TABLE 44.-Results for difference of longitude, Sault Ste. Marie and Ann Arbor, Mich.

[First Lieut. Charles S. Riché at Sault Ste. Marie; Prof. Asaph Hall, jr., at Ann Arbor.]

+4-2 28.060 +-2 28.103

+2 28.030

[Prof. Asaph Hall, jr., at Sault Ste. Marie; First Lieut. Charles S. Riché at Ann Arbor.]

Aug. 6.. +2 28.146

7.2 28. 117

+2 28.074

8.. 2 28. 132

+0.087

+0.069

"

8.

8.

Difference of longitude, Sault Ste. Marie observatory, west pier, west of "Detroit' m. observatory meridian circle at Ann Arbor, Mich.. 2 27.995 +0.036

The mean of the first five nights, July 10, 15, 19, 20, and 26, with First Lieut. Charles S. Riché, observer at Sault Ste. Marie, and Prof. Asaph Hall, jr., observer at Ann Arbor, gives 2 278.879 for the difference of time between the two places. The range in five nights is 0.295.

The mean of the second five nights, August 6, 7, 8, 9, and 12, with Prof. Asaph Hall, jr., observer at Sault Ste. Marie, and First Lieut. Charles S. Riché, observer at Ann Arbor, gives 2m 28.111 for the difference of time with a range of 0.105 in the five nights.

The mean of the ten nights' observed differences of time gives for the difference of longitude, Sault Ste. Marie west of Ann Arbor 2m 278.995 0.036, with a range of 0.295 in the ten nights, and for personal equation, Lieut Riché observes earlier than Prof. Hall 0.116.

The signals from Sault Ste. Marie give a result for difference of longitude greater by 0.084 on the average than the difference by signals from Ann Arbor. This difference, commonly called double the difference due to wave and armature time, is twice the apparent time of progression of a signal between the two places, due to the electro-static capacity of the telegraph wire, which is nearly in proportion to its length. The telegraph line between Sault Ste. Marie and Ann Arbor was continuous without repeaters.

In addition to the personal equation as derived from the results for difference of longitude with the interchange of observers, there were also made two direct determinations of the personal equation between First Lieut. Charles S. Riché and Prof. Asaph Hall, jr., one on the night of July 31 with Würdeman transit No. 1 at Sault Ste. Marie, and the other on the night of August 14 with the meridian circle at Ann Arbor.

On July 31 the method of observation was for one observer to observe a star over the first 3 wires and the other observer over the last 4. The observers interchanged wires on half the stars observed. On August 14 one observer observed the star over 3 wires, the other observer over 5 wires, and then the first observer took the star over the last 3 wires. On half the number of stars the observers interchanged wires. The observations of each observer on a star were reduced to the mean of the wires by means of the wire interval determined for each observer. The difference in the time of transit for the two observers gives the result for personal equation.

On July 31 the mean of 35 stars of less declination than 60° gave for personal equation

Riché observes earlier than Hall 0.144.

On August 14 the mean of 34 stars gave—
Riché observes earlier than Hall 08.098.

The mean of the two nights gives for personal equation

Riché observes earlier than Hall 0.121.

This result compares well with the result 08.116 for personal equation as derived from the difference of longitude with interchange of observers.

On the night of September 22 observations were made for the difference of longitude between Sault Ste. Marie and the Naval Observatory at Washington, D. C. Signals were successfully exchanged, but the observations were so broken by clouds that the work was not reduced.

AZIMUTH.

Observations for the azimuth of the line Observatory Sault Ste. Marie to station Azimuth were made by Mr. E. E. Heskell, U. S. assistant engineer, on four nights, March 2, 8, 14, and 19, by comparing the direction of the line with the direction of the star Polaris near western elongation. A few pointings on 51 Cephei near western elongation also were made on the night of March 19. The pointings to station Azimuth were made to a lamp accurately centered over the geodetic point. The length of the line Observatory to station Azimuth is 5 miles.

In determining the azimuth the large theodolite, Troughton & Simms No. 1, with a 14-inch horizontal circle, was used, reading with three microscopes. Pointings were made to the star direct and to the image reflected from mercury. The mean of the two readings is free of any error due to the axis of the pivots not being in a horizontal plane. The striding level was read during the observations, but no use was made of the readings in the reductions. The altitude of the light at station Azimuth was about 38' above the horizon. A correction for level was made to the readings on the mark deduced from the difference in the readings on the star direct and reflected. This was always small, never amounting to more than 0.3.

The method of observation was as follows: First the telescope of the theodolite was directed to the light on the distant station, bisecting it with the vertical wire, and the horizontal circle read; the telescope was then directed to the image of the star reflected from the mercury, and the time of bisection noted by the clock, and the horizontal circle read again; the telescope was then directed to the star, the time noted again, and the horizontal circle read. The observations were then repeated in the reverse order on the star, the image, and the light. In the next set the star was sighted on first, then the image reflected from mercury, and then the light; the observations were then repeated in the reverse order on the light, image, and the star. The telescope was then reversed by turning the telescope in a vertical plane around its pivot axis, the object glass passing through the nadir while the telescope was slightly lifted from the wyes to permit of the motion, and then the telescope revolved 180° in a horizontal plane and the observations repeated as described above. The observations thus made are for one position of the horizontal circle. After these observations the circle was shifted by revolving the whole instrument by means of the revolving trivet on which it was mounted. Observations were made in two positions of the circle every night.

Clock No. 256, Bond & Son, was used in noting the time of observation of the star and its reflection from mercury.

The clock correction was determined by Würdemann transit No. 1 from the observation of 4 time stars and 2 slow stars, usually before the observations for azimuth were begun. The transit was mounted on the same pier used for mounting the theodolite in observing for azimuth. The transit foot plates being firmly attached to the stone pier, it was possible to always place the instrument very nearly in the meridian without any special adjustment.

The observations for azimuth were reduced by finding the azimuth of the star at elongation and applying a correction depending on the interval between the time of elongation and the time of observation. The declinations and right ascensions used were taken from the Berlin Jahrbuch.

in whice

is the interval in time from elongation to the time of observation. This was used for intervals not exceeding twenty-five minutes. For deriving the correc