ninger. Den kunde ogsaa bestemmes, naar man kjendte 
den gjennemsnitlige Hastighed af Vandet over og under 
Grændsefladen. Man vilde da have Betingelsen for Vandets 
Continuitet udtrykt derved, at de øvre Strømningers Tver- 
snit forholder sig til de nedre Strømningers Tversnit som 
disses Middelhastighed til de førstes, og af Tversnittenes 
indbyrdes Størrelse kunde Beliggenheden af Grændselinien 
mellem begge bestemmes. 
At finde Middelhastigheden af Vandet 1 de øvre og 
nedre Stromme, eller Forholdet mellem begge, lader sig 
neppe gjøre med nogen synderlig Tilnærmelse til Nøjagtig- 
hed. Ydre og indre Friction spiller her en Rolle, hvis 
Virkning ikke lader sig bestemme. Vi kunne imidlertid 
ved Forsøg finde Grændser, inden hvilke Opgavens Løsning 
maa ligge. 
Tænke vi os, som i Fig. 2, at et verticalt Snit gjen- 
nem Havet har Formen af en Parabel, hvis Toppunkt ligger 
i Havets dybeste Punkt, B, saa ville vi søge den Dybde, 
i hvilken Grændsefladen N’ N vil ligge, dersom Gjennemsnits- 
Hastigheden i de øvre Lag var V og i de nedre Lag v. I 
saa Fald maatte Fladerummene TT N N og N N B for- 
holde sig som v til V. 
Kaldes Maximumsdybden H, Dybden af Grændsefladen 
h, og Havets halve Bredde i Overfladen A, i Grændsefladen 
a, saa har man 
det øvre Fladerum = 
2 oie 
= BIA ==) 
3 3 
det nedre = 5 (Hh)a 
HA — (H—h) a v 
liene - (HDG TV 
; E Ae a 
Indfores Relationen WO Hoy 
saa faar man 
h = VÆRE” 
EIN — 75 
Sættes H= 2000 Favne, saa faar man 
for ! = jl mn =>0,3340) /21 40) 1DAvne 
2 0.237 474 
3 O14 349 
4 0.138 276 
5 0.115 299. 
Da Middelhastigheden i det nedre Fladerum maa være 
mindre end i det øvre, saa bliver den allerstørste Dybde, 
i hvilken vi kunne søge Grændsefladen, 740 Favne. 
Naar man ser hen til, at i det nedre Tversnit den 
horizontale Hastighed er Nul rundt hele Tversnittets Om- 
kreds, medens den 1 det øvre Tversnit kun paa 3 Sider 
er Nul, nemlig i Axen, i Grændsefladen og ved Randen, 
men i Overfladen har et absolut Maximum, i Forbindelse 
med, at Gradienterne i de nedre Lag tilhøre den Axen 
nærmestliggende Del af Systemet, hvor disse overhovedet ere 
mindre, medens de i Overfladen voxe med Afstanden fra 
It might also be determined if we knew the average 
velocity of the water above and below the limiting surface. 
We should then have the condition of the water’s contin- 
uity expressed by the cross-section of the upper currents 
having to the cross-section of the lower the same ratio 
as the mean velocity of the latter has to that of the 
former; and from the relative areas of the cross-sections, 
the position of the limiting line between both might be 
determined. 
To find the mean velocity of the water in the upper 
and lower currents, or their ratio to each other, will 
hardly admit of being effected with any reasonable approach 
to correctness. Here, outer and inner friction play a part, 
the influence of which cannot be determined. Meanwhile, 
we can, on repeated trial, find limits within which the solu- 
tion of the problem must le. 
Now, if we imagine, as shown in fig 2, a vertical 
section through the sea having the form of a parabola, the 
vertex of which is at the deepest point of the ocean-bed, 
B, we shall seek the depth at which the limiting surface, 
N N’, will lie, assuming the average velocity in the upper 
strata to be V and in the lower strata v. Hence the 
areas TTN N and N N’ B must have the same ratio as 
v to V. 
Calling the maximum depth Å, the depth of the limit- 
ing surface h, and half 
face A, at the limiting 
the breadth of the sea at the sur- 
surface a, we have 
2 2 
the upper area = 3 HA — 3 (H—h) a 
2 
thegloverr == 3 (H—h) a: 
hence sd al Å 
(H—h) a SV 
2 a2 
Now, since HH 
we shall get 
Jo V VW 
i NWSE 
Putting H= 2000 fathoms, we get 
for Å =i K=030/Æ =W0 'evnoms 
2 0.237 474 
3 0.174 349 
4 0.138 276 
5 0.115 229 
Since the average velocity in the lower area must 
be less than in the upper, the greatest depth at which we 
can seek the limiting surface will be 740 fathoms. 
If we consider that m the lower cross-section the 
horizontal velocity is nil at the entire perimeter of the 
section, the upper cross-section it is nil 
on three sides only, viz., in the axis, at the limiting sur- 
face, and at the margin, but at the upper surface has 
an absolute maximum, besides that the gradients in the 
lower strata belong to the part of the system nearest the 
axis, where these on the whole are less, whereas at the 
whereas in 
