3 22 Proceedings of the Society of Arts, Sciences, &c. 



The commissioners charged by the society with the exa- 

 mination of this method proposed by M. Ducom (Messrs. 

 Lescan, Thibaut^ and Leupold,) have compared it with those 

 raost practised at sea, and particularly with Douves's method. 

 This last has been discussed at great length in a memoir by 

 M. Mendoza, inserted in the Connoissmice des Temps for 

 1 793 ; but the author of this memoir only employs the dif- 

 ferential formulae in the discussion of the errors which might 

 affect the elements of the calculation, which formulae always 

 suppose the errors to be extremely small. Much care and 

 attention in making the observations, and a sufficient know- 

 ledge of the instruments made use of, reduce the errors in 

 the altitudes, in the interval marked by the watch and in the 

 declination, so as to be effectually very small : but it is not 

 the same with errors which affect the latitude by account, 

 which in certain circumstances may be considerable. As 

 to the useful researches of M. Mendoza in his memoir, and 

 to which we must refer in the cases before cited, the com- 

 missioners have added the examination of the influence 

 which a considerable error in latitude might occasion. 



They have given in their report a formula which expresses 

 the error of the result given by Douves's method, in powers 

 of the error which affects the latitude by account. In using 

 this formula it will be necessary to take so many more terms 

 of the series, according as the error in latitude is greater. 



Among other consequences which this formula presents, 

 it shows that Douves's method will always give an error 

 which will be in a contrary sense to that which affects the 

 latitude by account, and that this error increases rapidly as 

 the latitude of the place of observation is greater, since the 

 successive powers of the tangent of the latitude enter into 

 his method. 



It appears from the reports made by the above gentle- 

 men that the method proposed by M. Ducom vvill give the 

 latitude very exactly, whatever may be the error in the lati- 

 tude by account, when, as the method require?, one of the 

 two altitudes shall have been taken exactly at the passage by 

 the prime vertical, or very near it. 



This method has one inconvenience, that it is not always 



practicable: 



