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guished geometrician, who calculated all the astronomical observations made by me since nay departure from Paris in 1798, to my return to Bordeaux in 1804. The longitude of Mexico (6h 45' £8") 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 Pluviose, year XIII, in which the calculations of the moon had not been corrected by the tables of M. Burg. 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 6h 45' 30".

Thirty-two distances from the moon to the sun, calculated by M. Oltmanns, from the newest lunar tables, give for longitude 6b 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 6h48' 24", the longitude of Mexico would be 6h 4.5' 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 6h 45' 331", the other 6h 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 resujts, 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' (/, 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 177-2, Velasquez gave to Mexico 2?8° Q1 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 17' 8, 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 Temascaltepee, and at Guanaxuato." M. Galeano, one of ^he 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' (f, 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 orthograpbica 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, 1 778,

lation. With the operations ofGama, Velasquez, and Galeano, I was totally unacquainted when I began my operations at Mexico. Moreover the detail of the observations of Don Dionisio Galeano was only communicated to me by M. Espinosa during the winter of 1804, after my return to Europe. These observations give a longitude apparently much more accurate than the one published by M. Antillon. '* I was ignorant (the learned director of the Deposito Hydrografico of Madrid writes me) during" your residence in Spain in 1799, of the observations of our common friend M. de Galeano. They consist of two emersions of satellites and the end of a lunar eclipse: they give me 101° 2/ S4"= 6h 4.5' 30"." But M. Oltmanns found on taking the medium of the three observations, and comparing the eclipse of the moon at five different places in Europe, 6h 45' Ay". The difference between my observations and those of the Spanish astronomer, a supposed difference of nearly half a degree, is consequently reduced to less than an arc of two minutes. It is satisfactory to find so great a harmony among observers, who, unknown to one another, employed such different methods. In the very minute maps of Thomas Jeffereys, published in 179+, Mexico is situated in 20° 2' of latitude, and 102° 52' 47' of longitude; while M. Arrowsmith, in his beautiful map of the West Indies in four sheets, makes the

longitude of Mexico 102° 8' O', and the latitude 19° 57', false 32 minutes.

Several Mexican geometricians of the seventeenth century guessed pretty nearly the true longitude of the capital. Father Diego Rodriguez, of the order of N. Seriora de la Merced, professor of mathematics at the imperial university of Mexico, and the astronomer Gabriel Lopez de Bonilla, adopted 7h 25' for the difference of meridians between Uranienburg and the capital, from whence there results the longitude of 101° 37' 45//=6h 46' 29*. But Don Carlos de Seguenza*, the celebrated successor of Rodriguez in the academical chair, was ignorant in 1681 of the observations on which Bonilla founded this result. He published a small treatise on the longitude of the city of Mexicof. He cites in it an observation of a lunar eclipse on the 20th December, 1619, by the engineer Henry Martinez, at Huehuetoca, to the north-west of Mexico. This is the same Dutch engineer who undertook the bold enterprize of the canal called le Desague

* Libra astronomica y filosofica escrita en 1681, por Don Carlos de Seguenza y Gongora, Catedratico de Matematicas de la Universidad de Mexico, y impresso en la misma Ciudad en 169O, §. 386.

f See the work above cited, §. 382, 385. I owe my acquaintance with this very rare book of Seguenza to M. Oteiza, who was kind enough to recalculate several old observations of the Mexican astronomers.

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