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Table showing discrepancies between stadia distances affected by "f+c" correction and computed distances.

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The mean discrepancy for the whole distance is 175 feet, or 1 in 2,133. This, it will be observed, approximates that obtained after application of the stadia-factor correction.

The results from the application of the f+c correction serve to indicate that the rod was graduated approximately correctly, as intended, and the stadia wires were fixed so as to read distances on the rod approximately in the proportion of 1 to 100. As the stadia-factor correction was systematic, the results obtained for distances along the boundary line by a direct adjustment of the original stadia distances to fit the triangulation exactly correspond to those which would have been obtained if the stadia-factor correction had been first applied and the remaining discrepancy afterwards adjusted to the triangulation.

The only check obtained with reference to vertical distances or measurements of height is that furnished by the portion of the line between the Northern Pacific and Great Northern railroads. Along the former road is a line of precise levels run by the United States Geological Survey from a mean sea-level connection at Tacoma, Washington. The stadia line was connected with a bench mark of the precise levels, and this bench mark is the datum upon which the elevation of the stadia line is based. The profile of the Great Northern Railway adjusted to the United States Geological Survey precise levels furnished an elevation at Leonia to which the stadia line was joined. The resulting discrepancy was 73 feet, which is greater than might reasonably be expected, but it is possible that some of the error may be in the railroad profile.

The details relating to the profile of the boundary line between these two railroads are as follows: Sum of horizontal components, 201,188 feet; sum of vertical components, 42,700 feet; discrepancy in closure, 73 feet; discrepancy referred to horizontal components equals 1 in 2,756; discrepancy referred to vertical components equals 1 in 585.

Extensive and careful experiments with the stadia were made by the

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The monument on the right was cut in ten sections for transportation on pack animals.

Boundary Commission engaged in the survey and re-marking of the boundary between the United States and Mexico west of the Rio Grande; and as the conclusions reached so nearly correspond to those arrived at in connection with the Idaho-Montana line, the following quotations are made:

The method by stadia is cheap and rapid; requires less cutting than that by chain; is carried on under the eye of an instrument man, presumably of a high order of intelligence; gives heights and angles, and enables objects to be located from the line which is being measured; is ordinarily more accurate than the chain, and can be successfully used where the chain can not be, experience on this survey having shown that the stadia lines over mountains, hills, and canyons were more accurate than those on level plains and wide valleys.

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In view of this proof of the inevitable change in the value of the interval, the common practice of painting a rod to correspond with the stadia interval of a certain hour and day and then continuing the use of such rod unchecked and unchanged during the widely different seasons of this country oftentimes-in fact, for many years at a time—is seen to be inviting the large systematic error which almost without exception characterizes such work. If this evidence be taken to prove the fact that even so-called fixed stadia wires actually change their relative positions, or, what amounts to the same thing, appear to change on account of the influence of differential refraction at different seasons, then the present method of painting the rod to correspond with the determined interval is objectionable because of the cost of regraduating and repainting the rod to correspond to such change in interval. A method entirely free from this objection of cost, and one which the writer has found to stand every test during several years of field use, is that which uses rods divided into true units of feet, yards, or meters and employs an interval factor in the computation of distances. With this system a change in the interval simply means the loss of an hour's time in the preparation of a new table for reduced or true distances corresponding to any rod reading.

MONUMENTS.

The monuments used along the meridional portion of the line are of two kinds-stone and iron. The stone monuments are of granite, 6 feet in length and 10 inches square, undressed except for spaces sufficient to permit cutting the words "Idaho" and "Montana," on opposite sides. These monuments are placed in the more prominent localities, and are monolithic in all cases where it was possible to transport them in one mass to the proper position; otherwise they were cut into ten sections, so that they could be carried on pack mules, and were bolted and cemented together when established in place. The monuments at the international boundary and at the summit of the Bitterroot Mountains, these being the terminal points of the meridional portion of the line, are of stone made from sections, as described, and monoliths are placed near the points at which the boundary line crosses the Northern Pacific and Great Northern railways. (See Pl. VII.) The iron monuments are hollow posts of wrought iron, 6 feet in length and about 4 inches in outer diameter, covered with a coat of asphaltum tar. At the bottom they are flared

to a width of 12 inches, to insure more secure planting. These posts are set to a depth of 3 feet below the surface of the ground, 3 feet remaining above ground, and a conical mound of earth being raised around them to a height of 2 feet. On the tops of the posts are riveted bronze caps, on which is cut appropriate lettering, and the number of the monument and the distance (in miles) from the international boundary are stamped in large figures. (See Pl. VIII.) In addition to the four stone monuments referred to, eighty-nine iron monuments were placed. The sites for the monuments were chosen with reference to the topographic features of the country, instead of being placed at even miles, as has usually been the custom on boundary lines, but there are few intervals greater than a mile between the monuments, the average interval being about three-fourths of a mile. They were placed generally on summits, or near streams, roads, or trails, and so as to be intervisible when possible. Between the monuments the line is thoroughly cut out, and adjacent trees are blazed, so that it can be readily recognized in any locality.

The stone monuments were quarried at Medical Lake, Washington, and cost $14.50 apiece delivered at the railroad station nearest the point at which they were established. The iron posts were made in St. Louis, and cost $2.08 delivered to the United States quartermaster at St. Louis.

Previous to the work herein referred to no attempt had ever been made to locate and mark the Idaho-Montana boundary line, but the engineers of the Northern Pacific and Great Northern railways had estimated the points at which it crossed their tracks and established marks according to this estimation. The accepted crossing on the Northern Pacific was found to be about one-fourth of a mile west of the true line and that of the Great Northern about 1 mile east of the true line along the railway track, but only about a half mile east thereof in direct longitude. Kootenai County, Idaho, spent a considerable sum of money in grading a road up the mountain from Leonia toward Sylvanite, which, when the boundary line was located soon after, was found to be in Flathead County, Montana.

Each monument is witnessed by pits and mounds wherever practicable, the pits being dug across the line distant 4 feet north and south of the post, and the mounds being 4 feet east and west thereof. The dimensions of the pits are 3 by 2 by 14 feet, and the mounds were constructed from the excavated material. The monuments are further witnessed, usually by four blazed bearing trees, one in each quadrant. The two trees in Idaho at post 48, for instance, were deeply engraved "Idaho P. 48 B. T.," and the two trees in Montana were marked in a corresponding manner. (See Pl. IX.) Under each monument was placed about a quart of charcoal. In the notes the distance and bearing to the witness trees were marked and the trees described,

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