392 



IV. 



TABLES 



FOR REDUCING BAROMETRICAL OBSERVATIONS TO THE LEVEL OF THE SEA, OR TO ANY 

 OTHER LEVEL, AND FOR COMPUTING DIFFERENCES OF ELEVATION MEASURED BY THE 

 BAROMETER, BY M. C. DIPPE. 



The following tables, published by M. C. Dippe, in the Astronomische Nachrichten, 

 No. 1056, November, 1856, are a modification and extension of Gauss's tables, 

 published in Schumacher's Jahrbuch, for 1836 and the following years, which are 

 based on the formula of Laplace. In this new form they answer a double purpose. 

 They give the means of solving a problem which often occurs in Meteorology, viz. : 

 The difference of elevation between two stations, and the temperature of the air at 

 both, being known, to reduce the height of the barometer at one of the stations to the 

 height it would have at the other. They are likewise adapted to the computation of 

 heights from barometrical observations. 



The formula of Laplace, which has been used, the Metres being reduced to Toises, 

 and the Centigrade degrees to degrees of Reaumur, reads as follows : 



A = 9407.73(l + '+/)(l+acos2c/.)(l + ^^)|log^-. + 21og(l+^^^^ 



Where t and t' =^ the temperatures of the air, in degrees of Reaumur, at the lower 

 and upper station, 

 b and b' = the height of the barometer, in any scale, reduced to the freezing 

 point, at the lower and upper station, 

 h = the difference of level, in toises, between the two stations, 

 r = the distance, in toises, of the lower station to the centre of the 



Earth, 

 (}> = the latitude of the place of observation, 

 a = the increase of gravity from the equator to the poles. 



Making, besides, m = the modulus of the common logarithms, the formula be- 

 comes, with sufficient accuracy, 



I /. I ^/ ; f 1 1 2 m) 1 1 



log b - log b' = h I g^^^-^3 . -— ,-^, - — [ • 1+700^-0 • 7T^ . 



' 400 "I" r 



Assuming r, or the radius of the Earth, at 45° latitude ^ 3266631 toises, and 

 a = 0.002595, instead of 0.002845 adopted in Gauss's tables, and making 



u = log b — lojT b\ 



( ^ 1 2m \ 



^ I" 400 



c = — ma COS 2 ^, 



I mh 



then the reduction of the height of the barometer to another level is given by the 

 formula, 

 D 52 



