394 BAROMETRICAL MEASUREMENT OF HEIGHTS. 



Example 1. 



Suppose the height of the barometer, reduced to the freezing point, to be I 1 = 

 295.39 Paris lines; the temperature of the air t' = 11. 8 Reaumur, and the latitude 

 cf> = 51 48'; the increase of heat downwards being 1 Reaumur for 100 toises. 

 What is the height of the barometer, reduced to the freezing point, at a station 

 lower by h = 498.2 toises ? 



In th' case t = t' -f- 4.98 = 16.78, and t + t' = 28.58. 

 Then 



log h = 2.69740 



Table I. for 28.58 gives a = 5.99538 



Table II. for 51 48' gives c = -f 0.00026 

 Table III. for 498 toises gives c' = 0.00007 



log u = 8.69297 10 



u = 0.04931 

 log V- = 2.47040 



log I = 2.51971 

 Barometer at the lower station b = 330.90 Paris lines. 



Example 2. 



Suppose the reduced barometer & = 598.6 millimetres ; the temperature of the 

 air t' = 18 .0 Centigrade = 14. 4 Reaumur; the difference of elevation h = 2217 

 metres , $ = 3. The temperature of the air at the lower station t = 27. 5 Cen- 

 tigrade = 22.0 Reaumur, and t + t' = 36 .4 Reaumur. 



TVi i 7, J log 2217 = 3.34577 



= I + 9.71018 



3.05595 v = 3.06 

 a = 5.98750 

 c = 0.00112 

 c' = _ 0.00015 



log u = 9.04218 10 



u = 0.11020 

 log V = 9/7T714 



log I = 9.88734 

 Barometer at the lower station b = 771.5 millimetres. 



2. For Computing Differences of Elevation from Barometrical Observations. 



Given the unreduced height of the barometer at the lower and upper station.! 

 B and B' ; the temperatures of the attached thermometers, T and T' ; the temperatures 

 of the air, t and t' ; and the latitude, $. 



To find A, or the difference of elevation between the two stations. 



Subtract (log B' 10 T 7 ) from (log B 10 T), paying due attention to the 

 nature of the signs of T and T', and taking the numbers 10 T and 10 T 1 as units ol 

 the fifth decimal. Calling then (log B 10 T) (log B 7 10 T') = w, or if the* 

 heights of the Barometers are reduced to the freezing point, log b log b' 

 take, 



In Table I., A with the argument t -f- *', and make v = log u + A. 

 In Table II., with the argument <, take c reversing the sign. 

 D 54 



