1825.] Baromeirica I Measurement of HeiglUs. 86 



versely as the volume, diminished in the ratio of 1 to 0*90909.* 

 The given heights of the barometer being, as in the preceding 

 example, 30*5 and 15*5 inches, we must augment the altitude 

 at 32°, or 17666 feet, one-tenth, or in the ratio of 90909 to 

 100000; equal either way to 194326 feet. At this temperature 



(12000 + -^th or) 13200 cubic feet of dry air supporting the 



pressure of 26*0988 inches, would be required to balance one of 

 mercury. 



The temperature of the air being 24 degrees below 32^F. or 

 at + 8° F. we must reduce the altitude at 32° one-twentieth, or 

 in the ratio of the densities,t viz. of 1 -05263 to 1, giving 1 6782*7 

 feet as the correct altitude of the object. 



We have hitherto supposed the stratum of air to be of uniform 

 temperature; a supposition seldom or ever confirmed by the 

 indications of the detached or exterior thermometers placed in 

 the shade, and freely exposed to the air at the summit and base. 

 Generally speaking, the temperature, especially when the dif- 

 ference of altitude is considerable, diminishes as we ascend. 

 The mean rate of the diminution, which is extremely variable at 

 different times and places, is usually estimated at 1° F. for an 

 elevation of 300 feet. My own numerous observations on alti- 

 tudes not exceeding 2000 feet, give 230 feet as the mean — a rate 

 of decrement differing little from that deduced from the observa- 

 tions of Mr. Dalton ; but as the diminution when within 100 or 

 200 feet of the summit, particularly when the mountain was an 

 extended ridge, and the thermometers w^ere placed on its lee- 

 ward side, was frequently double or treble that of the inferior 

 equal sections, the rate is evidently exaggerated, and some cor- 

 rection seems necessary in order to obtain a uniform decrement 

 from observations made on mountains of different altitudes. 



Supposing the decrement, whatever the rate, to be but 

 uniform, or in arithmetical progression ; that is, granting the 

 differences of temperature indicated by any number of thermo- 

 meters ranged on the side of the mountain at equal perpendicu- 

 lar distances to be the same, we shall commit no sensible error 

 in the calculation if we consider the mean density of the air the 

 same as that of another stratum uniformly of a temperature 

 equal to half the sum of the detached thermometers observed at 

 the base and summit of the mountain.J 



* See \ 20, p. 4S8, f Ibid. 



X If we expose 440 volumes of air 48 degrees above, and 440 volumes 48 degrees 

 beloitc the freezing point, to the mean temperature (equal to S£° F.), their volume collec- 

 tively will be greater by l-IOOth part than the sum of their volumes before the mixture 

 took place. 



For 400-0 volumes at 32° are equal to 440 volumes at + 80° 

 And 488-9 32 440 ~ 6 



88S-0 S80 31ean.ra 



