DETERMINATION OF ALTITUDES BY BAROMETER. 
119 
all causes of error do not affect the observations at both stations equally, particularly when 
distant from each other. This has rendered it necessary, in preparing our extended profiles, to 
adopt a new method founded upon a different principle. This is, to substitute for the variables 
in the formula their mean values for the whole time occupied by the survey, which is supposed 
to be long enough to insure great accuracy in absolute altitudes. At any rate, relative errors 
are thus eliminated. These mean values are found for the lower station by long continued 
observations ; for the upper station, the mean barometric reading is obtained by applying to 
the observed reading the horary and abnormal corrections, which reduce it to the mean for the 
desired period. The error of using with this value the observed air temperature is now 
apparent. It is virtually making the formula indeterminate, as, if the tables are correct, v/e 
shall have precisely the same values for all the other variables for every additional observation 
taken, and perhaps a different air temperature for each of them. But this algebraic result is as 
it should he, for the height of the mercurial column and the air temperature are, as above 
stated, mutually dependent variables requiring corresponding values. Hence, the theory of 
this method of computation, supposing the tables to be correct, plainly indicates that the mean 
air temperature for the time employed in the survey should he used in the formula. There is, 
however, a slight error in the abnormal table which modifies this result in practice. The 
horary table undoubtedly corrects the mercurial column for the effect produced by the changes 
in the heat of the sun during the day ; hut, although the abnormal curve is slightly affected by 
the difference in mean temperature from day to day, we cannot suppose that this change, 
depending so much upon local causes, extends uniformly over a large tract of country. Hence 
the abnormal table does not correct for it satisfactorily. This, together with the fact that we 
travelled over regions having widely different mean temperatures, which could not he deter¬ 
mined from our few observations, led me to use, in all cases, the mean daily air temperature. 
It was found by taking a mean of the observations at 7 a. m., 12 m., and 10 p. m., or of those 
at 7 a. m., J2 p. m., and 9 p. m.; either method being well known to give a closely approximate 
value. 
It is interesting to see how Mr. Blodget’s empirical table suggests the use of a mean tem¬ 
perature in the formula, although he bases upon it a widely different theory, and one which, 
however applicable it may he in particular cases to the old method of computation, appears to 
me to entirely fail in showing the cause of the error resulting from using the observed tempera¬ 
ture in the new method. This table reduces the temperature, when between 35° and 60° Fahr., 
to about 67° Fahr.; and when between 75° and 95° Fahr., to about 77° Fahr. Thus it not only 
approximates towards giving a mean temperature, hut it even indicates a higher mean tem¬ 
perature when the weather is warm than when it is cold. As this table is entirely empirical, 
being deduced by comparing altitudes found by the barometer and the level, it is by no means 
necessary to consider that it sustains the u surface temperature ” theory. It seems to me to 
confirm, as fully as could possibly he expected, considering the small number of observations 
from which it was deduced, the idea that the mean daily temperature should be used. 
In computing altitudes, the practical importance of an error in the air temperature at the 
upper station greatly depends upon its height above the lower ; an error of 1 ° Fahr. vitiating 
the result about one foot for each thousand feet of this height. 
