Allowing the perpendicular fall of the river Platte, from the mountains to its mouth, to be on an average nineteen inches per mile, (which appears reasonable from the rapidity of its current compared with that of the Missouri,) the fall of the Missouri from the place where it receives the Platte to its mouth, to be 16 inches per mile, which agrees with the result from _leveling_ at Engineer Cantonment--and that of the Mississippi from the mouth of the Missouri to the Gulf of Mexico to be 12 inches per mile, it would give for the height of the Platte at the base of the mountains, say at the place of the above observations, 3000 feet above the level of the ocean, and consequently the height of James's Peak would be 11507½ above the same level. This mountain was clothed in snow for a considerable distance below its summit, when the exploring party visited it, in the middle of July, and at the same time they experienced excessive heat at its base. * * * * * _Observations made on the Arkansa, at our camp, situated about twenty-five miles below the point where the river issues from the mountains._ _Equal altitudes of Sun to find error of watch, at noon._ | Time from Noon, | Time from Noon, | Error of Watch. | A.M. | P.M. | +------------------+--------------------+---------------- July 17, 1820. | 3ʰ 27´ 17˝ | 3ʰ 08´ 35˝ } | 15´ 03˝ slow. | 3 25 58 | 3 07 15 } | Mean time. | 3 24 36 | 3 05 54 } | +------------------+--------------------+---------------- July 17, 1820. | Meridian double altitude of Antares | 51° 28´ | Index error 3´ 22˝. Latitude } | | deduced } | 38 18 19 N. +---------------------------------------+---------------- _A mean of eight lunar observations. Distance of nearest limbs of sun and moon for calculating the longitude._ | Time per Watch, | Distance of Sun | | P.M. | and Moon. | Index Error. +------------------+------------------+------------- July 17, 1820. | 3ʰ 26´ 49˝ | 84° 08´ 30˝ | - 3´ 22˝ +------------------+------------------+------------- {xxxix} Assumed longitude 7ʰ 01´ west. Allowance to be made for error and rate of time-piece, as before. Longitude of Camp deduced, 7ʰ 02´ 39˝, or 105° 39´ 45˝ W. _Camp on the Arkansa, two miles below the river St. Charles, or third fork of Pike._