BAROMETRICAL MEASUREMENT OF HEIGHTS. 



1. log u = log h -f- a + c + c' ; 



2. log b log b 1 + M. 



Table I. contains the values of a for the argument t -f- t' ; 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 

 ;T 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 Z>', 



j 2. log h = log u + A + c + c', 



s.; in which A is the arithmetical complement of , and the corrections c and c' receive 

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

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

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



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

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

 oi ature of the attached thermometer in degrees of Reaumur, 



B B' 



& b :b ' = _ _ T : . -u 



and making = ft, 



u = log b log b' = (log B - T) (log B' ft T'). 

 Instead of /3 = 0.000098, we can write with sufficient accuracy 0.00010. 



USE OF THE TABLES. 



I, , 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- 



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



I 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', <, and b or b'. 

 To find b or b'. 



In Table I. with the argument t -{- 2', 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 -f- c' 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 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 -|- 9.71, and write 



log u = 9.71018 + log h + a + c + c' 10 (whole units). 

 Then again is log b log b' -J- u. 



B 55 



