118 
DETERMINATION OF ALTITUDES BY BAROMETER. 
exceedingly convenient, and, by not introducing logarithms, greatly diminish the liability to 
mistakes. The values assumed for a few of the quantities in the formula require notice. 
1. Reading of barometer and thermometer at lower station. —The mean reading of the barometer 
at the level of mean tide at Suisun hay, near Beniciq,, was uniformly assumed for the reading at 
the lower station. Its value was determined by computation from very numerous observations 
taken by the Medical Department of the army, at the United States hospital, near the water’s 
edge. It may be well to state that the altitude of the hospital above the level of mean tide, 
given as 64 feet in the returns sent to the Surgeon General’s office, is erroneous, and that the 
more accurate altitude of 81.5 feet was found, by careful measurement in 1854 by Lieutenant 
W. T. Welcker, Ordnance Corps, United States army, at the request of Lieutenant Williamson. 
This altitude was used in computing the barometric reading at the level of mean tide from that 
at the hospital. It is 30.057 inches, the temperature of the mercury being 32° Fahrenheit, 
and of the air 64° Fahrenheit. It was considered better to refer all the observations to this 
fixed base, partly because, by computing from camp to camp or station to station, all errors 
would be propagated through the whole succeeding work, and partly because the great prin¬ 
ciple of this method of computation being to reduce the observed to the mean reading, it would 
seem better to take for the lower station a mean reading very well determined than one deduced 
from a few observations, and depending for its accuracy upon the correctness of the horary and 
abnormal tables. This reasoning was verified by the test of the Canada de las Uvas observa¬ 
tions, which will be fully explained in a subsequent part of this chapter. 
2. Reading of thermometer at upper station. —It only remains to notice the air temperature at 
the upper station. As our method of computation differs in this from that of any of the Pacific 
railroad surveys yet published, I shall fully state the reasons which decided me to adopt the 
change. It had already been found that if, in this new method of computation, the observed 
air temperature was used, bad results were obtained, the very high temperatures giving too 
great altitudes, and the very low not great enough. To correct this source of error, Mr. L. 
Blodget constructed an empirical table of corrections, by comparing the results of a spirit 
level and a barometric survey of some passes in the Sierra Nevada, made by Lieutenant 
Williamson in 1853. Although the results obtained by using this table are doubtless more 
accurate than those given by the observed air temperature without this correction, still I cannot 
feel satisfied either with it or with the reasoning advanced to support it, based upon the 
difference between the “surface temperature” and that of the main body of the air. I think 
the source of the difficulty lies deeper, and that it may be anticipated from the very principle 
upon which the new method of computation is based. To understand this fully, it is necessary 
to refer to the formula used in computing altitudes from barometric observations, the tempera¬ 
ture of the mercury at both stations being the same. It contains, beside terms depending upon 
the geographical positions of the stations, two compound independent variables, each of which 
consists of two mutually dependent variables. These are the height of the mercurial column 
and the corresponding air temperature at each station ; and it must be carefully borne in mind 
that they are not four independent variables. The theory of the old method of computation was 
that, by taking simultaneous observations at both stations, all causes of error would affect them 
equally, and that by substituting these observed values for the variables, the formula would 
give a correct difference of altitude between the stations. This is slightly erroneous, for, as the 
ratio of the barometric readings enters into the formula, any error in them, even although it 
should affect both equally, would vitiate the result. A greater objection to the method is, that 
