136 



Ocean Magnetic Observations, 1905-16 



the zenith, but passes to one side by an angular distance {ZY) = y. However, the plane 

 contains the hne "peep-sight and vertical thread," EOH, which is the apparent azimuthal 

 direction of an object, S, in this inclined plane. But the true azimuthal direction of Sis 

 determined by the horizontal trace of a vertical plane ZOS passing through it, and the 

 correction a is the angle SZH between this vertical plane and a vertical plane containing 

 the Une "peep-sight and vertical thread." 



From the spherical triangle, SZH, there results 



sin SZ sin SH 



or 



sin SHZ sin SZH 



sin SH . „„„ cosSZ sin y 

 sm a = —. — 777i sm o/i/ = 



sinSZ" 



sin SZ cos y 



FiQ. 5. 



but as SHZ = y is less than 1° in instruments constructed with ordinary care, the arcs 

 may be substituted for sin a and tan y; introducing h, this equation becomes 



a = y tan h 



It is to be noted that if h is reckoned through the zenith when the Sun is behind the ob- 

 server, the formula may be considered general, so, when /i = 0° or 180°, a = 0, and when 

 /i = 90°, a becomes infinite, and for /i > 90°, tan /i is negative. 



Let the mirror be made parallel to a Une in the surface of the compass-bowl glass, which 

 line in turn is parallel to the line "peep-sight and vertical thread," that is, let the mirror be 

 rotated about its axis to a horizontal position. Next turn the azimuth cncle until the direc- 

 tion to a very distant object is at right angles to the line "peep-sight and vertical thread. 

 Then if angular measures are made with sextant or theodoUte between this distant object 

 and its reflections, as given by the mirror and compass-bowl glass, respectively, one-half the 



