The list of latitude pairs has been prepared with a view to observing latitude from time to time, for the purpose of detecting the change of latitude, if there is any. Recent determinations of latitude at various points over the surface of the earth by skilled observers and the elaborate investigations of the older observations of latitude and star declinations leave little doubt that there is a change of latitude with a period of about one year, and the amplitude of which is about 0.6. Two places on the earth's surface, 180° apart in longitude, show these small changes of latitude exactly opposite in phase. At Greenwich, for instance, when the latitude is at its greatest, at Honolulu it is at its least value. This would indicate that the pole of the earth describes a circle around its mean position in the period of the latitude change.

If there is any such motion of the pole there would be a corresponding change in the azimuth of a line on the earth's surface. The maximum change of azimuth will occur between the time the pole is farthest east and farthest west of its mean position, which corresponds to the time of greatest deviation of latitude from its mean position for a place 90 distant in longitude from the place of the azimuth.

Suppose the mean position or the center of the circle described by the pole to be at P on the surface of the earth and its position at its farthest west of its mean position as viewed from any other point S to be at P', then the change in the direction of the meridian through S due to the change in the position of the pole will be the angle P S P'.

The spherical triangle P S P', being right-angled at P', gives,

Taking for the position of the point S Sault Ste. Marie, of which the latitute is 46° 30' 06", S P is the co-latitude, P P is half the change of the latitude, 0.3 for a point 90° distant in longitude and the corresponding change in direction of the meridian is at Sault Ste. Marie, 0.44. The greatest change in the azimuth of the line will be twice the change in the direction of the meridian, or 0 ́.88.

To determine such a small change in the azimuth requires a very precise method of observation. The probable error of a very good measurement of a horizontal angle is about 10.5. The azimuth of a line determined in the usual way by means of a horizontal circle would not be any more accurate. The probable error of a latitude determination by means of the zenith telescope is only 10.08. The method of tracing the latitude change by observation of an azimuth would therefore not be of any great value as compared with the direct determinations of the latitude, unless some more accurate method of observing the azimuth can be devised than the one ordinarily in use.

In the ordinary method of determining the azimuth, the error is due to the errors of the circle used in observing the angle between the star and the mark, and the error due to observation of the star at an altitude, where a correction for level has to be applied for the inclination of the horizontal from observations with a striding level. The errors of graduation of the best circles are nearly of the same order as the change of azimuth to be determined.

The observatory at Sault Ste. Marie is well adapted for precise determination of azimuth. The stone pier for mounting the instrument is large and solid and well isolated from the surface layers of the earth, so that no tremors are transmitted. There is a concrete pier for holding a mercury dish, and the star can be observed direct, and reflected from Mercury, dispensing with the use of a striding level. A Azimuth is in the same vertical plane as Polaris at western elongation within 4', and the angle between it and the star can be determined with a micrometer, dispensing with the use of a horizontal circle.

The expression for the azimuth of a star at elongation is:

sin. A sec. o cos. d.

A azimuth of star.
platitude of place.

declination of star.

Supposing the azimuth and the latitude to vary and the declination of the star to remain constant, then differentiating the equation with respect A and it becomes:

For a change of latitude of 1" or d p=1" the corresponding change of azimuth of the star or d à is 0.033. There is, therefore, very little change of azimuth for a variation of latitude at a place. The change in the azimuth occurs, however, for a change of latitude at places 90° in longitude east and west of the place. Supposing the latitude to remain constant and the declination of the star to vary, then differentiating the equation with respect to A and & there results:

For Polaris, 6=88° 44′ 55′′ and a variation of 1" in 8 or d 8=1", this gives d A: 1.45".

The standard stars used in observing azimuth, their azimuths at western elongation for Sault Ste. Marie, their declinations and right ascensions are given in the following table:

Star.

Azimuth of stars at Sault Ste. Marie, Mich.

B.-REPORT OF MR. FRED MORLEY, ASSISTANT ENGINEER.

UNITED STATES ENGINEER OFFICE, Sault Ste. Marie, Mich., December 15, 1893.

SIR: I have the honor to submit the following report on the primary triangulation planned in connection with the resurvey of the St. Marys River, and which extends from the old Mackinac base line on the south side of the Straits of Mackinac northward to a connection with the triangulation system of the lake survey in the eastern end of Lake Superior.

A system of triangulation for expanding from a possible 4-mile base line on Batchewana Island to the primary triangles, and forming at the same time a part of the secondary system, planned in Whitefish, Batchewana, and Goulais bays is also

included.

This work, assigned to me by your letter of instructions dated April 19, 1893, was accomplished between April 17, when I reported for duty to General Poe in Detroit, and November 15, when my leave of absence from the University of Michigan expired.

Detail reports on all stations located and on the work in general having been furnished from time to time as the work progressed, as well as an annual report at the close of June, it seems unnecessary at this time to present more than a summary on the work as a whole.

