HYPSOMETRICAL TABLES. 



These values have been retained in the different formulse proposed later by Gauss, 

 in Schumacher's Jahrbuch for 1840, by Schmidt, Mathem. und Physische Geographie, 

 II. p. 205, and by Baily, Astronomical Tables, p. 183, which, therefore, only change 

 the form without changing the results. D'Aubuisson, in his formula and tables, Traite 

 de Geognosie, p. 488, only reduced the barometrical coefficient to its theoretical 

 value, which he determined to be 18365 metres, leaving unchanged the other coeffi- 

 cients of Laplace's formula. 



Bessel first introduced, in his formula, Astronomische Nachrichten, No. 356, a sep- 

 arate correction for the effect of moisture. The correction for the temperature of 

 the air is computed in his tables for two values of the coefficient, that of Gay-Lussac, 

 0.00375, and that of Rudberg, 0.00365. Laplace's barometrical coefficient is re- 

 tained, but the correction for the decrease of gravity is considerably modified. 



In Elie Ritter's formula, in the Memoires de la Societe de Physique de Geneve, 

 Tom. XIII. p. 343, the corrections for temperature and moisture are also separated ; 

 but other values of the barometrical and thermometrical coefficients, derived from 

 Regnault's determinations, are used, and a new method is proposed for applying the 

 correction due to the expansion of air, which is made proportional to the square of 

 the difference between the observed temperatures at each station. 



Baeyer's formula, recently published in Poggendorf 's Annalen der Physik und 

 Chemie, Tom. XCVIII. p. 371, does not belong to either of the two classes just men- 

 tioned ; for while it keeps Laplace's barometrical and thermometrical coefficients, it 

 corrects the effect of temperature by a method analogous to that of Ritter, and it en- 

 tirely neglects the effect of aqueous vapor. 



In the following set the tables of Delcros, Guyot, and Loomis develop the formula 

 of Laplace. The much larger tables of Delcros render unnecessary those of Olt- 

 manns, which are yearly reprinted in the Annuaire du Bureau des Longiiades. In- 

 stead of Gauss's tables will be found the tables of Dippe, which are computed from 

 the same formula, but are more extended. Baily's tables close the first series. The 

 tables of Plantamour, computed from Bessel's formula, are given here in preference to 

 Bessel's tables, because Plantamour substituted for Laplace's barometrical coefficient 

 that derived from the probably more accurate determination of the relative weight 

 of the air and mercuiy by Regnault, viz. 18404.8 metres. E. Ritter's tables, com- 

 puted from his own formula, give perhaps, in extreme cases, better results ; but 

 as, in ordinaiy circumstances, the altitudes obtained do not much differ from those 

 furnished by the less complicated tables of Plantamour, they were not reprinted 

 here. 



The miscellaneous tables which follow furnish useful materials for solving several 

 questions connected with the barometrical measurements. 



Regnault's table of Barometric Pressures corresponding to Temperatures of the 

 Boiling Point of Water, revised by Moritz, and its reduction to English measures, will 

 be found a valuable addition for thermometrical measurements of heights. 



The Appendix to the Hypsometrical Tables now offers, in a new form, a complete 

 series of tables for the comparison of the different measures of length generally used 

 for indicating altitudes, the convenience of which will be fully appreciated by those 

 who have attempted to collect and to use the abundant contributions furnished by all 

 civilized nations to that branch of geographical science. 



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