302 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 





sec. 

 The average rate of gain for chronometer No. 1631, daily, is 8.031 



Average rate at beginning and end of journey 7.010 



At Fort Leavenworth 10.000 



At Great SaltLake City 4.020 



h. m. s. 

 Time by sextant observations at Great Salt Lake City 7 49 43 



" " ** Fort Leavenworth 6 28 31 



Difference chronometer time 1 21 12 



** in mean time by assumed longitudes 1 09 17.1 



Chronometric gain 11 54.9 



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 ap- 

 plying it to the time given at Laramie, we have. 



Longitude, Great Salt Lake 112° 06' 08" 



«« Laramie 104° 40' 35" 



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 Fon- 

 taine 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 home- 

 ward journey. Relying 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 Chugwater, at 

 104° bOt' 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 



