beds, but with cross and letters U. S. cut on each. Bearings and distances to them are as follows: (1) N. 3° E. 60.72 feet; (2) S. 75° 30′ E. 32.4 feet; (3) S. 7° E. 60.9 feet; (4) S. 84 W. 44.7 feet. Distance between crosses on reference stones (1 to 2) 74.2 feet; (2 to 3) 57.6 feet; (3 to 4) 76.3 feet; (4 to 1) 80.5 feet.

Whitefish. This station is located on a small sand hill about 560 feet southwest of the center post of the Whitefish Point light tower. The tripod of the station is 40 feet high and set 5 feet in the sand. The geodetic point is a g-inch hole between the letters U. S. and the top of a stone 6 by 6 by 24 inches, set 6 feet below surface with an oil barrel around it. Post with nail in center set over it for a surface mark. Reference stones are two cut stones 2 feet long with tops dressed to 4 inches and letters U. S. cut on the side facing station. These are set in the ground at the foot of the sand hill and with the bearings and distances as follows: (1) N. 12° E. 120 feet; (2) S. 75 W. 120 feet. Center post of steel light tower N. 56 E. 560.8 feet. Astronomical post S. 34 E. 825.5 feet. Center of astronomical post to center post of steel light tower 1,007.36 feet.

Parisian.-Is on the highest point of the ridge that runs along the west side of Parisian Island. Top of tripod is 36 feet above ground. The geodetic point is a -inch hole between the letters U. S. and the top of a cut stone 6 by 6 by 24 inches and set 2 feet below the surface. Two reference stones (common field stones), with cross and letters U. S. cut on them, are set as follows: (1) Stone bears N. 18 30 E. 24 feet; (2) N. 72° W. 50 feet from the geodetic point.

North Gros Cap.-Is on the rock point that projects into Whitefish Bay and forms the southern limit of Goulais Bay. A4-foot station was put up here, setting on the solid rock. Geodetic point is a -inch hole drilled in the rock with a triangle (6-inch sides) cut around it. Reference marks are two crosses cut in the rock with letters U. S. near them. (1) Cut in sloping face of rock, bears nearly east and is 43.22 feet from geodetic point; (2) bears S. 60 E. 70.75 feet from geodetic point, and is cut in the vertical face of rock near a 6-inch oak tree.

Maple Island.-Is on the west shore of the island of the same name, about 40 feet from the water's edge. The station is about 35 feet high. The geodetic point is a well-shaped field stone about 6 by 5 by 24 inches, with a hole drilled in the top between the letters U. S. The stone is set with the top 6 inches below surface. But one reference mark was made; a cross and letters U. S. were cut on a large bowlder N. 6 W. and 104.2 feet from the geodetic point. Corbay Point light bears N. 9° 33′ W. from the station.

Maple Point.-Is on a projecting point on the south shore of Goulais Bay. The station consists of a 6-foot tripod set 2 feet in the ground. The geodetic point is the original Lake Survey mark, a lead center between the letters U. S. on the top of a cut stone 6 by 6 inches by (length unknown), set with top about 1 foot below surface and about 45 feet back from shore. Reference marks are a cross cut on a large bowlder in the water about 15 feet from shore, bearing N. 47 W. 61.9 feet from the geodetic point, and an 8-inch birch tree bearing S. 37° 30′ W. 36.55 feet.

Goulais River.-Is on the sandy shore a few hundred feet north of the middle mouth of the Goulais River and about 60 feet from shore. Station is a wooden post 12 inches by 8 feet, set with top about 42 inches above ground. This is the same point occupied by the old Lake Survey post. A long-necked bottle is set below this post, and is directly under the spot occupied by the center of the old post.

North Bay. Is about 2 miles north of the Goulais River station and about 30 feet from shore. The station consists of a 10-inch spruce tree cut off about 4 feet above ground and covered with a plank cap. A platform was built around the stump for observer to stand on. The geodetic point is 4-inch iron rod 6 inches long driven into the stump. Reference points are crosses on two bowlders near water's edge. (1) South 36.7 feet; (2) southwest 34.8 feet.

