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five: Cadiz, the most in use with navigators; Carthagena; the new observatory at the isle of Leon; the college of Nobles at Madrid, introduced by the beautiful maps of M. Antillon; and the point de la Galera at the island of Trinidad. To these five meridians might be added other two which pass through the Spanish possessions, and have been adopted by a great number of geographers: I mean the meridian of Teneriffe and of the island of Fer. The latter occasions inevitable confusion, d'Anville placing it between the town of Fer and Cape West. So that there are seven first meridians, without reckoning Toledo, in the sole dominions of the king of Spain.

I have followed, in the denomination of the seas which wash the coasts of Mexico, the ideas proposed by M. Fleurieu in his observations on the hydrographical division of the globe; a work in which the most enlarged views are united to a profound historical erudition. The Spanish names have often been added to facilitate the reading of travels written in Spanish.

In drawing up the map of Mexico, I began by assembling together all the points fixed by astronomical observations, from which I formed a view, which, for the better appretiating the degree of confidence which the results deserve, indicates the nature of the observation and the name of the observer. The number of these points amounts to 74, of which 50 are situated in the interior of

the country. Of this latter class there were only fifteen known before my arrival at Mexico in the month of April, 1803. It may be useful to discuss some of the thirty-three points whose position is determined by my own observations, and which are all comprised between the 16° 50′ and 20° 0′ of latitude, and the 98° 29′ and 103° 12′ of longitude. While we are fixing these positions, we shall enter into some historical details respecting the extraordinary errors which have been propagated to this day in the most recent and current maps.

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MEXICO.

Several meridian altitudes of the sun and stars gave me for the latitude of the capital at the convent of St. Augustin*, 9° 25′ 45". The longitude deduced from the eclipses of the satellites of Jupiter, from the distances from the moon to the sun, from transference of the time from Acapulco, and from a trigonometrical operation for estimating the difference of meridians between Mexico and the port of Vera Cruz, is 6" 45′ 42′′ or 101° 25′ 30′′. I shall observe once for all, that I rely on the numbers which result from the very careful calculations of M. Oltmanns, a distin

* The great gate of the cathedral church of Mexico is 12" farther north, and 10′′ farther east, than the convent of St. Augustin, near which I made my observations.

guished geometrician, who calculated all the astronomical observations made by me since my departure from Paris in 1798, to my return to Bordeaux in 1804. The longitude of Mexico (6h 45′ 28′′) indicated in the new astronomical tables published by the Bureau des Longitudes, is founded on an astronomical memoir which I presented to the first class of the institute, the fourth Pluviôse, year XIII, in which the calculations of the moon had not been corrected by the tables of M. Bürg. A year before I had fixed on a result which was still nearer to the true longitude; the medium of my observations printed at the Havannah was 101° 20′ 5′′.

Three emersions of the first satellite of Jupiter observed by me give for middle term, by the tables of M. Delambre, the longitude of 6o 45′ 30′′.

Thirty-two distances from the moon to the sun, calculated by M. Oltmanns, from the newest lunar tables, give for longitude 6 45′ 54′′.

The transference of time from Acapulco gives for the difference of meridians between the port and the capital of Mexico, 2′ 54′′ in time; consequently, supposing Acapulco 6" 48' 24", the longitude of Mexico would be 6h 45′ 29′′.

Two observations of satellites, the one at Lancaster in Pensylvania, the other at the Havannah, both corresponding to the emersion which I observed at Mexico, the 2d May, 1803, give in longitude, the one 6 45′ 33′′, the other 6 45′ 26′′.

The longitude of Guanaxuato determined by lunar distances, and connected by my chronometer with that of Mexico, gives for that capital 6h 45' 56".

From the trigonometrical operation, or rather from my attempt to connect the capital with the port of Vera Cruz, by means of the azimuths and angles of altitudes, taken on the volcanos of Orizaba and Popocatepec (according to the calculations of M. Oltmanns, and supposing Vera Cruz 6h 33′ 55′′), there results a longitude for Mexico of 6° 45′ 36".

All these results, obtained by ways so various and independent of one another, confirm the longitude that we assign to the capital of Mexico, which is more than a degree and a half different from what has been hitherto adopted; for the Knowledge of Times places Mexico in 1772, at 106h 1' 0", and again in 1804, at 102° 25' 45". The chart of the gulf of Mexico, published by the Deposito Hydrografico of Madrid in 1799, gives 103° 1' 27" to the capital; however, before I began to observe at Mexico, the true longitude was accurately enough known by three astronomers whose labours deserve to be better known, two of whom were born in Mexico. MM. Velasquez and Gama, so far back as 1778, had deduced from their observation of satellites the longitude of 101° 30', but having no corresponding observations, and calculating after the old tables of Wargentin,

they remained uncertain (as they themselves assured me) for more than a quarter of a degree. This curious result is contained in a small pamphlet printed at Mexico*, very little known in Europe. Velasquez, director of the supreme tribunal of mines, fixed the longitude of the capital at 101° 44' 0", as is proved by valuable manuscripts preserved by M. Costanzo at Vera Cruz. In a map of New Spain sketched in 1772, Velasquez gave to Mexico 278° g' of longitude, reckoning from the isle of Fer= 101° 51'. He says in a note to this map, "that before his voyage to California in 1768, all Mexico was placed in the South Sea; that his map is the first which offers the true position of the capital, and that he verified it by a great number of observations at Santa Rosa in California, at Temascaltepec, and at Guanaxuato." M. Galeano, one of the most able astronomers of the royal marine, had also found out the true position of Mexico, when he traversed the kingdom in 1791 to join the expedition of Malaspina. It is true that M. Antillon deduced the longitude of 101° 52′ C, from the observations of Galeano, a result which still differs from mine 1' 48" in time; but I suspect that this difference arises from some trivial error which may have crept into the calcu

* Descripcion orthographica universal del eclipse de sol del dia 24 de Junio de 1778, dedicada al Sr. Don Joacquin Velasquez de Leon, por Don Antonio de Leon y Gama, 1778,

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