Xl INTRODUCTION. 



j£ = 0.0000003 V and 



H being a constant depending on the variation of gravity with altitude 

 log | = log f + log ( I+ „g. 



7 



Since — is a very small fraction, we may write 

 K 



Nap. log (1 + f ) = f , and log (1 + f ) = f U, 

 M being the modulus of common logarithms. 

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



*(. + S)-fjri,Jf. 



With these substitutions the barometric formula becomes 



(I) *-*<* + <-^('+ t 7 i! )( I+i **')* 



(i + ^fif)logf,or 



(2) Z - K (1 + ofl) ( },(i+kcos2^-k'cos 2 2i, + C)(i + ^^Ax 



Vi- 0.378^ V K I 



( I+ f,/).og|. 



As a further simplification we shall put 



j8 = 0.378^, y = k cos 2 - &' cos 2 24, + C and y = ^=- M, 



and write for the second form, (2), the formula — 



Z = K (1 + ad) ( r ^) (1 + y) (1 + ^-°) (1 + n) log§- 



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

 quantity defined by the equation 



A X B n 



K - 



5 X ikf 



5„ is the normal barometric height of Laplace, 760 mm. 



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

 value adopted by the International Meteorological Committee, and which 

 has been employed in previous editions of these tables is A = 13.5956. The 



