SECTION II. 



COMPUTATION OF THE VALUES OF LOG 0'" FOR THE EARTH'S SURFACE. 



1. TAKING into account the spheroidal figure of the Earth, let r, 6', \ 

 be polar coordinates of a point referred to the Earth's centre as origin and 

 axis of figure as initial line. 



Also let a be the semi-axis major of the terrestrial meridian, 



& the angle from the axis of rotation, 

 and 6 the geographical colatitude of the point. 



a 4 sin 2 0+6 4 cos 2 

 Then r 2 = -r-r- 



r sin ff = 



r cos & = 



a" sin" 0+6* 



a? sin 6 



COB'S' 



icos 



__ 

 >/a"sin 1 0~+&'cos 1 0' 



af 



Also tan & = -^ tan 6, 



or tan 6 tan ff = 



, a 

 a cos v 



& 2 sin ff 



a 2 cos & 



cos = -. 



r + fe'sin'^' 



and 1* = 7.2 2 /)/ , 



If e be the eccentricity of the terrestrial meridian, 



& 2 = a 2 (l-e 2 ), 



and we have 



a 2 (l-e') 



~l-e 8 sin 2 ^' 

 A. n. 38 



