347 

 HYPSOMETRICAL TABLES 



FOR 



COMPUTING DIFFERENCES OF ELEVATION FROM BAROMETRICAL 



OBSERVATIONS. 



NUMEROUS determinations of altitude are one of the great desiderata of physical 

 science, and no more ready means for obtaining them is at the disposal of the scien- 

 tific man than the Barometer. A traveller, furnished with the improved and con- 

 venient instruments we can now command, and with some experience in using them, 

 can take a large number of barometric observations for determining heights, at the 

 cost of little trouble or time. It is, however, quite otherwise with the computations 

 by which the results are obtained. The prospect of that tedious and time-robbing 

 labor not only too often cools the zeal of the observer, but a vast amount of data 

 actually collected remain of no avail from the want of having been computed. 



The object of this much enlarged set of Hypsometrical Tables is to facilitate the 

 task of the computer. It contains practical tables adapted to the three usual baro- 

 metrical scales, and, among them, No. I., II., and V. are so disposed as to dispense 

 with ihe use of logarithms, and to reduce the computation to the simplest arithmeti- 

 cal operations. The others suppose the use of logarithms, a method which may still 

 be preferred by some observers. 



As these various tables represent the development of the principal formulae which 

 have been proposed, the computer is enabled to compare the results obtained by 

 each of them, and to select that which he most approves. 



These formula? may be referred to two classes, the respective types of which are 

 Laplace's and Bessel's formulae. 



Laplace, in the Mecanique Celeste, Tom. IV. p. 292, gave a complete solution of 

 the problem, and proposed a formula which soon superseded the older and less accu- 

 rate formulas of De Luc, Shuckburgh, and others. The coefficients which enter in it 

 were derived from the best determinations of the needed physical constants which 

 science could then furnish, the most important of which are the relative weight of 

 the air and of the mercury, and the rate of expansion of air by heat. The first was 

 assumed to be TIT ^^ T , according to the experiments of Biot and Arago ; and the ba- 

 rometrical coefficient deduced from it, 18317 metres. This coefficient was, how- 

 ever, empirically increased to 18336 metres, in order to adjust the results of the 

 formula to those furnished by the careful trigonometrical measurements made by 

 Ramond for the purpose of testing its correctness. It becomes 18393 metres when 

 including the correction due to the effect of the decrease of gravity with the height 

 on the density of the mercurial column and of the air. The coefficient expressing 

 the expansion of the air by heat, as determined by Gay-Lussac, viz. 0.00375 of its 

 bulk for one Centigrade degree, was adopted, but Laplace increased it to 0.004, in 

 order to take into the account the effect of the greater expansive power of the vapors 

 contained in the atmosphere. 



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