1825.] 



Barometrical Measurement of Heights. 



165 



be reciprocally as the two given numbers,* it is evident that the 

 natural numbers of a table of common logarithms vi^ill represent 

 the pressures jjor heights of th^ barometer, and the difference of 

 their corresponding logarithms, the difference of level, or altitude 

 of the strata (or stations), possibly in feet, but at all events in 

 some constant ratio of the scale of the barometer. 



We have demonstrated that when the pressures, as we ascend 

 a series of stations, are observed to diminish in geometrical 

 progression, the difference of level of the stations will be equal ; 

 and we shall find that if we affix to a series of numbers in 

 geometrical progression their corresponding logarithms, then 

 will the differences of the latter continue equal ; thus confirming* 

 the propriety of substituting logarithms in our calculations, for 

 the more tedious and less accurate method made use of in the 

 first instance. 



Example, 



The vertical height of a stratum of dry air of the temperature 

 of 32° F. intercepted by the pressures of 43-42945 inches, and 

 43-42946 inches, is equal to -0060095 foot ; but as the logarith- 

 mic difference of the pressures is only -0000001, we must multi- 

 ply the difference of the logarithms of the heights of the baro- 

 meter at the two stations by 60095, and the product will be 

 equal to their difference of level in feet. 



Lower barometer 30*5 in, 

 Upper barometer 15-5 



Example, 



Log. 1-4842998 

 1-1903317 



' Difference 0-2939681 x 60095 = 17666 ft. 



When the mean temperature differs from 32°, we must alter 

 the multiplier of the logarithmic difi'erences (termed the constant 

 coefficient) in the ratio of the variation of the volume of the air; 

 or we may multiply the altitude at 32° by the difference of that 

 temperature and the mean of the detached thermometers, and 



Log. of 15-00 M760913 



15-01 1-1763807 



Differences 00-01 000028 Diff. 00-01 0-0001447 



Hence 2894 is to 1447 in the inverse ratio of 15 to 30. 



Log. of 30-CO 1-4771213 



SO-01 1-47 7 -2660 