Mission.-Is about 1 mile north of the Indian settlement on Goulais Bay and about 20 feet from the shore. The station is a poplar stump treated as at North Bay. Reference points are crosses on two bowlders (rather small). (1) North 14.36 feet; (2) southwest 39.2 feet.

Buchanan.-Is on the edge of a bluff at the shore on Buchanan Point, about onehalf mile west of the Indian settlement in Goulais Bay. The station is a 6-foot tripod set 2 feet in the ground. The geodetic point is a -inch hole between the letters U. S. in top of a cut stone 6 by 6 by 24 inches set 18 inches under surface. Reference points are a 10-inch pine tree northeast 58.19 feet, and an 8-inch oak tree northwest 40.4 feet.

Goulais Point.-Is near the end of the point of land that separates Goulais Bay from Whitefish Bay, about 30 feet from shore. The station is a 4-foot tripod set 8 inches in the ground. The geodetic point is a 2-inch hole between the letters U. S. cut in the top of a stone 6 by 6 by 24 inches, and set 6 inches below the surface with a flat stone above it.

Sand Point.-Is on the long sandy point that projects out from north shore of Batchewana Bay toward the east end of Batchewana Island. The station is a 6-foot tripod

set about 23 feet in the sand. The geodetic point is a cross cut on the top of a dressed stone 4 by 4 by 24 inches, and set with top 6 inches above surface.

Crawford.-Is on the edge of a bluff near the shore, about one-fourth of a mile west of Crawford's landing, and about 14 miles northeast of Corbay Point light. The station is a 4-foot tripod. The geodetic point is a cross on a dressed stone 4 by 4 by 24 inches, set 6 inches above surface. Letters U. S. cut on side of stone.

South Parisian.-Is an 8-foot wooden post set 4 feet in the ground as near as it was possible to locate, where the old Lake Survey station was, on the south end of Parisian Island. The remains of the old station were found, but I could find nothing of the old geodetic point.

Salt Point.-Is on the extremity of a point of land on the south shore of Whitefish Bay, about 9 miles west of Iroquois Island and about 30 feet from shore; 20-foot tripod put up here; rest of station unfinished. The geodetic point is a g-inch hole between the letters U. S. in the top of a cut stone 6 by 6 by 24 inches, set with top 3 inches above surface of the ground.

Mamainse. Is the same point that the old lake survey used, and is on the highest peak in the vicinity, about 8 miles north of Batchewana Bay, and 8 miles east of Mamainse Point. The station is set on solid rock and is 28 feet high. The geodetic point is -inch hole between the letters U. S., cut in the flat top of a field stone, about 2 feet long, and set down to the solid rock, with top 6 inches below surface. Reference points are: (1) Center of top of old astronomical post southeast 68.44 feet; (2) cross and U. S. on rock just to left of line to astronomical post, 22.68 feet distant; (3) cross and U. S. on rock nearly south 43.84 feet.

South Gros Cap.-Mentioned in my report for the fiscal year ending June 30, 1893, as "Gros Cap.' The station has been changed from a 4-foot one to an 18-foot one. For descriptions of the rest of the stations built during 1893, see my annual report for that year.

A set of silver prints,* from negatives taken during the progress of the work, is submitted with this report.

Very respectfully, your obedient servant,

First Lieut. CHARLES S. RICHÉ,

Corps of Engineers, U. S. Army.

GLEN E. BALCH,
Assistant Engineer.

E. REPORT OF MR. E. E. HASKELL, ASSISTANT ENGINEER.

UNITED STATES ENGINEER OFFICE, Sault Ste. Marie, Mich., June 16, 1894. SIR: I have the honor to make the following report upon the field work of the angle reading and the reduction of the observations of the primary triangulation of the resurvey of St. Marys River, Michigan.

NARRATIVE.

The field work of the angle reading began July 5 and lasted until November 29, 1893. During this time the party occupied 11 stations, made 20 measures each of 91 primary angles and 8 measures each of 67 secondary angles, in addition to setting and frequently testing all of the targets used.

The interval from July 5 to 11 was employed in preparing and setting targets and in collecting the necessary outfit for the party. July 12, the instrument-Troughton & Simms theodolite No. 3-was taken to west base and mounted and the angle reading proper begun.

