Ancestral celestial Douwes formula

This page explains ancestral celestial Douwes formula, a logarithm-based method featured in the second part of my worksheet

View first Astronavigation and Logarithm Option from

In fact, this formula allows you to calculate the sun’s height using only logarithm tables, without the necessity of a scientific calculator.

Ancestral celestial Douwes formula, image douwes formula
log sinusvers = log versine (1 – cos ⍺ )

Table 1 = log cos; Table 2 = log versine; Table 3 cosine

The main objective of this website is to assist in determining your sea position with a sextant, with a primary focus on utilizing a scientific calculator, although the option to employ logarithm tables is also available.

However, understanding the Douwes formula is not a prerequisite for utilizing the tables.

Hence, you may skip this page without encountering any issues in utilizing the tables

Ancestral celestial Douwes formula, recommendation for the use of this website

Also, after starting the La Rochelle exercise, you will have the option of using a calculator or logarithm tables.

Oil on canvas. Metropolitan Museum of art

ancestral celestial Douwes formula: explanation Douwes formula

Douwes formula image  logarithm table
Ancestral celestial Douwes formula, the five tables in chronological order
The 5 tables in chronological order

Also, to work with this formula without a calculator we will use the logarithm tables and the natural sine and cosine tables

First part of the formula

Douwes formula image formula
log sinus verse = log versine

L = Dead reckoning latitude

D = Declination of the sun

 explanation same name/not same name

SAME NAME/NOT SAME NAME is part of the logarithm method.In this part we do not use the rule of signs .

Ancestral celestial Douwes formula: second part of the Douwes formula

logarithm 2nd term

Table 1 et 2

image douwes formula
log sinus verse = log versine
Ancestral celestial Douwes formula, image part of the worksheet

Ancestral celestial Douwes formula:

Table 3, 4 et 5

Finally, after having found log 2nd Term, we will seek with the help of table 4 (logarithms of whole numbers) the natural 2nd Term

Ancestral celestial Douwes formula, image douwes formula, table 4 (logarithms of whole numbers from 1000 to 10000
Douwes formula table 5
The use of table 5

Consequently, with the result natural cos (L+/-D) ⎼ natural 2eT = sin Hc, we will find the sin Hc.

example: sin Hc = 0,5

Hc = arcsin (0,5) = 30° (Table 5)

Additionally, here you can find a total of 4 exercises, all fully worked out and provided with the necessary table pages.

 example Hc with the tables

Two exercises Hc with logarithm tables and solutions

La Rochelle exercise option logarithm tables

Furthermore, after completing those four exercises, you can consider buying the solutions to the seven remaining exercises in the store, which will come with the complete logarithm tables