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, we 

 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 be, 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 be 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 ; but, 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 be 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 1a.m., 12 m., and 10 p. m., or of those 

 at 7 a. m., 2 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 be 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, but 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 " surface temperature " theory. It seems to me to 

 confirm, as fully as could possibly be 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. 



