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The errors of latitude are consequently of more than half a degree. It is difficult to conceive what is meant to be designed in the map of Arrowsmith bv the three mountains named Orizaba, False Orizaba, and Volcano of Tlascala. They are all indicated to the north-west of the port of Vera Cruz, while the true Pic d'Orizaba (and the Mexicans know but one, called in the Azteque language Citlaltepetl) lies to the south-west of Vera Cruz, between the city of Cordoba and the villages of San Andres, San Antonio, Huatusco, and St. Jean Coscomatepec. There is added to the False Orizaba the note "visible to the eye at 45 leagues distance." Now Citlaltepetl is the summit which navigators first see in approaching the coast of New Spain, consequently it might be inferred that the learned English geographer named it False Orizaba. But in this case, the latitudeof this problematical mountain would be a degree false, and Orizaba would be seven marine leagues to the north of the city of Xalappa, while in reality it is only twelve to the south-south-west. Or should the Pic d'Orizaba of Arrowsmith be the CofTre de Perotte? But the Coffre lies also to the south-east, and not to the south-west of the village of Perotte. This fable of two mountains of the name of Orizaba is to be found also in the atlas of Thomas JefFereys (The West-Indian atlas, London, 1794), where an attempt is made to convey minute information as to the roadfrom Vera Cruz to Mexico. The latitudes are there 36' false. The difference of longitude between the port and the capital is marked 2° 29' instead of 38 38' as in the map of Arrowsmith, and instead of 2° 56' 30" the result of my astronomical observations. It is also very improbable that the Volcano of Tlascala indicated in this new English map, is the Sierra de Tlascala, called in the country Malinche; for this Sierra is neither very remarkable for its elevation, nor very distant from la Puebla. This confusion is so much the more astonishing, as in 1803 the excellent observations of Don Jose Joacquin Ferrer, published in 1798, were known in London*, as well as the maps drawn up by the Deposito Hydrografico of Madrid; though even M. Antillon places it in 1802, in his map of North America, la Puebla 32' too much to the south.
t i * Ephemerides geographiques de M. de Zach, 17Q8, T. II. p. 393. It is from this map that I cite the results obtained by M. Ferrer. They sometimes differ from those indicated in the manuscripts, which that excellent and indefatigable observer bad, probably from less careful circulations, drawn up upon the spot, of which I am in possession of copies. I am bound to make this observation for the sake of those, who, having procured copies of my works, may be astonished at finding numbers in them differing from those now published by me. It is only after calculating carefully every observation that we can arrive at exact results.
POINTS SITUATED BETWEEN MEXICO, GUANAXUATO, AND VALLADOLID.
In two excursions which I made, the one to the mines of Moran and to the porphy retical summits (organos) of Actopan, the other to Guanaxuato and to the volcano of Jorullo in the kingdom of Mechoachan, I determined the position of ten points, whose longitudes are almost all founded on the transference of time. These points have enabled me to give with some accuracy a great part of the three intendancies of Mexico, Guanaxuato, and Valladolid. The longitude of the city of Guanaxuato was verified by distances from the moon to the sun. Its latitude, deduced from the observation of a de la Grue, is 21° O' 9". Fomachant gave me 21° O 28", and /3 de la Grue, 21° 0' 8''. The Jesuits in their map, engraved at la Puebla in 1755, placed Guanaxua to at22° 50' of latitude, and 112° 50' of longitude, an error of 9°! M. Velasquez, who observed the satellites of Jupiter at Guanaxuato, found this city 1° 48' to the east of Mexico, but at 20 45' 0" of latitude, as is proved by his manuscript map of New Spain. This error of latitude is so much the more extraordinary, as the difference in longitude which it indicates is to within an arc of l', the same with what results from my observations.
Latitude of Toluca by * de la Grue 19 16' 24'', by Fomahant, 19° 16' 3V. I endeavoured as much as possible constantly to observe the same stars to diminish any error from the uncertainty of the declination.
The position of Nevado de Toluca, the latitude ofPatequero, a city situated on the banks of the lake of the same name, of Salamanca, St. Juan del Rio, and Tisayuca, are founded on imperfect observations. There are circumstances in which the method of Douwes gives very inaccurate results; but in a country presenting so few fixed points we must often be contented with a simple approximation. I think I can venture to assert, that the longitudes of Queretaro, Salamanca, and San Juan del Rio, maybe confidently relied on.
Even in the valley of Mexico there are several very important points, the position of which was determined by Velasquez, the celebrated Mexican geometrician of the eighteenth century. This indefatigable man executed in 1773 an extensive survey along with a trigonometrical operation, to prove thatthe waters of the lake of Tezcuco might be conducted to the canal of Huehuetoca. M. Oteiza was kind enough to calculate for me the triangles of Velasquez, of which I possess the manuscripts. M. Oltmanns went over the same calculations. He subjected the positions of the signals to the latitude and longitude which we have here adopted for the convent of St. Augustin
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