The daily dispatch. [volume] (Richmond [Va.]) 1850-1884, 1876-04-04

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rna. Correcsien--AEair.
'' ApaIL 1, 1876.
x,,,o,s D;s,atch. The communicating
- - 10 II Nelson, and your remarks upea
a. n regard tothe error ia the calculator OF
=. "a = macs Of IJranus were read with much
snfatesl this morning, and cannot bat think |
Ana, re,, are wrong 10 several particulars.
Z. In the example you give your method o. |
Ending The error lie Incorrect; and even II
the method were right, you have made q
serious mistake ia your compuat,on.
You say Let the sun weiga LOO toss, aoa
!nssirr, as the mass OF Uranus I'D OF TINS, OF
a5 tons. New estimate the protaole error
In the denominsfor Of The fraction AZ l: 80
that we may say that this mass IS NOT less .aao
OF, sons. nor more than 335 toss. Then sou
Sav !. Inc tiifieFence is 13a tons, or less than
3. q OF the mass. ~,
I syes. this would Zoe less than of the
sun,s mss, which sou suppose to be 400
toms. but not less than IL Of The ptdaet's
Snass. 25 tons, aud the planets mass Is what
we are talking about, when we say, as 0id
the .Mos.thiy, "a 200 part of ITS value go
RIt This method OF calculating the error
e incorrect. III 33a and 20 tons are the
limits. between which the true weight hes,
Z then IL % tons Is assumed as the weight the
n Greatest possble error 10 one direction is "a
/. Tors and in The other FIVE tons; that Is, the
oreatest possible error 10 either direction is
II The q fJererce between the assumed msss ana
ghe estjma!sd limit 10 that difecuon.
4s cali your maihod spcorrect because,
i Yvhan COMPARED with the one just Given, II
4 gives an approximations 80 vide OF the anarK
ne 10 become practically useless.
Now, apply the method just given 70 Ihe
true figures 10 the case Of Uranus. The
greatest possible error in one direction is q
fraction representing the difference between
1.22e1e and l.22500, and in the other direc-
tion fraction representing the difference De-
tween 122600 and 22700. oo-ooo.
In the first case this fraction Is l-oOoSooo'
In the second case it is 1.51S02O0. go
Now. each of these is evidently 8 1raction
ofthe SIMS nass, as that Is the unit on Wnlcn
fh;s calculation Is based; ana 10 moo "naI
fraction of the planets mass eacn OF lneSe H.
xoe must multiply each of them by 2a600,
which gives us 1925 OF the planets mass as
the creates. possible error in one direction,
and 1927 of the planets mass 10 the other.
ASH 225 and 1927 are each less than 1'2o0
the Monthly says the error is @iWithin
1900" merely, as 1t seems to me, to ex'
press it in rourd numbers. and not, as you
think, because that is the difference OF the
denominaiors Of the fractions, which express
the limits, although that would be safe rule
In The msjority Of cases where the numera-
tors we're /.
You close by saying: $50 the mass Of
Uranus has been determined within 200 of
f.2250O of its value" You should have said,
. Within 1900 Of 1-22500 Of the value OF the
3 SUMS mass" as the SUMS mass is the unit;
& and this, as has been shown above, is the
same thing as saying within LOO OF the
planets mass.
In the VII. Book OF Paradise Lost, when
Milton is about TO relate the creation OF the
world, he calls upon the goddess Urania fol
: aid, afraid, as he confesses, lest without it
.r.,-s son the Aleisn plain FALL.
Erroneous there to wander and foriorn."
Following the illustrious example Of MIL
ton, and avoiding that disastrous plair
wbereon the Dispatch has fallen " erroneous
there 10 WANDER" cry out in humble inVo
cation,
49, "still govern thou my song.
Urania, and 1T audience find, though few"
80 BERTRAND.
K Our correspondent is right. 1t was oul
careless reading OF the extract from The
Popular Science Monthly that misled us
very careless reading it seems now to have
been, since we hsve come to understand the
meaning of the extract. Here is the ex
tract:
"From consideration of sll the measures
of Ursnus's satellites the author assigns Us
the macs of that planet 1-22600 of the mass OIL
the SUP, and he estimates the probable error
s of the denominator Of this fraction at 100
go that we may say that this mass is not less
Z than 1-22700, and not more than 1-22500 =
that is, the mass is determined within less
than, 1-20061art OF its value"
The fractions 1-225Oo, 1-2260O, and 1-2s70G
are fractions Of The mass Of the sun. The
fraction 1000 is fraction of the mass Of
Uranns. We read the extract as If the frac
-. tions bad all bad reference to the same OBJ
ject Hence our mistake. Our correspondent
sees, too, why we stated the error to be LOO
OF 1.22500. We had the sun in our eye,
large mote.
A FAILING Rock FROM LOOKOUT Noun