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in time for the absolute longitude. How many considerable cities are there in Spain, and in the most eastern and northern parts of Europe, which are still far from this accuracy of geographical position !

The very trifling expense of the execution of these three journies, above all of the first, would give a new face to the geography of New Spain. The positions of Acapulco, of Vera Cruz and Mexico, have been repeatedly verified by the operations of Galiano, of Espinosa and Cevallos, of Gama and Ferrer, and by my own. The officers of the royal marines stationed at the port of San Blas, could in a single excursion fix the important positions of the mines of Bolaños and of the city of Guadalaxara. The astronomical expedition

circles, there are not three places of the earth the latitude of which is known with the certainty of a second. In 1770, the lati. tude of Dresden was nearly three minutes false : that of the observatory of Berlin was uncertain till 1806, for nearly 25 seconds. In 1790 before the observations of Messrs. Barry and Henry, the position of the observatory of Manheim was false by a minute and 21 seconds of latitude, and yet father Christian Mayer had observed with a quadrant of Bird of 8 feet radius. (Ephemerides de Berlin, 1784, p. 158, and 1795, p. 96.) Before the observations of Le Monnier, we were ignorant of the true latitude of Paris for nearly 15 seconds. The astronomical journal of M. de Zach offers examples which serve to prove that an exercised observer, provided with a good sextant and an exact artificial horizon, may find the true latitude of a place to within seven or eight seconds.

which the government has entrusted to MM. de Cevallos and Herera, for surveying the coast of the gulph of Mexico, will determine the mouth of the Rio Huasacualco to the south-east of Vera Cruz. It would be easy for these able astronomers, who are provided with superb English instruments, to ascend this river, to which the project of a canal of communication between the At, lantic and South seas has given such celebrity; they would determine the breadth of this Mexican isthmus, in fixing the position of the port of Tehuantepec and of the bar of S. Francisco at the mouth of the Rio Chimalapa.

The means which I propose in this memoir could be easily carried into execution at a small expense. There does not exist on the globe a countryaffording greater advantages for trigonometrical operations. The great valley of Mexico, the vast plains of Zelaya and Salamanca, level as the surface of the waters which appear to have covered their soil for a long succession of ages; these plains, elevated 1700 metres* above the level of the ocean, and bounded by mountains visible at great distances, invite the astronomer to the measurement of several degrees of latitude towards the northern limits of the torrid zone. In the intendancy of Durango, in a part of that of S. Luis Potosi, triangles of an extraordinary extent might be traced over a surface covered with

* About 5570 feet. Trans.



grasses, and bare of wood; but to undertake the trigonometrical survey of the kingdom of New Spain, to wish to extend delicate operations over a surface five times larger than France, is to prevent the government from ever possessing a general map of its rich dominions, and to engage the court of Spain in a brilliant undertaking, but an undertaking of too great extent to be ever carried into complete execution. The scrupulous accuracy with which the officers of the Spanish marine examined the smallest sinuosities of the coast of South America has been censured*. This work was undoubt. edly both laborious and expensive; it appears to me, however, that it is unreasonable to blame those who presented to his catholic majesty so admirable a project of hydrographical survey. A marine chart can never be too minute. The safety of navigation, the facility of recognizing landing places, the necessary means of defence against an enemy who threatens disembarkation, all depend on the most intimate acquaintance with the coast, . and with the bottom of the sea. In the interior of a country it is sometimes of small consequence that the position of a city be exactly laid down to a minute of latitude; but on the coast, it is of the


* One of the most learned geographers of the age, Major Rennel, observes that the English possess very exact charts of the anchorages on the coast of Bengal, while there does not exist any thing like a tolerable chart of the English channel (Description of Hindostan, vol. 1. Preface.)

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 observation; 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 a:tronomically 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 eclipses, it would be of no les 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 ana gles of altitudes calculated by M. Oltmanns, have given the port of Vera Cruz Oll' 32" to the west of Mexico, while from purely astronomical observations there results a difference of meri. dians of on l' 47". In modifying the former result by several secondary operations at the pyramid of Cholula, we find even 0' 11' 41, yo ; so that in this particular case, on a distance of three degrees, the method of azimuths was only 7" false in timet.

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

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