
Tho differences in those results are conse-
bs avoided at present; 10 uncomfortable
changes in the positiona Of the Instruments, duo
to changes Of temperature aud to hurfaco vibra-
tiong; and to diTerouceH in the measure Of tho
baHo line between the two obBervatories,
There ara two otlnr elements in tho problem
which will enable uB to eliminate the ezror from
these computations:
!. Tho attraction Of the moon upon the equa.
tcrint protuhorance Of the oarth .csusos the
earth's axis to nutate Tor nod) to tho a1tcnt Of
9.22 seconds around tho mean place. Tho OK.
tent of this movement is obtained by obaorve-
tion. Now. 1t is proven BY csloul&ton that this
quantity Of mutation involves Tho fact that with
moon would bo to that Of tho earth aa to 81.5,
nearly; and that her mass for any other dis.
tanco must be proportional to the oubo Of the
cosecant Of tho parallax. Hor mass must DO
creator than by s1.5 II the distance bs grcater
2. The fall Of the moon towards tho earth,
from the tangent limo to the curve Of tho orbit,
ia duo to tho sum OF the attractions Of tho Garth
and moou. Tho earth alone attracts body, at
hor equatorial surface, with force equal 10 that
required to produce fall Of 16.10092 Ioot in tho
fist second OF time. II to this We add the pro-
portionnto quantity due to tho moon'a attractive
force, which is equal to her mnss compared With
that Of tho oarth, MD then divide tho urnount bY
the square Of the coaecant Of tho parailax, va
obtain tho total theoretical fall of tho moon
from tho tangent lino to tho curyo Of tho orbit,
10 eaeh second Of tilne: Ihis quantity ig din,in-
traotfon of tho sun.
Now, this last noted quantity must agroo with
tho actual difference betwcon the tAngont ind
the curve, which IL easily calculated II Ia equal
tiplicd Into tue squsro Of 3,14169, and that pro-
duct divided by the aquaro Of the number Of
seconds Of time 10 one sueroal revolution Of tho
moon. The result evidently increases In direct
An increaao Of ono second Of arc IN
tho paralla1 giving reduction ot 10 miles in Tho
distance, would involve decrease in tito total
attractive force, equivalent to that Which would
ESIx,%$t,
nearly one-fortioth part Of the whole.
When wo take as our unit the latost doter-
mfnation OF the enrth8 mean equatorial radius,
90, 924, 100 feet, or 8.962.01 miles, wo find that
the only yalues that wall giyo balance OF thoso
quantities Of force and distance are tho follow
ing:
MeAn equatorial paralla1, seconds. ......... 342oe7
Mean distance. miles .230,o15
Masa Of moon to earth, ,as.............,l 10 8lss
From thoao va1uoB 10 may obtain tho follow
ing:
Diameter OF moon, miles. 216o.Rs
Youtno OF moon 10 earth I'd. 10 40.2
Density, Garth bainy tlla unit 0.00k
Distance Of centre Of orbit frolu ths earth's
Moan % dls;anss % Of sentFs oi gravity rom -
eartha centre, miles. ....+...,........ 2900.85
may add that tho Inst noted quantity
Which is the extent to which the moon pushes
tho earth away from her average place
in the orbit dsond. Is fn0Tn y to to % suI!end an
This would glyo 81, TO- 600 miles for tho average
distance Of the Garth from the sun, or pAra1ax
OF B9O7 seconds. This determination (which las
possible error Of not more than 10000 miles
eIthor way) ia probably aa near the truth ~ any
tiat viii be obtained from observat.o,,s Of III
tranait Of VonuB on tho ssh Of next December,
The yaluo of the lunar pa1 allax thnt Ia now
most generally accepted Ia that rcoently deduced
BY Mr.. Adams from tho observations u1ado by
Mr: Broom At tho capo Of Good Hope, combined
With those msle a. European observatories.
This (9422.1 differs by u little more than two
seconds from the vaiue have deducod, aud
involves lineal difference Of aoout l4O miIos.
Buch hn extensive change should not 10 pro-
posed without good reasoD.
Cant Glnrt r NJ bsu ranap%1v r,rouod $~...