meridian of Chicago, which I consider well determined with reference to the meridian of Greenwich. I have already thus connected nine important points between Erie, Pennsylvania, and Prairie du Chien on the Mississippi river, and determined approximately their latitudes; but I have not time, at this moment, to add them here. I will, however, offer them at a future time, and as soon as I can arrange them in a brief form. They go to show that portions of the upper Mississippi river are laid down, even on the latest and most approved maps, several miles out of place in longitude. I wish to offer this paper, as it is, for publication in the Society's Proceedings, provided it be considered acceptable. J. D. GRAHAM, Member of the Society. CONTRIBUTIONS TO GEOGRAPHY, No. 2. On the Latitude and Longitude of four additional positions on Lake Michigan, and of MADISON, the Capital of the State of Wisconsin; from astronomical observations by Lieut. Colonel J. D. Graham, U. S. Corps of Topographical Engineers. Chicago, Illinois, December 14th, 1858. To the American Philosophical Society, Philadelphia. In my letter of the 29th ultimo, I offered for the consideration of the Society, and for publication in its Proceedings, some observations on the latitude and longitude of Chicago. I beg leave now to offer, for the same, the following observations in a brief form, made between the 20th of June and the 7th of September, 1858, for the determination of the geographical positions of the following places. Calling Chicago I, as already presented, I will enumerate the others, for convenient reference, as follows, viz: II. MICHIGAN CITY, INDIANA. III. WAUKEGAN, ILLINOIS. IV. RACINE, WISCONSIN. V. MILWAUKEE, WISCONSIN. VI. MADISON, THE CAPITAL OF WISCONSIN. The instruments used for the observations were all of a portable character, adapted to ready use at night, whenever I had occasion to halt in the course of a long journey by rail road. I will describe them as follows, viz:— 1. A sextant of 74 inches radius, made by Simms, of London, read ing by aid of the vernier to 10 seconds of arc. 2. An artificial horizon of quicksilver. 3. A sidereal chronometer No. 2557, by Parkinson and Frodsham, of London; beats half-seconds. 4. A mean solar chronometer No. 141, by Isaiah Lukens, of Philadelphia; beats half-seconds. This chronometer runs eight days without winding. It was made by Mr. Lukens about the year 1830 or 1831, while on a visit to London. It is one of the earliest chronometers, I know of, made by an American. It is now an excellent time-keeper. The latitudes, as will be seen, are derived from observed circummeridian altitudes of stars arranged in pairs, one of each pair passing the meridian to the north and the other to the south of the zenith. When it could be done, they were selected of such declinations as to cause them to pass the meridian at altitudes varying only a few degrees, say 2° to 3°. But this last mentioned advantage for a close elimination of errors could not always be secured on the occasions here presented. There is, however, an approximate elimination from having one of the stars of each pair to pass the meridian to the north and the other to the south of the zenith. The time stars were selected also in pairs, the one being observed eastward and the other westward of the meridian, and conformable, as nearly as was practicable under the circumstances attending each case, to the principle stated in my communication of the 29th ultimo. The longitudes are all derived from chronometrical comparisons with the meridian of Chicago. They rest, for accuracy, on the correctness of my determination, in the year 1842, of the longitude of the citadel of Quebec, west of Greenwich, already alluded to in my previous communications, and on the sextant observations for the time at Chicago and at the several places whose longitudes are sought. All the comparisons of time with the meridian of Chicago,-now assumed as a primary for my operations in our western country, were by means of electric signals transmitted forth and back along the telegraphic wires. The system adopted was as follows:-The night before visiting a place whose geographical position was to be ascertained, observations were made for the time at Chicago, with the sextant, the artificial horizon of quicksilver, and the sidereal chronometer. Both before VOL. VI.