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Show 802 APPENDIX B.- GEOGRAPHICAL POSITION. Allowing the entire change of the first day to be due to No. 1961, and taking the longitudes of the termini as stated above, The ayerage rate of gain for chronometer No. 1681, daily, is 8.081 Average rate at beginning and end of journey 7.010 At Fort Leavenworth „ M 10.000 At Great Salt Lake City „ 4.020 h. m. « . Time by sextant observations at Great Salt Lake City « . 7 49 43 " " " Fort Leavenworth. 6 28 81 Difference chronometer time. 1 21 12 " in mean time by assumed longitudes 1 09 17.1 Chronometrio gain 11 64.9 Time by sextant observations at Fort Laramie 7 17 29 The number of days between the respective observations, was, from Leavenworth to Laramie, fifty days; thence to Great Salt Lake City, thirty- nine days. The proportion of gain is therefore 6 min. 41.6 sec, and 5 min. 13.3 sec. Making these corrections, and converting into siderial time, the longitude of Laramie will be given at 105° 19' 50". But taking the rate at the termination of the journey, and applying it to the time given at Laramie, we have, Longitude, Great Salt Lake 112° 06' 08" " Laramie 104° 4C85" This would agree better with that of Fremont in 1842; but he observes in his book of 1843, that the longitudes of that year are thrown too far west collectively, and proposes to correct, at Fontaine qui Bouit: taking the amount of correction given at that station in 1845, at 15' 49", his observations place Laramie in 104° 31' 54", which is nearly that adopted in the accompanying map, resulting from measured distances and observations, on the homo-ward journey. Belying upon the accuracy of the map of 1845, we have checked the work made up from course and distance, measured by an odometer, at the crossing of the North Fork of the Platte, and reduced the longitude of Camp 32 on Ghugwater, at 104° 56' 45". The chronometric difference of this camp and Laramie is taken, on account of the good apparent work of the time- keepers and the winding of the road, at 25' 19", which gives the longitude of Fort Laramie at 104° 31' 26". Thence to Fort Leavenworth the intermediate points where latitudes were taken, we make up from course and distance as before. The lunars taken at Laramie and in the Salt Lake Valley, are |