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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 11 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 verti cal 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.

ADDENDUM.

As the primary triangulation ties in the tertiary triangulation of the river between Little Rapids and Point Iroquois, tying directly to it at each end and at several of the intermediate stations, and as many of these tertiary stations were used by the topographers in the course of their season's work, we have, in accordance with your suggestion, procured from Assistant Engineer Joseph Ripley, who executed this work, his computations of the triangle sides-given in Table No. 4-and have computed the geographical positions of the stations, and they will be found in Table No. 5.

The tertiary system must have been executed with great care, for Mr. Ripley's length of the primary line, Iroquois-South Gros Cap, on which it closes, agrees with the primary value within 0.47 of a meter. His azimuth of this line also agrees with the primary azimuth within 16".

These discrepancies have been distributed throughout the system, making it conform to the primary values, and it is the adjusted values that are given in the table. Very respectfully, your obedient servant,

First Lieut. CHARLES S. RICHÉ,

Corps of Engineers, U. S. Army.

E. E. HASKELL,
Assistant Engineer.

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TABLE NO. 2.-Geographical positions.—Primary stations.—The Clarke Spheroid of 1866.

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rilateral Michipicoten, Mamainse, Black Beaver Hill, Pantagreul will be completely read, and by reading the line East Sturgeon Mountain-Iroquois the angles of the quadrilateral Mamainse, Iroquois, Kings Mountain-East Sturgeon Mountain will be completely read. Possibly Whitefish can be seen from East Sturgeon Mountain. The triangle Mamainse, Black Beaver Hill-East Sturgeon remains. It is probable that the line East Sturgeon Mountain-Pantagruel can be read, though this was not determined, in which case the whole system would be made quadrilateral. These additional lines to be read are long and the resulting quadrilaterals not of good form. It is doubtful if any material advantage v'ould be gained in trying to make the system quadrilateral.

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The following quadrilateral and triangles form a branch system from the main chain to cover the lower portion of the St. Marys River:

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From the line Gaffney-Raber a reduction to the secondary system of triangles yet to be planned in the lower portion of the river and among the islands in Potogannissing Bay can be easily effected.

Secondary system in Whitefish and adjacent bays.

Form.

Vertices.

Quadrilateral
Do..

Do..
Do..

Triangle.
Hexagon

Triangle.

Whitefish, Parisian Island, Kings Mountain, Mamainse.

Whitefish, Parisian Island, Maple Island (12), South North Sandy (14).
South North Sandy (14), Maple Island (12), Rudder Head (9), Crawford (1).
South North Sandy (14), Rudder Head (9), West Batchewana (11), Crawford
(1).

Crawford (1), West Batchewana (11), Sand Point (3).

West Batchewana (11), Sand Point (3), Harmonie River (4), Perry (5), Island
(6), South Shore (8), East Batchewana (center of hexagon) (10).
West Batchewana (11), Rudder Head (9), South Shore (8).

By using the triangle South North Sandy (14), Maple Island (12), Crawford (1) for the third quadrilateral above, the cutting on the line Maple Island (12)-Rudder Head (9), which is considerable, is avoided. An 8-foot station would then be sufficient for Rudder Head (9).

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