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Show 53 For all ordinary purposes of map- construction, except where contours are wished with as close an approximation to accuracy as the means at our disposal will adraitr the differences of altitude, as derived from the aneroid feet- scale, are sufficient upon the scale of our maps for the proper representation by conventional signs of the general relief of the country ; but since continuous profiles were desired from which should be eliminated, as far as our knowledge and means would allow, the effects of periodic and non- periodic fluctuations in barometric height, it was necessary to carefully compute these observations by referring them to simultaneous observations at some fixed station whose altitude was known. In making these reductions, the first difficulty encountered arose from the fact that observations at the signal- stations were made at but few hours during the day, and, as a rule, at points of from 1,000 to 7,000 feet lower altitude than the moss of our aneroid observations, and although theoretically we could, by correcting for horary oscillation where this element was known, reduce our aneroid work to the mean of the day and refer these means to the observed means at the lower station, we were unable to determine the proper temperature to be used in the reductions, and where the difference of altitude was BO considerable the corrections from this term of the barometric formula were very large, and instrumental errors also materially affected the resulting absolute heights when such an inconstant and variable instrument as the aneroid was referred to another of entirely different character, and the profiles were found so discordant that it required considerable ingenuity to correct them and make them agree with the camps whose altitudes were derived from series of cistern- barometer and thermometer observations, referred to synchronous observations at a lower station. To lessen the labor of computation, to reduce the aneroid to its proper position as simply an adjunct of the mercurial barometer and the effect of instrumental errors and worth of compensation to a minimum, the method of computation now in use was proposed by Lieutenant Hoxie, and perfected and used to advantage by myself and assistants for all of our last season's aneroid work. The method is as follows: The altitudes of all camps are determined from a longer or shorter series of cistern-barometer, thermometer, and psychrometer observations, referred to synchronous observations at a lower station. The errors of the aneroid referred to the cistern at 32°. Fahrenheit are determined at each camp, and the mean error at two consecutive camps taken to correct all aneroid observations made between them, except where comparisons show that a sudden and great change in the error of the aneroid has occurred somewhere between the two camps, in which case the observations are rejected in toto, unless from our knowledge of the natural grades of the route we are enabled to locate the place in the profile where the change occurs, and to oorrect the observations before and after accordingly. The aneroid, watch, and thermometer are read upon leaving camp in the morning, and at a number of intermediate stations en route, and the profile closed by taking one or more careful readings upon arrival at the next camp. The observations are then, after correction for instrumental error, reduced to the mean of the day by the correction for horary oscillation, and each station referred to the preceding one, the mean of the observed temperatures at the two stations being taken for the mean temperature of the stratum between them. Thus, since the aneroid was referred constantly to its own indications, instrumental errors enter the results with only a differential value. Beginning at camp, the successive differences of altitude are then added, each to the altitude of the station preceding, and the profile carried over to the next camp by successive steps. The difference in the altitude of this camp as brought over from the preceding camp by the aneroid differences and that determined from the series of cistern- barometer observations is the error to be distributed throughout the profile to make the two coincide It is evident that, in thus computing this profile, we assume that there has been no non- periodic or abnormal fluctuation in the height of the barometer during the interval of time the profile was being measured, whereas in fact the air is seldom or never in a position of equilibrium, and the barometer is continually varyiug in height. Should the barometer bermw^, the difference of level between the two camps determined from this profile will be too great if we pass from a higher to a lower camp, and too small if we go from a lower to a higher, and rice versa if there be a falling barometer. In the first case, where the barometer is rising, the altitude of the second camp as determined from the profile will be too low by the amount in feet at that altitude of the abnormal oscillation, and vice versa when the barometer is falling, provided that the observations and computations are perfect. In distributing the errors, I have supposed that the abnormal or non- periodic oscillation is approximately a right line during the few hours the party may be engaged in running the profile- line, and that the error from this source in the altitude of each station is directly proportional to the time, or let- J£=. the difference, in feet, In the altitude of camp 2, carried by aneroid from camp 1 and that computed from synchronous observations of cistern- barometers; T=. entire interval of time, in minutes, between instant of leaving camp 1 and arriving in camp 2 |