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•207
For med Fçrdel at kunne anvende Piezometret som
Dybdemaaler maa man altsaa beregne Dybderne strengt
med de af de bedste Lodskud udledede Constanter. I dette
Tilfælde kan Piezomctret give en udmerket Control for
Lodskuddene, et Maal l’or disses Nøjagtighed og en
paalidelig Erstatning for mislykkede Lodskud, naar man er
sikker paa, at Instrumentet har været ved Bunden.
Hence, in order to use advantageously the piezometer
as a depth-meter, the depths must be rigorously computed
with the constants found from the best soundings. In that
case, the piezometer will afford an excellent means of
control for sounded depths, a measure of their precision, and
a trustworthy compensation for unsuccessful soundings,
provided it be quite certain that the instrument has been
at the bottom.
Man kan udvikle h i en Række efter Potentserne af
(m’—m), eller man kan opstille en herpaa grundet empirisk
Formel
We can develop h in a series progressing according
to the powers of (m’—m), or take an empirical formula
founded upon it. e. g.,
h = ■ , -— (m’—m) -
— (i -—ft eos 2 If)
ft cos 2 If)
(iii
+ CO. i*)1"’
-m)s +
og bestemme a, b og c ved de mindste Kvadraters Methode.
Man faar da følgende Betingelsesligninger [LogarithmerJ.
and determine a. b. and c by the method of least squares.
We shall then have the following conditional equations
[logarithms]: —
Endeligningerne blive
] 0.86491 fl 1 |i.74239] h- f- 2.61987J . : = [1.96848]
[’■52787I [3.06858] 14.60930! [2.61909!
[ 1.98677 1 3.98643I |s-q86io| 13.08493]
[2.00769! I4.02823J [6.04877] [3.10721]
I2.02566I 14.06426] 16.10286] I3.12483J
[2.02752 j 15-06797] [6.10843! [312808]
[2.070611 I4.15415I I6.23768I I317231]
|2.ioo86| 14.21462] I6.32839] [3.20104I
[2.12384! 14-26057] I6.39729] [3.22686]
I2.19312I 14-39908] ■ 16.60504] 13-297761
The normal equations will be
115344. a-f 14621307. b -f- 1912735673. c= «456854
14621307.«+ 1912740543. ft-f 257081182958. c = 184843697
1912735673. a.-f 257081182958. b -f 35422403423676. (’ = 24200418357
hvoraf (whence.) a= 12.25275 log a — 1.0882340
b— 0.003132885 log 7.4959306—10
c ——0.00000116585 log c — 4.0666447,, 10
. , o.oo s 1329 , , „ o.ooooo i 166
12.25275
- (1 -— ft cos 2 (f) 1 2 (l — ft cos 2 (f)
Indsættes i Ligningerne Værdierne af a, b og c faaes
1 and
(»’’-»)■ V(, _ liaxt2<ry
Substituting into the equations the values of a, b,
No. Ber. h Obs. h 0- n
(Comp.)
i 90.0 Fv. (Ftiis.) 93 Fv. (Fms. 1 +3.0 Fv. (Fms.
2 416.8 416 —0.8
3 1217.8 1216 — 1.8
4 1279-3 1280 +0.7
5 ■334-7 ■333 — ■•7
6 ■340.5 ■343 + 2.5
7 ■48.4.3 1487 + 2.7
8 ■594-5 ■590 — 4-5
9 ■ 683.7 1686 +2.3
10 1985.2 ■ 985 —0.2
M.F. + 2.02
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