BAROMETRICAL TABLES. XXI 



By substituting for Z its approximate value Z=K log ~, we have 

 With these substitutions the barometric formula becomes 



Z= A^Cl +ae)(™-g^)(l + ^ cos 2 <^)(l + ^^^°) 



b 



As a further simplification we shall put 



^ = 0.378 -j-1 y — k cos 2<^ and 7; = -^ i^/, 

 and write the formula — 



Z = A-Ci + a^) (^) (I +y) (i + -^4^) (I + ^) log§- 



Values of the co7istants. — The barometric constant K is a complex 

 quantity defined by the equation 



Ax Bn 



K 



8x M 



B„ is the normal barometric height of lyaplace, 760 mm. 



A is the density of mercury at the temperature of melting ice. M. 

 Marek {Travaux et Memoires du B^creau mternaiional des Poids et Mesures, 

 t. II, p. D 55) gives the value, A = 13-5956, and finds that different 

 specimens of mercury purified by different processes differ from this by 

 several units in the fourth decimal. The International Meteorological 

 Committee have taken the value 



A = 13-5958, 



and for the sake of uniformity this value is here adopted. 



8 is the density of dr}^ air at 0° C. and under the pressure of a column 



of mercury Bn at the sea level and at latitude 45.° The value adopted 



by the International Bureau of Weights and Measures {Travaux et Memoires, 



t. I, p. A 54) is 



S = 0.001293052. 



i^ (the modulus of common logarithms) — 0.4342945. 



These numbers give for the value of the baiometric constant 



K = 18400 metres. 



