The latitude and longitude and altitude of the main astronomical stations will be given in volume II of the quarto reports, now passing through the press.

It has not been found necessary to occupy further main astronomical stations for the purpose of checking positions determined by other means in the prosecution of work of 1877; but upon the completion of the observatory at Ogden and those contemplated-one at Denver, Col., another on the western slope of the Sierras, a number of points to the north and south of the present line of the Pacific Railroad, i. e., in Oregon, Idaho, Montana, Texas, New Mexico, and Arizona-may be occupied.

GEODETIC AND TOPOGRAPHICAL.

The sketches showing the triangulation in the Colorado, Utah, and California sections are added to as computations progress, and from time to time, as it covers a number of the regular atlas sheets, will be published, as well as the geographical positions, obtained by triangulation, of prominent points. The number of triangulation stations of the highest grade increases each year, and especially in areas where more numerous observations become necessary in order to gather data for delineation on maps of the larger scales. As usual, the areas occupied in the expedi tions of 1876 and 1877 follow strictly those authorized by the Chief of Engineers and the honorable the Secretary of War, in pursuance of projects submitted by the officer in charge, and are all laid within that part of the territory of the United States lying west of the one-hundredth meridian, as shown upon the progress map, and over which it is contemplated that topographical surveys in detail commensurate with the character and development of the various sections shall be prosecuted to completion.

The topographical assistants are now required to add to their notes careful data showing the natural resources of the region traversed, in order to collect information as to the general character and value of the areas still belonging to the Government, and it appears that the relative areas of arable, timber, grazing, mineral, and arid lands may be described and delineated.

The noticeable topographical results inaugurated during the year are about Lake Tahoe, in the Sierra Nevada, the topography of which, from data now gathered, warrant a projection on a scale of 1 inch to 1 mile, which has been completed at the hands of a special party engaged upon the high peaks and along the divides of the water courses of this peculiarly interesting lake region.

The plane-table sheets covering the entire Comstock mining district are drawn upon a scale of 1 inch to 500 feet, and will, after reduction, serve as a complete and connected contour map of this region so abundant in the precious metals.

As usual, when practicable, connections have been made with main and minor points of the land survey and monuments built in all cases of due importance. The areas covered by the expedition of 1876 are noted upon the progress map as parts of atlas sheets 47, 48, 56, 61, 62, 70, 77, and 78. Portions of the following basins are embraced, the "Great Interior Basin," and those of the Arkansas and Rio Grande Rivers, as well as the headwaters of a number of streams lining the western slopes of the Sierra Nevada between the latitudinal limits noted on the progress sheet. The gauge of the success of the expedition is better shown by the number and character of the observations made at the main geo

graphical stations than by the area covered, although the latter is not inconsiderable for so short a season.

A measured and developed base was laid out in the Carson Valley, and connected with the astronomical station established in 1873 at Virginia City, Nev. A description of the apparatus and method employed, by Dr. Kampf, being somewhat typical of that adopted for use upon the survey, is herewith given.

DESCRIPTION OF MEASURING-ROD.

The rod was decided upon by the officer in charge in the winter of 1875-76, upon consultation with Dr. Kampf, and constructed by Mr. Edward Kahler. It was made of wood, 20 feet in length, strengthened by a vertical cross-piece. Each end of the rod is provided with a scale 8 inches long, subdivided to 6 of an inch, so that by a magnifier it can be read to thousandths. At a point near the center an arc of a circle of 30° extension is fastened. An arm attached to the center of the circle, and movable by a micrometer screw, carries a level, so that after determining the zero-point on the face of the circle the inclination of the rod can be easily read to 5 minutes. The rod is placed for measurement on two iron-plates, weighing about 30 pounds each, and provided with three strong iron pins 2 inches long. In the center of the plate, on an elevated silver plane, is drawn a cross-line, which acts in the nature of the zero-point of the line.

METHOD OF COMPARISON.

