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These same insulated summits, situated in the midst of a vast plain, offer a still surer method of determining in a short space of time, to within à few seconds, the longitude of a great number of neighbouring places. Luminous signals, produced by the deflagration of a small quantity of gunpowder, may be observed at great distances by persons provided with proper means for finding and preserving the true time. Cassini de Thury and Lacaille were the first who successfully employed this method of luminous signals. M. de Zach has recently proved by his operations in Thuringia, that in favourable circumstances it will furnish in a few minutes positions comparable for accuracy to the results of a great number of observations of satellites or solar eclipses. In the kingdom of New Spain the signals might be given at Iztaccihuatl, or Siera Nevada of Mexico; on the rock called The Monk, an insulated summit of the volcano of Toluca, which I reached 29th September, 1803; on la Malriche near Tlascalar ; on the Coffre de Perotte; and on other mountains whose summits are accessible, and which are all elevated more than from three to four thousand metres * above the level of the sea.

entre Mexico et Vera Cruz, par MM. Oltmanns et Humboldt. (Zach, Monathliche Correspondenz, Novemb. 1806, p. 445, 454, 458.)

* From 9840 to 13,120 feet English. Trans.

The Spanish government having with extraordinary liberality made the most important sacrifices for the perfection of nautical astronomy, and for accurate surveys of the coast, we may expect that its next concern will be the geography of its vast American dominions, for which the royal marine would furnish both instruments, and astronomers skilled in observations. The school for mines of Mexico, in which mathematics are studied in a solid manner, spreads over the surface of this vast empire a great number of young men animated with the noblest zeal, and capable of using the in. struments with which they might be entrusted. It is by analogous means that the English East India Company have surveyed a territory whose surface equals that of England and France united *. We live no longer in times when governments dread to expose to foreign nations their territorial wealth in the Indies. The present king of Spain gave orders to publish, at the expense of the state, the survey of the coasts and ports; without fearing that the most minute plans of the Havannah, of Vera Cruz, and the mouth of the Rio Plata, should fall into the hands of the foreign nations whom events have made enemies of Spain. One of the finest maps, drawn up by the Deposito Hydrografico of Madrid, contains the most valuable details regarding the interior of Paraguay; details founded on

* Rennel's Hindostan, vol. i. p. 17.

the operations of the officers of the royal marine employed to settle the boundaries between the Portuguese and Spaniards. With the exception of the maps of Egypt and of some parts of the East Indies, the most accurate work which exists, of any European continental possession out of Europe, is the map of the kingdom of Quito, drawn up by Maldonado. Every thing proves, that for these fifteen years past the Spanish government, far from dreading the progress of geography, has published all the interesting materials which it possessed on the colonies in the two Indies.

Having indicated the means, apparently the most proper, for speedily completing the maps of the kingdom of New Spain, I shall give a succinct analysis of the materials employed by me in the geographical work which I offer to the public.

The general map of the kingdom of New Spain is drawn up, as all the other maps drawn up by me in the course of my expedition are, according to the projection of Mercator, with increasing la. titudes. This projection has the advantage of shewing at once the true distance of one place from another ; it is at the same time the most agreeable to the navigators who visit the colonies, and who, in fixing the position of their vessel by two mountains seen without difficulty, would wish their survey to correspond with the map. If I had had to choose among the stereographic projections, I should have given the preference to Murdoch's, which deserves to be generally followed. The scale of my map is 32 millimetres * for every degree of the equator. The scale of increasing latitudes is not founded on the tables of Don Jorge Juan, but on those which M. de Mendoza calcu. lated for the spheroid.

To give a more suitable form to the map of Mexico, the scale was only extended from the 15° to the 41° of north latitude, and from the 96° to the 117° of longitude. These limits did not admit of giving in the same map the intendancy of Merida or the peninsula of Yucatan, which belongs to the kingdom of New Spain. To in. clude in the map the most eastern point, which is Cape Catoche, or rather the island Cozumel, seven additional degrees of longitude are requisite, which would have forced me to comprize in the same map a portion of the kingdom of Guatimala, for which I have no data, all Louisiana, all western Florida, a part of the Tennessée, and of the Ohio.

It is in vain to seek, in this general map of New Spain, the Spanish establishments on the northwest coast of America, establishments which are insulated, and may be considered as colonies dependant on the metropolis of Mexico. To exhibit in the same map the missions of New California would have required an additional eight degrees of

* 1.25987 In. English. Trans.

VOL. I.

longitude ; for the most northern point of the kingdom is the presidio of San Francisco, situated, according to Vancouver, in 37° 48'30" of north latitude, and 124° 27' 45" of west longitude. Hence a map of New Spain, to deserve the name of a general map, should embrace the immense countries included within the 8yo and 125° of longitude, and within the 150 and 38° of latitude. To avoid the inconvenience of representing on a large scale countries which, in a political view, possess by no means the same interest, I wished to compress my labour within narrower bounds. I drew up, in a much smaller form, a second map, which not only exhibits in a coup d'ail all the territories which depend on the viceroyalty of Mexico, but which may also be consulted by those who wish to examine the different communications projected between the Atlantic ocean and the South sea. The motives which have occasioned this latter map to be extended to the port of Phi. ladelphia, and even to the mouth of the Rio San Juan at Choco, will be explained in the sequel of this work.

Although, according to the principles often laid down by me, I persist in preferring the new measures to the old, I have not however added to my maps the scale of centesimal degrees. The Bureau of Longitudes having constantly followed, both in the Knowledge of Times(Connoissance des Temps) and in the new Astronomical Tables lately pub.

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