Owing to the close proximity of the first four stations of the system to Sault Ste. Marie, the party did not go into camp until August 17, when they moved to ▲ azimuth. From August 17 to November 20, or the date on which the occupancy of A South Gros Cap was finished, the party lived in camp. On leaving South Gros Cap for Iroquois it was thought best, owing to the lateness of the season and the fact that there was a heavy fall of snow on the ground, to abandon camp and the party live with the light-keeper at Point Iroquois. Accordingly, at the request of Assistant Engineer David Molitor, my camp outfit and cook were turned over to him, he being engaged in topographic work in the vicinity, walking to and fro from his own camp, which was some 4 miles farther to the eastward.

The party finished the angle reading at A Iroquois on November 28, and on the next day moved everything to the office in Sault Ste. Marie, Mich., thus closing field work for the season.

With the exception of a short interval, when the services of a second observer's attendant was required, owing to heliotrope work and to the necessity of packing our instruments for some distance, the party consisted of the observer, one recorder, one observer's attendant, and, while living in camp, a cook-heliotropers when required.

Mr. J. A. Holwill was recorder from July 8 to September 18; Mr. Jacob Bainbridge, observer's attendant from July 5 to September 18, and recorder from September 19 to November 29; Mr. John M. Hogarth, second observer's attendant from August 30 to September 18, and observer's attendant from September 19 to October 23; Mr. Oliver McNeely, observer's attendant from November 11 to November 29, and Mr. James Doran, cook for all of the season spent in camp. To each I desire to express my thanks for efficient service rendered.

Beginning with the base stations of the "Soo" base the primary stations occupied were: West base, east base, Soo, Ste. Marie, azimuth, Korah, Rankin Mountain, Mirron, Larke, South Gros Cap, and Iroquois. For the relative position of these stations and an idea of the primary system of the river, see sketch, p. 4350, of the Report of the Chief of Engineers, U. S. Army, for 1893.

The secondary angles read from the primary stations were to stations of the river triangulation of the improvement work, to light-houses, to church spires, and to all prominent objects of a permanent character located in close proximity to the river. The weather throughout the season was fairly good. From what I gather from the reports of the U. S. Weather Observer at Sault Ste. Marie, Mich., the conditions did not differ much from those of an average season, and up to the time when lines became so long as to require the use of heliotropes-September 1-very good progress was made. From this time forward, however, the advancement was rather slow, a good reason for which will be found by examining the weather summary for the months of September, October, and November, an extract from which is here given.

During September there were 3 cloudless, 10 partly cloudy, and 17 cloudy days; during October 1 cloudless, 7 partly cloudy, and 23 cloudy days; and during November 1 cloudless, 6 partly cloudy, and 23 cloudy days; showing that during the 3 months there were 5 days when it was certain that a heliotrope could be used, 23 days when there was a possibility that it might be used, and 63 days when it was certain that it could not be used.

METHODS.

In regard to the methods adopted in the field work it may be stated that, while we have followed in a large measure those of previous work of this character, certain changes have been introduced with a view to lessening field work and also reducing the labor of the final computations.

In this direction the number of measures made of each primary angle or the number of positions of the circle on which the angles were read, has been reduced from what is common practice in this class of work, thus lessening the time required for the occupancy of stations.

It was thought that this change could be introduced in safety, in view of the fact that the instrument to be used (Troughton & Simms theodolite No. 3) is one of a high grade, with all of the refinements required for a first-class instrument, and it is believed that the results which will be exhibited later will prove that this change was warranted.

In mounting the instrument at stations and in setting of targets and heliotropes no eccentric positions, with one exception, have been allowed, thus avoiding the necessity of "reductions to center" and leaving the work so that at the end of every day's observations, the observer could tell exactly the value of his results. The exception noted was a target on the observatory which had to be eccentrically mounted to be seen from "Soo," for one over the center fell behind a chimney of a power house from which quantities of smoke were continually being emitted.

The usual precautions of having the instrument firmly mounted on a good support, of protecting it from the direct rays of the sun and from the wind, of seeing that all of its parts worked freely and that it was kept in good adjustment, were carefully attended to.

