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I-l!)
0.000139 Atmosfære eller 0.106min Kviksølvtryk. En saa
sterk Tilvæxt eller Aftagen med Dybden som den, vi have
regnet med, forekommer ikke i de større Dyb. Man kau
saaledes trygt regne med constant —.
Ved Studiet af Vandets Bevægelse i Havets Dyb
gjælder det at kjende Trykket i forskjellige Punkter af
samme Niveauflade. Havets Overflade vilde være en
Niveauflade, naar det var i Hvile og der paa hvert Punkt af
Overfladen var samme absolute Lufttryk. Den vilde da staa
lodret paa Tyngdens Retning i ethvert Punkt, men
Tyngdens Størrelse vilde aftage fra Polerne mod Æquator.
Igjennem hvert Punkt i Havet kan lægges en Niveauflade,
der er characteriseret derved, at der paa alle dens Punkter
hviler samme Tryk. T Forbindelse hermed staar, at
Afstanden mellem to paa hinanden følgen.le Niveauflader, maalt
langs Vertieallinion. er omvendt proportional med Tyngdens
Størrelse.
Antages Lufttrykket constant, Havvandets Tæthed lig
er p,,, h Vandtrykket i Bredden ep og Dybden li, og pK,„
Vandtrykket i 45° Bredde og Dybden //. saa er
the error will equal 0.000139 atmosphere, or 0.106 mm.
mercury-pressure. So considerable an increase or
diminution with depth as that we have assumed, does not occur
at great depths. Hence, we can safely compute with 2 as
constant.
For investigating the motion of the water in the depths
of the ocean, we must know the pressure at the various points
of the same surface of level. The surface of the sea would
be a surface of level were it at rest, and were each of
the points of the surface subjected to the same absolute
atmospheric pressure. Lt would then stand perpendicular
to the direction of gravity at every point; but the force
of gravity would diminish from the poles to the equator.
Through every point ol’ the sea can be laid a surface of level,
characterized by its having the same pressure at all of its
points. In connexion herewith we have the corollary, that
the distance between two consecutive surfaces of level,
measured along the vertical line, is inversely as the force
of gravity.
Assuming the atmospheric pressure constant, the
density of tlu> sea-water equal to 2:’, the water-pressure p (/,,
in the latitude <p and at the depth h, and the water-pressure
p4r,H on the 45th parallel of latitude and at the depth
H. then
a,. 2 (1— -1 eos 2 (f) (1 4 \ b. h) .
h - ,
Skulle begge disse Punkter tilhore samme Niveauflade,
maa p (/, h — Vu n
(1 - - eos 2 q) (1 -f I b. h)h = (1 + i b. H) H
H 1 + i b H
Te os 2 if 1 -I- \ b h
Da den midlere Tyngde i Bredden ip (g,,,,,) er lig
yr., (1 fl eos 2 (f i (1 -t- i bh) og i 45° Bredde (c/ ,„ ts) lig
f/i» (1 + i bH), har man eller Niveaufladens Afstand
ti g mill
fra Overfladens Niveauflade omvendt proportional meel
Tyngden. Da b er en meget liden Størrelse, kan man
sætte
h - ,
If both ol these points are to belong to the same
surface of level, we must have p,,, or
(1 — i eos 2 11) (1 + 4 b h) h = (1 -f 4 b H) H.
H 1 j+jbH
’ 1 — )<1 eos 2 ,p ’ 14 Ji h ’
The mean gravity in latitude ip (ffmi/) being equal to
r/45 (1 1 eos 2 <p) (1 4. i bh), and in latitude 45° (g„li:,)
equal to i/t:, (1 -f Å b H), we get or the di-
Ji gmf
stance of the surface of level in the deep from that of the
surface of the sea, inversely as the force of gravity. Since
b is but a small quantity, we can put
1 + * = 1 + i b H— i bh - i 6* hH
1 4. j b. h ^ -
idet man udelader Leddene med de højere Potenser af b.
Indsætter man her den tilnærmede Værdi af h — , •
1 — ,7 eos 2 rp
faar man
h = , " . «H \h[H- ,
1 — ß eos 2 ip \ 1
f ! b* /i- -f h b» h* H +.....- 1 4- $ h (H h).
excluding all terms with the higher powers of b. Now, if
we substitute here the approximate value of h zz - —
1 — .i eos 2 if
we get
\ H , //«ffom^f
2 If) 1 V eos 2 r| - ’ (1 — COS 2 If) ’ ’
In the extreme case that if = 80°, II — 2IKH) tatiinms,
the last tenu will = 0.00202 fathoms, which corresponds
Por (let extreme Tilfælde <( = 80», i/= 2000 Favne,
bliver det sidste Led = 0.00202 Favne, der svarer til
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