# NavList:

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

**Re: Double altitude method**

**From:**Ducruy Jacques

**Date:**2015 Aug 4, 10:17 -0700

Hi Paul,

Thank you again for your very interesting studies.

Few observations :

1) about Rosser : do you know the book of John Riddle (Treatise of navigation, edition 1859) ? It seems to me that the method for calculate latitude and longitude is the same of Rosser ; in the two cases, the base is the "Sumner line", with two calculations of longitude for each altitude.

2) about Johnson : I knew already "on finding latitude and longitude in cloudy weather" and I have seen the "symetry" with the method of Pagel. But, on the other hand, I was unaware of the other methods proposed by Johhson (as Borda method). The table I & II de Johnson are an interesting abbridged version of ABC and Perrin tables !

I disagree with you only on a little point : in note (8), you tell that Pagel was the first "user" of the coefficient Cotg Z/Cos L : Ducom used these coefficient in 1820 for facilitate the calculation of latitude by double altitude, for the Borda method as the Dunn method).

On the other hand, I have find a study of Henry Raper in "nautical magazine" of 1844 ; Raper proposed a simplification of the Sumner method, with only one calculation of longitude and a calculation of azimut by sinus formula : in my opinion, Raper is the "father" of the method of Johnson (also called "Lalande-Pagel" in France).

I add that Pagel had borrowed the method of Ducom for calculate the latitude (and the method of Ducom is a simplification of Dunn method) : but Ducom do not give the method for correcting the longitude after the calculation of the correction of latitude. The only differnce is the way to calculating the coefficient, called "Number N" by Ducom.

In summary, can I affirm that there are two approaches for a same problem : a "mathematical approach" by Pagel and a "graphical approach" (by projection) by Raper ? In the two case, the "common denominator" is the method of Dunn.

Best Regards

Jacques