Den sandsynlige 'Fejl af 1 Obs.: 0 = + 1.91 Favn. 
Den empiriske Formel tilfredsstiller altsaa Observationerne 
fuldkommen saa godt som den fysiske (0 = + 1.94) 
Man faar af Formelen 
adh he 12.25275 
d (m’—m)  S(1 — 800529) 
0.0062658 
Sættes som ovenfor d(m—m)= 0.081 mm, 
0.994 + 0.0005 (nm/—m) 
aar man ål == = : V 
N(1 — ? cos 2 g) å | 
en Størrelse. der, mellem Overfladen og 2000 Favne, holder | 
sig mellem 0.964 og 1.110 Favn. Med Piezometret og 
den empiriske Formel faar man altsaa Dybderne paa + 1 Fv. 
I den empiriske Formel er intet Hensyn taget til at 
Vandets Sammentrykkelighed er afhængig af Temperaturen. 
Det rene Vands Sammentrykkeligheds Variation med Tem- 
peraturen samt Havvandets Sammentrykkelighed og dens 
Variation med Temperaturen, gaar, da Temperaturen i Rege- 
len aftager med Dybden, ind i Coefficienterne for (m’—m)? 
og (m'—m)”. Formelen indeslutter en midlere Værdi af », 
passende for de høje Bredder i vort Nordhav. 
Sætter man, for at tage Hensyn til Temperaturens 
Indflydelse paa Vandets Sammentrykning 1 Piezometret, 
Ligningen for Dybden under Formen: 
Se 8re0s 
The probable error of I observation 0 = + 1.91 fathom. 
Hence the empirical formula satisfies the observations quite 
as well as the physical (0 = + 1.94). 
We get from the formula 
0.000003 498 
(19 --m) — ES Pesap 
DO ) (m’—m)?. 
Putting as befare d(m’—m) =0.081 mm., 
0.994 + 0.0005 (m’—m) 
S(k=PCw2M) ’ 
a quantity that ranges, between the surface and 2000 
fathoms, from 0.964 to 1.110 fathom. With the piezo- 
meter and the empirical formula, we can, therefore, deter- 
mine the depth within + 1 fathom. 
In the empirical formula, no regard has been taken 
to the compressibility of water being dependent on temper- 
ature. 
we have dh = 
The variation in compressibility of pure water with 
temperature, as also the compressibility of sea-water and 
its variation with temperature, will, the temperature decreas- 
ing as a rule with depth, be included in the coefficients for 
(m’—m)? and (m'—m)”. The formula involves a mean 
value of 7 adapted to the high latitudes of our North Ocean. 
If, that regard may be had to the influence of tem- 
perature on the compression of the water in the piezometer, 
we put the equation for depth under the form 
Nr — Pcos2 pyh=a(a + qt) (m’—m) + 0 (m’—m)? + ¢(m’—my’, 
idet Sammentrykkelighedseoeffierenten (7, = 7, (1 — 96) fore- 
| 
kommer i Nævneren af Coefficienten til (m’—m), har man 
KO nGG0 
= 0.0031702 
50.153 oud 
Man faar da folgende Verdier for log (Coeff. t. a) 
I 
No. t qt 
I 20.6 —+0.00 
2 0.77 FF 
3 —1 .35 —0.00 
4 =i Gå = 
5 —TI .42 — 
6 —I .20 — 
7 18 GÅ we 
8 — I .47 — 
9 =i 08S} a: 
10 = 050 = 
Factorerne b, c og h blive de samme som ovenfor. 
| 
1} 
i 
Endeligningerne blive: 
114352. 0 + 14557772. 0 + 
14557772 &@4- 1912740543. 0 
1904468269. a + 257081182958. b + 
the coefficient of compression (7, =1% (1 — q@)) occurring 
in the numerator of the coefficient of (m'—m), we have 
; log ¢= 7.50109—10. 
We then get the following values for log (coeff. for 
a): — 
ee eat) 
=" X(1 — 2 cos 2g) 
824 0.86847 
244 1.52893 
428 1.98491 
434 2.00580 
450 2.02370 
409 2.02574 
485 2.00850 
466 2.09883 
485 DANE 
378 2.19148 
The factors b, c, and h will be the same as above. 
The normal equations are 
1904468269. ¢= 1450504 
257081182958. C= 184843607 
35422403423676. C= 24200418357 
hvorat (whence) a= 12.089666 log a= 1.0824143 
b= 0.00660055 log 6 =7.8195832—10 
f = —0.000014704 log ¢6=5.1674405,—-10. 