-3 c and after these observations the sidereal and mean solar chronometers were compared. This gave the error of the first on sidereal, and of the second on mean solar time for the meridian of the Chicago obser. ving station. Immediately on returning to Chicago the same thing was again done. This gave a new determination of the errors for the second Chicago period, and also the rates of both chronometers during the elapsed time. Between these two periods the journey forth and back was made, and also the observations at the place whose position was sought, and the telegraphic signals exchanged, in the manner hereinafter reported. The mean solar chronometer was always left at Chicago, and the signals sent from that place, as well as those sent to Chicago, were noted by it there. The observations at the distant station, whose position was sought, and the telegraphic signals received at and sent from that station, were all noted there by the sidereal chronometer. These signals were always made by myself by pressing the telegraph key with the fingers, so as to produce the click of that key as nearly as possible in coincidence with a given beat of the chronometer. The signals at Chicago were always made by an experienced telegraph operator, who was, in the beginning, carried through a course of practice in making dots as nearly as possible in coincidence with the beats of the mean solar chronometer at every ten seconds of interval, for seven to ten and sometimes thirteen minutes as a series. It is remarkable how soon a person, with a good ear for cadence, or time, will acquire an accuracy in making these time-signals approaching almost to exactness. The results which will presently be presented will serve as evidence on this point. After the observations for the time, at the place visited, were com. pleted, the sidereal chronometer was carried to the telegraph office at that place. I then began by calling for a certain number of signals from Chicago at intervals of ten seconds apart, sufficient to insure two or three periods of coincidence in the beats of the two chronometers. This period of coincidence of beats having been thus ascertained, signals were sent from the distant station back to Chicago, at intervals that would ensure a coincidence with the beats of both chronometers. These intervals were easily ascertained by making allowance for the difference of the rates of the two chronometers affected by their proper algebraic signs of when gaining, and when losing, as well as for the gain of sidereal on mean solar time. Sometimes additional signals were called for from Chicago at stated moments, varying the interval two, three, or four seconds, each way, and sometimes throwing them into the half-second beats, and at others into the whole-second beats at that place, as tests upon the series. The reductions from Chicago mean solar to sidereal time, with the difference of the rates of the two chronometers incorporated into the calculations, give the fractions of a second which appear in the stated differences of longitude between the two stations-the signals corresponding to coincident beats of the two chronometers being the only ones used in the computations. I will now proceed to state, in a brief form, the observations and the results derived from them. The Observations for Time at Chicago. 1st. 1858, June 20th. At Chicago Observing Station No. 2, in latitude 41° 53' 50'.5 N.: longitude 5h. 50m. 31s.15 W. Sidereal chronometer No. 2557, fast: By 11 observations on a Lyræ, east (at 15h. 40m. sidereal) By 12 observations on a Bootis, west (at 16h. 13m. sidereal) Result-Chronometer No. 2557, fast of sidereal time for this station (at 15h. 56m. sidereal) By comparison-Chronometer No. 141, slow of mean solar time for this station (at 10h. 00m. mean time) 2d. June 22d. Same Station. Sidereal chronometer No. 2557, fast: By 14 observations on a Lyræ, E. (at 15h. 36m.) Result-Chronometer No. 2557, fast of sidereal time for this station (at 15h. 53m.) By comparison-Chronometer No. 141, slow of mean solar time for this station (at 9h. 48m. mean time) m. S. 59 18.93 59 18.32 3d. 1858, June 28th. Same Station. Sidereal chronometer No. 2557, fast: Result-Chronometer No. 2557, fast of sidereal time By comparison Chronometer No. 141, slow of mean solar time for this station (at 9h. 25m.) +1 00 07.56 4th. June 30th. At Chicago Observing Station No. 3, in latitude 41° 53′ 46′′.3 N., longitude 5h. 50m. 31s.2. W. Sidereal chronometer No. 2557, fast: By 10 observations on a Coronæ Borealis, W. 19h. 22m.) By 13 observations on Andromeda, E. (at 20h. 08m.) Result-Chronometer No. 2557, fast of sidereal time for this station (at 19h. 45m.) By comparison-Chronometer No. 141, slow of mean solar time for this station, (at 13h. 09m. mean time) 1 00 21.22 5th. 1858, July 3d. At Chicago Observing Station No. 2. Sidereal chronometer No. 2557, fast: By 6 observations on a Lyræ, E. (at h. m. S. By 14 observations on a Bootis, W. (at 16h. 38m.) Result-Chronometer No. 2557, fast of sidereal time for this station (at 16h. 40m.) By comparison-Chronometer No. 141, slow of mean solar time for this station (at 9h. 53m. mean time) |