The rod was compared daily, both before and after its use, with two steel standard rods, constructed by the United States Coast Survey, and of a normal length of 5 feet, at the temperature of 610.6 F. In place of the rod constructed by Mr. Kahler, a similar one, not quite 20 feet long, politely furnished by Mr. Adolf Sutro, of Sutro, Nev., consisting of very well seasoned and varnished wood, was used. A very simple apparatus was used, constructed for comparison, the standard steel rods being supported on two wooden blocks, and therefore elevated by the thickness of this support from the plane of measurement, two knifeblades were driven in a wooden board, 22 by 12 feet by 4 inches, being as much above the surface of the board as the polished plane at the end of the normal rod. The center of the sharp blade and the plane of the normal rod were brought into the same vertical plane, and by an assistant is kept in this position until the second rod is brought in contact with the first. Thus continuing, the fourth rod was found to reach over the knife-blade about 1 inches. A square block of wood was placed at the end, in contact with the normal rod, and by means of a small measure, 3 inches long, and divided to hundredths, the distance from the square block of wood to the blade of the knife was read, the temperature being always carefully noted and the measurement repeated.

The readings were made by Dr. Kampf and his assistant. After determining the distance between two points on the edges of the knifeblades, the measuring-rod was placed on top of the blades with the utmost care, and the scale on both ends read. In this manner the amount of over-lapping of the rod was obtained.

Observation made October 11, 1876, between knife-blades, 20 feet 1.537 inches, 550.8 Fahrenheit; reading of scales on rod, east end, 0.420 inch; west end, 0.140 inch; therefore the length of the rod was determined to be 20 feet + 0.997 inch, at 550.8 Fahrenheit.

DESCRIPTION OF METHOD OF MEASUREMENT.

Dr. Kampf was aided in the measurement by Mr. Louis Seckels and two laborers. The work was divided among the party as follows: The line was laid out in advance for one day's work, marked by iron pins 2 feet in length and about 180 feet apart. The base was measured on an old road, laid out about ten years ago, and running in a straight line for a distance of 33 miles. A fine line was tied to one pin and fastened to the next one. Two plates were laid down within the distance of 20 feet 2 inches, approximately, so that they were parallel with the line and tangent to it. One laborer takes the measuring-rod, bringing it near the plates, and the assistant being at the rear end, the laborer on the other, both grasp the rod at the same time and put it on top of the plates 18 of an inch distant from the cross on the ridge of the plates. Mr. Seckels reads the rear end of the scales at the same time that Dr. Kampf reads at the front end by means of a common magnifying-glass. The readings are then at once recorded. After that the level was read by Dr. Kampf and simultaneously with Mr. Seckels, who is now at the front end. He reads the rear end of the scales, and the readings are recorded by both. Then the readings are called out and in case of disagreement repeated. In the meanwhile the other laborer puts an auxiliary rod of 20 feet 2 inches in the position, so that the rear end may be in line with the mark on the plate driving the third plate in the ground. When the readings are finished the new plate is found in its proper position, the laborer brings the rods in front of both plates, and the operation is repeated. The other laborer takes meanwhile the first plate put down and brings it to the front, as No. 4. The thermometer is read from time to time on the shady and sunny side of the rod, to obtain its temperature. After a reasonable practice the rate of measurement may be assumed as 20 feet for each interval of one and one-half minutes.

CO-EFFICIENT OF EXPANSION.

The steel rods of the United States Coast Survey are of normal length at the temperature of 610.6 F. By means of the co-efficient of expansion for one degree, as given in Lee's tables, the distance of 201 feet is reduced by applying the temperature of the time of comparison. and thereby the distance between both knife blades is obtained. To this is added the readings of the scales of the rod, and the length of the rod for the observed temperature is found. The mean of the observa-, tions at low and high temperatures are taken, and from the difference of both lengths the factor of expansion is derived, as shown in the next table. The rod having been heavily saturated in a rain and snow storm on October 11, the observations taken afterward are not used for determination of expansion. The length of the rod was found from the comparisons to be 20ft 0in.9408 for 610.6 F.