Marine logarithm tables of whole numbers and example of how to use them
Marine logarithm tables:
This page only explains the use of this table, but you need to go to the page ‘Calculate Sun’s Altitude at Sea with Logarithm Tables‘ to see the full context.
The best way to calculate your position at sea using a sextant and logarithm tables is to start with the exercise ‘La Rochelle.’
After the general first part, make your choice between the calculator or the logarithm method.
Table of Logarithms of whole numbers
Here we see that we transform natural numbers into logarithmic numbers. Instead of multiplying, we add these logarithmic numbers to obtain a total logarithmic term.
Then, using Table IV (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)
The inputs obtained in the first part of the worksheet necessary to find the calculated altitude of the sun (Hc)
L = 16° 09′ N (D.R. latitude)
D = 19°21′.9 S (declination of the sun)
P = 42°15′.1 (NE) (polar angle)
The 29.37182 is called log 2nd term
TABLE IV
Marine logarithm tables:
Log 2nd Term = 29.37182
Mantissa = 37182
Characteristic = 29
The mantissa
With the Mantissa ( 37182), we will search for the whole number in the table of logarithms and whole numbers (Table IV)
Table 4 page 2200/2600
The use of the characteristic is to put the decimal point!
After finding the whole number, we have to put the decimal point!
Characteristic is 29 (see below for the decimal point)
Whole number = 2345
Characteristic = 29
natural second term = 0.2354
Conclusion
Table of Logarithms of Whole Numbers
We take the logarithm of natural numbers — in practice, we transform them into their logarithmic form. This replaces multiplication with addition.
The mantissa gives us the digits, and the characteristic tells us where to put the decimal point when converting back to a natural number. The small table above shows this clearly.
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 an example and two exercises completed in the interactive worksheet (tables) page in the calculated altitude section.
The idea is to continue with the concept of the DR position, and intercept but we no longer use the rule of signs (positive or negative)
It will be replaced by the notion same name or not same name.
method:
In principle, we adhere to the same Saint-Marc-Hilaire method.
These logarithm tables do not depend on time either.