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146
være rigtigst for de midterste og dybeste Dele af Havet.
Henimod Kysterne vil den være mindre rigtig, men her
blive Dybderne mindre og Tyngdens Tilvæxt selv mere og
mere forsvindende.
Tyngdens Tilvæxt med Tilnærmelsen til -lordens
Centrum beregnes saaledes
. M
.. Havet g„ =//,.(l + 1.45
„ Continent gh — g„ |l -+- 1.25
Angaaende den Nøjagtighed, hvormed Factoren b er
fundet, kan anstilles følgende Beregninger. Vi have
altsaa db = — b.
d,R
} d <l„ d0dD
) + ;
RD
li D9-’
Sættes dR = ± 500 Meter (den halve Forskjel
mellem Clarke’s og Listings Jordradius), d d„ = + 0.00005 og
d TJ — + {).]. saa faar man med de til Beregningen af ’b
brugte Constanter
db — ± 0.000000002 829.
Vi faa saaledes følgende Udtryk for Tyngdens
Størrelse i Bredden rp og Dybden h
g,ph = <U-, (1 –t eos 2 if) (1 4- b. h).
Havvandets Tæthed i Dybet er større end i
Overfladen, da Vandet sammentrykkes noget af Vægten af de
overliggende Vandlag. Er Trykket i et Punkt i Dybet p
Atmosfærer og Søvandets Sammentrykkelighedscoeffieient
for en Atmosfære iy, saa er, naar dets Tasthed under
almindeligt Luftryk, 1 Atmosfære, er S„ (tidligere betegnet
som S-,), dets Tæthed S,, under Trykket p
S„
1 -w ’
Det rene Vands Sammentrykkelighedscoeffieient er
afhængig af Temperaturen og af Trykket. Herom henvises
til IV Del af denne Afhandling "Om Piezometret som
Dybdemaaler og Vandets Sammentrykkelighed". Antager
man, at Søvandet følger de samme Love for
Sammentrykning, kan man sætte under Formen
- (,.„—0.159 t —0.0003141’1) (1 —0.00009325 p),
hvor t er Vandets Temperatur, p Vandtrykket i Atmosfærer
og il, Coefficienten ved 0° og almindeligt Lufttryk.
Regn ault1 fandt Sammentrykkelighedscoefficienten for
Søvand af en Temperatur af 17°.5 og specifisk Vægt 1.0264
and for continental attraction. It will prove most accurate
for the middle and the deepest parts of the sea. On
approaching the coast, it will be less accurate; but there
the depths are less, and consequently the increase of gravity
itself becomes more and more insensible.
The increase of gravity with the approach to the
centre of the earth is accordingly computed as follows: —
For the Atmosphere gh—g„ |l -f- 2
,. .. Ocean gh = g„ (l + 1.45
„ ,. Continent gh — g„ fl -f- 1.25 R j.
.Concerning the precision with which the factor b has
been found, the following computations can be made. We
have
b- ,
DI’
. j dR .,dd d„dl)
hence d b — b. R - o RJ> + A Rjyi.
Putting d R - ± 500 metres (half the difference
between Clarke’s and Listing’s values of the earth’s radius),
dd„-± 0.00005, and d D = ±0.1, we get, with the
constants made use of for calculating b,
db = ± 0.000000002 829.
Thus we have the following expression for the force
of gravity in latitude if and depth h
9ih (1—eos 2 if) (1 + ft. 70.
The density of sea-water in the deep is greater than
at the surface, the water being compressed to some extent
by the weight of the superincumbent strata. Assuming the
pressure at a given point in the deep to be p atmospheres, and
the coefficient of compression of sea-water for one
atmosphere to be ir then, provided its density under ordinary
atmospheric pressure, 1 atmosphere, be S„ (previously denoted
by S4„), its density, S,,, under the pressure p, is
S„
1~\p ’
The coefficient of compression of pure water depends on
temperature and on pressure. As to this .subject, the reader
is referred to Part IV of the present Memoir, viz., "The
Piezometer as a Depth-Meter and the Compressibility of Water."
Now, assuming sea-water subject to the same laws
regarding compression, we can put
/, = (>;„—0.159 t —0.0003141.*) (I—0.00009325 p),
in which t is the temperature of the water, p the
water-pressure in atmospheres, and ir the coefficient at <>° and
ordinary atmospheric pressure.
Regnault1 found the coefficient of compression for
sea-water with a temperature of 17°.5 and a specific
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