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 certam 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 3609 through an angle equal to 2 mn' where m is the number of equidistant microscopes and n the number of single results sought. In the present work m3 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 graduation, 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 se ondary 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 999 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 14 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, $319.22 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, |