388 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 i^^^i 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 11^315 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' of the thermometers attached to the ba- 

 rometers. We thus obtain an approximate altitude a. 



We then calculate the correction a g^^ for the temperature of the air, by mul- 

 tiplying the nine-hundredth part of a by the sum of the temperatures / and i' dimin- 

 ished by 64. This correction is of the same sign diS t -\- t' — 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 .^^^^g.^g arising 

 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 104^315 may be found in Part V. This correction is always additive. 



Example 1. 



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

 Mexico, in Latitude 21°, viz. 



Upper station. Lower station near the sea. 



Thermometer in open air, V = 70°. 3 t = 77°. 5 



Thermometer to barometer, T' = 70°.3 T — 77°.5 



Barometer, h' = 23.66 H = 30.046 



Required the difference in the height of the two stations. 

 D 48 



