74 Barometric Measurement of' the Height of Cheviot, 



suits, Mr Galbraith has inferred that the increase may be to- 

 lerably well represented by the common hyperbola, which satis- 

 fies the heights of Ramond, those by the Earl of Minto, and 

 some others very nearly. 



The equation to the hyperbola is 



!, = ^(^'-a')* (1.) 



y being the total height in feet, and x the ascent necessary to 

 depress the thermometer 1° of Fahrenheifs scale. 



If two values of ^ and y be taken from observations, that can 

 be depended upon, the values of a and h will become known. 

 Let 



^ y = 5000 feet, and x = 250 feet, 



y = 10,000 feet, and ixf = 300 feet, 



which, from the best observations, they are known to be nearly. 

 Now, if these be substituted in formula (1.), it will be found 



that — -zz-h^ nearly. But at the surface of the earth a^= x 



= 210 feet, as has been just found from experiments, whence 

 h = 55a = 55 X 210 = 11550, in round numbers, without sen- 

 sible error in the final results ; therefore a and b are known, 

 and consequently ^, the depression to any given height, y may 

 be computed. 



From the general equation 



it will be found that 



But b* = 133400000. Hence, if d be the depression, h the 

 height, and a = 210 feet, 



rf = 210(^1 + — — \^ (2.) 



V 133400000/ ^ ^ 



which is a general formula to compute the ascent in feet neces- 

 sary to depress Fahrenheit's thermometer one degree. 



In the Table in the margin are given the 

 corresponding numbers of feet required to de- 

 press the thermometer one degree by this for- 

 mula, that agree pretty well with observations, 

 in which, for the same height, there are often 

 considerable discrepancies, depending on causes 

 not well known. 20,000 



Heigh 

 In fee 



Height 

 feet 



5,000 

 10,000 



Depth 



Depi 

 infe< 



229 

 278 

 344 

 420 



