F-tafel, tafel zur vereinfachten berechnung von höhenstandlinien. Im auftage des Oberkommandos der Kriegsmarine herausgegeben von der
Deutschen seewarte.

Corporate Author: Deutsche Seewarte.

Language(s): German

Published: Hamburg, 1941.

Edition: 3. aufl.

Subjects: Azimuth.

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

Locate a Print Version: Find in a library

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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
Auflage.

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

and

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)

or

log sin h = V + log sin (d +
U).

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

hand
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
value

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

proportional parts.

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

Brown University

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