44 Mr W. Galbraith's Barometric Observations. 



the temperature at the bottom, and t' that at the top ; where- 

 fore, 



48237 { 1 + 00012 {t + = 48237 + 58 (^ + 0- 

 Or, to render the numbers more easily recollected, without 

 much affecting the accuracy of the result, if H be the height 

 required, 



H = {48000 + 60 (. + 0}{|=| +1(1^)' + &c.}...(A). 



This is correct only on the supposition that B and h are re- 

 duced by calculation, or approximate tables, to the same tem- 

 perature. But -it is known from experience, that the height 

 varies about 3 feet for every degree of difference of the attached 

 thermometers at top and bottom. Now, if t denote the tem- 

 perature of the attached thermometer at the bottom, and t that 

 at the top, then — 3 (t — </) must be the correction which is to 

 be subtracted, when t is greater than t, otherwise added. 

 Hence, finally, 



H = {48000+600+O}{|^ + |(|^)%&c.}-3(r-/)...(B). 



The term ^ i ^^ , ) will always be very small, except in 



great heights, and need seldom be attended to, as the error for 

 heights of about 



5,000 feet, it will be nearly ^-^^^ of the whole. 



10,000 ^1^ 



This term may therefore be safely rejected for any height 

 usually measured barometrically ; whence formula (B) becomes 



H = {48000 -^ 60 (^ + ^)||:=^ — 3 (r -r) (C). 



To assist the memory, if 48000 -f- 60 (< -f t') be denoted by c, 

 „ I by J, and — 3 (r — t') by e, formula (C) becomes 



n = cd — e (c). 



The whole of the numerical co-efficients are multiples of the 

 number 3, the last of them ; the second is twenty times the last, 

 or 20 X 3 = 60 ; and the first is eight hundred times the second, 

 or 800 X 60 = 48000, which is 16000 times the last, or 



