III. 



TABLE 



computing the diffekence in the heights of two places by means of 



the barometer. 



By Prof. Elias Loomis. 



This table was computed from the formula of Laplace, modified in accordance 

 with the results of more recent determinations. 

 Suppose that we have observed 



At the lower station. 



At the upper station. 



H, the height of the barometer, 



T, the temperature of the barometer, 



^, the temperature of the air, 



h\ the height of the barometer, 



T', the temperature of the barometer, 



t\ the temperature of the air. 



Represent by s the height of the lower station above the level of the sea, by L the 

 lal.tude of the place, and by h the observed height li' reduced to the temperature T. 

 The difference of level x between the two stations is given by the formula. 



60158. 6 ft. X log. ? X ^ 



\ \ buo ) 



(1 4- 0.00265 cos. 2 L) 



/, [ X + 52251 . s \ 

 \ y 20S8S629 r 10444315/ , 



But h represents the height h' reduced from the temperature T' to the temperature 

 T. The expansion of mercury for 1° Fahr. is 0.0001000 ; that of the brass which 

 forms the scale of the barometer is 0.0000104 ; the difference is 0.0000896. Hence 

 we have h = h' \\ -\- 0.0000896 (T — T')^ 



Therefore, 



60158. 6 ft. log. " = 60158.6 ft. log. " — 2.3409 ft. (T — T). 



Part I. of the accompanying Table furnishes in English feet the value of the ex- 

 pression 60158.6 log. H for heights of the barometer from 11 to 31 inches; only 

 they have all been diminished by the constant 27541.5 feet which does not change 

 the difference 



60158.6 log. H — 60158.6 log. h. 



Part II. furnishes the correction — 2.3109 (T — T') depending upon the differ- 

 ence T — T' of the temperatures of the barometers at the two stations. This cor- 

 D 49 