Measuring primary angles.-The programme followed throughout the work was to read each angle independently. The instrument having been carefully adjusted and leveled, the telescope was set on the left-hand target of any angle and the micrometers read. It was then set on the right-hand target and the micrometers again read, the difference between these readings being called a positive single result. The whole operation was then repeated in reverse order, beginning with the second target, giving a negative single result. The mean of these two results was called a combined result and is free from "station twist.

The instrument was then double reversed; that is, had its telescope turned 1802 n altitude and 180 in azimuth, and a second combined result obtained. The mean

of the two combined results was then taken for a single result, which was free from instrumental errors arising from imperfect adjustment for collimation, from inequality in the heights of the wyes and from inequality of the diameters of the pivots. The position of the circle on which these readings had been made, or the resulting angle, was designated as Position I. The circle was next shifted by means of the trivet 360° through an angle equal to where m is the number of equidistant microscopes 2 mn and n the number of single results sought. In the present work m— 3 and n=5, making the shift for the circle equal 120. A reading of the angle as outlined above, on this part of the circle, was designated Position II, and gave a second single result. The mean of the five single results obtained from the five positions of the circle, in addition to the errors eliminated noticed above, was free from periodic errors of gradnation, or, more properly speaking, those periodic errors that can be eliminated by the method of observing.

It will thus be seen that each angle was measured twenty times, giving ten pairs of combined results or five single results.

At each station, all the angles around the horizon, between stations, taken two and two completely closing the horizon, were read. When time and weather permitted, the sum angles of triangles forming quadrilaterals were also read, but were not considered as being absolutely necessary, but where read have been used in the adjust

ment.

The limits set upon the observations were that the sum of the angles closing the horizon should equal 360° within a 2", and that the sum of the three measured angles of a triangle should equal 180 within a 3".

Measuring secondary angles.-In reading angles to locate secondary points, the method followed has been to connect them with one or more of the primary stations by starting in with the first object on the left and reading around to each seeondary and the selected primary objects in the order of their azimuth, finally closing on the point of beginning. Then double reverse the instrument and read to all objects in reverse order. The mean of the forward and backward measures of any one angle of the first position of the circle was called a single result of Position I, and was free from "station twist," and from errors of the instrument arising from imperfect adjustment for collimation, from inequality in the heights of the wyes, and from inequality in the diameters of the pivots.

The circle was next shifted by means of the trivet through 15°, n, being made equal to four in the formula laid down under the primary work, and the readings again made in the same order, giving Position II.

The mean of the four single results obtained from the four positions of the circle, in addition to what has already been mentioned as eliminated, was free from periodic errors of graduation, or more properly those that can be eliminated by the method of observing.

So far as was possible each secondary point was read to from at least three primary stations, thereby securing a check on the location of each.

Measuring zenith distances.-At each station the zenith distance to all other stations of the primary system visible was read, four sets being taken to each station. With one exception no more than two sets were ever read to the same point on any one day. The time for them was limited to the interval between 8 a. m. and 4 p. m.

Form of target used.-The form of target used was one that originated on the work of the Mississippi River Commission in 1881 with the party of Assistant Engineer John Eisemann, of which the writer was a member while doing the triangulation of the river between Keokuk, Iowa, and Grafton, Ill. It is a phaseless one, and for this work has been made in sizes of 6, 8, 12, and 24 inches in diameter by 6 feet in length. To describe it briefly: A 6-inch target is made by taking one circular disk of No. 10 and three circular disks of No. 24 sheet iron that are 7 inches in diameter; through the center of the disk of No. 10 punch a 4-inch hole, for centering target; from this hole as a center strike a circle with 3-inch radius, and then at the 90° points of this circle punch 4-inch holes; using this disk as a pattern, punch holes in the other disks to correspond, omitting the center hole, which is not needed. Take the No. 10 disk for the bottom plate of the target, and in the holes at the 90points solder the ends of the rods of 4-inch round iron that are 6 feet in length, taking care to get them at right angles to the plate. Next slip these rods through the respective holes of one of the other disks, forcing it down to a point 2 feet from the bottom, where it is secured by solder. In like manner secure the two remaining disks at the 4-foot point and the top of the target, respectively, when the frame is complete.

