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"The base line of the triangulation of the twenty English miles to a point on the Colorado from its junction with the Gila," was measured by Lieut. N. Michler, corps topographical engineers, with two iron rods, "A" and "B," corresponding with rod "B," in the possession of Mr. R. D. Cutts, U. S. Coast Survey, the length of which is 4.0002457 metres at 32° Fahrenheit. The length of one metre, at 32° Fahrenheit, is equal to 39.3685034 inches at 62° Fahrenheit of the standard made by Troughton.

Rate of expansion of rods for 1° Fahrenheit, .000006963535.

The total length of the base, as computed by John O'Donoghue, computer, is 5,867 feet 5.9 inches.

Table showing the length of rods, at different temperatures, of the American and English Imperial

Standard.

Table showing the quantity to be taken from the length of the measuring-rod at the different ele

The point “F'” was Lieut. Michler's observatory, and distant from the junction of the Colorado and Gila, in a straight line, 104024.34 feet; the azimuth of this line, at the point "F"," is 36° 14′ 10′′ N. E., and its length is 1575.66 feet short of twenty miles. (See results of calculations of geodetic latitudes and longitudes of points of triangulation, &c.)

The latitude of point "F"," as obtained from triangulation, is 32° 29′ 42′′.64 N., and longitude 114° 48′ 09′′.51 west of Greenwich. The latitude used, however, is that obtained from observations with zenith telescope, and is 32° 29′ 41′′.65 N.; but the longitude taken is that obtained by triangulation.

The initial point, in the middle of the Colorado, was determined by prolonging the line from the junction, passing through "F"" 1575.66 feet, measured with the two iron rods, “A” and

Vol. I-22

"B," thus laying off a radius of twenty miles. At the extremity of this line, a perpendicular was erected, or, in other words, a tangent was drawn to the circumference of a circle with that radius and the junction as a centre, and, by means of the following table, the circle was described.

A table to lay out on the ground a portion of the circumference of a circle whose radius is twenty miles.

First take a point twenty miles from the mouth of the Gila, and having the direction of the line joining this point and the mouth of the Gila, protract a straight line, making an angle of 88° 34′ 02′′.8522 with this line; or prolong a line that will make an angle of 1° 25′ 57′′.1478 with the tangent to the circle at the point; then run 5,280 feet on this line, and this will give you a second point on the circle; then place your instrument alternately at the second and first points, and lay off the following angles with this chord of a mile long, and their intersections will be so many points in the circumference of the circle.

Having come to a point more than half way, reverse the readings, and they will give you other points commencing near the second point. The greatest distance of the periphery from this chord is about thirty-three feet.

III.-Tabulation of results for the latitude of astronomical station at the Initial Point on the Rio Colorado, twenty English miles below its junction with the Gila, derived from observations made with zenith telescope of Wurdemann, on sixteen pairs of stars. Observer, Lieut. N. Michler, Corps Topographical Engineers, U. S. Army. Computer, John O'Donoghue.

REMARKS.-The zenith telescope suffered very material injury in its transportation, in consequence of the counterpoise having been separated from the instrument by the breaking of a screw, and knocked about among the other parts. The tangent screws were mostly bent, the micrometer slightly injured, and the spider lines and levels all broken. Being in a country where the levels could not be replaced, the not very sensitive ones of a large bronze theodolite had to be substituted for those broken, and the other injuries repaired by such means as were at hand.

Computations from observations on Polaris, western elongation, for the determination of the value of one division of the micrometer attached to zenith telescope, by Wurdemann, for the U. S. Boundary Commission. March 23, 1855.

Computations for the value of one division of the micrometer, &c.-Continued.

Computations from observations on d Ursa Minoris, eastern elongation, for the value of one division of the micrometer. March 23, 1855.

Combination of results for the determination of one division of the micrometer, derived from observations on d Ursa Minoris near eastern elongation.

Value of one division of the micrometer from observations on Polaris (western elongation) and d Ursa Minoris (eastern elongation) is 0.63899.

Observer, Lieut. N. Michler, U. S. Topographical Engineers. Computer, Hugh Campbell,