# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Latitude by Polaris**

**From:**Ron Jones

**Date:**2016 Mar 26, 15:58 -0700

The 2002 Edition of Bowditch omitted an explanition of how the Polaris correction tables in in the Nauticak Almanac were constructed.

The following was taken from the 1977 Edition of Bowditch article 2027, pages 553 & 554 and may be of interest to any one interested in how the table were constructed:

Another special case of finding latitude is available in most of the northern hemisphere, it utilizes the fact that Polaris is less than **1°** from the north celestial pole. Since Polaris is never far from the north celestial pole, its observed altitude (**Ho**) , with suitable correction , is the observer's latitude. When Polaris is on the upper branch of observer's meridian ( **LHA = 0°** ) the observer's latitude is equal to the observed altitude minus the polar distance ( **p** ). When Polaris is on the lower branch of the observer's meridian ( **LHA = 180°** ) the observer's latitude is equal to the observed altitude plus the polar distance ( **p** ). When the **LAH** of Polaris is not **0°** or **180°** the Polaris correction is approximately defined by the polar distance ( **p** ) times the cosine of **LHA**. Thus the correction is a function of the **LHA** of Polaris, and hence also of the **LHA** of Aries, insofar as the difference between these quantities (the **SHA** of Polaris) can be considered a constant. Although this method provides sufficient accuracy, a higher degree of accuracy can be obtained by the use of the Polaris correction tables contained in the ** Nautical Almanac**.

The Nautical Almanac tables are based on the following formula:

Latitude - **Ho** = **p**•cos(**h**) + (**p**/2)•sin(**p**)•sin^{2}(**h**)•tan(latitude)

where **p** = polar distance of Polaris = 90° -Declination of Polaris

**h** = Local Hour Angle of Polaris = LHA of Aries + SHA of Polaris

The value of **a _{0}**, which is a function of

**LHA**Aries only, is the value of both terms of the above formula calculated for the mean values of

**SHA**and Dec. of Polaris, for a mean latitude of

**50°**, and adjusted by the addition of a constant (

**58.8'**). The value of

**a**which is a function of

_{1}**LHA**of Aries and latitude, is the excess of the value of the second term over its mean value for latitude 50°, increased by a constant (

**0.6'**) to make it always positive. The value of

**a**, which is a function of LAH Aries and date, is the correction to the first term for the variation of Polaris from its adopted mean position increased by a constant (

_{2}**0.6'**) to make it positive. The sum of the added constants is

**1°**, so that:

Latitude = corrected sextant altitude **-1° +a _{0} +a_{1} +a_{2}**

The ** Nautical Almanac** table at the top of each Polaris correction page (274→276) is entered with

**LHA**Aries, and the first correction (

**a**) is taken out by single interpolation. The second and third corrections (

_{0 }**a**and

_{1}**a**) are taken from the double entry tables without interpolation, using the

_{2 }**LAH**Aries column with the latitude for the second correction (

**a**) and with the month for the third correction (

_{1 }**a**).

_{2 }