sr 
Indsættes Værdierne af a, b og c i Ligningerne, faaes: 
Substituting the values of a, b and c into the equa- 
az | tions, we get: — 
(1 + qt) (m'—m) 
No. SG — famåm) bm —m) c(m—m)* ber. h obs. h. 0—B 
I 89.31 + 0.36 —o0.01 80.7 93 + 3.3 Fv. (Fims.) 
2 408.64 TB 0.60 415.8 416 +o.2 
3 1167.67 63.07 14.24 1217.4 1216 — 1.4 
4 12265021 70.44 16.45 1270.2 1280 0.8 
5 1276.76 76.53 18.63 1334-7 1333 = of) 
6 1282.77 77.16) 18.87 1341.1 1343 —-1.9 
7 1415.50 04.13 25.42 1484.2 1487 .+2.8 
8 1517.89 108.19 Bi RO 1594.8 1590 —4.8 
9 1600.07 120.27 36.71 1683.6 1686 +2.4 
10 1878.84 165.45 — 50.22 1985.1 1985 —0.1 
WE I => LOA 
0= + 1.794 Favn. (Fms.) 
Denne Formel giver saaledes en endnu mindre sandsyn- 
lig Fejl end den forrige. Rækkens Convergents er imidler- 
tid bleven adskillig mindre, idet 1 den forrige Formel Leddet 
c(m’—m) i Ligning No. 10 kun er: —4.7 Favne. 
Efter Formelen faar man: 
dh __ 12.089666 (1 + qt) 
0.01320110 
This formula gives accordingly a probable error still 
smaller than the preceding. The convergence of the 
series, however, has become considerably less, the term 
of the first formula, ¢ (m'—m)*, in equation No. 10, being 
but —4.7 fathoms. 
According to the formula, we get: — 
d (mm) SG = cos 2 ¢) 
s(1 — PB cos 2 9) 
0.00014112 : 
ss ~ (m'—m)?. 
5 (m' —m) S(a = B cos 2 9) 
Sættes (Putting) d (m'—m) = + 0.081 
0.9793 (1 + 2) 
(1 —( cos2¢) 
faaes (we get) dh = 
varierer fra 0.967 til 1.028 Favn. 
Efter Rækkeudviklingen af den rationelle Formel bliver 
en Størrelse, der mellem Overfladen og 2000 Favnes Dyb | 
| 
| 
(1 — Pcos2g)h= z 
a, (Å =m) 
Indsættes her Værdierne a, = 0.1769851, 1 = 50.153 
ne (6) 
Milliontedele, ; 5 9303:07 08 Middeltallet af m= 10.5661, 
faar man Factoren lig 12.1236(1 + qf), altsaa meget nær 
lig den af den sidste empiriske Formel fremgaaende. Un- 
dersøger man, hvad Værdi den empiriske Formel giver for 
Factoren c, saa findes ¢c = 0.00045472. Buchanan's Be- 
stemmelse, med hvilken der er regnet i den rationelle For- 
mel. er 0.000456. | 
0.001069 
(1 — £ cos 2 g) 
—(m’—m)+.... 
— (m’—m) — BSS ES STEN (m’—in)?, 
= (1 — P cos 2 9) 
a quantity that varies, between the surface and a depth of 
2000 fathoms, from 0.967 to 1.028 fathom. 
According to the rational formula developed im a 
series, we have 
I = sea) 
Th, E — m) H(t — qt) a (5 — m) No 
Substituting here the values a, = 0.1769851, 7, = 
ee 
50.153 millionths, =» = 9393-07, and the mean for m = 
10.5661, we get the factor equal to 12.1236 (1 + qf), 
therefore very nearly equal to that deduced from the last 
empirical formula. If we investigate what value the empirical 
formula gives to the factor c, we shall find ¢ = 0.00045472. 
Buchanan’s determination, with which I have computed in 
the rational formula, is 0.000456. 
Indleveret Marts 1886. 
Received March 1886. 
Translated into English by J. Hazeland. 
bo. 
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