BAROMETRICAL MEASUREMENT OF HEIGHTS. 393 



1. log u = log li -\- a -\- c -\- d -^ 



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



Table T. contains the values of a for the argument t-\- t' ; 10 units are to be sub- 

 tracted from the characteristic. 



Table II. gives the values of c for the argument (f>, or the correction for the 

 change of gravity in latitude, which is negative from 0° to 45°, j)ositwe 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 c' are given in units of the fifth decimal place. 



The difference of elevation of the two slatioiis is given by the formula, 



1. li = log b — log Z»', 



2. log li = log u -\- A. -\- c -\- d , 



in which A is the arithmetical complement of a, and the corrections c and d 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 Reaiwmr, 



b : b' = ^ : ^ 



14- 14-- ' 



I 4i40 I 4440 



and makmg ^^^^ = /3, 



u = log J — log b' = (log B — /3 T) — (log B' — yS T'). 

 Instead of /3 = 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 must 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, i, i', (^, 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 



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

 Then we have 



for a level lower by h toises, log b =: log b' -\- u; 

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



If h, or the difference of elevation, is given in metres, take d, which is always 

 negative, from Table 111. (for A) with the argument v = log h -\- 9.71, and write 



log u = 9.71018 -f log ;i -f a + c -f c' — 10 (whole units). 

 Then again is log b = log b' -^ u, 

 D 53 



