1843.] On Barometric Heights. 299 



On the reduction of mean temperature by elevation, Professor Leslie 

 has given the following formula as the result of his experiments on the 

 cold produced by diminution of barometric pressure. If B and b 

 denote the barometric pressure at the lower and upper stations ; then 

 will (-- -) 25 express on the Centigrade scale, the diminution of heat 

 in ascent (B). This formula cannot be universally true, though it 

 is known to give results agreeing very well with observation in mode- 

 rate elevations. For if we suppose three stations A, B, C, in the same 

 vertical line at which the barometer stands respectively at 30, 20, and 

 10 inches, it is obvious that the reduction of temperature between 

 A and B together with that between B and C must be the same as 

 the whole reduction from A to C. The formula gives (|^ — ^) 

 25=20.83 as the diminution from A to B ; and (^ -^)25=37.5 as 

 that from B to C : the sum of which is 58.33. But we have also 

 C - ^) 25 = 66 - 67 as the reduction from A to C. This differs so 

 much from the former result, that we may without any hesitation con- 

 clude that the formula cannot be strictly true. In order that the 

 diminution from A to C may be equal to the sura of the diminutions 

 from A to B and from B to C, it seems necessary to make it pro- 

 portional to the ratio of the densities, or as the logarithm of ~ ; that 

 is, as the difference of the logarithms of the barometers at the 

 two stations ; and if we assume that Leslie's formula gives results not 

 sensibly differing from the truth, at first, we shall have 115 log. — | 

 to be marked (C) as the expression for the diminution of temperature 

 on the Centigrade scale, or 207 log. -~ to be marked (D) on Fahren- 

 heit, which will give consistent results in all cases.* The diminution 

 of temperature is thus proportional to the approximate height in 

 barometric calculations, and if we calculate the approximate height 

 corresponding to a reduction of 1 degree in temperature, we shall 

 have 521.738 feet for 1° cent, and 289.86 feet for 1° Fahr., or in 

 round numbers 522 for 1° cent, and 290 for 1° Fahr. at the tempera- 

 ture of freezing. The numbers 522 and 290 will require a correction 

 for mean temperature, as in barometric measurements : This may be 

 done very simply. The expansion on a column of air of 522 feet for 

 1° cent, is just about 2 feet, and on 290 feet for 1° Fahr. the expansion 

 is 6 feet very nearly. Hence the corrected numbers may be found 



* If necessary the co-efficient may by corrected so as to agree with observation. 



