The Nautic-Astronomical and Universal Calculator: The mechanical solving of all Arithmetical problems, plane and spherical Trigonometry, including terrestrial and astronomical navigation [Reprint 2021 ed.] 9783112444207, 9783112444191

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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