TABLES FOR DETERMINING HEIGHTS. xlv 



IJ. being a constant depending on the variation of gravity with altitude 

 1 ^ = 0.0000003 ), and 



log^° = logf + log(l+4) 



7 



Since —- is a very small fraction, we may write 



XV 



Nap. log^i +^j 

 M being the modulus of common logarithms. 



fa„d.og(:+f) = f... 



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

 With these substitutions the barometric formula becomes 



(2) Z = K(i + ad)f ^ -Vi+/fecos2^-^'cos22</, + C)fi+^^^^)x 



Vi- 0.378^/ \ ^ J 



(.+fi/),o4». 



As a further simplification we shall put 



/3 == 0.3787 , y = k cos 2 (j) - k' cos^ 2(t> + C and rj = — M, 

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



Z = K{i + ae) (^) (I + y) (i + ^^°) (I + ^) log§. 



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

 quantity defined by the equation 



^ X B„ 



K 



d X M 



Bn 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 



