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167
blot tilsyneladende, idet Tæthedslladens Heldning trå
Kysten turde være noget sterkere end antaget i Kartet PI.
XLII. Eller den for den sydgaaende Strøm fornødne
Vandforsyning hentes fra de dybere liggende og koldere
Vandlag. Dette vilde bidrage til at forklare de forholdsvis
låve Temperaturer, som vi træffe paa Skotlands Østkyst
(Se Pl. XVI).
For at beregne Vandets Hastighed i Overfladen, gaa
vi ud fra Formelen
2 io sin (f
’ ♂4a (l — ß eos 2~qr>) ’
hvor u er Hastigheden og /; Heldningvinkelen af Overfladen
i et Plan lodret paa Ligetrykslinierne. Kaldes den til
Afstanden Aa;, regnet langs Normalen, svarende Stigning
af Overfladen A/i, saa er
tang ti
A/<
Aa-"
og
_A h gih (1 — ß eos 2 y)
— Aa; 2 co sin cp
Regnes A li i Meter, Aa; i Kilometer, saa faar man
_ A/t 1 gA5 (1 — ß eos 2 if) _ Ah 1
U ~ Aa; 1000 2 i„ sin rf ~ 2k
Meter per Secund.
Størrelsen k = 1000. — losuxif findes
bereg-9i s (1 — ß eos 2 tf)
net i Tabellen Side 120.
I Kartet PI. XLIII er Højdeforskjollen mellem
Lige-hojdelinierne, Ah, 0.1 Meter, og man faar
A./ = ,
i
20 k Aa-’ 20 k u
Efter denne sidste Formel er Skalaen paa PI. XLIII
beregnet. Til Venstre staar den opstigende Skala for
Kilometer. Parallel med den vise den hyperboliske Curves
vertieale Ordinater (Aa;) de Afstande mellem to
Lige-højdelinier, der svare til de forskjellige Hastigheder (u).
Skalaen for disse er den horizontale Grundlinie, inddelt
til at angive Hastigheden saavel i Meter pr. Secund som
i Kvartmil i 24 Timer. Den yderste Hyperbel gjælder for
55° Bredde, den inderste for 80°. Ved Abscissen for
0.01 m ere, øverst til Højre, Hyperblerne for de
mellemliggende 5 til 5 Grader antydede.
For at finde Strømhastigheden i et Punkt tager man
altsaa med Passeren Afstanden mellem de to nærmeste
Ligehøj deli nier, opsøger i Skalaen den vertieale Ordinat,
som passer hertil, Bredden taget i Betragtning, og aflæser
paa Hori/.ontalskalaen Hastigheden i Meter pr. Secund
eller i Kvartmil i 24 Timer.
inclination of the surface would appear to point
northward, whereas the motion must proceed along the coast
southward. This may indeed be only apparent, since
the slope of the surface of density from the coast is
possibly somewhat steeper than assumed in the map, PI. XLII.
Or the supply of water necessary for the current setting
south is derived from the deeper-lying and colder strata.
This would go far to explain the comparatively low
temperature met with off the east coast of Scotland (See Pl. XVI).
For computing the velocity of the water at the
surface, we have recourse to the following formula: —
2 to sin o"
tan i— - — • ti.
ffv, 11 — ß eos 2 if)
in which it represents the velocity and the angle of
inclination of the surface in a plane perpendicular to the
lines of equal pressure. Now, if we call A h the rise of
the surface corresponding to the distance A.»’, reckoned
along the normal, then
Ah
and
Aa:
we get n =.
t _ A/l (ft:, (1 — ß COS 2 if)
/\x 2 io sin (f
If A h be taken in metres, A x in kilometres, we
shall get
_ A /t_ 1 r/45 (1 - ß eos 2 if) _ Ah 1
?<_Aa- 1000 ’ 2 (o sin if ~~ 2k
metres per second.
The quantity k = 1000. wsin«f win ,)e
gi:, (1 — ß eos 2 (p)
found computed in the Table, p. 12(5.
In the map, PI. XLIII, the difference in height
between the lines of equal height, Ah, is 0.1 metre; hence
1 1
~ 20 k A x ’ 20kn
According to this last formula, the scale, PI. XLIII, has
been computed. To the left, we have the ascending scale for
kilometres. Parallel with this scale, the hyperbolical curve’s
vertical ordinates (Aa) show the distances between two
lines of equal height that correspond to the different
velocities (u). The scale for these velocities is the
horizontal base-line, graduated to indicate the velocity both in
metres per second and in nautical miles per 24 hours.
The outermost hyperbola refers to the 55th parallel of
latitude, the innermost to the 80th. At the abscissa for
0.01 m., in the upper corner to the right, the hyperbolas
for the interjacent 5 to 5 degrees are marked off.
To find the velocity of the current at any given
point, we measure accordingly, witli the compasses, the
distance between the two nearest lines of equal height,
seek out on the scale the vertical ordinate corresponding
to it — taking the latitude into account — and read off’ on
the horizontal scale the velocity in metres per second or
in nautical miles per 24 hours.
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