Annual Reports of the War Department

of the leveling instrument at the various stations. In any class of levels where but a single line is run it would be well to follow this method, as the single result will then be (partly) cleared of the error due to the leveling instrument settling. There are cases also when two lines are run, and in opposite directions, where it would be well to adopt this method, such, for example, as where the routes of the direct and reverse lines between two bench marks are not the same; also, when from rains or other causes the surface conditions are dissimilar for the two lines.

In the practice of precise levels the two cases above mentioned are of rare occurrence; in fact, they should be avoided altogether.

Let x be the aggregate sinking (or rising) of the leveling instruments between any two consecutive bench marks. Then when, for any reason, we think that x will change in size or sign between the direct and reverse leveling, it would be well to alternate the order of the sights at the successive stations. However, in precise leveling the routes and other conditions should be such that x will not change between bench marks. The method will tend to reduce the range in the results, and hence the probable error, and in precise levelling this is about all that can be said for it. As to using the top of the rail for rod support that, of course, must depend on the physical condition of the track and frequency of trains. When the change was first made in turning points at Pine City, stakes were driven at the side of the roadbed to avoid trains when they approached.

From some experiments made by taking the elevation of the rail before and after trains passed, there were some differences found. These differences were irregular in sign and nearly all within the limits of error in observing. After this no attention was paid to trains in this respect.

There may be individual movements of the rail, but on a stone or gravel ballasted track, well tied and spiked and laid with steel, such as was found between Pine City and St. Paul, I think the aggregate rod movement on the rail is less than for foot plates, stakes, or any kind of rod support that is practicable. With the completion of this line there will be two connections of the Mississippi River system of precise levels with the elevations of lakes Michigan and Superior, the first connection being that made between Savanna, Ill., and Chicago in 1882. (See Report of the Mississippi River Commission for 1883, p. 53, and Report for 1884, p. 116.) When the mean elevation of Lake Superior at the Duluth gauge is derived from the readings there, extending over a period of years, the two results can then be compared. Respectfully submitted.

Capt. CARL F. PALFREY,

JAMES A. PAIGE,
U. S. Assistant Engineer.

Secretary Mississippi River Commission.

Results of precise leveling, Duluth, Minn., to St. Paul, Minn., May 1 to September 25,

1891.

By Assistant Engineer JAMES A. PAIGE.