and 50 feet west of the center of the Chicago, Burlington and Northern Railway line to Fulton, on a 10-inch elm tree, being a spike in its root.

Elevation, 185.0472 meters. 607.116 feet.

P. B. M. 337 is in Savanna, Ill., about 65 feet below T. B. M. 354, on the line of the Chicago, Burlington and Northern Railway to Fulton, 600 feet below the crossing with the Chicago, Milwaukee and St. Paul Railway to Sabula, on land of A. Hershey, 12 feet back from top of bank of slough and 15 feet below Jones & Jordan's boat house, being a copper bolt in tile set 3 feet under ground.

Elevation, 184.6559 meters. 605.832 feet.

P. B. M. 338 is top of cap on iron pipe set over P. B. M. 337, standing about a foot above the surface of the ground.

Elevation, 185.8727 meters. 609.824 feet.

P. B. M. 64 is 24 miles east of the Chicago, Milwaukee and St. Paul Railway Junction House. Same as P. B. M. 64, given in the report of the Mississippi River Commission for 1884, page 137.

Elevation, 187.0818 meters. 613.791 feet.

APPENDIX 4 C.

Report of ASSISTANT ENGINEER JAS. A. PAIGE ON PRECISE LEVELS FROM DULUTH, MINNESOTA, TO ST. PAUL, MINNESOTA, WITH TABULATED RESULTS AND DESCRIPTIONS OF BENCHMARKS.

OFFICE MISSISSIPPI RIVER COMMISSION.

St. Louis, February 29, 1892.

SIR: I have the honor to report as follows on the precise leveling operations in my charge between Duluth and St. Paul, Minn.

In compliance with your instructions, I left St. Louis April 26, 1891, accompanied by Recorder L. D. Cabanne and Rodmen S. W. Shinkle and C. S. Farrar, arriving in Duluth the evening of the 27th. Two umbrella men and a teamster with team were employed at Duluth.

The organization of the party was: 1 observer, 1 recorder, 2 rodmen, 2 umbrella men, and a teamster with team, and a light wagon to carry the party to and from work.

Your instructions were to carry a line of precise levels from the U. S. Engineers' water gauge at Duluth by the most practicable route to St. Paul, Minn., and there connect with benchmarks established by Assistant O. W. Ferguson in starting his line down the Mississippi River.

The regular work of the season commenced April 30, and was completed to St. Paul September 25, and the levels there connected with Mr. Ferguson's permanent bench marks Nos. 68, 69, and 71. The party was disbanded on September 26, and on the 28th I reported to you at St. Louis for further duty in reducing the season's notes.

A description of various bench marks in Duluth was obtained of Capt. Fiske, Corps of Engineers, U. S. A., and they were connected with. These bench marks were used in establishing the Duluth water gauge and in maintaining it.

The instruments used were Kern level No. 2, with level vial No. 9, and Kern leveling rods Nos. 14 and 17. These instruments were used on the Mississippi River work, and are substantially the same as described in the Report of the Chief of Engineers for 1877, page 1190, and in subsequent reports.

The route of the levels was from the U.S. Engineers' water gauge at Duluth, Minn., to the St. Paul and Duluth Railway tracks; thence along the railway to Carlton, thence southward about 5 miles on the wagon road to the point where it joins the old military road between St. Paul and Superior; thence along the military road to Barnum, where the route again strikes the St. Paul and Duluth Railway; thence along the railway track to St. Paul.

Permanent bench marks were established from 4 to 6 miles apart, and elevations were taken at grade at railroad crossings and in front of various depots on the line. These bench marks consist of a slab of vitrified clay 18 inches square and 4 inches thick, into which is leaded vertically in the center of the upper face a copper bolt three-eighths of an inch thick and buried about 3.5 feet in the ground. Over this slab and surmounting the copper bolt is set a 4-inch wrought-iron pipe about 4 feet long, the lower end of which fits into a proper groove made in the slab. The top of the pipe is provided with a cap, which is fastened in place with brass bolts. The upper end of this pipe projects about 6 inches above the surface of the ground. (See illustrations of this bench mark, facing page 3485 of Report of Mississippi River Commission for 1891.) The top of the copper bolt in the slab beneath the ground is re

garded as the permanent bench mark, but the elevation of the top of the cap on the iron pipe is also determined. The party was subsisted at hotels, boarding houses, and such places as were available. The country passed through is but sparsely settled, there being no habitations north of Pine City outside the village along the line. This is an unsuitable method of subsisting a precise leveling party. On account of the irregular working hours, it is not possible to obtain suitable meals for the party, such as in camp, where one has entire control of his time. The hours of labor and rest are different to that of other occupations, and in order to arrange these details to suit the weather conditions a camp and cook are necessary. In the 156 miles of main line there were 62 miles over which there was no public road, and for this distance the team could not be used for transporting the party to and from work. Considerable use was made of the railway trains for about 30 miles in the vicinity of Hinckley, as the time-table suited the time of going to and from work.

The weather during the season was favorable for the work. There were but two days during which no work was done on account of rain, and eight days when work was interrupted by showers, but there were many days when the wind blew too hard for observing.

The methods used in observing during the first part of the season were about the same as those in use heretofore on this class of work. While reading the rod the vial bubble was kept at zero. No correction enters the reduction, therefore, for inclination of line of sight.

