HYPSOMETEICAL TABLES 



FOR 



COMPUTING DIFFERENCES OF ELEVATION FROM BAROMETRICAL 



OBSERVATIONS. 



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

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

 fic man than the Barometer. A traveller, furnished with the improved and con* 

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

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

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

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

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

 jtually 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 

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

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

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

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

 } preferred by some observers. 



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

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

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



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

 aplace's and Bessel's formulae. 



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

 e problem, and proposed a formula which soon superseded the older and less accu- 

 .te formula? of De Luc, Shuckburgh, and others. The coefficients which enter in it 

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

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

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

 turned to be nyi^r? according to the experiments of Biot and Arago ; and the ba- 



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

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

 rmula to those furnished by the careful trigonometrical measurements made by 

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

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

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

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

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

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

 >ntained in the atmosphere. 



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