114 DETERMINATION OF ALTITUDES BY BAROMETER. 



INTERPOLATION, AND APPROXIMATE TEST OF ACCURACY IN THE OBSERVER. 



Before proceeding to discuss the determination of altitudes, I shall explain the mechanical 

 method used in examining and studying observations taken at a fixed station. It is to repre- 

 sent them, the temperature of the mercury having been reduced to 32° Fahr., by a curve, of 

 which the abscissas denote the times of the observations, and the ordinates the corresponding 

 height of the mercurial column. By this means any great error in observation can be readily 

 detected by an abrupt change in the curve, and a very clear and comprehensive idea can be 

 obtained of the relations of the different observations to each other. This also furnishes the 

 best method of interpolating properly for intermediate readings. 



CORRECTIONS PREPARATORY TO COMPUTATION. 



1. For temperature of mercury. — In preparing observations for computation, the first step 

 taken was to reduce the observed readings of the barometer to what they would have been had 

 the temperature of the mercury been 32° Fahr. For this purpose the tables of Mr. A. Guyot, 

 published by the Smithsonian Institute, were used. 



2. For instrumental errors. — The correction for instrumental errors was then applied, and, 

 when more than. one barometer had been observed, a mean of the readings thus corrected was 

 taken, to eliminate, as far as possible, errors of observation. 



3 For horary oscillation. — The next step was to correct for the oscillations of the mercurial 

 column, due to the ever varying weight of the atmosphere. Of these there are two kinds, the 

 normal and abnormal. Although a monthly and a yearly normal oscillation, and also one 

 depending on the amount of moisture in the atmosphere, are supposed to exist, still, we practi- 

 cally know but one, called the horary variation. This is a kind of daily atmospheric tide, caused 

 principally by the heat of the sun, but greatly affected by the altitude and latitude of the place, 

 and, doubtless, by other circumstances. It is far from constant, even at the same locality, as 

 will be clearly shown by the result of our observations made at Fort Beading, in July and 

 November. 



Observations for the construction of a table of horary corrections should be taken hourly 

 with very great care, and continued, if possible, for a long period of time ; but this is not 

 absolutely necessary. A good one may be constructed from observations taken even for a single 

 day, when the mean temperature does not differ much from that of the season, and when there 

 is little or no abnormal oscillation. The latter condition is generally fulfilled when the 

 reading of the barometer, with the mercury reduced to 32° Fahr., is the same, or nearly the 

 same, at the last observation, as it was at the same hour on the preceding day. Even when 

 observations are taken for several days, the latter of these conditions must not be neglected ; 

 that is, the last observation, with the temperature of the mercury reduced to 32° Fahr., should 

 always be very nearly the same as that taken at the corresponding hour immediately preceding the 

 first observation used. This is manifestly necessary, as an abnormal change affects the horary 

 curve. For instance, if the mercury should, beside the horary change, uniformly descend for 

 one entire day and ascend for the next to the same height as before, the descending portion of 

 the horary curve on the first day will be lengthened, and the ascending shortened, and vice 

 versa on the second day. In a mean curve for the two days, these errors will balance each other. 



To construct a table of horary corrections, the observations, after the temperature of the 

 mercury has been reduced to 32° Fahr., should be represented by a curve, as already explained, 

 and examined to detect any errors of observation and to reject any portion in which the effect 



