F-tafel, tafel zur vereinfachten berechnung von höhenstandlinien. Im auftage des Oberkommandos der Kriegsmarine herausgegeben von der
Corporate Author: Deutsche Seewarte.
Published: Hamburg, 1941.
Edition: 3. aufl.
Note: In upper right corner of t.-p.: 2154.
Physical Description: xxiii, 88 p. 30 cm.
Original Format: Book
Original Classification Number: VK 563 .H19 1941
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F-Tafel. Tafel zur vereinfachten Berechnung von Höhenstandlinien. Im Auftrage des Oberkommandos der Kriegsmarine herausgegeben von der Deutschen Seewarte.
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29S[U].—Hamburg, Deutsche Seewarte, publication no. 2154, F-Tafel.
Tafel zur vereinfachten Berechnung von Höhenstandlinien. 3
Hamburg, August, 1941. xxiii, 88 p. 19.6 X 29.2 cm. In the third
edition there were extensions and corrections of the introductory material,
and of 8 of the 11 tables.
The method and principal table of this volume are similar in many respects to those of
H. O. 208 (Dreisonstok, see MTAC, v. 1, p. 79f). The astronomical triangle is divided
into two right spherical triangles by a perpendicular from the zenith upon the hour circle
of the star; U is the co-declination of the foot of the perpendicular, and V is log cos B,
where B is the angle subtended at the zenith by U. By Napier's rules,
tan U = cos I cot L
sin B = sin / cos L,
where /, L, and d are the local hour angle, latitude and declination respectively. By applying
another of Napier's rules to the right triangle of which the star is one vertex, the altitude,
h, may be found by
sin h = cos B sin (d + U)
log sin h = V + log sin (d +
For the determination of azimuth, Z, two more auxiliary quantities are introduced,
P which is the great circle distance from the star to the east- or west-point of the horizon,
and Gr. 4 which is the declination of the intersection of the hour circle of the star with the
prime vertical. Thus, sin t cosd ■>c osP and sin Z = cos P sec h. Also, tan Gr. S = tan L cos t.
82 RECENT MATHEMATICAL TABLES
In Table F I, with vertical argument, latitude 0(1°)70°, and horizontal argument,
local hour angle 0(4m)6h, three values per page, there are tabulated four quantities, U to
the nearest O'.l, V to 5D, Gr. 5 and P, each to the nearest 0?1. In the second part of
Table F I, the vertical argument is latitude, 70°(1°)90°, and the horizontal argument is
local hour angle 0(4m)6h, nine values per page, three in each horizontal section.
At ths bottom of the vertical columns in Table F I are azimuths; entering the left
column with altitude as argument, and moving across the pages horizontally until one
finds under P, the value already copied out, one can drop to the bottom of the column
and read off the azimuth angle. Since the tabulated values of the azimuth angle go up to
90° only, it is necessary to have another device to determine the quadrant. When the
hour angle is greater than 6b, the azimuth is measured from the elevated pole; when the
local hour angle is less than 6h and L and d are of opposite name, the azimuth is measured
from the depressed pole. If the local hour angle is less than 6h and L and d are of the same
name, the azimuth is measured from the elevated or depressed pole according as the declination
is greater or less than the quantity Gr. a.
In case the altitude is great, or the azimuth near 90°, the value of the azimuth may be
poorly determined by the use of Table F I. In such a case, it will be noted that the
of P lies below a dotted line running across the page. One must then use instead Table
F XI, which gives P to the nearest minute of arc and the variation in P corresponding to
1' change in d or h.
Table F II is a table of log sin x, x = [0(0'-1)6°(1')90°; 5D], with generous tables of
Tables F DI and F IV represent the principal advantages this volume possesses over
other similar tables; they permit one to determine the corrections (to the nearest 0!1) to
the computed altitude corresponding to slight changes in time (up to 2m by 10* steps) or latitude
(up to 30' by 1' steps) respectively. In both cases, one can interpolate very easily by a
shift of the decimal point. Table F III is a well-designed triple-entry table occupying only
five pages; one starts down the column at the left headed by the value nearest the assumed
latitude, stops at the value nearest the computed azimuth and moves to
the right to the
column headed by the number of seconds change in time. Table F IV is a small doubleentry
table on a single page; the vertical argument is azimuth 0(5°)20°(2°)90°, and the
horizontal argument is change in latitude, l'(l')10'(10')30'. These two tables allow one to
work either with an assumed position or with a dead reckoning position.
Table F V is for changing time into angular measure and conversely. Table F VI gives
the corrections for refraction, semi-diameter and parallax to be applied to the altitude
(3°-90°) of the lower- or upper-limb of the moon; there is a supplementary table for height
of eye. Table F VU gives the combined correction for refraction and height of eye (0-30
meters) to be applied to the altitudes (3°-90°) of fixed stars or planets. Table F VIH yields
the correction for refraction, semi-diameter and height of eye (0-30 meters) to be applied
to altitudes (3°-90°) of the
sun's lower limb; there are also two auxiliary tables to provide
corrections to the altitudes to take care of the varying semi-diameter of the sun through the
year, and for the case where the sun's upper limb was observed. The latter takes only a
very small amount of space and would seem to be quite worthwhile. Tables F IX and F X
provide similar corrections for use with the bubble sextant.
The tables are well printed on a good grade of paper. In a number of cases, the rules
needed to make decisions as to quadrants, etc. are printed on each page. As for the accuracy
of the tabulated values, only a few rounding off errors of a unit in the last place were
discovered in a brief examination.
Charles H. Smiley
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