Mr W. Galbraith's Barometric Observations. 43 



will be readily recollected, to procure the same advantage nearly 

 from the mercurial barometer, and then make a comparison of 

 the results derived from these two instruments, from heights, 

 where I have had an opportunity of employing them ; — the 

 first example, where they were used at different times, — the 

 other, where they were used conjointly, and read simultaneous- 



ly- . . . 



Since heights determined geometrically, are proportional to 

 the differences of the logarithms of the altitudes of the mercu- 

 rial columns, a formula may be derived from the usual series, 

 for the computation of logarithms, thus : — 



Let B be the altitude of the mercury at the lower station, 

 and b that at the upper ; then, ^ 



Log.B-log.5 = .M{|=j4l(|^J)'+&c.}....(l) 



To apply this to the purpose required here, it will be necessary 

 to obtain a constant factor, by which the difference of the log- 

 arithms must be multiplied, to give the heights in some known 

 measure, such as English fathoms, or rather feet, which are 

 now generally preferred. This number, from the observations 

 of Ramond and the experiments of Biot, is 60155 English 

 feet at the freezing point, or 32° of Fahrenheit's scale, and 2 M 

 is 0*86858896, or twice the logarithmetic modulus; conse- 

 quently 60,155 X 0-86858896 — 52,250, the constant co-effi- 

 cient at the freezing point. 



In this country, as Fahrenheit's thermometer is very gene- 

 rally used, it would therefore be more simple, if reduced to zero 

 of its scale. Now, the expansion or contraction of air in its 

 ordinary state, for 1° of Fahrenheit, is about 00024, whence 

 52250 X 00024 x 32 = 4013. Hence 52250 — 4013 = 

 48237, the co-efficient at zero of Fahrenheit's scale. 



In practice, the mean of the temperatures of the air at the 

 top and bottom is employed, wherefore, the result derived from 

 the logarithmic series must be multiplied by the factor depend- 

 ing upon the product of the mean temperature, and the varia-- 

 tion of the bulk of air for 1° increased by unity ; or it must be 



multiplied by 1 -f. 00024 C-^) = + 00012 (t + 0, t being 