These frames are then divided into three zones by stretching black and white cloth between the diagonals, the bottom and top zones being white with their planes at right angles to each other, and the middle zone black with its plane in either direction.

By this method of construction the target frames are very true and substantial,

but sizes larger than 12 inches in diameter need this modification: The disks made from the No. 24 iron should be replaced by a cross made from No. 10 band iron that is about 1 inches wide, for the reason that the large disks cast too large a shadow on the zones of cloth. Three-eighths inch round iron should be used for targets larger than 12 inches in diameter.

The target when set is secured in place at the bottom by a nail through the center hole, and otherwise by guy wires holding it plumb.

By using care they can, as a rule, be so placed as to need no change of position to be visible from all stations from which it is to be seen.

The first heliotropes used were camp-made affairs and answered every purpose, excepting the need of a telescope for picking up the direction of the distant station. About October 1 four Würdemann heliotropes arrived from the engineer depot at Willets Point, and these were used for the remainder of the season. They answered every purpose, but are more complicated than need be, requiring the services of a more or less skilled operator for their manipulation.

Instrument. The instrument used, as stated before, was Troughton & Simms theodolite No. 3, 14-inch circle. It was purchased in 1876 by the U. S. Lake Survey, and its constants were carefully determined by Mr. R. S. Woodward and will be found in the Report of the U. S. Lake Survey for 1879, Appendix No. 7 of Appendix M M. Mr. Woodward made a careful determination of the value of the graduative space 359°, 55' to 360°, and this space has been taken as the standard for all observations for

run.

On arriving at a new station the first leisure, after the instrument had been mounted, was utilized in making readings for run, measuring the standard space 10 times with the micrometer screw of each microscope.

Previous to taking the field I made a careful determination, by means of a leveltrier, of the value of one division of the striding and vertical circle level tubes, and, as will be seen by a comparison with the values given by Mr. Woodward, the vertical circle tube is undoubtedly the same one that was on the instrument when he examined it. There is some doubt about the other. His value for one division of the striding level for a space of about twelve divisions on either side of a central position and at 60° F. was 0.898. My determination was for a larger space each side of a central position, namely, about twenty divisions, and was made at a temperature of 63° F. and equals 0.763.

By Mr. Woodward's determination, the value of one division of the vertical circle level tube for a space of twenty divisions either side of a central position and at a temperature of 64° F. is 1.026. My determination was for a space of twenty-five divisions either side of a central position, made at a temperature of 73, and equals 1".110.

RESULTS.

Of the 11 stations occupied, all fell within the limits in summing the angles closing the horizon on first trial. The largest discrepancy was 1.82, the smallest 0.05, and the mean 1".04. At 5 stations the sum was in excess of 360 and at 6 stations less than 360°.

In the closing of triangles all fell within the limits on first trial. The greatest discrepancy was 2.98, the smallest 0.21, and the mean 1.43. Of the 18 triangles used in the reduced observations 7 closed large and 11 small.

Beginning with the base, the system of triangles, as far as the angles were meas ured, form a series of quadrilaterals. So in making the reduction of the observations it was thought best to adjust the system by quadrilaterals and thereby save a large amount of the labor that would be required to make a rigid adjustment of the system as a whole. I am of the opinion that a rigid adjustment could add but little, if anything, to the results except, perhaps, ornamental and deceptive precision, for the value of the work must lie in the observations themselves.

In reducing the work a local or station adjustment has first been made and these values of the angles used in making the quadrilateral adjustment.

The results of the computations of the triangulation will be found in Table No. 1, and the geographical positions of the primary stations in Table No. 2. The geographical positions of the secondary points observed from the primary stations will be found in Table No. 3.

All the computations throughout the work have been made independently by Mr. Thomas Russell and myself, and the results compared and made to check, leaving the probability of an error very small indeed.

COST OF THE ANGLE READING.

The total expense of the angle party, including all salaries for the field season, was $2,833.63, of which amount $26.47 is chargeable to expressage on and repairs of instruments, $349.22 cost of camp outfit and the necessary tools, etc., leaving $2,457.94 as the field expenses proper, or a cost of $223.45 per station.