Marine logarithm tables:
This page, devoted to the table of logarithms of whole numbers, serves as an intermediate reference.
To follow the full logic of the calculation, everything begins on the page Logarithm Tables and Celestial Navigation where you will find all the links related to the logarithmic method.
Logarithm tables of whole numbers and an example of how to use them
Table of Logarithms of whole numbers
Here we see how natural numbers are transformed into logarithmic numbers using the log cosine and log versine tables.
Instead of multiplying, we add these logarithmic numbers to obtain a total logarithmic term.
Then, using Table 4 (Logarithms of Whole Numbers), we convert this logarithmic term back into a natural number.
It’s like sending our numbers on a log trip and welcoming them back to the world of natural numbers!
These tables were developed by the author with the help of Google Sheets.
The five tables necessary to obtain the calculated height (Hc)
- Table 1: log cosine
- Table 2: log versine
- Table 3: natural cosine
- Table 4: logarithms of whole numbers
- Table 5: natural sine
Marine logarithm tables:
Example – Table 4: Logarithms of Whole Numbers
On this page, we focus only on how to use Table 4 to convert a logarithmic term into a natural term.
Log 2nd T ⇒ Nat 2nd T
Mantissa: the fractional part of a logarithm.
Characteristic: the integer part of that logarithm.
The 29.37182 is called log 2nd term
TABLE 4
Marine logarithm tables:
Log 2nd Term = 29.37182
Mantissa = 37182
Characteristic = 29
The mantissa
The mantissa is the decimal part of a logarithm, from the Latin word mantissa, meaning “an addition” or “something added.”
With the mantissa (37182), we search for the corresponding whole number in the Table of Logarithms of Whole Numbers (Table 4).
Table 4 page 2200/2600
The role of the characteristic is to determine the position of the decimal point.
After finding the whole number, we must place the decimal point.
Characteristic is 29 (see below for the decimal point)
Whole number = 2345
Characteristic = 29
Natural second term = 0.2354
In our specific use — that is, in our calculation grid, when adding the three logarithmic values — the characteristic of the result always falls into one of the following four cases: 26, 27, 28, or 29.
If you arrived from the page TWO EXERCISES TO CALCULATE THE ALTITUDE OF THE SUN (Hc), please return there after reviewing how Table 4 is used on this page.
Marine logarithm tables: recall
The purpose is to calculate the altitude of the sun (Hc) without a calculator.
The use of logarithm tables will replace multiplication with addition.
We will find a fully worked-out example and two completed exercises on the main page.
The idea is to continue using the concept of the DR position and the intercept, but without applying the rule of signs (positive or negative).
It is replaced by the concept of “same name” or “not same name”.
method:
In principle, we follow the same Saint-Marc-Hilaire method.
These logarithm tables are also independent of time.