When at Pine City your instructions were received, to the effect that the order of the sights at instrument stations be alternated so that the systematic error which frequently appears in precise levels would be avoided. The method was, at Station A, for example, to read the backsight first and then the foresight; at Station B, to read the foresight first and then the backsight; at Station C, read the backsight first and then the foresight, and so on. This method was followed from T. B. M. 121 to the end of the work at St. Paul.

At T. B. M. 121 another change was intrduced in the methods. The footplates were discarded and the top of the railroad rail was used as turning points. A mark was made on top of the rail, the rod placed thereon, and the details of the rodsman's operations between a fore and back sight to the same rod station were precisely the same as when footplates were used. On curves the inner rail was used and turning points always selected at least 6 feet from a joint. The St. Paul and Duluth Railway main line is ballasted with coarse sand and gravel, well tied and spiked, and laid with 60 and 63 pound steel.

Reduction of the notes.-All the compututions have been duplicated and the results compared with the field reduction. The sum of the "means of thread readings," which is the most important part of the computations, have been compared with the duplicate summation of the "thread readings."

This mean of thread readings or "mean-wire" column in the notebooks can be very well dispensed with. It is a useless and roundabout method of checking the reductions. The thread readings of the fore and back sights between the benches should be summed and one-third of their difference (in a three-wire instrument) will give the difference in elevation. This method avoids the remainders which frequently occur in deriving the mean wire, and which must be taken care of. The column of "thread readings" can be summed as often as necessary to avoid the possibility of an error, and the resulting labor is less than by the old method.

In all computations the shortest way, if it does not involve approximations or remainders, is the best way.

In platting the relative positions of the south and the north lines, where there were two or more lines in one direction, the mean of the lines in that direction has been platted.

In the tabulation of results column 2 gives the distances of the successive bench marks from the Duluth gange.

Column 5 gives the residuals, found by subtracting each result from the mean. Column 6 gives the probable error of the mean result in column 4.

Column 7 gives the probable error of the elevation of the permanent bench marks referred to the starting point.

The remaining columns are explained by their headings.

The

Instrumental constants.-The value of one division of the level vial and the inequality of the telescope collars were determined twice during the season. lengths of rods were compared with the metric scale in the Mississippi River Commission's office at St. Louis at the close of the season. This scale is the "U. S. Lake Survey, No. 1."

The error in the length of the rods thus found, if applied to the whole difference in elevation between Duluth and St. Paul, would amount to 0.3 millimeter. As the corrections due to rod length from bench to bench is much less than that due to fluctuations of length on account of temperature changes while at work, no rod correction has been applied. This temperature range was about from 30° to 95° F.

*The values of A do not enter the computations. All bench marks were such that the rods were placed directly upon them.

RESULTS.

Miles.

The distance from the Duluth gauge to permanent bench mark No. 69, at St:
Paul, is 251.23 kilometers..

156.2

Length of side line (3.60 kilometers).

2.2

Total (254.83 kilometers)..

158.4

The field season occupied 129 days, excluding Sundays, and the progress for completed work was 1.23 miles per day for the season.

From Hinckley southward a record was kept of the times between starting at one bench and closing on the next bench ahead.

Two hundred and eighty-seven and seven-tenths kilometers were run in 232.9 hours. This is an actual speed while at work of 1,231 meters per hour.

The probable error in the elevation of permanent bench mark No. "A," at St. Paul, is 15.7 millimeters. This gives a probable error in the work of 0.99 millimeters per kilometer. An inspection of the plat of the relative positions of the two lines shows that from the Duluth gange to T. B. M. 51, at Blackhoof River, there is a total divergence of 93.1 millimeters. For this portion of the line (53.2 kilometers long) the average departure of the lines is 1.8 millimeters per kilometer, the elevations by the south line being lower than by the north line. The ground leveled over was a newly constructed railroad bed and a light sandy wagon road. From T. B. M. 51 to Barnum the wagon road was mostly hard clay and gravel, and from Barnum to St. Paul the surface was a hard, well-settled railroad bed of coarse sand and gravel. From Duluth to T. B. M. 51 it was necessary to level 44 per cent of the distance more than twice. Now, if we reject all lines except the first two (south and north) we will get a result for T. B. M. 51 which differs but 9 millimeters from the adopted result by taking all the lines run. This is pretty good evidence of itself that a systematic error appears in the work up to this point. If this error had been eliminated by some change in the methods or by choosing another route, the probable error of 0.99 millimeter per kilometer would have been somewhat reduced. However, the result thus obtained for T. B. M. 51 would probably not have been any nearer the truth than the one we now have.

From T. B. M. 51 southward for 100 miles the general tendency of the lines is toward each other, the total discrepancy at T. B. M. 171 being 13.4 millimeters. From this point the lines again diverge, ending at St. Paul on P. B. M. 69 with a difference of 42.4 millimeters.

As to the method of alternating the order of the fore and back sights at successive instrument stations, it is not possible to discuss the effect of it on this piece of work, as it is combined with that due to a change in turning points from footplate to rail. They may be counterbalancing in effect, or they may be accumulative. From this season's results we can not determine their relative size or their signs. Alternating the order of the sights will tend to lessen the aggregate amount of settling

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.

are not in the main line of levels. In these reductions the value of 1 meter is 3.28086928 feet.]

Results of precise leveling, Duluth, Minn., to St. Paul, Minn., May 1 to September 25, 1891-Continued.

[Bench marks marked thus are not in the main line of levels. In these reductions the value of 1 meter is 3.28086928 feet.]