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Hello Paul,

Thank you very much for your answer.

Your study about "double altitude problem" is very intestesting ; can I made some observations ?

 1) Do you know the method proposed by Borda (see "traité du cercle à réflexion) : Borda made 2 calculations of hour angle with the first altitude and 2 calculations of latitude with the 2e altitude (taken near of the meridian), and a "règle de trois" give the latitude : this method had been simplified by Ducom (1806) => "méthode à un angle horaire".

2) the method of Fatio de Duillier had been use by Pezenas (1766), whitch is inclused in several treatises de navigation (Bezout-Rossel, Fournier, etc). The method proposed by Lynn on 1827 is a very near version (Lynn use the "nat versine formule", and Pezenas the rule of right angled triangle).

3) in my opinion, the method of Caillet (7) is a simplification of the method of Ducom (9) with use of "coef des circumméridienne"; I have find another version in the treatise of Constan (1904), but, in my opinion, these methods are only valable with altitude ex-meridian.

I am of course interested by your studies on double chronometer method.

About Louis Pagel, it seem that he use the formula de Ducom "at two hour angle" of Ducom for the calculation of latitude.

If :

P = HA of 1e altitude and P' = HA of 2e altitude (calculated for the estimed latitude)

I the ellapsed time

N and N' the coefficients (Cotg Z/Cos L) correspondant to P and P'

You have :

correction of Latitude : (I - (P'-P)) / (N' - N)

correction of mongitude : correction of latitude * N or N'

Have a nice evening

Jacques