Xlviii INTRODUCTION. 



sure at the upper station be 2.4 mb.; at the lower station 7.3 mb. 



Let the mean temperature of the air column be = 5°8 C. and the 



latitude 4> = 39° 25' N. 

 Table 57, with argument 448.6, gives 651 1 meters. 



Table 57, with argument 1000.3, gives 104 



Approximate value of Z 6407 meters. 



Table 61, with arguments 449 and 2.4 gives A = 0.3 

 Table 61, with arguments IOOO and 7.3 gives A = 0.4 

 Table 58, with = 5°8 + 07 = 6?5, and Z = 6407 gives 



6407 X 0.024 = 154 



Table 62 with Z = 6561 and <t> = 39 25', gives 19 



Table 63 with Z = 6561 and h = o, gives 7 



Corrected value of Z = 6587 meters. 



Table 64. Difference of height corresponding to a change of 0.1 inch in the 

 barometer — English measures. 



If we differentiate the barometric formula, page xlii, we shall obtain, 

 neglecting insensible quantities, 



d Z = - 26281 -^f ( 1 + 0.002039 (0 - 32 ) \ (1 + 0), 



in which B represents the mean pressure of the air column d Z. 

 Putting dB = 0.1 inch, 



dZ= -^^(1+0.002039(0-32°)) (1+0). 



The second member, taken positively, expresses the height of a column 

 of air in feet corresponding to a tenth of an inch in the barometer under 

 standard gravity. Since the last factor (1 + /3), as given on page xliii, is a 

 function of the temperature, the function has only two variables and admits 

 of convenient tabulation. 



Table 64, containing values of d Z for short intervals of the arguments 

 B and 0, has been taken from the Report of the U.S. Coast Survey, 1881, 

 Appendix 10, — Barometric hypsometry and reduction of the barometer to sea 

 level, by Wm. Ferrel.' 



The temperature argument is given for every 5 from 30 F. to 85 F. f 

 and the pressure argument for every 0.2 inch from 22.0 to 30.8 inches. 



This table may be used in computing small differences of altitude, and, 

 up to a thousand feet or more, very approximate results may be obtained. 



1 Due to the use of a slightly different value for the coefficient of expansion, Prof. 

 Ferrel's formula, upon which the table is computed, is 



dZ= _26^4 / I+aoo2034 (e- 3 2°)\ (I+/3). 



