BAROMETRICAL MEASUREMENT OF HEIGHTS. 393 



1. log u log h -f- a -\- c -\- c' ; 



2. log b = log b' + u. 



Table I. contains the values of a for the argument t -f- 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 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 c' are given in units of the fifth decimal place. 



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



1. u = log b log ', 



2. log h = log u -f- A -f- c -f- 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 L, and in Table III. the correction for A is found in another column, with the 

 more convenient argument v = log u -j- 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, arid T and T' the temper- 

 ature of the attached thermometer in degrees of Reaumur, 



> r y = _B_ : * 



1 + 4440 1 + 4440 



and making ^ = 0, 



u log b log V (log B /3T) (log B' /3 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, t, ', </>, and b or b'. 

 To find b or V. 



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

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

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



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



log h -\- a + c -\- c' 10 (whole units) = log u. 

 Then we have 



for a level lower by h toises, log b = log b' -f- u 5 

 for a level higher by h toises, log b 1 = 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 -f- log h + a + c + c' 10 (whole units). 

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

 D 53 



