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c From Mexico to Chiconautla, O' 20. (True distance 0° 15'.) d From the rock (Peñol) de los Baños to Zumpango, o' 92'. (True distance 0° 21'.) e From the Peñol de los Baños to San Christobal, 0° 13'. (True distance 0° 8'.) f From the village of Tehuiloyuca to Tezcuco O' 29'. (True distance 0° 21'.) Here are errors of 16,000, even of 20,000” metres, in distances which M. Velasquez, in a geodesical operation in 1773, had measured with great accuracy, and as to which there does not remain a doubt of a hundred metres f. And yet M. Alzate might have availed himself of the triangles of Velasquez, as was done by Don Luis Martin, M. Oltmanns, and myself, in constructing the map which is inserted in this work. I made no astronomical observation at Pachuca, but I did so at the Real de Meran, whose latitude is greater than that of Pachuca. I found the latitude of Moran 20° 10' 4", and yet M. Alzate makes Pachuca 20° 14'. The old city of Tula is placed in his map too far north by nearly a quarter of a degree. The plan of M. Mascaro, published in the Guia de Asevico (Mapa de las cercanias de A sevico ) only fourteen centimetres by tent, consequently it is about twelve times smaller than the one annexed

* About twelve miles and a half. Trans. t Aboubt 109 yards. Trans. ! About five inches and a half by four. Trans.


to this work. It may be considered as a copy of the plan of Siguenza and Alzate. The northern part of the valley has, however, been somewhat straitened. The summit of the volcano of Popocatepetl is distant from Huehuetoca, according to Father Alzate, 1° 14'; and according to M. Mascaro 1* 11'. The true distance is 1° 1', which results from connecting, by the triangles of Velasquez, Huehuetoca with the rock de los Baños, and this rock, by my astronomical observations, and by several azimuths, with the volcano of Popocatepetl and the pyramid of Cholula. There exist maps, according to which the waters of the lakes adjoining the city of Mexico do not run north-east towards the gulf of Mexico, as is really the case, but north-west to the South Sea. This error is to be found along with many others in the map of North America, published at London by M. Bower, geographer to the king. On my arrival at Mexico in the spring of the year 1800, I conceived the project of drawing up a map of the valley of Tenochtitlan. I proposed to fix, by astronomical observations, the limits of this valley, which has the form of a lengthened oval. I took besides a great number of angles of positions, from the tower of the cathedral of Mexico, the summit of the porphryry hills of Chapoltepec, and the Peñol de los Baños, the Wenta de Chalco, the summit of the mountain of Chicle, Huehuetoca, and Tissayuca. The position of the two volcanos of la Puebla and

the peak of Axusco was determined by a particular hypsometrical method, that is to say, by angles of altitude and azimuths. Having very little time to bestow on this work, I could not flatter myself with bringing together in my map the great number of small Indian villages, with which the banks of the lakes are covered. My principal aim was carefully to ascertain the form of the valley, and to draw up the physical map of a country in which I had measured a great number of elevations by means of the barometer. Circumstances of a favourable nature have enabled me to publish a topographical map from accurate materials. A respectable character, who, by a union rarely to be found in any country, possesses with a large fortune a strong love for the sciences, M. Don Jose Maria Fagoaga, wished to leave me a precious memorial of his country, in giving me at my departure from Mexico the sketch of a plan of the valley. On his invitation, one of my friends, Don Luis Martin, as good a mineralogist as he is an able engineer, drew up a map from the geodesical operations carried on at different times between the city of Mexico and the village of Huehuetoca, on account of the canals of Tezcuco, San Christobal, and Zumpango. M. Martin joined to these materials a part of the surveys communicated to him by me, in subjecting the delineation to the astronomical observations made by me at the extremities of the valley. The

numerous excursions which he had undertaken from a zeal for geology, enabled him to express, with a great deal of truth, the form and the relative height of the mountains which separate the plain of Mexico from those of Tula, Puebla, and Cuernavaca.

This map, which I owe to the obliging friendship of M. de Fagoaga, is not, however, the one which is inserted in this work. On examining and comparing it carefully, both with the triangulation of M. Velasquez, the detail of which I possess in an original manuscript, and with the table of astronomical positions ascertained by my observations, I perceived that the eastern bank of the lake of Tezcuco, and the whole northern part of the valley, required considerable alterations. M. Martin himself discovered the inaccuracy of his first sketch, and I engaged M. Oltmanns to reconstruct under his eye the map of the valley from the materials which I had collected. Every point was separately discussed; and when several surveys disagreed with one another, the mean term was adopted.

The following is the chain of the triangles measured by M. Velasquez, in 1773, from the rock of the baths (Peñol de los Baños), near the city of Mexico to the mountain of Sincoque, to the north of Huehuetoca. The angles were measured with an excellent English theodolite of ten inches di. ameter, provided with two glasses of twenty-eight inches in length.

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