In the early part of the season progress was delayed by the lateness of the spring and consequent unfavorable weather, as well as by the lack of suitable help and want of necessary instruments, and it was not until about the middle of June that these drawbacks were mainly removed. The use of only a small sailboat on the secondary work in Whitefish and adjacent bays was also a source of considerable delay. From about the middle of October to the middle of November the atmosphere continued so unfavorable for seeing as to greatly delay the work during that time.

South of Sault Ste. Marie much of the country back from the shore is quite accessible by roads, and so well settled up and provided with means of travel that little difficulty was experienced in securing accommodations and in getting from place to place. One and sometimes two men, in addition to myself, made up the party on this portion of the work.

North of Sault Ste. Marie the unsettled condition of the country made it necessary to procure a tent and other camp outfit and carry with us provisions for our subsistence. Journeys were made through the forests on foot. On two occasions Indian guides were employed. Two and, for a part of the time, three men were required in the reconnoissance of this section of country.

A field glass, a prismatic compass, a pocket sextant, creepers for climbing trees, and sectional maps of the country and charts of the lakes were provided for my use. A good aneroid barometer would frequently have been of service.

Mirrors were sometimes used in determining the intervisibility of stations by reflecting sunlight between them. The required heights of stations were most frequently determined by observations from tree tops.

THE SOUTHERN CONNECTION.

This is made on the old Mackinac base-line situated on the south side of the Straits of Mackinac and extending from McGulpins Point southeast about 4 miles. The buried stones marking the ends of this base have been found. These stones do not appear to have suffered the least change in position since they were set about forty years ago. The geodetic points on their upper surfaces, marking the exact ends of the base, also appear in perfect condition. No surface marks at the ends of the base remain to indicate their location. The northwest end stone of the base is about 16 feet out in front of the front door of the McGulpin Point light-house. The southeast end stone is in the highway leading from Mackinac City to Cheboygan, and about 24 miles from the former place, as indicated by the mile post on the Michigan Central Railroad, which runs parallel to the base along its southeast portion.

A remeasurement of this base-line is recommended. The southeast end of it is now occupied by a public highway, a portion of which is but little traveled. This half presents no obstruction to measurement, and little, if any, to the intervisibility of base ends. The northwest quarter of the base is occupied by a private road leading to McGulpin Point light-house, is little traveled, offers no obstructions to measurement, and can be cleared of obstructions to sight at small expense. The remaining mile having been allowed to grow up again since it was first cut out presents obstructions to measurement as well as to sight. This portion can, however, be reopened at probably less than half the expense required in the first cutting.

The system of quadrilaterals adopted in passing northward from the Mackinac base, it will be seen, closely agrees for a ways with the system formerly used in the survey of the Straits of Mackinac. The geodetic points of the former stations on Point St. Ignace, Rabbits Back Peak, and Mackinac Island, have been recovered, but with the possibility of the last named having been slightly disturbed. These points are to be reoccupied. Lack of time and unfavorable weather prevented my visiting Boiling Spring Point, Point St. Martin, and Point Fuyard to look for former stations on these points. There is little doubt but that the stations on the first two named points can be recovered, and possibly on all three points. These stations, if found, are to be reoccupied and, if not found, new stations in their immediate vicinity are to be used. A line from Mackinac Island to a station near the northeast end of Bois Blanc Island being determined through the above series of stations, the triangulation will be carried northward from this line to two inland stations,

and so on.

The average height of timber being about 80 feet, and the country comparatively even, high stations are required at the two inland points and near the northeast end of Bois Blanc Island to get above the timber and avoid cutting.

THE NORTHERN CONNECTION.

Of the old lake survey stations in the eastern end of Lake Superior, Mamainse, situated about 9 miles north of Batchewana Bay, was the last or most southerly station. Gargantua, located on the east coast of the lake, about 42 miles northwesterly of Mamainse, together with station Michipicoten, on the northwest side of Michipicoten Island, formed with Mamainse the vertices of the last triangle in the lateral chain of triangles in this end of the lake.

At Mamainse "the geodetic point was marked by a nail driven into a stake about 24 inches in diameter set about one foot below the ground surface." This stake was found, and, though its top portion was rotted away so that the nail itself was not recovered in place, the main portion of the stake was so well preserved that I feel confident that the place of the original geodetic point was recovered within less than half an inch. The astronomical stone post in the vicinity is still in place.

At Gargantua "the brass point about one-fourth of an inch in diameter set in the rock to mark the geodetic point" was found in place and in perfect condition. The "astronomical stone post" near by is also undisturbed. This station is on a hill only 431 feet above the lake, and unfortunately so situated that nothing can be seen from it to the eastward of the line from it to Mamainse owing to the higher hills but a short distance away on the easterly side of Gargantua Harbor. The line Mamainse-Gargantua could not, therefore, be used as at first anticipated as the direct line of connection.

The new station Pantagruel was therefore located on the higher hills about a mile from the northeast shore of Gargantua Harbor, about 2 miles eastward of station Gargantua, and the recovery of Michipicoten station sought for.

At Michipicoten the geodetic point is recorded as being "marked by a cross, cut in the solid surface rock." The tripod is still standing, though apparently tilted over southerly about 6 inches. I was unable to discover what appeared to me unmistakable marks, as described above, of the geodetic point.