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utmost importance to know the position of a cape, with all the accuracy which astronomical means admit of. In a hydrographical chart all the points should be equally well determined; for every one of them may serve as a point of departure or ob. servation; and there is none which is not connected with others: while, on the contrary, the maps which represent the interior of a country possess great merit, when they offer a certain number of places whose position has been astronomically fixed.

If it is desirable that the Spanish possessions in .

the interior of America should not be for some time surveyed with the same minute accuracy which has been displayed on the coast; if in the actual state of things it would be more useful merely to execute a provisory undertaking, founded on the use of sextants and chronometers, on lunar distances, on observations of satellites, and eclipscs, it would be of no less importance to unite to these purely astronomical means such other means as are furnished by the nature of the country and the great elevation of its insulated summits. When we know exactly the absolute height of these summits, whether by means of the barometer, or by geometrical operations, angles of altitudes and azimuths taken with the rising or setting sun may serve to connect these mountains with points whose latitude and longitude have been sufficiently verified. This method

furnishes perpendicular bases; and in estimating how much we may be deceived in the measurement of each base, it is easy to conclude by false suppositions what influence this error may have on the astronomical position either of the mountain itself, or of the other points which depend on it. An exact knowledge of the inferior limit of perpetual snow will often afford the same advantages as the measurement of an insulated summit. This is the method employed by me to verify the difference of longitude between the capital of Mexico and the port of Vera Cruz. Two great volcanos, that of la Puebla, called Popocatepetl, and the peak of Orizava, both visible from the platform of the ancient pyramid of Cholula, serve to connect two places distant from one another more than 16,000 * toises. The union of two geometrical measurements of the mountains, of the azimuths and angles of altitudes calculated by M. Oltmanns, have given the port of Vera Cruz 0 1 1/ 32” to the west of Mexico, while from purely astronomical observations there results a difference of meidians of 0 1 1' 47". In modifying the former

result by several secondary operations at the py-,

ramid of Cholula, we find even 0° 1 1/41, 37; so that in this particular case, on a distance of three degrees, the method of azimuths was only 7" false in timef.

* About 102,400 feet English, Trans. t Mémoire astronomique sur la différence des meridiens

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 a 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 of 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 Hum-
boldt. (Zach, Monathliche Correspondenz, Novemb, 1806,

p. 445, 454, 458.) -
* From 9840 to 13,120 feet English. Trans.

s & -* - —

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 instruments 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 governmentsdread 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 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 latitudes. 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,

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

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