74 



WISCOls'SIN' ACADEMY SCIEN"CES, AETS, AISTD LETTERS. 



atmosphere is of a uniform temperature, we may take the difference 

 of level of any two stations according to the equilibrium of elastic 

 fluids equal to a constant 60200 (at 32°) multiplied by the difference 

 of the logarithms of the readings in inches, thus: 

 (x = k (Log. B. — Log. b); ) 



Since the height of the mercury is affected by temperature, it is 

 necessary to reduce the observations to a common temperature. 



Mercury expands at 32° Fahr., about .0001 of its bulk for every 

 degree of heat, the rate of expansion varies, but this will not be 

 sensibly felt under ordinary circumstances. It is most easy, and 

 hence most proper to reduce the temperature of one reading to 

 that of the other, rather than to reduce both to a normal, and it will 

 be most convenient to reduce that which has the lowest tempera- 

 ture, which, as a rule, is at the highest station. 



The difference of temperature which will affect the height of the 

 mercury by expansion, will also affect it further by affecting the 

 density of the atmosphere. 



Air expands about .0021 of its bulk lor every degree from 32° 

 Fahr., and although this rate is not regular, it is safe to assume it 

 as such when applying to mean temperature. 



Where the distance between stations is great, or that the lati- 

 ude differs much from 45°, a correction must be made on account 

 of the difference of the force of gravit3^ Taking one practical ex- 

 ample and applying the two formulae before mentioned, the first 

 gives an altitude of 6143.50 feet, and the second 5960.1622 feet, both 

 of which are fair approximations. 



Examj^h. 



T+t 



-32^=29.5'^; T'— 1'=15°; 2 Lat.=89'^.50' 



1st. 55,000 (?=^1 =6143,50. 



\B+b/ 



2d. 60200 (Log. B— log. bM960, 1622. 



