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•209
Indsættos Værdierne af a. & og c i Ligningerne, faaes:
No. e(i +J?’)(<»’; — 1 COS -Ml) 2<r) b [m’—m)s c (m’—iji):i ber. h obs. h. 0—B
i 89.31 + 0.36 —0.01 89.7 93 +3.3 Fv. (A»,:
2 408.64 7-73 0.60 415-8 416 4-0.2
3 1167.67 63-97 14.24 1217.4 1216 — 1-4
4 1225.21 79-44 16.45 1279.2 1280 +0.8
5 1276.76 76-53 18.63 ■334-7 1333 — 1.7
6 1282.77 77-19 18.87 1341-1 1343 + 1.9
7 1415.50 94-13 25-42 1484.2 1487 +2.8
8 1517.89 108.19 31-32 ■594-8 1590 -4.8
9 1600.07 120.27 36.71 1683.6 1686 +2.4
10 1878.84 165.45 — 59-22 1985.1 1985 jr. f. —0.1 = ±l-94
ö = + 1-794 -Favn. (Ims.)
Denne Formel giver saaledes en endnu mindre
sandsynlig Fejl end den forrige. Bækkens Convergents er
imidlertid bleven adskillig mindre, idet i den forrige Formel Leddet
c (m’—m)* i Ligning No. 10 kun er —4.7 Favne.
Efter Formelen faar man:
This formula, gives accordingly a probable error still
smaller than the preceding. The convergence of the
series, however, has become considerably less, the term
of the first formula, c (m’—Hi)8, in equation No. 10, being
but 4.7 fathoms.
According to the formula, we set: —
dli _ 12.089666 (1 q †) 0.01320110 0.00014112 , , „
d (m’ -m) 2f (1 — ß eos 2 <p) 1 (1—,/cos 2 <f) 2(i — /f eos 2 g>)
faaes (we get) d h
Sættes (Putting) d(m’—m) = + 0.081
0.9793 (’i -)- g t) 0.001069
? (i — ft eos 2 if) - (i (i eos 2 if i
og 2000 Favnes Dvb
(m’—m) -
0.000003573
- (i — eos 2 ff)
(m’ — mY.
en Størrelse, der mellem Overfladen
varierer fra 0.967 til 1.028 Favn.
Efter Rækkeudviklingen af den rationelle Formel bliver
eos 2 <f) h =
(m’—m) -f
Indsættes her Van-dir
(
Milliontedele.
(Y.„ = O.I76985 I. t/n = 5O.I53
9303.07 og Middeltallet af m= 10.5661.
a quantity that varies, between the surface and a depth of
.2000 fathoms, from 0.967 to 1.028 fathom.
According to the rational formula developed in a
series, we have
+ ••
faar man Factoren lig 12.1236 (i -f- q t), altsaa meget nær
lig den af den sidste empiriske Formel fremgaaende.
Undersøger man, hvad Værdi den empiriske Formel giver for
Factoren c, saa findes c ~ 0.00045472. Buchanan’s
Bestemmelse, med hvilken der er regnet i den rationelle
Formel. er 0.000456.
_ 0 +<70
a„ ^ — m’) /,„ (1 — q t) a„ ^ — vi) 1
Substituting here the values a„ = 0.1769851, tr —
50.153 millionths, ^ = 9303.07, and the mean for m —
10.5661. we get the factor equal to 12.1236 (1 +?/).
therefore very nearly equal to that deduced from the last
empirical formula. If we investigate what value the empirical
formula gives to the factor c, we shall find c — 0.00045472.
Buchanan’s determination, with which I have computed in
the rational formula, is 0.000456.
Indleveret Marts 1886. Received March 1886.
Translated into English bv J. Hazeland.
Substituting the values of a, b and c into the
equations. we get: —
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