*The distances from Janos to Franklin were furnished by Mr. Chandler, assistant United States boundary commission.

A.-DETERMINATION OF BOUNDARY LINE FROM THE INITIAL POINT ON THE PACIFIC OCEAN TO JUNCTION OF THE GILA AND COLORADO.

1. Longitude of Camp Riley, near Initial Point, on the Pacific.

2. Longitude of junction of Gila and Colorado.

3. Latitude of Camp Riley,

4. Latitude of junction of Gila and Colorado.

5. Triangulation, transferring the determination at Camp Riley to Initial Point, on the Pacific.

6. Azimuth of straight line from Initial Point, on Pacific, to junction of Gila and Colorado.

B.-DETERMINATION OF BOUNDARY LINE FROM RIO COLORADO TO INTERSECTION OF 111TH MERIDIAN OF LONGITUDE WEST OF GREENWICH AND PARALLEL 31° 20′ N.

1. Azimuth line-astronomical positions.

2. Triangulation for determining longitude of Initial Point on the Colorado.

3. Tabulated results of latitude.

4. Distances between monuments.

C.-DETERMINATIONS OF THE BOUNDARY LINE ALONG PARALLELS 31° 47′ AND 31° 20′ N.

E.—TABLE OF LATITUDES AND LONGITUDES OF POINTS ON AND NEAR THE BOUNDARY LINE BETWEEN THE UNITED STATES AND MEXICO.

Vol. I-18

PREFACE.

I. CLASSES OF OBSERVATIONS.

The observations for the determination of the latitude and longitude were of two classes-the first being those which were made at primary stations with the largest instruments that could be conveniently transported by land; the second, those made at places of less importance, determined by reflecting instruments, and by the transmission of chronometers from the nearest primary stations, or by flashes of gunpowder, observed simultaneously. Eighteen stations of the first class were established across the continent at the following places, named in their order, from west to east:

1. Camp Riley, near initial point, on the Pacific coast; 2. Junction of the Gila and Colorado; 3. On the Colorado, where the line leaves that river; 4. Quitobaquita; 5. Los Nogales, near 111th meridian of longitude; 6. San Bernardino, near parallel 31° 20′; 7. San Luis springs, near parallel 31° 20'; 8. Agua del Perro; 9. Espia; 10. Carrizalillo, near parallel 31° 47'; 11. Frontera; 12. San Elceario; 13. Initial point of boundary on parallel 31° 47′; 14. Cañon where the San Antonio road leaves the Rio Bravo; 15. Presidio del Norte; 16. Eagle Pass, (Fort Duncan ;) 17. Ringgold Barracks; 18. Mouth of Rio Bravo.

I do not enumerate the very many points of lesser importance determined by the sextant and chronometer, as no special notice is required of the means used in their determination. It may be as well to state, however, that in all cases where observations were made for latitude with reflecting instruments, stars were taken, both north and south, and at altitudes as nearly equal as could be obtained; and when local time was obtained by these instruments, stars were taken both east and west, of nearly equal altitudes, and as near the prime vertical as they could be found. In this way we attempted to avoid the errors arising from refraction and from the eccentricity of the instrument.

In some cases, where I had direct comparisons with results obtained by the large instrument, I ascertained that the latitude of a place determined by the Gambey sextant in the proper hands, in a single night, might be relied upon to within 3" or 5"; and if the observation was repeated for two nights, the result might be relied upon to be within 2" of the true position.

II. LONGITUDE.

The longitudes of 1, 2, 4, 5, 10, 11, 12, 15, 16, 17, 18, were obtained by observations on the transit of the moon and moon culminating stars, with a telescope of forty-six inches' focal length, by Troughton & Simms, of London, and with a smaller one of thirty-six inches' focal length. Occultations were observed, whenever practicable; but, owing to the impossibility of obtaining corresponding observations, they proved of little value; indeed, but few were observable. Occultations are no doubt of the greatest value where corresponding observations at some established point are observed; but for the general purposes of a survey, conducted in distant regions, they are not a sure reliance. They occur too seldom; and to see the instant of immersion and emersion of a star requires great steadiness in the telescope, which in the field can be rarely obtained, owing to the difficulty of protecting the telescope from the wind, and of getting a firm support.