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 loioer station. — The mean reading of the barometer 

 at the level of mean tide at Suisun bay, near Benicia, 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 



