PREFACE. Vn 



Academy. It is very exact but too long for usual practice. I 

 afterwards adopted Dr. Mackay's methods, both for calcu- 

 lating the true and apparent altitudes of the objects, and for 

 reducing the apparent to the true distance, which are ren- 

 dered very concise by means of his table of natural versed 

 sines.* 



It is hoped that the following astronomical computations 

 will be found to correct many errors in the geography of the 

 country west of the Mississippi, as laid down even on some 

 of the latest and most approved maps. On Melish's latest 

 map of the United States and contiguous Spanish and British 

 Provinces, (entered according to the Act of Congress, June 

 16th, 1820,) we find the spot where Engineer Cantonment 

 was constructed, (three miles S. E. of the point known by the 

 name of the Council Bluff,) laid down in 41° 42' of N . latitude, 

 and 96° 50' of longitude W. of the meridian of Greenwich. 

 By fourteen meridian observations of the sun and stars I ob- 

 tained for the latitude of that place 41° 25' 03.9" N. and for- 

 ty-two distances of the moon from the sun and stars, together 

 with three eclipses of Jupiter's Satellites, gave me for the lon- 

 gitude 95° 43' 53" W. of Greenwich. The position of the 

 mouth of the river Platte is equally erroneous in longitude, 

 and 6' of latitude too far north, according to the same. We 

 find on the same map, that the highest peak between the head 

 waters of the Platte and Arkansa, is laid down in latitude 

 40° 42' N. and longitude 107° 20' W. whereas its position de- 

 termined from the observations of Major Long and Lieut. 

 Swift made near it, is 38° 53' N. lat. and 105° 52' W. long. 

 But by a map of Mexico, Louisiana, Mississippi Territory, 

 &c. by John H. Robinson, M. D. &c. &c. (published in Phi- 

 ladelphia in 1819,) who traversed the country with the expe- 

 dition under the gallant and enterprising Pike in 1806-7, the 

 position given this remarkable point is 41° 30' N. lat. and 

 111° 20' W. long, from Greenwich, which is too far north by 

 2° 37' of latitude, and too far west by 5° 28' of longitude ! ! 

 This will show what errors travellers are liable to commit in 

 laying down plans of countries they have explored unless 

 they have had recourse to astronomical observations for the 

 purpose of determining the geographical positions of remark- 

 able points. 



Considerable pains have been taken in overlooking the cal- 



♦The theoi'y and practice of finding the longitude at sea or on land, &c. by 

 Dr. Andrew Mackay, in 2 vols. London, 1810. 



