BAROMETRICAL MEASUREMENT OF HEIGHTS. 



1. log u = log h -\- a -\- c -}- c' ', 



2. log b = log b' -\- u. 



Table I. contains the values of a for the argument t-{- 1' ; 10 units are to be sub- 

 tracted from the characteristic. 



Table II. gives the values of c for the argument <^, or the correction for the 

 change of gravity in latitude, which is negative from 0° to 45°, positive from 45° 

 to 90°. 



Table III. furnishes the values of c' for the argument h in toises, or the correction 

 for the decrease of gravity on the vertical. Both in Tables II. and III. the values of 

 c and d are given in units of the fifth decimal place. 



The difference of elevation of the tioo stations is given by the formula, 



1. M = log b — log J', 



2. \og h = \og u -\- A. -\- c -^ c', 



in which A is the arithmetical complement of a, and the corrections c and c' receive 

 contrary signs. For the sake of convenience, the values of A have been placed in 

 Table I., and in Table III. the correction for A is found in another column, with the 

 more convenient argument v = log u -\- A. 



If the heights of the barometers have not been reduced to the freezing point, then, 

 B and B' being the unreduced heights of the barometers, and T and T' the temper- 

 ature of the attached thermometer in degrees of Reaumur, 



B B' 



b'.b' = 



A T 4440 ^ 4440 



and making ^^ = i3, 



u = \ogb — log b' = (log B — /3T) — (log B' — ^ T'). 

 Instead of iS = 0.000098, we can write with sufficient accuracy 0.00010. 



Use of the Tables. 



These tables can be used in any latitude, and for any barometrical scale ; but the 

 indications of the barometers 7nust be reduced to the freezing point ; and the tem- 

 peratures of the air must be given in degrees of Reaumur. The tables suppose the 

 use of logarithms with 5 decimals, such as those of Lalande, and give the results 

 in toises. 



I. For Reducing Barometrical Observations to another Level. 



Given h in toises, t., t', (f), and b or b'. 



To find b or b'. 

 In Table I. with the argument t -{- t', take a, 

 In Table II. with the argument </), take c. 

 In Table III. with the argument h, take c', 



the last two corrections being given in units of the fifth decimal, making 

 \oQ h -\- a -\- c -{- c' — 10 (whole units) = log u. 



Then v/e have 



for a level lower by h toises, log b — log 6' -}" « 5 

 for a level higher by h toises, log b' = log b — u. 



If A, or the difference of elevation, is given in metres, take c', which is always 

 negative, from Table III. (for A) with the argument v — log h -f 9.71, and write 



log u = 9.71018 -{- log /j -|- a 4- c 4- c' — 10 (whole units). 

 Then again is log b = log b' -\- u. 



D 55 



