BAROMETRICAL TABLES. XXXI 



TABLE 29. 



Table 29 gives the correction for the variation of gravity with altitude 

 In its effect on the weight of the air. 



The side argument is the same as in Table 28 ; the top argument is 

 the height of the lower station varying by intervals of 200 metres from o to 

 2000, with additional columns for 2500, 3000 and 4000 metres. 



Example : 



Let the barometric reading (reduced to 0° C. ) at the upper station 

 be 655.7 mm.; at the lower station, 772.4 mm. Let the mean 

 temperature of the air column be 6 = 12°. 2, C, the mean vapor 

 pressure <? = 9 mm. and the latitude <^ = 32° 



Table 25, with argument 655.7, gi^'^s 1179 metres. 



Table 25, " " 772-4. " — ^29 



Approximate value of Z = 1308 



Table 26, with Z= 1300 and 6 = i2.°3 C, gives 59 



Table 27, with c = (^mm. and Z= 1370, gives 7 



Table 28, with Z= 1370 and (^=32°, gives 5 



Table 29, with Z= 1370 and h^ = o, gives o 



Corrected value of Z = 1379 metres. 



TABLE 30. 



Table 30. Difference of height corresponding to a change of o.i inch in 

 the barometer — English measures. 



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

 neglecting insensible quantities, 



a'Z= — 26281 -o- (i +0.002039(^—32°)) (i +^)- 



in which B represents the mean pressure of the air column dZ. 

 Putting d B = 0.1 inch, 



^^__26^ (^1+0.002039 (^-32°) )(!+/?)• 



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 on the 

 parallel of 45° latitude. Since the last factor (i + /8), as given on page xxiii, 

 is a function of the temperature, the function has only two variables and 

 admits of convenient tabulation. 



Table 30, containing values oi dZ for short intervals of the arguments 

 B and 6, has been taken from the Report of the U. S. Coast Survey, i88i, 

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

 level, by Wm. Ferrel.* 



* Due to the use of a slightly different value for the coefl&cient of expansion, Prof. 

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



dZ = -^^^ 



("i + 0.002034 {Q — 32°)) (i + /3) • 



