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English Pages 67 [91] Year 1910
THE
NAUTIC-ASTRONOMICAL AND
UNIVERSAL CALCULATOR The mechanical solving of all Arithmetical problems, plain and spherical Trigonometry including terrestrial and astronomical navigation.
I. PART: Description of t h e Nautic=Astronomical Calculator and t h e solving of all p r o b l e m s in t h e whole m a t h e m a t i c s . II. PART: Applying t h e Calculator in t h e T e r r e s t r i a l Navigation. HI. PART; Applying t h e Calculator in t h e Astronomical Navigation.
[25] BY
R
NELTING.
Copy-right Right
HAMBURG
of translation
1909.
PUBLISHED B Y R . NELTING, HAMBURG 19, EMILIENSTRASSE 67.
reserved.
TABLE OF CONTENTS. PART I. DESCRIPTION AND DIRECTION TO U S E T H E CALCULATOR.
Pag
e
Chapter
1.
The nautic-astronomical or Universal Calculator
Chapter
2.
The scales of the calculator
3 4
Chapter
3.
The focussing and reading of the values of the scales
7
Chapter
4
The value of position in calculation
9
Chapter
5.
The reciprocal value
11
Chapter
6.
The multiplication
15 19
Chapter
7.
The division
Chapter
8.
The potencing
22
Chapter
9.
The extraction of the roots
24
Chapter 10.
The conversion into logarithms
26
Chapter 11.
The proportions
27
Chapter 12.
Combined methods of calculations
30
Chapter 13.
Formation of tables, formulas and the connection of the trigonometrical functions . . 36
PART II. E X A M P L E P R A C T I S E OF T E R R E S T R I A L NAVIGATION. Chapter 14.
Determination of speed and distances
39
Chapter 15.
The dead reckoning
42
Chapter 16.
The sailing in greatest circles
44
Chapter 17.
The calculation of current
47
Chapter 18.
The formation of tables
50
PART III. E X A M P L E P R A C T I S E OF ASTRONOMICAL NAVIGATION. Chapter 19.
Altimetry of stars. The azimuth of altitude of stars. The calculation of the position by the method of altitude
51
Chapter 20.
Finding the name of an observed star
54
Chapter 21.
Calculation of the longitude by chronometer
56
Chapter 22.
Calculation of azimuth
57
Chapter 23.
Calculation of latitude
59
Chapter 24.
Rising and setting of stars and their amplitude
61
Chapter 25.
Altitude and hour angle of a star in the 1st vertical
62
Chapter 26.
Altitude, azimuth, and hour angle of a star in the greatest digression
63
Chapter 27.
Differential formulas
64
Chapter 28.
Nautical tables and formulas
66
ABBREVIATIONS. 9 = Latitude,
b — 90 0 — 9
&
p = (90°— &) — pole distance
h
Declination,
z = (90 0 — li)
- Altitude, X
= Longitude
t
=.-- Hour angle
Az = q
zenith distance
Azimuth
= Parallactic angle
A ~~ Difference reap, error.
INTRODUCTION. T h e universal nautical and astronomical calculator is a logarithmic and nautical collection of tables of an unlimited extent never reached up to the present for the calculation of all sorts of mathematical problems and for the solution of all nautical calculations with a precision sufficient for all purposes of navigation.
The problems can almost all be solved by the use of proportions, con-
sequently without calculation.
In the cases where the solution of the problem is only possible by
calculation, as in those of altitude, longitude and latitude, the logarithmic solution of the problem is considerably simplified.
At the same time by the use of the instrument the mental strain involved
in the logarithmic calculation is greatly lessened, the calculations are made quicker and the security of the calculations is enhanced.
The nautical calculator contains the tables of the numbers, squares
and roots, of the trigonometrical functions sin, tang, cosec and ctg, together with their roots and squares, the tables of the reciprocal values of the figures, squares and roots and the tables of the logarithms of all the forenamed values. value.
The trigonometrical functions are given in time as well as in arc
The calculator moreover contains the tables for point, degree, arc and time, whereby the
direct change from degree measure into point measure and time values into arc values and the reverse conversion is rendered possible.
The calculations can be carried out direct with time, arc
or point measure. All scales of the instrument are in correlation with each other, whereby the trigonometrical functions enter reciprocally into relation, and thereby it becomes possible to pass from one function of the arc or of the time to another function of this value. By simple displacement of the
scales of the instrument towards each other all tables
can be composed as they appear necessary for navigation.
The arrangement of the scales of the
trigonometrical functions render possible the calculation and readings as well as the putting in of the values up to a fraction of a second, with regard to arc as well as with regard to time.
In spite of
the manifold repetition of the results of calculation the scales are clear and easily surveyable in their arrangement as well as in their representation. As the calculator enables the direct calculation with the squares and roots of all trigonometrical functions and co-functions, even the most difficult nautical problems can be solved, quicker, more securely and simply than by logarithmic calculation.
The instrument at every focussing shows
a table, and in this manner mathematical expressions can be rendered in form of a table by one single focussing, for instance:— a.x;
a.xs;
a.Vx;
x*.a;
V* (V (Va.x); a.x
'
a.x
Vb
b*
y
a a a —; —; —; yx x x
x.\'a;
x1 x —; —; a a2
x —ya
H< V?.-
a x2 h
!
x .a2;
, a
b