FOR THE EARTH'S SURFACE. 303 



iC 2 111 



The coefficient of - - is - - = - , 

 the coefficient of - - - is - - + - = 0, 



L * Zi . o Zi 4 4 



, . 4 .17,33 1 , 



the coefficient of ls o-7 + o~Q = -Q' &c -' &c - 



1./.O.4 Z 4 -j o o 



Hence to the 4th power of x we have 



If x log cos i// = log sec //, where /* is the angle of the vertical, we have 



1 1 111 



2 2t 28192 



sin 2 1// 



4. Also 1 cos //=,- . , 



1 + cos t/f 



hence log ( 1 - cos t/) = 2 log sin t/ - log 2 - log -- (1 + cos i/f) 



= 2 log sin i// log 2 + - log (sec //) nearly, 

 neglecting the square of log (sec i/). 



Or if a is the modulus of common logarithms, we have 



1 1 11 



i- 2i o i y 



1 1 (axf I (axY 



/v J_ \ / _ \ ' 



" 2 ^8 a 192 a 3 



l(log 10 8eci|<)' J 1 (Iog 10 sec^) 4 



OF J.Vti,n ~ \ *- T wo V / S '"filO J ^" f 



Z 8 ft 



By these formulae the values of log (1- cos \ji) and log(l + cos/) for 

 every 5th degree of geographical colatitude have been determined. 



