This result, and the results of the time-observations made at Chicago on the 16th and 19th of May, and the following telegraphic signals, give us a third determination of the longitude of Michigan City, as follows, viz- Determination of the difference of Longitude between Chicago and Michigan City, by electric signals for comparisons of time, May 17th, 1859. 08.307. Sidereal Chronometer No. 2557, fast, of Michigan City sidereal time (at 14h. 11m. 12s. sidereal time), 1h. 33m. 29s.89. Rate per sidereal day, -78.366; or per sidereal hour, Mean solar Chronometer No. 141, slow, of Chicago, mean solar time (at 10h. 27m. mean time), 4m. 41s.02. Rate per mean solar day, +0s.377; or per mean solar hour, + Os.0157. 1st.-Chicago signals recorded at both stations. 8. h. m. S. h. m. s. h. m. s. Chicago h. m. s. 14 11 12.61 14 08 19.03 h. m. 2d.-Michigan City signals recorded at both stations. Difference of Longitude by each signal.Michigan City east of the meridian of Chicago observing station No. 3. h. m. S. 0 02 53.58 0 02 53.577 h. m. s. h. m. 8. 15 56 44.5 10 34 20 15 59 45 10 37 20 16 02 45.5 10 40 20 h. m. s. Michigan City Michigan City h. m. s. h. m. 3. 2d Mean.-Electric signals sent from Michigan City to Chicago, Result:-Centre of Public Square in Michigan City is east, in longitude, of Chicago observing Station No. 3, by a mean of the two sets of signals, *It was cloudy at Chicago, May 18th, and no observations could be made on that night. Longitude of the centre of the public square of Michigan City, 5 47 37.64 We have here three determinations of the longitude of this position: one from observations in June, 1858, and two from observations in 1859, namely, April 28th and May 17th. The time-stars were much better selected in 1859 than in 1858, which will appear on a comparison of their north declinations. Those in 1859, were all observed near the prime vertical, but those of 1858 were observed before reaching the prime vertical, east or west, and on different sides of it, though at nearly equal altitudes. All things considered, we think the two results of 1859 are each entitled to twice the weight of that of 1858. On this principle the final result is presented, as follows, viz. SUMMARY.-Longitude of the Centre of this Public Square: Result adopted, giving the 2d and 3d determinations each a double weight. Longitude of the centre of the public square at Michi gan City, Indiana, west of the meridian of Greenwich, Equal, in arc, to Latitude of the same point, as before given, 5 47 37.56 86° 64' 23'.4 W. 41° 43' 08'.33 N. From our survey, based on the above result, and observed azimuths of Polaris for determining the true courses, we obtain the positions of other points in Michigan City. The following table shows them all: VOL. VII.-P In Talcott's map, accompanying his report on the survey of the Michigan and Ohio boundary of 1833, he lays down the position of Michigan City in latitude 41° 43' 10".8 N., and in longitude 86° 43' 26".9 5h. 46m. 53s.8 W. By our observations, his station, here, appears to be in latitude 41° 43' 10".52 N., and in longitude 86° 54′ 24" = 5h. 47m. 37s.6 W. While there is a remarkable agreement = in our observations of the latitude, we place the longitude 43s.76 of time, 10' 56.4 in arc, 9.42 miles, west of the position assigned to it on Talcott's map. = VI. MADISON, THE CAPITAL OF WISCONSIN. In our former paper, we gave an approximation to the geographical position of this place, derived from unsatisfactory observations made during unfavourable weather, which cut us off from a selection of pairs of stars well matched in declination for eliminating errors of observation, either for the determination of the latitude or the longitude. The approximate result then arrived at appears, from more accurate observations recently made, to have given the latitude too great by about 9.5, and the longitude too little by about 18.2 of time. This, however, was far more accurate than the position assigned to Madison on any of the maps extant. These more recent observations are now presented, as follows, viz: 1st. The Latitude. 1859, June 4th. At Madison Station No. 2.* 1. By 21 circum-meridian altitudes of a Virginis, south, combined with 17 altitudes of Polaris, north: latitude of station, 2. Same night-By 21 circum-meridian altitudes of Libræ, south, combined with 17 other altitudes of Polaris, north, observed at a later hour of the night than the 1st set, 43 04 25 43 04 25.24 Result adopted-Latitude of Madison station No. 2, 43 04 25.12 N. Reduction to the dome of the State Capital, Latitude of the dome of the State Capital, + 5.68 43 04 30.8 N. Here the stars are well paired with regard to their altitudes when observed, north and south, and the above result is, therefore, believed to be a pretty close approximation to the true latitude of this place. 2d. Observations for the Time. Same night (June 4th, 1859), and same station. Sidereal chronometer No. 2557, fast: By 10 observations on a Canum Vena- S. h. m. 1 45 43.15 * This station and its position relatively with that of the dome of the State Capital, will be found described in Vol. VI., at page 386 of the Society's Proceedings. Result adopted-Chronometer No. 2557, fast of sidereal time for this station (at 16h. 48m.) +1 45 42.64 The above result for the Madison time, and the results of the observations for the time at Chicago on the 3d and 6th of June, 1859, already given in their proper places, combined with the following telegraphic signals, give us a new result for the longitude of Madison, as follows, viz. Determination of the difference of Longitude between Chicago and Madison, Wisconsin, by electric signals for comparisons of time, June 4th, 1859. Sidereal Chronometer No. 2557, fast, of Madison sidereal time (at 15h. 57m. 45s. sidereal time), 1h. 45m. 42s.43. Rate per sidereal day, + 6s.086; or per sidereal hour, + Os.2535. Mean solar Chronometer No. 141, slow, of Chicago mean solar time (at 11h. 12m. 24s. mean time), 4m. 448.42. Rate per mean solar day, 0s.20; or per mean solar hour, 08.0083. 1st.-Chicago signals recorded at both stations. Times of signals given at Chicago by mean solar Chronometer No. 141. h. m. s. 11 07 40 11 10 40 11 25 40 1st Mean. h. m. 15 57 45.57 16 04 47.93 Electric signals sent from Chicago to Madison, Difference of Longitude by each signal.Madison is west of the me ridian of Chi cago observing station No. 3. h. m. S. 0 07 02.39 0 07 02.37 |