REDUCTION: OF THE BAROMETRIC OBSERVATIONS. 59 
made upon our line were developed into a curve; the absciss representing the times of obser- 
vation, and the ordinates, corresponding readings, or rather fluctuations, of the barometer ; the 
measured difference between the altitudes of any two ordinates being the true elevation or 
depression of the mercurial column after all the known corrections had been applied. This 
curve was found to be remarkably regular, so long as the observations from which it was plotted 
were made at the same station. But upon a change of place, the base being altered, the con- 
tinuity of the line was broken ; and observations made at the second station could not be com- 
pared with those taken a few hours before at the first, until the barometric movement for the 
intermediate time should be made known. This could be satisfactorily determined only by 
observations upon a barometer at rest during that period. Upon inquiry, it was ascertained 
that, subsequent to our first computations, barometric records had been received at the Surgeon 
General's office from various military posts in the vicinity of our route. To decide which of 
them would serve to connect the broken links of our series between consecutive stations, similar 
developments were made upon the diagram of other records covering the same periods of time. 
A comparison of them all showed which corresponded most nearly with our own. If day after 
day the oscillations at some fixed station were identical with those shown by the records made 
by us in two or more camps, it is fair to assume that, during our progress between those camps, 
the atmospheric dilatations were correctly represented in the same series. 
This principle being established, its application was easy. By a construction, more elaborate 
than has been attempted in the diagram, a complete curve of the variable pressure upon our 
whole route might be represented. Then, having drawn a horizontal line to denote the mean 
pressure, the abnormal error at any hour, during the required period, could be measured off 
above or below, and applied, with its proper sign, to the observation ; but, for the reduction 
of our profile, a simpler plan was adopted. Having, by the diagram, decided with which of 
the fixed barometric stations it was desirable to compare, the observations at that place were 
examined, and tables of the dilatations were made out, to be used as corrections. In deducing 
these lists of corrections, I am greatly indebted to Dr. R. H. Coolidge, United States army, and 
to Lorin Blodget, esq., for extending every facility and assistance that the Surgeon General's 
department could afford. 
For the determination of the profile of different portions of our line, corresponding observa- 
tions were compared, as follows, viz: 
From Fort Smith to Rio del Norte, with Fort Gibson. From Rio del Norte to Camp 73, 
(less satisfactorily,) with Fort Gibson. From Camp 73 to Camp 91, (Leroux's Spring,) with 
Great Salt Lake. From Leroux’s Spring to Camp 113, on Williams’ river, with Fort Yuma. 
From Camp 113 to Camp 134, (last on Rio Colorado,) with mean between Great Salt Lake and 
San Diego. From Camp 134 to the Pacific, with San Diego. 
Beside the comparisons above mentioned, the relative heights of many of the principal points 
were obtained by simultaneous observations at different stations along our route. "This was 
done whenever the party was divided for the purpose of making explorations in advance of the 
main survey ; and the duplicate sets of observations then taken have proved valuable tests to 
the results. 
The readings of the barometer being thus corrected for expansion, horary oscillations, and 
abnormal variations, the altitudes of the points of observation were deduced by the hypsometrical 
tables caleulated by Professor Loomis after the formula of Laplace. 'l'hese tables were convenient 
and highly satisfactory, except with reference to a single term of the corrections, viz: that 
relating to the air temperatures. For the want of corresponding observations, made at appro- 
priate fixed stations, the mean height of the mercurial column and mean temperature at the sea 
level in latitude 35° were assumed as the bases for comparison. It is evident that the observa- 
Hong obtained at the various points upon the survey should also be reduced to mean values, in 
order to be comparable with the assumed data. With regard to the barometer, this was accom- 
plished with some pretensions to accuracy. The air temperatures, however, in consequence of 
