TABLE FOR COMPUTING THE DIFFERENCE IN THE HEIGHTS 



rection is generally negative. It would be positive if T T' were negative ; that is 

 if the temperature T' of the barometer at the upper station exceeded the temperature 

 T at the lower station. 



Part III. gives the correction A X 0.00265 cos. 2 L, to be applied to the approx- 

 imate altitude A, and which arises from the variation of gravity from the latitude of 

 45 degrees, to the latitude L of the place of observation. This correction has the 

 same sign as cos. 2 L ; that is, it is positive from the equator to 45 degrees, and neg- 

 ative from 45 degrees to the pole. 



Part IV. gives the correction A X , which is always to be added to the ap- 



proximate height A, and which is due to the diminution of gravity on the vertical. 



Part V. furnishes for the approximate difference of level A the small correction 

 A X 1U4 44 31 5 corresponding to several values of the height s of the lower station. But 

 in place of s there has been substituted as the argument of the table, the height H of 

 the barometer at this station. 



Method of Computation. 



Take from Part I. the two numbers corresponding to the observed barometric 

 heights H and h'. From their difference subtract the correction 2.3409 (T T') 

 found in Part II. with the difference T T 7 of the thermometers attached to the ba- 

 rometers. We thus obtain an approximate altitude a. 



We then calculate the correction a ' + ^~ for the temperature of the air, by mul- 

 tiplying the nine-hundredth part of a by the sum of the temperatures t and t' dimin- 

 ished by 64. This correction is of the same sign as t -f- t 1 64. We thus obtain 

 a second approximate altitude A. 



With A and the latitude of the place L, we seek in Part III. the correction A x 

 0.00265 cos. 2 L arising from the variation of gravity with the latitude. 



For the approximate height A, Part IV. gives the correction A X ^0888629 ar i sm g 

 from the diminution of gravity on a vertical. This correction is always additive. 



Finally, when the height s of the lower station is considerable, the small correc- 

 tion A X 1(J44 S 4315 may be found in Part V. This correction is always additive. 



Example 1. 



M. Humboldt made the following observations on the mountain of Guanaxuato, in 

 Mexico, in Latitude 21, viz. 



Upper station. Lower station near the sea. 



Thermometer in open air, I' = 70. 3 t = 77.5 



Thermometer to barometer, T' 70.3 T 77,5 



Barometer, h 1 23.66 H = 30.046 



Required the difference in the height of the two stations. 

 D 48 



